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{
"id": 1005464535198605300,
"author_id": 805217272087838700,
"author_name": "Mathematics Bot",
"timestamp": "08/06/2022 09:17:05",
"content": "Available help channel!",
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"reference": null
},
{
"id": 1005465774485426300,
"author_id": 768747971272507400,
"author_name": "Inhumane",
"timestamp": "08/06/2022 09:22:01",
"content": "",
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"author_id": 805217272087838700,
"author_name": "Mathematics Bot",
"timestamp": "08/06/2022 09:22:02",
"content": "Pinned a message.",
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"id": 1005465781515063400,
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{
"id": 1005465811751813100,
"author_id": 768747971272507400,
"author_name": "Inhumane",
"timestamp": "08/06/2022 09:22:10",
"content": "How can I solve this",
"attachments": [],
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},
{
"id": 1005467412885414000,
"author_id": 768747971272507400,
"author_name": "Inhumane",
"timestamp": "08/06/2022 09:28:31",
"content": ".close",
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},
{
"id": 1005467415804649600,
"author_id": 805217272087838700,
"author_name": "Mathematics Bot",
"timestamp": "08/06/2022 09:28:32",
"content": "Channel closed",
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}
] |
help-9
|
7706b402c6d74c99b36a7aa15f1543c6
|
197,666 |
[
{
"id": 1005467633266724900,
"author_id": 926502640232321200,
"author_name": "Daphne",
"timestamp": "08/06/2022 09:29:24",
"content": "you still need help ?",
"attachments": [],
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"name": "Inhumane",
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"id": 1005467683644518500,
"author_id": 768747971272507400,
"author_name": "Inhumane",
"timestamp": "08/06/2022 09:29:36",
"content": "No",
"attachments": [],
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},
{
"id": 1005472855548502000,
"author_id": 805217272087838700,
"author_name": "Mathematics Bot",
"timestamp": "08/06/2022 09:50:09",
"content": "Available help channel!",
"attachments": [],
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"reference": null
},
{
"id": 1005473746179592200,
"author_id": 593796489948561400,
"author_name": "Berk.",
"timestamp": "08/06/2022 09:53:41",
"content": "what's the value of cot(-x)?",
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},
{
"id": 1005473748671012900,
"author_id": 805217272087838700,
"author_name": "Mathematics Bot",
"timestamp": "08/06/2022 09:53:42",
"content": "Pinned a message.",
"attachments": [],
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"channelId": 486844875632017400,
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}
},
{
"id": 1005473826055930000,
"author_id": 593796489948561400,
"author_name": "Berk.",
"timestamp": "08/06/2022 09:54:00",
"content": "or ctg(-x) same thing",
"attachments": [],
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"reference": null
},
{
"id": 1005473880451846100,
"author_id": 593796489948561400,
"author_name": "Berk.",
"timestamp": "08/06/2022 09:54:13",
"content": "cotangens",
"attachments": [],
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},
{
"id": 1005474001985998800,
"author_id": 220517274845577200,
"author_name": "ramonov",
"timestamp": "08/06/2022 09:54:42",
"content": "$\\whatis{\\cot(-x)}$",
"attachments": [],
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"reference": null
},
{
"id": 1005474055736021000,
"author_id": 510789298321096700,
"author_name": "TeXit",
"timestamp": "08/06/2022 09:54:55",
"content": "**โamonov**",
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"id": 1005474159867985900,
"author_id": 220517274845577200,
"author_name": "ramonov",
"timestamp": "08/06/2022 09:55:20",
"content": "it is unclear what you actually want",
"attachments": [],
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"reference": null
},
{
"id": 1005474201840402400,
"author_id": 593796489948561400,
"author_name": "Berk.",
"timestamp": "08/06/2022 09:55:30",
"content": "this",
"attachments": [
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{
"id": 1005474217858441300,
"author_id": 593796489948561400,
"author_name": "Berk.",
"timestamp": "08/06/2022 09:55:34",
"content": "is it -cotx",
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{
"id": 1005474232525918200,
"author_id": 593796489948561400,
"author_name": "Berk.",
"timestamp": "08/06/2022 09:55:37",
"content": "or is it just cotx",
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},
{
"id": 1005474619802800300,
"author_id": 593796489948561400,
"author_name": "Berk.",
"timestamp": "08/06/2022 09:57:10",
"content": "Ahhh nevermind i found it",
"attachments": [],
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},
{
"id": 1005474644515627100,
"author_id": 593796489948561400,
"author_name": "Berk.",
"timestamp": "08/06/2022 09:57:16",
"content": "its -cotx",
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},
{
"id": 1005474710538162300,
"author_id": 593796489948561400,
"author_name": "Berk.",
"timestamp": "08/06/2022 09:57:31",
"content": "Thanks",
"attachments": [],
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},
{
"id": 1005474735594942500,
"author_id": 593796489948561400,
"author_name": "Berk.",
"timestamp": "08/06/2022 09:57:37",
"content": ".close",
"attachments": [],
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"reference": null
},
{
"id": 1005474737020997600,
"author_id": 805217272087838700,
"author_name": "Mathematics Bot",
"timestamp": "08/06/2022 09:57:38",
"content": "Channel closed",
"attachments": [],
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"reference": null
}
] |
help-9
|
4dfea245a33c4cd5899deb365cd81fea
|
197,667 |
[
{
"id": 1005476274124361900,
"author_id": 805217272087838700,
"author_name": "Mathematics Bot",
"timestamp": "08/06/2022 10:03:44",
"content": "Available help channel!",
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},
{
"id": 1005482441798066300,
"author_id": 579296049819025400,
"author_name": "AG1LE",
"timestamp": "08/06/2022 10:28:15",
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"author_name": "Mathematics Bot",
"timestamp": "08/06/2022 10:28:15",
"content": "Pinned a message.",
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"id": 1005482539831541800,
"author_id": 579296049819025400,
"author_name": "AG1LE",
"timestamp": "08/06/2022 10:28:38",
"content": "where does the underlined inequality originate from?",
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{
"id": 1005482699504484500,
"author_id": 697730177962344400,
"author_name": "Tarek Ahmed",
"timestamp": "08/06/2022 10:29:16",
"content": "well actually -b/2a is the x-coordinate of the turning point of any quadratic equation ax^2+bx+c",
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{
"id": 1005482758530932700,
"author_id": 579296049819025400,
"author_name": "AG1LE",
"timestamp": "08/06/2022 10:29:30",
"content": "yeah the vertex right",
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{
"id": 1005482833348923500,
"author_id": 473405391167029250,
"author_name": "JamesH",
"timestamp": "08/06/2022 10:29:48",
"content": "the x coordinate of the axis of symmetry/vertex",
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{
"id": 1005482921488023600,
"author_id": 473405391167029250,
"author_name": "JamesH",
"timestamp": "08/06/2022 10:30:09",
"content": "what class is this for",
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"id": 1005482928123412600,
"author_id": 579296049819025400,
"author_name": "AG1LE",
"timestamp": "08/06/2022 10:30:11",
"content": "but why does x have to be less than -b/(2a) for the function to decrease",
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{
"id": 1005482987799969800,
"author_id": 473405391167029250,
"author_name": "JamesH",
"timestamp": "08/06/2022 10:30:25",
"content": "can you use calculus?",
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{
"id": 1005483005420257300,
"author_id": 579296049819025400,
"author_name": "AG1LE",
"timestamp": "08/06/2022 10:30:29",
"content": "i can",
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{
"id": 1005483029675909200,
"author_id": 579296049819025400,
"author_name": "AG1LE",
"timestamp": "08/06/2022 10:30:35",
"content": "but iโll prefer not to",
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{
"id": 1005483064157290600,
"author_id": 473405391167029250,
"author_name": "JamesH",
"timestamp": "08/06/2022 10:30:43",
"content": "its the first thing i would try",
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"id": 1005483080657666200,
"author_id": 579296049819025400,
"author_name": "AG1LE",
"timestamp": "08/06/2022 10:30:47",
"content": "the book is for calculus itself and calculus is introduced later",
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"id": 1005483123032727700,
"author_id": 579296049819025400,
"author_name": "AG1LE",
"timestamp": "08/06/2022 10:30:57",
"content": "this chapter is for functions",
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{
"id": 1005483149289078800,
"author_id": 473405391167029250,
"author_name": "JamesH",
"timestamp": "08/06/2022 10:31:03",
"content": "so no derivatives yet?",
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{
"id": 1005483167500746800,
"author_id": 579296049819025400,
"author_name": "AG1LE",
"timestamp": "08/06/2022 10:31:08",
"content": "nope",
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{
"id": 1005483191731224700,
"author_id": 579296049819025400,
"author_name": "AG1LE",
"timestamp": "08/06/2022 10:31:13",
"content": "just algebra",
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{
"id": 1005483446791045200,
"author_id": 473405391167029250,
"author_name": "JamesH",
"timestamp": "08/06/2022 10:32:14",
"content": "first off, after completing the square we can notice that the big ugly rational term is constant with respect to x",
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{
"id": 1005483515296620500,
"author_id": 579296049819025400,
"author_name": "AG1LE",
"timestamp": "08/06/2022 10:32:31",
"content": "right",
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{
"id": 1005483593189032000,
"author_id": 473405391167029250,
"author_name": "JamesH",
"timestamp": "08/06/2022 10:32:49",
"content": "so the functions decreasing/increasing behavior matches exactly the behavior of g(x) = a(x+b/2a)^2",
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{
"id": 1005483603913867400,
"author_id": 579296049819025400,
"author_name": "AG1LE",
"timestamp": "08/06/2022 10:32:52",
"content": "it remains constant for any x",
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{
"id": 1005483739717062800,
"author_id": 579296049819025400,
"author_name": "AG1LE",
"timestamp": "08/06/2022 10:33:24",
"content": "how?",
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"id": 1005483784839368800,
"author_id": 473405391167029250,
"author_name": "JamesH",
"timestamp": "08/06/2022 10:33:35",
"content": "take any function",
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"id": 1005483806465196000,
"author_id": 473405391167029250,
"author_name": "JamesH",
"timestamp": "08/06/2022 10:33:40",
"content": "add some constant to it",
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{
"id": 1005483855182045300,
"author_id": 579296049819025400,
"author_name": "AG1LE",
"timestamp": "08/06/2022 10:33:52",
"content": "it just changes the y axis",
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"id": 1005483863805526000,
"author_id": 579296049819025400,
"author_name": "AG1LE",
"timestamp": "08/06/2022 10:33:54",
"content": "or the range",
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{
"id": 1005483866594750500,
"author_id": 473405391167029250,
"author_name": "JamesH",
"timestamp": "08/06/2022 10:33:54",
"content": "all that changes is moving the WHOLE graph up/down, maintaining the same overall shape",
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{
"id": 1005483949033783400,
"author_id": 579296049819025400,
"author_name": "AG1LE",
"timestamp": "08/06/2022 10:34:14",
"content": "yeah yeah",
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{
"id": 1005483984718934100,
"author_id": 579296049819025400,
"author_name": "AG1LE",
"timestamp": "08/06/2022 10:34:22",
"content": "so the big ugly rational constant term",
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"id": 1005484012485230600,
"author_id": 579296049819025400,
"author_name": "AG1LE",
"timestamp": "08/06/2022 10:34:29",
"content": "just changes the range of the function",
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"id": 1005484107905650800,
"author_id": 473405391167029250,
"author_name": "JamesH",
"timestamp": "08/06/2022 10:34:52",
"content": "in particular, it can be ignored completely for the purposes of determining where the function is increasing/decreasing",
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"id": 1005484206207537300,
"author_id": 579296049819025400,
"author_name": "AG1LE",
"timestamp": "08/06/2022 10:35:15",
"content": "ookay",
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{
"id": 1005484277917561000,
"author_id": 579296049819025400,
"author_name": "AG1LE",
"timestamp": "08/06/2022 10:35:32",
"content": "so we eliminate the constant to focus on the term with x",
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"id": 1005484300763926700,
"author_id": 473405391167029250,
"author_name": "JamesH",
"timestamp": "08/06/2022 10:35:38",
"content": "now all we need to look at is the intervals where g(x) = a(x+b/2a)^2 would be inc/dec",
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"id": 1005484370448109700,
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"author_name": "AG1LE",
"timestamp": "08/06/2022 10:35:54",
"content": "exactly how do you do that?",
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"id": 1005484412290486400,
"author_id": 473405391167029250,
"author_name": "JamesH",
"timestamp": "08/06/2022 10:36:04",
"content": "well",
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{
"id": 1005484461879742500,
"author_id": 579296049819025400,
"author_name": "AG1LE",
"timestamp": "08/06/2022 10:36:16",
"content": "(x+b/(2a))^2 is positive for all x right",
"attachments": [],
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},
{
"id": 1005484495773896700,
"author_id": 473405391167029250,
"author_name": "JamesH",
"timestamp": "08/06/2022 10:36:24",
"content": "first we assume a is positive",
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},
{
"id": 1005484511917781000,
"author_id": 473405391167029250,
"author_name": "JamesH",
"timestamp": "08/06/2022 10:36:28",
"content": "and yes that is true",
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{
"id": 1005484521162027000,
"author_id": 579296049819025400,
"author_name": "AG1LE",
"timestamp": "08/06/2022 10:36:30",
"content": "yeah",
"attachments": [],
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},
{
"id": 1005484619543613600,
"author_id": 473405391167029250,
"author_name": "JamesH",
"timestamp": "08/06/2022 10:36:54",
"content": "ok",
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},
{
"id": 1005484676288356400,
"author_id": 473405391167029250,
"author_name": "JamesH",
"timestamp": "08/06/2022 10:37:07",
"content": "so that function is just a translation of a regular old parabola, y = ax^2",
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{
"id": 1005484711252066400,
"author_id": 473405391167029250,
"author_name": "JamesH",
"timestamp": "08/06/2022 10:37:16",
"content": "to the left by b/2a",
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{
"id": 1005484980488634400,
"author_id": 579296049819025400,
"author_name": "AG1LE",
"timestamp": "08/06/2022 10:38:20",
"content": "i think iโm getting it",
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{
"id": 1005485124256813000,
"author_id": 579296049819025400,
"author_name": "AG1LE",
"timestamp": "08/06/2022 10:38:54",
"content": "for x>b/2a",
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{
"id": 1005485162877952000,
"author_id": 579296049819025400,
"author_name": "AG1LE",
"timestamp": "08/06/2022 10:39:03",
"content": "the function will increase",
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},
{
"id": 1005485248320131100,
"author_id": 579296049819025400,
"author_name": "AG1LE",
"timestamp": "08/06/2022 10:39:24",
"content": "since the value inside the squared bracket is increasing",
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{
"id": 1005485288153419900,
"author_id": 579296049819025400,
"author_name": "AG1LE",
"timestamp": "08/06/2022 10:39:33",
"content": "unbounded",
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"timestamp": "08/06/2022 10:39:35",
"content": "right?",
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"timestamp": "08/06/2022 10:39:59",
"content": "that is true, continue",
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"timestamp": "08/06/2022 10:40:13",
"content": "but for",
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"timestamp": "08/06/2022 10:40:22",
"content": "x<b/2a",
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"timestamp": "08/06/2022 10:40:43",
"content": "the squared term decreases with decrease in x",
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"timestamp": "08/06/2022 10:41:01",
"content": "the mid i.e 0 occurs at x=-b/2a",
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"timestamp": "08/06/2022 10:41:43",
"content": "yes",
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"timestamp": "08/06/2022 10:41:50",
"content": "the last part",
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"timestamp": "08/06/2022 10:41:52",
"content": "wait the term is squared, for a negative x (x+b/(2a))^2 is positive",
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"timestamp": "08/06/2022 10:42:17",
"content": "yeah that is correct",
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"timestamp": "08/06/2022 10:42:23",
"content": "it should increase with an increase in magnitude of x",
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"timestamp": "08/06/2022 10:42:26",
"content": "the part i was saying yes to was the middle",
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"timestamp": "08/06/2022 10:42:33",
"content": "the key word there is **magnitude**",
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"timestamp": "08/06/2022 10:42:41",
"content": "absolutely",
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"timestamp": "08/06/2022 10:43:16",
"content": "when does a decrease to x necessarily increase its magnitude",
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"timestamp": "08/06/2022 10:43:47",
"content": "when the magnitude of x is greater than b/2a",
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"timestamp": "08/06/2022 10:44:10",
"content": "i.e the negative part of x axis to the left of b/2a",
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"timestamp": "08/06/2022 10:45:08",
"content": "you have the right ideas but either you arent writing carefully or you are slightly mixing some things up",
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"timestamp": "08/06/2022 10:45:30",
"content": "i think you probably have it",
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"timestamp": "08/06/2022 10:45:41",
"content": "what would the intervals of decrease and increase be then?",
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"timestamp": "08/06/2022 10:46:28",
"content": "x belongs to (-infinity,-b/2a) U (b/2a,infinity)",
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"timestamp": "08/06/2022 10:47:47",
"content": "is that where it decreases, or increases? and what happens to x between -b/2a and b/2a?",
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"timestamp": "08/06/2022 10:47:51",
"content": "you are close",
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"timestamp": "08/06/2022 10:48:43",
"content": "for a>0 \nthis interval is where it increases",
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"timestamp": "08/06/2022 10:48:45",
"content": "hey, would you please send the rest of the page? Iโd like to read the rest",
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"timestamp": "08/06/2022 10:48:51",
"content": "it decreases",
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"timestamp": "08/06/2022 10:49:07",
"content": "(ik it doesnโt have anything to do with your q, apologies)",
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"timestamp": "08/06/2022 10:49:29",
"content": "ok so hear me out for a second",
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"timestamp": "08/06/2022 10:49:40",
"content": "tysm",
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"timestamp": "08/06/2022 10:49:42",
"content": "sure",
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"timestamp": "08/06/2022 10:49:44",
"content": ":catlove:",
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"timestamp": "08/06/2022 10:50:00",
"content": "fix some arbitrary positive value a, and sketch the graph of g(x) = ax^2",
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"timestamp": "08/06/2022 10:50:36",
"content": "it really doesnt matter what value of a we choose, for simplicity we can look at the specific example a = 1",
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"timestamp": "08/06/2022 10:50:42",
"content": "taken",
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"timestamp": "08/06/2022 10:51:26",
"content": "the function we are looking at is a(x + b/2a)^2",
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"timestamp": "08/06/2022 10:51:42",
"content": "okay",
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"timestamp": "08/06/2022 10:51:54",
"content": "where b=0 a=1",
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"timestamp": "08/06/2022 10:52:03",
"content": "so the x-int is -b/2a",
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"timestamp": "08/06/2022 10:52:04",
"content": "how would we alter that graph to get the graph of a(x+b/2a)^2 froim that graph?",
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"timestamp": "08/06/2022 10:52:07",
"content": "hold on",
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"timestamp": "08/06/2022 10:52:14",
"content": "lets choose b = 2",
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"timestamp": "08/06/2022 10:52:17",
"content": "and a = 1",
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"timestamp": "08/06/2022 10:52:25",
"content": "then what is our function?",
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"timestamp": "08/06/2022 10:52:34",
"content": "(x+1)^2",
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"timestamp": "08/06/2022 10:53:19",
"content": "the graphs of (x+1)^2 and x^2 are very similar",
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"timestamp": "08/06/2022 10:53:27",
"content": "what is the difference?",
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"timestamp": "08/06/2022 10:53:38",
"content": "yes, this",
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"timestamp": "08/06/2022 10:53:39",
"content": "the values at -q and 1",
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"timestamp": "08/06/2022 10:53:43",
"content": "-1 and 1",
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"timestamp": "08/06/2022 10:53:54",
"content": "the values every where actually",
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"timestamp": "08/06/2022 10:53:59",
"content": "the graph pf (x+1)^2 shifts to the left",
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"timestamp": "08/06/2022 10:54:02",
"content": "on x axis",
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"timestamp": "08/06/2022 10:54:04",
"content": "yes",
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"timestamp": "08/06/2022 10:54:10",
"content": "by 1 unit",
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"timestamp": "08/06/2022 10:54:15",
"content": "ok",
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"timestamp": "08/06/2022 10:54:37",
"content": "and it is pretty clear that ax^2 is inc on [0,inf) and decreasing on (-inf,0], yeah?",
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"timestamp": "08/06/2022 10:54:50",
"content": "yeah",
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"timestamp": "08/06/2022 10:54:51",
"content": "yeah",
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"timestamp": "08/06/2022 10:55:20",
"content": "so all we do is pick the graph of ax^2 up and move it to the left by some number of units. the only thing that changes is that center point",
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"content": "okay",
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"timestamp": "08/06/2022 10:55:54",
"content": "that is our",
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"timestamp": "08/06/2022 10:56:02",
"content": "ugly constant term",
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"timestamp": "08/06/2022 10:56:06",
"content": "right?",
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"timestamp": "08/06/2022 10:56:22",
"content": "compare y=x^2 and y=2x^2",
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"timestamp": "08/06/2022 10:56:24",
"content": "some number of units",
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"timestamp": "08/06/2022 10:56:46",
"content": "graph just gets steeper",
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"timestamp": "08/06/2022 10:56:59",
"content": "yep",
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"timestamp": "08/06/2022 10:57:01",
"content": "without change in the intervals of increase and decrease",
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"timestamp": "08/06/2022 10:57:13",
"content": "im sending you a picture real quick",
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"timestamp": "08/06/2022 10:57:17",
"content": "sure",
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"timestamp": "08/06/2022 10:58:00",
"content": "this was for a 0 b term",
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"content": "however when b does not equal 0",
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"content": "b/2a has some value",
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"content": "and that value shifts the graph to",
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"content": "changing the orientation pf the parabola",
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"content": "depends on whether it is added or subtracted",
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"content": "and what about y=x^2+1",
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"content": "similar intervals of increase and decrease",
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"content": "it shifts the graph up the y axis bu 1 unit",
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"content": "now if the ugly constant term is taken to be 0",
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"content": "the parabolaโs vertex always touches x",
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"content": "hence before b/2a it decreases",
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"content": "and so it has a double root",
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"content": "and increases after b/2a",
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"content": "f(x+a) shifts the graph to left by a",
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"content": "we took b=2 and a=1",
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"content": "right right",
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"content": "itโs the negative of a",
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"content": "i.e -b/2a",
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"content": "exactly",
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"timestamp": "08/06/2022 11:02:54",
"content": "so that changes things slightly, doesnt it?",
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"content": "yes it does",
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"content": "OH I GOT IT",
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"content": "๐",
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"timestamp": "08/06/2022 11:03:47",
"content": "the phenomenon where f(x+a) shifts f(x) to the left",
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"content": "changes the vertex",
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"content": "to the left",
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"timestamp": "08/06/2022 11:04:04",
"content": "right ๐",
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"content": "instead of the intuitive right",
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"content": "will just change the range of the function",
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"content": "not the intervals in which it decreases and increases",
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"timestamp": "08/06/2022 11:05:23",
"content": "the minima occurs at x=-b/2a",
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"content": "for a>0",
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"content": "hence an upward parabola is minimum at the vertex",
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"content": "THANK YOU SO MUCH JAMES๐",
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"content": ".close",
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"content": "Channel closed",
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}
] |
help-9
|
c6c64d82d9074d2f9c314c9169c7c71f
|
197,668 |
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"author_id": 805217272087838700,
"author_name": "Mathematics Bot",
"timestamp": "08/06/2022 12:18:00",
"content": "Available help channel!",
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},
{
"id": 1005510390760870000,
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"timestamp": "08/06/2022 12:19:19",
"content": "Pinned a message.",
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"author_id": 679005078400663600,
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"timestamp": "08/06/2022 12:19:49",
"content": "I know that AB = CD because given and AB parallel to BC because given",
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"timestamp": "08/06/2022 12:20:18",
"content": "Ive proven that BAC = DCA because of coresponding alternate angles theorem",
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{
"id": 1005510730205892700,
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"timestamp": "08/06/2022 12:20:39",
"content": "and i know AC = CA because of reflexive property of equality",
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"id": 1005510840251859000,
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"timestamp": "08/06/2022 12:21:05",
"content": "but how do i prove that AD and BC are congruent and what do i need to do after",
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"timestamp": "08/06/2022 12:23:29",
"content": "Looks like you've got it",
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"timestamp": "08/06/2022 12:23:40",
"content": "This is a SAS congruence",
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"timestamp": "08/06/2022 12:25:46",
"content": "you could prove it",
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"content": "but you dont need to",
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"content": "why not?",
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"timestamp": "08/06/2022 12:26:07",
"content": "because",
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"timestamp": "08/06/2022 12:26:22",
"content": "you already have 2 sides and the angle between them",
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"author_name": "diet soup",
"timestamp": "08/06/2022 12:26:29",
"content": "right",
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"author_name": "Master Oogway",
"timestamp": "08/06/2022 12:26:32",
"content": "thats all you need for the triangle congruence",
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"id": 1005512321050878000,
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"author_name": "diet soup",
"timestamp": "08/06/2022 12:26:58",
"content": "so do i just say ABC = CDA and put SAS for the reason",
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},
{
"id": 1005512370816307300,
"author_id": 437166198166257660,
"author_name": "Master Oogway",
"timestamp": "08/06/2022 12:27:10",
"content": "no",
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},
{
"id": 1005512390139453600,
"author_id": 437166198166257660,
"author_name": "Master Oogway",
"timestamp": "08/06/2022 12:27:15",
"content": "say",
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},
{
"id": 1005512428609601700,
"author_id": 437166198166257660,
"author_name": "Master Oogway",
"timestamp": "08/06/2022 12:27:24",
"content": "1. AB=CD",
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},
{
"id": 1005512461123850400,
"author_id": 437166198166257660,
"author_name": "Master Oogway",
"timestamp": "08/06/2022 12:27:32",
"content": "2. AC=AC",
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},
{
"id": 1005512503243051000,
"author_id": 437166198166257660,
"author_name": "Master Oogway",
"timestamp": "08/06/2022 12:27:42",
"content": "3. BAC=DCA (angles)",
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"id": 1005512633778184200,
"author_id": 437166198166257660,
"author_name": "Master Oogway",
"timestamp": "08/06/2022 12:28:13",
"content": "after you write these 3",
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},
{
"id": 1005512660583993500,
"author_id": 437166198166257660,
"author_name": "Master Oogway",
"timestamp": "08/06/2022 12:28:19",
"content": "=>",
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},
{
"id": 1005512673556967400,
"author_id": 437166198166257660,
"author_name": "Master Oogway",
"timestamp": "08/06/2022 12:28:22",
"content": "SAS",
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},
{
"id": 1005512793769914600,
"author_id": 437166198166257660,
"author_name": "Master Oogway",
"timestamp": "08/06/2022 12:28:51",
"content": "triangle ABC=CDA",
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},
{
"id": 1005512930021888100,
"author_id": 679005078400663600,
"author_name": "diet soup",
"timestamp": "08/06/2022 12:29:24",
"content": "i have 1,2, and 3 and their reasons down",
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},
{
"id": 1005513043431657500,
"author_id": 679005078400663600,
"author_name": "diet soup",
"timestamp": "08/06/2022 12:29:51",
"content": "so now all i need to do is to write ABC = CDA and put SAS as the reason?",
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},
{
"id": 1005513100335775700,
"author_id": 437166198166257660,
"author_name": "Master Oogway",
"timestamp": "08/06/2022 12:30:04",
"content": "write an =>",
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},
{
"id": 1005513130660597800,
"author_id": 679005078400663600,
"author_name": "diet soup",
"timestamp": "08/06/2022 12:30:11",
"content": "?",
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},
{
"id": 1005513136796872800,
"author_id": 437166198166257660,
"author_name": "Master Oogway",
"timestamp": "08/06/2022 12:30:13",
"content": "and above it write SAS",
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},
{
"id": 1005513189955481700,
"author_id": 679005078400663600,
"author_name": "diet soup",
"timestamp": "08/06/2022 12:30:26",
"content": "what do you mean =>",
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},
{
"id": 1005513220771020900,
"author_id": 437166198166257660,
"author_name": "Master Oogway",
"timestamp": "08/06/2022 12:30:33",
"content": "its a symbol",
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},
{
"id": 1005513250978418700,
"author_id": 679005078400663600,
"author_name": "diet soup",
"timestamp": "08/06/2022 12:30:40",
"content": "ohhh",
"attachments": [],
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},
{
"id": 1005513276219719800,
"author_id": 679005078400663600,
"author_name": "diet soup",
"timestamp": "08/06/2022 12:30:46",
"content": "that symbol",
"attachments": [],
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},
{
"id": 1005513288290943100,
"author_id": 437166198166257660,
"author_name": "Master Oogway",
"timestamp": "08/06/2022 12:30:49",
"content": "yeah]",
"attachments": [],
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"reference": null
},
{
"id": 1005513293768691800,
"author_id": 679005078400663600,
"author_name": "diet soup",
"timestamp": "08/06/2022 12:30:50",
"content": "ok got it",
"attachments": [],
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},
{
"id": 1005513306049626200,
"author_id": 679005078400663600,
"author_name": "diet soup",
"timestamp": "08/06/2022 12:30:53",
"content": "thank you",
"attachments": [],
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"reference": null
},
{
"id": 1005513337003581400,
"author_id": 437166198166257660,
"author_name": "Master Oogway",
"timestamp": "08/06/2022 12:31:01",
"content": "np",
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"reference": null
},
{
"id": 1005513347027980300,
"author_id": 679005078400663600,
"author_name": "diet soup",
"timestamp": "08/06/2022 12:31:03",
"content": ".close",
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},
{
"id": 1005513348772802600,
"author_id": 805217272087838700,
"author_name": "Mathematics Bot",
"timestamp": "08/06/2022 12:31:03",
"content": "Channel closed",
"attachments": [],
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"reference": null
}
] |
help-9
|
4108470b2fd44ae4b53b180d10c3f6a8
|
197,669 |
[
{
"id": 1005514845510193300,
"author_id": 805217272087838700,
"author_name": "Mathematics Bot",
"timestamp": "08/06/2022 12:37:00",
"content": "Available help channel!",
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},
{
"id": 1005517390987133000,
"author_id": 712795809216725100,
"author_name": "Linc",
"timestamp": "08/06/2022 12:47:07",
"content": "Inequalities in Two Triangles",
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},
{
"id": 1005517392736161900,
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"content": "Pinned a message.",
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"id": 1005517436285628400,
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"author_name": "Linc",
"timestamp": "08/06/2022 12:47:18",
"content": "",
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"id": 1005517529696964600,
"author_id": 712795809216725100,
"author_name": "Linc",
"timestamp": "08/06/2022 12:47:40",
"content": "I was able to do the last one but I am struggling with this due it it being reversed?",
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},
{
"id": 1005517607656493200,
"author_id": 712795809216725100,
"author_name": "Linc",
"timestamp": "08/06/2022 12:47:59",
"content": "Not reversed -12",
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},
{
"id": 1005517755971285000,
"author_id": 712795809216725100,
"author_name": "Linc",
"timestamp": "08/06/2022 12:48:34",
"content": "if 2X -12 to make it 1 X would I do +24?",
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},
{
"id": 1005521532002512900,
"author_id": 805217272087838700,
"author_name": "Mathematics Bot",
"timestamp": "08/06/2022 13:03:34",
"content": "@Linc Has your question been resolved?",
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"id": 1005523379559878700,
"author_id": 712795809216725100,
"author_name": "Linc",
"timestamp": "08/06/2022 13:10:55",
"content": "im now doubting my answer haha",
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},
{
"id": 1005526993409949700,
"author_id": 712795809216725100,
"author_name": "Linc",
"timestamp": "08/06/2022 13:25:17",
"content": ".close",
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},
{
"id": 1005526995146383400,
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"timestamp": "08/06/2022 13:25:17",
"content": "Channel closed",
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}
] |
help-9
|
8fef783564584b54bbafb2ec02c30c9d
|
197,670 |
[
{
"id": 1005527248440410200,
"author_id": 805217272087838700,
"author_name": "Mathematics Bot",
"timestamp": "08/06/2022 13:26:17",
"content": "Available help channel!",
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},
{
"id": 1005532056828256300,
"author_id": 805217272087838700,
"author_name": "Mathematics Bot",
"timestamp": "08/06/2022 13:45:24",
"content": "Pinned a message.",
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"id": 1005532120384549000,
"author_id": 209300311091838980,
"author_name": "Peacemaker II",
"timestamp": "08/06/2022 13:45:39",
"content": "it's correct",
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},
{
"id": 1005532136050262000,
"author_id": 209300311091838980,
"author_name": "Peacemaker II",
"timestamp": "08/06/2022 13:45:43",
"content": "trust your gut",
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},
{
"id": 1005532177649389700,
"author_id": 977195783826841600,
"author_name": "VistaGuy",
"timestamp": "08/06/2022 13:45:53",
"content": "ln x*x^-1",
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},
{
"id": 1005532271635345500,
"author_id": 977195783826841600,
"author_name": "VistaGuy",
"timestamp": "08/06/2022 13:46:15",
"content": "when i diffrentiate this",
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},
{
"id": 1005532300634767400,
"author_id": 977195783826841600,
"author_name": "VistaGuy",
"timestamp": "08/06/2022 13:46:22",
"content": "i get",
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},
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"id": 1005532958121279600,
"author_id": 977195783826841600,
"author_name": "VistaGuy",
"timestamp": "08/06/2022 13:48:59",
"content": "",
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"id": 1005532962953117700,
"author_id": 977195783826841600,
"author_name": "VistaGuy",
"timestamp": "08/06/2022 13:49:00",
"content": "am i correct ?",
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"id": 1005533001037385900,
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"author_name": "VistaGuy",
"timestamp": "08/06/2022 13:49:09",
"content": "wish i could but im too paranoid",
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"id": 1005533023481110700,
"author_id": 977195783826841600,
"author_name": "VistaGuy",
"timestamp": "08/06/2022 13:49:14",
"content": "actually im always paranoid",
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},
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"id": 1005533561002131500,
"author_id": 977195783826841600,
"author_name": "VistaGuy",
"timestamp": "08/06/2022 13:51:22",
"content": "this is the answer i get when differentiate lnx*x^-1",
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"id": 1005533656665821200,
"author_id": 977195783826841600,
"author_name": "VistaGuy",
"timestamp": "08/06/2022 13:51:45",
"content": "so i just want to confirm if my answer is correct",
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"id": 1005533692782969000,
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"timestamp": "08/06/2022 13:51:54",
"content": "Channel closed",
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}
] |
help-9
|
273620a55d714bc78a597e80df9039ac
|
197,671 |
[
{
"id": 959621431946281000,
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"author_name": "Mathematics Bot",
"timestamp": "04/01/2022 21:12:58",
"content": "Available help channel!",
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},
{
"id": 959628390279807000,
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"content": "Pinned a message.",
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"id": 959628402283917300,
"author_id": 731447178572202000,
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"timestamp": "04/01/2022 21:40:40",
"content": "may i ask how to do e",
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"id": 959628416343212000,
"author_id": 731447178572202000,
"author_name": "yk3",
"timestamp": "04/01/2022 21:40:43",
"content": "cuz its weird",
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{
"id": 959628455178293200,
"author_id": 731447178572202000,
"author_name": "yk3",
"timestamp": "04/01/2022 21:40:52",
"content": "binomial expansion?",
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},
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"id": 959628476325978100,
"author_id": 731447178572202000,
"author_name": "yk3",
"timestamp": "04/01/2022 21:40:57",
"content": "then ill have to write a lot of terms aaa",
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"id": 959628536430338200,
"author_id": 490649542077841400,
"author_name": "tatpoj",
"timestamp": "04/01/2022 21:41:12",
"content": "No, luckily you don't have to do that lol",
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"id": 959628579392610300,
"author_id": 490649542077841400,
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"timestamp": "04/01/2022 21:41:22",
"content": "A simple u-substitution should do the trick",
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"id": 959628676209705000,
"author_id": 912691854410129400,
"author_name": "emre amag0ttenyiyen",
"timestamp": "04/01/2022 21:41:45",
"content": "B. Binomal theorem user",
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"timestamp": "04/01/2022 21:42:07",
"content": "we cannot use substitution",
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"id": 959628812126146600,
"author_id": 490649542077841400,
"author_name": "tatpoj",
"timestamp": "04/01/2022 21:42:17",
"content": "what",
"attachments": [],
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},
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"id": 959628825979940900,
"author_id": 731447178572202000,
"author_name": "yk3",
"timestamp": "04/01/2022 21:42:21",
"content": "yes",
"attachments": [],
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},
{
"id": 959628871949516800,
"author_id": 892725065127444500,
"author_name": "hellblaze_skyfire",
"timestamp": "04/01/2022 21:42:32",
"content": ",w u-substitution",
"attachments": [],
"mentions": [],
"reference": null
},
{
"id": 959628892107333600,
"author_id": 510789298321096700,
"author_name": "TeXit",
"timestamp": "04/01/2022 21:42:36",
"content": "Results provided by WolframAlpha",
"attachments": [],
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},
{
"id": 959628919659700200,
"author_id": 892725065127444500,
"author_name": "hellblaze_skyfire",
"timestamp": "04/01/2022 21:42:43",
"content": "โฆโฆโฆ",
"attachments": [],
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"reference": null
},
{
"id": 959628943223324800,
"author_id": 892725065127444500,
"author_name": "hellblaze_skyfire",
"timestamp": "04/01/2022 21:42:49",
"content": ",w u-substitution metghod",
"attachments": [],
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},
{
"id": 959628951603511300,
"author_id": 510789298321096700,
"author_name": "TeXit",
"timestamp": "04/01/2022 21:42:51",
"content": null,
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},
{
"id": 959629008226644000,
"author_id": 892725065127444500,
"author_name": "hellblaze_skyfire",
"timestamp": "04/01/2022 21:43:04",
"content": ",w u-substitution method",
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},
{
"id": 959629015616999400,
"author_id": 510789298321096700,
"author_name": "TeXit",
"timestamp": "04/01/2022 21:43:06",
"content": null,
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},
{
"id": 959629026505425000,
"author_id": 892725065127444500,
"author_name": "hellblaze_skyfire",
"timestamp": "04/01/2022 21:43:08",
"content": "โฆโฆโฆโฆโฆโฆโฆ",
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},
{
"id": 959629077025804300,
"author_id": 731447178572202000,
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"timestamp": "04/01/2022 21:43:21",
"content": "....",
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},
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"id": 959629097875677200,
"author_id": 490649542077841400,
"author_name": "tatpoj",
"timestamp": "04/01/2022 21:43:25",
"content": "I think they know what u-sub is. They said they're not allowed to use it",
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"author_name": "tatpoj",
"timestamp": "04/01/2022 21:43:40",
"content": "But why not?",
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"timestamp": "04/01/2022 21:43:49",
"content": "teacher said so",
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"id": 959629198627078100,
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"timestamp": "04/01/2022 21:43:50",
"content": "so",
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"id": 959629284094378000,
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"author_name": "yk3",
"timestamp": "04/01/2022 21:44:10",
"content": "should i ttake ln",
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"id": 959629314402431000,
"author_id": 731447178572202000,
"author_name": "yk3",
"timestamp": "04/01/2022 21:44:17",
"content": "and e^ the whole thing",
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"author_id": 490649542077841400,
"author_name": "tatpoj",
"timestamp": "04/01/2022 21:45:03",
"content": "Sorry, I'm at a loss if you're not supposed to do a substitution. I'll think about it",
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"id": 959629526290268300,
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"author_name": "yk3",
"timestamp": "04/01/2022 21:45:08",
"content": "lmao",
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"id": 959629528760725500,
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"author_name": "yk3",
"timestamp": "04/01/2022 21:45:08",
"content": "its ok",
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"id": 959629690136576000,
"author_id": 490649542077841400,
"author_name": "tatpoj",
"timestamp": "04/01/2022 21:45:47",
"content": "Out of curiosity, how did you do d then?",
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"id": 959629703059226800,
"author_id": 490649542077841400,
"author_name": "tatpoj",
"timestamp": "04/01/2022 21:45:50",
"content": "Did you actually divide them?",
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"id": 959629894348841000,
"author_id": 731447178572202000,
"author_name": "yk3",
"timestamp": "04/01/2022 21:46:35",
"content": "yes",
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"id": 959629902372536400,
"author_id": 731447178572202000,
"author_name": "yk3",
"timestamp": "04/01/2022 21:46:37",
"content": "long divison",
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"id": 959629925789356000,
"author_id": 731447178572202000,
"author_name": "yk3",
"timestamp": "04/01/2022 21:46:43",
"content": "does the job",
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},
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"id": 959630149207347200,
"author_id": 485903210272391200,
"author_name": "dldh06",
"timestamp": "04/01/2022 21:47:36",
"content": "Integration by parts",
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"id": 959630425523880000,
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"author_name": "yk3",
"timestamp": "04/01/2022 21:48:42",
"content": "no u sub",
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"id": 959630448697422000,
"author_id": 731447178572202000,
"author_name": "yk3",
"timestamp": "04/01/2022 21:48:48",
"content": "no by parts nice",
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"id": 959630483879248000,
"author_id": 731447178572202000,
"author_name": "yk3",
"timestamp": "04/01/2022 21:48:56",
"content": "just the basic integration rules",
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"id": 959630529085452400,
"author_id": 731447178572202000,
"author_name": "yk3",
"timestamp": "04/01/2022 21:49:07",
"content": "pain",
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"author_id": 490649542077841400,
"author_name": "tatpoj",
"timestamp": "04/01/2022 21:50:11",
"content": "I suppose you could do the binomial theorem, and just use sigma notation instead of writing all the terms explicitly",
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"timestamp": "04/01/2022 21:50:23",
"content": "...",
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"author_id": 490649542077841400,
"author_name": "tatpoj",
"timestamp": "04/01/2022 21:51:21",
"content": "If you can't use u sub or IBP, I can't think of anything else, and technically it wouldn't be that complicated",
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"timestamp": "04/01/2022 21:51:46",
"content": "what did u get after u sub tho",
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"id": 959631216531898400,
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"timestamp": "04/01/2022 21:51:51",
"content": "if u u sub",
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"author_id": 485903210272391200,
"author_name": "dldh06",
"timestamp": "04/01/2022 21:52:00",
"content": "I would ask your teacher for clarification, cause something to the 2022 is not fun",
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"timestamp": "04/01/2022 21:52:26",
"content": "You can do u=x+2, so x=u-2",
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"id": 959631366536974500,
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"timestamp": "04/01/2022 21:52:26",
"content": "pain",
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"id": 959631484329812100,
"author_id": 731447178572202000,
"author_name": "yk3",
"timestamp": "04/01/2022 21:52:54",
"content": "but without u sub tho",
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"author_name": "tatpoj",
"timestamp": "04/01/2022 21:53:11",
"content": "Oh, you asked what you get if you u sub",
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"author_id": 932314798559985700,
"author_name": "ayunami2000",
"timestamp": "04/01/2022 21:53:38",
"content": "someone plz help, im tryna solve this but i cant its pretty hard",
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"content": "@ayunami2000 go to an available channel",
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"timestamp": "04/01/2022 21:53:58",
"content": "in the section above",
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"author_name": "ayunami2000",
"timestamp": "04/01/2022 21:54:04",
"content": "ooh ok",
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"author_name": "tatpoj",
"timestamp": "04/01/2022 21:54:30",
"content": "@yk3 I'm not sure what you're asking now",
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"author_name": "yk3",
"timestamp": "04/01/2022 21:56:00",
"content": "wait",
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"id": 959632275530743800,
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"author_name": "yk3",
"timestamp": "04/01/2022 21:56:03",
"content": "can i",
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"id": 959632289065754600,
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"author_name": "yk3",
"timestamp": "04/01/2022 21:56:06",
"content": "take natural log",
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"id": 959632330442567700,
"author_id": 731447178572202000,
"author_name": "yk3",
"timestamp": "04/01/2022 21:56:16",
"content": "and make it sth like",
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"author_name": "yk3",
"timestamp": "04/01/2022 21:57:31",
"content": "",
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"timestamp": "04/01/2022 21:57:33",
"content": "@tatpoj",
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"author_name": "tatpoj",
"timestamp": "04/01/2022 21:58:12",
"content": "I mean, that is correct, but I don't see a clear way forward from there",
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"id": 959632896287735800,
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"author_name": "yk3",
"timestamp": "04/01/2022 21:58:31",
"content": "same",
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"id": 959633263956209700,
"author_id": 329749386315956200,
"author_name": "Sneaky",
"timestamp": "04/01/2022 21:59:59",
"content": "Could probably do something with binomial theorem and integrating it termwise if you apply binomial theorem smartly after integrating to get it into a better form.",
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"id": 959633414342971400,
"author_id": 490649542077841400,
"author_name": "tatpoj",
"timestamp": "04/01/2022 22:00:35",
"content": "That's pretty much what I was thinking. Just leave it in sigma notation instead of writing out each term",
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},
{
"id": 959633440913907800,
"author_id": 490649542077841400,
"author_name": "tatpoj",
"timestamp": "04/01/2022 22:00:41",
"content": "I mean obviously you're not going to write out over 2000 terms",
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"id": 959633482743677000,
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"author_name": "yk3",
"timestamp": "04/01/2022 22:00:51",
"content": "ok",
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},
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"id": 959633498174545900,
"author_id": 731447178572202000,
"author_name": "yk3",
"timestamp": "04/01/2022 22:00:55",
"content": "but whats the point of this question",
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},
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"id": 959633672833732600,
"author_id": 490649542077841400,
"author_name": "tatpoj",
"timestamp": "04/01/2022 22:01:36",
"content": "๐คทโโ๏ธ You'd have to ask your teacher. I'm not sure why you're being asked not to use particular techniques",
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},
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"id": 959633700813942800,
"author_id": 731447178572202000,
"author_name": "yk3",
"timestamp": "04/01/2022 22:01:43",
"content": "lmao",
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},
{
"id": 959633737677676500,
"author_id": 490649542077841400,
"author_name": "tatpoj",
"timestamp": "04/01/2022 22:01:52",
"content": "u-sub solves this problem very quickly",
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"id": 959633785731829900,
"author_id": 490649542077841400,
"author_name": "tatpoj",
"timestamp": "04/01/2022 22:02:03",
"content": "But honestly the binomial theorem isn't that bad either if you're comfortable with sigma notation",
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"id": 959633793302552700,
"author_id": 731447178572202000,
"author_name": "yk3",
"timestamp": "04/01/2022 22:02:05",
"content": "thats why i dont really like this question",
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"id": 959633858616238200,
"author_id": 731447178572202000,
"author_name": "yk3",
"timestamp": "04/01/2022 22:02:21",
"content": "but ok",
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"id": 959633886206390400,
"author_id": 731447178572202000,
"author_name": "yk3",
"timestamp": "04/01/2022 22:02:27",
"content": "thanks let me try",
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"id": 959633927574802400,
"author_id": 490649542077841400,
"author_name": "tatpoj",
"timestamp": "04/01/2022 22:02:37",
"content": "sure",
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"author_id": 805217272087838700,
"author_name": "Mathematics Bot",
"timestamp": "04/01/2022 22:17:27",
"content": "@yk3 Has your question been resolved?",
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"timestamp": "04/01/2022 22:32:28",
"content": "Channel closed",
"attachments": [],
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"reference": null
}
] |
help-9
|
0eafbbc05f4b4aad867c5d94162a9068
|
197,672 |
[
{
"id": 1005533722675785900,
"author_id": 977195783826841600,
"author_name": "VistaGuy",
"timestamp": "08/06/2022 13:52:01",
"content": "bruh",
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"reference": null
},
{
"id": 1005533726958178300,
"author_id": 977195783826841600,
"author_name": "VistaGuy",
"timestamp": "08/06/2022 13:52:02",
"content": "ok",
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},
{
"id": 1005533838488903800,
"author_id": 977195783826841600,
"author_name": "VistaGuy",
"timestamp": "08/06/2022 13:52:29",
"content": "lnx*x^-1 (differentiate)",
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},
{
"id": 1005533948207714400,
"author_id": 977195783826841600,
"author_name": "VistaGuy",
"timestamp": "08/06/2022 13:52:55",
"content": "im getting this",
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"id": 1005533966461308900,
"author_id": 977195783826841600,
"author_name": "VistaGuy",
"timestamp": "08/06/2022 13:52:59",
"content": "am i correct ?",
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},
{
"id": 1005533991417422000,
"author_id": 977195783826841600,
"author_name": "VistaGuy",
"timestamp": "08/06/2022 13:53:05",
"content": "just pls tell yes",
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},
{
"id": 1005564461869957100,
"author_id": 805217272087838700,
"author_name": "Mathematics Bot",
"timestamp": "08/06/2022 15:54:10",
"content": "Available help channel!",
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},
{
"id": 1005568466943742100,
"author_id": 761733743655911400,
"author_name": "rawlini",
"timestamp": "08/06/2022 16:10:05",
"content": "I am trying to solve this problem",
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"author_name": "Mathematics Bot",
"timestamp": "08/06/2022 16:10:05",
"content": "Pinned a message.",
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"id": 1005568509138452500,
"author_id": 761733743655911400,
"author_name": "rawlini",
"timestamp": "08/06/2022 16:10:15",
"content": "LEt me post my work",
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},
{
"id": 1005568683965419500,
"author_id": 761733743655911400,
"author_name": "rawlini",
"timestamp": "08/06/2022 16:10:56",
"content": "https://cdn.discordapp.com/attachments/958967215183523860/1005568618114842695/8556D232-0D44-44CF-B2AA-99482DDAF420.jpg",
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"id": 1005570792777596900,
"author_id": 761733743655911400,
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"timestamp": "08/06/2022 16:19:19",
"content": "kidding",
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},
{
"id": 1005570796338548700,
"author_id": 761733743655911400,
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"timestamp": "08/06/2022 16:19:20",
"content": "i got it",
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},
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"id": 1005570798284714100,
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"timestamp": "08/06/2022 16:19:20",
"content": "lol",
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"id": 1005570801409478800,
"author_id": 761733743655911400,
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"timestamp": "08/06/2022 16:19:21",
"content": ".close",
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},
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"id": 1005570803473060000,
"author_id": 805217272087838700,
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"timestamp": "08/06/2022 16:19:22",
"content": "Channel closed",
"attachments": [],
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}
] |
help-9
|
034c92f71a0c40aebec01b88f0c0c48e
|
197,673 |
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},
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"author_id": 425448181879537660,
"author_name": "allarkvarkk",
"timestamp": "08/06/2022 16:35:24",
"content": "Can someone explain this to me",
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"id": 1005574840457109600,
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"author_name": "Mathematics Bot",
"timestamp": "08/06/2022 16:35:24",
"content": "Pinned a message.",
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{
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"author_id": 425448181879537660,
"author_name": "allarkvarkk",
"timestamp": "08/06/2022 16:35:37",
"content": "I dont understand why n+1 was subbed in for n",
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},
{
"id": 1005578225088483300,
"author_id": 363399048037793800,
"author_name": "Corbak",
"timestamp": "08/06/2022 16:48:51",
"content": "Itโs because your sum start from zero instead of one",
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},
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"timestamp": "08/06/2022 16:51:54",
"content": "ohhhh i didnt see that",
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},
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"author_id": 425448181879537660,
"author_name": "allarkvarkk",
"timestamp": "08/06/2022 16:51:55",
"content": "thank youu",
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},
{
"id": 1005579008638976000,
"author_id": 425448181879537660,
"author_name": "allarkvarkk",
"timestamp": "08/06/2022 16:51:58",
"content": ".close",
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},
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"id": 1005579010241208400,
"author_id": 805217272087838700,
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"timestamp": "08/06/2022 16:51:58",
"content": "Channel closed",
"attachments": [],
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"reference": null
}
] |
help-9
|
32765a1059b94455a8f0201189372e27
|
197,674 |
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{
"id": 1005579264076300300,
"author_id": 805217272087838700,
"author_name": "Mathematics Bot",
"timestamp": "08/06/2022 16:52:59",
"content": "Available help channel!",
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},
{
"id": 1005580801917853700,
"author_id": 168539726813331460,
"author_name": "Nerokyi",
"timestamp": "08/06/2022 16:59:05",
"content": "Alright I need help for this problem.",
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"timestamp": "08/06/2022 16:59:06",
"content": "Pinned a message.",
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"author_name": "Foden",
"timestamp": "08/06/2022 16:59:19",
"content": "8",
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"author_id": 168539726813331460,
"author_name": "Nerokyi",
"timestamp": "08/06/2022 16:59:57",
"content": "So in the following I solved for delta x which was pretty simple. But I am confuse on how to really solve for delta y",
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},
{
"id": 1005581104947937300,
"author_id": 168539726813331460,
"author_name": "Nerokyi",
"timestamp": "08/06/2022 17:00:18",
"content": "I just don't know how to really proceed with it.",
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},
{
"id": 1005581375107240100,
"author_id": 168539726813331460,
"author_name": "Nerokyi",
"timestamp": "08/06/2022 17:01:22",
"content": "I tried plugging into the y=mx+b formula",
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},
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"id": 1005581483928453200,
"author_id": 261933205387477000,
"author_name": "riemann",
"timestamp": "08/06/2022 17:01:48",
"content": "Use the first equation given in the problem statement",
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},
{
"id": 1005581576316395500,
"author_id": 168539726813331460,
"author_name": "Nerokyi",
"timestamp": "08/06/2022 17:02:10",
"content": "Put it in the y=mx+b formula?",
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},
{
"id": 1005581672923803800,
"author_id": 261933205387477000,
"author_name": "riemann",
"timestamp": "08/06/2022 17:02:33",
"content": "> (so that delta y = ...)",
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},
{
"id": 1005581700954345600,
"author_id": 261933205387477000,
"author_name": "riemann",
"timestamp": "08/06/2022 17:02:40",
"content": "Very first line",
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},
{
"id": 1005581796173434900,
"author_id": 168539726813331460,
"author_name": "Nerokyi",
"timestamp": "08/06/2022 17:03:03",
"content": "mhm",
"attachments": [],
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},
{
"id": 1005582066383061100,
"author_id": 261933205387477000,
"author_name": "riemann",
"timestamp": "08/06/2022 17:04:07",
"content": "Do you understand the delta y equation?",
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"author_name": "Nerokyi",
"timestamp": "08/06/2022 17:04:27",
"content": "lemme do my work rq",
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},
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"author_name": "Nerokyi",
"timestamp": "08/06/2022 17:04:31",
"content": "then I will get back to you",
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},
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"author_name": "Nerokyi",
"timestamp": "08/06/2022 17:07:12",
"content": "Yeah I got the second one correct now by plugging in the 3 and 5.25 into the equation.",
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"timestamp": "08/06/2022 17:07:21",
"content": "Then subtract the two equation",
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"author_name": "Nerokyi",
"timestamp": "08/06/2022 17:07:30",
"content": "In which I got 2.8125",
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"timestamp": "08/06/2022 17:07:48",
"content": "So it would be like y=1.25 * 5.25",
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"timestamp": "08/06/2022 17:07:50",
"content": "and solve for y",
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"timestamp": "08/06/2022 17:08:00",
"content": "now I just need to find the y value",
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"author_name": "Nerokyi",
"timestamp": "08/06/2022 17:08:17",
"content": "by plugging finding the y=mx+b equation I presume",
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"timestamp": "08/06/2022 17:08:22",
"content": "For problem 3",
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"author_name": "riemann",
"timestamp": "08/06/2022 17:11:16",
"content": "Yea and you know m = delta y / delta x",
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},
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"id": 1005583952976826400,
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"timestamp": "08/06/2022 17:11:37",
"content": "Use the information in part a to find b",
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"timestamp": "08/06/2022 17:11:52",
"content": "alright",
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},
{
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"timestamp": "08/06/2022 17:19:04",
"content": "ok I did y=0.5x+0",
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"timestamp": "08/06/2022 17:19:13",
"content": "and put it in 5.25",
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"timestamp": "08/06/2022 17:19:16",
"content": "but I got it wrong",
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"author_name": "riemann",
"timestamp": "08/06/2022 17:24:13",
"content": "Where did you get that m=0.5 and b=0??????",
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"author_name": "Nerokyi",
"timestamp": "08/06/2022 17:26:29",
"content": "I got it by doing 1.5/3",
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"author_name": "Nerokyi",
"timestamp": "08/06/2022 17:26:32",
"content": "which got me 0.5",
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},
{
"id": 1005587727229661300,
"author_id": 168539726813331460,
"author_name": "Nerokyi",
"timestamp": "08/06/2022 17:26:37",
"content": "then I plugged it in",
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},
{
"id": 1005587736629092500,
"author_id": 168539726813331460,
"author_name": "Nerokyi",
"timestamp": "08/06/2022 17:26:39",
"content": "by doing",
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"author_id": 168539726813331460,
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"timestamp": "08/06/2022 17:26:49",
"content": "1.5=0.5 *3 + b",
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"timestamp": "08/06/2022 17:27:03",
"content": "which led me to get b = 0",
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"timestamp": "08/06/2022 17:27:04",
"content": "Nah. That's a point on the line, not the slope",
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"timestamp": "08/06/2022 17:27:07",
"content": "oh",
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"id": 1005587891822547100,
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"timestamp": "08/06/2022 17:27:16",
"content": "The slope is given by this",
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"id": 1005587976799137900,
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"timestamp": "08/06/2022 17:27:36",
"content": "Maybe I should have asked if you knew that first",
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"timestamp": "08/06/2022 17:27:46",
"content": "yeah I don't think I know that",
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"timestamp": "08/06/2022 17:27:47",
"content": ".-.",
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},
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"id": 1005588078066409600,
"author_id": 261933205387477000,
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"timestamp": "08/06/2022 17:28:00",
"content": "Slope is change in y over change in x",
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"timestamp": "08/06/2022 17:28:06",
"content": "m is slope",
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},
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"timestamp": "08/06/2022 17:28:17",
"content": "mhm",
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},
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"id": 1005588150569144400,
"author_id": 261933205387477000,
"author_name": "riemann",
"timestamp": "08/06/2022 17:28:18",
"content": "Change in y is delta y, change in x is delta x",
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},
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"id": 1005588172857671700,
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"timestamp": "08/06/2022 17:28:23",
"content": "wait",
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},
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"author_name": "Nerokyi",
"timestamp": "08/06/2022 17:28:25",
"content": "so I use the change",
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"timestamp": "08/06/2022 17:28:28",
"content": "not the actual",
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{
"id": 1005588231716339800,
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"timestamp": "08/06/2022 17:28:37",
"content": "like",
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},
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"timestamp": "08/06/2022 17:28:40",
"content": "Correct. Because that's the definition of slope",
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"id": 1005588244462837800,
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"timestamp": "08/06/2022 17:28:40",
"content": "x and",
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},
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"id": 1005588270975045800,
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"timestamp": "08/06/2022 17:28:46",
"content": "oh...",
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"id": 1005588350033461400,
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"author_name": "riemann",
"timestamp": "08/06/2022 17:29:05",
"content": "Slope is not y/x",
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},
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"id": 1005588378571518000,
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"author_name": "riemann",
"timestamp": "08/06/2022 17:29:12",
"content": "Change is important",
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},
{
"id": 1005588509635137500,
"author_id": 168539726813331460,
"author_name": "Nerokyi",
"timestamp": "08/06/2022 17:29:43",
"content": "so my slope is 1.25",
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},
{
"id": 1005588600508919900,
"author_id": 168539726813331460,
"author_name": "Nerokyi",
"timestamp": "08/06/2022 17:30:05",
"content": "since I divide 2.8125 by 2.25",
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},
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"id": 1005588713151135900,
"author_id": 168539726813331460,
"author_name": "Nerokyi",
"timestamp": "08/06/2022 17:30:32",
"content": "then how do I solve for b?",
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"timestamp": "08/06/2022 17:34:05",
"content": ".",
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},
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"timestamp": "08/06/2022 17:36:47",
"content": "Got it right",
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},
{
"id": 1005590289987162100,
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"author_name": "Nerokyi",
"timestamp": "08/06/2022 17:36:48",
"content": "thanks",
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},
{
"id": 1005590349898596500,
"author_id": 168539726813331460,
"author_name": "Nerokyi",
"timestamp": "08/06/2022 17:37:02",
"content": "it was 4.3125",
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},
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"author_name": "Nerokyi",
"timestamp": "08/06/2022 17:37:07",
"content": "I can't read for my life.",
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"timestamp": "08/06/2022 17:37:09",
"content": ".close",
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},
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"id": 1005590381842399400,
"author_id": 805217272087838700,
"author_name": "Mathematics Bot",
"timestamp": "08/06/2022 17:37:09",
"content": "Channel closed",
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}
] |
help-9
|
94ba044f4bdc4e068105049b90402a70
|
197,675 |
[
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"timestamp": "08/06/2022 17:38:10",
"content": "Available help channel!",
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},
{
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"author_id": 342475274622861300,
"author_name": "Witchy Scholar (Evena)",
"timestamp": "08/06/2022 17:45:19",
"content": "Is this proof correct?",
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"timestamp": "08/06/2022 17:45:20",
"content": "Pinned a message.",
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"timestamp": "08/06/2022 17:59:59",
"content": "what are you trying to prove",
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"timestamp": "08/06/2022 18:00:42",
"content": "sqrt(10) == sqrt(2.5) * 2",
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"timestamp": "08/06/2022 18:01:33",
"content": "i dont think so",
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"author_id": 473405391167029250,
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"timestamp": "08/06/2022 18:01:47",
"content": "why are you writing (3^2+1)^2",
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"timestamp": "08/06/2022 18:01:52",
"content": "that is 100",
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"timestamp": "08/06/2022 18:02:13",
"content": "oh i see what you meant",
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"id": 1005596691203895400,
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"timestamp": "08/06/2022 18:02:14",
"content": "but",
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"timestamp": "08/06/2022 18:02:26",
"content": "this is not how you write a proof",
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"timestamp": "08/06/2022 18:02:29",
"content": "you start with one of the things",
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"timestamp": "08/06/2022 18:02:35",
"content": "do algebra, and get to the other thing",
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"timestamp": "08/06/2022 18:02:49",
"content": "you have equality between the things",
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"timestamp": "08/06/2022 18:03:42",
"content": "to start",
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"author_name": "JamesH",
"timestamp": "08/06/2022 18:04:12",
"content": "or wait",
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"timestamp": "08/06/2022 18:04:19",
"content": "ok maybe the does make sense",
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"author_name": "JamesH",
"timestamp": "08/06/2022 18:04:25",
"content": "but it is much more complicated than it needs to be",
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"author_name": "Witchy Scholar (Evena)",
"timestamp": "08/06/2022 18:04:35",
"content": "I don't know what an actual proof is. I start with two things which are equal, using the two triangles with equal hypotenuses.",
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"timestamp": "08/06/2022 18:04:57",
"content": "just write 2.5 = 5/2",
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"timestamp": "08/06/2022 18:05:22",
"content": "which means 2 * sqrt(5/2) = sqrt(4 * 5/2) = sqrt(10)",
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"author_name": "Witchy Scholar (Evena)",
"timestamp": "08/06/2022 18:07:07",
"content": "Wait, you can just square a multiplication to get it inside a sqrt?",
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"id": 1005597938849947800,
