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{
"id": 1036152689039519700,
"author_id": 805217272087838700,
"author_name": "Mathematics Bot",
"timestamp": "10/30/2022 01:40:51",
"content": "Available help channel!",
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"id": 1036154656969199600,
"author_id": 618992877846134800,
"author_name": "SnowZillin",
"timestamp": "10/30/2022 01:48:41",
"content": "hey in the squeeze therum it says the two squeezing lines cant intersect eachother, why?\nusing limits you still get the same answer",
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"id": 1036154661125750800,
"author_id": 805217272087838700,
"author_name": "Mathematics Bot",
"timestamp": "10/30/2022 01:48:42",
"content": "Pinned a message.",
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{
"id": 1036154903644622800,
"author_id": 329749386315956200,
"author_name": "Sneaky",
"timestamp": "10/30/2022 01:49:39",
"content": "What is your statement of the squeeze theorem? I dont remember a part about lines not intersecting each other in the squeeze theorem.",
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{
"id": 1036155001338351700,
"author_id": 331558346333224960,
"author_name": "jan Niku",
"timestamp": "10/30/2022 01:50:03",
"content": "youd want them to be above and below the thing theyre squeezing :thonk:",
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{
"id": 1036155010540638200,
"author_id": 618992877846134800,
"author_name": "SnowZillin",
"timestamp": "10/30/2022 01:50:05",
"content": "it was taught on khan academy, it says you cant have intersecting lines that cross it",
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{
"id": 1036155052240416900,
"author_id": 618992877846134800,
"author_name": "SnowZillin",
"timestamp": "10/30/2022 01:50:15",
"content": "you get the same answer tho",
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{
"id": 1036155074814160900,
"author_id": 331558346333224960,
"author_name": "jan Niku",
"timestamp": "10/30/2022 01:50:20",
"content": "sometimes",
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{
"id": 1036155093684322300,
"author_id": 618992877846134800,
"author_name": "SnowZillin",
"timestamp": "10/30/2022 01:50:25",
"content": "when do you not",
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{
"id": 1036155107923984400,
"author_id": 331558346333224960,
"author_name": "jan Niku",
"timestamp": "10/30/2022 01:50:28",
"content": "im wondering if you mean like",
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{
"id": 1036155145580449900,
"author_id": 331558346333224960,
"author_name": "jan Niku",
"timestamp": "10/30/2022 01:50:37",
"content": "do you mean the thing you are squeezing cant cross the lines?",
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{
"id": 1036155193638780900,
"author_id": 331558346333224960,
"author_name": "jan Niku",
"timestamp": "10/30/2022 01:50:48",
"content": "or the two lines that are doing the squeezing cant cross",
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},
{
"id": 1036155217965760500,
"author_id": 618992877846134800,
"author_name": "SnowZillin",
"timestamp": "10/30/2022 01:50:54",
"content": "no the red and yellow lines cant intersect",
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{
"id": 1036155250505166800,
"author_id": 618992877846134800,
"author_name": "SnowZillin",
"timestamp": "10/30/2022 01:51:02",
"content": "two lines that are squeezing",
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{
"id": 1036155286169321500,
"author_id": 331558346333224960,
"author_name": "jan Niku",
"timestamp": "10/30/2022 01:51:11",
"content": "wtf thats red and yellow :flonshed:",
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{
"id": 1036155301348528100,
"author_id": 331558346333224960,
"author_name": "jan Niku",
"timestamp": "10/30/2022 01:51:14",
"content": "oh are there 3 lines",
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{
"id": 1036155311217705000,
"author_id": 618992877846134800,
"author_name": "SnowZillin",
"timestamp": "10/30/2022 01:51:17",
"content": "up abovr",
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{
"id": 1036155317614030800,
"author_id": 618992877846134800,
"author_name": "SnowZillin",
"timestamp": "10/30/2022 01:51:18",
"content": "my b",
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{
"id": 1036155339571212300,
"author_id": 331558346333224960,
"author_name": "jan Niku",
"timestamp": "10/30/2022 01:51:23",
"content": "i cant see the color sorry",
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{
"id": 1036155374811762700,
"author_id": 618992877846134800,
"author_name": "SnowZillin",
"timestamp": "10/30/2022 01:51:32",
"content": "LOL i cant see :(",
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{
"id": 1036155405627310100,
"author_id": 618992877846134800,
"author_name": "SnowZillin",
"timestamp": "10/30/2022 01:51:39",
"content": "🦯",
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{
"id": 1036155508740083700,
"author_id": 331558346333224960,
"author_name": "jan Niku",
"timestamp": "10/30/2022 01:52:04",
"content": "",
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{
"id": 1036155519028695200,
"author_id": 618992877846134800,
"author_name": "SnowZillin",
"timestamp": "10/30/2022 01:52:06",
"content": "anyways why is it not allowed",
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{
"id": 1036155520085667800,
"author_id": 331558346333224960,