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"timestamp": "08/06/2022 18:07:11",
"content": "yes",
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"id": 1005597963877367800,
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"timestamp": "08/06/2022 18:07:17",
"content": "only a positive one",
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"id": 1005598196959031400,
"author_id": 342475274622861300,
"author_name": "Witchy Scholar (Evena)",
"timestamp": "08/06/2022 18:08:13",
"content": "Woah! How have I not come across this? haha, thank you very much.",
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"timestamp": "08/06/2022 18:08:17",
"content": "no problem",
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"timestamp": "08/06/2022 18:08:24",
"content": "it follows from exponent rules",
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"author_name": "JamesH",
"timestamp": "08/06/2022 18:10:11",
"content": "in particular, if we want to rewrite x * y^(1/2), we can write x = (x^2)^(1/2), then use the exponent law that a^n * b^n = (ab)^n",
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"timestamp": "08/06/2022 18:10:51",
"content": "this lets you write it x*y^(1/2) = (x^2)^(1/2) * y^(1/2) = (x^2y)^(1/2)",
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"timestamp": "08/06/2022 18:11:11",
"content": "but x has to be positive, otherwise it doesnt make sense",
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"timestamp": "08/06/2022 18:11:24",
"content": "you would have to factor out the negative and leave it outside",
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"timestamp": "08/06/2022 18:16:00",
"content": "or alternatively, $2\\sqrt{2.5}=\\sqrt{4}\\cdot\\sqrt{2.5}=\\sqrt{4\\cdot2.5}=\\sqrt{10}$",
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"timestamp": "08/06/2022 18:16:03",
"content": "**lirmirit**",
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"timestamp": "08/06/2022 18:17:20",
"content": "Okay, thank you. that makes a lot of sense.",
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"timestamp": "08/06/2022 18:18:42",
"content": "How might I simplify this then?",
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"timestamp": "08/06/2022 18:21:24",
"content": "you mean $2\\cdot(5/2)^2=0.5^2+3.5^2$",
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"timestamp": "08/06/2022 18:21:27",
"content": "**lirmirit**",
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"timestamp": "08/06/2022 18:22:03",
"content": "yes, thank you.",
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"id": 1005602128317919400,
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"author_name": "lirmirit",
"timestamp": "08/06/2022 18:23:50",
"content": "$2\\cdot\\left(\\frac{5}{2}\\right)^2=2\\cdot\\frac{25}{4}=\\frac{25}{2}$",
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"id": 1005602138740768900,
"author_id": 510789298321096700,
"author_name": "TeXit",
"timestamp": "08/06/2022 18:23:53",
"content": "**lirmirit**",
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"timestamp": "08/06/2022 18:24:37",
"content": "$0.5^2+3.5^2=\\frac{1}{4}+\\frac{49}{4}=\\frac{50}{4}=\\frac{25}{2}$",
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},
{
"id": 1005602335789154300,
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"timestamp": "08/06/2022 18:24:40",
"content": "**lirmirit**",
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"timestamp": "08/06/2022 18:25:39",
"content": "Okay, thank you.",
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"timestamp": "08/06/2022 18:40:39",
"content": "@Witchy Scholar (Evena) Has your question been resolved?",
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"content": "Channel closed",
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}
] |
help-9
|
acd8a5f320f342bab5033b4eb0064d70
|
197,676 |
[
{
"id": 1005610388836065400,
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"author_name": "Mathematics Bot",
"timestamp": "08/06/2022 18:56:40",
"content": "Available help channel!",
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},
{
"id": 1005614565477851100,
"author_id": 726966851254616200,
"author_name": "NoNameGuy",
"timestamp": "08/06/2022 19:13:15",
"content": "can someone please help me with this",
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"content": "Pinned a message.",
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"timestamp": "08/06/2022 19:13:58",
"content": "I understand that he's 6 times more likely to lose than win and 3 times more likely to lose then draw",
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{
"id": 1005616679625183400,
"author_id": 102893616577384450,
"author_name": "Tymelord14",
"timestamp": "08/06/2022 19:21:39",
"content": "First you want to find probability of loss, we're told $P(W)=6P(L)$, $P(D)=3P(L)$ but we're also subject to the constraint $P(W)+P(L)+P(D)=1$ since these are all the possible outcomes. This is sufficient info to find $P(L)$, then $P(L \\text{ and } L)=P(L)^2$ by assumption of independence of the games.",
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"timestamp": "08/06/2022 19:22:12",
"content": "**Tymelord14**",
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"timestamp": "08/06/2022 19:22:55",
"content": "Why is P(W)+P(L)+P(D) = 1 ?",
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"id": 1005617378090029200,
"author_id": 689108355632988300,
"author_name": "nisrine",
"timestamp": "08/06/2022 19:24:26",
"content": "because W L and D are the only possibilities",
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"author_id": 102893616577384450,
"author_name": "Tymelord14",
"timestamp": "08/06/2022 19:25:05",
"content": "and the events are mutually exclusive",
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"id": 1005617629815373800,
"author_id": 102893616577384450,
"author_name": "Tymelord14",
"timestamp": "08/06/2022 19:25:26",
"content": "mike can't win and lose, for example",
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"author_name": "NoNameGuy",
"timestamp": "08/06/2022 19:27:07",
"content": "Ohhh I get it now",
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},
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"id": 1005618073685999600,
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"author_name": "NoNameGuy",
"timestamp": "08/06/2022 19:27:12",
"content": "and then I sub in the losses",
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"timestamp": "08/06/2022 19:27:15",
"content": "get 1/10",
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"author_name": "NoNameGuy",
"timestamp": "08/06/2022 19:27:27",
"content": "then do 1/10*1/10 to get the chances that mike loses both games?",
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"timestamp": "08/06/2022 19:28:24",
"content": "That sounds good to me",
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"timestamp": "08/06/2022 19:28:34",
"content": "ok ty",
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},
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"id": 1005620957089628200,
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"timestamp": "08/06/2022 19:38:39",
"content": ".close",
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},
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"id": 1005620958876405900,
"author_id": 805217272087838700,
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"timestamp": "08/06/2022 19:38:40",
"content": "Channel closed",
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}
] |
help-9
|
18a42b3fa7f447a3b2cc2f2bac484b69
|
197,677 |
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"timestamp": "08/06/2022 19:43:52",
"content": "Not sure how to do these",
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"timestamp": "08/06/2022 19:53:41",
"content": "Whats part a",
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"timestamp": "08/06/2022 19:58:53",
"content": "@kunalch Has your question been resolved?",
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"timestamp": "08/06/2022 19:59:16",
"content": "I already got the answer",
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"timestamp": "08/06/2022 19:59:43",
"content": "Linear approximation assumes you have a line to reference",
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"content": "",
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"author_name": "GarlicBredFries",
"timestamp": "08/06/2022 19:59:52",
"content": "Oh wait",
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"author_name": "kunalch",
"timestamp": "08/06/2022 20:00:06",
"content": "hmm",
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"author_name": "GarlicBredFries",
"timestamp": "08/06/2022 20:00:26",
"content": "You get the tangent line approximation",
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"author_name": "kunalch",
"timestamp": "08/06/2022 20:00:47",
"content": "So find the tangent line of V?",
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"timestamp": "08/06/2022 20:01:25",
"content": "You do dV/dt",
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"timestamp": "08/06/2022 20:01:28",
"content": "Yeah",
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"author_id": 652747647521914900,
"author_name": "kunalch",
"timestamp": "08/06/2022 20:02:55",
"content": "Find the derivative of v?",
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"author_name": "kunalch",
"timestamp": "08/06/2022 20:02:59",
"content": "or of the tangent line",
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"timestamp": "08/06/2022 20:04:34",
"content": "@GarlicBredFries",
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"timestamp": "08/06/2022 20:04:50",
"content": "Find the derivative to get the tangent line",
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"timestamp": "08/06/2022 20:05:24",
"content": "Ok",
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"author_name": "kunalch",
"timestamp": "08/06/2022 20:05:27",
"content": "Partials",
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},
{
"id": 1005629726875996300,
"author_id": 907667015756574800,
"author_name": "Asagao ๆ้ก",
"timestamp": "08/06/2022 20:13:30",
"content": "you'd need a tangent plane",
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"author_id": 907667015756574800,
"author_name": "Asagao ๆ้ก",
"timestamp": "08/06/2022 20:13:32",
"content": "not a line",
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"author_name": "Mathematics Bot",
"timestamp": "08/06/2022 20:13:53",
"content": "Channel closed",
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}
] |
help-9
|
f3ec3db9ab194f74a04ad4b6f87bcdbe
|
197,678 |
[
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"author_name": "Asagao ๆ้ก",
"timestamp": "08/06/2022 20:14:45",
"content": "partial derivatives*",
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"content": "Available help channel!",
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"id": 1005670072624353400,
"author_id": 375220847448686600,
"author_name": "FarFromFury",
"timestamp": "08/06/2022 22:53:49",
"content": "thought i had the solution for the formula for A, but a later question gives a value for A(w) and finding w is negative, which can't be true",
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"content": "Pinned a message.",
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"author_id": 375220847448686600,
"author_name": "FarFromFury",
"timestamp": "08/06/2022 22:55:06",
"content": "is it right that adding the area of both the semicircle and rectangle would be the total cross-sectional area?",
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},
{
"id": 1005670640654757900,
"author_id": 375220847448686600,
"author_name": "FarFromFury",
"timestamp": "08/06/2022 22:56:05",
"content": "i gave L an arbitrary number to satisfy",
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"author_name": "FarFromFury",
"timestamp": "08/06/2022 23:00:30",
"content": "would the width (in blue) have an effect on area of the semicircle? as the radius of 25 doesn't extend to the exterior",
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"author_id": 349354952961032200,
"author_name": "Umbraleviathan",
"timestamp": "08/06/2022 23:07:48",
"content": "Are you finding the blue area?",
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},
{
"id": 1005673830280351700,
"author_id": 349354952961032200,
"author_name": "Umbraleviathan",
"timestamp": "08/06/2022 23:08:45",
"content": "And is the thickness of the curve also the same as the width?",
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},
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"id": 1005674050074456200,
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"author_name": "Umbraleviathan",
"timestamp": "08/06/2022 23:09:38",
"content": "Because that's an assumption I guess you can make from the given information",
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"id": 1005674097486864500,
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"author_name": "Umbraleviathan",
"timestamp": "08/06/2022 23:09:49",
"content": "In that case, the larger circle's radius is 25+w",
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"author_name": "Umbraleviathan",
"timestamp": "08/06/2022 23:10:06",
"content": "The length of the rectangular base would be 50+2w",
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"author_name": "FarFromFury",
"timestamp": "08/06/2022 23:11:32",
"content": "if i'm interpreting the question properly, it wants the cross sectional area of the plastic wall, which should be the blue",
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"id": 1005674636765319300,
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"author_name": "Umbraleviathan",
"timestamp": "08/06/2022 23:11:57",
"content": "Yeah so I'm asking about the thickness of the blue semicircle; is that also w",
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"timestamp": "08/06/2022 23:12:07",
"content": "That's assuming the blue as uniform thickness",
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"author_name": "FarFromFury",
"timestamp": "08/06/2022 23:12:09",
"content": "yeah, all uniform for w",
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"author_name": "Umbraleviathan",
"timestamp": "08/06/2022 23:12:30",
"content": "Then your larger semicircle's radius is 25+w, and the length (diameter) is 50+2w",
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"id": 1005675929881821200,
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"timestamp": "08/06/2022 23:17:06",
"content": "Finding the area shouldn't be too hard if it's a semicircle ring slapped onto a rectangle",
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"author_name": "Mathematics Bot",
"timestamp": "08/06/2022 23:27:10",
"content": "@FarFromFury Has your question been resolved?",
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"timestamp": "08/06/2022 23:27:28",
"content": "if i've got it right, if w=5, finding the area of the blue for the semicircle is the area of the total semicircle, 25+5, the subtracted from the area of the semicircle with radius 25",
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"timestamp": "08/06/2022 23:27:44",
"content": "then add that to the area of the rectangle",
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"timestamp": "08/06/2022 23:27:58",
"content": "and that should be the cross-sectional area of the blue in total",
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"timestamp": "08/06/2022 23:29:08",
"content": "Channel closed",
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}
] |
help-9
|
aa1e86952edb434ea119f35a17a12b75
|
197,679 |
[
{
"id": 1005712509862424600,
"author_id": 805217272087838700,
"author_name": "Mathematics Bot",
"timestamp": "08/07/2022 01:42:27",
"content": "Available help channel!",
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},
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"id": 1005714400801456100,
"author_id": 805217272087838700,
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"timestamp": "08/07/2022 01:49:58",
"content": "Pinned a message.",
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{
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"author_id": 910777539444744200,
"author_name": "Mr. Gamer",
"timestamp": "08/07/2022 01:50:16",
"content": "Whats the problem",
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},
{
"id": 1005714546268315600,
"author_id": 865065944644190200,
"author_name": "Moon Knight",
"timestamp": "08/07/2022 01:50:33",
"content": "i dont get it",
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},
{
"id": 1005714593076748300,
"author_id": 910777539444744200,
"author_name": "Mr. Gamer",
"timestamp": "08/07/2022 01:50:44",
"content": "What is the question asking you to do",
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},
{
"id": 1005714635246284800,
"author_id": 865065944644190200,
"author_name": "Moon Knight",
"timestamp": "08/07/2022 01:50:54",
"content": "dis one",
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},
{
"id": 1005714665491419100,
"author_id": 865065944644190200,
"author_name": "Moon Knight",
"timestamp": "08/07/2022 01:51:01",
"content": "um",
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},
{
"id": 1005714673821290500,
"author_id": 865065944644190200,
"author_name": "Moon Knight",
"timestamp": "08/07/2022 01:51:03",
"content": "-2pq",
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},
{
"id": 1005714683694686200,
"author_id": 865065944644190200,
"author_name": "Moon Knight",
"timestamp": "08/07/2022 01:51:05",
"content": "pr",
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},
{
"id": 1005714701293981700,
"author_id": 865065944644190200,
"author_name": "Moon Knight",
"timestamp": "08/07/2022 01:51:10",
"content": "-4pq",
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},
{
"id": 1005714713621045400,
"author_id": 865065944644190200,
"author_name": "Moon Knight",
"timestamp": "08/07/2022 01:51:13",
"content": "is that is",
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},
{
"id": 1005714718880702500,
"author_id": 865065944644190200,
"author_name": "Moon Knight",
"timestamp": "08/07/2022 01:51:14",
"content": "it",
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},
{
"id": 1005715070170431500,
"author_id": 220517274845577200,
"author_name": "ramonov",
"timestamp": "08/07/2022 01:52:38",
"content": "you posted 3 expressions",
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},
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"id": 1005715150822715400,
"author_id": 220517274845577200,
"author_name": "ramonov",
"timestamp": "08/07/2022 01:52:57",
"content": "can you clearly rewrite your result",
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},
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"id": 1005715352073805800,
"author_id": 865065944644190200,
"author_name": "Moon Knight",
"timestamp": "08/07/2022 01:53:45",
"content": "nvm",
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},
{
"id": 1005715356645605500,
"author_id": 865065944644190200,
"author_name": "Moon Knight",
"timestamp": "08/07/2022 01:53:46",
"content": "is ok",
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},
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"author_id": 805217272087838700,
"author_name": "Mathematics Bot",
"timestamp": "08/07/2022 01:53:51",
"content": "Channel closed",
"attachments": [],
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}
] |
help-9
|
e94b7d2769224bddbec2fbceb40f78f5
|
197,680 |
[
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"id": 1005716923587240000,
"author_id": 805217272087838700,
"author_name": "Mathematics Bot",
"timestamp": "08/07/2022 01:59:59",
"content": "Available help channel!",
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},
{
"id": 1005718657608986600,
"author_id": 393418159589163000,
"author_name": "Edward NewGate",
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"timestamp": "08/07/2022 02:06:53",
"content": "Pinned a message.",
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"id": 1005718745022480400,
"author_id": 697730177962344400,
"author_name": "Tarek Ahmed",
"timestamp": "08/07/2022 02:07:14",
"content": "Factor by grouping",
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},
{
"id": 1005718832343679000,
"author_id": 393418159589163000,
"author_name": "Edward NewGate",
"timestamp": "08/07/2022 02:07:34",
"content": "oki",
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},
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"id": 1005718846583345200,
"author_id": 393418159589163000,
"author_name": "Edward NewGate",
"timestamp": "08/07/2022 02:07:38",
"content": "thanks!",
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},
{
"id": 1005718887612031100,
"author_id": 697730177962344400,
"author_name": "Tarek Ahmed",
"timestamp": "08/07/2022 02:07:48",
"content": "Np",
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},
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"id": 1005718957174571000,
"author_id": 393418159589163000,
"author_name": "Edward NewGate",
"timestamp": "08/07/2022 02:08:04",
"content": "./close",
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"id": 1005718967521906700,
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"author_name": "Edward NewGate",
"timestamp": "08/07/2022 02:08:07",
"content": ".close",
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"content": "Channel closed",
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"mentions": [],
"reference": null
}
] |
help-9
|
38cf682354664f00b238ca53b7884af9
|
197,681 |
[
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"id": 1005725351168704600,
"author_id": 805217272087838700,
"author_name": "Mathematics Bot",
"timestamp": "08/07/2022 02:33:29",
"content": "Available help channel!",
"attachments": [],
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},
{
"id": 1005726348133810300,
"author_id": 756062513011097600,
"author_name": "Acrab",
"timestamp": "08/07/2022 02:37:26",
"content": "Hi, for part a, does it mean I'm going to find the distance such that (the norm of velocity) = c? How can I get to this then",
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"timestamp": "08/07/2022 02:37:27",
"content": "Pinned a message.",
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"author_id": 826318983413366800,
"author_name": "Cogwheels of the mind",
"timestamp": "08/07/2022 02:50:25",
"content": "Probably means\n$fโ(t)\\sqrt{\\sum_{i}r_{i}โ(f(t))^{2}}=c$ ?",
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},
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"id": 1005729624380166300,
"author_id": 510789298321096700,
"author_name": "TeXit",
"timestamp": "08/07/2022 02:50:28",
"content": "**Cogwheels of the mind**",
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"author_id": 756062513011097600,
"author_name": "Acrab",
"timestamp": "08/07/2022 02:50:59",
"content": "right",
"attachments": [],
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},
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"id": 1005729835961823200,
"author_id": 756062513011097600,
"author_name": "Acrab",
"timestamp": "08/07/2022 02:51:18",
"content": "I tried to find a such function, but I didn't get it",
"attachments": [],
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},
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"id": 1005730001351618600,
"author_id": 756062513011097600,
"author_name": "Acrab",
"timestamp": "08/07/2022 02:51:57",
"content": "any suggestions?",
"attachments": [],
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"author_name": "Cogwheels of the mind",
"timestamp": "08/07/2022 02:52:43",
"content": "Idk, not familiar",
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"id": 1005730362921603200,
"author_id": 756062513011097600,
"author_name": "Acrab",
"timestamp": "08/07/2022 02:53:24",
"content": "ok, thx",
"attachments": [],
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},
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"id": 1005731570935672800,
"author_id": 756062513011097600,
"author_name": "Acrab",
"timestamp": "08/07/2022 02:58:12",
"content": "@Helpers can I have some help on how to do this please",
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},
{
"id": 1005734321329553400,
"author_id": 756062513011097600,
"author_name": "Acrab",
"timestamp": "08/07/2022 03:09:07",
"content": ".close",
"attachments": [],
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},
{
"id": 1005734322696888400,
"author_id": 805217272087838700,
"author_name": "Mathematics Bot",
"timestamp": "08/07/2022 03:09:08",
"content": "Channel closed",
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}
] |
help-9
|
bce11829f38645aba56cee1fdfa2e147
|
197,682 |
[
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"id": 959641691437019300,
"author_id": 805217272087838700,
"author_name": "Mathematics Bot",
"timestamp": "04/01/2022 22:33:28",
"content": "Available help channel!",
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"reference": null
},
{
"id": 959642455303680000,
"author_id": 270824453334761470,
"author_name": "1Kลtare",
"timestamp": "04/01/2022 22:36:30",
"content": "",
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"timestamp": "04/01/2022 22:36:31",
"content": "Pinned a message.",
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"author_id": 270824453334761470,
"author_name": "1Kลtare",
"timestamp": "04/01/2022 22:37:25",
"content": "is foil method correct here or is it simply 9x^2",
"attachments": [],
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},
{
"id": 959643095060860900,
"author_id": 200013547491688450,
"author_name": "a disappointing son",
"timestamp": "04/01/2022 22:39:03",
"content": "FOIL is only applicable when multiplying binomials",
"attachments": [],
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},
{
"id": 959643158768148500,
"author_id": 270824453334761470,
"author_name": "1Kลtare",
"timestamp": "04/01/2022 22:39:18",
"content": "whats a binomial?",
"attachments": [],
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},
{
"id": 959643273213923300,
"author_id": 200013547491688450,
"author_name": "a disappointing son",
"timestamp": "04/01/2022 22:39:45",
"content": "an expression with two terms",
"attachments": [],
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},
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"author_id": 270824453334761470,
"author_name": "1Kลtare",
"timestamp": "04/01/2022 22:41:09",
"content": "oh so it would be 3x+4 for example in the bracket? so when multiplying by itself then foil would apply?",
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},
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"id": 959643711178960900,
"author_id": 200013547491688450,
"author_name": "a disappointing son",
"timestamp": "04/01/2022 22:41:30",
"content": "if you were expanding (3x+4)(3x+4), FOIL would apply, yes",
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"id": 959643796390424600,
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"author_name": "1Kลtare",
"timestamp": "04/01/2022 22:41:50",
"content": "i see so it was as simple as 9x^2?",
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},
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"id": 959643807610183700,
"author_id": 200013547491688450,
"author_name": "a disappointing son",
"timestamp": "04/01/2022 22:41:53",
"content": "yes",
"attachments": [],
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},
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"id": 959643829059854500,
"author_id": 270824453334761470,
"author_name": "1Kลtare",
"timestamp": "04/01/2022 22:41:58",
"content": "thank you",
"attachments": [],
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},
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"id": 959643887557820500,
"author_id": 270824453334761470,
"author_name": "1Kลtare",
"timestamp": "04/01/2022 22:42:12",
"content": ".close",
"attachments": [],
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},
{
"id": 959643889139081200,
"author_id": 805217272087838700,
"author_name": "Mathematics Bot",
"timestamp": "04/01/2022 22:42:12",
"content": "Channel closed",
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}
] |
help-9
|
0bd88e06ffe747f39213b3cd177c3f8c
|
197,683 |
[
{
"id": 1005751197933781000,
"author_id": 805217272087838700,
"author_name": "Mathematics Bot",
"timestamp": "08/07/2022 04:16:11",
"content": "Available help channel!",
"attachments": [],
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},
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"id": 1005751424178729000,
"author_id": 610844733194895400,
"author_name": "Foremost",
"timestamp": "08/07/2022 04:17:05",
"content": "I am haunted by the sense that some effectively imperceptible error in our system of mathematics has rendered humanity incapable of achieving those loftier things which are truly sought for our attainment.\n\nConsider the follow which some could perhaps call \"semantic discrepancies\":\n\nConsider the multiplication of a quantity of three with a quantity of two:\n3x2 = 2 + 2 + 2 = 6\n2x3 = 3 + 3 = 6\n3x2 =! 2x3 because (2 + 2 + 2) =! (3 + 3) although both (2 + 2 + 2) and (3 + 3) = 6.\nMade simpler: we cannot correctly state that a quantity of three instanced twice is equivalent to a quantity of two instanced thrice although both quantities compound as six.\n\nTwo groups of three bananas and thee groups of two bananas cannot be called an exact or perfect equivalenc(y).\n(๐ ๐ ๐)(๐ ๐ ๐)\nversus\n(๐ ๐ )(๐๐)(๐๐)\nwhich both make for\n(๐ ๐ ๐๐ ๐๐)\n\nNow evidenced, let us consider 1x0:\n1x0 = one instance of zero = 0. This checks out.\nBut then let us consider 0x0:\n0x0 = no instances of zero which cannot = 0 because 0 = 1(0) = one time (of) zero which =! 0x0.\nWould it now be more correct then for us to say that 0x0 cannot = 0 (which = 1(0)) and therefore must instead = any N where Nโ 0?\nI posit that 0(0) = N where Nโ 0 or 0โNโโคE where E = nonzero.\n\nFurther consider any 0xN or Nx0.\nNow Nx0 must then equal N time(s) of zero,\nand 0xN must then equal no times (of) N where if 0โN then 0xN must yield ร = {} (empty set/null set) else any unforeseen nonordinal implementation.\n\nI know this is a bit convuluted and I wish I could have explained it better, but does anyone have any unenimical thoughts regarding these things (t)herementioned?\n\nI am haunted by the sense that some effectively imperceptible error in our system of mathematics has rendered humanity incapable of achieving those loftier things which are truly fit for our attainment.\n\ntl;dr zero times zero cannot equal zero because zero equals one times zero which does not equal zero times zeros. zero times (of) zero therefore must equal any nonzero.",
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"author_id": 805217272087838700,
"author_name": "Mathematics Bot",
"timestamp": "08/07/2022 04:17:05",
"content": "Pinned a message.",
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"id": 1005751958856007800,
"author_id": 610844733194895400,
"author_name": "Foremost",
"timestamp": "08/07/2022 04:19:12",
"content": "FORMATTING ISSUE One sec to correct.",
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},
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"id": 1005752643693596700,
"author_id": 984319941417251000,
"author_name": "๐๐๐ถ๐๐๐ถ๐",
"timestamp": "08/07/2022 04:21:56",
"content": "a little hard to read right now with the *'s, but non-injective functions exist",
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},
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"id": 1005752971340034000,
"author_id": 610844733194895400,
"author_name": "Foremost",
"timestamp": "08/07/2022 04:23:14",
"content": "I just finished correcting those. Apologies. But what is a \"non-injective function\"?",
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"id": 1005753017083105300,
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"author_name": "Foremost",
"timestamp": "08/07/2022 04:23:25",
"content": "google brb",
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"author_id": 984319941417251000,
"author_name": "๐๐๐ถ๐๐๐ถ๐",
"timestamp": "08/07/2022 04:23:29",
"content": "a function that sends two different things to the same thing",
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"id": 1005753254828834800,
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"author_name": "Foremost",
"timestamp": "08/07/2022 04:24:21",
"content": "That makes sense to me. I strill struggle to comprehend basic functions...lol...but how does this pertain to the above musings though? .0.",
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"author_name": "๐๐๐ถ๐๐๐ถ๐",
"timestamp": "08/07/2022 04:24:37",
"content": "multiplication is a function",
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"id": 1005753368788082700,
"author_id": 984319941417251000,
"author_name": "๐๐๐ถ๐๐๐ถ๐",
"timestamp": "08/07/2022 04:24:49",
"content": "it takes in two numbers and sends something out",
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"author_name": "๐๐๐ถ๐๐๐ถ๐",
"timestamp": "08/07/2022 04:25:43",
"content": "non-injective functions are everywhere though, the bigger idea you are thinking about isn't very specific to multiplication",
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"id": 1005753815150121000,
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"author_name": "Foremost",
"timestamp": "08/07/2022 04:26:35",
"content": "Yeah, I think that multiplication was just the best (most simple) \"peephole\" into the idea, so to speak lol",
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"timestamp": "08/07/2022 04:26:43",
"content": "if that makes sense lol",
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"author_name": "๐๐๐ถ๐๐๐ถ๐",
"timestamp": "08/07/2022 04:28:32",
"content": "ok so... if we call the multiplication function \\*, then we could write \\*(0,1) = 0. But typically (like, always) people write 0\\*1 in place of \\*(0,1)",
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"author_name": "๐๐๐ถ๐๐๐ถ๐",
"timestamp": "08/07/2022 04:29:38",
"content": "for a function to send (0,0) and (1,0) and (9,0) to the same thing is perfectly fine",
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"author_name": "๐๐๐ถ๐๐๐ถ๐",
"timestamp": "08/07/2022 04:30:35",
"content": "the squaring function sends -4 and 4 to 16, but that's ok. No one thinks that means -4 = 4",
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"author_id": 805217272087838700,
"author_name": "Mathematics Bot",
"timestamp": "08/07/2022 04:41:43",
"content": "@Foremost Has your question been resolved?",
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"timestamp": "08/07/2022 04:42:05",
"content": "eh. meh. i guess kinda sorta not really lol",
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"timestamp": "08/07/2022 05:12:06",
"content": "@Foremost Has your question been resolved?",
"attachments": [],
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"author_name": "Saccharine",
"timestamp": "08/07/2022 05:16:41",
"content": "if you're interested in the standard logical constructions of math, then you should note that \"multiplication\" is just something we define as (perhaps) f: ZxZ -> Z",
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"author_id": 704179090395103200,
"author_name": "Saccharine",
"timestamp": "08/07/2022 05:17:26",
"content": "perhaps you appeal to some intuition about our reality, but in reality, the multiplication in mathematics is just some function that's defined and that maps onto the set of integers",
"attachments": [],
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},
{
"id": 1005766794973298800,
"author_id": 704179090395103200,
"author_name": "Saccharine",
"timestamp": "08/07/2022 05:18:10",
"content": "one could define something like \"two-multiplication\" which is just g(p, q) = f(p, q) + f(p, q), i.e. 2 times p times q",
"attachments": [],
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},
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"id": 1005767040398786600,
"author_id": 704179090395103200,
"author_name": "Saccharine",
"timestamp": "08/07/2022 05:19:08",
"content": "so your assertion that mathematics has some fundamental error because it doesn't align with your intuition about bananas is missing a pretty crucial step: why that should be true anyway",
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"id": 1005767450555588600,
"author_id": 704179090395103200,
"author_name": "Saccharine",
"timestamp": "08/07/2022 05:20:46",
"content": "of course, there are issues with how you define \"perfect equivalence\" and all of those things, and the idea that 3 + 3 is not equal to 2 + 2 + 2 is also very debatable, but you have a more fundamental error in your logic, and that is you haven't shown that the definition of multiplication is inconsistent with commonly accepted properties (or that multiplication, as defined, cannot exist). you've instead leveled criticism at perhaps its *applicability* to situations involving bananas",
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"author_id": 805217272087838700,
"author_name": "Mathematics Bot",
"timestamp": "08/07/2022 05:42:06",
"content": "Channel closed",
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}
] |
help-9
|
b17b84cdcafe4e20aa47e3fb08c04044
|
197,684 |
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"author_name": "Mathematics Bot",
"timestamp": "08/07/2022 05:43:07",
"content": "Available help channel!",
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},
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"author_id": 852470857569402900,
"author_name": "Teek0505",
"timestamp": "08/07/2022 06:25:04",
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"timestamp": "08/07/2022 06:25:05",
"content": "Pinned a message.",
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"author_id": 852470857569402900,
"author_name": "Teek0505",
"timestamp": "08/07/2022 06:25:19",
"content": "Something is wrong with the numerator",
"attachments": [],
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},
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"timestamp": "08/07/2022 06:25:28",
"content": "Help please",
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"author_name": "Teek0505",
"timestamp": "08/07/2022 06:39:47",
"content": "I just need someone to confirm my answer.",
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"timestamp": "08/07/2022 06:44:06",
"content": "Ohm",
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"timestamp": "08/07/2022 06:44:15",
"content": "Resistors",
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"timestamp": "08/07/2022 06:44:16",
"content": "Hmm",
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"author_name": "Mathematics Bot",
"timestamp": "08/07/2022 06:54:47",
"content": "@Teek0505 Has your question been resolved?",
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"timestamp": "08/07/2022 06:54:58",
"content": "Lol",
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"content": ":sippy:",
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"timestamp": "08/07/2022 06:55:39",
"content": "Ah yes",
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"content": ":bleakkekw:",
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"timestamp": "08/07/2022 06:57:35",
"content": "My attempt",
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"timestamp": "08/07/2022 07:01:39",
"content": "Maybe try at helpers if u want",
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"content": "@Helpers",
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"timestamp": "08/07/2022 07:33:33",
"content": "@Teek0505 Has your question been resolved?",
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"timestamp": "08/07/2022 07:38:54",
"content": "idk if this formula could help",
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"timestamp": "08/07/2022 07:43:02",
"content": "No idts. Thanks tho",
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"author_name": "smermla9",
"timestamp": "08/07/2022 07:50:09",
"content": "welcome",
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"author_name": "Teek0505",
"timestamp": "08/07/2022 08:16:59",
"content": "@Helpers",
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"id": 1005821220513648600,
"author_id": 363399048037793800,
"author_name": "Corbak",
"timestamp": "08/07/2022 08:54:26",
"content": "Did you try to rewrite the denominator as a double sum ?",
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"author_id": 363399048037793800,
"author_name": "Corbak",
"timestamp": "08/07/2022 08:58:10",
"content": "Try to sum from 1 to n the sin(j/n) times the sum from 1 to j-1 of sin(i/n)",
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"author_name": "Corbak",
"timestamp": "08/07/2022 09:00:06",
"content": "Then you can simplify sin(k/n) as sin((k-1 +1)/n)",
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"timestamp": "08/07/2022 09:20:06",
"content": "@Teek0505 Has your question been resolved?",
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"timestamp": "08/07/2022 09:20:33",
"content": "I did this",
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"timestamp": "08/07/2022 09:30:48",
"content": "@Corbak",
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"timestamp": "08/07/2022 09:39:16",
"content": "Seems correct to me",
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"timestamp": "08/07/2022 09:41:36",
"content": "Ohk thanks.",
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"timestamp": "08/07/2022 09:41:45",
"content": "Book's solution",
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"timestamp": "08/07/2022 09:41:52",
"content": "If you wanted to see.",
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"author_name": "Corbak",
"timestamp": "08/07/2022 09:43:50",
"content": "The only problem is the integral ln(sin(x)) at 0",
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"author_name": "Corbak",
"timestamp": "08/07/2022 09:44:32",
"content": "If it diverges it might be another limit",
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"id": 1005834446282432600,
"author_id": 363399048037793800,
"author_name": "Corbak",
"timestamp": "08/07/2022 09:46:59",
"content": "And i donโt undertand why the log disapear with un",
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"author_id": 363399048037793800,
"author_name": "Corbak",
"timestamp": "08/07/2022 09:49:05",
"content": "The solution proposed isnโt correct",
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"author_name": "Mathematics Bot",
"timestamp": "08/07/2022 11:41:52",
"content": "@Teek0505 Has your question been resolved?",
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"timestamp": "08/07/2022 12:07:29",
"content": "Yep I understand.",
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"timestamp": "08/07/2022 12:07:32",
"content": "Thanks for confirming.",
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"timestamp": "08/07/2022 12:07:35",
"content": ".close",
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"content": "Channel closed",
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}
] |
help-9
|
41cfb2a6880d489f81e64add1fc6896f
|
197,685 |
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"timestamp": "08/07/2022 12:08:35",
"content": "Available help channel!",
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"id": 1005876454858432500,
"author_id": 998257141943128000,
"author_name": "JChapman",
"timestamp": "08/07/2022 12:33:55",
"content": "find the value of",
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"content": "Pinned a message.",
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"id": 1005876843376812000,
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"timestamp": "08/07/2022 12:35:27",
"content": "I have tried this",
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"id": 1005876866214805500,
"author_id": 998257141943128000,
"author_name": "JChapman",
"timestamp": "08/07/2022 12:35:33",
"content": "but am now unsure on where to go",
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"id": 1005879093197295600,
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"timestamp": "08/07/2022 12:44:24",
"content": "Have been directed to this by a prof but cant get a clear understanding",
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"content": "@JChapman Has your question been resolved?",
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"content": ".close",
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] |
help-9
|
e3ce6dcf66954dd9bffd3653f114dd88
|
197,686 |
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"content": "Available help channel!",
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{
"id": 1005892350058446800,
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"author_name": "ุชุง ุฆุจุงุช",
"timestamp": "08/07/2022 13:37:04",
"content": "I feel like the SAT math is so hard anyone got any tips to practicing it and learning the material? where to start and how to start?",
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"id": 1005892352084291700,
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"timestamp": "08/07/2022 13:40:28",
"content": "Just start with jee material",
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"timestamp": "08/07/2022 13:41:03",
"content": "100% sure u will get full marks in maths section if u practice it well",
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"id": 1005894748428579000,
"author_id": 757971959538647000,
"author_name": "Tech support",
"timestamp": "08/07/2022 13:46:36",
"content": "I dont have the SAT in my country, but I have something similar, so everything I stated here may not work 100% in the SAT. One thing I have found helped me is to learn how the problems are structured generally, usualy very similar problems apear on every test, it often helps when you get stuck to ask yourself \"what kind of trick do they want me to use here\". Often then answer can be found without even crunching the numbers, as long as the answers are diferent enough. Things like this made me go from 54/80 to 77/80 in score in just a few weeks\n(for me its 40x2 multiple choice questions in 55x2 minutes)",
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"id": 1005895108375355400,
"author_id": 831433025471774700,
"author_name": "cleverdumb [2756956]",
"timestamp": "08/07/2022 13:48:02",
"content": "just have this in mind: The guy who made the questions is evil and hates you and wants you to fail so be careful of his/her traps and dont fall into them context-wise it shouldnt be too hard just do some materials about it",
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"id": 1005895624027279500,
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"timestamp": "08/07/2022 13:50:05",
"content": "Yeah\nThe goal of theese tests arent for everyone to get 100%, they want to be able to diferentiate between the person with 50% and 80%, not 94% vs 97%",
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"timestamp": "08/07/2022 13:55:05",
"content": "@ุชุง ุฆุจุงุช Has your question been resolved?",
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"timestamp": "08/07/2022 13:55:49",
"content": "what's that",
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"author_id": 994286722357674100,
"author_name": "Twerkingbee",
"timestamp": "08/07/2022 13:56:39",
"content": "One of the world's toughest exams",
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"author_name": "ุชุง ุฆุจุงุช",
"timestamp": "08/07/2022 14:01:18",
"content": "I see thank you, also to you guys @cleverdumb [2756956] @Tech support",
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"content": "np :)",
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"timestamp": "08/07/2022 14:31:19",
"content": "@ุชุง ุฆุจุงุช Has your question been resolved?",
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"content": "@ุชุง ุฆุจุงุช Has your question been resolved?",
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}
] |
help-9
|
b608571774954ff0800938933b73244a
|
197,687 |
[
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"author_name": "Mathematics Bot",
"timestamp": "08/07/2022 16:43:05",
"content": "Available help channel!",
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"reference": null
},
{
"id": 1005943422919659800,
"author_id": 1003266905303421000,
"author_name": "F-22 Ranchu Squadron",
"timestamp": "08/07/2022 17:00:01",
"content": "Hi, so if 27 pumps empty a dam of capacity 'x' in 6 days or 23 pumps in 9 days while flowing water enters the dam at a constant rate at the same time, how do we find how much each pump makes and then how many should be connected to the dam so the water volume remains constant?",
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"id": 1005943425130045400,
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"timestamp": "08/07/2022 17:15:01",
"content": "@F-22 Ranchu Squadron Has your question been resolved?",
"attachments": [],
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"author_name": "F-22 Ranchu Squadron",
"timestamp": "08/07/2022 17:19:58",
"content": "?",
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{
"id": 1005949840934580400,
"author_id": 1003266905303421000,
"author_name": "F-22 Ranchu Squadron",
"timestamp": "08/07/2022 17:25:31",
"content": "Pls help",
"attachments": [],
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},
{
"id": 1005950589475233800,
"author_id": 1003266905303421000,
"author_name": "F-22 Ranchu Squadron",
"timestamp": "08/07/2022 17:28:30",
"content": "Anyone??",
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"author_id": 805217272087838700,
"author_name": "Mathematics Bot",
"timestamp": "08/07/2022 17:58:30",
"content": "@F-22 Ranchu Squadron Has your question been resolved?",
"attachments": [],
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"author_name": "Tymelord14",
"timestamp": "08/07/2022 18:03:53",
"content": "Are you given the initial amount of water in the dam? If not that's fine, we can figure it out along the way",
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"content": "@F-22 Ranchu Squadron",
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"timestamp": "08/07/2022 18:28:30",
"content": "Channel closed",
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] |
help-9
|
088c7df6da014f3b8e5a1bd07c6efc90
|
197,688 |
[
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"author_name": "Mathematics Bot",
"timestamp": "08/07/2022 18:29:30",
"content": "Available help channel!",
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{
"id": 1005970809300455600,
"author_id": 211057300427898880,
"author_name": "notableboyscouts",
"timestamp": "08/07/2022 18:48:50",
"content": "I donโt think any of these answers are correct",
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"timestamp": "08/07/2022 18:48:51",
"content": "Pinned a message.",
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"id": 1005971237115281400,
"author_id": 761155030513352700,
"author_name": "Bungo",
"timestamp": "08/07/2022 18:50:32",
"content": "what answer do you get?",
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"id": 1005971333831737300,
"author_id": 211057300427898880,
"author_name": "notableboyscouts",
"timestamp": "08/07/2022 18:50:56",
"content": "27.9",
"attachments": [],
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},
{
"id": 1005971457483997200,
"author_id": 764959481070616600,
"author_name": "Toby",
"timestamp": "08/07/2022 18:51:25",
"content": "set your calculator to radians mode",
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},
{
"id": 1005971470205337600,
"author_id": 761155030513352700,
"author_name": "Bungo",
"timestamp": "08/07/2022 18:51:28",
"content": "are you sure you used radians mode?",
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{
"id": 1005971580066734100,
"author_id": 211057300427898880,
"author_name": "notableboyscouts",
"timestamp": "08/07/2022 18:51:54",
"content": "Ohhh",
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{
"id": 1005971600006463500,
"author_id": 211057300427898880,
"author_name": "notableboyscouts",
"timestamp": "08/07/2022 18:51:59",
"content": "Nvm itโs in degree mode",
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"id": 1005971628536107000,
"author_id": 761155030513352700,
"author_name": "Bungo",
"timestamp": "08/07/2022 18:52:06",
"content": "easy mistake to make",
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{
"id": 1005972558849515500,
"author_id": 211057300427898880,
"author_name": "notableboyscouts",
"timestamp": "08/07/2022 18:55:48",
"content": "Also would two expressions that are the exact same count as cofunctions?",
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"id": 1005972610791788500,
"author_id": 211057300427898880,
"author_name": "notableboyscouts",
"timestamp": "08/07/2022 18:56:00",
"content": "Or do they have to be two different expressions that have the same value",
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"id": 1005973182118903800,
"author_id": 211057300427898880,
"author_name": "notableboyscouts",
"timestamp": "08/07/2022 18:58:16",
"content": "@Bungo",
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"id": 1005973229971714200,
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"author_name": "dldh06",
"timestamp": "08/07/2022 18:58:28",
"content": "Just don't have it in gradian mode",
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"timestamp": "08/07/2022 19:13:16",
"content": "@notableboyscouts Has your question been resolved?",
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"timestamp": "08/07/2022 19:14:52",
"content": "Channel closed",
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help-9
|
97ffce29e9d04b82904e778766a7fcba
|
197,689 |
[
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"id": 1005977613824700400,
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"author_name": "Mathematics Bot",
"timestamp": "08/07/2022 19:15:53",
"content": "Available help channel!",
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},
{
"id": 1005989455477358600,
"author_id": 835939107367682000,
"author_name": "A.L.I.C.E",
"timestamp": "08/07/2022 20:02:56",
"content": "I have an assignment about ODEs and 2nd question is:\n> A thermometer that marks 15Fยฐ is carried to a room where temperature is 81Fยฐ. A minute later thermometer marks 30Fยฐ\n> \n> (a) Find thermometer function in time that marks temperature\n> \n> (b) Find how much thermometer will mark if 5 minutes pass\n> \n> (c) How much time will it have to happen to thermometer marks 45Fยฐ\n\nI had used linear approximation such that `T(t) = 15Fยฐ/m ร (t + 1m)` I mean, that works XD\n\nBut my question is, as I didn't use sort of ODE to solve it, even I don't see any ODE in question, such as speed of thermometer `dT/dt` is not mentioned, so what I did is it okay, or is there a sort of ODE in the question statement?",
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"timestamp": "08/07/2022 20:02:56",
"content": "Pinned a message.",
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"author_name": "Mathematics Bot",
"timestamp": "08/07/2022 20:17:56",
"content": "@A.L.I.C.E Has your question been resolved?",
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"id": 1005996480563257300,
"author_id": 189001310937284600,
"author_name": "Tom",
"timestamp": "08/07/2022 20:30:51",
"content": "It's not in the question and idk if it's expected knowledge for your assignment but I think that \ndT/dt = a * (T - room_temp)\nwould be the appropriate ODE",
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"id": 1005996541607149700,
"author_id": 835939107367682000,
"author_name": "A.L.I.C.E",
"timestamp": "08/07/2022 20:31:06",
"content": "Yeah",
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{
"id": 1005996688172908700,
"author_id": 835939107367682000,
"author_name": "A.L.I.C.E",
"timestamp": "08/07/2022 20:31:40",
"content": "I didn't use that because as we're not physics class but math instead XD",
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"id": 1005997037076107300,
"author_id": 189001310937284600,
"author_name": "Tom",
"timestamp": "08/07/2022 20:33:04",
"content": "yeah, seems strange to ask a question that's testing your physics knowledge but idk how else to get an ODE",
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"id": 1005997107209064600,
"author_id": 835939107367682000,
"author_name": "A.L.I.C.E",
"timestamp": "08/07/2022 20:33:20",
"content": "XD",
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},
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"id": 1005997205607424000,
"author_id": 835939107367682000,
"author_name": "A.L.I.C.E",
"timestamp": "08/07/2022 20:33:44",
"content": "Thanks you for answering btw!",
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"id": 1005997288751108200,
"author_id": 835939107367682000,
"author_name": "A.L.I.C.E",
"timestamp": "08/07/2022 20:34:04",
"content": ".close",
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"author_name": "Mathematics Bot",
"timestamp": "08/07/2022 20:34:04",
"content": "Channel closed",
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}
] |
help-9
|
ffe611a64f01492d93c0314415d00973
|
197,690 |
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"timestamp": "08/07/2022 20:35:05",
"content": "Available help channel!",
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},
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"id": 1006008618618990600,
"author_id": 994461493502431200,
"author_name": "vanessa.v",
"timestamp": "08/07/2022 21:19:05",
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"content": "Pinned a message.",
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"id": 1006008623048179800,
"author_id": 994461493502431200,
"author_name": "vanessa.v",
"timestamp": "08/07/2022 21:19:06",
"content": ",rotate",
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},
{
"id": 1006008625413763200,
"author_id": 510789298321096700,
"author_name": "TeXit",
"timestamp": "08/07/2022 21:19:07",
"content": "",
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"author_name": "dldh06",
"timestamp": "08/07/2022 21:19:30",
"content": "That's a test?",
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},
{
"id": 1006008822453784600,
"author_id": 994461493502431200,
"author_name": "vanessa.v",
"timestamp": "08/07/2022 21:19:54",
"content": "its a practice test that my teacher gave the grade 12s",
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},
{
"id": 1006008881379561500,
"author_id": 994461493502431200,
"author_name": "vanessa.v",
"timestamp": "08/07/2022 21:20:08",
"content": "well it was a test for them, but practice test for me",
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},
{
"id": 1006008923637162000,
"author_id": 994461493502431200,
"author_name": "vanessa.v",
"timestamp": "08/07/2022 21:20:18",
"content": "so not for marks",
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},
{
"id": 1006009026854801500,
"author_id": 485903210272391200,
"author_name": "dldh06",
"timestamp": "08/07/2022 21:20:42",
"content": "So what exactly is your question?",
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{
"id": 1006009209369919500,
"author_id": 994461493502431200,
"author_name": "vanessa.v",
"timestamp": "08/07/2022 21:21:26",
"content": "just looking at how i answered each question, does it look correct? or am i using an incorrect solving method",
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},
{
"id": 1006009492208615600,
"author_id": 485903210272391200,
"author_name": "dldh06",
"timestamp": "08/07/2022 21:22:33",
"content": "I'm gonna be honest, it's hard to read because it's kinda small",
"attachments": [],
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},
{
"id": 1006009605790384300,
"author_id": 994461493502431200,
"author_name": "vanessa.v",
"timestamp": "08/07/2022 21:23:00",
"content": "no worries i will try to send a clearer pic",
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},
{
"id": 1006009762762211300,
"author_id": 994461493502431200,
"author_name": "vanessa.v",
"timestamp": "08/07/2022 21:23:38",
"content": ",rotate",
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},
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"timestamp": "08/07/2022 21:23:46",
"content": "is that better or still not good",
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},
{
"id": 1006009825571897300,
"author_id": 485903210272391200,
"author_name": "dldh06",
"timestamp": "08/07/2022 21:23:53",
"content": "A lot better",
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},
{
"id": 1006009860464316400,
"author_id": 994461493502431200,
"author_name": "vanessa.v",
"timestamp": "08/07/2022 21:24:01",
"content": "great",
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},
{
"id": 1006010420156436600,
"author_id": 485903210272391200,
"author_name": "dldh06",
"timestamp": "08/07/2022 21:26:14",
"content": "I'm gonna be honest, I don't recall this stuff, sorry. I thought I could help somehow, and also to mention that it was hard to read",
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},
{
"id": 1006010525043413100,
"author_id": 994461493502431200,
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"timestamp": "08/07/2022 21:26:39",
"content": "sorry my handwriting isnt great loll",
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},
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"author_id": 994461493502431200,
"author_name": "vanessa.v",
"timestamp": "08/07/2022 21:26:59",
"content": "no problem though, ill tryn find help elsewhere for now",
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},
{
"id": 1006010620778401800,
"author_id": 994461493502431200,
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"timestamp": "08/07/2022 21:27:02",
"content": ".close",
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},
{
"id": 1006010623513088000,
"author_id": 805217272087838700,
"author_name": "Mathematics Bot",
"timestamp": "08/07/2022 21:27:03",
"content": "Channel closed",
"attachments": [],
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"reference": null
}
] |
help-9
|
a78c6068375042fea8699596028df030
|
197,691 |
[
{
"id": 1006010661194694800,
"author_id": 485903210272391200,
"author_name": "dldh06",
"timestamp": "08/07/2022 21:27:12",
"content": "Nah, the handwriting was fine, it's just that when you zoomed in, it made it blurry",
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"reference": null
},
{
"id": 1006010714042933200,
"author_id": 994461493502431200,
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"timestamp": "08/07/2022 21:27:25",
"content": "ohh",
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},
{
"id": 1006010801494163500,
"author_id": 485903210272391200,
"author_name": "dldh06",
"timestamp": "08/07/2022 21:27:45",
"content": "For the original, that's what happened",
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},
{
"id": 1006010806518956000,
"author_id": 994461493502431200,
"author_name": "vanessa.v",
"timestamp": "08/07/2022 21:27:47",
"content": "okay if i have trouble with anything ill send later on",
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},
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"id": 1006010847254040600,
"author_id": 994461493502431200,
"author_name": "vanessa.v",
"timestamp": "08/07/2022 21:27:56",
"content": "and make it clearer",
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},
{
"id": 1006075664434208800,
"author_id": 805217272087838700,
"author_name": "Mathematics Bot",
"timestamp": "08/08/2022 01:45:30",
"content": "Available help channel!",
"attachments": [],
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"reference": null
},
{
"id": 1006079542303129600,
"author_id": 701704062994743400,
"author_name": "sLoct",
"timestamp": "08/08/2022 02:00:54",
"content": "Hello",
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},
{
"id": 1006079544391897100,
"author_id": 805217272087838700,
"author_name": "Mathematics Bot",
"timestamp": "08/08/2022 02:00:55",
"content": "Pinned a message.",
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"channelId": 486844875632017400,
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{
"id": 1006079574330847400,
"author_id": 701704062994743400,
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"timestamp": "08/08/2022 02:01:02",
"content": "",
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"id": 1006079609000951900,
"author_id": 701704062994743400,
"author_name": "sLoct",
"timestamp": "08/08/2022 02:01:10",
"content": "I don't understand what 4b is asking me",
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},
{
"id": 1006079632489070600,
"author_id": 701704062994743400,
"author_name": "sLoct",
"timestamp": "08/08/2022 02:01:16",
"content": "What does the square mean",
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},
{
"id": 1006079713225220100,
"author_id": 701704062994743400,
"author_name": "sLoct",
"timestamp": "08/08/2022 02:01:35",
"content": "I did 4a",
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"id": 1006081735508906000,
"author_id": 261933205387477000,
"author_name": "riemann",
"timestamp": "08/08/2022 02:09:37",
"content": "the second derivative",
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{
"id": 1006081978782720000,
"author_id": 261933205387477000,
"author_name": "riemann",
"timestamp": "08/08/2022 02:10:35",
"content": "so if $y = f(x) = 5x^3$, then",
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},
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"id": 1006081980624027600,
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"timestamp": "08/08/2022 02:10:36",
"content": "$\\frac{d^2y}{dx^2} = f''(x) = 5(3)(2)x = 30x$",
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},
{
"id": 1006081988148609000,
"author_id": 510789298321096700,
"author_name": "TeXit",
"timestamp": "08/08/2022 02:10:38",
"content": "**riemann**",
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"id": 1006081998244298800,
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"timestamp": "08/08/2022 02:10:40",
"content": "**riemann**",
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"author_name": "Mathematics Bot",
"timestamp": "08/08/2022 02:16:35",
"content": "@sLoct Has your question been resolved?",
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"id": 1006085726435295200,
"author_id": 701704062994743400,
"author_name": "sLoct",
"timestamp": "08/08/2022 02:25:29",
"content": "ic",
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},
{
"id": 1006085734719045800,
"author_id": 701704062994743400,
"author_name": "sLoct",
"timestamp": "08/08/2022 02:25:31",
"content": "thank you",
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},
{
"id": 1006085765295505500,
"author_id": 701704062994743400,
"author_name": "sLoct",
"timestamp": "08/08/2022 02:25:38",
"content": ".close",
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},
{
"id": 1006085767489142800,
"author_id": 805217272087838700,
"author_name": "Mathematics Bot",
"timestamp": "08/08/2022 02:25:39",
"content": "Channel closed",
"attachments": [],
"mentions": [],
"reference": null
}
] |
help-9
|
ff2ea1f2119c4291a05b01434887400f
|
197,692 |
[
{
"id": 1006088309598064800,
"author_id": 805217272087838700,
"author_name": "Mathematics Bot",
"timestamp": "08/08/2022 02:35:45",
"content": "Available help channel!",
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},
{
"id": 1006089278650056800,
"author_id": 805217272087838700,
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"content": "Pinned a message.",
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"id": 1006090489365266600,
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"timestamp": "08/08/2022 02:44:24",
"content": "try squares",
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},
{
"id": 1006091116254347400,
"author_id": 261933205387477000,
"author_name": "riemann",
"timestamp": "08/08/2022 02:46:54",
"content": "$a n^2$",
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"timestamp": "08/08/2022 02:46:57",
"content": "**riemann**",
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"id": 1006091586637148300,
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"timestamp": "08/08/2022 02:48:46",
"content": "solves this problem",
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{
"id": 1006091709580578800,
"author_id": 826318983413366800,
"author_name": "Cogwheels of the mind",
"timestamp": "08/08/2022 02:49:15",
"content": "Use Lagrange polynomial to obtain a polynomial f such that f(1)=2,โฆ,f(5)=50 then ฮฃf(k)",
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"id": 1006092109541036000,
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"timestamp": "08/08/2022 02:50:51",
"content": "just use what i suggested",
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"id": 1006092154986319900,
"author_id": 826318983413366800,
"author_name": "Cogwheels of the mind",
"timestamp": "08/08/2022 02:51:02",
"content": "Oh",
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},
{
"id": 1006092168382926800,
"author_id": 826318983413366800,
"author_name": "Cogwheels of the mind",
"timestamp": "08/08/2022 02:51:05",
"content": "See it now๐",
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},
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"id": 1006092191254466600,
"author_id": 826318983413366800,
"author_name": "Cogwheels of the mind",
"timestamp": "08/08/2022 02:51:10",
"content": "2n^2",
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},
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"id": 1006092304496472200,
"author_id": 261933205387477000,
"author_name": "riemann",
"timestamp": "08/08/2022 02:51:37",
"content": "cog working on too many hard problems to do simple ones anymore",
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},
{
"id": 1006092352038903800,
"author_id": 826318983413366800,
"author_name": "Cogwheels of the mind",
"timestamp": "08/08/2022 02:51:49",
"content": "๐",
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},
{
"id": 1006092618716954600,
"author_id": 805217272087838700,
"author_name": "Mathematics Bot",
"timestamp": "08/08/2022 02:52:52",
"content": "Channel closed",
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}
] |
help-9
|
8f1917767efe49cb810af2812a9ab63b
|
197,693 |
[
{
"id": 959645205269725200,
"author_id": 270824453334761470,
"author_name": "1Kลtare",
"timestamp": "04/01/2022 22:47:26",
"content": ".reopen",
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},
{
"id": 959645211800256600,
"author_id": 805217272087838700,
"author_name": "Mathematics Bot",
"timestamp": "04/01/2022 22:47:27",
"content": "โ
",
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"reference": null
},
{
"id": 959645401009520800,
"author_id": 270824453334761470,
"author_name": "1Kลtare",
"timestamp": "04/01/2022 22:48:12",
"content": "so is this a binomial? or still a polynomial because itโs still considered one number having the b attached to it",
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},
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"id": 959645416373239800,
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{
"id": 959645466872660000,
"author_id": 200013547491688450,
"author_name": "a disappointing son",
"timestamp": "04/01/2022 22:48:28",
"content": "still on term",
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},
{
"id": 959645474514690000,
"author_id": 270824453334761470,
"author_name": "1Kลtare",
"timestamp": "04/01/2022 22:48:30",
"content": "monomial* not sure what theyโre called",
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},
{
"id": 959645494290821100,
"author_id": 200013547491688450,
"author_name": "a disappointing son",
"timestamp": "04/01/2022 22:48:35",
"content": "if it's a binomial it'll have a + or - in between terms",
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},
{
"id": 959645504243908600,
"author_id": 270824453334761470,
"author_name": "1Kลtare",
"timestamp": "04/01/2022 22:48:37",
"content": "ah i see thought so",
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},
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"id": 959645522946322400,
"author_id": 270824453334761470,
"author_name": "1Kลtare",
"timestamp": "04/01/2022 22:48:42",
"content": "thanks again",
"attachments": [],
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"reference": null
},
{
"id": 959645541304774700,
"author_id": 270824453334761470,
"author_name": "1Kลtare",
"timestamp": "04/01/2022 22:48:46",
"content": ".close",
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},
{
"id": 959645542667927700,
"author_id": 805217272087838700,
"author_name": "Mathematics Bot",
"timestamp": "04/01/2022 22:48:46",
"content": "Channel closed",
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}
] |
help-9
|
208c8d380c2b497c9400633b18d80f82
|
197,694 |
[
{
"id": 1006097204156571600,
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"author_name": "Mathematics Bot",
"timestamp": "08/08/2022 03:11:05",
"content": "Available help channel!",
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},
{
"id": 1006097817095393300,
"author_id": 899691752531828900,
"author_name": "Doctor beak",
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"timestamp": "08/08/2022 03:13:32",
"content": "Pinned a message.",
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"id": 1006097952470749200,
"author_id": 899691752531828900,
"author_name": "Doctor beak",
"timestamp": "08/08/2022 03:14:04",
"content": "I need help with the right one",
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},
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"timestamp": "08/08/2022 03:14:57",
"content": "is this a test?",
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"id": 1006098233732382800,
"author_id": 899691752531828900,
"author_name": "Doctor beak",
"timestamp": "08/08/2022 03:15:11",
"content": "No",
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},
{
"id": 1006098291651514400,
"author_id": 899691752531828900,
"author_name": "Doctor beak",
"timestamp": "08/08/2022 03:15:25",
"content": "It's homework",
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},
{
"id": 1006098320474771500,
"author_id": 899691752531828900,
"author_name": "Doctor beak",
"timestamp": "08/08/2022 03:15:32",
"content": "For the holidays",
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},
{
"id": 1006098513127546900,
"author_id": 899691752531828900,
"author_name": "Doctor beak",
"timestamp": "08/08/2022 03:16:17",
"content": "Oh I think I found a mistake ๐
",
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"id": 1006098521444843500,
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"author_name": "riemann",
"timestamp": "08/08/2022 03:16:19",
"content": "mistake on c term",
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"author_name": "Doctor beak",
"timestamp": "08/08/2022 03:16:33",
"content": "Yeah ty",
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},
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"id": 1006098620170371200,
"author_id": 899691752531828900,
"author_name": "Doctor beak",
"timestamp": "08/08/2022 03:16:43",
"content": "So it's -160",
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},
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"id": 1006098634468761700,
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"author_name": "Doctor beak",
"timestamp": "08/08/2022 03:16:46",
"content": ".close",
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},
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"id": 1006098636268114000,
"author_id": 805217272087838700,
"author_name": "Mathematics Bot",
"timestamp": "08/08/2022 03:16:47",
"content": "Channel closed",
"attachments": [],
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"reference": null
}
] |
help-9
|
2878645167ff4a63945378af6417e990
|
197,695 |
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"id": 1006123680092409900,
"author_id": 805217272087838700,
"author_name": "Mathematics Bot",
"timestamp": "08/08/2022 04:56:18",
"content": "Available help channel!",
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},
{
"id": 1006130670642401300,
"author_id": 437174082665185300,
"author_name": "Yash ;)",
"timestamp": "08/08/2022 05:24:04",
"content": "How do I proceed here?",
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"timestamp": "08/08/2022 05:24:05",
"content": "Pinned a message.",
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"author_id": 826318983413366800,
"author_name": "Cogwheels of the mind",
"timestamp": "08/08/2022 05:25:40",
"content": "Real polynomial? And donโt know what ฮป is",
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"id": 1006131391701995600,
"author_id": 482237034736386050,
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"content": "a real or complex number quiet surely",
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},
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"id": 1006131423905849300,
"author_id": 826318983413366800,
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"timestamp": "08/08/2022 05:27:04",
"content": "Really",
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"id": 1006131444562800600,
"author_id": 826318983413366800,
"author_name": "Cogwheels of the mind",
"timestamp": "08/08/2022 05:27:09",
"content": "Between two roots",
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},
{
"id": 1006131478532460500,
"author_id": 826318983413366800,
"author_name": "Cogwheels of the mind",
"timestamp": "08/08/2022 05:27:17",
"content": "What does โbetweenโ mean",
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},
{
"id": 1006131504558112800,
"author_id": 826318983413366800,
"author_name": "Cogwheels of the mind",
"timestamp": "08/08/2022 05:27:23",
"content": "If itโs complex numbers",
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"id": 1006131732304625700,
"author_id": 482237034736386050,
"author_name": "EnzoL",
"timestamp": "08/08/2022 05:28:18",
"content": "mh",
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},
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"id": 1006131738067619800,
"author_id": 482237034736386050,
"author_name": "EnzoL",
"timestamp": "08/08/2022 05:28:19",
"content": "yeah",
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"id": 1006131739242025000,
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"content": "so its real",
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"author_id": 482237034736386050,
"author_name": "EnzoL",
"timestamp": "08/08/2022 05:28:20",
"content": "no order relation in complexs",
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},
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"id": 1006131804274708500,
"author_id": 826318983413366800,
"author_name": "Cogwheels of the mind",
"timestamp": "08/08/2022 05:28:35",
"content": "And he still hasnโt told us what ฮป is",
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"timestamp": "08/08/2022 05:29:46",
"content": "so it might be a real",
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"timestamp": "08/08/2022 05:30:17",
"content": "coeffs are real to",
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"timestamp": "08/08/2022 05:30:21",
"content": "so it seems logic imo",
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"content": "@Yash ;) Has your question been resolved?",
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"content": "@Cogwheels of the mind lambda is a real number",
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"timestamp": "08/08/2022 05:44:52",
"content": "And yeah the polynomial is also real",
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"content": "Answer given is A,C,D",
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"content": "Does โbetweenโ include those two roots?",
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"timestamp": "08/08/2022 06:04:44",
"content": "A is true because",
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"timestamp": "08/08/2022 06:05:18",
"content": "Things in option A is the derivative of $e^{ฮปx}ฯ(x)$",
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"timestamp": "08/08/2022 06:05:20",
"content": "**Cogwheels of the mind**",
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"timestamp": "08/08/2022 06:06:25",
"content": "Now $e^{ฮปx}ฯ(x)$ also has the same roots with $ฯ(x)$, by rolle theorem",
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"timestamp": "08/08/2022 06:06:27",
"content": "**Cogwheels of the mind**",
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"author_name": "Samsyet",
"timestamp": "08/08/2022 06:07:15",
"content": "i think using rolles and intermediate value theorem u can get all the results",
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"timestamp": "08/08/2022 06:07:25",
"content": "basically all of them are about how the derivative of polynomials behave",
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"timestamp": "08/08/2022 06:07:35",
"content": "$f(x)=e^{ฮปx}ฯ(x)$, apply rolle theorem on f we have $fโ(t)=0$ for some t between two roots",
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"timestamp": "08/08/2022 06:07:38",
"content": "**Cogwheels of the mind**",
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"timestamp": "08/08/2022 06:08:28",
"content": "Not sure about that, maybe some of them we can find counterexamples",
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"timestamp": "08/08/2022 06:09:13",
"content": "oh wait maybe u can form differential equations for all of them and then check",
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"timestamp": "08/08/2022 06:09:16",
"content": "that might work",
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"timestamp": "08/08/2022 06:10:24",
"content": "Maybe not",
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"timestamp": "08/08/2022 06:10:32",
"content": "For option A it worked because",
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"timestamp": "08/08/2022 06:10:52",
"content": "e^ฮปxฯ(x) also have the same roots",
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"timestamp": "08/08/2022 06:10:58",
"content": "So I applied rolle theorem",
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"timestamp": "08/08/2022 06:23:24",
"content": "@Yash ;) Has your question been resolved?",
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"timestamp": "08/08/2022 06:33:14",
"content": "Two roots are $a<b$. let $q(x)=ฯโ(x)+p(x)ฯ(x)$ then $ฯ(x)=u(x)v(x)$ where $u(x)=e^{-\\int_{a}^{x} p(t)dt}. v(x)=\\int_{a}^{x}e^{\\int_{a}^{t}p(s)ds}q(t)dt$ now $ฯ(a)=0=ฯ(b)$ we have $v(a)=0=v(b)$ and $vโ(x)= e^{\\int_{a}^{x}p(s)ds}q(x)$ so apply rolle theorem on v we obtain that $q(x)=0$ for some x between a and b",
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"timestamp": "08/08/2022 06:33:35",
"content": "**Cogwheels of the mind**",
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"timestamp": "08/08/2022 06:41:03",
"content": "How about option B? What if two roots a<0<b this case",
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"timestamp": "08/08/2022 06:47:24",
"content": ":catThin4K:",
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"timestamp": "08/08/2022 06:50:39",
"content": "No,it is excluding them",
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"timestamp": "08/08/2022 06:51:28",
"content": "i thought u can do B like this, if u solve x*phi'(x)+lambda\\*phi(x)=0, u get x^-(lambda)=phi(x), which isnt a polynomial all the time",
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"timestamp": "08/08/2022 06:51:30",
"content": "hence its false",
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"timestamp": "08/08/2022 06:52:36",
"content": "Doesnโt seem valid. ฯ doesnโt always satisfy xฯโ+ฮปฯ=0",
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"timestamp": "08/08/2022 06:52:51",
"content": "thats what i said",
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"timestamp": "08/08/2022 06:52:56",
"content": "if some phi satisfied it",
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"timestamp": "08/08/2022 06:53:04",
"content": "it would be of the form x^-lambda",
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"timestamp": "08/08/2022 06:53:12",
"content": "hence it wont always even be a polynomial",
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"timestamp": "08/08/2022 06:53:29",
"content": "and so it cant satisfy that condition",
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"timestamp": "08/08/2022 06:53:29",
"content": ":catThin4K:",
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"id": 1006153215659757600,
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"author_name": "Yash ;)",
"timestamp": "08/08/2022 06:53:40",
"content": "Hmm I think you're right",
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"timestamp": "08/08/2022 06:53:53",
"content": "No I mean no one said there exists such an equation,xฯโ+ฮปฯ=0 we just hope there exists one point that it holds",
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"timestamp": "08/08/2022 06:54:15",
"content": "we have to show this holds for all phi(x)",
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"timestamp": "08/08/2022 06:54:22",
"content": "as it didnt specify any condition on it",
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"timestamp": "08/08/2022 06:54:24",
"content": "What",
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"id": 1006153439732056000,
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"author_name": "Samsyet",
"timestamp": "08/08/2022 06:54:33",
"content": "hence if we find a counterexample, its enough to show that it wont always hold",
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"id": 1006153481238884500,
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"author_name": "Samsyet",
"timestamp": "08/08/2022 06:54:43",
"content": "we are told phi(x) is just a polynomial",
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"timestamp": "08/08/2022 06:54:44",
"content": "nothing else",
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"author_name": "Samsyet",
"timestamp": "08/08/2022 06:55:00",
"content": "hence we cant make any arbitrary restrictions on it",
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"id": 1006153671932919900,
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"author_name": "Cogwheels of the mind",
"timestamp": "08/08/2022 06:55:28",
"content": "So I donโt understand your way to construct a counterexample",
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"author_name": "Samsyet",
"timestamp": "08/08/2022 06:55:36",
"content": ":catThin4K:",
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"id": 1006153721312456700,
"author_id": 852947058905579500,
"author_name": "Samsyet",
"timestamp": "08/08/2022 06:55:40",
"content": "what do u find weird",
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"id": 1006153877000818800,
"author_id": 437174082665185300,
"author_name": "Yash ;)",
"timestamp": "08/08/2022 06:56:17",
"content": "No we don't have to show this for all x,we only have to check if that equation has a root between the two roots of phi(x) or not",
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"author_name": "Cogwheels of the mind",
"timestamp": "08/08/2022 06:56:36",
"content": "Why xฯโ+ฮปฯ=0 holds for some point make you think xฯโ+ฮปฯ=0 holds for some open interval",
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"timestamp": "08/08/2022 06:56:52",
"content": "hmm",
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"author_name": "Cogwheels of the mind",
"timestamp": "08/08/2022 06:57:09",
"content": "If there is no condition xฯโ+ฮปฯ=0 holds on an interval I donโt have this differential equation",
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"id": 1006154158119866500,
"author_id": 437174082665185300,
"author_name": "Yash ;)",
"timestamp": "08/08/2022 06:57:24",
"content": "Yuppp",
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"timestamp": "08/08/2022 06:58:29",
"content": "i didnt say that",
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"timestamp": "08/08/2022 07:00:46",
"content": "Anyway, my counterexample is ฯ(x)=x^2-1 and ฮป=-1 xฯโ(x)+ฮปฯ(x)=2x^2-(x^2-1)=x^2+1 doesnโt have real root",
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"id": 1006155128920887400,
"author_id": 826318983413366800,
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"timestamp": "08/08/2022 07:01:16",
"content": "So ACD are true B is false",
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"timestamp": "08/08/2022 07:01:59",
"content": "Still havenโt got your idea, I suppose thatโs itโฆ already found a counterexample so โฆ",
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"id": 1006156442576896000,
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"timestamp": "08/08/2022 07:06:29",
"content": ":coCatThink:",
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"timestamp": "08/08/2022 07:06:52",
"content": "my idea was showing that no polynomial that satisfies that condition can have more than one root, but w/e",
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"timestamp": "08/08/2022 07:06:56",
"content": "ur example works just as fine",
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"timestamp": "08/08/2022 07:57:24",
"content": "@Yash ;) Has your question been resolved?",
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"timestamp": "08/08/2022 08:25:42",
"content": "Channel closed",
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}
] |
help-9
|
4c6bc11303e84400a9e1615e935201fc
|
197,696 |
[
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"timestamp": "08/08/2022 08:26:42",
"content": "Available help channel!",
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},
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"id": 1006180691488297100,
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"timestamp": "08/08/2022 08:42:52",
"content": "I can not derive the 6x/4 it is the concern that prevents me from succeeding the exercise.",
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"id": 1006180823642419200,
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"timestamp": "08/08/2022 08:43:22",
"content": "6xโด/4",
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"timestamp": "08/08/2022 08:43:27",
"content": "*",
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"id": 1006180845029179400,
"author_id": 841679117350994000,
"author_name": "Not Trout",
"timestamp": "08/08/2022 08:43:27",
"content": "uh",
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"author_id": 841679117350994000,
"author_name": "Not Trout",
"timestamp": "08/08/2022 08:43:30",
"content": "think of it like",
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"id": 1006180926834876400,
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"timestamp": "08/08/2022 08:43:46",
"content": "$\\frac{6}{4} * x^4$",
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"author_name": "TeXit",
"timestamp": "08/08/2022 08:43:49",
"content": "**Not Trout**",
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"timestamp": "08/08/2022 08:43:58",
"content": "i think you can derive that ^-^",
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"author_name": "lil king",
"timestamp": "08/08/2022 08:44:45",
"content": "uโ . v - u.vโ on v ?",
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"content": "@Not Trout its about derivative",
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"timestamp": "08/08/2022 08:49:07",
"content": "?",
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"timestamp": "08/08/2022 08:49:10",
"content": "no as in just derive it",
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"id": 1006182286682767400,
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"author_name": "Not Trout",
"timestamp": "08/08/2022 08:49:11",
"content": "as",
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"id": 1006182362310267000,
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"timestamp": "08/08/2022 08:49:29",
"content": "$\\frac{d}{dx}(\\frac{6}{4}x^4)$",
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"timestamp": "08/08/2022 08:49:43",
"content": "Ah ok",
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"timestamp": "08/08/2022 08:49:47",
"content": "**Not Trout**",
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"timestamp": "08/08/2022 08:50:12",
"content": ".close",
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"id": 1006182548491210900,
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"timestamp": "08/08/2022 08:50:13",
"content": "Channel closed",
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}
] |
help-9
|
170f9defe70b44e58897849a0b80f2ec
|
197,697 |
[
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"content": "Available help channel!",
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"timestamp": "08/08/2022 09:28:18",
"content": "How do you do this",
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"content": "why is it 33(11x+9)",
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help-9
|
a85cd768f5ad4e869affb3feff3e8085
|
197,698 |
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"content": "Available help channel!",
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{
"id": 1006197536622657800,
"author_id": 818876716726091800,
"author_name": "Merciless_Admiral",
"timestamp": "08/08/2022 09:49:46",
"content": "Plz tag me if you know solution",
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"content": "Pinned a message.",
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"id": 1006197822594498700,
"author_id": 764959481070616600,
"author_name": "Toby",
"timestamp": "08/08/2022 09:50:55",
"content": "sum of two cubes",
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"author_id": 818876716726091800,
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"content": "?",
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"id": 1006198141571309700,
"author_id": 764959481070616600,
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"timestamp": "08/08/2022 09:52:11",
"content": "factor the sum of two cubes",
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"id": 1006198280218222700,
"author_id": 764959481070616600,
"author_name": "Toby",
"timestamp": "08/08/2022 09:52:44",
"content": "$x^3+y^3=(x+y)(x^2-xy+y^2)$",
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"timestamp": "08/08/2022 09:52:46",
"content": "**Toby**",
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"timestamp": "08/08/2022 09:52:57",
"content": "Ok...",
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"author_id": 818876716726091800,
"author_name": "Merciless_Admiral",
"timestamp": "08/08/2022 09:53:17",
"content": "Then?",
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"id": 1006198528713961600,
"author_id": 764959481070616600,
"author_name": "Toby",
"timestamp": "08/08/2022 09:53:43",
"content": "then divide the two numbers to get what you want?",
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"id": 1006198597563449300,
"author_id": 764959481070616600,
"author_name": "Toby",
"timestamp": "08/08/2022 09:53:59",
"content": "(x^3+y^3)/(x+y)",
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},
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"id": 1006198848357675100,
"author_id": 818876716726091800,
"author_name": "Merciless_Admiral",
"timestamp": "08/08/2022 09:54:59",
"content": "Ok, u mean divide x^3+y^3 by x+y get value of remaining and then find for what is asked, right?",
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"author_name": "Toby",
"timestamp": "08/08/2022 09:56:09",
"content": "huh?",
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"author_id": 818876716726091800,
"author_name": "Merciless_Admiral",
"timestamp": "08/08/2022 09:56:29",
"content": "Solve this, get value and put in what is asked...",
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"timestamp": "08/08/2022 09:56:40",
"content": "why do you need to solve it lol",
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"id": 1006199287786524800,
"author_id": 764959481070616600,
"author_name": "Toby",
"timestamp": "08/08/2022 09:56:44",
"content": "I already did it for you",
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"id": 1006199295357223000,
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"author_name": "Toby",
"timestamp": "08/08/2022 09:56:46",
"content": "the question is just asking you to divide 100010111 by 11111",
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"id": 1006199379369152500,
"author_id": 818876716726091800,
"author_name": "Merciless_Admiral",
"timestamp": "08/08/2022 09:57:06",
"content": "Yeah, i meant this only",
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"author_name": "Merciless_Admiral",
"timestamp": "08/08/2022 09:57:14",
"content": "Thanks!",
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"author_id": 818876716726091800,
"author_name": "Merciless_Admiral",
"timestamp": "08/08/2022 09:57:19",
"content": ". close",
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},
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"id": 1006199446847099000,
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"content": "yw",
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"author_name": "Mathematics Bot",
"timestamp": "08/08/2022 10:12:20",
"content": "@Merciless_Admiral Has your question been resolved?",
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"timestamp": "08/08/2022 10:26:18",
"content": "Channel closed",
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}
] |
help-9
|
772e5468c8dd400d927d355c6880c000
|
197,699 |
[
{
"id": 1006206981851316200,
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"author_name": "Mathematics Bot",
"timestamp": "08/08/2022 10:27:18",
"content": "Available help channel!",
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},
{
"id": 1006207576456831000,
"author_id": 412739317887139840,
"author_name": "Goose on a Moose",
"timestamp": "08/08/2022 10:29:40",
"content": "Can someone help me solve for X?",
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"content": "Pinned a message.",
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"author_id": 412739317887139840,
"author_name": "Goose on a Moose",
"timestamp": "08/08/2022 10:30:13",
"content": "So far I got AX+BXC=D",
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},
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"id": 1006207736721178800,
"author_id": 412739317887139840,
"author_name": "Goose on a Moose",
"timestamp": "08/08/2022 10:30:18",
"content": "not sure how to isolate for X",
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},
{
"id": 1006210767432990800,
"author_id": 132304137583984640,
"author_name": "Denascite",
"timestamp": "08/08/2022 10:42:21",
"content": "I would probably just set X=(a, b; c, d) and then set up 4 equations for a,b,c,d",
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"timestamp": "08/08/2022 10:42:40",
"content": "good idea. thanks",
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},
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"timestamp": "08/08/2022 10:43:18",
"content": ".close",
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},
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"author_name": "Mathematics Bot",
"timestamp": "08/08/2022 10:43:18",
"content": "Channel closed",
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}
] |
help-9
|
c6bcb568bc39429298dca53340eb097b
|
197,700 |
[
{
"id": 1006211260284670000,
"author_id": 805217272087838700,
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"timestamp": "08/08/2022 10:44:18",
"content": "Available help channel!",
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"id": 1006215000601415800,
"author_id": 342475274622861300,
"author_name": "Witchy Scholar (Evena)",
"timestamp": "08/08/2022 10:59:10",
"content": "In base negabinary, how can you solve something like 1101 + 110?",
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"id": 1006215003453526100,
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"timestamp": "08/08/2022 10:59:11",
"content": "Pinned a message.",
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"author_name": "Witchy Scholar (Evena)",
"timestamp": "08/08/2022 11:01:02",
"content": "Converting it to base 10 and then solving it is super easy, but I don't want to need to do that.",
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"content": "@Witchy Scholar (Evena) Has your question been resolved?",
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"timestamp": "08/08/2022 11:46:15",
"content": "@Witchy Scholar (Evena) Has your question been resolved?",
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"id": 1006230698996269200,
"author_id": 363984127977848800,
"author_name": "Anoma",
"timestamp": "08/08/2022 12:01:33",
"content": "Do you know how to do it in base 2?",
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"timestamp": "08/08/2022 12:02:18",
"content": "Yes",
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},
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"id": 1006231063275770000,
"author_id": 342475274622861300,
"author_name": "Witchy Scholar (Evena)",
"timestamp": "08/08/2022 12:03:00",
"content": "1101 + 110 = 10011",
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{
"id": 1006231257627246700,
"author_id": 363984127977848800,
"author_name": "Anoma",
"timestamp": "08/08/2022 12:03:46",
"content": "It's almost the same, except the carry is multiplied by -1",
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},
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"id": 1006231304506986600,
"author_id": 363984127977848800,
"author_name": "Anoma",
"timestamp": "08/08/2022 12:03:57",
"content": "Like this",
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"id": 1006232306798821500,
"author_id": 342475274622861300,
"author_name": "Witchy Scholar (Evena)",
"timestamp": "08/08/2022 12:07:56",
"content": "But sometimes the cary seems to be 11. like with 11+11",
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"author_name": "Witchy Scholar (Evena)",
"timestamp": "08/08/2022 12:10:40",
"content": "Ah, wrong one. 111 + 111 which has a cary of 11 and a cary of 10",
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"author_id": 363984127977848800,
"author_name": "Anoma",
"timestamp": "08/08/2022 12:12:26",
"content": "Ah yes if you have a carry of -1 => 1 in the result and 1 in the carry",
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"id": 1006233882842120300,
"author_id": 363984127977848800,
"author_name": "Anoma",
"timestamp": "08/08/2022 12:14:12",
"content": "(because -1 = 1 + (-2) )",
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"author_id": 342475274622861300,
"author_name": "Witchy Scholar (Evena)",
"timestamp": "08/08/2022 12:17:11",
"content": "But why does 1+1+1+1 seem to give a cary of 10?",
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"id": 1006235329667276800,
"author_id": 342475274622861300,
"author_name": "Witchy Scholar (Evena)",
"timestamp": "08/08/2022 12:19:57",
"content": "Figured it out! Thank you.",
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{
"id": 1006237238394376300,
"author_id": 342475274622861300,
"author_name": "Witchy Scholar (Evena)",
"timestamp": "08/08/2022 12:27:32",
"content": "Is that the same for all negative bases?",
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"id": 1006239667949154400,
"author_id": 342475274622861300,
"author_name": "Witchy Scholar (Evena)",
"timestamp": "08/08/2022 12:37:11",
"content": "How do decimals work?",
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"author_id": 342475274622861300,
"author_name": "Witchy Scholar (Evena)",
"timestamp": "08/08/2022 12:40:59",
"content": "Nvmd",
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},
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"id": 1006243088622170100,
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"author_name": "Anoma",
"timestamp": "08/08/2022 12:50:47",
"content": "Yes but when, like the -1 in the result, if we have a negative number, we have to remember that for example if in base -6 we have -2, -2 = 4+(-6) so the (-6) becomes 1 in the carry and the result is 4",
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"timestamp": "08/08/2022 12:55:08",
"content": "14+14=12",
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"timestamp": "08/08/2022 13:55:08",
"content": "@Witchy Scholar (Evena) Has your question been resolved?",
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"timestamp": "08/08/2022 14:05:50",
"content": "Channel closed",
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] |
help-9
|
5d34609ede6e475cae538471c829aa69
|
197,701 |
[
{
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"content": "Available help channel!",
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{
"id": 1006262959607124000,
"author_id": 300298101623619600,
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"timestamp": "08/08/2022 14:09:45",
"content": "hello",
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"timestamp": "08/08/2022 14:09:46",
"content": "Pinned a message.",
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{
"id": 1006263060555644900,
"author_id": 333544771421470700,
"author_name": "ๅผตๅๆฃ",
"timestamp": "08/08/2022 14:10:09",
"content": "what do you need help with?",
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},
{
"id": 1006263114326614100,
"author_id": 333544771421470700,
"author_name": "ๅผตๅๆฃ",
"timestamp": "08/08/2022 14:10:21",
"content": "pls don't occupy a help channel to just say hello",
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{
"id": 1006263132542488700,
"author_id": 300298101623619600,
"author_name": "999999999",
"timestamp": "08/08/2022 14:10:26",
"content": "so im supposed to calculate the difference between\n4,5celcius and -18,4",
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{
"id": 1006263148388556900,
"author_id": 300298101623619600,
"author_name": "999999999",
"timestamp": "08/08/2022 14:10:30",
"content": "how do I do it",
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},
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"id": 1006263323664318600,
"author_id": 994286722357674100,
"author_name": "Twerkingbee",
"timestamp": "08/08/2022 14:11:11",
"content": ":bleak:",
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{
"id": 1006263350851813400,
"author_id": 300298101623619600,
"author_name": "999999999",
"timestamp": "08/08/2022 14:11:18",
"content": "its not for me I dont know",
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},
{
"id": 1006263359747924000,
"author_id": 300298101623619600,
"author_name": "999999999",
"timestamp": "08/08/2022 14:11:20",
"content": "just help man",
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},
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"id": 1006263467814174800,
"author_id": 994286722357674100,
"author_name": "Twerkingbee",
"timestamp": "08/08/2022 14:11:46",
"content": "-18.4-4.5",
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},
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"id": 1006263515117539300,
"author_id": 300298101623619600,
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"timestamp": "08/08/2022 14:11:57",
"content": "but its -18,4",
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"id": 1006263517915140200,
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"author_name": "Twerkingbee",
"timestamp": "08/08/2022 14:11:58",
"content": "Absolute difference would be ^",
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},
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"author_id": 994286722357674100,
"author_name": "Twerkingbee",
"timestamp": "08/08/2022 14:12:06",
"content": ", is .",
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"id": 1006263594456993800,
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"timestamp": "08/08/2022 14:12:16",
"content": "okay but",
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"id": 1006263612140179500,
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"timestamp": "08/08/2022 14:12:20",
"content": "its -18.4",
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},
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"id": 1006263649318486000,
"author_id": 994286722357674100,
"author_name": "Twerkingbee",
"timestamp": "08/08/2022 14:12:29",
"content": ".",
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},
{
"id": 1006263674316533900,
"author_id": 300298101623619600,
"author_name": "999999999",
"timestamp": "08/08/2022 14:12:35",
"content": "so u just do it like that",
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"id": 1006263682860331100,
"author_id": 994286722357674100,
"author_name": "Twerkingbee",
"timestamp": "08/08/2022 14:12:37",
"content": "Without sign",
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},
{
"id": 1006263694193328300,
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"author_name": "999999999",
"timestamp": "08/08/2022 14:12:40",
"content": "18.4-4.5",
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"id": 1006263721418559700,
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"timestamp": "08/08/2022 14:12:46",
"content": "Yeah",
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},
{
"id": 1006263814339186700,
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"author_name": "Twerkingbee",
"timestamp": "08/08/2022 14:13:08",
"content": "Russians write like that",
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{
"id": 1006263837856645200,
"author_id": 220517274845577200,
"author_name": "ramonov",
"timestamp": "08/08/2022 14:13:14",
"content": "no",
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"id": 1006263878503632900,
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"author_name": "Twerkingbee",
"timestamp": "08/08/2022 14:13:24",
"content": "Lol",
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},
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"id": 1006263890109268000,
"author_id": 994286722357674100,
"author_name": "Twerkingbee",
"timestamp": "08/08/2022 14:13:26",
"content": "I have few",
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},
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"id": 1006263906488037500,
"author_id": 994286722357674100,
"author_name": "Twerkingbee",
"timestamp": "08/08/2022 14:13:30",
"content": "Ruski friends",
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},
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"id": 1006263961479545000,
"author_id": 220517274845577200,
"author_name": "ramonov",
"timestamp": "08/08/2022 14:13:43",
"content": "you'd do\n4.5 - (-18.4)",
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},
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"id": 1006264061677277300,
"author_id": 220517274845577200,
"author_name": "ramonov",
"timestamp": "08/08/2022 14:14:07",
"content": "or | -18.4 - 4.5|",
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},
{
"id": 1006264088361439400,
"author_id": 994286722357674100,
"author_name": "Twerkingbee",
"timestamp": "08/08/2022 14:14:14",
"content": "Lol wait",
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},
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"id": 1006264106627641300,
"author_id": 994286722357674100,
"author_name": "Twerkingbee",
"timestamp": "08/08/2022 14:14:18",
"content": "I didnt put sign",
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},
{
"id": 1006264113736994800,
"author_id": 994286722357674100,
"author_name": "Twerkingbee",
"timestamp": "08/08/2022 14:14:20",
"content": "Looll",
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"author_name": "Twerkingbee",
"timestamp": "08/08/2022 14:14:40",
"content": "Ok nao its fine",
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"id": 1006264204908581000,
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"timestamp": "08/08/2022 14:14:41",
"content": "So its",
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"id": 1006264249909256300,
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"timestamp": "08/08/2022 14:14:52",
"content": "+22,9?",
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"id": 1006264360269783000,
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"author_name": "ramonov",
"timestamp": "08/08/2022 14:15:18",
"content": "depends on the wording",
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"author_name": "ramonov",
"timestamp": "08/08/2022 14:15:42",
"content": "the difference between the two temps is 22.9ยฐC",
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"timestamp": "08/08/2022 14:29:52",
"content": "@999999999 Has your question been resolved?",
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"timestamp": "08/08/2022 14:44:53",
"content": "Channel closed",
"attachments": [],
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}
] |
help-9
|
1c8782dc01894656a1c7a1f5ce6e4e4e
|
197,702 |
[
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"timestamp": "08/08/2022 14:45:53",
"content": "Available help channel!",
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},
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"id": 1006273869423857700,
"author_id": 207962451168198660,
"author_name": "Emhyr Var Emreis",
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"content": "Pinned a message.",
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"id": 1006273919206031400,
"author_id": 207962451168198660,
"author_name": "Emhyr Var Emreis",
"timestamp": "08/08/2022 14:53:18",
"content": "I have zero idea how Iโd even begin to solve this",
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},
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"id": 1006274169039769700,
"author_id": 207962451168198660,
"author_name": "Emhyr Var Emreis",
"timestamp": "08/08/2022 14:54:17",
"content": "Derivative of absolute value is (x*xโ)/|x|",
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"author_name": "Emhyr Var Emreis",
"timestamp": "08/08/2022 14:54:30",
"content": "x times derivative of x divided by absolute value of x",
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},
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"id": 1006274301034512500,
"author_id": 207962451168198660,
"author_name": "Emhyr Var Emreis",
"timestamp": "08/08/2022 14:54:49",
"content": "With x possibly being any function",
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},
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"id": 1006274341475983500,
"author_id": 207962451168198660,
"author_name": "Emhyr Var Emreis",
"timestamp": "08/08/2022 14:54:58",
"content": "But I donโt think this gives me any solution",
"attachments": [],
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},
{
"id": 1006274430948884600,
"author_id": 207962451168198660,
"author_name": "Emhyr Var Emreis",
"timestamp": "08/08/2022 14:55:20",
"content": "Wellโฆ I couldnโt reach a solution through this*",
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},
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"id": 1006274470824124700,
"author_id": 207962451168198660,
"author_name": "Emhyr Var Emreis",
"timestamp": "08/08/2022 14:55:29",
"content": "And I have no idea what else to do",
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"id": 1006274511739556000,
"author_id": 207962451168198660,
"author_name": "Emhyr Var Emreis",
"timestamp": "08/08/2022 14:55:39",
"content": "I tried to turn it into a piecewise function too",
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},
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"id": 1006274608854483100,
"author_id": 207962451168198660,
"author_name": "Emhyr Var Emreis",
"timestamp": "08/08/2022 14:56:02",
"content": "y = 0 when x = 1, x = 1-sqrt(3), and when x = 1 + sqrt(3)",
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"timestamp": "08/08/2022 15:11:02",
"content": "@Emhyr Var Emreis Has your question been resolved?",
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"author_name": "Toby",
"timestamp": "08/08/2022 15:11:12",
"content": "we have the normal critical points when f'(x)=0 (which is equivalent to when x^3-3x^2+2 has critical points, ie without the absolute values), and we have the critical points arising from when f'(x) is undefined, ie when f(x)=0 (when the non-absolute value function changes sign)",
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"timestamp": "08/08/2022 15:26:02",
"content": "Channel closed",
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] |
help-9
|
b7f2016b65bf4c7ea286aeca5197d9cf
|
197,703 |
[
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"timestamp": "08/08/2022 15:27:03",
"content": "Available help channel!",
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"id": 1006288896264511500,
"author_id": 240225041353146370,
"author_name": "bobbyt",
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"author_id": 349354952961032200,
"author_name": "Umbraleviathan",
"timestamp": "08/08/2022 15:54:00",
"content": "Replace y^2 using y",
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"author_name": "Umbraleviathan",
"timestamp": "08/08/2022 15:54:07",
"content": "Solve for x",
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"author_name": "bobbyt",
"timestamp": "08/08/2022 15:57:56",
"content": "okay let me try",
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"timestamp": "08/08/2022 16:08:39",
"content": "How can I solve for x via factoring when the coefficient of the first term is greater than 1? Could you tell me please? Iโd appreciate",
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"timestamp": "08/08/2022 16:23:39",
"content": "@bobbyt Has your question been resolved?",
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"timestamp": "08/08/2022 16:25:03",
"content": "$$(2x+1)^2 = 4x^2 + 4x+1$$",
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"author_name": "TeXit",
"timestamp": "08/08/2022 16:25:05",
"content": "**Umbraleviathan**",
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"content": "wtf",
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"content": "Foiling",
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"timestamp": "08/08/2022 16:30:12",
"content": "AB AbBa ab",
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help-9
|
2d691182cb39472699483a3440f4d5ed
|
197,704 |
[
{
"id": 959647731784245400,
"author_id": 805217272087838700,
"author_name": "Mathematics Bot",
"timestamp": "04/01/2022 22:57:28",
"content": "Available help channel!",
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},
{
"id": 959655372568793200,
"author_id": 775985060721590300,
"author_name": "Kitara",
"timestamp": "04/01/2022 23:27:50",
"content": "Can someone give an example of **how to calculate a problem related in Coulomb's Law?**",
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"id": 959655375076991000,
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"content": "Pinned a message.",
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"id": 959658114121080800,
"author_id": 200013547491688450,
"author_name": "a disappointing son",
"timestamp": "04/01/2022 23:38:43",
"content": "google?",
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"id": 959659373225979900,
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"author_name": "Mathematics Bot",
"timestamp": "04/01/2022 23:43:44",
"content": "@Kitara Has your question been resolved?",
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"id": 959661161035481100,
"author_id": 800622149903056900,
"author_name": "Shen",
"timestamp": "04/01/2022 23:50:50",
"content": "^^",
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"id": 959661431664558100,
"author_id": 956973920991473700,
"author_name": "ymme",
"timestamp": "04/01/2022 23:51:54",
"content": "Examples here: https://byjus.com/jee/coulombs-law/",
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"timestamp": "04/01/2022 23:58:44",
"content": "Channel closed",
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] |
help-9
|
aa458f5c856941078e773005b0a9e0a7
|
197,705 |
[
{
"id": 1006312079411646500,
"author_id": 805217272087838700,
"author_name": "Mathematics Bot",
"timestamp": "08/08/2022 17:24:56",
"content": "Available help channel!",
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},
{
"id": 1006321755251540100,
"author_id": 531934659693641700,
"author_name": "Chaosas",
"timestamp": "08/08/2022 18:03:23",
"content": "Hi. I loved the math back in the school and I have to relearn a lot now I a started programming. I have one mathematical problem i can not remember how to solve: The numbers does not matter I Just want to find out the way to solve it, might as well use x/y/z instead of real numbers. I hope i can express the problem in the right way:\n\nimagine i have 3 workers (Brick Layers) who work at the different speed.\nWorker A Places 1 brick every 2 minutes.\nWorker B Places 1 Brick Every 3 Minutes\nWorker C Places 1 Brick Every 5 Minutes\n\nHow long would it take for all 3 of them working together to place 100 Bricks?\n\nNote that the amount of workers in my programming formula will change so there could be more variables, yet idea would stay the same. Thank you in advance for help!",
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"timestamp": "08/08/2022 18:03:23",
"content": "Pinned a message.",
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"id": 1006322145078563000,
"author_id": 697730177962344400,
"author_name": "Tarek Ahmed",
"timestamp": "08/08/2022 18:04:55",
"content": "Each worker has their own rate of working",
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},
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"id": 1006322288678928500,
"author_id": 697730177962344400,
"author_name": "Tarek Ahmed",
"timestamp": "08/08/2022 18:05:30",
"content": "Just add their rates",
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"id": 1006322436603650200,
"author_id": 697730177962344400,
"author_name": "Tarek Ahmed",
"timestamp": "08/08/2022 18:06:05",
"content": "Then find the time they take to reach 100 bricks using the rate",
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"id": 1006322473119273000,
"author_id": 531934659693641700,
"author_name": "Chaosas",
"timestamp": "08/08/2022 18:06:14",
"content": "could you give me example please?",
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"id": 1006322485987397600,
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"author_name": "Tarek Ahmed",
"timestamp": "08/08/2022 18:06:17",
"content": "Ok",
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},
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"id": 1006322536205783200,
"author_id": 697730177962344400,
"author_name": "Tarek Ahmed",
"timestamp": "08/08/2022 18:06:29",
"content": "Letโs say Abby places a brick a minute",
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},
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"id": 1006322578492768300,
"author_id": 697730177962344400,
"author_name": "Tarek Ahmed",
"timestamp": "08/08/2022 18:06:39",
"content": "And Carl places4 bricks a minute",
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},
{
"id": 1006322654640357400,
"author_id": 697730177962344400,
"author_name": "Tarek Ahmed",
"timestamp": "08/08/2022 18:06:57",
"content": "Abbyโs rate is 1 brick/minute and Carl is 4 bricks/minute",
"attachments": [],
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},
{
"id": 1006322722533560400,
"author_id": 697730177962344400,
"author_name": "Tarek Ahmed",
"timestamp": "08/08/2022 18:07:13",
"content": "So Abby + Carl working together would do 5 bricks/minute",
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},
{
"id": 1006322804720934900,
"author_id": 697730177962344400,
"author_name": "Tarek Ahmed",
"timestamp": "08/08/2022 18:07:33",
"content": "So we want to know at 5 bricks per minute, how long would it take for them to reach 100 bricks",
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},
{
"id": 1006322862455529600,
"author_id": 697730177962344400,
"author_name": "Tarek Ahmed",
"timestamp": "08/08/2022 18:07:46",
"content": "We have a linear equation",
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},
{
"id": 1006322882600784000,
"author_id": 697730177962344400,
"author_name": "Tarek Ahmed",
"timestamp": "08/08/2022 18:07:51",
"content": "5x=100",
"attachments": [],
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},
{
"id": 1006322919015710800,
"author_id": 697730177962344400,
"author_name": "Tarek Ahmed",
"timestamp": "08/08/2022 18:08:00",
"content": "5 is the rate they work at",
"attachments": [],
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},
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"id": 1006322952117166200,
"author_id": 697730177962344400,
"author_name": "Tarek Ahmed",
"timestamp": "08/08/2022 18:08:08",
"content": "x is the time they take",
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},
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"id": 1006322956546359400,
"author_id": 531934659693641700,
"author_name": "Chaosas",
"timestamp": "08/08/2022 18:08:09",
"content": "yeh i understand that",
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},
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"id": 1006322980810404000,
"author_id": 697730177962344400,
"author_name": "Tarek Ahmed",
"timestamp": "08/08/2022 18:08:15",
"content": "Ok",
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},
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"id": 1006323003828731900,
"author_id": 697730177962344400,
"author_name": "Tarek Ahmed",
"timestamp": "08/08/2022 18:08:20",
"content": "If 5x=100 what is x",
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"author_name": "Chaosas",
"timestamp": "08/08/2022 18:08:46",
"content": "problem is that i have the time of how long it takes to place 1 brick instead of how many over 1 minute",
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"id": 1006323170111930500,
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"author_name": "Tarek Ahmed",
"timestamp": "08/08/2022 18:09:00",
"content": "What do you mean",
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"author_name": "Chaosas",
"timestamp": "08/08/2022 18:09:04",
"content": "and the precice time will vary a lot",
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"author_name": "Chaosas",
"timestamp": "08/08/2022 18:09:20",
"content": "ok let me give you in a bit more complex way",
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"timestamp": "08/08/2022 18:09:22",
"content": "Same thing",
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"author_name": "Tarek Ahmed",
"timestamp": "08/08/2022 18:09:35",
"content": "Just add all of their rates",
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"author_name": "Chaosas",
"timestamp": "08/08/2022 18:09:43",
"content": "A: 1 brick every 34 sec",
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"id": 1006323393198563500,
"author_id": 531934659693641700,
"author_name": "Chaosas",
"timestamp": "08/08/2022 18:09:53",
"content": "B: 1 brick every 52 sec",
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},
{
"id": 1006323444159348900,
"author_id": 531934659693641700,
"author_name": "Chaosas",
"timestamp": "08/08/2022 18:10:05",
"content": "C: 1 brick every 39 sec",
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},
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"id": 1006323477676044300,
"author_id": 531934659693641700,
"author_name": "Chaosas",
"timestamp": "08/08/2022 18:10:13",
"content": "and there could be 100 of these",
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},
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"id": 1006323539680428000,
"author_id": 697730177962344400,
"author_name": "Tarek Ahmed",
"timestamp": "08/08/2022 18:10:28",
"content": "So your problem is having an accurate decimal result?",
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"id": 1006323565676736500,
"author_id": 531934659693641700,
"author_name": "Chaosas",
"timestamp": "08/08/2022 18:10:34",
"content": "yep",
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"id": 1006323601449959400,
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"author_name": "Tarek Ahmed",
"timestamp": "08/08/2022 18:10:43",
"content": "Ok",
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},
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"author_id": 697730177962344400,
"author_name": "Tarek Ahmed",
"timestamp": "08/08/2022 18:11:01",
"content": "Well you could try finding the least common multiple of all the numbers in the bottom",
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"author_name": "Chaosas",
"timestamp": "08/08/2022 18:11:21",
"content": "I was looking for some formula were if i have 100 of these, i would not need to try the comon one ๐",
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},
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"id": 1006323819440509000,
"author_id": 531934659693641700,
"author_name": "Chaosas",
"timestamp": "08/08/2022 18:11:35",
"content": "sample is of 3 but what if i have a lot more ?",
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},
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"id": 1006327595283005600,
"author_id": 805217272087838700,
"author_name": "Mathematics Bot",
"timestamp": "08/08/2022 18:26:35",
"content": "@Chaosas Has your question been resolved?",
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"id": 1006333068883275900,
"author_id": 936816135830114300,
"author_name": "Sunil Chhetri",
"timestamp": "08/08/2022 18:48:20",
"content": "5x^2 + 6x + 1 = 0\n(5x + 1)(x + 1) = 0\nx = -1/5 and x = -1",
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"author_id": 936816135830114300,
"author_name": "Sunil Chhetri",
"timestamp": "08/08/2022 18:48:33",
"content": "If you are still stuck, then please ask. Thanks.",
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},
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"id": 1006333249871675500,
"author_id": 531934659693641700,
"author_name": "Chaosas",
"timestamp": "08/08/2022 18:49:03",
"content": "i bielieve that persons problem was solved already",
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"timestamp": "08/08/2022 19:19:03",
"content": "@Chaosas Has your question been resolved?",
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"timestamp": "08/08/2022 19:20:59",
"content": "Channel closed",
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}
] |
help-9
|
ac670da6429e40ff90b72ecad3aa2c1f
|
197,706 |
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"id": 1006341539003379700,
"author_id": 805217272087838700,
"author_name": "Mathematics Bot",
"timestamp": "08/08/2022 19:21:59",
"content": "Available help channel!",
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},
{
"id": 1006342304451285100,
"author_id": 921012659388809200,
"author_name": "Rooms By The Sea",
"timestamp": "08/08/2022 19:25:02",
"content": "Anyone able to tell me where I'm going wrong with 7iii)",
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"content": "Pinned a message.",
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"author_name": "Rooms By The Sea",
"timestamp": "08/08/2022 19:25:33",
"content": "My second x-value is incorrect but my first is correct",
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"id": 1006342566318448600,
"author_id": 921012659388809200,
"author_name": "Rooms By The Sea",
"timestamp": "08/08/2022 19:26:04",
"content": "how do I get the correct second x-value ?",
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},
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"id": 1006345360588943500,
"author_id": 921012659388809200,
"author_name": "Rooms By The Sea",
"timestamp": "08/08/2022 19:37:10",
"content": "@Helpers",
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},
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"author_id": 437818258372952060,
"author_name": "caden_the_cadet",
"timestamp": "08/08/2022 19:37:53",
"content": "!15min",
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"id": 1006345538867830900,
"author_id": 805217272087838700,
"author_name": "Mathematics Bot",
"timestamp": "08/08/2022 19:37:53",
"content": "Please only use the @Helpers ping **once** if your question has not been answered **for 15 minutes**. Please do not ping or DM individual users about your question.",
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{
"id": 1006345602944221200,
"author_id": 921012659388809200,
"author_name": "Rooms By The Sea",
"timestamp": "08/08/2022 19:38:08",
"content": "sorry",
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"id": 1006346068641972200,
"author_id": 182179228840755200,
"author_name": "iCaird",
"timestamp": "08/08/2022 19:39:59",
"content": "$|2x|$ is $2x$ if $x$ is positive or $-2x$ if $x$ is negative, not sure why you're talking about y and -y",
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},
{
"id": 1006346080662851600,
"author_id": 510789298321096700,
"author_name": "TeXit",
"timestamp": "08/08/2022 19:40:02",
"content": "**ฮฃAC**",
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"timestamp": "08/08/2022 19:41:58",
"content": "I see now",
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"timestamp": "08/08/2022 19:42:05",
"content": "thank you",
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"author_name": "Mathematics Bot",
"timestamp": "08/08/2022 19:57:05",
"content": "@Rooms By The Sea Has your question been resolved?",
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"timestamp": "08/08/2022 20:12:06",
"content": "Channel closed",
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}
] |
help-9
|
1bdd9d7e42454f92b5a69371095ed7ea
|
197,707 |
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"timestamp": "08/08/2022 20:13:06",
"content": "Available help channel!",
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{
"id": 1006363051026550800,
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"content": "Pinned a message.",
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"author_id": 730443144302428200,
"author_name": "Percy Potter",
"timestamp": "08/08/2022 20:48:01",
"content": "so i know that the last number has to be 1, 3 or 9",
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"id": 1006363243222151300,
"author_id": 730443144302428200,
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"timestamp": "08/08/2022 20:48:14",
"content": "but idk how to find the total combinations",
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{
"id": 1006363481244717000,
"author_id": 533543009774731260,
"author_name": "2 3 5 7",
"timestamp": "08/08/2022 20:49:11",
"content": "How many options do you have for the last degit?",
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"id": 1006363569081831400,
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"timestamp": "08/08/2022 20:49:32",
"content": "3",
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"id": 1006363596655177900,
"author_id": 533543009774731260,
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"timestamp": "08/08/2022 20:49:38",
"content": "No",
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"id": 1006363609418440800,
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"timestamp": "08/08/2022 20:49:41",
"content": "Ye",
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{
"id": 1006363621556756500,
"author_id": 730443144302428200,
"author_name": "Percy Potter",
"timestamp": "08/08/2022 20:49:44",
"content": "typo myb",
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"id": 1006363758706303000,
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"author_name": "2 3 5 7",
"timestamp": "08/08/2022 20:50:17",
"content": "Now you select one of the 3 \nHow many options do you have for the second last ?",
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"id": 1006363831670427800,
"author_id": 600510288067952600,
"author_name": "GarlicBredFries",
"timestamp": "08/08/2022 20:50:34",
"content": "err",
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"id": 1006363881612005400,
"author_id": 600510288067952600,
"author_name": "GarlicBredFries",
"timestamp": "08/08/2022 20:50:46",
"content": "the next digit you should worry about is the 10k digit",
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"timestamp": "08/08/2022 20:51:01",
"content": "4",
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"timestamp": "08/08/2022 20:51:06",
"content": "Ye",
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"author_name": "Percy Potter",
"timestamp": "08/08/2022 20:51:12",
"content": "sorry?",
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"timestamp": "08/08/2022 20:51:15",
"content": "Third last ?",
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"author_id": 600510288067952600,
"author_name": "GarlicBredFries",
"timestamp": "08/08/2022 20:51:17",
"content": "the 10k digit cannot be 0",
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"timestamp": "08/08/2022 20:51:49",
"content": "3",
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"author_name": "2 3 5 7",
"timestamp": "08/08/2022 20:52:27",
"content": "Tbh i hate where the question is not clear wether 0123 counts in your set",
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"id": 1006364411264499700,
"author_id": 730443144302428200,
"author_name": "Percy Potter",
"timestamp": "08/08/2022 20:52:52",
"content": "wdym 0123?",
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"id": 1006364684527607800,
"author_id": 730443144302428200,
"author_name": "Percy Potter",
"timestamp": "08/08/2022 20:53:58",
"content": "k wait i think i get it",
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},
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"id": 1006364748947923000,
"author_id": 730443144302428200,
"author_name": "Percy Potter",
"timestamp": "08/08/2022 20:54:13",
"content": "first, one odd at the end is 4! combos",
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"id": 1006364777876041900,
"author_id": 730443144302428200,
"author_name": "Percy Potter",
"timestamp": "08/08/2022 20:54:20",
"content": "then second odd number at the end also 4! combos",
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"id": 1006364788445687800,
"author_id": 730443144302428200,
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"timestamp": "08/08/2022 20:54:22",
"content": "then 3rd",
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"author_id": 730443144302428200,
"author_name": "Percy Potter",
"timestamp": "08/08/2022 20:54:27",
"content": "so would it be 4! x 3",
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"id": 1006364827507249300,
"author_id": 730443144302428200,
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"timestamp": "08/08/2022 20:54:32",
"content": "=72",
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"author_name": "Percy Potter",
"timestamp": "08/08/2022 20:54:32",
"content": "?",
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"author_id": 726966851254616200,
"author_name": "NoNameGuy",
"timestamp": "08/08/2022 20:59:11",
"content": "That should be right",
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"author_name": "Percy Potter",
"timestamp": "08/08/2022 20:59:46",
"content": "k thx",
"attachments": [],
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},
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"author_id": 726966851254616200,
"author_name": "NoNameGuy",
"timestamp": "08/08/2022 20:59:52",
"content": "np",
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"author_name": "Percy Potter",
"timestamp": "08/08/2022 21:00:00",
"content": "what abt this q?",
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"timestamp": "08/08/2022 21:00:01",
"content": "",
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"author_name": "NoNameGuy",
"timestamp": "08/08/2022 21:01:35",
"content": "I think ik how to get to the answer just gives away the answer for you though",
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"timestamp": "08/08/2022 21:01:42",
"content": "i think it should be 5k",
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"timestamp": "08/08/2022 21:01:50",
"content": "maybe",
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"author_name": "Percy Potter",
"timestamp": "08/08/2022 21:01:54",
"content": "cuz 50k more till 6 digits",
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"author_name": "Percy Potter",
"timestamp": "08/08/2022 21:01:57",
"content": "then /10",
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"author_name": "Percy Potter",
"timestamp": "08/08/2022 21:02:00",
"content": "so 5k",
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"author_name": "NoNameGuy",
"timestamp": "08/08/2022 21:02:20",
"content": "I think it's also 5k but I'm new to permuations kind of",
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"author_name": "Percy Potter",
"timestamp": "08/08/2022 21:02:29",
"content": "oh ok",
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"author_name": "Percy Potter",
"timestamp": "08/08/2022 21:02:47",
"content": "how would u get to the answer \"straight away\" then",
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"timestamp": "08/08/2022 21:02:54",
"content": "was just thinking",
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"timestamp": "08/08/2022 21:02:58",
"content": "and would it also be 5k?",
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"timestamp": "08/08/2022 21:03:06",
"content": "100k-50k",
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"author_name": "NoNameGuy",
"timestamp": "08/08/2022 21:03:13",
"content": "right",
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"author_name": "NoNameGuy",
"timestamp": "08/08/2022 21:03:18",
"content": "but we'd get 50k",
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"author_name": "NoNameGuy",
"timestamp": "08/08/2022 21:03:37",
"content": "So we'd have to go in a range between 10k and 50k again",
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"timestamp": "08/08/2022 21:03:42",
"content": "So just the numbers between that",
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"timestamp": "08/08/2022 21:03:48",
"content": "I'd assume it's 5k",
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"timestamp": "08/08/2022 21:03:50",
"content": "I think",
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"timestamp": "08/08/2022 21:04:03",
"content": "yea",
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"author_name": "NoNameGuy",
"timestamp": "08/08/2022 21:04:14",
"content": "in your case we'd just go from 50 001 to 99 999",
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"author_name": "Percy Potter",
"timestamp": "08/08/2022 21:04:40",
"content": "yea but has to be divisible by 10",
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"author_name": "NoNameGuy",
"timestamp": "08/08/2022 21:05:04",
"content": "Every time numbers gets bigger",
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"author_name": "NoNameGuy",
"timestamp": "08/08/2022 21:05:09",
"content": "like to 10 at the end",
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"author_name": "NoNameGuy",
"timestamp": "08/08/2022 21:05:13",
"content": "ok here's what I'd do",
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"id": 1006367566933000300,
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"author_name": "NoNameGuy",
"timestamp": "08/08/2022 21:05:25",
"content": "how many 10s are in 1000",
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"author_name": "Percy Potter",
"timestamp": "08/08/2022 21:05:50",
"content": ".100",
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"id": 1006367692913115100,
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"author_name": "NoNameGuy",
"timestamp": "08/08/2022 21:05:55",
"content": "good",
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"author_name": "NoNameGuy",
"timestamp": "08/08/2022 21:06:33",
"content": "So we know 100 10s in a 1000",
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"timestamp": "08/08/2022 21:06:42",
"content": "Multiply that by 50 and we get teh answer",
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"id": 1006367927446032400,
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"timestamp": "08/08/2022 21:06:51",
"content": "the 100 10s part I meant",
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"id": 1006368091858550900,
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"author_name": "Percy Potter",
"timestamp": "08/08/2022 21:07:30",
"content": "right",
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},
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"id": 1006368103279640700,
"author_id": 730443144302428200,
"author_name": "Percy Potter",
"timestamp": "08/08/2022 21:07:33",
"content": "so 5000",
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},
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"id": 1006368140483100700,
"author_id": 726966851254616200,
"author_name": "NoNameGuy",
"timestamp": "08/08/2022 21:07:42",
"content": "yeah",
"attachments": [],
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},
{
"id": 1006368146829086800,
"author_id": 726966851254616200,
"author_name": "NoNameGuy",
"timestamp": "08/08/2022 21:07:43",
"content": "basically",
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"id": 1006368380313424000,
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"author_name": "Percy Potter",
"timestamp": "08/08/2022 21:08:39",
"content": "nice",
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},
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"id": 1006368384297992300,
"author_id": 730443144302428200,
"author_name": "Percy Potter",
"timestamp": "08/08/2022 21:08:40",
"content": "thx",
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},
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"id": 1006369853894033500,
"author_id": 730443144302428200,
"author_name": "Percy Potter",
"timestamp": "08/08/2022 21:14:30",
"content": ".close",
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},
{
"id": 1006369855496278100,
"author_id": 805217272087838700,
"author_name": "Mathematics Bot",
"timestamp": "08/08/2022 21:14:30",
"content": "Channel closed",
"attachments": [],
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"reference": null
}
] |
help-9
|
1fd58f2076714b2598a4cc87e1e3ac7c
|
197,708 |
[
{
"id": 1006370108802871300,
"author_id": 805217272087838700,
"author_name": "Mathematics Bot",
"timestamp": "08/08/2022 21:15:31",
"content": "Available help channel!",
"attachments": [],
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"reference": null
},
{
"id": 1006370720625995800,
"author_id": 156929189348376580,
"author_name": "Bira",
"timestamp": "08/08/2022 21:17:57",
"content": "Hello! Im trying to solve this Diffie-Hellman protocol problem. Im stuck on the mod chart section. Where i put the question mark, i dont think its correct. I know im supposed to subract by the mod to get a remainder but i think that product is way too large",
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"timestamp": "08/08/2022 21:17:57",
"content": "Pinned a message.",
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{
"id": 1006371557725184100,
"author_id": 156929189348376580,
"author_name": "Bira",
"timestamp": "08/08/2022 21:21:16",
"content": "i also saw this same question posted to chegg however they didnt show all the work involved so it doesnt help me much other than give me the end result",
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"id": 1006373708648169500,
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"author_name": "tatpoj",
"timestamp": "08/08/2022 21:29:49",
"content": "I don't have the knowledge to help you with this question, but it seems like it might be over the heads of a lot of people here. You might have more luck if you scroll down and post it in the relevant university or advanced mathematics channel",
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"timestamp": "08/08/2022 21:30:35",
"content": "alright thanks",
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},
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"id": 1006373908603224000,
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"author_name": "Bira",
"timestamp": "08/08/2022 21:30:37",
"content": ".close",
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},
{
"id": 1006373909840547800,
"author_id": 805217272087838700,
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"timestamp": "08/08/2022 21:30:37",
"content": "Channel closed",
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}
] |
help-9
|
dae54a0d57c74a18a0a33e16562d306e
|
197,709 |
[
{
"id": 1006374163537211400,
"author_id": 805217272087838700,
"author_name": "Mathematics Bot",
"timestamp": "08/08/2022 21:31:38",
"content": "Available help channel!",
"attachments": [],
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"reference": null
},
{
"id": 1006377042041901200,
"author_id": 938223451850825700,
"author_name": "phi_psi",
"timestamp": "08/08/2022 21:43:04",
"content": "For relations $P:A \\to B$ and $R:C \\to D$, and $\\varphi :\\equiv P \\land R$, can we say that $\\varphi$ has a domain, and, if so, is its domain $A \\cup C$?",
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},
{
"id": 1006377044239732900,
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"author_name": "Mathematics Bot",
"timestamp": "08/08/2022 21:43:04",
"content": "Pinned a message.",
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{
"id": 1006377052942897200,
"author_id": 510789298321096700,
"author_name": "TeXit",
"timestamp": "08/08/2022 21:43:07",
"content": "**scope\\_phi**",
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"id": 1006378090768908400,
"author_id": 331558346333224960,
"author_name": "jan Niku",
"timestamp": "08/08/2022 21:47:14",
"content": "how is that and functioning here :thonk: just curious",
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},
{
"id": 1006378150969737200,
"author_id": 938223451850825700,
"author_name": "phi_psi",
"timestamp": "08/08/2022 21:47:28",
"content": "What do you mean?",
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},
{
"id": 1006378164680937500,
"author_id": 331558346333224960,
"author_name": "jan Niku",
"timestamp": "08/08/2022 21:47:32",
"content": "tempted to say it should be intersection",
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},
{
"id": 1006378230879625300,
"author_id": 331558346333224960,
"author_name": "jan Niku",
"timestamp": "08/08/2022 21:47:47",
"content": "for phi := P \\land R",
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},
{
"id": 1006378247874945000,
"author_id": 331558346333224960,
"author_name": "jan Niku",
"timestamp": "08/08/2022 21:47:51",
"content": "whats the land doing",
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},
{
"id": 1006378316422463500,
"author_id": 938223451850825700,
"author_name": "phi_psi",
"timestamp": "08/08/2022 21:48:08",
"content": "It's just a conjunction. logical and",
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},
{
"id": 1006378354074726400,
"author_id": 331558346333224960,
"author_name": "jan Niku",
"timestamp": "08/08/2022 21:48:17",
"content": "ah, okay",
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},
{
"id": 1006378384164651100,
"author_id": 331558346333224960,
"author_name": "jan Niku",
"timestamp": "08/08/2022 21:48:24",
"content": "in that case yea i dont think the domain can be the union",
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},
{
"id": 1006378405178134500,
"author_id": 331558346333224960,
"author_name": "jan Niku",
"timestamp": "08/08/2022 21:48:29",
"content": "i think it has to be intersection",
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},
{
"id": 1006378593305231400,
"author_id": 938223451850825700,
"author_name": "phi_psi",
"timestamp": "08/08/2022 21:49:14",
"content": "But couldn't it just be false everywhere that isn't the intersection?",
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},
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"id": 1006378633792847900,
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"author_name": "phi_psi",
"timestamp": "08/08/2022 21:49:23",
"content": "I think you're right though",
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},
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"id": 1006378668202917900,
"author_id": 331558346333224960,
"author_name": "jan Niku",
"timestamp": "08/08/2022 21:49:32",
"content": "well youd have to run a relation somewhere its not defined right",
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},
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"id": 1006378715116212400,
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"author_name": "jan Niku",
"timestamp": "08/08/2022 21:49:43",
"content": "to me that seems like itd break it",
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},
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"id": 1006378726994485400,
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"author_name": "jan Niku",
"timestamp": "08/08/2022 21:49:46",
"content": "cant say ive run into this before though",
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},
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"id": 1006378738679812200,
"author_id": 331558346333224960,
"author_name": "jan Niku",
"timestamp": "08/08/2022 21:49:48",
"content": "at least not with relations",
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},
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"id": 1006378808330432500,
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"author_name": "jan Niku",
"timestamp": "08/08/2022 21:50:05",
"content": "seems like T land undefined would be undefined",
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"id": 1006378809479663600,
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"author_name": "phi_psi",
"timestamp": "08/08/2022 21:50:05",
"content": "idk what you mean by \"run a relation somewhere its not defined\"",
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"id": 1006378867126173800,
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"author_name": "jan Niku",
"timestamp": "08/08/2022 21:50:19",
"content": "like idk we can make an example",
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"id": 1006378871605702800,
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"author_name": "phi_psi",
"timestamp": "08/08/2022 21:50:20",
"content": "Ohhhh right ok",
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},
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"id": 1006378911585800200,
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"author_name": "jan Niku",
"timestamp": "08/08/2022 21:50:30",
"content": "but if your domains dont perfectly overlap",
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},
{
"id": 1006378938303533000,
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"author_name": "phi_psi",
"timestamp": "08/08/2022 21:50:36",
"content": "Yeah, that's definitely right",
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},
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"author_name": "jan Niku",
"timestamp": "08/08/2022 21:50:37",
"content": "you may choose an input thats only in one domain",
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"id": 1006378955231739900,
"author_id": 331558346333224960,
"author_name": "jan Niku",
"timestamp": "08/08/2022 21:50:40",
"content": "but it will be in the union",
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},
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"id": 1006379056880693200,
"author_id": 938223451850825700,
"author_name": "phi_psi",
"timestamp": "08/08/2022 21:51:04",
"content": "yeah, ok",
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},
{
"id": 1006379065550315500,
"author_id": 938223451850825700,
"author_name": "phi_psi",
"timestamp": "08/08/2022 21:51:06",
"content": "thanks",
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},
{
"id": 1006379075369177200,
"author_id": 331558346333224960,
"author_name": "jan Niku",
"timestamp": "08/08/2022 21:51:09",
"content": "np",
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},
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"author_id": 938223451850825700,
"author_name": "phi_psi",
"timestamp": "08/08/2022 21:51:15",
"content": ".close",
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},
{
"id": 1006379103957565400,
"author_id": 805217272087838700,
"author_name": "Mathematics Bot",
"timestamp": "08/08/2022 21:51:16",
"content": "Channel closed",
"attachments": [],
"mentions": [],
"reference": null
}
] |
help-9
|
1fc4de687ab24701ab22ca60b3fb9625
|
197,710 |
[
{
"id": 1006394028155207800,
"author_id": 805217272087838700,
"author_name": "Mathematics Bot",
"timestamp": "08/08/2022 22:50:34",
"content": "Available help channel!",
"attachments": [],
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"reference": null
},
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"id": 1006397070678175700,
"author_id": 168539726813331460,
"author_name": "Nerokyi",
"timestamp": "08/08/2022 23:02:39",
"content": "Hey, can someone help me on the following problem? I know for the last 2 problems that it is a positive vlaue",
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"content": "Pinned a message.",
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"author_id": 168539726813331460,
"author_name": "Nerokyi",
"timestamp": "08/08/2022 23:03:10",
"content": "But how would it look like with the context.",
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},
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"id": 1006398284501356500,
"author_id": 168539726813331460,
"author_name": "Nerokyi",
"timestamp": "08/08/2022 23:07:29",
"content": "In which I don't know how to express it with intervals",
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},
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"id": 1006400003557818400,
"author_id": 492817322105634800,
"author_name": "marco.py",
"timestamp": "08/08/2022 23:14:18",
"content": "maybe radius can only be positive",
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},
{
"id": 1006400143278473200,
"author_id": 492817322105634800,
"author_name": "marco.py",
"timestamp": "08/08/2022 23:14:52",
"content": "so interval would be [0, โ)",
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},
{
"id": 1006400170658902000,
"author_id": 492817322105634800,
"author_name": "marco.py",
"timestamp": "08/08/2022 23:14:58",
"content": "the ) means its not included",
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},
{
"id": 1006400191198400600,
"author_id": 492817322105634800,
"author_name": "marco.py",
"timestamp": "08/08/2022 23:15:03",
"content": "because you cant include infinity",
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},
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"id": 1006400227974062100,
"author_id": 349354952961032200,
"author_name": "Umbraleviathan",
"timestamp": "08/08/2022 23:15:12",
"content": "Pretty much yeah",
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},
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"id": 1006400243664949200,
"author_id": 349354952961032200,
"author_name": "Umbraleviathan",
"timestamp": "08/08/2022 23:15:16",
"content": "Although",
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},
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"id": 1006400259808829400,
"author_id": 349354952961032200,
"author_name": "Umbraleviathan",
"timestamp": "08/08/2022 23:15:19",
"content": "You can't have a 0 radius either",
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},
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"id": 1006400378419548200,
"author_id": 492817322105634800,
"author_name": "marco.py",
"timestamp": "08/08/2022 23:15:48",
"content": "no circle lol",
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},
{
"id": 1006400417153957900,
"author_id": 349354952961032200,
"author_name": "Umbraleviathan",
"timestamp": "08/08/2022 23:15:57",
"content": "Circlen't",
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},
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"id": 1006400569193275400,
"author_id": 349354952961032200,
"author_name": "Umbraleviathan",
"timestamp": "08/08/2022 23:16:33",
"content": "Although if this is on a graph and you're one of those pesky Polar Graph sycophants, I guess you can have a negative radius",
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},
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"id": 1006400582912856000,
"author_id": 349354952961032200,
"author_name": "Umbraleviathan",
"timestamp": "08/08/2022 23:16:36",
"content": "I mean it doesn't do shit",
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},
{
"id": 1006400617109008500,
"author_id": 349354952961032200,
"author_name": "Umbraleviathan",
"timestamp": "08/08/2022 23:16:45",
"content": "But \"ooh I guess you have can negative radii aaa ooo spooky\"",
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},
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"id": 1006401233533280300,
"author_id": 492817322105634800,
"author_name": "marco.py",
"timestamp": "08/08/2022 23:19:12",
"content": "@Nerokyi",
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"id": 1006401376378691700,
"author_id": 349354952961032200,
"author_name": "Umbraleviathan",
"timestamp": "08/08/2022 23:19:46",
"content": "Well he does have DND on",
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},
{
"id": 1006401379931267100,
"author_id": 349354952961032200,
"author_name": "Umbraleviathan",
"timestamp": "08/08/2022 23:19:47",
"content": "Hm",
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},
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"id": 1006401495769567400,
"author_id": 492817322105634800,
"author_name": "marco.py",
"timestamp": "08/08/2022 23:20:14",
"content": "damn yeah",
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},
{
"id": 1006401531165294700,
"author_id": 349354952961032200,
"author_name": "Umbraleviathan",
"timestamp": "08/08/2022 23:20:23",
"content": "Whelp his loss ig",
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},
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"id": 1006402231379177500,
"author_id": 168539726813331460,
"author_name": "Nerokyi",
"timestamp": "08/08/2022 23:23:10",
"content": "huh",
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},
{
"id": 1006402610321965000,
"author_id": 168539726813331460,
"author_name": "Nerokyi",
"timestamp": "08/08/2022 23:24:40",
"content": "oh yeah it was [0,inf)",