"author_name": "jan Niku",
"timestamp": "10/30/2022 01:52:06",
"content": "it is almost time to bring him back",
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{
"id": 1036155565241544800,
"author_id": 618992877846134800,
"author_name": "SnowZillin",
"timestamp": "10/30/2022 01:52:17",
"content": "where did u find that lol",
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{
"id": 1036155585063829600,
"author_id": 331558346333224960,
"author_name": "jan Niku",
"timestamp": "10/30/2022 01:52:22",
"content": "a friend made it",
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{
"id": 1036155592009601000,
"author_id": 331558346333224960,
"author_name": "jan Niku",
"timestamp": "10/30/2022 01:52:23",
"content": "on my request",
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{
"id": 1036155642538377200,
"author_id": 618992877846134800,
"author_name": "SnowZillin",
"timestamp": "10/30/2022 01:52:36",
"content": "odd request",
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{
"id": 1036155668215898200,
"author_id": 618992877846134800,
"author_name": "SnowZillin",
"timestamp": "10/30/2022 01:52:42",
"content": "but worth it",
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{
"id": 1036155685139918800,
"author_id": 331558346333224960,
"author_name": "jan Niku",
"timestamp": "10/30/2022 01:52:46",
"content": "i cant tell which lines you mean",
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{
"id": 1036155722578276400,
"author_id": 331558346333224960,
"author_name": "jan Niku",
"timestamp": "10/30/2022 01:52:55",
"content": "they are the lines that are above and below the function?",
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{
"id": 1036155787673866400,
"author_id": 618992877846134800,
"author_name": "SnowZillin",
"timestamp": "10/30/2022 01:53:10",
"content": "wait what colors can u see?",
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{
"id": 1036155813636616200,
"author_id": 618992877846134800,
"author_name": "SnowZillin",
"timestamp": "10/30/2022 01:53:16",
"content": "or i can name then",
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{
"id": 1036155842224996400,
"author_id": 331558346333224960,
"author_name": "jan Niku",
"timestamp": "10/30/2022 01:53:23",
"content": "i guess what im saying is it it would help me and possibly you if you are more specific",
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{
"id": 1036155876437925900,
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"author_name": "jan Niku",
"timestamp": "10/30/2022 01:53:31",
"content": "because the squeeze theorem doesnt have colors in its statement",
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{
"id": 1036155892988649500,
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"author_name": "jan Niku",
"timestamp": "10/30/2022 01:53:35",
"content": "and i dont think it says cross",
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"id": 1036155911124832300,
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"author_name": "SnowZillin",
"timestamp": "10/30/2022 01:53:40",
"content": "",
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"id": 1036155987813470200,
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"author_name": "jan Niku",
"timestamp": "10/30/2022 01:53:58",
"content": "right so it depends where the limit is i guess :thonk:",
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"id": 1036156012610195500,
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"author_name": "SnowZillin",
"timestamp": "10/30/2022 01:54:04",
"content": "the colors are just to represent different lines",
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{
"id": 1036156075361189900,
"author_id": 331558346333224960,
"author_name": "jan Niku",
"timestamp": "10/30/2022 01:54:19",
"content": "lets say the thing youre trying to squeeze is g",
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"author_name": "SnowZillin",
"timestamp": "10/30/2022 01:54:21",
"content": "but you can say about lines that dont intersect with the same exceptions",
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"id": 1036156135201308700,
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"author_name": "jan Niku",
"timestamp": "10/30/2022 01:54:33",
"content": "then what you really want is some function that is always as big or bigger than it",
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"id": 1036156148811841500,
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"author_name": "jan Niku",
"timestamp": "10/30/2022 01:54:36",
"content": "ga",
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"id": 1036156182580183000,
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"author_name": "jan Niku",
"timestamp": "10/30/2022 01:54:44",
"content": "and some functions thats always smaller than or as small as it",
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"id": 1036156186485071900,
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"author_name": "jan Niku",
"timestamp": "10/30/2022 01:54:45",
"content": "gb",
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"author_name": "SnowZillin",
"timestamp": "10/30/2022 01:54:54",
"content": "x<=y<=z right",
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"id": 1036156241128472600,
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"author_name": "jan Niku",
"timestamp": "10/30/2022 01:54:58",
"content": "so that gb <= g <= ga",
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{