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"author_name": "Nerokyi",
"timestamp": "08/08/2022 23:24:43",
"content": ".close",
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},
{
"id": 1006402626126086100,
"author_id": 805217272087838700,
"author_name": "Mathematics Bot",
"timestamp": "08/08/2022 23:24:44",
"content": "Channel closed",
"attachments": [],
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}
] |
help-9
|
b777930567044df7aeefda6b53327c28
|
197,711 |
[
{
"id": 1006402775241998300,
"author_id": 349354952961032200,
"author_name": "Umbraleviathan",
"timestamp": "08/08/2022 23:25:19",
"content": "Lmao I guess they allow you to have no circle as an option",
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"author_name": "Mathematics Bot",
"timestamp": "08/09/2022 03:12:02",
"content": "Available help channel!",
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},
{
"id": 1006461459712196600,
"author_id": 203063245135806460,
"author_name": "aardoc",
"timestamp": "08/09/2022 03:18:31",
"content": "Why is statement I not true?",
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"id": 1006461461536706600,
"author_id": 805217272087838700,
"author_name": "Mathematics Bot",
"timestamp": "08/09/2022 03:18:31",
"content": "Pinned a message.",
"attachments": [],
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{
"id": 1006461630558777300,
"author_id": 203063245135806460,
"author_name": "aardoc",
"timestamp": "08/09/2022 03:19:11",
"content": "Isn't f'(x) = 2 for x < 3?",
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},
{
"id": 1006461839695151100,
"author_id": 437818258372952060,
"author_name": "caden_the_cadet",
"timestamp": "08/09/2022 03:20:01",
"content": "Because of the discontinuity between the two, it is not differentiable at that point",
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},
{
"id": 1006462263798005800,
"author_id": 437818258372952060,
"author_name": "caden_the_cadet",
"timestamp": "08/09/2022 03:21:42",
"content": "@aardoc",
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{
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{
"id": 1006462648143061100,
"author_id": 203063245135806460,
"author_name": "aardoc",
"timestamp": "08/09/2022 03:23:14",
"content": "But then why is statement II true?",
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},
{
"id": 1006463015090143200,
"author_id": 203063245135806460,
"author_name": "aardoc",
"timestamp": "08/09/2022 03:24:41",
"content": "like why is it not differentiable from the left but it is from the right",
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},
{
"id": 1006463299312947300,
"author_id": 437818258372952060,
"author_name": "caden_the_cadet",
"timestamp": "08/09/2022 03:25:49",
"content": "because it can be approached from the right I believe",
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},
{
"id": 1006463318736765000,
"author_id": 437818258372952060,
"author_name": "caden_the_cadet",
"timestamp": "08/09/2022 03:25:54",
"content": "Iโm not sure",
"attachments": [],
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},
{
"id": 1006463882166009900,
"author_id": 203063245135806460,
"author_name": "aardoc",
"timestamp": "08/09/2022 03:28:08",
"content": "is there anyone else who knows why",
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},
{
"id": 1006465330689888400,
"author_id": 203063245135806460,
"author_name": "aardoc",
"timestamp": "08/09/2022 03:33:54",
"content": "@Helpers",
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},
{
"id": 1006465587351924700,
"author_id": 437818258372952060,
"author_name": "caden_the_cadet",
"timestamp": "08/09/2022 03:34:55",
"content": "!15min",
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},
{
"id": 1006465588438249500,
"author_id": 805217272087838700,
"author_name": "Mathematics Bot",
"timestamp": "08/09/2022 03:34:55",
"content": "Please only use the @Helpers ping **once** if your question has not been answered **for 15 minutes**. Please do not ping or DM individual users about your question.",
"attachments": [],
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},
{
"id": 1006467041189969900,
"author_id": 203063245135806460,
"author_name": "aardoc",
"timestamp": "08/09/2022 03:40:41",
"content": "it has been 15 minutes",
"attachments": [],
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},
{
"id": 1006470816961155100,
"author_id": 805217272087838700,
"author_name": "Mathematics Bot",
"timestamp": "08/09/2022 03:55:42",
"content": "@aardoc Has your question been resolved?",
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"id": 1006474592866554000,
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"author_name": "Mathematics Bot",
"timestamp": "08/09/2022 04:10:42",
"content": "Channel closed",
"attachments": [],
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"reference": null
}
] |
help-9
|
dbb633e17d1d4f5eab7c87522ff6682c
|
197,712 |
[
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"id": 1006474848303857700,
"author_id": 805217272087838700,
"author_name": "Mathematics Bot",
"timestamp": "08/09/2022 04:11:43",
"content": "Available help channel!",
"attachments": [],
"mentions": [],
"reference": null
},
{
"id": 1006477449808322600,
"author_id": 385735450465271800,
"author_name": "jacksoniga",
"timestamp": "08/09/2022 04:22:03",
"content": "",
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"timestamp": "08/09/2022 04:22:04",
"content": "Pinned a message.",
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"id": 1006477531031019500,
"author_id": 385735450465271800,
"author_name": "jacksoniga",
"timestamp": "08/09/2022 04:22:22",
"content": "did anyone get 40/3",
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},
{
"id": 1006477836770619500,
"author_id": 826318983413366800,
"author_name": "Cogwheels of the mind",
"timestamp": "08/09/2022 04:23:35",
"content": "Me too",
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},
{
"id": 1006479113277685800,
"author_id": 909734400990785500,
"author_name": "แฒผแฒผ",
"timestamp": "08/09/2022 04:28:40",
"content": "not me",
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"timestamp": "08/09/2022 04:29:03",
"content": "40/3 is correct guys",
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},
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"id": 1006479216398843900,
"author_id": 385735450465271800,
"author_name": "jacksoniga",
"timestamp": "08/09/2022 04:29:04",
"content": "nvm",
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},
{
"id": 1006479262804611200,
"author_id": 385735450465271800,
"author_name": "jacksoniga",
"timestamp": "08/09/2022 04:29:15",
"content": "i realised i was integrating wrong for my answer",
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},
{
"id": 1006479595501015000,
"author_id": 909734400990785500,
"author_name": "แฒผแฒผ",
"timestamp": "08/09/2022 04:30:35",
"content": "the question meant this area right?",
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"id": 1006479766288875600,
"author_id": 909734400990785500,
"author_name": "แฒผแฒผ",
"timestamp": "08/09/2022 04:31:15",
"content": "oh wait",
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{
"id": 1006479779295400000,
"author_id": 909734400990785500,
"author_name": "แฒผแฒผ",
"timestamp": "08/09/2022 04:31:18",
"content": "I see",
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"id": 1006479925534011400,
"author_id": 909734400990785500,
"author_name": "แฒผแฒผ",
"timestamp": "08/09/2022 04:31:53",
"content": "ya 40/3",
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},
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"id": 1006480806954418200,
"author_id": 385735450465271800,
"author_name": "jacksoniga",
"timestamp": "08/09/2022 04:35:23",
"content": "๐",
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},
{
"id": 1006480878672810000,
"author_id": 385735450465271800,
"author_name": "jacksoniga",
"timestamp": "08/09/2022 04:35:40",
"content": ".close",
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},
{
"id": 1006480880409247900,
"author_id": 805217272087838700,
"author_name": "Mathematics Bot",
"timestamp": "08/09/2022 04:35:41",
"content": "Channel closed",
"attachments": [],
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}
] |
help-9
|
6a0d7a0bb60e47ab96286c3ecb0fda89
|
197,713 |
[
{
"id": 1006505852536111200,
"author_id": 805217272087838700,
"author_name": "Mathematics Bot",
"timestamp": "08/09/2022 06:14:55",
"content": "Available help channel!",
"attachments": [],
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"reference": null
},
{
"id": 1006519209016176600,
"author_id": 711962128306929700,
"author_name": "SpartanGodofWar",
"timestamp": "08/09/2022 07:07:59",
"content": "anybody available for help",
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},
{
"id": 1006519211578896400,
"author_id": 805217272087838700,
"author_name": "Mathematics Bot",
"timestamp": "08/09/2022 07:08:00",
"content": "Pinned a message.",
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"author_id": 510059806875451400,
"author_name": "Shoใปใทใง",
"timestamp": "08/09/2022 07:08:09",
"content": "post your question",
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},
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"author_name": "SpartanGodofWar",
"timestamp": "08/09/2022 07:09:10",
"content": "I can type 32 pages in 6 hours on a computer. How so i find\n1. time taken by me to type 1 page\n2. Number of pages I can type in 1 hour\n3. number of pages I can type in 1 minute",
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"timestamp": "08/09/2022 07:12:09",
"content": "The basic idea is to get speed.",
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"author_name": "Chai T. Rex",
"timestamp": "08/09/2022 07:12:16",
"content": "The amount of work over time it takes.",
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"timestamp": "08/09/2022 07:12:53",
"content": "So, you have 32/6 pages/hour.",
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"timestamp": "08/09/2022 07:13:01",
"content": "That's the answer to question 2.",
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"author_name": "Chai T. Rex",
"timestamp": "08/09/2022 07:13:11",
"content": "Then, you can only do 1/60 of that number of pages in a minute.",
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"timestamp": "08/09/2022 07:13:32",
"content": "Then, you can flip it over: 6/32 hours/page.",
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"author_name": "Chai T. Rex",
"timestamp": "08/09/2022 07:13:40",
"content": "And that's the answer to question 1.",
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"author_name": "Shoใปใทใง",
"timestamp": "08/09/2022 07:14:23",
"content": "i know this is wrong to ask but could you help me in #help-6๏ฝlong-wang-้พ็ I have been waiting for over half an hour :')",
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"timestamp": "08/09/2022 07:14:27",
"content": "Ok, let me digest all that ๐ญ",
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"timestamp": "08/09/2022 07:14:48",
"content": "@Shoใปใทใง @Chai T. Rex thanks guys",
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"timestamp": "08/09/2022 07:16:33",
"content": "can you explain to me how this part works? ๐",
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"author_name": "Shoใปใทใง",
"timestamp": "08/09/2022 07:17:17",
"content": "if 6 hrs equals 32 pages",
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"author_name": "Shoใปใทใง",
"timestamp": "08/09/2022 07:17:56",
"content": "then you find the equivalent of 1hr/ how many pages",
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"timestamp": "08/09/2022 07:18:13",
"content": "therefore dividing 32 by 6",
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"author_name": "Chai T. Rex",
"timestamp": "08/09/2022 07:18:59",
"content": "Well, the speed will be in pages/hour, right?",
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"author_name": "Chai T. Rex",
"timestamp": "08/09/2022 07:19:08",
"content": "So, you put the pages on top of the fraction and the hours on the bottom.",
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"author_name": "Chai T. Rex",
"timestamp": "08/09/2022 07:19:20",
"content": "(32 pages)/(6 hours)",
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"author_name": "SpartanGodofWar",
"timestamp": "08/09/2022 07:19:22",
"content": "no i want to kno simply, hpw long does it take me to write 1 page",
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"author_name": "Chai T. Rex",
"timestamp": "08/09/2022 07:19:40",
"content": "OK, so you want to know time per page.",
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"author_name": "Chai T. Rex",
"timestamp": "08/09/2022 07:19:49",
"content": "So, you put time on the top of the fraction and pages on the bottom.",
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"author_name": "SpartanGodofWar",
"timestamp": "08/09/2022 07:19:53",
"content": "yes time for page",
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"timestamp": "08/09/2022 07:19:58",
"content": "(6 hours)/(32 pages)",
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"author_name": "Chai T. Rex",
"timestamp": "08/09/2022 07:20:04",
"content": "So, 6/32 hours per page.",
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"author_name": "SpartanGodofWar",
"timestamp": "08/09/2022 07:20:23",
"content": "oh yes, its starting to make sense",
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"author_name": "Chai T. Rex",
"timestamp": "08/09/2022 07:20:26",
"content": "You put what units you want to get as the answer on top and the other units on bottom.",
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"author_name": "Chai T. Rex",
"timestamp": "08/09/2022 07:20:44",
"content": "Also, they'll probably do something else in future problems.",
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"author_id": 537482727557955600,
"author_name": "Chai T. Rex",
"timestamp": "08/09/2022 07:20:58",
"content": "Like they'll say five people are working together, how much work can they all do or whatever.",
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"id": 1006522520905728100,
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"author_name": "Chai T. Rex",
"timestamp": "08/09/2022 07:21:09",
"content": "You just add their speeds together to see how fast they all are together.",
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"timestamp": "08/09/2022 07:21:21",
"content": "Thanks T Rex, my thinking isw more clear now. Also thanks Sho\\",
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"timestamp": "08/09/2022 07:21:26",
"content": "You're welcome.",
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"author_name": "Shoใปใทใง",
"timestamp": "08/09/2022 07:21:31",
"content": ":') i didnt do much",
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"author_name": "SpartanGodofWar",
"timestamp": "08/09/2022 07:21:45",
"content": "I'll solve it right now , fingers crossed",
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"author_name": "Shoใปใทใง",
"timestamp": "08/09/2022 07:22:01",
"content": "use .close when you're finished",
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"timestamp": "08/09/2022 07:22:45",
"content": "thanks, i'll do. I'm new here ๐",
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"author_name": "SpartanGodofWar",
"timestamp": "08/09/2022 07:32:03",
"content": "Guys follow up\n1. 32/6 gives me 5.3 and I understand , I can type 5.3 pages per hour.\n2. 6/32 gives me 0.1875, **I cant make sense of this number** ๐ฆ",
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"author_id": 510059806875451400,
"author_name": "Shoใปใทใง",
"timestamp": "08/09/2022 07:33:12",
"content": "its just that",
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"author_name": "Shoใปใทใง",
"timestamp": "08/09/2022 07:33:27",
"content": "you can type 0.1875 of a page in an hour",
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"timestamp": "08/09/2022 07:34:07",
"content": "oh yeah , its so clear now",
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"timestamp": "08/09/2022 07:34:34",
"content": "follow up, can I futhur use this information to find how many pages I can type in a minute?",
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"timestamp": "08/09/2022 07:34:38",
"content": "yes",
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"timestamp": "08/09/2022 07:35:11",
"content": "0.1875/60 = 0.003125",
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"author_id": 510059806875451400,
"author_name": "Shoใปใทใง",
"timestamp": "08/09/2022 07:35:31",
"content": "wait",
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"id": 1006526142657867800,
"author_id": 510059806875451400,
"author_name": "Shoใปใทใง",
"timestamp": "08/09/2022 07:35:32",
"content": "nvm",
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"author_id": 510059806875451400,
"author_name": "Shoใปใทใง",
"timestamp": "08/09/2022 07:35:34",
"content": "im an itidot",
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"id": 1006526150996144100,
"author_id": 711962128306929700,
"author_name": "SpartanGodofWar",
"timestamp": "08/09/2022 07:35:34",
"content": "why it should be multiply and not divide?",
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"id": 1006526158550081500,
"author_id": 510059806875451400,
"author_name": "Shoใปใทใง",
"timestamp": "08/09/2022 07:35:36",
"content": "sorry",
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"id": 1006526188124110800,
"author_id": 510059806875451400,
"author_name": "Shoใปใทใง",
"timestamp": "08/09/2022 07:35:43",
"content": "yep",
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"author_id": 510059806875451400,
"author_name": "Shoใปใทใง",
"timestamp": "08/09/2022 07:35:45",
"content": "youre right",
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"timestamp": "08/09/2022 07:35:46",
"content": "no i'm bigger idiot",
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"timestamp": "08/09/2022 07:36:04",
"content": "@Shoใปใทใง 0.003125 what does this number mean now?",
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"author_name": "Shoใปใทใง",
"timestamp": "08/09/2022 07:36:43",
"content": "its just the amount of pages you can type in a minute. so its 1/60th of the amount you could type in an hour",
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"id": 1006526445994135700,
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"timestamp": "08/09/2022 07:36:45",
"content": "it means I can type 0.003125 page in a minute",
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"id": 1006526460498018300,
"author_id": 510059806875451400,
"author_name": "Shoใปใทใง",
"timestamp": "08/09/2022 07:36:48",
"content": "yes",
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"author_name": "SpartanGodofWar",
"timestamp": "08/09/2022 07:37:49",
"content": "ok, so how do i find in what Time can I type 1 page",
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"id": 1006526817487831000,
"author_id": 510059806875451400,
"author_name": "Shoใปใทใง",
"timestamp": "08/09/2022 07:38:13",
"content": "didnt you- do it? in question 1",
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"author_name": "Shoใปใทใง",
"timestamp": "08/09/2022 07:38:21",
"content": "awit",
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"author_id": 510059806875451400,
"author_name": "Shoใปใทใง",
"timestamp": "08/09/2022 07:38:23",
"content": "sory",
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"author_id": 510059806875451400,
"author_name": "Shoใปใทใง",
"timestamp": "08/09/2022 07:38:52",
"content": "if you want one page",
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"author_name": "Shoใปใทใง",
"timestamp": "08/09/2022 07:39:06",
"content": "oh",
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"timestamp": "08/09/2022 07:39:17",
"content": "Then, you can flip it over: 6/32 hours/page.\nAnd that's the answer to question 1. \nT rex answered it but I didnt understand",
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"author_name": "Shoใปใทใง",
"timestamp": "08/09/2022 07:39:25",
"content": "i think you mixed it around",
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"author_name": "Shoใปใทใง",
"timestamp": "08/09/2022 07:39:42",
"content": "wait or im an idiot",
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"author_name": "Shoใปใทใง",
"timestamp": "08/09/2022 07:39:46",
"content": "let me think",
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"author_id": 510059806875451400,
"author_name": "Shoใปใทใง",
"timestamp": "08/09/2022 07:40:02",
"content": "if you wnat one page",
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"timestamp": "08/09/2022 07:40:11",
"content": "No, its clear to me how many pages I can type in 1 hour and 1 minute.",
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"author_name": "Shoใปใทใง",
"timestamp": "08/09/2022 07:40:16",
"content": "you have to divide how many hours it took to do 32 by 32",
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"id": 1006527362659254400,
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"author_name": "SpartanGodofWar",
"timestamp": "08/09/2022 07:40:23",
"content": "But, how much time will it take me to type 1 page",
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"timestamp": "08/09/2022 07:41:24",
"content": "๐ญ",
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"timestamp": "08/09/2022 07:41:37",
"content": "for example if it took 6 minutes to make 3 page (this is just an example)",
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"timestamp": "08/09/2022 07:42:24",
"content": "then one page would be 6/3",
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"content": "1/2 what?",
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"timestamp": "08/09/2022 07:43:00",
"content": "sorr",
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"author_name": "Shoใปใทใง",
"timestamp": "08/09/2022 07:43:08",
"content": "my fingers arent working",
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"author_name": "SpartanGodofWar",
"timestamp": "08/09/2022 07:43:34",
"content": "yes i can type 1 page in 2 minutees, it makes sense now",
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"author_name": "Shoใปใทใง",
"timestamp": "08/09/2022 07:44:18",
"content": "you divide the amount of time by the pages",
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"timestamp": "08/09/2022 07:44:20",
"content": "so, if I can type **36**( making it easier) in 6 hours, how loong does it take me to type 1 page?\n\\",
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"author_name": "Shoใปใทใง",
"timestamp": "08/09/2022 07:44:24",
"content": "my brain isnt working",
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"timestamp": "08/09/2022 07:44:50",
"content": "yes ultimately I have to put page in denominator",
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"content": "Time/page",
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"timestamp": "08/09/2022 07:45:41",
"content": "its just equivalent fractions",
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"author_name": "SpartanGodofWar",
"timestamp": "08/09/2022 07:46:30",
"content": "I came up with solution that it takes me 11 minutes and 25 seconds to type 1 page. Am i right otr wrong?",
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"author_name": "Shoใปใทใง",
"timestamp": "08/09/2022 07:46:49",
"content": "for the actual question?",
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"author_name": "SpartanGodofWar",
"timestamp": "08/09/2022 07:47:00",
"content": "ok let me do it for actual question",
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"author_name": "SpartanGodofWar",
"timestamp": "08/09/2022 07:47:23",
"content": "yes for actual question, 11 minutes and 25 seconds",
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"timestamp": "08/09/2022 07:47:38",
"content": "here's how I did it",
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"timestamp": "08/09/2022 07:48:24",
"content": "6 hours = 360 minutes\nTime/Page\n360/32 = 11.25\nIs this right? @Shoใปใทใง",
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"timestamp": "08/09/2022 07:49:20",
"content": "yep",
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"timestamp": "08/09/2022 07:49:29",
"content": "thank you so much @Shoใปใทใง",
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"timestamp": "08/09/2022 07:49:32",
"content": "unbelievable",
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"timestamp": "08/09/2022 07:50:08",
"content": ".close",
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"id": 1006529817539248300,
"author_id": 805217272087838700,
"author_name": "Mathematics Bot",
"timestamp": "08/09/2022 07:50:08",
"content": "Channel closed",
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}
] |
help-9
|
154cae11cfa64ab09bc624ac7d0215f7
|
197,714 |
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"author_name": "Mathematics Bot",
"timestamp": "08/09/2022 07:57:09",
"content": "Available help channel!",
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"timestamp": "08/09/2022 08:07:55",
"content": "hey",
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"timestamp": "08/09/2022 08:07:55",
"content": "Pinned a message.",
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"content": "this is in linear equations",
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"content": "how do i solve this",
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"timestamp": "08/09/2022 08:08:59",
"content": "should i get 10p towards 5p and make it 5p-10p or should i get 5p towards LHS and make it 10p - 5p?",
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"content": "both work, but its easier to keep the p positive and move the 5p to the 10p (this will avoid dividing by -1)",
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"timestamp": "08/09/2022 08:10:58",
"content": "ohk",
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"timestamp": "08/09/2022 08:14:52",
"content": "for the first 4 questions i got the asnwers as",
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"timestamp": "08/09/2022 08:15:25",
"content": "1a. z <5.5\n2a. x > 0.625\n3a. t > 0.333\n4a. S > 1.2",
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"timestamp": "08/09/2022 08:15:35",
"content": "are these correct?",
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"author_id": 915145402859278300,
"author_name": "Deep.",
"timestamp": "08/09/2022 08:16:38",
"content": "Idk but first is wrong ig",
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"author_name": "Deep.",
"timestamp": "08/09/2022 08:17:28",
"content": "It should be negative",
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"timestamp": "08/09/2022 08:17:45",
"content": "ye",
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"timestamp": "08/09/2022 08:17:51",
"content": "i forgot to type negative",
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"timestamp": "08/09/2022 08:18:16",
"content": "last question if u dont mind",
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"timestamp": "08/09/2022 08:18:32",
"content": "what should exactly should i do here?",
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"author_name": "EnzoL",
"timestamp": "08/09/2022 08:18:58",
"content": "solve each one",
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"author_name": "EnzoL",
"timestamp": "08/09/2022 08:19:10",
"content": "and see if the solution is y>=2",
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"timestamp": "08/09/2022 08:19:12",
"content": "or not",
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"author_id": 408715646956863500,
"author_name": "D.",
"timestamp": "08/09/2022 08:19:20",
"content": "no need",
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"id": 1006537262143635500,
"author_id": 408715646956863500,
"author_name": "D.",
"timestamp": "08/09/2022 08:19:43",
"content": "u can see u need a positive 7y on the right",
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"timestamp": "08/09/2022 08:20:10",
"content": "yeah ofc u can see and do things but seems like the exercise is done for this",
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"id": 1006537387855315100,
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"author_name": "D.",
"timestamp": "08/09/2022 08:20:13",
"content": "so your option can be reduced",
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"author_name": "EnzoL",
"timestamp": "08/09/2022 08:20:19",
"content": "with the questions that he asked",
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"timestamp": "08/09/2022 08:20:32",
"content": "theres no point not solving every single equation",
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"timestamp": "08/09/2022 08:20:49",
"content": "i mean its good for him",
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"timestamp": "08/09/2022 08:21:36",
"content": "ohk",
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"timestamp": "08/09/2022 08:21:40",
"content": "i thaught the same",
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"timestamp": "08/09/2022 08:21:44",
"content": "just i got confused",
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"timestamp": "08/09/2022 08:21:48",
"content": "its okay dw",
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"timestamp": "08/09/2022 08:21:52",
"content": "ok",
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"timestamp": "08/09/2022 08:22:05",
"content": "tell me what u got when you think you're right",
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"content": "ok",
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"timestamp": "08/09/2022 08:24:24",
"content": "yup",
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"timestamp": "08/09/2022 08:26:05",
"content": "should i do this in number line format",
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"content": "bro should i make an number line for this",
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"content": "yh",
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"timestamp": "08/09/2022 08:28:07",
"content": "thx",
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"content": "so i got the answer 3",
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"content": "idk how it is wanted",
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"content": "this is the question",
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"content": "so i got the correct",
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"content": "but i forgot the number line part",
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"content": "so it it correct?",
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"content": "3 to infinite",
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"content": "but try to specify that r is not 3",
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"content": "isnt r = 3",
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"content": "i mean",
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"content": "and before 0 you forgot the -",
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"content": "r < 3",
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"content": "no",
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"content": "r > 3",
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"timestamp": "08/09/2022 08:38:31",
"content": "ye",
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"timestamp": "08/09/2022 08:38:39",
"content": "how?",
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"content": "24 < 8r",
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"content": "3 < r",
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"timestamp": "08/09/2022 08:39:02",
"content": "so r cant be 3",
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"content": "-8r > -24",
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"content": "r > -24/-8 = 3",
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"content": "r > 3",
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"timestamp": "08/09/2022 08:40:07",
"content": "could u explain me the concept in vc",
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"content": "cant",
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"timestamp": "08/09/2022 08:40:15",
"content": "in vacations rn",
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"content": "ohk",
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"content": "sorry",
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"timestamp": "08/09/2022 08:40:28",
"content": "but lemme write it",
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"content": "so basically in",
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"content": "could u send me ur working",
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"content": "didnt do any but wait",
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"content": "with the number line",
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"content": "imma write it down",
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"content": "the ] means that it is not equal to 3",
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"content": "[ means that it can be equal",
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"content": "i did the exact thing",
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"timestamp": "08/09/2022 08:43:03",
"content": "equal or infinitwe",
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"content": "its not equal",
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"timestamp": "08/09/2022 08:43:16",
"content": "it cant be equal to 3",
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"content": "wdym",
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"content": "r > 3",
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"timestamp": "08/09/2022 08:43:25",
"content": "yr",
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"timestamp": "08/09/2022 08:43:26",
"content": "ye",
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"timestamp": "08/09/2022 08:43:29",
"content": "bc r is more",
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"content": "r >= 3",
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"content": "means",
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"content": "r = 3 or r > 3",
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"timestamp": "08/09/2022 08:43:46",
"content": "so when ever we r trying to find r value",
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"timestamp": "08/09/2022 08:43:58",
"content": "r is always bigger in every question",
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"content": "mmh",
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"content": "nah",
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"timestamp": "08/09/2022 08:44:06",
"content": "it depends",
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"timestamp": "08/09/2022 08:44:17",
"content": "here u found y >=2",
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"timestamp": "08/09/2022 08:44:28",
"content": "so y can be = 2",
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"timestamp": "08/09/2022 08:44:33",
"content": "exactly",
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"timestamp": "08/09/2022 08:44:38",
"content": "so y is bigger",
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"timestamp": "08/09/2022 08:44:45",
"content": "or any variable is bigger than constant",
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"timestamp": "08/09/2022 08:44:46",
"content": "or equal",
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"timestamp": "08/09/2022 08:44:52",
"content": "yes",
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"timestamp": "08/09/2022 08:44:58",
"content": "thx",
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"timestamp": "08/09/2022 08:45:27",
"content": "try to replace r=3 in 15 + 7r < 15r - 9",
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"timestamp": "08/09/2022 08:45:29",
"content": "you will have",
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"timestamp": "08/09/2022 08:45:41",
"content": "15 + 7x3 < 15x 3 - 9",
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"timestamp": "08/09/2022 08:45:48",
"content": "36 < 36",
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"content": "for b part is the asnwer",
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"content": "p > 1",
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"author_name": "EnzoL",
"timestamp": "08/09/2022 08:47:36",
"content": "1 >= p",
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"author_name": "RacerVFX",
"timestamp": "08/09/2022 08:47:44",
"content": "how is 1 bigger?",
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"author_name": "RacerVFX",
"timestamp": "08/09/2022 08:47:47",
"content": "than p",
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"author_name": "EnzoL",
"timestamp": "08/09/2022 08:47:54",
"content": "3 - 2p >= p",
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"content": "3 >= 3p",
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"timestamp": "08/09/2022 08:48:14",
"content": "u said variable is bigger than constant",
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"content": "non",
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"timestamp": "08/09/2022 08:48:19",
"content": "it depends",
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"timestamp": "08/09/2022 08:48:22",
"content": "of the sign",
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"timestamp": "08/09/2022 08:48:27",
"content": "ohk",
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"author_name": "EnzoL",
"timestamp": "08/09/2022 08:48:37",
"content": "a > b means a is NOT EQUAL but GREATER than b",
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"timestamp": "08/09/2022 08:48:46",
"content": "ohk",
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"author_name": "EnzoL",
"timestamp": "08/09/2022 08:48:52",
"content": "a >= b means that a is greater or equal than b",
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"timestamp": "08/09/2022 08:49:22",
"content": "gotchu",
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"author_name": "EnzoL",
"timestamp": "08/09/2022 08:49:28",
"content": "3 - 2p >= p \n3 >= 3p\n1 >= p",
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"timestamp": "08/09/2022 08:49:40",
"content": "exactky",
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"timestamp": "08/09/2022 08:49:44",
"content": ":)",
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"timestamp": "08/09/2022 08:49:51",
"content": "so more than 1 or equal",
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"timestamp": "08/09/2022 08:49:55",
"content": "for number lline right?",
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"timestamp": "08/09/2022 08:50:19",
"content": "no",
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"timestamp": "08/09/2022 08:50:23",
"content": "1 >= p",
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"author_name": "RacerVFX",
"timestamp": "08/09/2022 08:50:33",
"content": "1 is bigger",
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"timestamp": "08/09/2022 08:50:37",
"content": "my bad equal",
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"author_name": "EnzoL",
"timestamp": "08/09/2022 08:50:39",
"content": "yea",
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"timestamp": "08/09/2022 08:50:44",
"content": "bigger or equal",
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"id": 1006545069458849800,
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"timestamp": "08/09/2022 08:50:45",
"content": "but it still is equal",
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"timestamp": "08/09/2022 08:50:45",
"content": "yeah",
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"content": "exactky",
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"timestamp": "08/09/2022 08:50:53",
"content": "thats what i said",
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"timestamp": "08/09/2022 08:50:55",
"content": "meant*",
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"timestamp": "08/09/2022 08:51:00",
"content": "okok",
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"timestamp": "08/09/2022 08:51:01",
"content": "so yeah",
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"author_name": "EnzoL",
"timestamp": "08/09/2022 08:51:04",
"content": "p can be",
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"timestamp": "08/09/2022 08:51:10",
"content": "every values",
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"author_name": "EnzoL",
"timestamp": "08/09/2022 08:51:14",
"content": "that are before 1",
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"author_name": "EnzoL",
"timestamp": "08/09/2022 08:51:22",
"content": "in the number line",
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"author_name": "EnzoL",
"timestamp": "08/09/2022 08:51:26",
"content": "and also can be 1 !",
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"timestamp": "08/09/2022 08:51:39",
"content": "ye",
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"timestamp": "08/09/2022 08:51:41",
"content": "done",
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"timestamp": "08/09/2022 08:54:09",
"content": "right?",
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"author_name": "RacerVFX",
"timestamp": "08/09/2022 08:54:11",
"content": "",
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"author_id": 805217272087838700,
"author_name": "Mathematics Bot",
"timestamp": "08/09/2022 09:09:11",
"content": "@RacerVFX Has your question been resolved?",
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"timestamp": "08/09/2022 09:13:31",
"content": "is this correct?",
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"author_name": "RacerVFX",
"timestamp": "08/09/2022 09:13:42",
"content": "i need to know that and then it will be over",
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"author_id": 695670158890500100,
"author_name": "Pinball Wizard",
"timestamp": "08/09/2022 09:19:07",
"content": "Which question",
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"author_name": "Pinball Wizard",
"timestamp": "08/09/2022 09:19:56",
"content": "This",
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"author_name": "Pinball Wizard",
"timestamp": "08/09/2022 09:21:03",
"content": "This will to -infinity if p โค 1",
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"author_name": "EnzoL",
"timestamp": "08/09/2022 09:21:35",
"content": "the solutions are EVERY negative number, and from 0 to 1",
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"timestamp": "08/09/2022 09:21:58",
"content": "you did the opposite",
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"author_name": "Pinball Wizard",
"timestamp": "08/09/2022 09:22:07",
"content": "Negative numbers from 0 to 1 ???",
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"timestamp": "08/09/2022 09:22:13",
"content": "nah",
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"timestamp": "08/09/2022 09:22:16",
"content": "every negative",
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"id": 1006553013416120400,
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"author_name": "EnzoL",
"timestamp": "08/09/2022 09:22:19",
"content": "+ from 0 to 1",
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"author_name": "Pinball Wizard",
"timestamp": "08/09/2022 09:22:26",
"content": "How 0",
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"timestamp": "08/09/2022 09:22:37",
"content": "And 0 to 1 is all positive",
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"author_name": "EnzoL",
"timestamp": "08/09/2022 09:22:40",
"content": "yeah",
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"author_name": "EnzoL",
"timestamp": "08/09/2022 09:22:46",
"content": "the solutions are",
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"content": "EVERY negative",
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"timestamp": "08/09/2022 09:22:50",
"content": "So pi",
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"author_name": "EnzoL",
"timestamp": "08/09/2022 09:22:56",
"content": "so -oo to 0",
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"author_name": "Pinball Wizard",
"timestamp": "08/09/2022 09:23:01",
"content": "Yesl",
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"timestamp": "08/09/2022 09:23:04",
"content": "and",
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"timestamp": "08/09/2022 09:23:04",
"content": "Yeah",
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"timestamp": "08/09/2022 09:23:06",
"content": "0 to 1",
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"author_name": "EnzoL",
"timestamp": "08/09/2022 09:23:12",
"content": "thats what i said",
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"timestamp": "08/09/2022 09:23:24",
"content": "]-oo, 1] if u prefer :)",
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"timestamp": "08/09/2022 09:23:36",
"content": "Hmm i don't know the question tho",
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"timestamp": "08/09/2022 09:23:41",
"content": "So no idea",
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"timestamp": "08/09/2022 09:23:42",
"content": "trust xd",
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"timestamp": "08/09/2022 09:23:47",
"content": "Lol",
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"timestamp": "08/09/2022 09:24:07",
"content": "(-oo, 1]",
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"timestamp": "08/09/2022 09:28:04",
"content": "???",
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"author_name": "EnzoL",
"timestamp": "08/09/2022 09:28:13",
"content": "what does ( means",
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"author_name": "EnzoL",
"timestamp": "08/09/2022 09:28:38",
"content": "if u mean that it is not in the set",
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"timestamp": "08/09/2022 09:28:49",
"content": "] means the same in my langage",
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"timestamp": "08/09/2022 09:43:42",
"content": "@RacerVFX Has your question been resolved?",
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"timestamp": "08/09/2022 10:13:42",
"content": "Channel closed",
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}
] |
help-9
|
89f7de54d1d34f3eafec047ae4e07069
|
197,715 |
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"id": 959663402303750100,
"author_id": 805217272087838700,
"author_name": "Mathematics Bot",
"timestamp": "04/01/2022 23:59:44",
"content": "Available help channel!",
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"reference": null
},
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"id": 959664693276991500,
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"timestamp": "04/02/2022 00:04:55",
"content": "may i ask how to do c",
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"author_id": 186287358285447170,
"author_name": "Ara",
"timestamp": "04/02/2022 00:10:33",
"content": "this is a graph of $\\sqrt{4-x^2}$ on $x \\in [-2,2]$",
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"timestamp": "04/02/2022 00:10:51",
"content": "**Ara**",
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"timestamp": "04/02/2022 00:12:42",
"content": "this is a graph of $|x|\\leq y\\leq \\sqrt{4-x^2}$",
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"timestamp": "04/02/2022 00:12:45",
"content": "**Ara**",
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"timestamp": "04/02/2022 00:13:04",
"content": "ohh",
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"timestamp": "04/02/2022 00:13:07",
"content": "so its a sector",
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"timestamp": "04/02/2022 00:13:14",
"content": "yeah",
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"author_name": "Umbraleviathan",
"timestamp": "04/02/2022 00:15:28",
"content": "I'm gonna let $a = \\sqrt2$\n\n$\\int_{-a}^{a}\\sqrt{4 - x^2}dx - (\\int_{-a}^{0} -x dx + \\int_{0}^{a} x dx)$",
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"content": "**Umbraleviathan**",
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"author_name": "Umbraleviathan",
"timestamp": "04/02/2022 00:16:13",
"content": "I split the integral up",
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"timestamp": "04/02/2022 00:16:18",
"content": "And then I split |x|",
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"author_name": "yk3",
"timestamp": "04/02/2022 00:17:08",
"content": "the sector is more straightforward tho",
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"author_name": "Umbraleviathan",
"timestamp": "04/02/2022 00:17:20",
"content": "Could you do sector area?",
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"author_id": 349354952961032200,
"author_name": "Umbraleviathan",
"timestamp": "04/02/2022 00:17:24",
"content": "Would that be valid",
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"id": 959667864426664000,
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"author_name": "yk3",
"timestamp": "04/02/2022 00:17:28",
"content": "yes",
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"timestamp": "04/02/2022 00:17:35",
"content": "results from geometry",
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"author_id": 349354952961032200,
"author_name": "Umbraleviathan",
"timestamp": "04/02/2022 00:17:44",
"content": "Oh",
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"author_name": "Umbraleviathan",
"timestamp": "04/02/2022 00:17:47",
"content": "I guess lol",
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"author_name": "yk3",
"timestamp": "04/02/2022 00:17:52",
"content": "lmao",
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"id": 959667987508494300,
"author_id": 349354952961032200,
"author_name": "Umbraleviathan",
"timestamp": "04/02/2022 00:17:57",
"content": "You know what",
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"author_id": 349354952961032200,
"author_name": "Umbraleviathan",
"timestamp": "04/02/2022 00:18:04",
"content": "Yes.",
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"id": 959668085487452200,
"author_id": 349354952961032200,
"author_name": "Umbraleviathan",
"timestamp": "04/02/2022 00:18:21",
"content": "Do a sector instead lol",
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"author_name": "yk3",
"timestamp": "04/02/2022 00:19:46",
"content": "lmao",
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"author_name": "yk3",
"timestamp": "04/02/2022 00:19:48",
"content": "how about d",
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},
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"author_name": "yk3",
"timestamp": "04/02/2022 00:19:51",
"content": "i cant sector it",
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"author_name": "yk3",
"timestamp": "04/02/2022 00:19:52",
"content": "lemme see",
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"author_name": "yk3",
"timestamp": "04/02/2022 00:20:57",
"content": "d is a mess",
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"timestamp": "04/02/2022 00:24:08",
"content": "do u have any ideas on d",
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"timestamp": "04/02/2022 00:26:18",
"content": "example of area for a=1",
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"timestamp": "04/02/2022 00:26:35",
"content": "hint",
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"content": "oh",
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"timestamp": "04/02/2022 00:29:38",
"content": "lemme try",
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"timestamp": "04/02/2022 00:35:30",
"content": "is it",
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"content": "yes",
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"content": "@yk3 Has your question been resolved?",
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] |
help-9
|
763c78eb54a741aa9f13416e079f209d
|
197,716 |
[
{
"id": 1006578228309262500,
"author_id": 805217272087838700,
"author_name": "Mathematics Bot",
"timestamp": "08/09/2022 11:02:30",
"content": "Available help channel!",
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},
{
"id": 1006578799888056300,
"author_id": 676937377738129400,
"author_name": "SmokeChef22",
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"content": "Pinned a message.",
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"author_id": 676937377738129400,
"author_name": "SmokeChef22",
"timestamp": "08/09/2022 11:04:58",
"content": "Anyone mind confirming my work?",
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},
{
"id": 1006580531875545100,
"author_id": 531535537362829300,
"author_name": "Eric Tao",
"timestamp": "08/09/2022 11:11:40",
"content": "what are you trying to prove",
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},
{
"id": 1006580541010755700,
"author_id": 531535537362829300,
"author_name": "Eric Tao",
"timestamp": "08/09/2022 11:11:42",
"content": "I'm confused",
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},
{
"id": 1006581040791425300,
"author_id": 676937377738129400,
"author_name": "SmokeChef22",
"timestamp": "08/09/2022 11:13:41",
"content": "if a,b,c are integers of the modulos in the question",
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},
{
"id": 1006581076908585000,
"author_id": 676937377738129400,
"author_name": "SmokeChef22",
"timestamp": "08/09/2022 11:13:50",
"content": "there must exits x,y that are also integer",
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},
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"id": 1006581198786662400,
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"author_name": "SmokeChef22",
"timestamp": "08/09/2022 11:14:19",
"content": "so b=0 mod 2, x,y,a,c = 1 mod 2",
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},
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"id": 1006581250091401300,
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"author_name": "Eric Tao",
"timestamp": "08/09/2022 11:14:31",
"content": "okay lemme look through your work",
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},
{
"id": 1006581262464602200,
"author_id": 676937377738129400,
"author_name": "SmokeChef22",
"timestamp": "08/09/2022 11:14:34",
"content": "ty",
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},
{
"id": 1006581317724540900,
"author_id": 676937377738129400,
"author_name": "SmokeChef22",
"timestamp": "08/09/2022 11:14:47",
"content": "i have another proof that extends from this one that im polishing down",
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},
{
"id": 1006581388893491200,
"author_id": 676937377738129400,
"author_name": "SmokeChef22",
"timestamp": "08/09/2022 11:15:04",
"content": "I dont really write things in the \"normal\" way. so any help on thats appreciated too",
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},
{
"id": 1006581465758314500,
"author_id": 676937377738129400,
"author_name": "SmokeChef22",
"timestamp": "08/09/2022 11:15:22",
"content": "in this case its an elementary proof, it should be just fine?",
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},
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"id": 1006581515196575900,
"author_id": 531535537362829300,
"author_name": "Eric Tao",
"timestamp": "08/09/2022 11:15:34",
"content": "yeah I noticed some things, lemme give you all the feedback after I finish reading it though",
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},
{
"id": 1006582697075953800,
"author_id": 531535537362829300,
"author_name": "Eric Tao",
"timestamp": "08/09/2022 11:20:16",
"content": "do you know bezout's lemma?",
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},
{
"id": 1006582796439011300,
"author_id": 531535537362829300,
"author_name": "Eric Tao",
"timestamp": "08/09/2022 11:20:40",
"content": "I can't really figure out your thought process here",
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},
{
"id": 1006583094918266900,
"author_id": 531535537362829300,
"author_name": "Eric Tao",
"timestamp": "08/09/2022 11:21:51",
"content": "I would solve this using bezout's lemma",
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},
{
"id": 1006583109296324700,
"author_id": 531535537362829300,
"author_name": "Eric Tao",
"timestamp": "08/09/2022 11:21:54",
"content": "there is a nice and elegant proof",
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},
{
"id": 1006583251554553900,
"author_id": 676937377738129400,
"author_name": "SmokeChef22",
"timestamp": "08/09/2022 11:22:28",
"content": "people mention it",
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},
{
"id": 1006583318353018900,
"author_id": 676937377738129400,
"author_name": "SmokeChef22",
"timestamp": "08/09/2022 11:22:44",
"content": "its similar, but bezouts lemma involves only 2 fixed variable for x,y",
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"timestamp": "08/09/2022 11:22:46",
"content": "this deals with 3",
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"content": "look at this",
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"content": "im constantly trying to make it easier to read, i dont think i can do anymore",
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"author_name": "Eric Tao",
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"content": "I don't understand that.. you define d in terms of x and then k in terms of d and then x in terms of k",
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"content": "start at the top and work down",
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"author_name": "Eric Tao",
"timestamp": "08/09/2022 11:23:48",
"content": "you at no point prove that x exists",
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"timestamp": "08/09/2022 11:23:52",
"content": "I did",
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"timestamp": "08/09/2022 11:23:55",
"content": "x is in terms of d",
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"timestamp": "08/09/2022 11:24:05",
"content": "line 4",
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"timestamp": "08/09/2022 11:24:08",
"content": "there are a couple numerical errors",
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"author_name": "Eric Tao",
"timestamp": "08/09/2022 11:24:23",
"content": "and also, you use the same name for multiple different variables which is confusing",
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"author_name": "Eric Tao",
"timestamp": "08/09/2022 11:24:30",
"content": "for example you substitute 2a - 1 for a",
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"author_name": "Eric Tao",
"timestamp": "08/09/2022 11:24:49",
"content": "and then here it should be x+1 instead of x-1",
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"timestamp": "08/09/2022 11:24:54",
"content": "thats because there are restrictions set on those numbers in the question",
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"timestamp": "08/09/2022 11:25:02",
"content": "so we use their modular form",
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"author_name": "Eric Tao",
"timestamp": "08/09/2022 11:25:05",
"content": "no, a โ 2a - 1",
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"timestamp": "08/09/2022 11:25:12",
"content": "its actualy + or minus 1",
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"author_name": "Eric Tao",
"timestamp": "08/09/2022 11:25:15",
"content": "a is equal to 2n-1 for some number n",
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"author_name": "Eric Tao",
"timestamp": "08/09/2022 11:25:30",
"content": "the only number where a = 2a-1 is a=1",
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"author_name": "SmokeChef22",
"timestamp": "08/09/2022 11:25:41",
"content": "all those shows is that x must be odd",
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"timestamp": "08/09/2022 11:25:52",
"content": "you already know that x is odd",
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"author_name": "Eric Tao",
"timestamp": "08/09/2022 11:25:57",
"content": "that doesn't help you prove the existence of x",
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"timestamp": "08/09/2022 11:26:16",
"content": "I would suggest manipulating the equation into a form that you can use bezout's lemma on",
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"timestamp": "08/09/2022 11:26:22",
"content": "and then the proof immediately follows",
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"timestamp": "08/09/2022 11:26:42",
"content": "(the tricky part is making sure that x and y are odd)",
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"timestamp": "08/09/2022 11:26:50",
"content": "(if you use bezout's lemma)",
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"timestamp": "08/09/2022 11:32:52",
"content": "i dont think bezouts will help here, bezouts only applies for 2 fixed integers a,b. this needs to deal with a,b,c",
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"timestamp": "08/09/2022 11:33:42",
"content": "bezout's definitely applies here, hint: try manipulating it into the form a times something + b times something = something times gcd(a,b)",
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"timestamp": "08/09/2022 11:34:19",
"content": "then, apply bezout's identity",
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"author_name": "SmokeChef22",
"timestamp": "08/09/2022 11:37:51",
"content": "i think you just dont understand my method, can i explain this more in private?",
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"author_name": "Eric Tao",
"timestamp": "08/09/2022 11:45:14",
"content": "what do you mean in private",
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"author_name": "Eric Tao",
"timestamp": "08/09/2022 11:45:51",
"content": "also yes I don't understand your method, but I've been looking at it and I don't think it is correct; you never prove that there must exist an x or y",
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"author_name": "Eric Tao",
"timestamp": "08/09/2022 11:46:06",
"content": "you assume the existence of x",
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"timestamp": "08/09/2022 11:47:03",
"content": "Y is assumed from that start",
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"timestamp": "08/09/2022 11:47:21",
"content": "then we find x = 4ak+-1",
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"timestamp": "08/09/2022 11:47:49",
"content": "and thats an integer",
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"author_name": "Eric Tao",
"timestamp": "08/09/2022 11:49:20",
"content": "no, we don't assume y exists, and also, you defined k in terms of x",
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"author_name": "Eric Tao",
"timestamp": "08/09/2022 11:49:24",
"content": "and then defined x in terms of k",
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"timestamp": "08/09/2022 11:49:36",
"content": "which is circular logic if you want to show that x exists",
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"timestamp": "08/09/2022 11:49:58",
"content": "this is unture",
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"author_name": "Eric Tao",
"timestamp": "08/09/2022 11:50:09",
"content": "how are you defining k then?",
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"timestamp": "08/09/2022 11:50:15",
"content": "k is defined by d, and d is defined by x",
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"timestamp": "08/09/2022 11:50:22",
"content": "exactly how its written",
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"timestamp": "08/09/2022 11:50:29",
"content": "yes",
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"timestamp": "08/09/2022 11:50:32",
"content": "so k is defined in terms of x",
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"author_name": "Eric Tao",
"timestamp": "08/09/2022 11:50:39",
"content": "but then you use k in the definition of x at the end",
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"timestamp": "08/09/2022 11:50:42",
"content": "do you see why this is circular",
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"timestamp": "08/09/2022 11:50:46",
"content": "nah",
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"timestamp": "08/09/2022 11:50:55",
"content": "x -->a",
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"author_name": "SmokeChef22",
"timestamp": "08/09/2022 11:51:47",
"content": "eureka, i see what you are missing ๐",
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"author_name": "SmokeChef22",
"timestamp": "08/09/2022 11:51:56",
"content": "its my fault for missing it ๐",
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"author_name": "SmokeChef22",
"timestamp": "08/09/2022 11:53:30",
"content": "ahhh",
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"author_name": "Eric Tao",
"timestamp": "08/09/2022 11:53:33",
"content": "I recommend using bezout's identity though, you can make like a 4-line proof of this using it",
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"timestamp": "08/09/2022 11:53:43",
"content": "you also are missing the part about k being an arbritary number",
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"timestamp": "08/09/2022 11:53:51",
"content": "for all k",
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"timestamp": "08/09/2022 11:54:32",
"content": "x=2d+-1; d=2ak x is defined in terms of a and k",
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"timestamp": "08/09/2022 11:54:48",
"content": "therefore we can substitute for x",
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"timestamp": "08/09/2022 11:55:08",
"content": "since a is known to also be an integer",
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"timestamp": "08/09/2022 11:55:25",
"content": "you understand it?",
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"author_name": "Toby",
"timestamp": "08/09/2022 11:55:38",
"content": "Easy way to test if your proof works. If we give you a=3, b=8, c=5 (for example). Will you be able to find x and y with your proof?",
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"timestamp": "08/09/2022 11:56:59",
"content": "yes easily",
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"author_name": "Eric Tao",
"timestamp": "08/09/2022 11:57:01",
"content": "a is not determined by x, a is given..",
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"author_name": "Eric Tao",
"timestamp": "08/09/2022 11:57:16",
"content": "what are x and y?",
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"timestamp": "08/09/2022 11:57:21",
"content": "yes we start with a , b ,c and y is an integer",
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"timestamp": "08/09/2022 11:57:30",
"content": "then find X that is an integer",
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"timestamp": "08/09/2022 11:57:49",
"content": "so we know theres x,y",
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"timestamp": "08/09/2022 11:58:33",
"content": "gimme a few i seen something i can add",
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"timestamp": "08/09/2022 11:59:48",
"content": "theres infinitely many actually",
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"timestamp": "08/09/2022 12:00:03",
"content": "okay can you find one such pair x,y that works though",
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"timestamp": "08/09/2022 12:00:15",
"content": "no infinitely many",
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"timestamp": "08/09/2022 12:00:23",
"content": "yes, but can you give one example",
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"timestamp": "08/09/2022 12:00:25",
"content": "yeah , but lets start small and find one pair",
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"timestamp": "08/09/2022 12:00:32",
"content": "for your one above?",
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"timestamp": "08/09/2022 12:00:47",
"content": "funny thing is i have other methods of doing this ๐",
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"author_name": "SmokeChef22",
"timestamp": "08/09/2022 12:00:55",
"content": "but tis way much easier",
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"timestamp": "08/09/2022 12:02:23",
"content": "sure, but if your proof is valid (though it doesn't make much sense to me), you should be able to generate an x and y such that what you want holds",
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"author_name": "Toby",
"timestamp": "08/09/2022 12:03:53",
"content": "like, you said x=2d-1, where d=2a'k. But what is k concretely?",
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"author_name": "Toby",
"timestamp": "08/09/2022 12:04:29",
"content": "surely not every k works",
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"author_name": "Toby",
"timestamp": "08/09/2022 12:06:26",
"content": "I think you have to use bezout's (or at least some sort of division algorithm) to prove the statement",
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"author_name": "SmokeChef22",
"timestamp": "08/09/2022 12:10:34",
"content": "im almost done just making sure i write things in correct",
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"author_name": "Eric Tao",
"timestamp": "08/09/2022 12:11:38",
"content": "if you decide to use bezout's lemma, here is a hint: ||observe that you can manipulate the equation into the form (-x)a + yb = c gcd(a,b)||",
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"timestamp": "08/09/2022 12:15:54",
"content": "",
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"timestamp": "08/09/2022 12:15:56",
"content": "here ya go",
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"author_id": 531535537362829300,
"author_name": "Eric Tao",
"timestamp": "08/09/2022 12:16:31",
"content": "what are values for k and n?",
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"author_name": "Eric Tao",
"timestamp": "08/09/2022 12:16:32",
"content": "as numbers",
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"author_name": "SmokeChef22",
"timestamp": "08/09/2022 12:16:58",
"content": "ax give x",
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"author_name": "Eric Tao",
"timestamp": "08/09/2022 12:17:28",
"content": "can you like",
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"author_name": "Eric Tao",
"timestamp": "08/09/2022 12:17:30",
"content": "give explicitly",
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"author_name": "Eric Tao",
"timestamp": "08/09/2022 12:17:33",
"content": "k = this number, and n = this number",
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"author_name": "SmokeChef22",
"timestamp": "08/09/2022 12:17:39",
"content": "every single K gives an integer solution",
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"timestamp": "08/09/2022 12:17:48",
"content": "okay",
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"author_name": "Eric Tao",
"timestamp": "08/09/2022 12:17:51",
"content": "but",
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"author_name": "Eric Tao",
"timestamp": "08/09/2022 12:17:55",
"content": "k=1 doesn't",
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"author_name": "Eric Tao",
"timestamp": "08/09/2022 12:18:03",
"content": "because then y is not an integer",
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"timestamp": "08/09/2022 12:18:12",
"content": "if k =1 its not even",
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"author_name": "SmokeChef22",
"timestamp": "08/09/2022 12:18:20",
"content": "and it says K is even",
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"timestamp": "08/09/2022 12:18:28",
"content": "k=2n",
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"author_name": "Eric Tao",
"timestamp": "08/09/2022 12:18:28",
"content": "okay",
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"author_name": "Eric Tao",
"timestamp": "08/09/2022 12:19:10",
"content": "is x = 4ak + 1 or 4ak-1",
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"author_name": "Eric Tao",
"timestamp": "08/09/2022 12:19:19",
"content": "it can't be both simultaneously",
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"author_name": "SmokeChef22",
"timestamp": "08/09/2022 12:19:36",
"content": "+1",
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"author_name": "Eric Tao",
"timestamp": "08/09/2022 12:19:39",
"content": "okay",
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"author_name": "Toby",
"timestamp": "08/09/2022 12:19:54",
"content": ",calc (3*(4*3*2-1)+5)/8",
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"author_name": "TeXit",
"timestamp": "08/09/2022 12:20:53",
"content": "Result:\n```\n9.25\n```",
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"author_name": "Eric Tao",
"timestamp": "08/09/2022 12:20:54",
"content": "x = 4ak+1\ny = 9/4 k + 1/2\nlet k=2, then\nx = 8a+1 = 25\ny = 9/4 2 + 1/2 = 5\nbut\nax/b + c/b = 3*25/8 + 5/8 = 10 โ 5\nso the choice of x and y does not work",
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"timestamp": "08/09/2022 12:21:05",
"content": "unless I miscalculated somewhere",
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"timestamp": "08/09/2022 12:21:48",
"content": "x=8a+2",
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"author_name": "Eric Tao",
"timestamp": "08/09/2022 12:22:06",
"content": "but then x is even",
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"timestamp": "08/09/2022 12:24:08",
"content": "your mistake is, you assume K must be even for all a,b,c",
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"author_name": "SmokeChef22",
"timestamp": "08/09/2022 12:24:21",
"content": "for your example of a,b,c it happend that K is even",
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"author_name": "Eric Tao",
"timestamp": "08/09/2022 12:24:22",
"content": ":| you just said it works for any even k",
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"author_name": "SmokeChef22",
"timestamp": "08/09/2022 12:24:37",
"content": "yes but you need a,b,c to determine x,y,k",
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"timestamp": "08/09/2022 12:24:42",
"content": "yes",
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"author_name": "Eric Tao",
"timestamp": "08/09/2022 12:24:47",
"content": "I let a=3, b=8, c=5",
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"author_name": "SmokeChef22",
"timestamp": "08/09/2022 12:24:50",
"content": "so you cant say K is this",
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"author_name": "Eric Tao",
"timestamp": "08/09/2022 12:24:55",
"content": "then what is k",
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"timestamp": "08/09/2022 12:24:58",
"content": "K decides what it is based on a b c",
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"timestamp": "08/09/2022 12:24:58",
"content": "if a=3, b=8, c=5",
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"author_name": "SmokeChef22",
"timestamp": "08/09/2022 12:26:50",
"content": "in your example, k=2n for all n",
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"author_name": "Toby",
"timestamp": "08/09/2022 12:27:46",
"content": "ok, tell us what n is then",
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"timestamp": "08/09/2022 12:27:56",
"content": "18n+2=4 y",
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"timestamp": "08/09/2022 12:28:19",
"content": "as a number please, you can choose any that work",
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"author_name": "Toby",
"timestamp": "08/09/2022 12:28:29",
"content": "we are defining y based off n, not the other way round, right?",
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"timestamp": "08/09/2022 12:29:01",
"content": "abc defines n. n defines y",
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"timestamp": "08/09/2022 12:29:12",
"content": "same deal for x",
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"author_name": "SmokeChef22",
"timestamp": "08/09/2022 12:29:22",
"content": "except is k for x",
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"author_name": "Eric Tao",
"timestamp": "08/09/2022 12:29:48",
"content": "okay what is n then",
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"author_name": "Eric Tao",
"timestamp": "08/09/2022 12:29:50",
"content": "as a number",
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"timestamp": "08/09/2022 12:29:59",
"content": "if a=3, b=8, c=5",
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"author_name": "SmokeChef22",
"timestamp": "08/09/2022 12:30:30",
"content": "in your example y=5",
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"id": 1006600395105251300,
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"author_name": "SmokeChef22",
"timestamp": "08/09/2022 12:30:35",
"content": "then theres infinitely many more",
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"id": 1006600484901105800,
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"author_name": "Eric Tao",
"timestamp": "08/09/2022 12:30:57",
"content": "but what is n",
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"id": 1006600502898872400,
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"author_name": "SmokeChef22",
"timestamp": "08/09/2022 12:31:01",
"content": "2",
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"author_name": "Toby",
"timestamp": "08/09/2022 12:31:34",
"content": "but 10โ 5 ^",
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"timestamp": "08/09/2022 12:31:41",
"content": "n = 2,4,6,8,10,12,14, etc....",
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"id": 1006600734470582500,
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"author_name": "Eric Tao",
"timestamp": "08/09/2022 12:31:56",
"content": "if n = 2 then y is not even an integer...",
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"author_name": "SmokeChef22",
"timestamp": "08/09/2022 12:32:21",
"content": "18n+2=4 yif n=2 how is this not an integer?",
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"author_name": "Eric Tao",
"timestamp": "08/09/2022 12:32:35",
"content": "if you keep insisting that you're right against the evidence then we can't really help you :/",
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"timestamp": "08/09/2022 12:32:37",
"content": "it equals 20, and 20/4 = 5",
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"timestamp": "08/09/2022 12:32:49",
"content": "18*2 + 2 is 38",
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"timestamp": "08/09/2022 12:32:52",
"content": "not 20",
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"timestamp": "08/09/2022 12:33:13",
"content": "my bad n=1",
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"timestamp": "08/09/2022 12:33:18",
"content": "okay",
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"timestamp": "08/09/2022 12:33:26",
"content": "but if n=1 then the equation doesn't hold",
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"timestamp": "08/09/2022 12:33:42",
"content": "because you get x = 25 and y = 5",
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"timestamp": "08/09/2022 12:33:51",
"content": "18n+2=4 y",
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"author_name": "SmokeChef22",
"timestamp": "08/09/2022 12:34:00",
"content": "where u get 25?",
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"author_name": "Eric Tao",
"timestamp": "08/09/2022 12:34:21",
"content": "because k = 2 and x = 4ak+1 from what you said",
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"timestamp": "08/09/2022 12:34:23",
"content": "i told you, you applied k wrong for x",
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"timestamp": "08/09/2022 12:34:29",
"content": ":/",
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"timestamp": "08/09/2022 12:34:36",
"content": "you said k = 2n though",
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"timestamp": "08/09/2022 12:34:51",
"content": "and n = 1",
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"timestamp": "08/09/2022 12:34:56",
"content": "so k = 2",
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"content": "ahhhh ok",
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"content": "so heres the confusion",
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"content": "@Eric Tao",
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"content": "i make a mistake, heres your solution",
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"timestamp": "08/09/2022 12:49:56",
"content": "right, so can you say a specific y and x that works?",
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"timestamp": "08/09/2022 12:50:11",
"content": "we would just have to substitue",
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"timestamp": "08/09/2022 12:50:13",
"content": "because f=1 gives y=10, x=193. Which doesn't work",
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"timestamp": "08/09/2022 12:50:21",
"content": "we know f=1-> infinity",
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"timestamp": "08/09/2022 12:50:39",
"content": "f=1 should give 10 x=5",
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"timestamp": "08/09/2022 12:50:46",
"content": "additionally y is not odd",
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"timestamp": "08/09/2022 12:51:05",
"content": "y doesnt have to be odd",
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"timestamp": "08/09/2022 12:51:10",
"content": "yes it does",
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"timestamp": "08/09/2022 12:51:16",
"content": "nope",
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"timestamp": "08/09/2022 12:51:17",
"content": "you said it had to be",
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"timestamp": "08/09/2022 12:51:23",
"content": "-_-",
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"timestamp": "08/09/2022 12:51:31",
"content": "on that picture it assuredly does not",
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"timestamp": "08/09/2022 12:51:50",
"content": "*which picture*",
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"timestamp": "08/09/2022 12:52:08",
"content": "I'm gonna stop commenting on this question since you don't seem to want to listen to our suggestions, but the hints I gave involving bezout's identity are sufficient to prove the statement in your original picture",
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"timestamp": "08/09/2022 12:52:24",
"content": "that was an error",
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"timestamp": "08/09/2022 12:52:29",
"content": "y was supposed to ne x",
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"author_name": "Eric Tao",
"timestamp": "08/09/2022 12:52:33",
"content": "if you need any clarification on anything I said then let me know",
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"timestamp": "08/09/2022 12:52:43",
"content": "dont worry about that, you asked for solutions to a special case",
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"timestamp": "08/09/2022 12:53:07",
"content": "i fixed that already, im working on this one now for your example case",
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"timestamp": "08/09/2022 12:53:26",
"content": "above picture is correct",
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"timestamp": "08/09/2022 12:54:01",
"content": "substitute for X when you know y and youll get 3=x for y=10",
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"timestamp": "08/09/2022 12:55:49",
"content": "need me to give you the new expression for x?",
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"timestamp": "08/09/2022 12:55:54",
"content": "x for f",
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"timestamp": "08/09/2022 12:58:50",
"content": "for the sake of our sanity, I'm going to sketch out how to get an actual solution for a=3, b=8, c=5. \n\nWe wish to find x,y odd such that -ax+by=c.\n\nWe have that gcd(a,b)=1. So by the euclidean algorithm we have 3a-b=1. Now, we multiply this by c to get 15a-5b=c. Since -15 and -5 are both odd, these are our x and y respectively.\n\nIn the case that y is even (note that x is automatically odd), we can add an appropriate amount of 1s to y",
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"timestamp": "08/09/2022 12:59:02",
"content": "feel free to take it or leave it",
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"timestamp": "08/09/2022 12:59:18",
"content": "thats exactly what the above says pretty much",
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"timestamp": "08/09/2022 12:59:37",
"content": "damn, quick reading skills!",
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"timestamp": "08/09/2022 12:59:38",
"content": "theres just one extra variable in the above",
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"timestamp": "08/09/2022 13:00:06",
"content": "like i said, this situation is for ANY 3 fixed variables",
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"timestamp": "08/09/2022 13:00:18",
"content": "yours deals with 2 fixed 3 varaible",
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"timestamp": "08/09/2022 13:00:25",
"content": "your algorithm did not manage to generate any numbers for x and y that work ยฏ\\_(ใ)_/ยฏ",
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"timestamp": "08/09/2022 13:00:32",
"content": "x=3 y=10",
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"timestamp": "08/09/2022 13:01:07",
"content": "but not for 4ak-1",
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"timestamp": "08/09/2022 13:01:10",
"content": "x changed",
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"timestamp": "08/09/2022 13:01:21",
"content": "thats why i asked if you needed me to show you the new X there",
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"timestamp": "08/09/2022 13:02:05",
"content": "I dont see how x=3 and y=10 gives the desired solution, but ok",
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"timestamp": "08/09/2022 13:02:56",
"content": "Yeah I think we should just drop this, this is getting nowhere",
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"timestamp": "08/09/2022 13:03:20",
"content": "hm",
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"author_name": "Eric Tao",
"timestamp": "08/09/2022 13:03:35",
"content": "You asked us to verify if your solution was correct; we told you it was wrong; you continue to insist it's right; what was the point of asking in the first place?",
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"timestamp": "08/09/2022 13:03:36",
"content": "we tried ยฏ\\_(ใ)_/ยฏ",
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"timestamp": "08/09/2022 13:09:25",
"content": "i know i appreciate it,",
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"timestamp": "08/09/2022 13:10:02",
"content": "its not that im saying im right, i know for a fact just via numerical analysis this sitation is right, im just trying to translate languages",
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"timestamp": "08/09/2022 13:10:11",
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"timestamp": "08/09/2022 13:10:26",
"content": "this?",
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"timestamp": "08/09/2022 13:10:52",
"content": "thats your a,b,c",
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"author_name": "Eric Tao",
"timestamp": "08/09/2022 13:13:25",
"content": "I'm confused now.. if there was a typo in your original question, what question are you trying to solve now",
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"timestamp": "08/09/2022 13:13:53",
"content": "thats stuffs all correct except for that one issue with x not being set odd",
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"timestamp": "08/09/2022 13:14:23",
"content": "set x=odd y=integer, everythings ok",
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"timestamp": "08/09/2022 13:15:35",
"content": "okay so given a (odd), b (even), c (odd), you want to find x (odd) and y (integer) such that ax/b + c/b = y where a and b are coprime?",
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"timestamp": "08/09/2022 13:15:57",
"content": "I think thats how i should have stated things, yes",
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"timestamp": "08/09/2022 13:16:37",
"content": "and right now your formula is that x = 4ak + 1, y = 9n/4 + 1 where k = 4n and n can be what?",
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"timestamp": "08/09/2022 13:17:48",
"content": "no, that was an incorrect solution to you example",
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"timestamp": "08/09/2022 13:17:59",
"content": "ive corrected it, last picture",
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"timestamp": "08/09/2022 13:18:39",
"content": "but that applies for your a,b,c",
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"timestamp": "08/09/2022 13:18:51",
"content": "should it be k = 16f",
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"timestamp": "08/09/2022 13:18:56",
"content": "if k=4n and n = 4f",
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"timestamp": "08/09/2022 13:19:16",
"content": "now that i see it",
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"timestamp": "08/09/2022 13:19:18",
"content": "absolutely!",
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"timestamp": "08/09/2022 13:19:32",
"content": "makes it neater",
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"timestamp": "08/09/2022 13:19:44",
"content": "okay so you're saying that x = 32af + 1, and y = 9f + 1",
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"timestamp": "08/09/2022 13:19:49",
"content": "where f is any integer?",
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"timestamp": "08/09/2022 13:20:03",
"content": "precisely",
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"timestamp": "08/09/2022 13:20:15",
"content": "okay",
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"timestamp": "08/09/2022 13:20:18",
"content": "let me check if it works",
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"content": "wait",
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"content": "31anf",
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"timestamp": "08/09/2022 13:20:43",
"content": "32*",
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"timestamp": "08/09/2022 13:20:51",
"content": "is x = 4ak + 1?",
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"timestamp": "08/09/2022 13:21:02",
"content": "if so then it should be x = 64af + 1",
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"timestamp": "08/09/2022 13:21:11",
"content": "thats still a number thats 1 mod 4",
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"timestamp": "08/09/2022 13:21:15",
"content": "^^",
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"timestamp": "08/09/2022 13:22:11",
"content": "i think for this one n can be anything also tbh",
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"timestamp": "08/09/2022 13:22:16",
"content": "but i dunno",
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"timestamp": "08/09/2022 13:23:29",
"content": "okay wait what is your solution in general then",
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"timestamp": "08/09/2022 13:23:32",
"content": "for any a,b,c",
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"timestamp": "08/09/2022 13:23:54",
"content": "that, save your self right now",
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"timestamp": "08/09/2022 13:24:02",
"content": "ill use what we are doing now to make it better ๐",
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"timestamp": "08/09/2022 13:24:12",
"content": "lets just make sure the individual example is understood",
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"timestamp": "08/09/2022 13:24:17",
"content": "by us all ๐",
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"timestamp": "08/09/2022 13:26:10",
"content": "okay so since a = 3, your solution is x = 12k + 1 and y = 9f + 1 where f is any integer and k = 16f?",
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"timestamp": "08/09/2022 13:26:27",
"content": "for a=3, b=8, c=5",
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"timestamp": "08/09/2022 13:27:29",
"content": "for all f",
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"timestamp": "08/09/2022 13:27:45",
"content": "๐",
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"timestamp": "08/09/2022 13:28:05",
"content": "General solution isnt that difficult",
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"timestamp": "08/09/2022 13:28:18",
"content": "i just need to find my mistakes and reflect the numbers",
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"timestamp": "08/09/2022 13:29:55",
"content": "I still don't think this satisfies the equation, for example if you let f = 1",
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"timestamp": "08/09/2022 13:29:58",
"content": "let me put a=3",
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"timestamp": "08/09/2022 13:32:46",
"content": "those should be your values of x",
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"timestamp": "08/09/2022 13:32:49",
"content": "for all f",
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"timestamp": "08/09/2022 13:33:17",
"content": "unfortunately if you calculate it out for any fโ 0, you'll see that ax/b + c/b โ y",
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"timestamp": "08/09/2022 13:33:21",
"content": "for the values of x and y that you gave",
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"timestamp": "08/09/2022 13:33:41",
"content": "for example if f=1, then y = 10 but ax/b + c/b = 37",
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"timestamp": "08/09/2022 13:33:51",
"content": "i made an error",
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"timestamp": "08/09/2022 13:37:10",
"content": "@Eric Tao i appreciate this, one moment i think i got it better now",
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"timestamp": "08/09/2022 13:38:26",
"content": "Okay!",
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"timestamp": "08/09/2022 13:40:49",
"content": "like your question, your are a top level guy certainly",
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"timestamp": "08/09/2022 13:41:03",
"content": "because i see exactly how far down the rabbit hole i gotta go with this one",
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"timestamp": "08/09/2022 13:43:31",
"content": "lets see if this is far enough, let me know",
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"timestamp": "08/09/2022 13:44:25",
"content": "this one i think f is now dependent on x,y again correct?",
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"timestamp": "08/09/2022 13:44:33",
"content": "or it always was anyways, i know thats the case",
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"timestamp": "08/09/2022 13:44:40",
"content": "are you saying it works for any f?",
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"timestamp": "08/09/2022 13:45:12",
"content": "im not sure",
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"timestamp": "08/09/2022 13:45:22",
"content": "i think f is dependent on x and y now",
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"timestamp": "08/09/2022 13:45:40",
"content": "like for these systems, i know with numbers thats the case",
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"timestamp": "08/09/2022 13:45:44",
"content": "well x and y are what we are trying to find",
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"timestamp": "08/09/2022 13:45:45",
"content": "but thats not enough",
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"timestamp": "08/09/2022 13:46:00",
"content": "so if f is dependent on them, then we can't figure out what x and y are! we want some way to figure out what x and y are",
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"timestamp": "08/09/2022 13:46:30",
"content": "yup, i already seen that, been working on it before you mentioned it ๐",
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"timestamp": "08/09/2022 13:46:35",
"content": "i think im on track now",
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"timestamp": "08/09/2022 13:48:18",
"content": "if i think back really hard, i think i actually learned this step in high school algrebra a long time ago ^^",
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"timestamp": "08/09/2022 13:48:30",
"content": "just gotta give em factors",
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"timestamp": "08/09/2022 13:49:19",
"content": "if this line of reasoning doesn't work, we can use the bezout's identity approach I outlined earlier",
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"timestamp": "08/09/2022 13:49:26",
"content": "which is far simpler (only takes maybe like 4-5 lines of proof)",
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"timestamp": "08/09/2022 13:51:11",
"content": "i wanna prove this ๐",
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"timestamp": "08/09/2022 13:51:19",
"content": "then you show me the short way? deal?",
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"timestamp": "08/09/2022 13:51:45",
"content": "i need to do it this way, because this has very important implications ๐",
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"timestamp": "08/09/2022 13:52:07",
"content": "okay",
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"timestamp": "08/09/2022 13:57:44",
"content": "im here",
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"content": "i think this is they way to go",
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"timestamp": "08/09/2022 13:58:57",
"content": "x and y arent equal btw thats an error",
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"timestamp": "08/09/2022 13:59:21",
"content": "so is f still any integer?",
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"timestamp": "08/09/2022 14:00:26",
"content": "no f is 24q",
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"timestamp": "08/09/2022 14:01:06",
"content": "should be solutions here for all q",
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"timestamp": "08/09/2022 14:01:19",
"content": "okay",
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"timestamp": "08/09/2022 14:01:24",
"content": "since we kind of ended up where we started here",
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"timestamp": "08/09/2022 14:01:28",
"content": "so for example f = 24 would be a solution?",
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"timestamp": "08/09/2022 14:01:29",
"content": "just f changed to q",
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"timestamp": "08/09/2022 14:01:42",
"content": "possible thats there is a > <",
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"timestamp": "08/09/2022 14:02:23",
"content": "i just know x doesnt equal y if x>1",
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"timestamp": "08/09/2022 14:03:25",
"content": "test for Q, since q defines f",
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"timestamp": "08/09/2022 14:03:45",
"content": "okay I think this solution works for all integers f",
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"timestamp": "08/09/2022 14:03:47",
"content": "number computer says we have hit a loop",
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"timestamp": "08/09/2022 14:03:57",
"content": "can i dm you?",
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"content": "assuming a=3, b=8, c=5",
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"content": "it should ๐",
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"content": "let's just talk about it in this channel",
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"content": "well",
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"content": "do you know where this situation pertains to?",
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"timestamp": "08/09/2022 14:04:33",
"content": "and what we have done?",
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"content": "what do you mean where this situation pertains to",
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"content": "what have we done lol",
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"timestamp": "08/09/2022 14:05:39",
"content": "ok let me add this method to something a bit deeper",
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"content": "oh wait i know what to do",
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"content": "i can show you, gimme a bit",
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"timestamp": "08/09/2022 14:07:05",
"content": "@Eric Tao safe to assume the method is correct, and we can extend it to any a,b,c in the given parameters?",
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"timestamp": "08/09/2022 14:08:06",
"content": "the 8 and 3 are derivatives of a,b,c",
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"timestamp": "08/09/2022 14:08:19",
"content": "so generalizing is easy",
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"timestamp": "08/09/2022 14:08:30",
"content": "i have to do that now ๐",
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"timestamp": "08/09/2022 14:09:58",
"content": "well I'm not sure about your method so I'm honestly not sure how you got the correct answer ๐
like for example I'm not sure how you got the last line here",
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"content": "i got lucky and chose 4 xD",
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"timestamp": "08/09/2022 14:11:41",
"content": "LOL",
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"timestamp": "08/09/2022 14:11:47",
"content": "yeah I'm not sure how generalizable this method is",
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"timestamp": "08/09/2022 14:11:47",
"content": "any 2^even",
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"timestamp": "08/09/2022 14:11:52",
"content": "it seems to involve some guess and check",
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"timestamp": "08/09/2022 14:12:04",
"content": "for this one yeah",
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"timestamp": "08/09/2022 14:12:13",
"content": "this is the lazy way for a particiular example",
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"timestamp": "08/09/2022 14:12:23",
"content": "lemme do for q= a,b,c ^^",
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"timestamp": "08/09/2022 14:14:48",
"content": "im just writing things wrong is all",
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"timestamp": "08/09/2022 14:25:27",
"content": "ok i found integer k",
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"timestamp": "08/09/2022 14:38:25",
"content": "@Eric Tao are you stil lurking around?",
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"timestamp": "08/09/2022 14:38:33",
"content": "yeah",
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"timestamp": "08/09/2022 14:39:44",
"content": "you ready? start to finsih then tell me ๐",
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"timestamp": "08/09/2022 14:40:14",
"content": "i think thats where we needed to go",
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"timestamp": "08/09/2022 14:40:49",
"content": "wait so what is your formula for y",
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"timestamp": "08/09/2022 14:41:00",
"content": "we set y = integer",
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"timestamp": "08/09/2022 14:41:09",
"content": "so it's any integer?",
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"timestamp": "08/09/2022 14:41:15",
"content": "a,b,c = integers of their modular forms",
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"timestamp": "08/09/2022 14:41:17",
"content": "y is any",
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"timestamp": "08/09/2022 14:41:31",
"content": "okay",
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"timestamp": "08/09/2022 14:41:46",
"content": "i have 37 other lines, i can now delete xD",
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"timestamp": "08/09/2022 14:41:47",
"content": "wait but if y is any integer then x is not necessarily an integer",
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"timestamp": "08/09/2022 14:41:53",
"content": "not nessecarilly",
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"timestamp": "08/09/2022 14:41:58",
"content": "so y can't be any integer",
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"timestamp": "08/09/2022 14:42:02",
"content": "but it will for some y",
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"timestamp": "08/09/2022 14:42:06",
"content": "we showed that part already",
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"timestamp": "08/09/2022 14:42:33",
"content": "d=2ak sets x for a,y",
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"timestamp": "08/09/2022 14:43:28",
"content": "okay wait so what is an example of a y where it works",
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"timestamp": "08/09/2022 14:43:38",
"content": "we end up at the second line before we apply the modular forms",
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"timestamp": "08/09/2022 14:44:42",
"content": "i think solutions are found for x= a mod y for the integers",
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"timestamp": "08/09/2022 14:45:27",
"content": "hmm were you telling me to delete x without telling me?",
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"timestamp": "08/09/2022 14:45:42",
"content": "no I'm just asking",
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"timestamp": "08/09/2022 14:46:02",
"content": "given a,b,c how would you calculate a y",
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"timestamp": "08/09/2022 14:56:31",
"content": "almost there ๐",
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"timestamp": "08/09/2022 15:11:31",
"content": "@SmokeChef22 Has your question been resolved?",
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"timestamp": "08/09/2022 15:17:47",
"content": "@Eric Tao y= something pretty cool",
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"timestamp": "08/09/2022 15:20:58",
"content": "wait",
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"timestamp": "08/09/2022 15:21:02",
"content": "there is a y in your expression for what y is",
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"timestamp": "08/09/2022 15:21:03",
"content": "๐ญ",
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"author_id": 676937377738129400,
"author_name": "SmokeChef22",
"timestamp": "08/09/2022 15:22:17",
"content": "y is the same y",
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"timestamp": "08/09/2022 15:22:19",
"content": "some integer",
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"timestamp": "08/09/2022 15:22:41",
"content": "this is y for a,b,c",
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"timestamp": "08/09/2022 15:22:48",
"content": "im doing the expansions now",
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"timestamp": "08/09/2022 15:38:14",
"content": "@Eric Tao we can resolve for b->a,c",
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"timestamp": "08/09/2022 15:45:31",
"content": "ive got maybe 12 lines left",
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"content": "almost there",
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] |
help-9
|
0b1d38b27a8d424d862b6e8a6db5946d
|
197,717 |
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"timestamp": "08/09/2022 16:16:50",
"content": "Available help channel!",
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"author_name": "placement",
"timestamp": "08/09/2022 16:19:08",
"content": "I've done the first part, but I am stuck on where to start with proving h is onto",
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"timestamp": "08/09/2022 16:19:44",
"content": "If we were given that f o h is onto, I think I would have a way to start the proof, but because that information isn't given, i don't really know where to start",
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"author_id": 1001814625781817300,
"author_name": "Katieee",
"timestamp": "08/09/2022 16:20:01",
"content": "Hello",
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"author_id": 1001814625781817300,
"author_name": "Katieee",
"timestamp": "08/09/2022 16:20:37",
"content": "Do you know linear algebra?",
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"id": 1006658356653600900,
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"timestamp": "08/09/2022 16:20:55",
"content": "yea a bit",
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"author_id": 1001814625781817300,
"author_name": "Katieee",
"timestamp": "08/09/2022 16:20:58",
"content": "Use it",
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"author_name": "themateo713",
"timestamp": "08/09/2022 16:21:20",
"content": "What",
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"author_id": 182179228840755200,
"author_name": "iCaird",
"timestamp": "08/09/2022 16:21:22",
"content": "Linear algebra won't be much help here, these are set functions",
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"timestamp": "08/09/2022 16:21:25",
"content": "lol",
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"author_name": "themateo713",
"timestamp": "08/09/2022 16:21:38",
"content": "This is best proved in elementary terms",
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"author_name": "SmokeChef22",
"timestamp": "08/09/2022 16:22:10",
"content": "@Eric Tao u here",
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"author_id": 697730177962344400,
"author_name": "Tarek Ahmed",
"timestamp": "08/09/2022 16:22:15",
"content": "Is onto surjective",
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"author_name": "SmokeChef22",
"timestamp": "08/09/2022 16:22:17",
"content": "i think i got the endpoint",
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"timestamp": "08/09/2022 16:22:18",
"content": "yea",
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"author_name": "Eric Tao",
"timestamp": "08/09/2022 16:22:26",
"content": "@SmokeChef22 this is someone else's channel",
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"author_name": "Eric Tao",
"timestamp": "08/09/2022 16:22:37",
"content": "open another one if you wanna talk",
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"author_name": "SmokeChef22",
"timestamp": "08/09/2022 16:22:49",
"content": "ok",
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"author_name": "Fractal",
"timestamp": "08/09/2022 16:22:59",
"content": "the idea here is to prove h is \"right cancelling\"\nyou can cancel it from the right and make any two functions equal in that sense\nthink of what would happen if h *was not* onto",
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"author_name": "SmokeChef22",
"timestamp": "08/09/2022 16:23:02",
"content": "ill open it with a pdf, sorry to interrupt",
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"timestamp": "08/09/2022 16:27:14",
"content": "if it wasn't onto, then there would exist some x s.t h(x) does not map to an element in the codomain, right?",
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"author_name": "Fractal",
"timestamp": "08/09/2022 16:27:23",
"content": "an awfully suggestive drawing",
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"timestamp": "08/09/2022 16:27:58",
"content": "no",
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"author_name": "Fractal",
"timestamp": "08/09/2022 16:28:18",
"content": "there would exist some y where there would be no x mapped *to* it",
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"author_name": "themateo713",
"timestamp": "08/09/2022 16:28:22",
"content": "h not surjective <=> there exists y in Y such that no x in X verifies h(x) = y",
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"timestamp": "08/09/2022 16:28:31",
"content": "^ this is what i meant",
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"author_name": "Fractal",
"timestamp": "08/09/2022 16:28:53",
"content": "but thats a different statement",
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"author_name": "Fractal",
"timestamp": "08/09/2022 16:29:12",
"content": "notice what you said implies the function maps somewhere else other than the codomain, as I understand it",
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"author_name": "Fractal",
"timestamp": "08/09/2022 16:29:29",
"content": "functions always map to their codomain by defintion/restriction",
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"timestamp": "08/09/2022 16:30:12",
"content": "i see now",
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"timestamp": "08/09/2022 16:32:47",
"content": "do you think it would be an easier approach to prove this by contradiction?",
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"author_name": "Fractal",
"timestamp": "08/09/2022 16:33:16",
"content": "maybe\nId try to construct maps similar to the drawing",
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"timestamp": "08/09/2022 16:33:41",
"content": "that would be my first idea",
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"author_name": "Fractal",
"timestamp": "08/09/2022 16:34:29",
"content": "my hint is to take maps from h(X) and try to extend them",
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"author_name": "themateo713",
"timestamp": "08/09/2022 16:34:38",
"content": "That's the idea yes",
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"timestamp": "08/09/2022 16:35:41",
"content": "meaning we want to form something like h o f? what do you mean by extend",
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"author_name": "Fractal",
"timestamp": "08/09/2022 16:38:34",
"content": "like take some map $\\tilde f: h(X) \\to Z$ and create bigger maps $f,g : Y \\to Z$ that are the same as $\\tilde f$ when *restricted* to $h(X)$",
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"timestamp": "08/09/2022 16:38:37",
"content": "**Fractal**",
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"timestamp": "08/09/2022 16:39:06",
"content": "I think the drawing helps more than words",
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"timestamp": "08/09/2022 16:39:12",
"content": "if its even understandable",
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"timestamp": "08/09/2022 16:42:38",
"content": "im still confused, sorry",
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"timestamp": "08/09/2022 16:42:50",
"content": "should i not use any previous information from the rest of the proof?",
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"author_name": "Fractal",
"timestamp": "08/09/2022 16:43:58",
"content": "what previous information?",
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"timestamp": "08/09/2022 16:44:43",
"content": "",
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"timestamp": "08/09/2022 16:44:56",
"content": "i am going to get eaten alive with my proof writing skills",
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"timestamp": "08/09/2022 16:45:09",
"content": "if thats not readable i can also type it up in latex",
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"timestamp": "08/09/2022 16:47:58",
"content": "that seems almost correct",
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"timestamp": "08/09/2022 16:48:04",
"content": "i just cant get",
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"author_name": "Fractal",
"timestamp": "08/09/2022 16:48:05",
"content": "but your reasoning is a bit backwards",
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"id": 1006665197374685400,
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"timestamp": "08/09/2022 16:48:05",
"content": "the onto part",
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"id": 1006665212809728100,
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"timestamp": "08/09/2022 16:48:09",
"content": "oh no",
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"author_name": "Fractal",
"timestamp": "08/09/2022 16:48:32",
"content": "you should choose y *after* assuming h is not onto",
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"author_name": "Fractal",
"timestamp": "08/09/2022 16:48:56",
"content": "your h is already not onto\nsince its image is in Y\\\\{y} right?",
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"timestamp": "08/09/2022 16:49:19",
"content": "wait",
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"timestamp": "08/09/2022 16:49:23",
"content": "you have the right idea",
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"timestamp": "08/09/2022 16:49:45",
"content": "h maps to Y\\ {y} yes",
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"timestamp": "08/09/2022 16:50:02",
"content": "that would be not onto\nif you made that for *every* x",
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"timestamp": "08/09/2022 16:50:09",
"content": "that is where your idea is coming from",
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"author_name": "Fractal",
"timestamp": "08/09/2022 16:50:30",
"content": "all you need is to explicit that z is *different* than z'",
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"id": 1006665850289406000,
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"author_name": "Fractal",
"timestamp": "08/09/2022 16:50:41",
"content": "(hence the 2 element hypothesis)",
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"timestamp": "08/09/2022 16:51:12",
"content": "can i start with",
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"id": 1006666016530645100,
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"timestamp": "08/09/2022 16:51:21",
"content": "suppose Z has 2 elements? and just say that z,z' in Z",
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"timestamp": "08/09/2022 16:51:33",
"content": "that loses generality though i think",
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"timestamp": "08/09/2022 16:51:43",
"content": "it has at least 2 elements by hypothesis",
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"timestamp": "08/09/2022 16:51:51",
"content": "you dont need to suppose anything to use that, fren",
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"timestamp": "08/09/2022 16:52:14",
"content": ".__.",
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"timestamp": "08/09/2022 16:52:22",
"content": "sorry",
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"timestamp": "08/09/2022 16:52:22",
"content": "lol",
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"author_name": "placement",
"timestamp": "08/09/2022 16:52:46",
"content": "ok let me rewrite it and see what i get",
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"timestamp": "08/09/2022 16:52:48",
"content": "thanks for all the help",
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"id": 1006669037507461100,
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"author_name": "placement",
"timestamp": "08/09/2022 17:03:21",
"content": "@Fractal is this a bit more clear?",
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"author_name": "Fractal",
"timestamp": "08/09/2022 17:06:43",
"content": "a few things\nyou should not choose just *any* y\nthat y should be precisely the (or one of the) y that is not *reached* by h\n\nanother thing I dont get is why did you suppose f o h is different than g o h\nyou already showed they were equal (kind of)\nf(g(x)) = f(h(x)) for any x",
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"timestamp": "08/09/2022 17:10:03",
"content": "i guess the 2nd part is a bit redundant, but my thinking was that i didn't cover the case where f o h noteq g o h, so i wanted to cover it to further solidify my previous point",
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"content": "also did you mean f(h(x))=g(h(x)) or did i make an error",
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"id": 1006670816257257500,
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"author_name": "Fractal",
"timestamp": "08/09/2022 17:10:25",
"content": "error",
"attachments": [],
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"author_name": "Fractal",
"timestamp": "08/09/2022 17:10:46",
"content": "I dont get exactly what you mean by that",
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"id": 1006671049288581200,
"author_id": 196875895179444220,
"author_name": "placement",
"timestamp": "08/09/2022 17:11:21",
"content": "f noteq g",
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"id": 1006671092766752900,
"author_id": 196875895179444220,
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"timestamp": "08/09/2022 17:11:31",
"content": "as f(y) noteq g(y)",
"attachments": [],
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"id": 1006671245133221900,
"author_id": 196875895179444220,
"author_name": "placement",
"timestamp": "08/09/2022 17:12:07",
"content": "so when i suppose that f o h = g o h, i wanted to give the case where f o h noteq g o h to reinforce that this only happens at y",
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"id": 1006671276628246700,
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"timestamp": "08/09/2022 17:12:15",
"content": "unless that is not needed",
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"id": 1006674462734827600,
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"author_name": "placement",
"timestamp": "08/09/2022 17:24:55",
"content": "i think i've gotten all the help i need, thank you for helping me out",
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"timestamp": "08/09/2022 17:24:57",
"content": ".close",
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"author_name": "Mathematics Bot",
"timestamp": "08/09/2022 17:24:57",
"content": "Channel closed",
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}
] |
help-9
|
2ba3c0177b6b4ed0bc1ae81c9ceb9ccf
|
197,718 |
[
{
"id": 1006679715869896700,
"author_id": 805217272087838700,
"author_name": "Mathematics Bot",
"timestamp": "08/09/2022 17:45:47",
"content": "Available help channel!",
"attachments": [],
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"reference": null
},
{
"id": 1006683763700404400,
"author_id": 933153827648045200,
"author_name": "AuHasard",
"timestamp": "08/09/2022 18:01:52",
"content": "Given the function f(x) = (9 cos(x+13))ยฒ with the domain of function being (โโ,โ), determine the range of function [a, b] for the function.",
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"id": 1006683767500439700,
"author_id": 805217272087838700,
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"timestamp": "08/09/2022 18:01:53",
"content": "Pinned a message.",
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"author_id": 933153827648045200,
"author_name": "AuHasard",
"timestamp": "08/09/2022 18:01:56",
"content": "Can someone help me w this one",
"attachments": [],
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},
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"id": 1006684019443900500,
"author_id": 182179228840755200,
"author_name": "iCaird",
"timestamp": "08/09/2022 18:02:53",
"content": "You've got to think about what possible values f(x) can take if x can be anything",
"attachments": [],
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},
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"id": 1006685401492234200,
"author_id": 933153827648045200,
"author_name": "AuHasard",
"timestamp": "08/09/2022 18:08:23",
"content": "Well, -1โคcos(x)โค1 right?",
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},
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"id": 1006685423579435000,
"author_id": 933153827648045200,
"author_name": "AuHasard",
"timestamp": "08/09/2022 18:08:28",
"content": "That's the range iirc",
"attachments": [],
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},
{
"id": 1006685608011382900,
"author_id": 182179228840755200,
"author_name": "iCaird",
"timestamp": "08/09/2022 18:09:12",
"content": "That's the range of cos(x) yes",
"attachments": [],
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},
{
"id": 1006685744011677800,
"author_id": 933153827648045200,
"author_name": "AuHasard",
"timestamp": "08/09/2022 18:09:44",
"content": "So (9*1)^2 = 81, and (9\\*-1)^2 = 81",
"attachments": [],
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},
{
"id": 1006685877898059900,
"author_id": 933153827648045200,
"author_name": "AuHasard",
"timestamp": "08/09/2022 18:10:16",
"content": "What do you think?",
"attachments": [],
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},
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"id": 1006685962677526700,
"author_id": 182179228840755200,
"author_name": "iCaird",
"timestamp": "08/09/2022 18:10:36",
"content": "So I think that shows the *biggest* it can be is 81",
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"id": 1006685981354762200,
"author_id": 182179228840755200,
"author_name": "iCaird",
"timestamp": "08/09/2022 18:10:41",
"content": "What about the lowest?",
"attachments": [],
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},
{
"id": 1006686130202226800,
"author_id": 933153827648045200,
"author_name": "AuHasard",
"timestamp": "08/09/2022 18:11:16",
"content": "Wellโฆ we can see that 9 and cos are put within the same brackets, and if you square a negative number we get a positive number.",
"attachments": [],
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},
{
"id": 1006686153908420700,
"author_id": 933153827648045200,
"author_name": "AuHasard",
"timestamp": "08/09/2022 18:11:22",
"content": "So what do we do?",
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"id": 1006686255632887800,
"author_id": 182179228840755200,
"author_name": "iCaird",
"timestamp": "08/09/2022 18:11:46",
"content": "So we know it's always positive",
"attachments": [],
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},
{
"id": 1006686306300084200,
"author_id": 182179228840755200,
"author_name": "iCaird",
"timestamp": "08/09/2022 18:11:58",
"content": "Well",
"attachments": [],
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},
{
"id": 1006686334812963000,
"author_id": 182179228840755200,
"author_name": "iCaird",
"timestamp": "08/09/2022 18:12:05",
"content": "Non-negative",
"attachments": [],
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},
{
"id": 1006686351602757600,
"author_id": 182179228840755200,
"author_name": "iCaird",
"timestamp": "08/09/2022 18:12:09",
"content": "Can it ever be 0?",
"attachments": [],
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},
{
"id": 1006686432817053800,
"author_id": 933153827648045200,
"author_name": "AuHasard",
"timestamp": "08/09/2022 18:12:28",
"content": "Yes",
"attachments": [],
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},
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"id": 1006686449804005400,
"author_id": 933153827648045200,
"author_name": "AuHasard",
"timestamp": "08/09/2022 18:12:32",
"content": "[0, 81]?",
"attachments": [],
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},
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"id": 1006686563410915500,
"author_id": 182179228840755200,
"author_name": "iCaird",
"timestamp": "08/09/2022 18:13:00",
"content": "Was going to add about cos being continuous",
"attachments": [],
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},
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"id": 1006686606993924200,
"author_id": 182179228840755200,
"author_name": "iCaird",
"timestamp": "08/09/2022 18:13:10",
"content": "And ยฒ",
"attachments": [],
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},
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"id": 1006686642926518300,
"author_id": 510789298321096700,
"author_name": "TeXit",
"timestamp": "08/09/2022 18:13:19",
"content": "**AuHasard**",
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"id": 1006686755795243100,
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"author_name": "iCaird",
"timestamp": "08/09/2022 18:13:45",
"content": "Sure it's intermediate value theorem no?",
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"author_name": "AuHasard",
"timestamp": "08/09/2022 18:14:17",
"content": "So guys",
"attachments": [],
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"id": 1006686906177835000,
"author_id": 933153827648045200,
"author_name": "AuHasard",
"timestamp": "08/09/2022 18:14:21",
"content": "[0, 81]?",
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"id": 1006686941812641800,
"author_id": 182179228840755200,
"author_name": "iCaird",
"timestamp": "08/09/2022 18:14:30",
"content": "I agree",
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"author_name": "AuHasard",
"timestamp": "08/09/2022 18:14:42",
"content": "",
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"author_name": "AuHasard",
"timestamp": "08/09/2022 18:14:51",
"content": "Do I answer like that?",
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"id": 1006687075829022800,
"author_id": 182179228840755200,
"author_name": "iCaird",
"timestamp": "08/09/2022 18:15:02",
"content": "Put the brackets in",
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},
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"id": 1006687100537684100,
"author_id": 182179228840755200,
"author_name": "iCaird",
"timestamp": "08/09/2022 18:15:08",
"content": "I would assume",
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"id": 1006687125569274000,
"author_id": 933153827648045200,
"author_name": "AuHasard",
"timestamp": "08/09/2022 18:15:14",
"content": "Alright thanks",
"attachments": [],
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},
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"id": 1006687146511441900,
"author_id": 933153827648045200,
"author_name": "AuHasard",
"timestamp": "08/09/2022 18:15:19",
"content": ".close",
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},
{
"id": 1006687147832639500,
"author_id": 805217272087838700,
"author_name": "Mathematics Bot",
"timestamp": "08/09/2022 18:15:19",
"content": "Channel closed",
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}
] |
help-9
|
a124f7d1421240e48b821cfb61332500
|
197,719 |
[
{
"id": 1006687400770146300,
"author_id": 805217272087838700,
"author_name": "Mathematics Bot",
"timestamp": "08/09/2022 18:16:19",
"content": "Available help channel!",
"attachments": [],
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"reference": null
},
{
"id": 1006691956828668000,
"author_id": 933153827648045200,
"author_name": "AuHasard",
"timestamp": "08/09/2022 18:34:25",
"content": "Are these functional graphs (check link) https://imgur.com/a/D91kyNN",
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},
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"id": 1006691959454318700,
"author_id": 805217272087838700,
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"timestamp": "08/09/2022 18:34:26",
"content": "Pinned a message.",
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{
"id": 1006693617689166000,
"author_id": 261933205387477000,
"author_name": "riemann",
"timestamp": "08/09/2022 18:41:01",
"content": "what's a functional graph",
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},
{
"id": 1006693633191325700,
"author_id": 261933205387477000,
"author_name": "riemann",
"timestamp": "08/09/2022 18:41:05",
"content": "graph of a function?",
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},
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"id": 1006693982048370700,
"author_id": 933153827648045200,
"author_name": "AuHasard",
"timestamp": "08/09/2022 18:42:28",
"content": "Yes",
"attachments": [],
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"reference": null
},
{
"id": 1006694174936027400,
"author_id": 261933205387477000,
"author_name": "riemann",
"timestamp": "08/09/2022 18:43:14",
"content": "https://mathworld.wolfram.com/VerticalLineTest.html",
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},
{
"id": 1006696394544918500,
"author_id": 933153827648045200,
"author_name": "AuHasard",
"timestamp": "08/09/2022 18:52:03",
"content": ".close",
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},
{
"id": 1006696396285558800,
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"timestamp": "08/09/2022 18:52:04",
"content": "Channel closed",
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}
] |
help-9
|
c78bce3b32dd4f56a0f41422e0837f4f
|
197,720 |
[
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"author_name": "iCaird",
"timestamp": "08/09/2022 18:52:43",
"content": "It's like slamming a door in your face @riemann",
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"timestamp": "08/09/2022 18:53:04",
"content": "Available help channel!",
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},
{
"id": 1006704866036559900,
"author_id": 94991937047633920,
"author_name": "Revolution",
"timestamp": "08/09/2022 19:25:43",
"content": "I've been trying to make use of this result from a mathematics paper, for doing some hobbyist programming in computer graphics, it works *almost perfectly*, and I was wondering if anyone knew enough about vector math to resolve an issue.\n\nThe paper is `Lee, S.-W., & Mittra, R. (1983). Fourier transform of a polygonal shape function and its application in electromagnetics. IEEE Transactions on Antennas and Propagation, 31(1), 99โ103.)`\n\nThis is the result from the paper:\n```latex\n$S(u, v) = \\sum_{n=1}^{N} e^{j\\overrightarrow{w}\\dotproduct\\overrightarrow{\\gamma_{n}}}\\left[\\dfrac{\\hat{n}\\cross\\hat{a}_{n}\\dotproduct\\hat{a}_{n-1}}{(\\overrightarrow{w}\\dotproduct\\hat{a}_{n})(\\overrightarrow{w}\\dotproduct\\hat{a}_{n-1})}\\right]\\\\Where:\\\\\\hat{n}=+\\hat{x}\\hat{y}=+\\hat{z}\\\\\\overrightarrow{\\gamma}_{n}=x_{n}\\hat{x}+y_{n}\\hat{y}=\\textrm{vector from origin 0 to corner n}\\\\\\\\\\hat{a}_{n}=\\dfrac{\\overrightarrow{\\gamma}_{n+1}-\\overrightarrow{\\gamma}_{n}}{\\absolutevalue{\\overrightarrow{\\gamma}_{n+1}-\\overrightarrow{\\gamma}_{n}}}\\\\\\overrightarrow{w}=\\hat{x}u+\\hat{y}v$\n```\nSee the image for the diagram from the paper showing what this applies to.\n\nWhat I'm running into is that, if you think about it, whenever the arguments to S(u, v) produce a vector which is perpendicular to any of the sides of the polygon, the denominator of that big fraction is zero due to the w vector and the side vector's dot product being zero. Based on generating some results of this function, it seems a lot like this creates a *hole* rather than an asymptote in the function, as I'm not getting any odd behavior approaching one of these spots until floating-point errors kick in.\n\nI've tried going through a few steps but I'm not good enough with reasoning about Vector multiplication and such to resolve this. I remember from normal algebra that removing holes from equations is doable in certain circumstances. Is there a different form of the fraction shown that removes the holes?",
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"timestamp": "08/09/2022 19:25:44",
"content": "Pinned a message.",
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"timestamp": "08/09/2022 19:25:47",
"content": "**Revolution**",
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"author_name": "riemann",
"timestamp": "08/09/2022 19:26:13",
"content": "holy shit",
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{
"id": 1006705016821776500,
"author_id": 331558346333224960,
"author_name": "jan Niku",
"timestamp": "08/09/2022 19:26:19",
"content": ":blobsweat:",
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"content": "sir this is a wendy's",
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"timestamp": "08/09/2022 19:26:47",
"content": "okay you see this part",
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"timestamp": "08/09/2022 19:27:10",
"content": "\"I remember from normal algebra that removing holes from equations is doable in certain circumstances\"",
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"content": "explain that",
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"timestamp": "08/09/2022 19:27:54",
"content": "like when the function isn't necessarily in its simplest form, so you get a divide by zero in precisely one spot not affecting the rest of the function",
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"timestamp": "08/09/2022 19:28:48",
"content": "like `(x + 1)(x + 2)/(x+2)` has a hole at `-2` despite the simplest form `(x+1)` not having a hole",
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"content": "ah okay. like\n$\\frac{\\sin(x)}{x}$ is undefined at zero, but $\\lim_{x\\ra 0}\\frac{sin(x)}{x} = 1$",
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"timestamp": "08/09/2022 19:29:03",
"content": "**riemann**",
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"timestamp": "08/09/2022 19:29:11",
"content": "yeah exactly",
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"content": "right right. so you want to do that for your fraction",
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"content": "yes",
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"content": "what does this mean",
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"timestamp": "08/09/2022 19:30:43",
"content": "where da hole tho",
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"timestamp": "08/09/2022 19:30:56",
"content": "gotta unpack all their variables to find it :monkey:",
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"timestamp": "08/09/2022 19:31:05",
"content": "n is a unit vector",
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"timestamp": "08/09/2022 19:31:39",
"content": "oh and this is called a removable singularity",
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"timestamp": "08/09/2022 19:32:40",
"content": "n is the unit vector representing the cross product between the x and y unit vectors, the places its used it basically rotates the vector by 90 degrees",
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"content": "this is $(\\hat{n} \\cross \\hat{a}_n) \\cdot \\hat{a}_{n-1}$, right?",
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"timestamp": "08/09/2022 19:32:51",
"content": "**riemann**",
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"timestamp": "08/09/2022 19:33:07",
"content": "lemme check",
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"timestamp": "08/09/2022 19:33:19",
"content": "yes",
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"timestamp": "08/09/2022 19:33:21",
"content": "what about it",
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"content": "okay so it's just $\\hat{z}$",
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"content": "**riemann**",
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"timestamp": "08/09/2022 19:33:48",
"content": "but sec u need more on a_n",
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"content": "yeah, the paper had a + for unambiguity I suppose",
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"timestamp": "08/09/2022 19:34:16",
"content": "where are the recursive/iterative definitions of $x_n, y_n$",
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"timestamp": "08/09/2022 19:34:19",
"content": "**riemann**",
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"content": "the hole exists any time the these two vectors are perpendicular for any side n $\\\\\\overrightarrow{w}\\\\\\hat{a}_{n}$",
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"timestamp": "08/09/2022 19:36:00",
"content": "**Revolution**",
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"content": "this makes it look like $\\hat{a}_n \\cdot \\hat{z}$ = 0",
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"content": "**riemann**",
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"timestamp": "08/09/2022 19:36:51",
"content": "since the $\\vec{\\gamma}$ terms only have $x$ and $y$ components",
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"content": "**riemann**",
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"timestamp": "08/09/2022 19:36:56",
"content": "that would be the case",
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"timestamp": "08/09/2022 19:37:33",
"content": "so then $\\hat{n} \\cross \\hat{a}_n = \\vec{0}$",
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"timestamp": "08/09/2022 19:37:45",
"content": "**riemann**",
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"timestamp": "08/09/2022 19:37:54",
"content": "no?",
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"timestamp": "08/09/2022 19:37:55",
"content": "and this whole thing is zero?",
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"timestamp": "08/09/2022 19:38:01",
"content": "it means it only has x and y components",
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"timestamp": "08/09/2022 19:38:02",
"content": "oh i'm dumb",
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"timestamp": "08/09/2022 19:39:02",
"content": "in my programming I'm using a 2D geometric algebra where $\\hat{n}$ is the unit bivector",
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"timestamp": "08/09/2022 19:39:04",
"content": "**Revolution**",
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"timestamp": "08/09/2022 19:39:42",
"content": "no idea what that means",
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"timestamp": "08/09/2022 19:39:54",
"content": "does it not mean $\\hat{n} = \\hat{z}$ ?",
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"content": "**riemann**",
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"timestamp": "08/09/2022 19:41:25",
"content": "it means $\\hat{z}$ isn't considered and instead $\\hat{x}\\crossproduct\\hat{y} = \\hat{x}\\hat{y} = -\\hat{y}\\hat{x}$",
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"timestamp": "08/09/2022 19:41:27",
"content": "**Revolution**",
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"timestamp": "08/09/2022 19:42:11",
"content": "if they're equal why does it matter to your removable singularity problem?",
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"timestamp": "08/09/2022 19:42:16",
"content": "it doesnt",
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"timestamp": "08/09/2022 19:42:31",
"content": "you were asking about it though",
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"timestamp": "08/09/2022 19:42:50",
"content": "yea just funky notation",
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"content": "i think from here, you should try to expand the triple product in the numerator and then factor",
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"content": "or use one of the identities here:\n<https://en.wikipedia.org/wiki/Triple_product>",
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"timestamp": "08/09/2022 19:46:08",
"content": "and the express the denominators and numerators in as few variables as possible. you know $\\hat{a}_n$ in terms of $x_n$ and $y_n$ so plug those in.",
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"timestamp": "08/09/2022 19:46:11",
"content": "**riemann**",
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"timestamp": "08/09/2022 19:46:21",
"content": "alright lemme go try that on pen and paper",
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"timestamp": "08/09/2022 19:46:22",
"content": "few independent* variables",
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"author_id": 94991937047633920,
"author_name": "Revolution",
"timestamp": "08/09/2022 19:53:48",
"content": "dot product distributes like normal multiplication right?",
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"id": 1006713639509700600,
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"author_name": "Revolution",
"timestamp": "08/09/2022 20:00:35",
"content": "give me a few minutes to slam something out in latex",
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"id": 1006714477061886100,
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"author_name": "Revolution",
"timestamp": "08/09/2022 20:03:55",
"content": "```latex\n$\\overrightarrow{w}\\dotproduct\\hat{a}_{n}=\\dfrac{\\overrightarrow{w}\\dotproduct x_{n+1}\\hat{x}+\\overrightarrow{w}\\dotproduct y_{n+1}\\hat{y}-\\overrightarrow{w}\\dotproduct x_{n}\\hat{x}-\\overrightarrow{w}\\dotproduct y_{n}\\hat{y}}{\\absolutevalue{x_{n+1}\\hat{x}+y_{n+1}\\hat{y}-x_{n}\\hat{x}-y_{n}\\hat{y}}}$\n```",
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"id": 1006714512390488200,
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"author_name": "Revolution",
"timestamp": "08/09/2022 20:04:03",
"content": "does that look correct?",
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"id": 1006715258326491100,
"author_id": 94991937047633920,
"author_name": "Revolution",
"timestamp": "08/09/2022 20:07:01",
"content": "oh wait",
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"id": 1006715426782331000,
"author_id": 510789298321096700,
"author_name": "TeXit",
"timestamp": "08/09/2022 20:07:41",
"content": "**Revolution**",
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"author_name": "Revolution",
"timestamp": "08/09/2022 20:07:46",
"content": "yeah there we go",
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"id": 1006719055836750000,
"author_id": 94991937047633920,
"author_name": "Revolution",
"timestamp": "08/09/2022 20:22:06",
"content": "and I think purely in terms of components that would come out tooooo",
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"id": 1006719527523995600,
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"author_name": "Revolution",
"timestamp": "08/09/2022 20:23:59",
"content": "```latex\n$\\dfrac{ux_{n+1}+vy_{n+1}-ux_n-vy_n}{\\sqrt{(x_{n+1}-x_n)^2+(y_{n+1}-y_n)^2}}$\n```",
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"id": 1006719537535782900,
"author_id": 510789298321096700,
"author_name": "TeXit",
"timestamp": "08/09/2022 20:24:01",
"content": "**Revolution**",
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"id": 1006719934425993200,
"author_id": 94991937047633920,
"author_name": "Revolution",
"timestamp": "08/09/2022 20:25:36",
"content": "which is still 0 when the vectors are perpendicular I think?",
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},
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"id": 1006719936602849300,
"author_id": 261933205387477000,
"author_name": "riemann",
"timestamp": "08/09/2022 20:25:36",
"content": "Looks like you can just write delta x and use that instead",
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"id": 1006721333079580700,
"author_id": 94991937047633920,
"author_name": "Revolution",
"timestamp": "08/09/2022 20:31:09",
"content": "I'll do that, lemme work out some numerator stuff",
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"id": 1006724984607088800,
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"author_name": "Revolution",
"timestamp": "08/09/2022 20:45:40",
"content": "```latex\n$because\\\\a\\dotproduct(b\\crossproduct c)=b\\dotproduct(c\\crossproduct a)\\\\(\\hat{n}\\crossproduct\\hat{a}_n)\\dotproduct\\hat{a}_{n-1}=\\hat{a}_{n-1}\\dotproduct(\\hat{n}\\crossproduct\\hat{a}_n)=\\hat{n}\\dotproduct(\\hat{a}_n\\crossproduct\\hat{a}_{n-1})\\\\\\textrm{which because both vectors here only have z components}\\\\numerator=\\hat{a}_n\\crossproduct\\hat{a}_{n-1}\\textrm{ treated as a scalar}$\n```",
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"id": 1006724997529731200,
"author_id": 510789298321096700,
"author_name": "TeXit",
"timestamp": "08/09/2022 20:45:43",
"content": "**Revolution**",
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"timestamp": "08/09/2022 20:45:47",
"content": "hows that look",
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"author_id": 805217272087838700,
"author_name": "Mathematics Bot",
"timestamp": "08/09/2022 21:00:47",
"content": "@Revolution Has your question been resolved?",
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"id": 1006729185638744000,
"author_id": 94991937047633920,
"author_name": "Revolution",
"timestamp": "08/09/2022 21:02:21",
"content": "wait and so hold on",
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"id": 1006729290731229200,
"author_id": 94991937047633920,
"author_name": "Revolution",
"timestamp": "08/09/2022 21:02:47",
"content": "because both of these are the norms of certain vectors and they only have x and y components isnt their cross product just the angle between them",
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"id": 1006730243907780600,
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"author_name": "Revolution",
"timestamp": "08/09/2022 21:06:34",
"content": "im getting pretty tired so im gonna close the channel for now, thanks for the help",
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},
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"id": 1006730296567267300,
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"author_name": "Revolution",
"timestamp": "08/09/2022 21:06:46",
"content": ".close",
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"content": "Channel closed",
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}
] |
help-9
|
4ac2b367bc494b14adce170dc5244681
|
197,721 |
[
{
"id": 1006730551312531600,
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"author_name": "Mathematics Bot",
"timestamp": "08/09/2022 21:07:47",
"content": "Available help channel!",
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},
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"id": 1006731531458453600,
"author_id": 282250535967391740,
"author_name": "Skishy",
"timestamp": "08/09/2022 21:11:41",
"content": "how do I find dy/dx of x^2",
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"id": 1006731533505269900,
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"author_id": 573905759134548000,
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"timestamp": "08/09/2022 21:12:45",
"content": "power rule",
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"id": 1006731984166469600,
"author_id": 277133612812468220,
"author_name": "HeadShotCem",
"timestamp": "08/09/2022 21:13:29",
"content": "@Skishy",
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"timestamp": "08/09/2022 21:13:32",
"content": "$\\frac d {dx}[x^n] = n ยท x^{n - 1}$",
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"content": "**Nonna**",
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"timestamp": "08/09/2022 21:14:06",
"content": ":catThink:",
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"id": 1006732687735799900,
"author_id": 760284651385913300,
"author_name": "JHVBT",
"timestamp": "08/09/2022 21:16:16",
"content": "Try plugging in x^2 into the definition of d/dx",
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"timestamp": "08/09/2022 21:16:28",
"content": "That might give a more intuitive feel for the derivative",
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"content": "@Skishy Has your question been resolved?",
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"timestamp": "08/09/2022 21:41:41",
"content": "Channel closed",
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}
] |
help-9
|
6a16c27878f94c569067f6be2aa612fb
|
197,722 |
[
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"content": "Available help channel!",
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"timestamp": "08/09/2022 21:47:52",
"content": "How would I solve for this?",
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"content": "ok",
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"timestamp": "08/09/2022 21:57:39",
"content": "i dont understand sorry",
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"timestamp": "08/09/2022 21:57:44",
"content": "how did u get m=1/4",
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"content": "@Deleted User Has your question been resolved?",
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"timestamp": "08/09/2022 22:18:38",
"content": "Channel closed",
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] |
help-9
|
972aa3f970aa4aa6aa4ddd24467ccd24
|
197,723 |
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{
"id": 1006769667970433000,
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"content": "Available help channel!",
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"id": 1006779816500006900,
"author_id": 577631194439745500,
"author_name": "elpisav._",
"timestamp": "08/10/2022 00:23:33",
"content": "while estimating the limit how do i round these numbers with the decimal? if itโs .500 would i round it up to 1?",
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"timestamp": "08/10/2022 00:25:53",
"content": "No",
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"id": 1006780475785883800,
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"author_name": "Eric Tao",
"timestamp": "08/10/2022 00:26:10",
"content": "do you see how f(x) is getting closer and closer to the same number",
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"id": 1006780502545543200,
"author_id": 531535537362829300,
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"timestamp": "08/10/2022 00:26:16",
"content": "the closer x gets to 0",
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"id": 1006780619524677600,
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"content": "yes",
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"id": 1006780740786213000,
"author_id": 531535537362829300,
"author_name": "Eric Tao",
"timestamp": "08/10/2022 00:27:13",
"content": "what number does f(x) get close to",
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"id": 1006781499057639400,
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"author_name": "elpisav._",
"timestamp": "08/10/2022 00:30:14",
"content": "so from the left side it decrease closer to the .499 and on the right side it increases so would the rounded number be 0?",
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"id": 1006782943810814000,
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"timestamp": "08/10/2022 00:35:58",
"content": "Let me put it this way",
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"id": 1006782976849367200,
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"author_name": "Eric Tao",
"timestamp": "08/10/2022 00:36:06",
"content": "what is the most logical number to put in place of the question mark",
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"id": 1006783021447401500,
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"timestamp": "08/10/2022 00:36:17",
"content": "based on the pattern that the numbers follow",
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"timestamp": "08/10/2022 00:37:46",
"content": ".4999?",
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"id": 1006783643886293000,
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"timestamp": "08/10/2022 00:38:45",
"content": "yep you could say that",
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"timestamp": "08/10/2022 00:38:48",
"content": "or 0.500",
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"author_name": "Eric Tao",
"timestamp": "08/10/2022 00:39:07",
"content": "based on just the info in the table you can't actually tell the exact answer lol, but both of those are logical answers",
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"id": 1006784311111983200,
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"author_name": "elpisav._",
"timestamp": "08/10/2022 00:41:24",
"content": "so i could put down .500 as the โlimitโ bc there isnโt an exact answer ?",
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"id": 1006785376867848300,
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"author_name": "citrusmunch",
"timestamp": "08/10/2022 00:45:39",
"content": "it turns out for this the exact value can be found, just not with plugging in values from the table",
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"timestamp": "08/10/2022 00:45:59",
"content": "the question is nudging you towards that exact value which is `1/2`",
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"timestamp": "08/10/2022 00:47:26",
"content": "ohhhh okay thank you very much !!",
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"timestamp": "08/10/2022 00:47:29",
"content": ".close",
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}
] |
help-9
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5fcc8a7a881b4fab9ff12f3abcd7bddc
|
197,724 |
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"content": "Available help channel!",
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},
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"id": 1006792896265076700,
"author_id": 224873001873571840,
"author_name": ".neds",
"timestamp": "08/10/2022 01:15:31",
"content": "How do i do a ratio test on this series?",
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"timestamp": "08/10/2022 01:15:32",
"content": "Pinned a message.",
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"id": 1006792973033427000,
"author_id": 224873001873571840,
"author_name": ".neds",
"timestamp": "08/10/2022 01:15:50",
"content": "i dont get what im supposed to do with the pi/2e",
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},
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"id": 1006796232758407200,
"author_id": 485164773647056900,
"author_name": "Gooaaa",
"timestamp": "08/10/2022 01:28:47",
"content": "Nothing",
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"id": 1006796240463331300,
"author_id": 485164773647056900,
"author_name": "Gooaaa",
"timestamp": "08/10/2022 01:28:49",
"content": "Let it si",
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},
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"id": 1006796245106426000,
"author_id": 485164773647056900,
"author_name": "Gooaaa",
"timestamp": "08/10/2022 01:28:50",
"content": "So",
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},
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"author_name": "Mathematics Bot",
"timestamp": "08/10/2022 01:33:50",
"content": "@.neds Has your question been resolved?",
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"author_name": ".neds",
"timestamp": "08/10/2022 01:34:22",
"content": "so do i just ignore it during the ratio test?",
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"timestamp": "08/10/2022 01:35:24",
"content": "No u just let it so in ratio test",
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"id": 1006798120488804500,
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"timestamp": "08/10/2022 01:36:17",
"content": "okey",
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},
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"id": 1006798126545375400,
"author_id": 224873001873571840,
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"timestamp": "08/10/2022 01:36:18",
"content": "ty",
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},
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"id": 1006798135349227600,
"author_id": 224873001873571840,
"author_name": ".neds",
"timestamp": "08/10/2022 01:36:20",
"content": ".close",
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},
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"id": 1006798136808841200,
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"author_name": "Mathematics Bot",
"timestamp": "08/10/2022 01:36:21",
"content": "Channel closed",
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}
] |
help-9
|
3a9403f4e50942c9bc95d147995ee4a7
|
197,725 |
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"id": 1006810749894676500,
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"timestamp": "08/10/2022 02:26:28",
"content": "Available help channel!",
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},
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"id": 1006831650019221500,
"author_id": 335329581190086660,
"author_name": "SMorcrux",
"timestamp": "08/10/2022 03:49:31",
"content": "Hey guys, quick question: are there any interesting rules that are derived from the continuum hypothesis? Say the axiom of choice does a lot of things like ensure every vector space has a basis, what does CH do?",
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},
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"content": "Pinned a message.",
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"content": "@SMorcrux Has your question been resolved?",
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"content": "Channel closed",
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] |
help-9
|
6ee060a5234e4c6a9d5ef7310bc2a0db
|
197,726 |
[
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"id": 959701812271784000,
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"author_name": "Mathematics Bot",
"timestamp": "04/02/2022 02:32:22",
"content": "Available help channel!",
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},
{
"id": 959706082182312000,
"author_id": 528537640618950660,
"author_name": "bono",
"timestamp": "04/02/2022 02:49:20",
"content": "",
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"timestamp": "04/02/2022 02:49:20",
"content": "Pinned a message.",
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"id": 959706131591204900,
"author_id": 528537640618950660,
"author_name": "bono",
"timestamp": "04/02/2022 02:49:32",
"content": "Can someone please help me with part ii?",
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"id": 959707442114084900,
"author_id": 757890033238671400,
"author_name": "Sabertoothed Rat",
"timestamp": "04/02/2022 02:54:44",
"content": "just write cos(2ฮ) in that form and complete square",
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"timestamp": "04/02/2022 03:04:32",
"content": "@bono Has your question been resolved?",
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"content": "Channel closed",
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}
] |
help-9
|
9327e79a14534017b88b589331623691
|
197,727 |
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"id": 1006839454163538000,
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"author_name": "Mathematics Bot",
"timestamp": "08/10/2022 04:20:32",
"content": "Available help channel!",