"id": 1036156298674327600,
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"author_name": "jan Niku",
"timestamp": "10/30/2022 01:55:12",
"content": "then if you show that gb and ga approach the same limit",
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"id": 1036156353749725200,
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"author_name": "jan Niku",
"timestamp": "10/30/2022 01:55:25",
"content": "**because g is always between them** you can conclude that g shares this limit too",
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"id": 1036156379360145400,
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"author_name": "jan Niku",
"timestamp": "10/30/2022 01:55:31",
"content": "once lines start crossing you uhh",
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"author_name": "SnowZillin",
"timestamp": "10/30/2022 01:55:35",
"content": "ye but why does that matter at the end of the day we want to find the initial lines not follow rules",
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"id": 1036156398561660900,
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"author_name": "jan Niku",
"timestamp": "10/30/2022 01:55:36",
"content": "i guess it depends on which lines cross",
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{
"id": 1036156433118543900,
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"author_name": "SnowZillin",
"timestamp": "10/30/2022 01:55:44",
"content": "it would break that rule tho",
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{
"id": 1036156509865902100,
"author_id": 331558346333224960,
"author_name": "jan Niku",
"timestamp": "10/30/2022 01:56:02",
"content": "i wonder if what youre asking is uhh",
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{
"id": 1036156521400250500,
"author_id": 618992877846134800,
"author_name": "SnowZillin",
"timestamp": "10/30/2022 01:56:05",
"content": "but none the less the same answer can be got with crossing lines",
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{
"id": 1036156531416252400,
"author_id": 331558346333224960,
"author_name": "jan Niku",
"timestamp": "10/30/2022 01:56:07",
"content": "okay so the limit may be or not be something",
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{
"id": 1036156565696294900,
"author_id": 331558346333224960,
"author_name": "jan Niku",
"timestamp": "10/30/2022 01:56:16",
"content": "what is important is that the squeeze theorem has conditions",
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{
"id": 1036156596620898300,
"author_id": 331558346333224960,
"author_name": "jan Niku",
"timestamp": "10/30/2022 01:56:23",
"content": "and if theyre satisfied, you get something for free",
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{
"id": 1036156622000631800,
"author_id": 331558346333224960,
"author_name": "jan Niku",
"timestamp": "10/30/2022 01:56:29",
"content": "if theyre not, you may still get the something",
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{
"id": 1036156684864847900,
"author_id": 331558346333224960,
"author_name": "jan Niku",
"timestamp": "10/30/2022 01:56:44",
"content": "but its not because the squeeze theorem",
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"id": 1036156782374039600,
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"author_name": "SnowZillin",
"timestamp": "10/30/2022 01:57:07",
"content": "so your saying crossing lines means a special rare case is violated?",
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"id": 1036156865039568900,
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"author_name": "SnowZillin",
"timestamp": "10/30/2022 01:57:27",
"content": "but maybe sometimes it works",
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"id": 1036156867287724000,
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"author_name": "jan Niku",
"timestamp": "10/30/2022 01:57:28",
"content": "idk what you mean special or rare",
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"author_name": "jan Niku",
"timestamp": "10/30/2022 01:57:42",
"content": "its not clear what lines would be crossing but i think any of these lines crossing is a problem",
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{
"id": 1036156960778760300,
"author_id": 331558346333224960,
"author_name": "jan Niku",
"timestamp": "10/30/2022 01:57:50",
"content": "it means some condition of the squeeze theorem isnt being satisfied",
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{
"id": 1036156982769496000,
"author_id": 618992877846134800,
"author_name": "SnowZillin",
"timestamp": "10/30/2022 01:57:55",
"content": "yes",
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{
"id": 1036157013257896100,
"author_id": 331558346333224960,
"author_name": "jan Niku",
"timestamp": "10/30/2022 01:58:02",
"content": "which condition depends on which lines",
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{
"id": 1036157083424407600,
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"author_name": "SnowZillin",
"timestamp": "10/30/2022 01:58:19",
"content": "but why does it matter if the condition of no crossing lines is violated",
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{
"id": 1036157111148748800,
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"author_name": "jan Niku",
"timestamp": "10/30/2022 01:58:26",
"content": "if gb crosses ga something has gone horribly wrong",
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{