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"author_name": "DharMannVEVO",
"timestamp": "08/10/2022 04:34:12",
"content": "It's about trigonometric identities and the book is showing a procedure and apparently idk how did \n(sin theta/tan theta)^2 + (sin theta)^2 = 1\nWent to this",
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"content": "Pinned a message.",
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"author_id": 191148988089630720,
"author_name": "Twentycents",
"timestamp": "08/10/2022 04:35:59",
"content": "They factored by $\\sin(\\theta)^2$",
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"timestamp": "08/10/2022 04:36:02",
"content": "**Twenty**",
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"author_name": "DharMannVEVO",
"timestamp": "08/10/2022 04:39:12",
"content": "So basically sin (0)^2 + sin (0)^2 = 2 sin (0)^2?",
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"timestamp": "08/10/2022 04:45:56",
"content": "ye",
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"timestamp": "08/10/2022 04:46:10",
"content": "and then sin theta is factored out just like any other thing",
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"timestamp": "08/10/2022 04:54:13",
"content": "@DharMannVEVO Has your question been resolved?",
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"author_name": "DharMannVEVO",
"timestamp": "08/10/2022 05:02:47",
"content": "Wait, sry I still don't get it",
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"author_name": "cleverdumb [2756956]",
"timestamp": "08/10/2022 05:13:01",
"content": "a + a = 2a\nsin(a) + sin(a) = 2 sin(a)",
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"timestamp": "08/10/2022 05:13:44",
"content": "Oh okay",
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"author_name": "DharMannVEVO",
"timestamp": "08/10/2022 05:14:25",
"content": "Wait arggh I still don't know how did the author figure this out",
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"timestamp": "08/10/2022 05:14:56",
"content": "ab + ac = a (b+c)",
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"author_name": "cleverdumb [2756956]",
"timestamp": "08/10/2022 05:15:03",
"content": "that applies to all things",
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"author_name": "DharMannVEVO",
"timestamp": "08/10/2022 05:15:24",
"content": "Alright",
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"author_name": "DharMannVEVO",
"timestamp": "08/10/2022 05:15:56",
"content": "U also gotta take the tan theta in the denominator as well",
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"timestamp": "08/10/2022 05:16:09",
"content": "so it means $sin^2(\\theta) + sin^2(\\theta) \\cdot \\frac{1}{tan^2(\\theta)}$",
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"author_name": "DharMannVEVO",
"timestamp": "08/10/2022 05:16:20",
"content": "Which would make\n\nsin theta / tan theta + sin theta times tan theta/ tan theta",
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"timestamp": "08/10/2022 05:16:29",
"content": "Yeah",
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"author_name": "TeXit",
"timestamp": "08/10/2022 05:16:40",
"content": "**cleverdumb [2756956]**",
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"timestamp": "08/10/2022 05:18:46",
"content": "Ahhh so that's why it's related to here",
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"timestamp": "08/10/2022 05:18:51",
"content": "ye",
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"author_id": 756698895425208300,
"author_name": "DharMannVEVO",
"timestamp": "08/10/2022 05:18:56",
"content": "What happens next?",
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"author_name": "DharMannVEVO",
"timestamp": "08/10/2022 05:19:02",
"content": "It's (2 sin theta) ^2 now right?",
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"author_name": "cleverdumb [2756956]",
"timestamp": "08/10/2022 05:19:37",
"content": "and then it converts to $sin^2(\\theta) \\cdot (\\frac{1}{tan^2(\\theta)}+1)$",
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"author_name": "TeXit",
"timestamp": "08/10/2022 05:19:45",
"content": "**cleverdumb [2756956]**",
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"timestamp": "08/10/2022 05:20:07",
"content": "no square it before doubling it",
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"timestamp": "08/10/2022 05:20:40",
"content": "a + ab = a(b+1)",
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"timestamp": "08/10/2022 05:21:48",
"content": "$2(sin^2(\\theta))$",
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"author_name": "TeXit",
"timestamp": "08/10/2022 05:21:54",
"content": "**cleverdumb [2756956]**",
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"timestamp": "08/10/2022 05:22:07",
"content": "but it will never happen so no",
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"timestamp": "08/10/2022 05:25:31",
"content": "So, it's basically this when you remove the squares?",
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"timestamp": "08/10/2022 05:25:41",
"content": "I assumed to put them onto the 1 earlier at rhs, becoming radical of 1",
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"author_id": 831433025471774700,
"author_name": "cleverdumb [2756956]",
"timestamp": "08/10/2022 05:28:05",
"content": "i am not too sure",
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},
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"id": 1006856970810179600,
"author_id": 756698895425208300,
"author_name": "DharMannVEVO",
"timestamp": "08/10/2022 05:30:08",
"content": "Ohkay",
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},
{
"id": 1006857094617649300,
"author_id": 756698895425208300,
"author_name": "DharMannVEVO",
"timestamp": "08/10/2022 05:30:37",
"content": "@Helpers may I ask how did the second part went from that to the third part?\nThanks",
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},
{
"id": 1006858690604839000,
"author_id": 482237034736386050,
"author_name": "EnzoL",
"timestamp": "08/10/2022 05:36:58",
"content": "sinยฒ/tanยฒ = sinยฒ * 1/tanยฒ right?",
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},
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"id": 1006858780664930300,
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"author_name": "DharMannVEVO",
"timestamp": "08/10/2022 05:37:19",
"content": "Yeah",
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},
{
"id": 1006858780690092000,
"author_id": 482237034736386050,
"author_name": "EnzoL",
"timestamp": "08/10/2022 05:37:19",
"content": "sinยฒ = sinยฒ*1",
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},
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"id": 1006858836805701600,
"author_id": 756698895425208300,
"author_name": "DharMannVEVO",
"timestamp": "08/10/2022 05:37:33",
"content": "What's *1?",
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},
{
"id": 1006858847773802500,
"author_id": 756698895425208300,
"author_name": "DharMannVEVO",
"timestamp": "08/10/2022 05:37:35",
"content": "Times 1?",
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},
{
"id": 1006858860012769300,
"author_id": 482237034736386050,
"author_name": "EnzoL",
"timestamp": "08/10/2022 05:37:38",
"content": "yup",
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},
{
"id": 1006859104549089300,
"author_id": 482237034736386050,
"author_name": "EnzoL",
"timestamp": "08/10/2022 05:38:37",
"content": "so sinยฒ + sinยฒ/tanยฒ = 1 x sinยฒ + sinยฒ x 1/tanยฒ",
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},
{
"id": 1006859250712199200,
"author_id": 482237034736386050,
"author_name": "EnzoL",
"timestamp": "08/10/2022 05:39:11",
"content": "so you can factorize by sinยฒ",
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},
{
"id": 1006859286208598100,
"author_id": 482237034736386050,
"author_name": "EnzoL",
"timestamp": "08/10/2022 05:39:20",
"content": "if you know what that means",
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},
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"id": 1006859854431928300,
"author_id": 756698895425208300,
"author_name": "DharMannVEVO",
"timestamp": "08/10/2022 05:41:35",
"content": "I finally got it",
"attachments": [],
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"author_name": "DharMannVEVO",
"timestamp": "08/10/2022 05:41:40",
"content": "Thanks",
"attachments": [],
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},
{
"id": 1006859915538743300,
"author_id": 756698895425208300,
"author_name": "DharMannVEVO",
"timestamp": "08/10/2022 05:41:50",
"content": "That was pretty big brain",
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},
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"author_id": 756698895425208300,
"author_name": "DharMannVEVO",
"timestamp": "08/10/2022 05:41:56",
"content": ".close",
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},
{
"id": 1006859941992210600,
"author_id": 805217272087838700,
"author_name": "Mathematics Bot",
"timestamp": "08/10/2022 05:41:56",
"content": "Channel closed",
"attachments": [],
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"reference": null
}
] |
help-9
|
d136011e36ef497ebf8911b8014b896e
|
197,728 |
[
{
"id": 1006865195886444500,
"author_id": 805217272087838700,
"author_name": "Mathematics Bot",
"timestamp": "08/10/2022 06:02:49",
"content": "Available help channel!",
"attachments": [],
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"reference": null
},
{
"id": 1006866459043053600,
"author_id": 775278256961355800,
"author_name": "Radiance",
"timestamp": "08/10/2022 06:07:50",
"content": "does anyone know how to calculate the surface area of a cylindar 7cm r,6 cm h with a 2.5cm r and 2xm h cylindar on top?",
"attachments": [],
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},
{
"id": 1006866460842397800,
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"author_name": "Mathematics Bot",
"timestamp": "08/10/2022 06:07:50",
"content": "Pinned a message.",
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{
"id": 1006866559211421700,
"author_id": 775278256961355800,
"author_name": "Radiance",
"timestamp": "08/10/2022 06:08:14",
"content": "this was one of my tutoring questions and im kinda stuck",
"attachments": [],
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},
{
"id": 1006866781786357800,
"author_id": 775278256961355800,
"author_name": "Radiance",
"timestamp": "08/10/2022 06:09:07",
"content": "how do you calculate the cylinder on top with the bottom one together?",
"attachments": [],
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},
{
"id": 1006868261465489400,
"author_id": 498831265814806500,
"author_name": "Ayn",
"timestamp": "08/10/2022 06:15:00",
"content": "A cylinder is basically a stack of circles",
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{
"id": 1006868291123429400,
"author_id": 498831265814806500,
"author_name": "Ayn",
"timestamp": "08/10/2022 06:15:07",
"content": "Would you agree?",
"attachments": [],
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},
{
"id": 1006868483356754000,
"author_id": 498831265814806500,
"author_name": "Ayn",
"timestamp": "08/10/2022 06:15:53",
"content": "@Radiance wake up",
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"id": 1006868734150979700,
"author_id": 498831265814806500,
"author_name": "Ayn",
"timestamp": "08/10/2022 06:16:52",
"content": "Cylinder info:\nRadius - 7 cm\nHeight - 6 cm\n\nSmaller cylinder info:\nRadius - 2.5 cm\nHeight - 2 cm",
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},
{
"id": 1006870557595271200,
"author_id": 805217272087838700,
"author_name": "Mathematics Bot",
"timestamp": "08/10/2022 06:24:07",
"content": "@Radiance Has your question been resolved?",
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"timestamp": "08/10/2022 06:39:07",
"content": "Channel closed",
"attachments": [],
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}
] |
help-9
|
5fbb6e8a805c46b6957684c98cbe4c38
|
197,729 |
[
{
"id": 1006874586316542000,
"author_id": 805217272087838700,
"author_name": "Mathematics Bot",
"timestamp": "08/10/2022 06:40:08",
"content": "Available help channel!",
"attachments": [],
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"reference": null
},
{
"id": 1006875648645669000,
"author_id": 756698895425208300,
"author_name": "DharMannVEVO",
"timestamp": "08/10/2022 06:44:21",
"content": "This is about the identities",
"attachments": [],
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},
{
"id": 1006875651019657300,
"author_id": 805217272087838700,
"author_name": "Mathematics Bot",
"timestamp": "08/10/2022 06:44:22",
"content": "Pinned a message.",
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"author_id": 756698895425208300,
"author_name": "DharMannVEVO",
"timestamp": "08/10/2022 06:46:10",
"content": "So like the book is showing a procedure and then I don't know what happened from the first part to the second part",
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"id": 1006876850217291900,
"author_id": 485164773647056900,
"author_name": "Gooaaa",
"timestamp": "08/10/2022 06:49:07",
"content": "Multiplied both sides by sin ^-2",
"attachments": [],
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},
{
"id": 1006877337129857200,
"author_id": 801338293241118700,
"author_name": "Atomic",
"timestamp": "08/10/2022 06:51:04",
"content": "and cot = 1/tan",
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},
{
"id": 1006877429798813800,
"author_id": 801338293241118700,
"author_name": "Atomic",
"timestamp": "08/10/2022 06:51:26",
"content": "use the hexagon",
"attachments": [],
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},
{
"id": 1006877557007859700,
"author_id": 756698895425208300,
"author_name": "DharMannVEVO",
"timestamp": "08/10/2022 06:51:56",
"content": "Where did that come from?",
"attachments": [],
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}
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{
"id": 1006877662758834300,
"author_id": 689888565521678300,
"author_name": "darryl",
"timestamp": "08/10/2022 06:52:21",
"content": "Hi! I'm trying to learn discrete math & logic on my own, and following along with a university course that's been posted on YouTube. I'm currently learning about logical equivalencies, and am a bit confused about one problem in particular. The prof walked through the solution, but the jump between step 2 and 3, where said she combined the Commutative and Associative laws, is not clear at all to me. I can see how the commutative law might be applied to show that \"(ยฌp โจ ยฌq) โจ (p โจ q) โก (p โจ q) โจ (ยฌp โจ ยฌq)\", but no idea where the associative law (which says \"(pโจq)โจr=pโจ(qโจr)\" ) comes in to get to give us \"โก (p โจ ยฌp) โจ (q โจ ยฌq)\" ... can anyone help break up these steps or explain? Thanks! (ps https://www.youtube.com/watch?v=u5y1zte2w_4&list=PLl-gb0E4MII28GykmtuBXNUNoej-vY5Rz&index=10&t=627s at 9:10 if anyone wants to take a look at the video",
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"id": 1006877690105704400,
"author_id": 801338293241118700,
"author_name": "Atomic",
"timestamp": "08/10/2022 06:52:28",
"content": "https://youtu.be/T7D1W1oD8wo",
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"id": 1006877793134588000,
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"timestamp": "08/10/2022 06:52:52",
"content": "multiplied both sides by 1/sin^2(x)",
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"author_name": "DharMannVEVO",
"timestamp": "08/10/2022 06:53:05",
"content": "Also, appreciate it you took my pic as your pfp much love :quillen:",
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"id": 1006878136606150700,
"author_id": 801338293241118700,
"author_name": "Atomic",
"timestamp": "08/10/2022 06:54:14",
"content": "do u still need help?",
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},
{
"id": 1006878155761516500,
"author_id": 801338293241118700,
"author_name": "Atomic",
"timestamp": "08/10/2022 06:54:19",
"content": "if not do .close",
"attachments": [],
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},
{
"id": 1006878247759384600,
"author_id": 756698895425208300,
"author_name": "DharMannVEVO",
"timestamp": "08/10/2022 06:54:41",
"content": "Is that how you just do it?",
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"id": 1006878286326026200,
"author_id": 801338293241118700,
"author_name": "Atomic",
"timestamp": "08/10/2022 06:54:50",
"content": "yes",
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},
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"id": 1006878311294701700,
"author_id": 756698895425208300,
"author_name": "DharMannVEVO",
"timestamp": "08/10/2022 06:54:56",
"content": "No, sry I mean I still don't know",
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"id": 1006878392727117800,
"author_id": 801338293241118700,
"author_name": "Atomic",
"timestamp": "08/10/2022 06:55:15",
"content": "or in other words. Divide both sides by sin^2(x)",
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"author_name": "DharMannVEVO",
"timestamp": "08/10/2022 06:56:28",
"content": "Ahh so basically it's just like multiplying on both sides like in algebra to get the x\nBut 1/sin (x) ^2 instead?",
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"id": 1006878791127289900,
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"timestamp": "08/10/2022 06:56:50",
"content": "yes",
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},
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"id": 1006878814208536600,
"author_id": 756698895425208300,
"author_name": "DharMannVEVO",
"timestamp": "08/10/2022 06:56:56",
"content": "Ohkay, thanks",
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},
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"author_name": "DharMannVEVO",
"timestamp": "08/10/2022 06:56:58",
"content": ".close",
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},
{
"id": 1006878825847722100,
"author_id": 805217272087838700,
"author_name": "Mathematics Bot",
"timestamp": "08/10/2022 06:56:58",
"content": "Channel closed",
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}
] |
help-9
|
30796eaef04243cc89fddf3a4f82f909
|
197,730 |
[
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"timestamp": "08/10/2022 06:57:59",
"content": "Available help channel!",
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},
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"id": 1006879327859785700,
"author_id": 689888565521678300,
"author_name": "darryl",
"timestamp": "08/10/2022 06:58:58",
"content": "@Helpers ๐ thanks!",
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},
{
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"timestamp": "08/10/2022 07:10:36",
"content": ".close",
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},
{
"id": 1006882257472061400,
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"timestamp": "08/10/2022 07:10:37",
"content": "Channel closed",
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}
] |
help-9
|
76a93a0164ca4369a9d1ba1e43a4a4da
|
197,731 |
[
{
"id": 1006882511688843400,
"author_id": 805217272087838700,
"author_name": "Mathematics Bot",
"timestamp": "08/10/2022 07:11:37",
"content": "Available help channel!",
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},
{
"id": 1006886220602818600,
"author_id": 388490547204980740,
"author_name": "Tako",
"timestamp": "08/10/2022 07:26:22",
"content": "hey guy",
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"content": "Pinned a message.",
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{
"id": 1006886286180745300,
"author_id": 388490547204980740,
"author_name": "Tako",
"timestamp": "08/10/2022 07:26:37",
"content": "the answer says that half of the river is equal to x",
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},
{
"id": 1006886330380320800,
"author_id": 388490547204980740,
"author_name": "Tako",
"timestamp": "08/10/2022 07:26:48",
"content": "but how did they prove/know that?",
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},
{
"id": 1006886658538483800,
"author_id": 388490547204980740,
"author_name": "Tako",
"timestamp": "08/10/2022 07:28:06",
"content": ".close",
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},
{
"id": 1006886660081979500,
"author_id": 805217272087838700,
"author_name": "Mathematics Bot",
"timestamp": "08/10/2022 07:28:06",
"content": "Channel closed",
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}
] |
help-9
|
271b82790c8643f6bbdf133c9047be8a
|
197,732 |
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"id": 1006886666138558600,
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"timestamp": "08/10/2022 07:28:08",
"content": "bro im stupid",
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"author_name": "Tako",
"timestamp": "08/10/2022 07:28:10",
"content": "it was in the question",
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"timestamp": "08/10/2022 07:28:15",
"content": "i cant read fr",
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"id": 1006886873693692000,
"author_id": 388490547204980740,
"author_name": "Tako",
"timestamp": "08/10/2022 07:28:57",
"content": ".reopen",
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"id": 1006886877841866800,
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"author_name": "Mathematics Bot",
"timestamp": "08/10/2022 07:28:58",
"content": "โ
",
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"id": 1006886882505936900,
"author_id": 388490547204980740,
"author_name": "Tako",
"timestamp": "08/10/2022 07:28:59",
"content": "wait no nvm",
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"id": 1006890083867168800,
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"author_name": "Tako",
"timestamp": "08/10/2022 07:41:43",
"content": "@Helpers",
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"author_id": 388490547204980740,
"author_name": "Tako",
"timestamp": "08/10/2022 07:45:21",
"content": "imma go do some other work please ping me if u answer",
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"id": 1006891069885132800,
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"author_name": "Tako",
"timestamp": "08/10/2022 07:45:38",
"content": "the answer says that half of the river is equal to x\nbut how did they prove/know that?",
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"timestamp": "08/10/2022 08:00:38",
"content": "@Tako Has your question been resolved?",
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"timestamp": "08/10/2022 08:15:38",
"content": "Channel closed",
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}
] |
help-9
|
07030278e08748518ea555ff81a28361
|
197,733 |
[
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"id": 1006917215351742500,
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"author_name": "Mathematics Bot",
"timestamp": "08/10/2022 09:29:31",
"content": "Available help channel!",
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"id": 1006929363377332400,
"author_id": 686029440135725000,
"author_name": "4634",
"timestamp": "08/10/2022 10:17:48",
"content": "Given Kepler's law\n```T^2 = ca^3```\n`T` is the orbital period of a planet, `c` is a constant, and `a` is the distance from the planet to the sun.\n\nIf planet 1 has twice the orbital distance of planet 2, how can I show that the ratio between the distances to the sun is equal to\n```a_1 = (4^(1/3))a_2```",
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"author_name": "4634",
"timestamp": "08/10/2022 10:18:20",
"content": "I'm solving similar numeric problems, but not sure how to derive this solution from just the equation itself",
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"id": 1006929848742191200,
"author_id": 686029440135725000,
"author_name": "4634",
"timestamp": "08/10/2022 10:19:43",
"content": "In general I don't understand how to find how much the right side of the equation would increase by if we increase the left by some factor. The book doesn't elaborate how to do it",
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"id": 1006931321400086700,
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"author_name": "hsp",
"timestamp": "08/10/2022 10:25:34",
"content": "$$\\frac{T_1^2}{a_1^3} = \\frac{T_2^2}{a_2^3}$$\nrearranging,\n$$\\left(\\frac{a_2}{a_1}\\right)^3 = \\left(\\frac{T_2}{T_1}\\right)^2$$",
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"timestamp": "08/10/2022 10:25:37",
"content": "**hsp**",
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"timestamp": "08/10/2022 10:26:10",
"content": "the ratio of orbital periods T2/T1 is given",
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"timestamp": "08/10/2022 10:32:34",
"content": "That clarifies it perfectly, thank you!",
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"timestamp": "08/10/2022 10:32:47",
"content": ".close",
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"content": "Channel closed",
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] |
help-9
|
9f88d03d025b4c2ea170601a6ba5e2aa
|
197,734 |
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"content": "Available help channel!",
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"author_id": 797077265472290800,
"author_name": "MO",
"timestamp": "08/10/2022 10:41:19",
"content": ". Rotate",
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},
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"author_name": "MO",
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"content": ".rotate",
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"author_id": 797077265472290800,
"author_name": "MO",
"timestamp": "08/10/2022 10:41:49",
"content": "Its messy but is a proof justified to say assume bca is 90",
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"id": 1006935545663991900,
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"author_name": "MO",
"timestamp": "08/10/2022 10:42:22",
"content": "Then using that say that BCA must equal 3alpja",
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"id": 1006935572159398000,
"author_id": 797077265472290800,
"author_name": "MO",
"timestamp": "08/10/2022 10:42:28",
"content": "So alphabet equal 30",
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"id": 1006935608062640100,
"author_id": 797077265472290800,
"author_name": "MO",
"timestamp": "08/10/2022 10:42:36",
"content": "And if that's satisfied in the other graph",
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"id": 1006935630170824700,
"author_id": 797077265472290800,
"author_name": "MO",
"timestamp": "08/10/2022 10:42:42",
"content": "Does it count as a priof",
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"id": 1006935652107042800,
"author_id": 797077265472290800,
"author_name": "MO",
"timestamp": "08/10/2022 10:42:47",
"content": "Tnat bca is 90",
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"timestamp": "08/10/2022 10:57:47",
"content": "@MO Has your question been resolved?",
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"timestamp": "08/10/2022 11:12:47",
"content": "Channel closed",
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] |
help-9
|
758b92fff685409c8cfd8164e06ca879
|
197,735 |
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"content": "Available help channel!",
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"timestamp": "08/10/2022 11:22:10",
"content": "Is this true?",
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"author_id": 483962566977126400,
"author_name": "MarveI",
"timestamp": "08/10/2022 11:22:50",
"content": "no",
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"timestamp": "08/10/2022 11:22:52",
"content": "no",
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"timestamp": "08/10/2022 11:23:03",
"content": "$\\fdream$",
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"author_name": "TeXit",
"timestamp": "08/10/2022 11:23:06",
"content": "**โamonov**",
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"timestamp": "08/10/2022 11:23:17",
"content": "oh",
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"timestamp": "08/10/2022 11:23:31",
"content": "wew, that became a command",
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"timestamp": "08/10/2022 11:23:37",
"content": "i really wish it was like that",
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"author_name": "Stormerz",
"timestamp": "08/10/2022 11:24:34",
"content": "So you solve whats within the parentheses first?",
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"author_name": "ramonov",
"timestamp": "08/10/2022 11:24:54",
"content": "solve is not the appropriate word",
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"author_name": "Arthur1102",
"timestamp": "08/10/2022 11:24:59",
"content": "a^(-1) = 1/a",
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"author_name": "ramonov",
"timestamp": "08/10/2022 11:25:21",
"content": "you could combine the stuff inside the parentheses into a single fraction first if you want",
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"author_name": "ramonov",
"timestamp": "08/10/2022 11:25:31",
"content": "some might consider that simplifying",
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"author_id": 193696227617931260,
"author_name": "Stormerz",
"timestamp": "08/10/2022 11:26:27",
"content": "but a and b in the equations are not unknown constants they are notations, i just didnt know how to write notations",
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"content": "xd",
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"author_name": "Arthur1102",
"timestamp": "08/10/2022 11:26:31",
"content": "a/b + c/d = (ad + bc)/bd",
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"author_name": "ramonov",
"timestamp": "08/10/2022 11:26:35",
"content": "but i tried not to use that here as split form isn't really objectively simpler than the combined form",
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"timestamp": "08/10/2022 11:27:20",
"content": "First, make 1/ra + 1/rb a single fraction",
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"timestamp": "08/10/2022 11:27:28",
"content": "Using this",
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"timestamp": "08/10/2022 11:27:49",
"content": "And since this is true for a not 0, you will see the result",
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"author_name": "MarveI",
"timestamp": "08/10/2022 11:28:09",
"content": "do you need an explanation on how he got that equation?",
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"timestamp": "08/10/2022 11:28:27",
"content": "sure ๐",
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"author_name": "MarveI",
"timestamp": "08/10/2022 11:28:32",
"content": "ok so",
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"timestamp": "08/10/2022 11:28:49",
"content": "first you'll need to find a common multiple of both denominators",
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"timestamp": "08/10/2022 11:28:56",
"content": "Thank you Marvel",
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"author_id": 483962566977126400,
"author_name": "MarveI",
"timestamp": "08/10/2022 11:29:00",
"content": "since, you dont know the value of those denominator",
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"author_name": "MarveI",
"timestamp": "08/10/2022 11:29:13",
"content": "you multiply them together so it's divisible by both",
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"author_name": "MarveI",
"timestamp": "08/10/2022 11:30:09",
"content": "e.g \"a common multiple of **\"a\"** and **\"b\"** is **\"a * b\"**\"",
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"timestamp": "08/10/2022 11:30:55",
"content": "you can divide a * b by both \"a\" and \"b\" thus it's a common multiple of both values/variables",
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"timestamp": "08/10/2022 11:31:19",
"content": "oh",
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"timestamp": "08/10/2022 11:31:23",
"content": "okay",
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"author_name": "Stormerz",
"timestamp": "08/10/2022 11:31:25",
"content": "i get it",
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},
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"id": 1006947910526701700,
"author_id": 193696227617931260,
"author_name": "Stormerz",
"timestamp": "08/10/2022 11:31:30",
"content": "nice",
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},
{
"id": 1006947919666098300,
"author_id": 193696227617931260,
"author_name": "Stormerz",
"timestamp": "08/10/2022 11:31:32",
"content": "close.",
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},
{
"id": 1006947943321972900,
"author_id": 193696227617931260,
"author_name": "Stormerz",
"timestamp": "08/10/2022 11:31:37",
"content": ".close",
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},
{
"id": 1006947944609616000,
"author_id": 805217272087838700,
"author_name": "Mathematics Bot",
"timestamp": "08/10/2022 11:31:38",
"content": "Channel closed",
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}
] |
help-9
|
b80fc615e0dc422398ac05525937cc98
|
197,736 |
[
{
"id": 1006967939917955200,
"author_id": 805217272087838700,
"author_name": "Mathematics Bot",
"timestamp": "08/10/2022 12:51:05",
"content": "Available help channel!",
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},
{
"id": 1006973971952058500,
"author_id": 710880757505327100,
"author_name": "Alexnd",
"timestamp": "08/10/2022 13:15:03",
"content": "Hi there! I have a simple question for math enthusiasts, but unfortunately my latest math class are a bit dated now and I am struggling with an Excel formula ๐ฆ\n\nI have a number (let's say 9000) that I want to weight according to another column by +/- 20% depending on this other column number (5 means no weight, 1 means substract 20%, 10 means add 20%).\n\nSo for instance I would have these columns:\nSalary (in US$) : 9000\nMotivation (from 1 to 10): 10\nIn this case, the employee motivation is 10 out of 10, so I'd like the final result to be 9000+20% = $10800\nIf I had a motivation of 3 instead of 10, I would then have 9000-10% = $8100\nIf I had 1, then the result would be 9000-20% = $7200\n\nWhat kind of algorithm should I be looking for to achieve this?\n\nThank you.",
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},
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"id": 1006973973914992600,
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"timestamp": "08/10/2022 13:15:04",
"content": "Pinned a message.",
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"id": 1006974767611527300,
"author_id": 764959481070616600,
"author_name": "Toby",
"timestamp": "08/10/2022 13:18:13",
"content": "your weight scale is not linear",
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},
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"id": 1006974824507248600,
"author_id": 764959481070616600,
"author_name": "Toby",
"timestamp": "08/10/2022 13:18:26",
"content": "5 is not in the middle of 1 and 10",
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},
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"id": 1006974988902990000,
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"author_name": "Toby",
"timestamp": "08/10/2022 13:19:06",
"content": "I guess you want 0 to 10",
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},
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"id": 1006975487127584900,
"author_id": 764959481070616600,
"author_name": "Toby",
"timestamp": "08/10/2022 13:21:04",
"content": "In `B3`, ```B$1*(40*B$2/10-20)```",
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"author_name": "Toby",
"timestamp": "08/10/2022 13:22:40",
"content": "10 is because your scale is out of 10. 40=(20-(-20)) because the range of values is 20 to -20. then -20 because if the weight was 0, we want -20.",
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"id": 1006975892825833500,
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"author_name": "Alexnd",
"timestamp": "08/10/2022 13:22:41",
"content": "right",
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"author_name": "Alexnd",
"timestamp": "08/10/2022 13:23:04",
"content": "let me try this! thank you for your help ๐",
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"id": 1006976014599078000,
"author_id": 764959481070616600,
"author_name": "Toby",
"timestamp": "08/10/2022 13:23:10",
"content": "yw, hope it works",
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},
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"author_name": "Mathematics Bot",
"timestamp": "08/10/2022 13:38:05",
"content": "@Alexnd Has your question been resolved?",
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"timestamp": "08/10/2022 13:53:05",
"content": "Channel closed",
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"reference": null
}
] |
help-9
|
110730cd2003456f9f3eb73df8e74657
|
197,737 |
[
{
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"author_id": 805217272087838700,
"author_name": "Mathematics Bot",
"timestamp": "04/02/2022 03:20:32",
"content": "Available help channel!",
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},
{
"id": 959714011300102100,
"author_id": 846382043885338600,
"author_name": "aphilethesky",
"timestamp": "04/02/2022 03:20:50",
"content": "yo",
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},
{
"id": 959714012667469800,
"author_id": 805217272087838700,
"author_name": "Mathematics Bot",
"timestamp": "04/02/2022 03:20:51",
"content": "Pinned a message.",
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"author_name": "aphilethesky",
"timestamp": "04/02/2022 03:21:28",
"content": "solve the inequality for X",
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},
{
"id": 959717697246093300,
"author_id": 391270706186420200,
"author_name": "illuminator3",
"timestamp": "04/02/2022 03:35:29",
"content": "what have you done so far",
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},
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"author_name": "Mathematics Bot",
"timestamp": "04/02/2022 03:40:29",
"content": "@aphilethesky Has your question been resolved?",
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"timestamp": "04/02/2022 03:41:42",
"content": "oh nvm i did it",
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"timestamp": "04/02/2022 03:41:47",
"content": "just forgot to close the channel",
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"timestamp": "04/02/2022 03:41:49",
"content": ".close",
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},
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"id": 959719294181183500,
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"timestamp": "04/02/2022 03:41:50",
"content": "Channel closed",
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}
] |
help-9
|
70bd8c5aa009403291967fef3eca4429
|
197,738 |
[
{
"id": 1006983795746033700,
"author_id": 805217272087838700,
"author_name": "Mathematics Bot",
"timestamp": "08/10/2022 13:54:05",
"content": "Available help channel!",
"attachments": [],
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},
{
"id": 1006985047426994200,
"author_id": 215090636192350200,
"author_name": "ูุนู
ุงู",
"timestamp": "08/10/2022 13:59:04",
"content": "I thought determinants were linear in every row so that det(A) + det(B) = det(A+B) is true, but this is not the case, am i misunderstanding multilinearity?",
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"content": "Pinned a message.",
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"id": 1006985171502895200,
"author_id": 261933205387477000,
"author_name": "riemann",
"timestamp": "08/10/2022 13:59:33",
"content": "Are A and B rows?",
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"author_id": 215090636192350200,
"author_name": "ูุนู
ุงู",
"timestamp": "08/10/2022 13:59:38",
"content": "ex. det(I+I) \\neq det(2I)",
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"author_id": 215090636192350200,
"author_name": "ูุนู
ุงู",
"timestamp": "08/10/2022 13:59:40",
"content": "No theyre matrices",
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"id": 1006985265954443400,
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"author_name": "riemann",
"timestamp": "08/10/2022 13:59:56",
"content": "where does it say the determinant is linear in matrices?",
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"id": 1006986762024915100,
"author_id": 215090636192350200,
"author_name": "ูุนู
ุงู",
"timestamp": "08/10/2022 14:05:52",
"content": "then im not sure how to interpret summing two determinant rows",
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"author_id": 215090636192350200,
"author_name": "ูุนู
ุงู",
"timestamp": "08/10/2022 14:07:03",
"content": "isn't det(Ri)+det(Rj) = Det(Ri+Rj) for every row the same as saying Det(A)+det(B)=det(A+B)?",
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"timestamp": "08/10/2022 14:07:12",
"content": "determinant is only defined for matrices",
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"id": 1006987255941963800,
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"author_name": "everg",
"timestamp": "08/10/2022 14:07:50",
"content": "of order nxn",
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"author_id": 628203740494823400,
"author_name": "R00tKiT",
"timestamp": "08/10/2022 14:07:57",
"content": "and only square matrices",
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"timestamp": "08/10/2022 14:08:20",
"content": "det(AB)=det(A)det(B) is true though",
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"timestamp": "08/10/2022 14:08:21",
"content": "<https://math.stackexchange.com/questions/3189406/determinant-is-linear-as-a-function-of-each-of-the-rows-of-the-matrix>",
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ุงู",
"timestamp": "08/10/2022 14:14:26",
"content": "Im still a bit confused, whats wrong with saying \nif every row ri was summed with a row xi then you'd have det(x1+r1,x2+r2,....xn+rn) = det(x,....,xn)+det(r1,....,rn)",
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"timestamp": "08/10/2022 14:15:24",
"content": "you can't write det (x1, .., xn) because determinants are undefined for rows",
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ุงู",
"timestamp": "08/10/2022 14:16:14",
"content": "Why not? If a matrix M nxn with rows x1,...,xn we can think of the determinant as a function of the rows",
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ุงู",
"timestamp": "08/10/2022 14:16:26",
"content": "as stated here",
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"timestamp": "08/10/2022 14:18:12",
"content": "even if we do that, it doesn't follow that det (A+B) = det(A) + det(B)",
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ุงู",
"timestamp": "08/10/2022 14:18:43",
"content": "Okey sure, i know that and ive provided a counterexample to show that thats false.",
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ุงู",
"timestamp": "08/10/2022 14:18:49",
"content": "but where am i going wrong here",
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"timestamp": "08/10/2022 14:19:40",
"content": "det(x1+r1,x2+r2,....xn+rn) = det (x1, x2+r2, ..., xn+rn) + det (r1, x2+r2, ..., xn+rn))",
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"timestamp": "08/10/2022 14:19:40",
"content": "do the full calculation for n=3",
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"timestamp": "08/10/2022 14:33:49",
"content": "@ูุนู
ุงู Has your question been resolved?",
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"content": "Channel closed",
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] |
help-9
|
38a7e26751434a3ba14415cc791c6c95
|
197,739 |
[
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"content": "Available help channel!",
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"timestamp": "08/10/2022 14:51:50",
"content": "trying to figure out how to start this one since the video lectures were god awful",
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"id": 1006998496328552600,
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"timestamp": "08/10/2022 14:52:30",
"content": "What does reflexive mean",
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"author_name": "tiberiusrox",
"timestamp": "08/10/2022 15:00:31",
"content": "it means that it relates to itself",
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"content": "so am I evaluating wheather a * a is greater than or equal to 0?",
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"content": "yes",
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"timestamp": "08/10/2022 15:01:08",
"content": "So is (a,a) in R for any integer a",
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"timestamp": "08/10/2022 15:01:11",
"content": "Yee",
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"timestamp": "08/10/2022 15:01:33",
"content": "Are there actually people who actually write equivalence relations like that ?",
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"timestamp": "08/10/2022 15:01:37",
"content": "In general",
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"timestamp": "08/10/2022 15:01:49",
"content": "ok so it's reflexive. and if a*b then b*a in general so it is symetric?",
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"timestamp": "08/10/2022 15:02:19",
"content": "It's what they really are under the bonnet",
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"timestamp": "08/10/2022 15:02:27",
"content": "Symmetric is aRb <=> bRa for all a and b",
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"timestamp": "08/10/2022 15:02:29",
"content": "I know",
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"timestamp": "08/10/2022 15:03:09",
"content": "If you're a hard-core set theorist you probably would",
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"timestamp": "08/10/2022 15:03:11",
"content": "But don't people always use aRb rather than (a, b) in R ?",
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"timestamp": "08/10/2022 15:03:18",
"content": "Ok",
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"author_name": "tiberiusrox",
"timestamp": "08/10/2022 15:03:26",
"content": "it's confusing because I know how to evaluate one operator",
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"timestamp": "08/10/2022 15:03:29",
"content": "I mean always is a strong word like, people use whatever",
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"timestamp": "08/10/2022 15:03:45",
"content": "aRb or a~b are more common yeah",
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"timestamp": "08/10/2022 15:03:47",
"content": "is the operator * or is it <=?",
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"timestamp": "08/10/2022 15:04:07",
"content": "What do you mean",
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"timestamp": "08/10/2022 15:04:34",
"content": "we are finding properties of relations with respect to an operator typically",
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"timestamp": "08/10/2022 15:04:59",
"content": "so 4 = 4 is a relation involing the '=' operator",
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"timestamp": "08/10/2022 15:05:17",
"content": "I mean relations are just defined by some conditions",
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"timestamp": "08/10/2022 15:05:28",
"content": "They don't have to rely on some 'operator'",
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"timestamp": "08/10/2022 15:05:36",
"content": "Binary relationships are always functions whose codomain is {true, false}",
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"timestamp": "08/10/2022 15:05:51",
"content": "ok I am confused then",
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"timestamp": "08/10/2022 15:06:44",
"content": "Like the whole statement aRb iff ab>=0 is the entire relation",
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"timestamp": "08/10/2022 15:06:50",
"content": "for symetry does a*b need to be b*a? and is the <= operator just telling me the variable should remain equal to or greater than 0?",
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"timestamp": "08/10/2022 15:06:58",
"content": "oh",
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"timestamp": "08/10/2022 15:07:09",
"content": "wtf why would they write it as ab then",
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"timestamp": "08/10/2022 15:07:20",
"content": "You should be checking that if ab>=0 then ba>=0",
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"timestamp": "08/10/2022 15:07:44",
"content": "Bc this is the same as checking if aRb then bRa",
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"timestamp": "08/10/2022 15:07:45",
"content": "well it's clearly true",
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"timestamp": "08/10/2022 15:07:49",
"content": "I agree",
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"timestamp": "08/10/2022 15:07:56",
"content": "Not much to do there",
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"timestamp": "08/10/2022 15:08:48",
"content": "but for reflexive is it just if a >= 0 then a>=0?",
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"timestamp": "08/10/2022 15:09:09",
"content": "Reflexive is just aRa for any a",
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"timestamp": "08/10/2022 15:09:18",
"content": "So a*a>=0 for any a",
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"author_name": "tiberiusrox",
"timestamp": "08/10/2022 15:09:27",
"content": "and transitive is a little tough because there is no c",
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"timestamp": "08/10/2022 15:09:43",
"content": "There never is",
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"author_name": "tiberiusrox",
"timestamp": "08/10/2022 15:10:06",
"content": "so if a*b >= 0 and b*c >= 0 then ac >=0?",
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"timestamp": "08/10/2022 15:10:06",
"content": "You make it yourself",
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"timestamp": "08/10/2022 15:10:34",
"content": "You need to check if aRb and bRc then is aRc?",
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"id": 1007003089540223000,
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"author_name": "iCaird",
"timestamp": "08/10/2022 15:10:45",
"content": "Not quite what you have",
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"author_name": "tiberiusrox",
"timestamp": "08/10/2022 15:11:29",
"content": "i fixed it",
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"author_name": "themateo713",
"timestamp": "08/10/2022 15:11:49",
"content": "btw, with a bit of thinking there's a much simpler way to do all this",
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"timestamp": "08/10/2022 15:12:16",
"content": "well before you show me",
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"timestamp": "08/10/2022 15:12:26",
"content": "transitive would be true right?",
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"timestamp": "08/10/2022 15:12:34",
"content": "Sure but why",
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"author_name": "tiberiusrox",
"timestamp": "08/10/2022 15:12:35",
"content": "cuz I cant think of a c that would make it false",
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"timestamp": "08/10/2022 15:12:40",
"content": "Almost. 0 is a special case",
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"timestamp": "08/10/2022 15:12:54",
"content": "Just bc you can't think of a counterexample doesn't mean you can say its true!",
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"timestamp": "08/10/2022 15:13:04",
"content": "yea",
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"id": 1007003685685035000,
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"author_name": "iCaird",
"timestamp": "08/10/2022 15:13:07",
"content": "We want to look at ac",
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"id": 1007003714827079800,
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"author_name": "iCaird",
"timestamp": "08/10/2022 15:13:14",
"content": "We only know about ab and bc",
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"author_name": "tiberiusrox",
"timestamp": "08/10/2022 15:13:37",
"content": "would you use algebra?",
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"id": 1007003820544512100,
"author_id": 182179228840755200,
"author_name": "iCaird",
"timestamp": "08/10/2022 15:13:40",
"content": "What could we do with ab and bc to get ac to appear somewhere",
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"author_name": "tiberiusrox",
"timestamp": "08/10/2022 15:15:13",
"content": "or we could do (ab >=0 /\\ bc>=0 ) -> ac>=0",
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"id": 1007004276373070100,
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"timestamp": "08/10/2022 15:15:28",
"content": "??",
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"author_name": "iCaird",
"timestamp": "08/10/2022 15:15:35",
"content": "You haven't done anything there",
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"id": 1007004318441934800,
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"timestamp": "08/10/2022 15:15:38",
"content": "yea it's not meaningful",
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"timestamp": "08/10/2022 15:16:14",
"content": "just think about doing an operation to ab and bc to make ac appear *somewhere*",
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"timestamp": "08/10/2022 15:16:48",
"content": "(ab*bc)/b",
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"id": 1007004725918564400,
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"author_name": "iCaird",
"timestamp": "08/10/2022 15:17:15",
"content": "Dont divide by b",
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"timestamp": "08/10/2022 15:17:18",
"content": "But good for timesing",
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"id": 1007004773947543700,
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"author_name": "iCaird",
"timestamp": "08/10/2022 15:17:27",
"content": "abยฒc",
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"id": 1007004805606146200,
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"author_name": "tiberiusrox",
"timestamp": "08/10/2022 15:17:34",
"content": "oh",
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"timestamp": "08/10/2022 15:17:38",
"content": "Is this >=0?",
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"author_name": "tiberiusrox",
"timestamp": "08/10/2022 15:18:08",
"content": "well b^2 alone is >=0",
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"timestamp": "08/10/2022 15:18:21",
"content": "Right thats going to come in handy in a second",
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"id": 1007005036917817300,
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"author_name": "iCaird",
"timestamp": "08/10/2022 15:18:30",
"content": "First we need to know that abยฒc>=0",
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"timestamp": "08/10/2022 15:18:36",
"content": "(Hint use our assumptions)",
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"author_name": "tiberiusrox",
"timestamp": "08/10/2022 15:19:11",
"content": "well cant you just divide by a and then divide by c?",
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"id": 1007005336865087600,
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"author_name": "iCaird",
"timestamp": "08/10/2022 15:19:41",
"content": "we can avoid dividing altogether",
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"id": 1007005378850082800,
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"author_name": "iCaird",
"timestamp": "08/10/2022 15:19:51",
"content": "ab>=0 and bc>=0",
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"id": 1007005413910253700,
"author_id": 182179228840755200,
"author_name": "iCaird",
"timestamp": "08/10/2022 15:19:59",
"content": "So abยฒc>=0",
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"id": 1007005527634624600,
"author_id": 182179228840755200,
"author_name": "iCaird",
"timestamp": "08/10/2022 15:20:27",
"content": "And we know bยฒ>=0 so we must have ac>=0",
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"timestamp": "08/10/2022 15:20:37",
"content": "oh ok",
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"author_name": "tiberiusrox",
"timestamp": "08/10/2022 15:20:38",
"content": "thanks",
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"author_name": "tiberiusrox",
"timestamp": "08/10/2022 15:21:46",
"content": "and then anti symmetry was like if they are equal or something right?",
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"author_name": "iCaird",
"timestamp": "08/10/2022 15:22:01",
"content": "Honestly, no idea lemme look it up",
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"timestamp": "08/10/2022 15:23:10",
"content": "Anti symmetric means if aRb and bRa then a=b",
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"timestamp": "08/10/2022 15:23:43",
"content": "A relation *can* be both symmetric and antisymmetric",
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"author_name": "tiberiusrox",
"timestamp": "08/10/2022 15:25:13",
"content": "just because a*b and b*a are both >=0 does not mean a=b though",
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"timestamp": "08/10/2022 15:25:28",
"content": "I agree",
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"author_name": "tiberiusrox",
"timestamp": "08/10/2022 15:26:41",
"content": "and finally an equivelnce relation is just = right?",
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"timestamp": "08/10/2022 15:26:47",
"content": "Very few though no ?",
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"timestamp": "08/10/2022 15:27:04",
"content": "No idea just learnt what antisymmetric meant",
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"timestamp": "08/10/2022 15:27:18",
"content": "It has a very specific definition that should be in your notes",
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"timestamp": "08/10/2022 15:27:44",
"content": "There always exists some function f such that aRb <=> f(a) = f(b), if R is an ER",
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"timestamp": "08/10/2022 15:28:45",
"content": "It seems only relations consisting of elements (a,a)",
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"timestamp": "08/10/2022 15:28:57",
"content": "ER <=> reflexive, symmetric, transitive",
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"timestamp": "08/10/2022 15:29:09",
"content": "That's what I thought yeah",
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"timestamp": "08/10/2022 15:29:45",
"content": "There's also the empty relation",
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"timestamp": "08/10/2022 15:30:28",
"content": "Don't say that about me and my gf",
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"timestamp": "08/10/2022 15:30:37",
"content": "lmao",
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"timestamp": "08/10/2022 15:30:52",
"content": "You can say it to me though. No gf to be offended",
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"timestamp": "08/10/2022 15:31:54",
"content": "Symmetric + antisymmetric <=> for every a, if there's b such that aRb, then a=b",
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"timestamp": "08/10/2022 15:32:19",
"content": "So it's a \"subset of =\" in all technicality",
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"author_name": "tiberiusrox",
"timestamp": "08/10/2022 15:32:37",
"content": "oh equvilance relation means symmetric, reflexive and transitive",
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"timestamp": "08/10/2022 15:32:45",
"content": "Yes",
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"timestamp": "08/10/2022 15:35:32",
"content": "As such, the only antisymmetric equivalence relation is =",
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"author_name": "tiberiusrox",
"timestamp": "08/10/2022 15:37:10",
"content": "can I get help on a related question or do I have to post another thread?",
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"timestamp": "08/10/2022 15:37:19",
"content": "You can keep it here",
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"timestamp": "08/10/2022 15:37:24",
"content": "yay ty",
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"timestamp": "08/10/2022 15:37:26",
"content": "You should know that by now",
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"timestamp": "08/10/2022 15:37:27",
"content": "",
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"timestamp": "08/10/2022 15:37:45",
"content": "its harder to tell when it's in this form",
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"timestamp": "08/10/2022 15:37:57",
"content": "symmetric is super easy to see",
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"author_name": "riemann",
"timestamp": "08/10/2022 15:38:29",
"content": "damn ๐ง for that burn",
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"timestamp": "08/10/2022 15:38:52",
"content": "and I assume reflexive would only be true if it was like only (1,1),(2,2),(3,3) etc",
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"timestamp": "08/10/2022 15:39:04",
"content": "They're all easy except transitivity",
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"timestamp": "08/10/2022 15:39:50",
"content": "so it's not reflexive and it's not symmetric which also means that it's not anti-symmetric",
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"timestamp": "08/10/2022 15:40:07",
"content": "Why that implication ?",
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"timestamp": "08/10/2022 15:40:37",
"content": "because anti-symmetric means aRb and bRa then a=b",
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"timestamp": "08/10/2022 15:40:53",
"content": "Where does this not hold?",
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"author_name": "tiberiusrox",
"timestamp": "08/10/2022 15:40:59",
"content": "oh wait",
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"author_name": "tiberiusrox",
"timestamp": "08/10/2022 15:41:04",
"content": "logic",
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"timestamp": "08/10/2022 15:41:10",
"content": "Ha ha",
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"id": 1007010768224530400,
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"author_name": "tiberiusrox",
"timestamp": "08/10/2022 15:41:16",
"content": "if the premise is false then it's still true",
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"id": 1007010787711270900,
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"timestamp": "08/10/2022 15:41:21",
"content": "Yes",
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"timestamp": "08/10/2022 15:41:58",
"content": "False => whatever is a tautology",
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"timestamp": "08/10/2022 15:42:33",
"content": "so it's not symmetric and not reflexive but it is ant-symmetric",
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"timestamp": "08/10/2022 15:42:38",
"content": "what about transitive",
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"author_name": "tiberiusrox",
"timestamp": "08/10/2022 15:43:01",
"content": "so if aRb and bRc then aRc",
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"timestamp": "08/10/2022 15:43:18",
"content": "we have to make a new set",
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"timestamp": "08/10/2022 15:44:23",
"content": "f* transitivity on tables",
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"timestamp": "08/10/2022 15:44:56",
"content": "It's like O(n^3) to check",
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"timestamp": "08/10/2022 15:45:23",
"content": "Happens to be very fast here but f that nonetheless",
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"timestamp": "08/10/2022 15:47:52",
"content": "so what's the simple method",
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"timestamp": "08/10/2022 15:48:16",
"content": "For transitivity idk",
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"timestamp": "08/10/2022 15:48:29",
"content": "Here it's nice because R is sparse",
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"author_name": "iCaird",
"timestamp": "08/10/2022 15:48:43",
"content": "Yeah theres a reason there's only 3 x's",
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"timestamp": "08/10/2022 15:48:48",
"content": "Just check manually",
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"timestamp": "08/10/2022 15:49:10",
"content": "how",
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"timestamp": "08/10/2022 15:49:40",
"content": "there are three x's does that mean one is a and one is b and one is c?",
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"timestamp": "08/10/2022 15:50:09",
"content": "There's only 3 b values. Only 1 of them is nontrivial. Just apply the definition",
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"timestamp": "08/10/2022 15:50:56",
"content": "ok so 2,2 3,3 and 3,1",
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"timestamp": "08/10/2022 15:51:29",
"content": "just confused as how to relate them to each other",
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"timestamp": "08/10/2022 15:54:08",
"content": "You'd do.something like okay I know 1R3, now i need to look for 3R(something), okay well the only thing I can see is 3R3. Transitivity would then say 1R3, ah yep that is true",
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"timestamp": "08/10/2022 15:54:15",
"content": "Repeat for others",
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"timestamp": "08/10/2022 15:56:39",
"content": "Youre basically searching the table for all the ways you can find aRb and bRc and then seeing if aRc",
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"timestamp": "08/10/2022 15:56:56",
"content": "but two messes it up right",
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"timestamp": "08/10/2022 15:57:25",
"content": "No",
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"timestamp": "08/10/2022 15:59:15",
"content": "ok so 3R1 and 3R3 and 3R3 so that is true, but I have to check the others too right?",
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"timestamp": "08/10/2022 15:59:56",
"content": "2R2 okay so we look for 2R(something), our only option is again 2R2. Transitivity would say 2R2 ah great that's true",
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"timestamp": "08/10/2022 16:02:09",
"content": "ok i dont see how this could not be transitive",
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"timestamp": "08/10/2022 16:02:43",
"content": "Well that's probably bc it is transitive",
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"timestamp": "08/10/2022 16:02:48",
"content": "haha",
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"id": 1007016193154109400,
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"timestamp": "08/10/2022 16:02:49",
"content": "But you need to check",
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"timestamp": "08/10/2022 16:02:49",
"content": "ok",
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"timestamp": "08/10/2022 16:02:50",
"content": "ty",
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"timestamp": "08/10/2022 16:02:57",
"content": "i checked all 3",
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"author_name": "iCaird",
"timestamp": "08/10/2022 16:03:39",
"content": "Okay cool, transitive it is then!",
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},
{
"id": 1007016519877808100,
"author_id": 282616879137423360,
"author_name": "tiberiusrox",
"timestamp": "08/10/2022 16:04:07",
"content": "any idea what R^2 means?",
"attachments": [],
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},
{
"id": 1007016614287392900,
"author_id": 182179228840755200,
"author_name": "iCaird",
"timestamp": "08/10/2022 16:04:30",
"content": "What context",
"attachments": [],
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},
{
"id": 1007016948640526300,
"author_id": 282616879137423360,
"author_name": "tiberiusrox",
"timestamp": "08/10/2022 16:05:50",
"content": "",
"attachments": [
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"fileName": "unknown.png",
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"id": 1007017474505572500,
"author_id": 182179228840755200,
"author_name": "iCaird",
"timestamp": "08/10/2022 16:07:55",
"content": "I have no idea sorry, search your notes for what Rยฒ means",
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},
{
"id": 1007017502729048200,
"author_id": 282616879137423360,
"author_name": "tiberiusrox",
"timestamp": "08/10/2022 16:08:02",
"content": "ok",
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},
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"id": 1007017519573373000,
"author_id": 282616879137423360,
"author_name": "tiberiusrox",
"timestamp": "08/10/2022 16:08:06",
"content": "thanks for the help though",
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},
{
"id": 1007017539873820800,
"author_id": 282616879137423360,
"author_name": "tiberiusrox",
"timestamp": "08/10/2022 16:08:10",
"content": ".close",
"attachments": [],
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},
{
"id": 1007017541887066100,
"author_id": 805217272087838700,
"author_name": "Mathematics Bot",
"timestamp": "08/10/2022 16:08:11",
"content": "Channel closed",
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}
] |
help-9
|
5039e912c3dd4ca28dde4b2345f35f6d
|
197,740 |
[
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"id": 1007017795080429700,
"author_id": 805217272087838700,
"author_name": "Mathematics Bot",
"timestamp": "08/10/2022 16:09:11",
"content": "Available help channel!",
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},
{
"id": 1007025724340846700,
"author_id": 402114534552371200,
"author_name": "hotemogirl",
"timestamp": "08/10/2022 16:40:42",
"content": "can someone help me understand equation on straight lines like rise over run",
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},
{
"id": 1007025726681268400,
"author_id": 805217272087838700,
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"timestamp": "08/10/2022 16:40:42",
"content": "Pinned a message.",
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"timestamp": "08/10/2022 16:41:03",
"content": "https://gyazo.com/8eb64419b58ceecafcd3accdd45b578e",
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"id": 1007025848869716100,
"author_id": 402114534552371200,
"author_name": "hotemogirl",
"timestamp": "08/10/2022 16:41:12",
"content": "it says like equation at the bottom but idk how to work it out",
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"id": 1007025992541421700,
"author_id": 244806629839732740,
"author_name": "~Martin",
"timestamp": "08/10/2022 16:41:46",
"content": "for straight lines the equation always follows this format:\ny=mx+b\nwhere m is the gradient and b is the y-intercept",
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"timestamp": "08/10/2022 16:41:57",
"content": "wdym slope",
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"timestamp": "08/10/2022 16:42:05",
"content": "gradient",
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"author_name": "hotemogirl",
"timestamp": "08/10/2022 16:42:09",
"content": "oh",
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"id": 1007026137299419300,
"author_id": 402114534552371200,
"author_name": "hotemogirl",
"timestamp": "08/10/2022 16:42:20",
"content": "whats y",
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"id": 1007026188218282100,
"author_id": 244806629839732740,
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"timestamp": "08/10/2022 16:42:32",
"content": "you have an x axis and a y axis",
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"timestamp": "08/10/2022 16:42:39",
"content": "ye ye",
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"timestamp": "08/10/2022 16:42:44",
"content": "the y-intercept is where the line intercepts the y axis",
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"timestamp": "08/10/2022 16:42:51",
"content": "ye",
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"timestamp": "08/10/2022 16:42:54",
"content": "for example the red line intercepts the y axis at y=1",
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"timestamp": "08/10/2022 16:43:02",
"content": "ye i see",
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"timestamp": "08/10/2022 16:43:12",
"content": "ah you mean what is the y in y=mx+b?",
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"author_name": "hotemogirl",
"timestamp": "08/10/2022 16:43:14",
"content": "ye",
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"timestamp": "08/10/2022 16:43:20",
"content": "but i understand its just",
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"timestamp": "08/10/2022 16:43:20",
"content": "f(x)=y",
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"timestamp": "08/10/2022 16:43:22",
"content": "like the answer",
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"timestamp": "08/10/2022 16:43:29",
"content": "in other words, y is the function of the line",
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"timestamp": "08/10/2022 16:43:35",
"content": "ye i think i get that",
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"author_name": "hotemogirl",
"timestamp": "08/10/2022 16:43:51",
"content": "but liike i dont get how like A is 1/2 x + 5",
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"timestamp": "08/10/2022 16:44:12",
"content": "for a given value for x, you put it into the formula for y and it gives you the value for y such that the pair (x,y) is on the line",
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"timestamp": "08/10/2022 16:44:46",
"content": "f(x)=y=mx+b\nif we have m and b (m=1/2, b=5) we can just put them into the equation",
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"id": 1007026894077706200,
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"author_name": "hotemogirl",
"timestamp": "08/10/2022 16:45:21",
"content": "ohh",
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"author_name": "hotemogirl",
"timestamp": "08/10/2022 16:45:25",
"content": "so u take the rise over run",
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"id": 1007026936742154200,
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"timestamp": "08/10/2022 16:45:31",
"content": "plus the y intercept",
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"id": 1007026951791333400,
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"author_name": "~Martin",
"timestamp": "08/10/2022 16:45:34",
"content": "exactly",
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"author_name": "hotemogirl",
"timestamp": "08/10/2022 16:45:42",
"content": "ohh man i was being dumb",
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"id": 1007027073728139300,
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"author_name": "hotemogirl",
"timestamp": "08/10/2022 16:46:04",
"content": "its late and im stressing over the math test tmrw but i get it now",
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"timestamp": "08/10/2022 16:46:33",
"content": "haha",
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"timestamp": "08/10/2022 16:46:35",
"content": "good luck^^",
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"author_name": "hotemogirl",
"timestamp": "08/10/2022 16:46:37",
"content": "https://gyazo.com/04c2681d2aa878cee4663de00b5ba89f",
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"id": 1007027220780425300,
"author_id": 402114534552371200,
"author_name": "hotemogirl",
"timestamp": "08/10/2022 16:46:39",
"content": "sorry",
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},
{
"id": 1007027230511222900,
"author_id": 402114534552371200,
"author_name": "hotemogirl",
"timestamp": "08/10/2022 16:46:41",
"content": "what about this one",
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{
"id": 1007027289000779800,
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"author_name": "hotemogirl",
"timestamp": "08/10/2022 16:46:55",
"content": "its the answer at the bottom im looking at a memo",
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"timestamp": "08/10/2022 16:47:15",
"content": "do you have problems with the gradient or with the y intercept?",
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"author_name": "hotemogirl",
"timestamp": "08/10/2022 16:47:18",
"content": "is it the same thing bcs you go 1 right and then 3 up",
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"timestamp": "08/10/2022 16:47:23",
"content": "and that equals 3",
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},
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"id": 1007027433314197500,
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"author_name": "hotemogirl",
"timestamp": "08/10/2022 16:47:29",
"content": "and ur y intercept is 3",
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"id": 1007027433628766200,
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"timestamp": "08/10/2022 16:47:29",
"content": "yes",
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"id": 1007027459545374800,
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"timestamp": "08/10/2022 16:47:36",
"content": "correct",
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"timestamp": "08/10/2022 16:47:38",
"content": "ohh ye i get it",
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"id": 1007027530118737900,
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"timestamp": "08/10/2022 16:47:52",
"content": "so when its like 3/1 u just write 3",
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"author_name": "hotemogirl",
"timestamp": "08/10/2022 16:48:06",
"content": "how do i know which one to put first the 1 or the 3, is it always up first bcs its rise",
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"id": 1007027657441018000,
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"timestamp": "08/10/2022 16:48:23",
"content": "it is always up first",
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"id": 1007027663166243000,
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"timestamp": "08/10/2022 16:48:24",
"content": "correct",
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"author_name": "hotemogirl",
"timestamp": "08/10/2022 16:49:23",
"content": "do u always have to put the x after the number",
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"id": 1007027914870624400,
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"timestamp": "08/10/2022 16:49:24",
"content": "like 3 x",
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"timestamp": "08/10/2022 16:49:25",
"content": "also you can take any segment of the line you want",
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"timestamp": "08/10/2022 16:49:30",
"content": "yes",
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"timestamp": "08/10/2022 16:49:42",
"content": "the formula is always y=gradient*x+intercept",
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"timestamp": "08/10/2022 16:50:05",
"content": "surely here u ran first then rise",
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"timestamp": "08/10/2022 16:50:27",
"content": "wdym?",
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"author_name": "hotemogirl",
"timestamp": "08/10/2022 16:50:28",
"content": "but do u always just go the one that goes up",
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"timestamp": "08/10/2022 16:50:36",
"content": "like here did u go down then run?",
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"timestamp": "08/10/2022 16:50:57",
"content": "didnt u work it out like u ran 2 steps positvie then 6 steps up",
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"timestamp": "08/10/2022 16:51:10",
"content": "the general idea is that you just draw a triangle and look at the sides\nthen divide the vertical line by the horizontal line",
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"timestamp": "08/10/2022 16:51:24",
"content": "ohh ok",
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"timestamp": "08/10/2022 16:52:00",
"content": "so you could just as well draw the triangle like this",
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"timestamp": "08/10/2022 16:52:10",
"content": "thats just a visual thing",
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"timestamp": "08/10/2022 16:52:21",
"content": "oh it doesnt matter where its drawn?",
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"timestamp": "08/10/2022 16:52:26",
"content": "in the end always do vertical/horizontal",
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"timestamp": "08/10/2022 16:52:30",
"content": "correct",
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"timestamp": "08/10/2022 16:52:41",
"content": "this is because the line has the same gradient at every point",
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"timestamp": "08/10/2022 16:52:44",
"content": "yo",
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"timestamp": "08/10/2022 16:52:47",
"content": "yo",
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"author_name": "Kira_",
"timestamp": "08/10/2022 16:52:57",
"content": "any help in thiss",
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"timestamp": "08/10/2022 16:53:03",
"content": "ima kms",
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"content": "@Kira_ pls get your own channel\nif you dont know how than you can look at #โhow-to-get-help",
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"timestamp": "08/10/2022 16:53:51",
"content": "dw lol",
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"content": "https://gyazo.com/41964770cf01f01765f5d243026f15f0",
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"timestamp": "08/10/2022 16:54:11",
"content": "this one goes down tho so its negative or what",
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"timestamp": "08/10/2022 16:54:24",
"content": "ah ok so",
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"timestamp": "08/10/2022 16:55:24",
"content": "yep",
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"timestamp": "08/10/2022 16:55:34",
"content": "but then it aint rise over run",
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"author_name": "hotemogirl",
"timestamp": "08/10/2022 16:55:40",
"content": "bcs it goes down?",
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"timestamp": "08/10/2022 16:55:46",
"content": "still is",
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"author_name": "hotemogirl",
"timestamp": "08/10/2022 16:55:47",
"content": "or do u start at the bottom",
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"id": 1007029726566691000,
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"author_name": "~Martin",
"timestamp": "08/10/2022 16:56:36",
"content": "you start at any point and generally always go to the right from there",
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"author_name": "~Martin",
"timestamp": "08/10/2022 16:56:54",
"content": "so in this case you start at (0,2) and go to (5,-1)",
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"timestamp": "08/10/2022 16:57:07",
"content": "so yo have a rise of -3 and a run of 5",
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"timestamp": "08/10/2022 16:57:14",
"content": "ohh",
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"timestamp": "08/10/2022 16:57:22",
"content": "so its still rise just negative rise",
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"id": 1007030064233324700,
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"timestamp": "08/10/2022 16:57:57",
"content": "yes",
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"author_name": "hotemogirl",
"timestamp": "08/10/2022 16:58:16",
"content": "https://gyazo.com/6e34d5868a21e89e06d58648112eaa7b",
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"timestamp": "08/10/2022 16:58:21",
"content": "surely if its always rise over run",
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"timestamp": "08/10/2022 16:58:33",
"content": "this would be 4/2 which is 2",
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"id": 1007030231934177300,
"author_id": 402114534552371200,
"author_name": "hotemogirl",
"timestamp": "08/10/2022 16:58:37",
"content": "not -2?",
"attachments": [],
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{
"id": 1007030515544621200,
"author_id": 244806629839732740,
"author_name": "~Martin",
"timestamp": "08/10/2022 16:59:44",
"content": "if we start at the top left of the triangle, we have a rise of -4 and a run of 2\nif we start at the bottem right of the triangle we have a run of -2 and a rise of 4",
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"author_name": "hotemogirl",
"timestamp": "08/10/2022 17:00:14",
"content": "ohh ye ye",
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"author_name": "hotemogirl",
"timestamp": "08/10/2022 17:00:23",
"content": "just threw me off bcs netiher of them said negative",
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"author_name": "hotemogirl",
"timestamp": "08/10/2022 17:02:18",
"content": "https://gyazo.com/d0dd38e980d78a14fe830ca39fffdf20",
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"author_name": "hotemogirl",
"timestamp": "08/10/2022 17:02:26",
"content": "in these are they trying to get to the center always?",
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"author_name": "hotemogirl",
"timestamp": "08/10/2022 17:03:07",
"content": "wait nvm",
"attachments": [],
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"author_name": "hotemogirl",
"timestamp": "08/10/2022 17:03:12",
"content": "do u have to start at the red line",
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"timestamp": "08/10/2022 17:03:36",
"content": "maybe this helps\nfor the gradient it doesnt really matter which way we go\nif we instead of going from A to B, we go from B to A, what happens is that the sign of the rise changes but so does the sign of the run\nso in total the sign of the gradient doesnt change",
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"timestamp": "08/10/2022 17:03:52",
"content": "ye thats what i thought",
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"timestamp": "08/10/2022 17:04:27",
"content": "bcs like for the first one you have to either go negative 4 down and then run 3 or plus 4 up then negative 3 run, its the same answer",
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"timestamp": "08/10/2022 17:05:52",
"content": "but like for those you have to start on the redline or is that a always",
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"timestamp": "08/10/2022 17:08:27",
"content": "you always start somewhere on the line, correct",
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"author_name": "hotemogirl",
"timestamp": "08/10/2022 17:08:49",
"content": "you explain stuff better than my teachers",
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{
"id": 1007032976275689600,
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"author_name": "~Martin",
"timestamp": "08/10/2022 17:09:31",
"content": "i doubt that",
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{
"id": 1007033011847565400,
"author_id": 244806629839732740,
"author_name": "~Martin",
"timestamp": "08/10/2022 17:09:39",
"content": "teachers usually cover a broader spectrum",
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"timestamp": "08/10/2022 17:09:50",
"content": "thats why you can easily get lost in all of that information",
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"timestamp": "08/10/2022 17:10:09",
"content": "ye ig that makes sense but this is better if u dont understand something",
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"timestamp": "08/10/2022 17:10:24",
"content": "ty tho",
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"timestamp": "08/10/2022 17:11:04",
"content": "np^^",
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"author_name": "hotemogirl",
"timestamp": "08/10/2022 17:12:57",
"content": ".close",
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},
{
"id": 1007033841225060400,
"author_id": 805217272087838700,
"author_name": "Mathematics Bot",
"timestamp": "08/10/2022 17:12:57",
"content": "Channel closed",
"attachments": [],
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}
] |
help-9
|
a1b87e44a0014e328adedc553e719e54
|
197,741 |
[
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"id": 1007033978898878500,
"author_id": 402114534552371200,
"author_name": "hotemogirl",
"timestamp": "08/10/2022 17:13:30",
"content": "isnt it 12g4h5",
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"author_name": "Mathematics Bot",
"timestamp": "08/10/2022 17:13:57",
"content": "Available help channel!",
"attachments": [],
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"reference": null
},
{
"id": 1007034432189890700,
"author_id": 402114534552371200,
"author_name": "hotemogirl",
"timestamp": "08/10/2022 17:15:18",
"content": "?",
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"timestamp": "08/10/2022 17:15:19",
"content": "Pinned a message.",
"attachments": [],
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"author_name": "hotemogirl",
"timestamp": "08/10/2022 17:16:16",
"content": "u can open a help channel on the available ones",
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"timestamp": "08/10/2022 17:16:17",
"content": ".close",
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},
{
"id": 1007034681339945000,
"author_id": 805217272087838700,
"author_name": "Mathematics Bot",
"timestamp": "08/10/2022 17:16:17",
"content": "Channel closed",
"attachments": [],
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"reference": null
}
] |
help-9
|
59d408eed82b49feb4be8a557d35711c
|
197,742 |
[
{
"id": 1007034805751386100,
"author_id": 402114534552371200,
"author_name": "hotemogirl",
"timestamp": "08/10/2022 17:16:47",
"content": "ill explain",
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"author_name": "hotemogirl",
"timestamp": "08/10/2022 17:16:49",
"content": "@nirajiswife",
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"id": 1007034904321732600,
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"author_name": "hotemogirl",
"timestamp": "08/10/2022 17:17:10",
"content": "so you got to take apart the sum bascially",
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{
"id": 1007034918259400700,
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"timestamp": "08/10/2022 17:17:14",
"content": "so numbers first",
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{
"id": 1007034926157279400,
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"author_name": "hotemogirl",
"timestamp": "08/10/2022 17:17:16",
"content": "3 x 4",
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{
"id": 1007034963201359900,
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"author_name": "hotemogirl",
"timestamp": "08/10/2022 17:17:25",
"content": "which is 12",
"attachments": [],
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},
{
"id": 1007035019014983700,
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"author_name": "hotemogirl",
"timestamp": "08/10/2022 17:17:38",
"content": "then the g's",
"attachments": [],
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{
"id": 1007035043857838200,
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"author_name": "hotemogirl",
"timestamp": "08/10/2022 17:17:44",
"content": "g x g3",
"attachments": [],
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},
{
"id": 1007035057136992500,
"author_id": 402114534552371200,
"author_name": "hotemogirl",
"timestamp": "08/10/2022 17:17:47",
"content": "is g4",
"attachments": [],
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},
{
"id": 1007035103270146200,
"author_id": 402114534552371200,
"author_name": "hotemogirl",
"timestamp": "08/10/2022 17:17:58",
"content": "g3 is bascially just g x g x g",
"attachments": [],
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{
"id": 1007035149411700900,
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"author_name": "hotemogirl",
"timestamp": "08/10/2022 17:18:09",
"content": "so times by another g will just make it 4",
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"timestamp": "08/10/2022 17:18:21",
"content": "i mean times",
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},
{
"id": 1007035301266456600,
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"author_name": "hotemogirl",
"timestamp": "08/10/2022 17:18:45",
"content": "do you understand it now",
"attachments": [],
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},
{
"id": 1007035430400704500,
"author_id": 402114534552371200,
"author_name": "hotemogirl",
"timestamp": "08/10/2022 17:19:16",
"content": "in a circle",
"attachments": [],
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},
{
"id": 1007035436004290600,
"author_id": 402114534552371200,
"author_name": "hotemogirl",
"timestamp": "08/10/2022 17:19:17",
"content": "?",
"attachments": [],
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},
{
"id": 1007035574332436500,
"author_id": 402114534552371200,
"author_name": "hotemogirl",
"timestamp": "08/10/2022 17:19:50",
"content": "is there like a question to answer",
"attachments": [],
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},
{
"id": 1007035714300551300,
"author_id": 402114534552371200,
"author_name": "hotemogirl",
"timestamp": "08/10/2022 17:20:24",
"content": "so work out the circumference?",
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{
"id": 1007035799939858400,
"author_id": 402114534552371200,
"author_name": "hotemogirl",
"timestamp": "08/10/2022 17:20:44",
"content": "what have they given us to help answer it",
"attachments": [],
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{
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"timestamp": "08/10/2022 17:21:16",
"content": "this is a diagram of a circle right",
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{
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"timestamp": "08/10/2022 17:21:17",
"content": "https://gyazo.com/6503a3c1435e5a8a6eb22379c9ad336d",
"attachments": [],
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},
{
"id": 1007035996120035300,
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"timestamp": "08/10/2022 17:21:31",
"content": "so circumference is the entire outer part",
"attachments": [],
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{
"id": 1007036098846924900,
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"timestamp": "08/10/2022 17:21:55",
"content": "so what did they give us?",
"attachments": [],
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"id": 1007036296683847800,
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"author_name": "hotemogirl",
"timestamp": "08/10/2022 17:22:42",
"content": "but then whats the question if they are giving us the raidius",
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"author_name": "~Martin",
"timestamp": "08/10/2022 17:23:35",
"content": "",
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"timestamp": "08/10/2022 17:24:16",
"content": "ohh mbb",
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"author_name": "hotemogirl",
"timestamp": "08/10/2022 17:24:40",
"content": "you have to do 2xPixRadius",
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"id": 1007036799316676600,
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"timestamp": "08/10/2022 17:24:42",
"content": "for the circumference you have c=2 pi r=2 d",
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"timestamp": "08/10/2022 17:24:42",
"content": "i think",
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"id": 1007036879620804700,
"author_id": 244806629839732740,
"author_name": "~Martin",
"timestamp": "08/10/2022 17:25:01",
"content": "so in your case\nc=2 * pi * 4",
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"author_id": 805217272087838700,
"author_name": "Mathematics Bot",
"timestamp": "08/10/2022 17:25:20",
"content": "Available help channel!",
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},
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"id": 1007037014849360000,
"author_id": 805217272087838700,
"author_name": "Mathematics Bot",
"timestamp": "08/10/2022 17:25:34",
"content": "Pinned a message.",
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"author_id": 402114534552371200,
"author_name": "hotemogirl",
"timestamp": "08/10/2022 17:25:41",
"content": "nah its fine",
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"id": 1007037137717317600,
"author_id": 402114534552371200,
"author_name": "hotemogirl",
"timestamp": "08/10/2022 17:26:03",
"content": "do you know Pi",
"attachments": [],
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"id": 1007037258647470300,
"author_id": 402114534552371200,
"author_name": "hotemogirl",
"timestamp": "08/10/2022 17:26:32",
"content": "So you have to do 2 x Pi x Radius",
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},
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"id": 1007037290163491000,
"author_id": 402114534552371200,
"author_name": "hotemogirl",
"timestamp": "08/10/2022 17:26:39",
"content": "for cirumference",
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"author_name": "hotemogirl",
"timestamp": "08/10/2022 17:27:12",
"content": "i just see it as a rule but it could be bcs you need 2 radiuses to span the whole circle",
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"author_name": "hotemogirl",
"timestamp": "08/10/2022 17:27:31",
"content": "https://gyazo.com/226c3da8a397be345bc8b1cd7eb37bce",
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"author_name": "hotemogirl",
"timestamp": "08/10/2022 17:28:02",
"content": "i think the right way is radius x Pi x 2 but either way works",
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"id": 1007037749628506100,
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"author_name": "hotemogirl",
"timestamp": "08/10/2022 17:28:29",
"content": "ye ill try",
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"id": 1007037954994221000,
"author_id": 402114534552371200,
"author_name": "hotemogirl",
"timestamp": "08/10/2022 17:29:18",
"content": "sorry could u send a picture of the question",
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{
"id": 1007038239397392400,
"author_id": 402114534552371200,
"author_name": "hotemogirl",
"timestamp": "08/10/2022 17:30:26",
"content": "have you learnt about canceling out",
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{
"id": 1007038344519241700,
"author_id": 402114534552371200,
"author_name": "hotemogirl",
"timestamp": "08/10/2022 17:30:51",
"content": "ok anyway",
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},
{
"id": 1007038350559019000,
"author_id": 402114534552371200,
"author_name": "hotemogirl",
"timestamp": "08/10/2022 17:30:52",
"content": "whats 9 divided by 3",
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"id": 1007038368749715500,
"author_id": 402114534552371200,
"author_name": "hotemogirl",
"timestamp": "08/10/2022 17:30:56",
"content": "the line is just divide",
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"id": 1007038532122058900,
"author_id": 402114534552371200,
"author_name": "hotemogirl",
"timestamp": "08/10/2022 17:31:35",
"content": "i cant really see how many A's there are but i think its 3a and 2a right",
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"id": 1007038670689280100,
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"author_name": "hotemogirl",
"timestamp": "08/10/2022 17:32:08",
"content": "so then with the 3 a you can cancel out the 2 a and have 1a left over at the top",
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"id": 1007038773651067000,
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"author_name": "hotemogirl",
"timestamp": "08/10/2022 17:32:33",
"content": "you have 3 a's at the top right",
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"id": 1007038870900195500,
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"author_name": "hotemogirl",
"timestamp": "08/10/2022 17:32:56",
"content": "so lets say they are having a fight for example",
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"id": 1007038920975990900,
"author_id": 402114534552371200,
"author_name": "hotemogirl",
"timestamp": "08/10/2022 17:33:08",
"content": "the 3 a's attack the 2'a's",
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},
{
"id": 1007038943981736100,
"author_id": 402114534552371200,
"author_name": "hotemogirl",
"timestamp": "08/10/2022 17:33:14",
"content": "and 1a gets left over right",
"attachments": [],
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"id": 1007038981243928700,
"author_id": 402114534552371200,
"author_name": "hotemogirl",
"timestamp": "08/10/2022 17:33:23",
"content": "so he stays at the top",
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},
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"id": 1007039009148645400,
"author_id": 402114534552371200,
"author_name": "hotemogirl",
"timestamp": "08/10/2022 17:33:29",
"content": "ye",
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},
{
"id": 1007039047870451700,
"author_id": 402114534552371200,
"author_name": "hotemogirl",
"timestamp": "08/10/2022 17:33:38",
"content": "so far we should have 3a at the top",
"attachments": [],
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},
{
"id": 1007039069311738000,
"author_id": 402114534552371200,
"author_name": "hotemogirl",
"timestamp": "08/10/2022 17:33:44",
"content": "then there is 1 b on both sides",
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},
{
"id": 1007039097828819000,
"author_id": 402114534552371200,
"author_name": "hotemogirl",
"timestamp": "08/10/2022 17:33:50",
"content": "which just cancel eachother out",
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},
{
"id": 1007039115134505100,
"author_id": 402114534552371200,
"author_name": "hotemogirl",
"timestamp": "08/10/2022 17:33:54",
"content": "so they fight and they both go out",
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},
{
"id": 1007039166242099300,
"author_id": 402114534552371200,
"author_name": "hotemogirl",
"timestamp": "08/10/2022 17:34:07",
"content": "yup",
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},
{
"id": 1007039204255084700,
"author_id": 402114534552371200,
"author_name": "hotemogirl",
"timestamp": "08/10/2022 17:34:16",
"content": "so the answer should be 3a",
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{
"id": 1007039224953974800,
"author_id": 402114534552371200,
"author_name": "hotemogirl",
"timestamp": "08/10/2022 17:34:21",
"content": "ye u dont have to write the 1",
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},
{
"id": 1007039302204674200,
"author_id": 402114534552371200,
"author_name": "hotemogirl",
"timestamp": "08/10/2022 17:34:39",
"content": "bcs 3 and 3 x 1 is the same answer",
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},
{
"id": 1007039405015453800,
"author_id": 402114534552371200,
"author_name": "hotemogirl",
"timestamp": "08/10/2022 17:35:04",
"content": "do you understand it",
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},
{
"id": 1007039570174546000,
"author_id": 402114534552371200,
"author_name": "hotemogirl",
"timestamp": "08/10/2022 17:35:43",
"content": "ok ill try otherwise there is people that are way better at explaining then me",
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},
{
"id": 1007039849011880000,
"author_id": 402114534552371200,
"author_name": "hotemogirl",
"timestamp": "08/10/2022 17:36:49",
"content": "so here they give us the diameter",
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},
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"id": 1007039881576448100,
"author_id": 402114534552371200,
"author_name": "hotemogirl",
"timestamp": "08/10/2022 17:36:57",
"content": "https://gyazo.com/226c3da8a397be345bc8b1cd7eb37bce",
"attachments": [],
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},
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"id": 1007039904896786400,
"author_id": 402114534552371200,
"author_name": "hotemogirl",
"timestamp": "08/10/2022 17:37:03",
"content": "you can look at this picture again",
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},
{
"id": 1007039952888016900,
"author_id": 402114534552371200,
"author_name": "hotemogirl",
"timestamp": "08/10/2022 17:37:14",
"content": "you basically take the diameter and x by Pi",
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},
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"id": 1007040124514730000,
"author_id": 402114534552371200,
"author_name": "hotemogirl",
"timestamp": "08/10/2022 17:37:55",
"content": "there is no radius this time they didnt give it to us",
"attachments": [],
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},
{
"id": 1007040172011040800,
"author_id": 402114534552371200,
"author_name": "hotemogirl",
"timestamp": "08/10/2022 17:38:06",
"content": "instead they gave the diameter which is basically 2 raidiuses",
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},
{
"id": 1007040256157175900,
"author_id": 402114534552371200,
"author_name": "hotemogirl",
"timestamp": "08/10/2022 17:38:26",
"content": "as you can see diameter spans over the whole circle while raidius only half",
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},
{
"id": 1007040327095431300,
"author_id": 402114534552371200,
"author_name": "hotemogirl",
"timestamp": "08/10/2022 17:38:43",
"content": "try diameter x pi",
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},
{
"id": 1007040461694844900,
"author_id": 402114534552371200,
"author_name": "hotemogirl",
"timestamp": "08/10/2022 17:39:15",
"content": "what does it say the answer is",
"attachments": [],
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},
{
"id": 1007040527381831700,
"author_id": 402114534552371200,
"author_name": "hotemogirl",
"timestamp": "08/10/2022 17:39:31",
"content": "its right",
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},
{
"id": 1007040554623828100,
"author_id": 402114534552371200,
"author_name": "hotemogirl",
"timestamp": "08/10/2022 17:39:38",
"content": "you just have to round of to 1 decimal place",
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},
{
"id": 1007040583564537900,
"author_id": 402114534552371200,
"author_name": "hotemogirl",
"timestamp": "08/10/2022 17:39:45",
"content": "so i think 28.3",
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},
{
"id": 1007040687633596500,
"author_id": 402114534552371200,
"author_name": "hotemogirl",
"timestamp": "08/10/2022 17:40:09",
"content": "dw just remember to read the question carefully",
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},
{
"id": 1007040859113525400,
"author_id": 402114534552371200,
"author_name": "hotemogirl",
"timestamp": "08/10/2022 17:40:50",
"content": "dw man",
"attachments": [],
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},
{
"id": 1007040989866758300,
"author_id": 402114534552371200,
"author_name": "hotemogirl",
"timestamp": "08/10/2022 17:41:21",
"content": "ye there is also way better people at explaining, i was just asking for help before u came",
"attachments": [],
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"reference": null
},
{
"id": 1007041143755771900,
"author_id": 402114534552371200,
"author_name": "hotemogirl",
"timestamp": "08/10/2022 17:41:58",
"content": "happy i could help",
"attachments": [],
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},
{
"id": 1007041226844934100,
"author_id": 402114534552371200,
"author_name": "hotemogirl",
"timestamp": "08/10/2022 17:42:18",
"content": "have a good one",
"attachments": [],
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},
{
"id": 1007041245685743600,
"author_id": 402114534552371200,
"author_name": "hotemogirl",
"timestamp": "08/10/2022 17:42:22",
"content": "remember to close it",
"attachments": [],
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},
{
"id": 1007041265944244400,
"author_id": 402114534552371200,
"author_name": "hotemogirl",
"timestamp": "08/10/2022 17:42:27",
"content": "by doing .close",
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},
{
"id": 1007041310563250300,
"author_id": 805217272087838700,
"author_name": "Mathematics Bot",
"timestamp": "08/10/2022 17:42:38",
"content": "Channel closed",
"attachments": [],
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"reference": null
}
] |
help-9
|
a7e3836494994abdb054391d55150fbc
|
197,743 |
[
{
"id": 1007041563924385800,
"author_id": 805217272087838700,
"author_name": "Mathematics Bot",
"timestamp": "08/10/2022 17:43:38",
"content": "Available help channel!",
"attachments": [],
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"reference": null
},
{
"id": 1007043244816859300,
"author_id": 448474477869924350,
"author_name": "dopamine",
"timestamp": "08/10/2022 17:50:19",
"content": "for net change theorem im confused about finding displacement",
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"reference": null
},
{
"id": 1007043246750449700,
"author_id": 805217272087838700,
"author_name": "Mathematics Bot",
"timestamp": "08/10/2022 17:50:19",
"content": "Pinned a message.",
"attachments": [],
"mentions": [],
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"messageId": 1007043244816859300,
"channelId": 486844875632017400,
"guildId": null
}
},
{
"id": 1007045808081883300,
"author_id": 261933205387477000,
"author_name": "riemann",
"timestamp": "08/10/2022 18:00:30",
"content": "show the whole original question",
"attachments": [],
"mentions": [
{
"id": 448474477869924350,
"name": "dopamine",
"discriminator": "9669",
"nickname": "dopamine",
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}
],
"reference": null
},
{
"id": 1007045893914099700,
"author_id": 448474477869924350,
"author_name": "dopamine",
"timestamp": "08/10/2022 18:00:51",
"content": "oh im not workin goff a q",
"attachments": [],
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"reference": null
},
{
"id": 1007045937060925400,
"author_id": 448474477869924350,
"author_name": "dopamine",
"timestamp": "08/10/2022 18:01:01",
"content": "im just wondering what the formula is",
"attachments": [],
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},
{
"id": 1007045954827980900,
"author_id": 448474477869924350,
"author_name": "dopamine",
"timestamp": "08/10/2022 18:01:05",
"content": "im just confused cause",
"attachments": [],
"mentions": [],
"reference": null
},
{
"id": 1007046015590863000,
"author_id": 261933205387477000,
"author_name": "riemann",
"timestamp": "08/10/2022 18:01:20",
"content": "then what's your question",
"attachments": [],
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"reference": null
},
{
"id": 1007046076903215100,
"author_id": 448474477869924350,
"author_name": "dopamine",
"timestamp": "08/10/2022 18:01:34",
"content": "velocity t is โซabย = F(b) - F(a) right",
"attachments": [],
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},
{
"id": 1007046106724696000,
"author_id": 448474477869924350,
"author_name": "dopamine",
"timestamp": "08/10/2022 18:01:41",
"content": "but then what is displacement",
"attachments": [],
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},
{
"id": 1007046145295523800,
"author_id": 448474477869924350,
"author_name": "dopamine",
"timestamp": "08/10/2022 18:01:51",
"content": "is it the same thing but you just take the absolute value?",
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},
{
"id": 1007046301369761900,
"author_id": 281105694013259780,
"author_name": "citrusmunch",
"timestamp": "08/10/2022 18:02:28",
"content": "just so we're on the same page <https://math.libretexts.org/Bookshelves/Calculus/Map%3A_Calculus__Early_Transcendentals_(Stewart)/05%3A_Integrals/5.04%3A_Indefinite_Integrals_and_the_Net_Change_Theorem>",
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},
{
"id": 1007046521281335400,
"author_id": 448474477869924350,
"author_name": "dopamine",
"timestamp": "08/10/2022 18:03:20",
"content": "oh sorry",
"attachments": [],
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},
{
"id": 1007046525559517200,
"author_id": 448474477869924350,
"author_name": "dopamine",
"timestamp": "08/10/2022 18:03:21",
"content": "i meant",
"attachments": [],
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},
{
"id": 1007046536007536600,
"author_id": 281105694013259780,
"author_name": "citrusmunch",
"timestamp": "08/10/2022 18:03:24",
"content": "so if you go out to groceries and come back home you're net displacement is zero",
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},
{
"id": 1007046539803373700,
"author_id": 448474477869924350,
"author_name": "dopamine",
"timestamp": "08/10/2022 18:03:25",
"content": "totaly displacement",
"attachments": [],
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},
{
"id": 1007046558686126100,
"author_id": 448474477869924350,
"author_name": "dopamine",
"timestamp": "08/10/2022 18:03:29",
"content": "distance *",
"attachments": [],
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"reference": null
},
{
"id": 1007046639527149800,
"author_id": 448474477869924350,
"author_name": "dopamine",
"timestamp": "08/10/2022 18:03:48",
"content": "",
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"timestamp": "08/10/2022 18:03:49",
"content": "this one",
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"author_name": "citrusmunch",
"timestamp": "08/10/2022 18:04:05",
"content": "ok sure, very related concepts",
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"timestamp": "08/10/2022 18:04:10",
"content": "and like you said it involves abs value",
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"author_name": "citrusmunch",
"timestamp": "08/10/2022 18:04:27",
"content": "are you confused about the language used, or how to compute these?",
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"author_name": "dopamine",
"timestamp": "08/10/2022 18:04:49",
"content": "how to compute",
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"timestamp": "08/10/2022 18:05:05",
"content": "|v(t)|=v(t).",
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"timestamp": "08/10/2022 18:05:17",
"content": "usually you have to know the function",
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"timestamp": "08/10/2022 18:05:24",
"content": "and take the cases for when it's positive or negative",
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"content": "in fact, abs value is a piecewise function anyway",
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"timestamp": "08/10/2022 18:07:19",
"content": "in this example its a and then b",
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"timestamp": "08/10/2022 18:07:32",
"content": "so when you integrate, it's a *signed* integral, meaning it keeps track of how much negative and how much positive there are",
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"timestamp": "08/10/2022 18:07:41",
"content": "but for total displacement we want to add that negative area",
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"timestamp": "08/10/2022 18:07:45",
"content": "instead of taking it away",
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"author_name": "citrusmunch",
"timestamp": "08/10/2022 18:08:00",
"content": "since we're discussing movement in different directions for these kind of questions",
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"timestamp": "08/10/2022 18:08:46",
"content": "but we don't want movement in opposite directions to cancel out, we still want to consider that movement\nlike doubling back when you walked the wrong way up a mountain lol you can't just forget that",
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"timestamp": "08/10/2022 18:09:38",
"content": "what did you mean by\n> a and then b",
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"timestamp": "08/10/2022 18:22:19",
"content": "@dopamine Has your question been resolved?",
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"timestamp": "08/10/2022 18:26:09",
"content": "Is it usually good to graph it",
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"timestamp": "08/10/2022 18:26:17",
"content": "And I understand why the first bound becomes positive",
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"timestamp": "08/10/2022 18:26:25",
"content": "Cause itโs in the negative part of the graph",
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"timestamp": "08/10/2022 18:37:19",
"content": "Channel closed",
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}
] |
help-9
|
0469a2a3a8be403984371e1f48588c7c
|
197,744 |
[
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"author_id": 805217272087838700,
"author_name": "Mathematics Bot",
"timestamp": "08/10/2022 18:38:20",
"content": "Available help channel!",
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},
{
"id": 1007059116075778000,
"author_id": 759245748751171600,
"author_name": "crescentshrey",
"timestamp": "08/10/2022 18:53:23",
"content": "what is this eq for?",
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"content": "Pinned a message.",
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"author_name": "Toby",
"timestamp": "08/10/2022 18:54:51",
"content": "looks like a first degree taylor polynomial in two variables",
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"id": 1007059569916248000,
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"timestamp": "08/10/2022 18:55:11",
"content": "ie, a linear approximation to f",
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"timestamp": "08/10/2022 18:55:36",
"content": "In other words, the plane that best fits a curve, at some point (x0, y0)",
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"timestamp": "08/10/2022 18:57:28",
"content": "ok cool thanks",
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"timestamp": "08/10/2022 18:57:31",
"content": ".close",
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},
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"content": "Channel closed",
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}
] |
help-9
|
127225cdeb4b4867b678a85245f471cd
|
197,745 |
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"timestamp": "08/10/2022 19:07:45",
"content": "Stuck on this one",
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"id": 1007063973784469500,
"author_id": 251788903730642940,
"author_name": "hello2248",
"timestamp": "08/10/2022 19:12:41",
"content": "What's the area you want to integrate over?",
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"content": "Aka write the bounds of the integrals",
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"author_id": 251788903730642940,
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"timestamp": "08/10/2022 19:13:49",
"content": "Or is it the actual integrating that you're stuck on",
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"content": "Im stuck on what should the bounds be",
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"id": 1007065533738406000,
"author_id": 531535537362829300,
"author_name": "Eric Tao",
"timestamp": "08/10/2022 19:18:53",
"content": "okay so you're stuck on how to describe the triangle?",
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"id": 1007065573013856300,
"author_id": 531535537362829300,
"author_name": "Eric Tao",
"timestamp": "08/10/2022 19:19:02",
"content": "what does x range from in the triangle",
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"id": 1007065581381492900,
"author_id": 531535537362829300,
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"timestamp": "08/10/2022 19:19:04",
"content": "what to what",
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"timestamp": "08/10/2022 19:22:09",
"content": "0 to 4?",
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"timestamp": "08/10/2022 19:26:31",
"content": "@Eric Tao",
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"timestamp": "08/10/2022 19:26:57",
"content": "yup! and then what does y range from",
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"timestamp": "08/10/2022 19:26:59",
"content": "in terms of x",
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"author_name": "Eric Tao",
"timestamp": "08/10/2022 19:27:09",
"content": "hint: rearrange x+y=a to y=a-x",
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"timestamp": "08/10/2022 19:28:50",
"content": "4-x, SQRT(-x^2 + 16)",
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"author_name": "Eric Tao",
"timestamp": "08/10/2022 19:29:40",
"content": "we're only focused on y right now",
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"id": 1007068259159384000,
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"author_name": "Eric Tao",
"timestamp": "08/10/2022 19:29:43",
"content": "we will think about z later",
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"author_name": "Eric Tao",
"timestamp": "08/10/2022 19:29:53",
"content": "right now all that is relevant is the triangle on the xy-plane",
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"timestamp": "08/10/2022 19:29:56",
"content": "do you get what I mean",
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"author_name": "Eric Tao",
"timestamp": "08/10/2022 19:30:16",
"content": "so don't worry about z = x^2 + y^2 yet",
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"timestamp": "08/10/2022 19:30:19",
"content": "y = 4 - x, SQRT(-y^2 + 16)",
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"timestamp": "08/10/2022 19:30:34",
"content": "no",
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"author_name": "Eric Tao",
"timestamp": "08/10/2022 19:30:39",
"content": "where are you getting the sqrt(-y^2 + 16) from",
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"timestamp": "08/10/2022 19:30:47",
"content": "Oh sorry",
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"timestamp": "08/10/2022 19:30:53",
"content": "what is the smallest that y can be",
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"content": "y = SQRT(z - x^2)",
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"content": "0",
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"timestamp": "08/10/2022 19:31:37",
"content": "yup",
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"timestamp": "08/10/2022 19:31:41",
"content": "and then what is the largest that y can be",
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"timestamp": "08/10/2022 19:31:42",
"content": "in terms of x",
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"content": "4",
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"timestamp": "08/10/2022 19:31:57",
"content": "in general yes, but let's say I just give you a specific x",
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"content": "like x = 2 for example",
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"author_name": "Eric Tao",
"timestamp": "08/10/2022 19:32:10",
"content": "how would you figure out the largest value for y",
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"timestamp": "08/10/2022 19:32:41",
"content": "Plug it into the equation",
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"timestamp": "08/10/2022 19:33:37",
"content": "which equation",
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"content": "x + y = 4",
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"timestamp": "08/10/2022 19:34:02",
"content": "yep",
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"content": "so what is the biggest y can be",
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"timestamp": "08/10/2022 19:34:11",
"content": "in terms of x",
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"content": "2",
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"timestamp": "08/10/2022 19:34:20",
"content": "yep, so there you did 4 - 2 right",
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"author_name": "Eric Tao",
"timestamp": "08/10/2022 19:34:25",
"content": "what is it in general for some arbitrary x",
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"author_name": "kunalch",
"timestamp": "08/10/2022 19:34:35",
"content": "y = 4-x",
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},
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"id": 1007069653056634900,
"author_id": 531535537362829300,
"author_name": "Eric Tao",
"timestamp": "08/10/2022 19:35:15",
"content": "yep!",
"attachments": [],
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},
{
"id": 1007069681473032300,
"author_id": 531535537362829300,
"author_name": "Eric Tao",
"timestamp": "08/10/2022 19:35:22",
"content": "so what are the bounds on the integrals",
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},
{
"id": 1007069953536561200,
"author_id": 652747647521914900,
"author_name": "kunalch",
"timestamp": "08/10/2022 19:36:27",
"content": "0, 4 , 4-x, SQRT(z - x^2)",
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"id": 1007070414171803800,
"author_id": 531535537362829300,
"author_name": "Eric Tao",
"timestamp": "08/10/2022 19:38:17",
"content": "well",
"attachments": [],
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},
{
"id": 1007070433008435200,
"author_id": 531535537362829300,
"author_name": "Eric Tao",
"timestamp": "08/10/2022 19:38:21",
"content": "x ranges from 0 to 4 that's correct",
"attachments": [],
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},
{
"id": 1007070449898889300,
"author_id": 531535537362829300,
"author_name": "Eric Tao",
"timestamp": "08/10/2022 19:38:25",
"content": "but what did we say y ranges from",
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},
{
"id": 1007070462565687300,
"author_id": 531535537362829300,
"author_name": "Eric Tao",
"timestamp": "08/10/2022 19:38:28",
"content": "what is the minimum and maximum",
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},
{
"id": 1007070539451486300,
"author_id": 652747647521914900,
"author_name": "kunalch",
"timestamp": "08/10/2022 19:38:47",
"content": "0, 2",
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},
{
"id": 1007070749493838000,
"author_id": 531535537362829300,
"author_name": "Eric Tao",
"timestamp": "08/10/2022 19:39:37",
"content": "no I mean in terms of x",
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},
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"id": 1007070843467210900,
"author_id": 652747647521914900,
"author_name": "kunalch",
"timestamp": "08/10/2022 19:39:59",
"content": "4 - x",
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},
{
"id": 1007071027886559200,
"author_id": 531535537362829300,
"author_name": "Eric Tao",
"timestamp": "08/10/2022 19:40:43",
"content": "yep",
"attachments": [],
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},
{
"id": 1007071039450267600,
"author_id": 531535537362829300,
"author_name": "Eric Tao",
"timestamp": "08/10/2022 19:40:46",
"content": "so the minimum is what",
"attachments": [],
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},
{
"id": 1007071052985286800,
"author_id": 531535537362829300,
"author_name": "Eric Tao",
"timestamp": "08/10/2022 19:40:49",
"content": "and the maximum is what",
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},
{
"id": 1007071146916720800,
"author_id": 652747647521914900,
"author_name": "kunalch",
"timestamp": "08/10/2022 19:41:11",
"content": "min = 4 -x",
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},
{
"id": 1007071520977334300,
"author_id": 652747647521914900,
"author_name": "kunalch",
"timestamp": "08/10/2022 19:42:41",
"content": "max = x^2 + y^2",
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},
{
"id": 1007071634164814000,
"author_id": 652747647521914900,
"author_name": "kunalch",
"timestamp": "08/10/2022 19:43:08",
"content": "Im not sure for max hmm",
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},
{
"id": 1007071674803441800,
"author_id": 531535537362829300,
"author_name": "Eric Tao",
"timestamp": "08/10/2022 19:43:17",
"content": "no",
"attachments": [],
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},
{
"id": 1007071712858357900,
"author_id": 531535537362829300,
"author_name": "Eric Tao",
"timestamp": "08/10/2022 19:43:26",
"content": "what is the lowest y can be",
"attachments": [],
"mentions": [],
"reference": null
},
{
"id": 1007071724673695700,
"author_id": 531535537362829300,
"author_name": "Eric Tao",
"timestamp": "08/10/2022 19:43:29",
"content": "for any given x",
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},
{
"id": 1007071737923522600,
"author_id": 652747647521914900,
"author_name": "kunalch",
"timestamp": "08/10/2022 19:43:32",
"content": "0",
"attachments": [],
"mentions": [],
"reference": null
},
{
"id": 1007071828688244700,
"author_id": 652747647521914900,
"author_name": "kunalch",
"timestamp": "08/10/2022 19:43:54",
"content": "Equation or number?",
"attachments": [],
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},
{
"id": 1007071879510622200,
"author_id": 652747647521914900,
"author_name": "kunalch",
"timestamp": "08/10/2022 19:44:06",
"content": "min = 4 -x this should be good right?",
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},
{
"id": 1007072063623811100,
"author_id": 531535537362829300,
"author_name": "Eric Tao",
"timestamp": "08/10/2022 19:44:50",
"content": "okay I think you're confused",
"attachments": [],
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},
{
"id": 1007072076500320300,
"author_id": 531535537362829300,
"author_name": "Eric Tao",
"timestamp": "08/10/2022 19:44:53",
"content": "lemme just draw a picture",
"attachments": [],
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"reference": null
},
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"id": 1007072335259504600,
"author_id": 531535537362829300,
"author_name": "Eric Tao",
"timestamp": "08/10/2022 19:45:55",
"content": "",
"attachments": [
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"url": "https://cdn.discordapp.com/attachments/486844875632017408/1007072334571647022/IMG_20220810_194554_688.jpg",
"fileName": "IMG_20220810_194554_688.jpg",
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},
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"id": 1007072383288483800,
"author_id": 531535537362829300,
"author_name": "Eric Tao",
"timestamp": "08/10/2022 19:46:06",
"content": "do you see how the green region is bounded by a line below and a line above",
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},
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"id": 1007072402884276400,
"author_id": 652747647521914900,
"author_name": "kunalch",
"timestamp": "08/10/2022 19:46:11",
"content": "ye",
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},
{
"id": 1007072534786744400,
"author_id": 531535537362829300,
"author_name": "Eric Tao",
"timestamp": "08/10/2022 19:46:42",
"content": "okay",
"attachments": [],
"mentions": [],
"reference": null
},
{
"id": 1007072555057819800,
"author_id": 531535537362829300,
"author_name": "Eric Tao",
"timestamp": "08/10/2022 19:46:47",
"content": "what is the equation of the line it's bounded below by",
"attachments": [],
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"reference": null
},
{
"id": 1007072564637606000,
"author_id": 531535537362829300,
"author_name": "Eric Tao",
"timestamp": "08/10/2022 19:46:49",
"content": "y = what",
"attachments": [],
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},
{
"id": 1007072581091852300,
"author_id": 652747647521914900,
"author_name": "kunalch",
"timestamp": "08/10/2022 19:46:53",
"content": "4 -x",
"attachments": [],
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"reference": null
},
{
"id": 1007072711039791200,
"author_id": 531535537362829300,
"author_name": "Eric Tao",
"timestamp": "08/10/2022 19:47:24",
"content": "no",
"attachments": [],
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},
{
"id": 1007072750738870300,
"author_id": 531535537362829300,
"author_name": "Eric Tao",
"timestamp": "08/10/2022 19:47:34",
"content": "I mean the equation of the line that's on the bottom of the green region",
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"reference": null
},
{
"id": 1007072817407340500,
"author_id": 652747647521914900,
"author_name": "kunalch",
"timestamp": "08/10/2022 19:47:50",
"content": "y = 0",
"attachments": [],
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},
{
"id": 1007072960533778600,
"author_id": 531535537362829300,
"author_name": "Eric Tao",
"timestamp": "08/10/2022 19:48:24",
"content": "yep!",
"attachments": [],
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"reference": null
},
{
"id": 1007072987754791000,
"author_id": 531535537362829300,
"author_name": "Eric Tao",
"timestamp": "08/10/2022 19:48:30",
"content": "and then what's the equation of the line that's on the top of the green region",
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},
{
"id": 1007073028498260100,
"author_id": 652747647521914900,
"author_name": "kunalch",
"timestamp": "08/10/2022 19:48:40",
"content": "y = 4-x",
"attachments": [],
"mentions": [],
"reference": null
},
{
"id": 1007073044956713100,
"author_id": 531535537362829300,
"author_name": "Eric Tao",
"timestamp": "08/10/2022 19:48:44",
"content": "yep",
"attachments": [],
"mentions": [],
"reference": null
},
{
"id": 1007073050698731600,
"author_id": 531535537362829300,
"author_name": "Eric Tao",
"timestamp": "08/10/2022 19:48:45",
"content": "exactly",
"attachments": [],
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},
{
"id": 1007073063029985400,
"author_id": 531535537362829300,
"author_name": "Eric Tao",
"timestamp": "08/10/2022 19:48:48",
"content": "so what are the bounds on y",
"attachments": [],
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"reference": null
},
{
"id": 1007073086669062300,
"author_id": 652747647521914900,
"author_name": "kunalch",
"timestamp": "08/10/2022 19:48:54",
"content": "Max - 4 - x",
"attachments": [],
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},
{
"id": 1007073106076123300,
"author_id": 652747647521914900,
"author_name": "kunalch",
"timestamp": "08/10/2022 19:48:59",
"content": "min - 0",
"attachments": [],
"mentions": [],
"reference": null
},
{
"id": 1007073114120794200,
"author_id": 531535537362829300,
"author_name": "Eric Tao",
"timestamp": "08/10/2022 19:49:00",
"content": "yes!!!!",
"attachments": [],
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},
{
"id": 1007073126577885200,
"author_id": 531535537362829300,
"author_name": "Eric Tao",
"timestamp": "08/10/2022 19:49:03",
"content": "okay awesome",
"attachments": [],
"mentions": [],
"reference": null
},
{
"id": 1007073143837438100,
"author_id": 531535537362829300,
"author_name": "Eric Tao",
"timestamp": "08/10/2022 19:49:08",
"content": "now do you understand how to write the integral",
"attachments": [],
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},
{
"id": 1007073172962689200,
"author_id": 652747647521914900,
"author_name": "kunalch",
"timestamp": "08/10/2022 19:49:14",
"content": "Let check with you",
"attachments": [],
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"reference": null
},
{
"id": 1007073182307586000,
"author_id": 531535537362829300,
"author_name": "Eric Tao",
"timestamp": "08/10/2022 19:49:17",
"content": "kk",
"attachments": [],
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"reference": null
},
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"id": 1007073418660806700,
"author_id": 652747647521914900,
"author_name": "kunalch",
"timestamp": "08/10/2022 19:50:13",
"content": "",
"attachments": [
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"url": "https://cdn.discordapp.com/attachments/486844875632017408/1007073418040070164/unknown.png",
"fileName": "unknown.png",
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"id": 1007073511828893700,
"author_id": 652747647521914900,
"author_name": "kunalch",
"timestamp": "08/10/2022 19:50:35",
"content": "is that correct so far",
"attachments": [],
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},
{
"id": 1007073612030816400,
"author_id": 531535537362829300,
"author_name": "Eric Tao",
"timestamp": "08/10/2022 19:50:59",
"content": "4-x",
"attachments": [],
"mentions": [],
"reference": null
},
{
"id": 1007073619672834000,
"author_id": 531535537362829300,
"author_name": "Eric Tao",
"timestamp": "08/10/2022 19:51:01",
"content": "not x-4",
"attachments": [],
"mentions": [],
"reference": null
},
{
"id": 1007073634952687600,
"author_id": 531535537362829300,
"author_name": "Eric Tao",
"timestamp": "08/10/2022 19:51:05",
"content": "but otherwise yes!",
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},
{
"id": 1007073819229438100,
"author_id": 652747647521914900,
"author_name": "kunalch",
"timestamp": "08/10/2022 19:51:49",
"content": "Ok",
"attachments": [],
"mentions": [],
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},
{
"id": 1007073898321432700,
"author_id": 652747647521914900,
"author_name": "kunalch",
"timestamp": "08/10/2022 19:52:07",
"content": "I got the wrong answer",
"attachments": [],
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"reference": null
},
{
"id": 1007073903048400900,
"author_id": 652747647521914900,
"author_name": "kunalch",
"timestamp": "08/10/2022 19:52:09",
"content": "https://www.symbolab.com/solver/step-by-step/%5Cint_%7B0%7D%5E%7B4%7D%5Cint_%7B0%7D%5E%7B4-%20x%7Ddydx%20?or=input",
"attachments": [],
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},
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"id": 1007073960552304800,
"author_id": 652747647521914900,
"author_name": "kunalch",
"timestamp": "08/10/2022 19:52:22",
"content": "",
"attachments": [
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"url": "https://cdn.discordapp.com/attachments/486844875632017408/1007073959579234384/unknown.png",
"fileName": "unknown.png",
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"id": 1007074020312744000,
"author_id": 531535537362829300,
"author_name": "Eric Tao",
"timestamp": "08/10/2022 19:52:36",
"content": "you have to insert the function you are integrating too",
"attachments": [],
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},
{
"id": 1007074046522970100,
"author_id": 531535537362829300,
"author_name": "Eric Tao",
"timestamp": "08/10/2022 19:52:43",
"content": "what function are you integrating here?",
"attachments": [],
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},
{
"id": 1007074125199708300,
"author_id": 652747647521914900,
"author_name": "kunalch",
"timestamp": "08/10/2022 19:53:01",
"content": "x^2 + y^2",
"attachments": [],
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"reference": null
},
{
"id": 1007074150743035900,
"author_id": 531535537362829300,
"author_name": "Eric Tao",
"timestamp": "08/10/2022 19:53:08",
"content": "yep!",
"attachments": [],
"mentions": [],
"reference": null
},
{
"id": 1007074317969936400,
"author_id": 652747647521914900,
"author_name": "kunalch",
"timestamp": "08/10/2022 19:53:47",
"content": "Ok ur the best",
"attachments": [],
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"reference": null
},
{
"id": 1007074352073801900,
"author_id": 652747647521914900,
"author_name": "kunalch",
"timestamp": "08/10/2022 19:53:56",
"content": "thx!",
"attachments": [],
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"reference": null
},
{
"id": 1007074382012743800,
"author_id": 531535537362829300,
"author_name": "Eric Tao",
"timestamp": "08/10/2022 19:54:03",
"content": "no problem!",
"attachments": [],
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},
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"id": 1007074435888582800,
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"author_name": "kunalch",
"timestamp": "08/10/2022 19:54:16",
"content": "",
"attachments": [
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"id": 1007074545863229400,
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"author_name": "kunalch",
"timestamp": "08/10/2022 19:54:42",
"content": "For this one I got the intercepts as z = 5, x = 5, y =2.5",
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},
{
"id": 1007074655057752200,
"author_id": 652747647521914900,
"author_name": "kunalch",
"timestamp": "08/10/2022 19:55:08",
"content": "Then how can I use integration here",
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},
{
"id": 1007074795608883300,
"author_id": 531535537362829300,
"author_name": "Eric Tao",
"timestamp": "08/10/2022 19:55:41",
"content": "first draw what it looks like if you project it onto the xy axis",
"attachments": [],
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},
{
"id": 1007076774838026200,
"author_id": 652747647521914900,
"author_name": "kunalch",
"timestamp": "08/10/2022 20:03:33",
"content": "Ok",
"attachments": [],
"mentions": [],
"reference": null
},
{
"id": 1007076912604123300,
"author_id": 652747647521914900,
"author_name": "kunalch",
"timestamp": "08/10/2022 20:04:06",
"content": "What should I use to graph",
"attachments": [],
"mentions": [],
"reference": null
},
{
"id": 1007076926671822800,
"author_id": 652747647521914900,
"author_name": "kunalch",
"timestamp": "08/10/2022 20:04:09",
"content": "any recs",
"attachments": [],
"mentions": [],
"reference": null
},
{
"id": 1007077010213970000,
"author_id": 531535537362829300,
"author_name": "Eric Tao",
"timestamp": "08/10/2022 20:04:29",
"content": "pencil and paper",
"attachments": [],
"mentions": [],
"reference": null
},
{
"id": 1007078107871727600,
"author_id": 652747647521914900,
"author_name": "kunalch",
"timestamp": "08/10/2022 20:08:51",
"content": "The 3D function?",
"attachments": [],
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},
{
"id": 1007078129845665800,
"author_id": 652747647521914900,
"author_name": "kunalch",
"timestamp": "08/10/2022 20:08:56",
"content": "That might be hard right",
"attachments": [],
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"reference": null
},
{
"id": 1007078297231962200,
"author_id": 531535537362829300,
"author_name": "Eric Tao",
"timestamp": "08/10/2022 20:09:36",
"content": "it is a good exercise for you",
"attachments": [],
"mentions": [],
"reference": null
},
{
"id": 1007078327481282600,
"author_id": 531535537362829300,
"author_name": "Eric Tao",
"timestamp": "08/10/2022 20:09:43",
"content": "you should learn how to visualize these functions",
"attachments": [],
"mentions": [],
"reference": null
},
{
"id": 1007078499305140200,
"author_id": 531535537362829300,
"author_name": "Eric Tao",
"timestamp": "08/10/2022 20:10:24",
"content": "it doesn't have to be perfect or anything, it just needs to be good enough so you can imagine what it looks like in your head",
"attachments": [],
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"reference": null
},
{
"id": 1007079493355196500,
"author_id": 652747647521914900,
"author_name": "kunalch",
"timestamp": "08/10/2022 20:14:21",
"content": "ok",
"attachments": [],
"mentions": [],
"reference": null
},
{
"id": 1007082498875985900,
"author_id": 652747647521914900,
"author_name": "kunalch",
"timestamp": "08/10/2022 20:26:18",
"content": "got it",
"attachments": [],
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},
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"id": 1007082509210767400,
"author_id": 652747647521914900,
"author_name": "kunalch",
"timestamp": "08/10/2022 20:26:20",
"content": "then what",
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},
{
"id": 1007082820096766000,
"author_id": 652747647521914900,
"author_name": "kunalch",
"timestamp": "08/10/2022 20:27:35",
"content": "How do I set up the integral, im a little lost",
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},
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"id": 1007082962514350200,
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"author_name": "Eric Tao",
"timestamp": "08/10/2022 20:28:08",
"content": "okay what does it look like if you project it onto the xy axis",
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"timestamp": "08/10/2022 20:42:35",
"content": "@kunalch Has your question been resolved?",
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"timestamp": "08/10/2022 20:57:35",
"content": "Channel closed",
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}
] |
help-9
|
86269e481af24be491f0ed294beb4f98
|
197,746 |
[
{
"id": 1007094947134058600,
"author_id": 652747647521914900,
"author_name": "kunalch",
"timestamp": "08/10/2022 21:15:46",
"content": ".reopen",
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},
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"id": 1007094953765261400,
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"author_name": "Mathematics Bot",
"timestamp": "08/10/2022 21:15:47",
"content": "โ
",
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},
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"id": 1007096354096545900,
"author_id": 652747647521914900,
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"content": "Like a rectangle shape",
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"timestamp": "08/10/2022 21:21:55",
"content": "not quite",
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},
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"id": 1007096535525372000,
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"author_name": "Eric Tao",
"timestamp": "08/10/2022 21:22:05",
"content": "can you show me your drawing",
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},
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"content": "@kunalch Has your question been resolved?",
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"timestamp": "08/10/2022 21:51:22",
"content": "Channel closed",
"attachments": [],
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}
] |
help-9
|
99a3d5f6c3b84c3faca0b3861ea580db
|
197,747 |
[
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"author_id": 805217272087838700,
"author_name": "Mathematics Bot",
"timestamp": "08/10/2022 22:44:42",
"content": "Available help channel!",
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},
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"id": 1007120132604170400,
"author_id": 908079803574411300,
"author_name": "DaKing",
"timestamp": "08/10/2022 22:55:51",
"content": "triangle symbol is delta",
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"author_name": "DaKing",
"timestamp": "08/10/2022 22:56:12",
"content": "srry bot boi",
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},
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"id": 1007120454399578100,
"author_id": 209300311091838980,
"author_name": "Peacemaker II",
"timestamp": "08/10/2022 22:57:07",
"content": "triangle symbol is a function",
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"timestamp": "08/10/2022 22:57:14",
"content": "oh",
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"id": 1007120493201084400,
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"timestamp": "08/10/2022 22:57:16",
"content": "shit",
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"timestamp": "08/10/2022 22:57:22",
"content": "f(a, b)",
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"id": 1007120590471180300,
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"author_name": "DaKing",
"timestamp": "08/10/2022 22:57:40",
"content": "i still dk tho",
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"author_id": 209300311091838980,
"author_name": "Peacemaker II",
"timestamp": "08/10/2022 22:57:46",
"content": "not sure what is the difference between f(a, b) and \"a [symbol] b\" actually",
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"id": 1007120621941039200,
"author_id": 841679117350994000,
"author_name": "Not Trout",
"timestamp": "08/10/2022 22:57:47",
"content": "treat triangle symbol",
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},
{
"id": 1007120626235998200,
"author_id": 841679117350994000,
"author_name": "Not Trout",
"timestamp": "08/10/2022 22:57:48",
"content": "like",
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},
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"id": 1007120650672033800,
"author_id": 841679117350994000,
"author_name": "Not Trout",
"timestamp": "08/10/2022 22:57:54",
"content": "something like addition",
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{
"id": 1007120657009606700,
"author_id": 841679117350994000,
"author_name": "Not Trout",
"timestamp": "08/10/2022 22:57:56",
"content": "so let's say",
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{
"id": 1007120662361559000,
"author_id": 841679117350994000,
"author_name": "Not Trout",
"timestamp": "08/10/2022 22:57:57",
"content": "a + b",
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},
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"id": 1007120674659246200,
"author_id": 841679117350994000,
"author_name": "Not Trout",
"timestamp": "08/10/2022 22:58:00",
"content": "adds each other",
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},
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"id": 1007120684977234000,
"author_id": 841679117350994000,
"author_name": "Not Trout",
"timestamp": "08/10/2022 22:58:02",
"content": "similarly",
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{
"id": 1007120715717288000,
"author_id": 841679117350994000,
"author_name": "Not Trout",
"timestamp": "08/10/2022 22:58:10",
"content": "$a \\triangle b = a^2 + ab - b^2$",
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},
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"id": 1007120738307817600,
"author_id": 841679117350994000,
"author_name": "Not Trout",
"timestamp": "08/10/2022 22:58:15",
"content": "so you plug in the value of `a` and `b`",
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},
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"id": 1007120762878050400,
"author_id": 510789298321096700,
"author_name": "TeXit",
"timestamp": "08/10/2022 22:58:21",
"content": "**Not Trout -\\_-**",
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"author_id": 908079803574411300,
"author_name": "DaKing",
"timestamp": "08/10/2022 22:58:33",
"content": "ok ok",
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"author_id": 209300311091838980,
"author_name": "Peacemaker II",
"timestamp": "08/10/2022 22:58:38",
"content": "@Not Trout do you know why they didn't just write f(a,b)?",
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"timestamp": "08/10/2022 22:59:18",
"content": "no clue but its easier to understand i guess",
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"author_name": "Not Trout",
"timestamp": "08/10/2022 22:59:24",
"content": "f(a, b) is like multivariable function or something idk",
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"id": 1007121034719281200,
"author_id": 841679117350994000,
"author_name": "Not Trout",
"timestamp": "08/10/2022 22:59:26",
"content": "๐ญ",
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},
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"id": 1007121102490841200,
"author_id": 841679117350994000,
"author_name": "Not Trout",
"timestamp": "08/10/2022 22:59:42",
"content": "in this context i guess theyh aev a similar definition",
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"author_id": 908079803574411300,
"author_name": "DaKing",
"timestamp": "08/10/2022 22:59:42",
"content": "yea trye",
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{
"id": 1007121142936506500,
"author_id": 209300311091838980,
"author_name": "Peacemaker II",
"timestamp": "08/10/2022 22:59:51",
"content": "I mean it's literally the same thing I think (unless I'm mistaken)\nf(a,b) is just a function with 2 inputs",
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"id": 1007121178646810600,
"author_id": 841679117350994000,
"author_name": "Not Trout",
"timestamp": "08/10/2022 23:00:00",
"content": "but there might be a bunch of implications with the functions compared to using it as operations i guess",
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"id": 1007121209986658400,
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"timestamp": "08/10/2022 23:00:07",
"content": "maybe",
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},
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"id": 1007123080474263700,
"author_id": 908079803574411300,
"author_name": "DaKing",
"timestamp": "08/10/2022 23:07:33",
"content": "@Helpers",
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},
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"author_name": "DaKing",
"timestamp": "08/10/2022 23:12:56",
"content": "@Peacemaker II",
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"timestamp": "08/10/2022 23:13:08",
"content": "@Not Trout",
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"author_id": 841679117350994000,
"author_name": "Not Trout",
"timestamp": "08/10/2022 23:13:19",
"content": "?",
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"id": 1007124560539295700,
"author_id": 908079803574411300,
"author_name": "DaKing",
"timestamp": "08/10/2022 23:13:26",
"content": "help again",
"attachments": [],
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},
{
"id": 1007124778026533000,
"author_id": 710970577556340900,
"author_name": "theworstbesttourist_20",
"timestamp": "08/10/2022 23:14:18",
"content": "If you think of a triangle b as the function a^2 + ab - b^2 , where a is the first number in the phrase and b is the second number, then this is just the expression a^2 + ab - b^2 evaluated more than once",
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"id": 1007124827955531800,
"author_id": 710970577556340900,
"author_name": "theworstbesttourist_20",
"timestamp": "08/10/2022 23:14:30",
"content": "Start with 3 triangle 2",
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},
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"id": 1007124872113160200,
"author_id": 710970577556340900,
"author_name": "theworstbesttourist_20",
"timestamp": "08/10/2022 23:14:40",
"content": "Which number is a, and which number is b?",
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"id": 1007125029483446300,
"author_id": 908079803574411300,
"author_name": "DaKing",
"timestamp": "08/10/2022 23:15:18",
"content": "theyre just variables",
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},
{
"id": 1007125162799398900,
"author_id": 710970577556340900,
"author_name": "theworstbesttourist_20",
"timestamp": "08/10/2022 23:15:50",
"content": "Yes, plug them into a^2 + ab - b^2",
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},
{
"id": 1007125283817660400,
"author_id": 710970577556340900,
"author_name": "theworstbesttourist_20",
"timestamp": "08/10/2022 23:16:19",
"content": "Evaluate for whatever number that is, then do it again with (that result) triangle 13",
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},
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"id": 1007125461249310700,
"author_id": 908079803574411300,
"author_name": "DaKing",
"timestamp": "08/10/2022 23:17:01",
"content": "its one",
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"id": 1007125520812609500,
"author_id": 908079803574411300,
"author_name": "DaKing",
"timestamp": "08/10/2022 23:17:15",
"content": "what now",
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},
{
"id": 1007125912837431300,
"author_id": 710970577556340900,
"author_name": "theworstbesttourist_20",
"timestamp": "08/10/2022 23:18:49",
"content": "It's not one",
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},
{
"id": 1007126042542088200,
"author_id": 710970577556340900,
"author_name": "theworstbesttourist_20",
"timestamp": "08/10/2022 23:19:20",
"content": "Which number is equal to a in whatever this expression is?",
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},
{
"id": 1007126049877921800,
"author_id": 908079803574411300,
"author_name": "DaKing",
"timestamp": "08/10/2022 23:19:21",
"content": "how",
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},
{
"id": 1007126166626369500,
"author_id": 908079803574411300,
"author_name": "DaKing",
"timestamp": "08/10/2022 23:19:49",
"content": "it is one \\",
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},
{
"id": 1007126189552443400,
"author_id": 908079803574411300,
"author_name": "DaKing",
"timestamp": "08/10/2022 23:19:55",
"content": "it dont matter",
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},
{
"id": 1007126340132143100,
"author_id": 908079803574411300,
"author_name": "DaKing",
"timestamp": "08/10/2022 23:20:30",
"content": "4+6-9=1\\\\",
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},
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"id": 1007126500467818600,
"author_id": 710970577556340900,
"author_name": "theworstbesttourist_20",
"timestamp": "08/10/2022 23:21:09",
"content": "Your a and b are swapped",
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},
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"id": 1007126515210780700,
"author_id": 908079803574411300,
"author_name": "DaKing",
"timestamp": "08/10/2022 23:21:12",
"content": "OH",
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},
{
"id": 1007126580688064600,
"author_id": 908079803574411300,
"author_name": "DaKing",
"timestamp": "08/10/2022 23:21:28",
"content": "11",
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},
{
"id": 1007126674216865800,
"author_id": 710970577556340900,
"author_name": "theworstbesttourist_20",
"timestamp": "08/10/2022 23:21:50",
"content": "Now you can do 11 ๐บ 13",
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},
{
"id": 1007126978337448000,
"author_id": 908079803574411300,
"author_name": "DaKing",
"timestamp": "08/10/2022 23:23:03",
"content": "95?",
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},
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"id": 1007127062915588100,
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"author_name": "theworstbesttourist_20",
"timestamp": "08/10/2022 23:23:23",
"content": "Eyyy you got it",
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},
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"id": 1007127139017044100,
"author_id": 908079803574411300,
"author_name": "DaKing",
"timestamp": "08/10/2022 23:23:41",
"content": "thx",
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},
{
"id": 1007127156255637500,
"author_id": 908079803574411300,
"author_name": "DaKing",
"timestamp": "08/10/2022 23:23:45",
"content": ".close",
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},
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"id": 1007127158596063200,
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"author_name": "Mathematics Bot",
"timestamp": "08/10/2022 23:23:46",
"content": "Channel closed",
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}
] |
help-9
|
8ca9600f2ffa4451b6d4d15491cb78f6
|
197,748 |
[
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"timestamp": "04/02/2022 03:42:50",
"content": "Available help channel!",
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"content": "Pinned a message.",
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}
] |
help-9
|
de04da07c95244ae9388cbe096dc1e24
|
197,749 |
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"author_id": 710970577556340900,
"author_name": "theworstbesttourist_20",
"timestamp": "08/10/2022 23:24:37",
"content": "@Helpers is there a rule for people making irrelevant comments and then deleting?",
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"timestamp": "08/10/2022 23:24:43",
"content": "Like \"Nerds\", @ Fate?#2152 has done that like 4 times in this question alone",
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] |
help-9
|
50ef072741954cab88c1e6717a7b5c19
|
197,750 |
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"content": "Available help channel!",
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"content": "I've got that $\\sum\\limits_{n=1}^{4} \\frac{(-1)^{n+1}}{n} = \\frac{7}{12}$\n\nand $\\sum\\limits_{n=1}^{5} \\frac{(-1)^{n+1}}{n} = \\frac{47}{60} $\n\nAnd that, by the alternating series test, $\\sum\\limits_{n=1}^{\\infty} \\frac{(-1)^{n+1}}{n}$ converges. However, I'm not sure what it converges to and if that will uphold my inequality. \n\nThanks in advance!",
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"content": "**TallKoala**",
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"content": "@TallKoala Has your question been resolved?",
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"content": "@Helpers",
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"author_id": 261933205387477000,
"author_name": "riemann",
"timestamp": "08/11/2022 00:32:01",
"content": "use taylor's remainder theorem",
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"author_name": "TallKoala",
"timestamp": "08/11/2022 00:37:20",
"content": "Would that qualify as \"grouping\"?",
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"timestamp": "08/11/2022 00:37:53",
"content": "you did the grouping here already",
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"timestamp": "08/11/2022 00:38:33",
"content": "oh ok, I thought I needed to also show that the sum is in the middle by grouping, which i didn't understand how to do.",
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"content": "@TallKoala Has your question been resolved?",
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"timestamp": "08/11/2022 01:10:11",
"content": "I think I managed to do the whole thing by grouping",
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"timestamp": "08/11/2022 01:10:14",
"content": "Does this look good?",
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"timestamp": "08/11/2022 01:18:45",
"content": ".close",
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] |
help-9
|
6dbc8490bf6a43c092ec1f4553dbed69
|
197,751 |
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"timestamp": "08/11/2022 01:19:45",
"content": "Available help channel!",
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"id": 1007159775475286100,
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"author_id": 623494823093207000,
"author_name": "muppetman",
"timestamp": "08/11/2022 01:33:28",
"content": "I dont know how to do this",
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"id": 1007160031189418100,
"author_id": 623494823093207000,
"author_name": "muppetman",
"timestamp": "08/11/2022 01:34:23",
"content": "i know i can get answer if i put it in form (x-x0)^2+(y-y0)^2=r^2",
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"id": 1007160059303825500,
"author_id": 623494823093207000,
"author_name": "muppetman",
"timestamp": "08/11/2022 01:34:30",
"content": "but i dont know how to get to that point",
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"id": 1007160064286675000,
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"author_name": "Gooaaa",
"timestamp": "08/11/2022 01:34:31",
"content": "Yes",
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"author_name": "muppetman",
"timestamp": "08/11/2022 01:34:54",
"content": "is taht really you",
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"id": 1007160200354091000,
"author_id": 623494823093207000,
"author_name": "muppetman",
"timestamp": "08/11/2022 01:35:03",
"content": "how are u so ripped",
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},
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"id": 1007160455380348900,
"author_id": 485164773647056900,
"author_name": "Gooaaa",
"timestamp": "08/11/2022 01:36:04",
"content": "Lots of math",
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"id": 1007161215916716200,
"author_id": 485164773647056900,
"author_name": "Gooaaa",
"timestamp": "08/11/2022 01:39:06",
"content": "((sqrt(3)x-2sqrt(3))^2= 3x^2-12x+12",
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"id": 1007161654833848300,
"author_id": 623494823093207000,
"author_name": "muppetman",
"timestamp": "08/11/2022 01:40:50",
"content": "?",
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"id": 1007161666791805000,
"author_id": 623494823093207000,
"author_name": "muppetman",
"timestamp": "08/11/2022 01:40:53",
"content": "where is the y",
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"timestamp": "08/11/2022 01:55:53",
"content": "@muppetman Has your question been resolved?",
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"author_name": "Gooaaa",
"timestamp": "08/11/2022 01:58:47",
"content": "Do that yourself haha",
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"author_id": 485164773647056900,
"author_name": "Gooaaa",
"timestamp": "08/11/2022 01:58:50",
"content": "Same way",
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"author_name": "muppetman",
"timestamp": "08/11/2022 01:59:36",
"content": "@Helpers",
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"author_name": "muppetman",
"timestamp": "08/11/2022 01:59:52",
"content": "what do you mean same way",
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"timestamp": "08/11/2022 02:00:18",
"content": "",
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"timestamp": "08/11/2022 02:00:28",
"content": "need help solving this",
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},
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"id": 1007166667677237400,
"author_id": 623494823093207000,
"author_name": "muppetman",
"timestamp": "08/11/2022 02:00:45",
"content": "how do i put in form (x-h)^2+(y-k)^2=r^2",
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"id": 1007173118097371100,
"author_id": 623494823093207000,
"author_name": "muppetman",
"timestamp": "08/11/2022 02:26:23",
"content": "@Helpers",
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},
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"id": 1007173225341538300,
"author_id": 209300311091838980,
"author_name": "Peacemaker II",
"timestamp": "08/11/2022 02:26:49",
"content": "complete the square?",
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"author_name": "muppetman",
"timestamp": "08/11/2022 02:29:36",
"content": "how?",
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"id": 1007173990604873900,
"author_id": 623494823093207000,
"author_name": "muppetman",
"timestamp": "08/11/2022 02:29:51",
"content": "how do i convert the form",
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"id": 1007178076003778700,
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"author_name": "riemann",
"timestamp": "08/11/2022 02:46:05",
"content": "factor first",
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"author_name": "wideputin",
"timestamp": "08/11/2022 02:52:02",
"content": "3x^2 can be expressed (root3x)^2 then you can divide -12x by 2root3 x to see what the constant is to complete the square and then do the same with y",
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"timestamp": "08/11/2022 03:02:02",
"content": "@muppetman Has your question been resolved?",
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"content": "Channel closed",
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] |
help-9
|
188e794383a44d018351fa452276d7d4
|
197,752 |
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"timestamp": "08/11/2022 03:33:03",
"content": "Available help channel!",
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"id": 1007193221484523500,
"author_id": 897732241516531700,
"author_name": "mc768",
"timestamp": "08/11/2022 03:46:16",
"content": "how to do this",
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"content": "Pinned a message.",
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"author_id": 897732241516531700,
"author_name": "mc768",
"timestamp": "08/11/2022 03:46:52",
"content": "i try to square (x-y^2) but it doesnt solve the problem",
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"id": 1007193477911691400,
"author_id": 704179090395103200,
"author_name": "Saccharine",
"timestamp": "08/11/2022 03:47:17",
"content": "perhaps if you write y^2 = x-4",
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"id": 1007193502842630100,
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"author_name": "Saccharine",
"timestamp": "08/11/2022 03:47:23",
"content": "and then plug that into the second equation",
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"id": 1007193523436650500,
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"author_name": "Saccharine",
"timestamp": "08/11/2022 03:47:28",
"content": "to get x^2 + (x-4)^2 = 15",
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"author_name": "Saccharine",
"timestamp": "08/11/2022 03:47:30",
"content": "does that help?",
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"author_name": "mc768",
"timestamp": "08/11/2022 03:47:36",
"content": "i will try",
"attachments": [],
"mentions": [],
"reference": null
},
{
"id": 1007194275018182700,
"author_id": 897732241516531700,
"author_name": "mc768",
"timestamp": "08/11/2022 03:50:27",
"content": "uh i think it doesnt help",
"attachments": [],
"mentions": [],
"reference": null
},
{
"id": 1007194316508246000,
"author_id": 704179090395103200,
"author_name": "Saccharine",
"timestamp": "08/11/2022 03:50:37",
"content": "what part are you stuck on now?",
"attachments": [],
"mentions": [],
"reference": null
},
{
"id": 1007194437501337600,
"author_id": 897732241516531700,
"author_name": "mc768",
"timestamp": "08/11/2022 03:51:06",
"content": "if i sub (x-4)^2 the result will be 4-sqrt14/2 and 4+sqrt14/2",
"attachments": [],
"mentions": [],
"reference": null
},
{
"id": 1007194555185102800,
"author_id": 704179090395103200,
"author_name": "Saccharine",
"timestamp": "08/11/2022 03:51:34",
"content": ",w solve x^2 + (x-4)^2 = 15",
"attachments": [],
"mentions": [],
"reference": null
},
{
"id": 1007194566983680000,
"author_id": 510789298321096700,
"author_name": "TeXit",
"timestamp": "08/11/2022 03:51:37",
"content": "Results provided by WolframAlpha",
"attachments": [],
"mentions": [],
"reference": null
},
{
"id": 1007194721908703200,
"author_id": 704179090395103200,
"author_name": "Saccharine",
"timestamp": "08/11/2022 03:52:14",
"content": "hm sure that gives you some values for x",
"attachments": [],
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"reference": null
},
{
"id": 1007194743861682300,
"author_id": 704179090395103200,
"author_name": "Saccharine",
"timestamp": "08/11/2022 03:52:19",
"content": "then you can solve for y, right?",
"attachments": [],
"mentions": [],
"reference": null
},
{
"id": 1007194783539798000,
"author_id": 704179090395103200,
"author_name": "Saccharine",
"timestamp": "08/11/2022 03:52:29",
"content": "though I'm sure there are a few issues with the roots",
"attachments": [],
"mentions": [],
"reference": null
},
{
"id": 1007195041405616100,
"author_id": 897732241516531700,
"author_name": "mc768",
"timestamp": "08/11/2022 03:53:30",
"content": "same",
"attachments": [],
"mentions": [],
"reference": null
},
{
"id": 1007195059852148900,
"author_id": 897732241516531700,
"author_name": "mc768",
"timestamp": "08/11/2022 03:53:35",
"content": "x=y2+4",
"attachments": [],
"mentions": [],
"reference": null
},
{
"id": 1007195098896924800,
"author_id": 897732241516531700,
"author_name": "mc768",
"timestamp": "08/11/2022 03:53:44",
"content": "y4+y4+8y2+16=15",
"attachments": [],
"mentions": [],
"reference": null
},
{
"id": 1007195138784763900,
"author_id": 897732241516531700,
"author_name": "mc768",
"timestamp": "08/11/2022 03:53:53",
"content": "and 2y2 (y2+4)=-1",
"attachments": [],
"mentions": [],
"reference": null
},
{
"id": 1007195244170858500,
"author_id": 897732241516531700,
"author_name": "mc768",
"timestamp": "08/11/2022 03:54:18",
"content": "wait i will give the full picture",
"attachments": [],
"mentions": [],
"reference": null
},
{
"id": 1007195375196717000,
"author_id": 897732241516531700,
"author_name": "mc768",
"timestamp": "08/11/2022 03:54:50",
"content": "nvm i can solve it my own",
"attachments": [],
"mentions": [],
"reference": null
},
{
"id": 1007195390002614300,
"author_id": 897732241516531700,
"author_name": "mc768",
"timestamp": "08/11/2022 03:54:53",
"content": ".close",
"attachments": [],
"mentions": [],
"reference": null
},
{
"id": 1007195391449632900,
"author_id": 805217272087838700,
"author_name": "Mathematics Bot",
"timestamp": "08/11/2022 03:54:54",
"content": "Channel closed",
"attachments": [],
"mentions": [],
"reference": null
}
] |
help-9
|
69d5317534e247e8bbfe376d9d1ebc35
|
197,753 |
[
{
"id": 1007195749525766100,
"author_id": 805217272087838700,
"author_name": "Mathematics Bot",
"timestamp": "08/11/2022 03:56:19",
"content": "Available help channel!",
"attachments": [],
"mentions": [],
"reference": null
},
{
"id": 1007206376763818100,
"author_id": 922907687237341200,
"author_name": "SpicebagKing",
"timestamp": "08/11/2022 04:38:33",
"content": "hello",
"attachments": [],
"mentions": [],
"reference": null
},
{
"id": 1007206379070705700,
"author_id": 805217272087838700,
"author_name": "Mathematics Bot",
"timestamp": "08/11/2022 04:38:33",
"content": "Pinned a message.",
"attachments": [],
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"reference": {
"messageId": 1007206376763818100,
"channelId": 486844875632017400,
"guildId": null
}
},
{
"id": 1007206400587481100,
"author_id": 922907687237341200,
"author_name": "SpicebagKing",
"timestamp": "08/11/2022 04:38:38",
"content": "i need help",
"attachments": [],
"mentions": [],
"reference": null
},
{
"id": 1007206448826171400,
"author_id": 922907687237341200,
"author_name": "SpicebagKing",
"timestamp": "08/11/2022 04:38:50",
"content": "",
"attachments": [
{
"id": 1007206447408492700,
"url": "https://cdn.discordapp.com/attachments/486844875632017408/1007206447408492616/IMG_1983.jpg",
"fileName": "IMG_1983.jpg",
"fileSizeBytes": 1275047
}
],
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},
{
"id": 1007206544540180600,
"author_id": 922907687237341200,
"author_name": "SpicebagKing",
"timestamp": "08/11/2022 04:39:13",
"content": "q20 - 31",
"attachments": [],
"mentions": [],
"reference": null
},
{
"id": 1007206571085930500,
"author_id": 922907687237341200,
"author_name": "SpicebagKing",
"timestamp": "08/11/2022 04:39:19",
"content": "then q34",
"attachments": [],
"mentions": [],
"reference": null
},
{
"id": 1007206672822968300,
"author_id": 922907687237341200,
"author_name": "SpicebagKing",
"timestamp": "08/11/2022 04:39:43",
"content": "algabraic fractions",
"attachments": [],
"mentions": [],
"reference": null
},
{
"id": 1007206972598276100,
"author_id": 922907687237341200,
"author_name": "SpicebagKing",
"timestamp": "08/11/2022 04:40:55",
"content": "@Helpers",
"attachments": [],
"mentions": [],
"reference": null
},
{
"id": 1007209263971696600,
"author_id": 922907687237341200,
"author_name": "SpicebagKing",
"timestamp": "08/11/2022 04:50:01",
"content": "close",
"attachments": [],
"mentions": [],
"reference": null
},
{
"id": 1007209276269408300,
"author_id": 922907687237341200,
"author_name": "SpicebagKing",
"timestamp": "08/11/2022 04:50:04",
"content": ".clode",
"attachments": [],
"mentions": [],
"reference": null
},
{
"id": 1007209289355624600,
"author_id": 922907687237341200,
"author_name": "SpicebagKing",
"timestamp": "08/11/2022 04:50:07",
"content": ".close",
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"mentions": [],
"reference": null
},
{
"id": 1007209291171766300,
"author_id": 805217272087838700,
"author_name": "Mathematics Bot",
"timestamp": "08/11/2022 04:50:08",
"content": "Channel closed",
"attachments": [],
"mentions": [],
"reference": null
}
] |
help-9
|
8d8f65b9977a440c8fe48368b04f2c74
|
197,754 |
[
{
"id": 1007209544105082900,
"author_id": 805217272087838700,
"author_name": "Mathematics Bot",
"timestamp": "08/11/2022 04:51:08",
"content": "Available help channel!",
"attachments": [],
"mentions": [],
"reference": null
},
{
"id": 1007219075782557700,
"author_id": 656180648297627600,
"author_name": "karo",
"timestamp": "08/11/2022 05:29:00",
"content": "6x โก 15y mod 12 is true only when 2x โก y mod 4.\n\nCould someone maybe explain? I kind of see a correlation but I'm not sure. I thought it might have something to do with shortening but I think I might be wrong.",
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},
{
"id": 1007219078286544900,
"author_id": 805217272087838700,
"author_name": "Mathematics Bot",
"timestamp": "08/11/2022 05:29:01",
"content": "Pinned a message.",
"attachments": [],
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"messageId": 1007219075782557700,
"channelId": 486844875632017400,
"guildId": null
}
},
{
"id": 1007219906317647900,
"author_id": 656180648297627600,
"author_name": "karo",
"timestamp": "08/11/2022 05:32:18",
"content": "I think 6x โก 15y mod 12 shortened is 2x โก 5y mod 2, so it's not exactly the second congruence.",
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},
{
"id": 1007220010432864400,
"author_id": 533543009774731260,
"author_name": "2 3 5 7",
"timestamp": "08/11/2022 05:32:43",
"content": "I don't think thats how it works",
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"reference": null
},
{
"id": 1007220084110020700,
"author_id": 656180648297627600,
"author_name": "karo",
"timestamp": "08/11/2022 05:33:01",
"content": "Could you elaborate maybe",
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},
{
"id": 1007220224174587900,
"author_id": 533543009774731260,
"author_name": "2 3 5 7",
"timestamp": "08/11/2022 05:33:34",
"content": "How did you get mod 2 in the end ?",
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"reference": null
},
{
"id": 1007220331691397100,
"author_id": 533543009774731260,
"author_name": "2 3 5 7",
"timestamp": "08/11/2022 05:34:00",
"content": "It should be mod 4",
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"reference": null
},
{
"id": 1007220431016706200,
"author_id": 656180648297627600,
"author_name": "karo",
"timestamp": "08/11/2022 05:34:24",
"content": "Not sure what it's called in English but I divided it by finding the biggest common divider of 6 and 12 which is 2",
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},
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"id": 1007220566119415900,
"author_id": 656180648297627600,
"author_name": "karo",
"timestamp": "08/11/2022 05:34:56",
"content": "oh wait",
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},
{
"id": 1007220589808857200,
"author_id": 533543009774731260,
"author_name": "2 3 5 7",
"timestamp": "08/11/2022 05:35:01",
"content": "But that's not a factor of 15",
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},
{
"id": 1007220620360159400,
"author_id": 656180648297627600,
"author_name": "karo",
"timestamp": "08/11/2022 05:35:09",
"content": "I think you're right, I'm gonna look again",
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},
{
"id": 1007220835012067300,
"author_id": 533543009774731260,
"author_name": "2 3 5 7",
"timestamp": "08/11/2022 05:36:00",
"content": "2x = 5y in mod 4",
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},
{
"id": 1007220924182954000,
"author_id": 656180648297627600,
"author_name": "karo",
"timestamp": "08/11/2022 05:36:21",
"content": "it's mod 4 because you can divide 6 and 15 by 3 and the biggest divider of 12 and 3 is 3",
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},
{
"id": 1007220945938821100,
"author_id": 656180648297627600,
"author_name": "karo",
"timestamp": "08/11/2022 05:36:26",
"content": "but then there's still the 5y",
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"reference": null
},
{
"id": 1007220964825764000,
"author_id": 533543009774731260,
"author_name": "2 3 5 7",
"timestamp": "08/11/2022 05:36:31",
"content": "Yes",
"attachments": [],
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},
{
"id": 1007220974632063100,
"author_id": 656180648297627600,
"author_name": "karo",
"timestamp": "08/11/2022 05:36:33",
"content": "in the second conogruence there is only y",
"attachments": [],
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},
{
"id": 1007221044513361900,
"author_id": 533543009774731260,
"author_name": "2 3 5 7",
"timestamp": "08/11/2022 05:36:50",
"content": "Hint : you can write 5y as : \nY + 4Y",
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},
{
"id": 1007221319785525400,
"author_id": 656180648297627600,
"author_name": "karo",
"timestamp": "08/11/2022 05:37:55",
"content": "ohhh wait so the 4y is redundant because it can be divided by 4 right",
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"reference": null
},
{
"id": 1007221719179722800,
"author_id": 533543009774731260,
"author_name": "2 3 5 7",
"timestamp": "08/11/2022 05:39:31",
"content": "Yes",
"attachments": [],
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"reference": null
},
{
"id": 1007221929469542500,
"author_id": 656180648297627600,
"author_name": "karo",
"timestamp": "08/11/2022 05:40:21",
"content": "ohhhhh",
"attachments": [],
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"reference": null
},
{
"id": 1007221942882938900,
"author_id": 656180648297627600,
"author_name": "karo",
"timestamp": "08/11/2022 05:40:24",
"content": "ok thank you :)",
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"reference": null
},
{
"id": 1007221967692251300,
"author_id": 656180648297627600,
"author_name": "karo",
"timestamp": "08/11/2022 05:40:30",
"content": ".close",
"attachments": [],
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},
{
"id": 1007221969479020500,
"author_id": 805217272087838700,
"author_name": "Mathematics Bot",
"timestamp": "08/11/2022 05:40:30",
"content": "Channel closed",
"attachments": [],
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"reference": null
}
] |
help-9
|
f55beedb97c6471a9c72174aa05f7ac0
|
197,755 |
[
{
"id": 1007222222374568000,
"author_id": 805217272087838700,
"author_name": "Mathematics Bot",
"timestamp": "08/11/2022 05:41:31",
"content": "Available help channel!",
"attachments": [],
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"reference": null
},
{
"id": 1007233379818807300,
"author_id": 729392148377501700,
"author_name": "S.Bolt",
"timestamp": "08/11/2022 06:25:51",
"content": "",
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"id": 1007233381714641000,
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"author_name": "Mathematics Bot",
"timestamp": "08/11/2022 06:25:51",
"content": "Pinned a message.",
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{
"id": 1007234926929785000,
"author_id": 764959481070616600,
"author_name": "Toby",
"timestamp": "08/11/2022 06:32:00",
"content": "hint: cot^-1(x) is less than 1 when x> 1/tan(1)",
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},
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"id": 1007237155598377100,
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"author_name": "Mathematics Bot",
"timestamp": "08/11/2022 06:40:51",
"content": "@S.Bolt Has your question been resolved?",
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"timestamp": "08/11/2022 06:55:51",
"content": "Channel closed",
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}
] |
help-9
|
b58b22afe909415cab91a55f09feacb6
|
197,756 |
[
{
"id": 1007241184013451300,
"author_id": 805217272087838700,
"author_name": "Mathematics Bot",
"timestamp": "08/11/2022 06:56:51",
"content": "Available help channel!",
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"reference": null
},
{
"id": 1007247716847460500,
"author_id": 759245748751171600,
"author_name": "crescentshrey",
"timestamp": "08/11/2022 07:22:49",
"content": "",
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"content": "Pinned a message.",
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{
"id": 1007247748162130000,
"author_id": 759245748751171600,
"author_name": "crescentshrey",
"timestamp": "08/11/2022 07:22:56",
"content": "how would i set up my integral to begin with",
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},
{
"id": 1007247909999349900,
"author_id": 759245748751171600,
"author_name": "crescentshrey",
"timestamp": "08/11/2022 07:23:35",
"content": "for the integrand i would say \nr^3 d z d r d theta",
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},
{
"id": 1007248304016457700,
"author_id": 759245748751171600,
"author_name": "crescentshrey",
"timestamp": "08/11/2022 07:25:09",
"content": "i assume cylindrical is the best coordinate system to use",
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},
{
"id": 1007248744363872400,
"author_id": 183668144404037630,
"author_name": "Ann",
"timestamp": "08/11/2022 07:26:54",
"content": "spherical is better",
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},
{
"id": 1007248827515945000,
"author_id": 759245748751171600,
"author_name": "crescentshrey",
"timestamp": "08/11/2022 07:27:14",
"content": "oh wow",
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},
{
"id": 1007249085004255400,
"author_id": 759245748751171600,
"author_name": "crescentshrey",
"timestamp": "08/11/2022 07:28:15",
"content": "would the limits be\n0 to 2pi for phi and theta\nrho is 2 to 5?",
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},
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"id": 1007252861274558500,
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"timestamp": "08/11/2022 07:43:15",
"content": "@crescentshrey Has your question been resolved?",
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{
"id": 1007253016992293000,
"author_id": 521464336284254200,
"author_name": "Gamer Dio",
"timestamp": "08/11/2022 07:43:53",
"content": "ฯ and ฮธ isn't both 0 to 2ฯ",
"attachments": [],
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},
{
"id": 1007255461441060900,
"author_id": 759245748751171600,
"author_name": "crescentshrey",
"timestamp": "08/11/2022 07:53:35",
"content": "why? i thought this would be over all 8 octants",
"attachments": [],
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"id": 1007255621999014000,
"author_id": 521464336284254200,
"author_name": "Gamer Dio",
"timestamp": "08/11/2022 07:54:14",
"content": "Consider just varying ฯ. If ฯ goes from 0 to 2ฯ, that draws out a disc, right?",
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},
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"id": 1007255683760148500,
"author_id": 759245748751171600,
"author_name": "crescentshrey",
"timestamp": "08/11/2022 07:54:28",
"content": "yeah",
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},
{
"id": 1007255934097162400,
"author_id": 521464336284254200,
"author_name": "Gamer Dio",
"timestamp": "08/11/2022 07:55:28",
"content": "Now consider varying ฮธ. This will rotate the disc, yes? This'll take some visualization, but do you see that you don't need to rotate a full 360 for that disc to trace out a sphere?",
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},
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"id": 1007256559186882600,
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"author_name": "crescentshrey",
"timestamp": "08/11/2022 07:57:57",
"content": "oh yeah theta should be half",
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},
{
"id": 1007256761473958000,
"author_id": 759245748751171600,
"author_name": "crescentshrey",
"timestamp": "08/11/2022 07:58:45",
"content": "it could be even a quarter",
"attachments": [],
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"reference": null
},
{
"id": 1007256788028117100,
"author_id": 759245748751171600,
"author_name": "crescentshrey",
"timestamp": "08/11/2022 07:58:52",
"content": "0 to pi/2 for theta",
"attachments": [],
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},
{
"id": 1007256879438778400,
"author_id": 521464336284254200,
"author_name": "Gamer Dio",
"timestamp": "08/11/2022 07:59:13",
"content": "No, it's gotta be 0 to ฯ to trace a full sphere",
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},
{
"id": 1007256937760559100,
"author_id": 759245748751171600,
"author_name": "crescentshrey",
"timestamp": "08/11/2022 07:59:27",
"content": "no yeah its pi i will be missing out on two octants",
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},
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"id": 1007257007352459300,
"author_id": 759245748751171600,
"author_name": "crescentshrey",
"timestamp": "08/11/2022 07:59:44",
"content": "ok thanks I get it",
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},
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"author_id": 759245748751171600,
"author_name": "crescentshrey",
"timestamp": "08/11/2022 08:00:24",
"content": ".close",
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},
{
"id": 1007257177020453000,
"author_id": 805217272087838700,
"author_name": "Mathematics Bot",
"timestamp": "08/11/2022 08:00:24",
"content": "Channel closed",
"attachments": [],
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}
] |
help-9
|
274676dccf344afe9421fef1e8ad613e
|
197,757 |
[
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"id": 1007267453639864400,
"author_id": 805217272087838700,
"author_name": "Mathematics Bot",
"timestamp": "08/11/2022 08:41:15",
"content": "Available help channel!",
"attachments": [],
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"reference": null
},
{
"id": 1007275127777530100,
"author_id": 640436986624344000,
"author_name": "ahhhhhh",
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"content": "",
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"id": 1007275129958563800,
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"timestamp": "08/11/2022 09:11:45",
"content": "Pinned a message.",
"attachments": [],
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"messageId": 1007275127777530100,
"channelId": 486844875632017400,
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"id": 1007275199596597400,
"author_id": 640436986624344000,
"author_name": "ahhhhhh",
"timestamp": "08/11/2022 09:12:01",
"content": "I'm a bit confused by this question",
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},
{
"id": 1007275644759056400,
"author_id": 700275680226705400,
"author_name": "Fibdg",
"timestamp": "08/11/2022 09:13:47",
"content": "Do you know what tangent means?",
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},
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"id": 1007275745451712600,
"author_id": 640436986624344000,
"author_name": "ahhhhhh",
"timestamp": "08/11/2022 09:14:11",
"content": "in terms of a circle graph not really",
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},
{
"id": 1007275814821306500,
"author_id": 700275680226705400,
"author_name": "Fibdg",
"timestamp": "08/11/2022 09:14:28",
"content": "Ok, so tangent means that the line and the circle share one point",
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},
{
"id": 1007275855283757200,
"author_id": 700275680226705400,
"author_name": "Fibdg",
"timestamp": "08/11/2022 09:14:38",
"content": "The line barely touches the circle basically",
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},
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"id": 1007275892449493100,
"author_id": 640436986624344000,
"author_name": "ahhhhhh",
"timestamp": "08/11/2022 09:14:47",
"content": "ah",
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},
{
"id": 1007275913509085300,
"author_id": 640436986624344000,
"author_name": "ahhhhhh",
"timestamp": "08/11/2022 09:14:52",
"content": "i see",
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},
{
"id": 1007276017473290200,
"author_id": 700275680226705400,
"author_name": "Fibdg",
"timestamp": "08/11/2022 09:15:16",
"content": "Does this help or are you still stuck",
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},
{
"id": 1007276067167416300,
"author_id": 640436986624344000,
"author_name": "ahhhhhh",
"timestamp": "08/11/2022 09:15:28",
"content": "I'm still stuck",
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},
{
"id": 1007276264568148000,
"author_id": 700275680226705400,
"author_name": "Fibdg",
"timestamp": "08/11/2022 09:16:15",
"content": "If a line is tangent to a circle, it means it's distance from the center of the circle is exactly the radius",
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"id": 1007276344561897500,
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"author_name": "Fibdg",
"timestamp": "08/11/2022 09:16:34",
"content": "So set up this equation with m as a variable and then solve",
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},
{
"id": 1007276510710857700,
"author_id": 640436986624344000,
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"timestamp": "08/11/2022 09:17:14",
"content": "Ah ok",
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},
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"id": 1007276530788999200,
"author_id": 640436986624344000,
"author_name": "ahhhhhh",
"timestamp": "08/11/2022 09:17:19",
"content": "I understand now",
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},
{
"id": 1007276543887806600,
"author_id": 640436986624344000,
"author_name": "ahhhhhh",
"timestamp": "08/11/2022 09:17:22",
"content": "Thanks",
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},
{
"id": 1007276590067101800,
"author_id": 640436986624344000,
"author_name": "ahhhhhh",
"timestamp": "08/11/2022 09:17:33",
"content": ".close",
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},
{
"id": 1007276591660937200,
"author_id": 805217272087838700,
"author_name": "Mathematics Bot",
"timestamp": "08/11/2022 09:17:33",
"content": "Channel closed",
"attachments": [],
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"reference": null
}
] |
help-9
|
5b74b1fa5927494fb5c002a2332f98bb
|
197,758 |
[
{
"id": 1007277654111682700,
"author_id": 805217272087838700,
"author_name": "Mathematics Bot",
"timestamp": "08/11/2022 09:21:47",
"content": "Available help channel!",
"attachments": [],
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"reference": null
},
{
"id": 1007279345720639500,
"author_id": 905739286916247600,
"author_name": "sxm!",
"timestamp": "08/11/2022 09:28:30",
"content": ".help",
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"reference": null
},
{
"id": 1007279346492383400,
"author_id": 805217272087838700,
"author_name": "Mathematics Bot",
"timestamp": "08/11/2022 09:28:30",
"content": "**Commands:**\nclopen: `.close`, `.reopen`\nfactoids: `.tag`\nhelp: `.help`\n\nType `.help <command name>` for more info on a command.",
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{
"id": 1007279463094026400,
"author_id": 905739286916247600,
"author_name": "sxm!",
"timestamp": "08/11/2022 09:28:58",
"content": "hi",
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},
{
"id": 1007279465694499000,
"author_id": 805217272087838700,
"author_name": "Mathematics Bot",
"timestamp": "08/11/2022 09:28:58",
"content": "Pinned a message.",
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},
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"id": 1007279530987229200,
"author_id": 905739286916247600,
"author_name": "sxm!",
"timestamp": "08/11/2022 09:29:14",
"content": "plese help me with this",
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},
{
"id": 1007279559223279600,
"author_id": 905739286916247600,
"author_name": "sxm!",
"timestamp": "08/11/2022 09:29:21",
"content": "",
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"id": 1007280055057141800,
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"author_name": "sxm!",
"timestamp": "08/11/2022 09:31:19",
"content": "@Helpers",
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},
{
"id": 1007281266980290700,
"author_id": 905739286916247600,
"author_name": "sxm!",
"timestamp": "08/11/2022 09:36:08",
"content": "@Helpers",
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"author_id": 805217272087838700,
"author_name": "Mathematics Bot",
"timestamp": "08/11/2022 09:36:36",
"content": "Please only use the @Helpers ping **once** if your question has not been answered **for 15 minutes**. Please do not ping or DM individual users about your question.",
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"id": 1007281806384574600,
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"timestamp": "08/11/2022 09:38:17",
"content": ".close",
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"id": 1007281808376864800,
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"timestamp": "08/11/2022 09:38:17",
"content": "Channel closed",
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] |
help-9
|
6c8241b0f84d44c6b5ce9a2e8c536e6d
|
197,759 |
[
{
"id": 959722564660375700,
"author_id": 731447178572202000,
"author_name": "yk3",
"timestamp": "04/02/2022 03:54:50",
"content": "",
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"id": 959722595538837500,
"author_id": 731447178572202000,
"author_name": "yk3",
"timestamp": "04/02/2022 03:54:57",
"content": "may i ask how to do this?",
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},
{
"id": 959722614320955400,
"author_id": 812978986442817500,
"author_name": "ฮtomFPS",
"timestamp": "04/02/2022 03:55:02",
"content": "Can any of you guys help me understand this",
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"id": 959722631546949600,
"author_id": 731447178572202000,
"author_name": "yk3",
"timestamp": "04/02/2022 03:55:06",
"content": "without u sub",
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},
{
"id": 959722651461484500,
"author_id": 731447178572202000,
"author_name": "yk3",
"timestamp": "04/02/2022 03:55:10",
"content": "and ibp",
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},
{
"id": 959722683363377200,
"author_id": 198191547970355200,
"author_name": "sills",
"timestamp": "04/02/2022 03:55:18",
"content": "#โhow-to-get-help",
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"author_id": 812978986442817500,
"author_name": "ฮtomFPS",
"timestamp": "04/02/2022 03:55:23",
"content": "Oh bruh",
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},
{
"id": 959722724857630700,
"author_id": 812978986442817500,
"author_name": "ฮtomFPS",
"timestamp": "04/02/2022 03:55:28",
"content": "I thought I had it",
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"reference": null
},
{
"id": 959722732109574300,
"author_id": 812978986442817500,
"author_name": "ฮtomFPS",
"timestamp": "04/02/2022 03:55:30",
"content": "Sorry ๐",
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},
{
"id": 959722742574370800,
"author_id": 198191547970355200,
"author_name": "sills",
"timestamp": "04/02/2022 03:55:32",
"content": "its ok",
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},
{
"id": 959722759636783100,
"author_id": 198191547970355200,
"author_name": "sills",
"timestamp": "04/02/2022 03:55:36",
"content": "it happens",
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},
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"id": 959722777189974000,
"author_id": 198191547970355200,
"author_name": "sills",
"timestamp": "04/02/2022 03:55:40",
"content": "@yk3 do you know what method you need/want to use",
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"id": 959723147765092400,
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"timestamp": "04/02/2022 03:57:09",
"content": "dk",
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"id": 959724548956229600,
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"author_name": "yk3",
"timestamp": "04/02/2022 04:02:43",
"content": ".close",
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},
{
"id": 959725060833280000,
"author_id": 805217272087838700,
"author_name": "Mathematics Bot",
"timestamp": "04/02/2022 04:04:45",
"content": "Available help channel!",
"attachments": [],
"mentions": [],
"reference": null
},
{
"id": 959726503531266000,
"author_id": 241927037135224830,
"author_name": "Sup?",
"timestamp": "04/02/2022 04:10:29",
"content": "@yk3 Still here?",
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"id": 959726504860848100,
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"author_name": "Mathematics Bot",
"timestamp": "04/02/2022 04:10:29",
"content": "Pinned a message.",
"attachments": [],
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"channelId": 486844875632017400,
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"id": 959726737829265400,
"author_id": 731447178572202000,
"author_name": "yk3",
"timestamp": "04/02/2022 04:11:25",
"content": "yes i am",
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},
{
"id": 959726774047100900,
"author_id": 241927037135224830,
"author_name": "Sup?",
"timestamp": "04/02/2022 04:11:33",
"content": "Rewrite the integral as",
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},
{
"id": 959726801184251900,
"author_id": 241927037135224830,
"author_name": "Sup?",
"timestamp": "04/02/2022 04:11:40",
"content": "(x+2 - 2)(x+2)^(2022)",
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},
{
"id": 959726810994712600,
"author_id": 241927037135224830,
"author_name": "Sup?",
"timestamp": "04/02/2022 04:11:42",
"content": "Distribute",
"attachments": [],
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},
{
"id": 959726820733911000,
"author_id": 241927037135224830,
"author_name": "Sup?",
"timestamp": "04/02/2022 04:11:44",
"content": "and then integrate",
"attachments": [],
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},
{
"id": 959726950933483600,
"author_id": 731447178572202000,
"author_name": "yk3",
"timestamp": "04/02/2022 04:12:15",
"content": "ara has her way",
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{
"id": 959726951684251800,
"author_id": 731447178572202000,
"author_name": "yk3",
"timestamp": "04/02/2022 04:12:16",
"content": "tho",
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{
"id": 959726996999516200,
"author_id": 731447178572202000,
"author_name": "yk3",
"timestamp": "04/02/2022 04:12:26",
"content": "yeah",
"attachments": [],
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},
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"id": 959727002502430700,
"author_id": 731447178572202000,
"author_name": "yk3",
"timestamp": "04/02/2022 04:12:28",
"content": "same way",
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"id": 959727042771943400,
"author_id": 731447178572202000,
"author_name": "yk3",
"timestamp": "04/02/2022 04:12:37",
"content": "but you'll eventually have to u sub",
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"id": 959727047054348300,
"author_id": 241927037135224830,
"author_name": "Sup?",
"timestamp": "04/02/2022 04:12:38",
"content": "that answer is wrong tho",
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"id": 959727052318191600,
"author_id": 241927037135224830,
"author_name": "Sup?",
"timestamp": "04/02/2022 04:12:40",
"content": "no",
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{
"id": 959727065781923800,
"author_id": 241927037135224830,
"author_name": "Sup?",
"timestamp": "04/02/2022 04:12:43",
"content": "No u-sub required",
"attachments": [],
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},
{
"id": 959727107238416400,
"author_id": 731447178572202000,
"author_name": "yk3",
"timestamp": "04/02/2022 04:12:53",
"content": "she didnt integrate",
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},
{
"id": 959727153237336000,
"author_id": 241927037135224830,
"author_name": "Sup?",
"timestamp": "04/02/2022 04:13:04",
"content": "ah",
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"id": 959727830114115600,
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"timestamp": "04/02/2022 04:15:45",
"content": "mm",
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"timestamp": "04/02/2022 04:28:04",
"content": "@Sup? Has your question been resolved?",
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"timestamp": "04/02/2022 04:28:09",
"content": "Channel closed",
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}
] |
help-9
|
b4e92ef154dc47c1abb8bf97d3468b8c
|
197,760 |
[
{
"id": 1007282061830271000,
"author_id": 805217272087838700,
"author_name": "Mathematics Bot",
"timestamp": "08/11/2022 09:39:17",
"content": "Available help channel!",
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"reference": null
},
{
"id": 1007282665793269900,
"author_id": 854969885658316800,
"author_name": "babario",
"timestamp": "08/11/2022 09:41:41",
"content": "how can i find <AOB",
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"content": "Pinned a message.",
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"author_id": 854969885658316800,
"author_name": "babario",
"timestamp": "08/11/2022 09:42:50",
"content": "oh, n the midpoint of AB connected to O is 15cm",
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},
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"id": 1007283660640227500,
"author_id": 764959481070616600,
"author_name": "Toby",
"timestamp": "08/11/2022 09:45:39",
"content": "use the cos rule",
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},
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"id": 1007283666763915400,
"author_id": 437166198166257660,
"author_name": "Master Oogway",
"timestamp": "08/11/2022 09:45:40",
"content": "draw it pls",
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},
{
"id": 1007283693666185300,
"author_id": 510789298321096700,
"author_name": "TeXit",
"timestamp": "08/11/2022 09:45:46",
"content": "**Toby**",
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"id": 1007283694127550500,
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"author_name": "Master Oogway",
"timestamp": "08/11/2022 09:45:47",
"content": "wtf",
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},
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"id": 1007283730777374700,
"author_id": 437166198166257660,
"author_name": "Master Oogway",
"timestamp": "08/11/2022 09:45:55",
"content": "bro",
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},
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"id": 1007283743544836200,
"author_id": 437166198166257660,
"author_name": "Master Oogway",
"timestamp": "08/11/2022 09:45:58",
"content": "put that again pls",
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},
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"id": 1007283820543877200,
"author_id": 764959481070616600,
"author_name": "Toby",
"timestamp": "08/11/2022 09:46:17",
"content": "why lol",
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},
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"id": 1007283840332607500,
"author_id": 437166198166257660,
"author_name": "Master Oogway",
"timestamp": "08/11/2022 09:46:21",
"content": "its so cool",
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},
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"id": 1007283844875038800,
"author_id": 437166198166257660,
"author_name": "Master Oogway",
"timestamp": "08/11/2022 09:46:23",
"content": "pls",
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},
{
"id": 1007283864915431400,
"author_id": 764959481070616600,
"author_name": "Toby",
"timestamp": "08/11/2022 09:46:27",
"content": "ill dm you the source",
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},
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"id": 1007283883047407600,
"author_id": 437166198166257660,
"author_name": "Master Oogway",
"timestamp": "08/11/2022 09:46:32",
"content": "ok",
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},
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"id": 1007284165827379300,
"author_id": 854969885658316800,
"author_name": "babario",
"timestamp": "08/11/2022 09:47:39",
"content": "any other ways tat does not involve trigo?",
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"id": 1007284220483350700,
"author_id": 764959481070616600,
"author_name": "Toby",
"timestamp": "08/11/2022 09:47:52",
"content": "actually, you could probably avoid the cos rule and split the triangle in half",
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},
{
"id": 1007284269065982100,
"author_id": 764959481070616600,
"author_name": "Toby",
"timestamp": "08/11/2022 09:48:04",
"content": "and just use the normal cos in a right angle triangle",
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},
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"id": 1007284313966006300,
"author_id": 510789298321096700,
"author_name": "TeXit",
"timestamp": "08/11/2022 09:48:14",
"content": "**Toby**",
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"id": 1007284504043471100,
"author_id": 182179228840755200,
"author_name": "iCaird",
"timestamp": "08/11/2022 09:49:00",
"content": "If you have a problem asking you to find an angle and you're only given lengths, there is pretty much no avoiding trigonometry",
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"author_name": "babario",
"timestamp": "08/11/2022 09:49:24",
"content": "ok then",
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},
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"id": 1007284620011774100,
"author_id": 854969885658316800,
"author_name": "babario",
"timestamp": "08/11/2022 09:49:27",
"content": "thx a lot",
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},
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"id": 1007284640974917800,
"author_id": 854969885658316800,
"author_name": "babario",
"timestamp": "08/11/2022 09:49:32",
"content": ".close",
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},
{
"id": 1007284643688616000,
"author_id": 805217272087838700,
"author_name": "Mathematics Bot",
"timestamp": "08/11/2022 09:49:33",
"content": "Channel closed",
"attachments": [],
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"reference": null
}
] |
help-9
|
5ffba10f928444b881be601dba71f288
|
197,761 |
[
{
"id": 1007285194581102600,
"author_id": 805217272087838700,
"author_name": "Mathematics Bot",
"timestamp": "08/11/2022 09:51:44",
"content": "Available help channel!",
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},
{
"id": 1007288549701320800,
"author_id": 271969786219462660,
"author_name": "femboyteacup",
"timestamp": "08/11/2022 10:05:04",
"content": "in a lattice model, I have N lattice sites occupied by n1, n2, and n3 particles. If no other pparticles have been placed on the lattice, how many ways can i place n1 particles on the lattice?",
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},
{
"id": 1007288551584583700,
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"author_name": "Mathematics Bot",
"timestamp": "08/11/2022 10:05:05",
"content": "Pinned a message.",
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}
},
{
"id": 1007288680622346400,
"author_id": 271969786219462660,
"author_name": "femboyteacup",
"timestamp": "08/11/2022 10:05:35",
"content": "I'm struggling to wrap my head around how this works and how to use factorials",
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},
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"id": 1007292456578056200,
"author_id": 805217272087838700,
"author_name": "Mathematics Bot",
"timestamp": "08/11/2022 10:20:36",
"content": "@femboyteacup Has your question been resolved?",
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"id": 1007296847431340200,
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"author_name": "femboyteacup",
"timestamp": "08/11/2022 10:38:03",
"content": "",
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{
"id": 1007296864489570300,
"author_id": 271969786219462660,
"author_name": "femboyteacup",
"timestamp": "08/11/2022 10:38:07",
"content": "this is the question in question",
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},
{
"id": 1007297140407664600,
"author_id": 764959481070616600,
"author_name": "Toby",
"timestamp": "08/11/2022 10:39:12",
"content": "there are N spots, you need to choose n1 of these spots to place the type 1 particles",
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},
{
"id": 1007297245433041000,
"author_id": 271969786219462660,
"author_name": "femboyteacup",
"timestamp": "08/11/2022 10:39:37",
"content": "yes",
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},
{
"id": 1007297298142859300,
"author_id": 271969786219462660,
"author_name": "femboyteacup",
"timestamp": "08/11/2022 10:39:50",
"content": "So presumably N-n1",
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},
{
"id": 1007297340698263700,
"author_id": 764959481070616600,
"author_name": "Toby",
"timestamp": "08/11/2022 10:40:00",
"content": "have you heard of the nCk choose function?",
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},
{
"id": 1007297370247143400,
"author_id": 271969786219462660,
"author_name": "femboyteacup",
"timestamp": "08/11/2022 10:40:07",
"content": "whats that?",
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},
{
"id": 1007297437100163200,
"author_id": 764959481070616600,
"author_name": "Toby",
"timestamp": "08/11/2022 10:40:23",
"content": "https://en.wikipedia.org/wiki/Binomial_coefficient",
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},
{
"id": 1007297509258969100,
"author_id": 271969786219462660,
"author_name": "femboyteacup",
"timestamp": "08/11/2022 10:40:40",
"content": "ah yes im familiar",
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},
{
"id": 1007297604972986400,
"author_id": 764959481070616600,
"author_name": "Toby",
"timestamp": "08/11/2022 10:41:03",
"content": "so the answer to (i) is N choose n1",
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},
{
"id": 1007297875782402000,
"author_id": 271969786219462660,
"author_name": "femboyteacup",
"timestamp": "08/11/2022 10:42:08",
"content": "oh wow",
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},
{
"id": 1007297950726246500,
"author_id": 271969786219462660,
"author_name": "femboyteacup",
"timestamp": "08/11/2022 10:42:26",
"content": "so I'm looking at\n\nN! / n1!(N-n1)!",
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},
{
"id": 1007298152057028700,
"author_id": 764959481070616600,
"author_name": "Toby",
"timestamp": "08/11/2022 10:43:14",
"content": "yup",
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},
{
"id": 1007298681118146700,
"author_id": 271969786219462660,
"author_name": "femboyteacup",
"timestamp": "08/11/2022 10:45:20",
"content": "so with the n1 particles in place, would adding the n2 particles do the binomial function as\n( N-n1 \n n2 )",
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},
{
"id": 1007298746083717100,
"author_id": 271969786219462660,
"author_name": "femboyteacup",
"timestamp": "08/11/2022 10:45:35",
"content": "(idk how to write the nCk brackets)",
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},
{
"id": 1007298883296182400,
"author_id": 764959481070616600,
"author_name": "Toby",
"timestamp": "08/11/2022 10:46:08",
"content": "yup",
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},
{
"id": 1007298895317061800,
"author_id": 764959481070616600,
"author_name": "Toby",
"timestamp": "08/11/2022 10:46:11",
"content": "thats correct",
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},
{
"id": 1007298957677957100,
"author_id": 764959481070616600,
"author_name": "Toby",
"timestamp": "08/11/2022 10:46:26",
"content": "${N-n_1}\\choose{n_2}$",
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"reference": null
},
{
"id": 1007298969346527200,
"author_id": 510789298321096700,
"author_name": "TeXit",
"timestamp": "08/11/2022 10:46:29",
"content": "**Toby**",
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"id": 1007299034354028700,
"author_id": 271969786219462660,
"author_name": "femboyteacup",
"timestamp": "08/11/2022 10:46:44",
"content": "thats the one",
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},
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"id": 1007306585124651100,
"author_id": 805217272087838700,
"author_name": "Mathematics Bot",
"timestamp": "08/11/2022 11:16:44",
"content": "@femboyteacup Has your question been resolved?",
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"timestamp": "08/11/2022 11:42:38",
"content": "Channel closed",
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}
] |
help-9
|
a3684997f3914e309fca99a03f33b9cf
|
197,762 |
[
{
"id": 1007313352449605800,
"author_id": 805217272087838700,
"author_name": "Mathematics Bot",
"timestamp": "08/11/2022 11:43:38",
"content": "Available help channel!",
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},
{
"id": 1007315823305699300,
"author_id": 250371559808565250,
"author_name": "Mimir",
"timestamp": "08/11/2022 11:53:27",
"content": "I have a question relating to part B",
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"timestamp": "08/11/2022 11:53:27",
"content": "Pinned a message.",
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{
"id": 1007315826484981800,
"author_id": 250371559808565250,
"author_name": "Mimir",
"timestamp": "08/11/2022 11:53:28",
"content": "Of this question",
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},
{
"id": 1007315988854886500,
"author_id": 250371559808565250,
"author_name": "Mimir",
"timestamp": "08/11/2022 11:54:06",
"content": "In the answer booklet, it says",
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},
{
"id": 1007316023655010300,
"author_id": 250371559808565250,
"author_name": "Mimir",
"timestamp": "08/11/2022 11:54:15",
"content": "Would this be the venn diagram",
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},
{
"id": 1007316063505096700,
"author_id": 250371559808565250,
"author_name": "Mimir",
"timestamp": "08/11/2022 11:54:24",
"content": "Because the answer booklet has somethin different",
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},
{
"id": 1007316075484029000,
"author_id": 250371559808565250,
"author_name": "Mimir",
"timestamp": "08/11/2022 11:54:27",
"content": "Which I dont get",
"attachments": [],
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"reference": null
},
{
"id": 1007316141837914100,
"author_id": 250371559808565250,
"author_name": "Mimir",
"timestamp": "08/11/2022 11:54:43",
"content": "so its P((AUB)`)",
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},
{
"id": 1007316876478652500,
"author_id": 834653553167302700,
"author_name": "ArshiyaKhan",
"timestamp": "08/11/2022 11:57:38",
"content": "whats your final answer",
"attachments": [],
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},
{
"id": 1007317123149877200,
"author_id": 250371559808565250,
"author_name": "Mimir",
"timestamp": "08/11/2022 11:58:37",
"content": "Mine was 2.56 percent",
"attachments": [],
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"reference": null
},
{
"id": 1007317137242734600,
"author_id": 250371559808565250,
"author_name": "Mimir",
"timestamp": "08/11/2022 11:58:40",
"content": "But the answer booklet",
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"reference": null
},
{
"id": 1007317250321154000,
"author_id": 250371559808565250,
"author_name": "Mimir",
"timestamp": "08/11/2022 11:59:07",
"content": "",
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"id": 1007317261486399500,
"author_id": 250371559808565250,
"author_name": "Mimir",
"timestamp": "08/11/2022 11:59:10",
"content": "they dod",
"attachments": [],
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"author_id": 250371559808565250,
"author_name": "Mimir",
"timestamp": "08/11/2022 11:59:30",
"content": "1-P(AโฉB)",
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"id": 1007317387072254100,
"author_id": 250371559808565250,
"author_name": "Mimir",
"timestamp": "08/11/2022 11:59:40",
"content": "I did 1-(AUB), I counted everything",
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"id": 1007318035482296300,
"author_id": 834653553167302700,
"author_name": "ArshiyaKhan",
"timestamp": "08/11/2022 12:02:14",
"content": "I agree, but maybe I'm making a mistake too ๐ (it's unlikely!)",
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"id": 1007318381189406700,
"author_id": 250371559808565250,
"author_name": "Mimir",
"timestamp": "08/11/2022 12:03:37",
"content": "Can I call helpers then",
"attachments": [],
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},
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"id": 1007318388667850900,
"author_id": 250371559808565250,
"author_name": "Mimir",
"timestamp": "08/11/2022 12:03:38",
"content": "in a bit",
"attachments": [],
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},
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"id": 1007318395651358800,
"author_id": 250371559808565250,
"author_name": "Mimir",
"timestamp": "08/11/2022 12:03:40",
"content": "I need to make sure",
"attachments": [],
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"author_id": 834653553167302700,
"author_name": "ArshiyaKhan",
"timestamp": "08/11/2022 12:03:46",
"content": "this is gotta be the case that maximum 1 photocopier works",
"attachments": [],
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"id": 1007318623347560600,
"author_id": 250371559808565250,
"author_name": "Mimir",
"timestamp": "08/11/2022 12:04:34",
"content": "no thats the case where both, or one photocopier doesnt work",
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"author_id": 834653553167302700,
"author_name": "ArshiyaKhan",
"timestamp": "08/11/2022 12:06:32",
"content": "this is the same ๐ isn't it?",
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"id": 1007319423352307800,
"author_id": 250371559808565250,
"author_name": "Mimir",
"timestamp": "08/11/2022 12:07:45",
"content": "no, max one photocopier working is P(AUB)",
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"id": 1007319488867352600,
"author_id": 250371559808565250,
"author_name": "Mimir",
"timestamp": "08/11/2022 12:08:01",
"content": "Cause it would cover A and B",
"attachments": [],
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},
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"id": 1007319612624482300,
"author_id": 834653553167302700,
"author_name": "ArshiyaKhan",
"timestamp": "08/11/2022 12:08:30",
"content": "- AโฉB",
"attachments": [],
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"id": 1007319708023922700,
"author_id": 834653553167302700,
"author_name": "ArshiyaKhan",
"timestamp": "08/11/2022 12:08:53",
"content": "both won't work at the same time",
"attachments": [],
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},
{
"id": 1007319739539919000,
"author_id": 834653553167302700,
"author_name": "ArshiyaKhan",
"timestamp": "08/11/2022 12:09:01",
"content": "thats maximum 1",
"attachments": [],
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},
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"id": 1007319757516701700,
"author_id": 250371559808565250,
"author_name": "Mimir",
"timestamp": "08/11/2022 12:09:05",
"content": "oh",
"attachments": [],
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},
{
"id": 1007319760591130800,
"author_id": 250371559808565250,
"author_name": "Mimir",
"timestamp": "08/11/2022 12:09:06",
"content": "ye",
"attachments": [],
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},
{
"id": 1007319763162239100,
"author_id": 250371559808565250,
"author_name": "Mimir",
"timestamp": "08/11/2022 12:09:06",
"content": "mb",
"attachments": [],
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},
{
"id": 1007319776349147100,
"author_id": 250371559808565250,
"author_name": "Mimir",
"timestamp": "08/11/2022 12:09:09",
"content": "I was thinking min 1",
"attachments": [],
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},
{
"id": 1007320499799470100,
"author_id": 250371559808565250,
"author_name": "Mimir",
"timestamp": "08/11/2022 12:12:02",
"content": "Yeagh I think textbook is wrong",
"attachments": [],
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},
{
"id": 1007320509370863600,
"author_id": 250371559808565250,
"author_name": "Mimir",
"timestamp": "08/11/2022 12:12:04",
"content": "theres no way",
"attachments": [],
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},
{
"id": 1007320536872927400,
"author_id": 250371559808565250,
"author_name": "Mimir",
"timestamp": "08/11/2022 12:12:11",
"content": "thanks for ur help Im just gonna move on",
"attachments": [],
"mentions": [],
"reference": null
},
{
"id": 1007320548256272400,
"author_id": 250371559808565250,
"author_name": "Mimir",
"timestamp": "08/11/2022 12:12:13",
"content": "@ArshiyaKhan",
"attachments": [],
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{
"id": 1007320553767587800,
"author_id": 250371559808565250,
"author_name": "Mimir",
"timestamp": "08/11/2022 12:12:15",
"content": ".close",
"attachments": [],
"mentions": [],
"reference": null
},
{
"id": 1007320555747291300,
"author_id": 805217272087838700,
"author_name": "Mathematics Bot",
"timestamp": "08/11/2022 12:12:15",
"content": "Channel closed",
"attachments": [],
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"reference": null
}
] |
help-9
|
4d92f7f67f2d43cda50e17fd396cc50b
|
197,763 |
[
{
"id": 1007320728040906800,
"author_id": 834653553167302700,
"author_name": "ArshiyaKhan",
"timestamp": "08/11/2022 12:12:56",
"content": "btw if you enjou when diagram, you may like this",
"attachments": [
{
"id": 1007320727239807100,
"url": "https://cdn.discordapp.com/attachments/486844875632017408/1007320727239807056/unknown.png",
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"author_id": 834653553167302700,
"author_name": "ArshiyaKhan",
"timestamp": "08/11/2022 12:13:09",
"content": "@Mimir",
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"id": 1007320796823290000,
"author_id": 250371559808565250,
"author_name": "Mimir",
"timestamp": "08/11/2022 12:13:13",
"content": "Oh",
"attachments": [],
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},
{
"id": 1007325701013246000,
"author_id": 805217272087838700,
"author_name": "Mathematics Bot",
"timestamp": "08/11/2022 12:32:42",
"content": "Available help channel!",
"attachments": [],
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"reference": null
},
{
"id": 1007327491054125000,
"author_id": 215090636192350200,
"author_name": "ูุนู
ุงู",
"timestamp": "08/11/2022 12:39:49",
"content": "How do i go about the following exercise:\n\nWrite det(\n\\begin{pmatrix}\n1+x & 1+x+x^2 & 1+x+x^2+x^3 \\\\\n1+y & 1+y+y^2 & 1+y+y^2+y^3 \\\\\n1+z & 1+z+z^2 & 1+z+z^2+z^3 \\\\\n\\end{pmatrix}\n)\n\nas the product of as many possible factors (note: its possible to write this as a product of four facots)",
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"id": 1007327493130309800,
"author_id": 805217272087838700,
"author_name": "Mathematics Bot",
"timestamp": "08/11/2022 12:39:49",
"content": "Pinned a message.",
"attachments": [],
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"id": 1007327506514313300,
"author_id": 510789298321096700,
"author_name": "TeXit",
"timestamp": "08/11/2022 12:39:52",
"content": "**ูุนู
ุงู**\nCompile Error! Click the :errors: reaction for more information.\n(You may edit your message to recompile.)",
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"author_id": 215090636192350200,
"author_name": "ูุนู
ุงู",
"timestamp": "08/11/2022 12:41:49",
"content": "I thought of disolving the matrix Z into the sum of several matrices and then writing the determinant as det(Z) = det(A+B+C) = det(A.B.C.(B^-1C^-1+A^-1C^1+A^-1B^-1) = det(A).det(B).det(C).det(B^-1C^-1+A^-1C^1+A^-1B^-1)",
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},
{
"id": 1007328037752279200,
"author_id": 215090636192350200,
"author_name": "ูุนู
ุงู",
"timestamp": "08/11/2022 12:41:59",
"content": "but i feel like thats either wrong or far to complicated",
"attachments": [],
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},
{
"id": 1007328116965908500,
"author_id": 215090636192350200,
"author_name": "ูุนู
ุงู",
"timestamp": "08/11/2022 12:42:18",
"content": "i bet it has something to do with the polynomial of rising degree in every row",
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"id": 1007328458113822700,
"author_id": 215090636192350200,
"author_name": "ูุนู
ุงู",
"timestamp": "08/11/2022 12:43:39",
"content": "While waiting on a response im gonna try applying the leibniz formula and see if i can maybe factor out an x y and z from every sum",
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"id": 1007332233801117700,
"author_id": 215090636192350200,
"author_name": "ูุนู
ุงู",
"timestamp": "08/11/2022 12:58:39",
"content": "Okey that didnt work",
"attachments": [],
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},
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"id": 1007332233847251100,
"author_id": 805217272087838700,
"author_name": "Mathematics Bot",
"timestamp": "08/11/2022 12:58:39",
"content": "@ูุนู
ุงู Has your question been resolved?",
"attachments": [],
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ุงู",
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ุงู",
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"id": 1007332288566132900,
"author_id": 215090636192350200,
"author_name": "ูุนู
ุงู",
"timestamp": "08/11/2022 12:58:52",
"content": "@Helpers",
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},
{
"id": 1007333425901998200,
"author_id": 132304137583984640,
"author_name": "Denascite",
"timestamp": "08/11/2022 13:03:24",
"content": "well I would probably start with subtracting the second column from the third and the first from the second",
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"id": 1007333459141869600,
"author_id": 132304137583984640,
"author_name": "Denascite",
"timestamp": "08/11/2022 13:03:32",
"content": "then you can split it up into two determinants",
"attachments": [],
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},
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"id": 1007333581179326600,
"author_id": 132304137583984640,
"author_name": "Denascite",
"timestamp": "08/11/2022 13:04:01",
"content": "one of them is the vandermonde determinant so that is nice. not sure about the other one",
"attachments": [],
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},
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"id": 1007333860150878200,
"author_id": 215090636192350200,
"author_name": "ูุนู
ุงู",
"timestamp": "08/11/2022 13:05:07",
"content": "ohh yeahhh i forgot you can do column operations on determinants",
"attachments": [],
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},
{
"id": 1007333998676152300,
"author_id": 215090636192350200,
"author_name": "ูุนู
ุงู",
"timestamp": "08/11/2022 13:05:40",
"content": "you can do that on matrices too right? as long as you stick with either row/column operations for the whole process",
"attachments": [],
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},
{
"id": 1007336193085690000,
"author_id": 285006840893538300,
"author_name": "Kero",
"timestamp": "08/11/2022 13:14:23",
"content": "hmm hey",
"attachments": [],
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ุงู",
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ุงู",
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"id": 1007336204997500900,
"author_id": 285006840893538300,
"author_name": "Kero",
"timestamp": "08/11/2022 13:14:26",
"content": "what's u question",
"attachments": [],
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},
{
"id": 1007341549639712800,
"author_id": 805217272087838700,
"author_name": "Mathematics Bot",
"timestamp": "08/11/2022 13:35:40",
"content": "@ูุนู
ุงู Has your question been resolved?",
"attachments": [],
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ุงู",
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ุงู",
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{
"id": 1007351861931692200,
"author_id": 215090636192350200,
"author_name": "ูุนู
ุงู",
"timestamp": "08/11/2022 14:16:39",
"content": "Sorry went to have to dinner",
"attachments": [],
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},
{
"id": 1007351900410228900,
"author_id": 215090636192350200,
"author_name": "ูุนู
ุงู",
"timestamp": "08/11/2022 14:16:48",
"content": "How would i do that?",
"attachments": [],
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{
"id": 1007351912573698200,
"author_id": 215090636192350200,
"author_name": "ูุนู
ุงู",
"timestamp": "08/11/2022 14:16:51",
"content": "Using my method?",
"attachments": [],
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},
{
"id": 1007352517258137600,
"author_id": 132304137583984640,
"author_name": "Denascite",
"timestamp": "08/11/2022 14:19:15",
"content": "I suggest you look up properties of the determinant",
"attachments": [],
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},
{
"id": 1007352538229645400,
"author_id": 215090636192350200,
"author_name": "ูุนู
ุงู",
"timestamp": "08/11/2022 14:19:20",
"content": "yeah i just got it",
"attachments": [],
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},
{
"id": 1007352552158929000,
"author_id": 215090636192350200,
"author_name": "ูุนู
ุงู",
"timestamp": "08/11/2022 14:19:24",
"content": "like while you were typing",
"attachments": [],
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},
{
"id": 1007352584576700500,
"author_id": 215090636192350200,
"author_name": "ูุนู
ุงู",
"timestamp": "08/11/2022 14:19:31",
"content": "been doing to much linear algebra its getting to me",
"attachments": [],
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},
{
"id": 1007356796295462900,
"author_id": 215090636192350200,
"author_name": "ูุนู
ุงู",
"timestamp": "08/11/2022 14:36:16",
"content": "For the other matrix r1=(x x^2 x^3) r2= (y y^2 ...) .... , can i just do row operations 1/x 1/y and 1/z for their respetive row and then use the vandermonde matrix again?",
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"id": 1007357502247153800,
"author_id": 132304137583984640,
"author_name": "Denascite",
"timestamp": "08/11/2022 14:39:04",
"content": "that's the one I meant with vandermonde",
"attachments": [],
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},
{
"id": 1007357527924674700,
"author_id": 132304137583984640,
"author_name": "Denascite",
"timestamp": "08/11/2022 14:39:10",
"content": "the other isn't vandermonde",
"attachments": [],
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},
{
"id": 1007357637186310100,
"author_id": 132304137583984640,
"author_name": "Denascite",
"timestamp": "08/11/2022 14:39:36",
"content": "but yeah, divide by x etc",
"attachments": [],
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},
{
"id": 1007359085030686800,
"author_id": 215090636192350200,
"author_name": "ูุนู
ุงู",
"timestamp": "08/11/2022 14:45:21",
"content": "well i end up with a vandermonde if i do that",
"attachments": [],
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},
{
"id": 1007359143910326400,
"author_id": 215090636192350200,
"author_name": "ูุนู
ุงู",
"timestamp": "08/11/2022 14:45:35",
"content": "nvm",
"attachments": [],
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},
{
"id": 1007359146900848800,
"author_id": 215090636192350200,
"author_name": "ูุนู
ุงู",
"timestamp": "08/11/2022 14:45:36",
"content": "well",
"attachments": [],
"mentions": [],
"reference": null
},
{
"id": 1007359151728496600,
"author_id": 215090636192350200,
"author_name": "ูุนู
ุงู",
"timestamp": "08/11/2022 14:45:37",
"content": "no",
"attachments": [],
"mentions": [],
"reference": null
},
{
"id": 1007359514980401200,
"author_id": 358244735220973600,
"author_name": "TheTntExpress",
"timestamp": "08/11/2022 14:47:04",
"content": "Hello",
"attachments": [],
"mentions": [],
"reference": null
},
{
"id": 1007359742999539700,
"author_id": 215090636192350200,
"author_name": "ูุนู
ุงู",
"timestamp": "08/11/2022 14:47:58",
"content": "right now i have \n\n\\begin{pmatrix} \n1&x^2&x^3\\\\\n1&y^2&y^3\\\\\n1&z^2&z^3\\\\\n\\end{pmatrix}\n\n+\n\n\\begin{pmatrix} \nx&x^2&x^3\\\\\ny&y^2&y^3\\\\\nz&z^2&z^3\\\\\n\\end{pmatrix}",
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},
{
"id": 1007359757402771600,
"author_id": 510789298321096700,
"author_name": "TeXit",
"timestamp": "08/11/2022 14:48:02",
"content": "**ูุนู
ุงู**\nCompile Error! Click the :errors: reaction for more information.\n(You may edit your message to recompile.)",
"attachments": [
{
"id": 1007359757495050200,
"url": "https://cdn.discordapp.com/attachments/486844875632017408/1007359757495050300/215090636192350209.png",
"fileName": "215090636192350209.png",
"fileSizeBytes": 30547
}
],
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},
{
"id": 1007359842287091800,
"author_id": 215090636192350200,
"author_name": "ูุนู
ุงู",
"timestamp": "08/11/2022 14:48:22",
"content": "Which i think i can bring to this: (given that x,y and z are not 0)",
"attachments": [],
"mentions": [],
"reference": null
},
{
"id": 1007360164065710200,
"author_id": 215090636192350200,
"author_name": "ูุนู
ุงู",
"timestamp": "08/11/2022 14:49:38",
"content": "\\begin{pmatrix} \n1&x^2&x^3\\\\\n1&y^2&y^3\\\\\n1&z^2&z^3\\\\\n\\end{pmatrix}\n\n+\n1/x . 1/y . 1/z .\n\\begin{pmatrix} \n1&x&x^2\\\\\n1&y&y^2\\\\\n1&z&z^2\\\\\n\\end{pmatrix}",
"attachments": [],
"mentions": [],
"reference": null
},
{
"id": 1007360180431900900,
"author_id": 510789298321096700,
"author_name": "TeXit",
"timestamp": "08/11/2022 14:49:42",
"content": "**ูุนู
ุงู**\nCompile Error! Click the :errors: reaction for more information.\n(You may edit your message to recompile.)",
"attachments": [
{
"id": 1007360180071182300,
"url": "https://cdn.discordapp.com/attachments/486844875632017408/1007360180071182399/215090636192350209.png",
"fileName": "215090636192350209.png",
"fileSizeBytes": 28696
}
],
"mentions": [],
"reference": null
},
{
"id": 1007360280138875000,
"author_id": 215090636192350200,
"author_name": "ูุนู
ุงู",
"timestamp": "08/11/2022 14:50:06",
"content": "Hello",
"attachments": [],
"mentions": [
{
"id": 358244735220973600,
"name": "TheTntExpress",
"discriminator": "4134",
"nickname": "TheTntExpress",
"isBot": false
}
],
"reference": null
},
{
"id": 1007360352897478700,
"author_id": 215090636192350200,
"author_name": "ูุนู
ุงู",
"timestamp": "08/11/2022 14:50:23",
"content": "Interpret the matrices as determinants, no idea how to do determinants in LaTeX",
"attachments": [],
"mentions": [
{
"id": 132304137583984640,
"name": "Denascite",
"discriminator": "8952",
"nickname": "Denascite",
"isBot": false
}
],
"reference": null
},
{
"id": 1007360433423925200,
"author_id": 215090636192350200,
"author_name": "ูุนู
ุงู",
"timestamp": "08/11/2022 14:50:43",
"content": "so that way i have 1 vandermonde and then one not really vandermonde but looks suspiciously alot like vandermonde",
"attachments": [],
"mentions": [],
"reference": null
},
{
"id": 1007363872900001900,
"author_id": 215090636192350200,
"author_name": "ูุนู
ุงู",
"timestamp": "08/11/2022 15:04:23",
"content": "@Helpers",
"attachments": [],
"mentions": [],
"reference": null
},
{
"id": 1007364497964552300,
"author_id": 215090636192350200,
"author_name": "ูุนู
ุงู",
"timestamp": "08/11/2022 15:06:52",
"content": "No idea how to continue on from there",
"attachments": [],
"mentions": [],
"reference": null
},
{
"id": 1007364590297952300,
"author_id": 215090636192350200,
"author_name": "ูุนู
ุงู",
"timestamp": "08/11/2022 15:07:14",
"content": "The second matrix reduces to the vandermonde but no idea what to do with the first :bleakcat:",
"attachments": [],
"mentions": [],
"reference": null
},
{
"id": 1007368984305336400,
"author_id": 105878844061286400,
"author_name": "Namington",
"timestamp": "08/11/2022 15:24:41",
"content": "please do not ping mods for math help",
"attachments": [],
"mentions": [],
"reference": null
},
{
"id": 1007369000294039700,
"author_id": 215090636192350200,
"author_name": "ูุนู
ุงู",
"timestamp": "08/11/2022 15:24:45",
"content": "srry someone was being mean",
"attachments": [],
"mentions": [],
"reference": null
},
{
"id": 1007369024688115800,
"author_id": 215090636192350200,
"author_name": "ูุนู
ุงู",
"timestamp": "08/11/2022 15:24:51",
"content": "but they deleted it",
"attachments": [],
"mentions": [],
"reference": null
},
{
"id": 1007369088978407600,
"author_id": 105878844061286400,
"author_name": "Namington",
"timestamp": "08/11/2022 15:25:06",
"content": "oh i see",
"attachments": [],
"mentions": [],
"reference": null
},
{
"id": 1007369093516624000,
"author_id": 105878844061286400,
"author_name": "Namington",
"timestamp": "08/11/2022 15:25:07",
"content": "sorry",
"attachments": [],
"mentions": [],
"reference": null
},
{
"id": 1007369103624900700,
"author_id": 105878844061286400,
"author_name": "Namington",
"timestamp": "08/11/2022 15:25:10",
"content": "i'll address it",
"attachments": [],
"mentions": [],
"reference": null
},
{
"id": 1007369152425644200,
"author_id": 215090636192350200,
"author_name": "ูุนู
ุงู",
"timestamp": "08/11/2022 15:25:21",
"content": "no its okey it wasnt a big deal",
"attachments": [],
"mentions": [],
"reference": null
},
{
"id": 1007369540491038800,
"author_id": 215090636192350200,
"author_name": "ูุนู
ุงู",
"timestamp": "08/11/2022 15:26:54",
"content": ".close",
"attachments": [],
"mentions": [],
"reference": null
},
{
"id": 1007369542575599600,
"author_id": 805217272087838700,
"author_name": "Mathematics Bot",
"timestamp": "08/11/2022 15:26:54",
"content": "Channel closed",
"attachments": [],
"mentions": [],
"reference": null
}
] |
help-9
|
076f1ee40e52417cb0cc2d6641e5775b
|
197,764 |
[
{
"id": 1007376064294694900,
"author_id": 805217272087838700,
"author_name": "Mathematics Bot",
"timestamp": "08/11/2022 15:52:49",
"content": "Available help channel!",
"attachments": [],
"mentions": [],
"reference": null
},
{
"id": 1007380589894176800,
"author_id": 215090636192350200,
"author_name": "ูุนู
ุงู",
"timestamp": "08/11/2022 16:10:48",
"content": "I have no idea how to prove the following, can i maybe get a hint?\n\nFor an nxn matrix A and a real scalar c:\n\ndet(cI-A) = c^n-det(A)",
"attachments": [],
"mentions": [],
"reference": null
},
{
"id": 1007380592054259700,
"author_id": 805217272087838700,
"author_name": "Mathematics Bot",
"timestamp": "08/11/2022 16:10:49",
"content": "Pinned a message.",
"attachments": [],
"mentions": [],
"reference": {
"messageId": 1007380589894176800,
"channelId": 486844875632017400,
"guildId": null
}
},
{
"id": 1007380813148602400,
"author_id": 215090636192350200,
"author_name": "ูุนู
ุงู",
"timestamp": "08/11/2022 16:11:42",
"content": "I know the determinant of (cI) = c^n but i cant get further then that",
"attachments": [],
"mentions": [],
"reference": null
},
{
"id": 1007380890277646500,
"author_id": 215090636192350200,
"author_name": "ูุนู
ุงู",
"timestamp": "08/11/2022 16:12:00",
"content": "i dont see how i can split up the determinant either",
"attachments": [],
"mentions": [],
"reference": null
},
{
"id": 1007381352666124400,
"author_id": 132304137583984640,
"author_name": "Denascite",
"timestamp": "08/11/2022 16:13:50",
"content": "who says that is true?",
"attachments": [],
"mentions": [],
"reference": null
},
{
"id": 1007381389253021700,
"author_id": 132304137583984640,
"author_name": "Denascite",
"timestamp": "08/11/2022 16:13:59",
"content": "if it were then computing eigenvalues would be really easy",
"attachments": [],
"mentions": [],
"reference": null
},
{
"id": 1007381398019113100,
"author_id": 132304137583984640,
"author_name": "Denascite",
"timestamp": "08/11/2022 16:14:01",
"content": "I'd love that",
"attachments": [],
"mentions": [],
"reference": null
},
{
"id": 1007381480500121700,
"author_id": 215090636192350200,
"author_name": "ูุนู
ุงู",
"timestamp": "08/11/2022 16:14:21",
"content": "Oh",
"attachments": [],
"mentions": [],
"reference": null
},
{
"id": 1007381549395747000,
"author_id": 215090636192350200,
"author_name": "ูุนู
ุงู",
"timestamp": "08/11/2022 16:14:37",
"content": "i really hate the prove or disprove the following type of questions",
"attachments": [],
"mentions": [],
"reference": null
},
{
"id": 1007381568786006100,
"author_id": 215090636192350200,
"author_name": "ูุนู
ุงู",
"timestamp": "08/11/2022 16:14:42",
"content": "but hey i learn.",
"attachments": [],
"mentions": [],
"reference": null
},
{
"id": 1007381575870197800,
"author_id": 215090636192350200,
"author_name": "ูุนู
ุงู",
"timestamp": "08/11/2022 16:14:43",
"content": "thanks!",
"attachments": [],
"mentions": [],
"reference": null
},
{
"id": 1007381580685254800,
"author_id": 215090636192350200,
"author_name": "ูุนู
ุงู",
"timestamp": "08/11/2022 16:14:45",
"content": ".close",
"attachments": [],
"mentions": [],
"reference": null
},
{
"id": 1007381582920831100,
"author_id": 805217272087838700,
"author_name": "Mathematics Bot",
"timestamp": "08/11/2022 16:14:45",
"content": "Channel closed",
"attachments": [],
"mentions": [],
"reference": null
}
] |
help-9
|
57bf0cb6057e4e5ca2e218e924f2f313
|
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