"id": 1036157137975509000,
"author_id": 331558346333224960,
"author_name": "jan Niku",
"timestamp": "10/30/2022 01:58:32",
"content": "if g crosses ga or g crosses gb",
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{
"id": 1036157161388122200,
"author_id": 331558346333224960,
"author_name": "jan Niku",
"timestamp": "10/30/2022 01:58:38",
"content": "you maybe just have a little more work to do",
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{
"id": 1036157169537667100,
"author_id": 618992877846134800,
"author_name": "SnowZillin",
"timestamp": "10/30/2022 01:58:40",
"content": "but you get the same answer",
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{
"id": 1036157201577951200,
"author_id": 618992877846134800,
"author_name": "SnowZillin",
"timestamp": "10/30/2022 01:58:47",
"content": "screws over the theorum formula",
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{
"id": 1036157245983051800,
"author_id": 331558346333224960,
"author_name": "jan Niku",
"timestamp": "10/30/2022 01:58:58",
"content": "whats important to understand is like",
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{
"id": 1036157278870569100,
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"author_name": "jan Niku",
"timestamp": "10/30/2022 01:59:06",
"content": "okay you tried one case and got the same answer",
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"timestamp": "10/30/2022 01:59:10",
"content": "or maybe you try a hundred cases",
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"content": "whats cool about a theorem is it gives you a set of conditions",
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"content": "and then says something is always true",
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"content": "but if you only follow the rules it will be harder to create your own rules",
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"content": "this question is an outlet to question athority and i think authority is wrong",
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"content": "squeeze theorem isnt a rule",
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"content": "its not even a property",
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"content": "its just a consequence",
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"content": "its like",
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"content": "a result",
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"content": "i mean like a rule as in thats what ur supposed to do",
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"content": "there are no rules in the squeeze theorem lol",
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"timestamp": "10/30/2022 02:01:12",
"content": "do it this way because you are taught this way",
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"content": "your supposed to not cross lines",
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"timestamp": "10/30/2022 02:01:40",
"content": "i think thats a rule maybe not technically",
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"content": "i think the not crossing lines is a mnemonic they are trying to give you",
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"content": "regardless if its a free correct answer, i want to know why my answer would give an incorect one",
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"timestamp": "10/30/2022 02:02:06",
"content": "and its supposed to tell you whether or not youve correctly bounded the function",
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"content": "mnemonic?",
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"timestamp": "10/30/2022 02:02:14",
"content": ",w mnemonic",
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"timestamp": "10/30/2022 02:02:18",
"content": "Results provided by WolframAlpha",
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"timestamp": "10/30/2022 02:02:30",
"content": "so you dont have to remember a complicated definition",
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"timestamp": "10/30/2022 02:02:33",
"content": "and thats the only use",
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"content": "if you roughly get the idea",
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"content": "of the lines crossing?",
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"timestamp": "10/30/2022 02:02:42",
"content": "that would be a rational explination",
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"timestamp": "10/30/2022 02:02:47",
"content": "Where did you see whatever you are concerned about?",
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"content": "my brain",
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"content": "they said khan academy",
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"timestamp": "10/30/2022 02:03:10",
"content": "ig that would be a good explination for the rule",
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"content": "i mean if you create an upper and lower bound of something",
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"timestamp": "10/30/2022 02:03:18",
"content": "and things start crossing each other",
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"timestamp": "10/30/2022 02:03:19",
"content": "ye calc 1 squeeze theorum",
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"timestamp": "10/30/2022 02:03:21",
"content": "something has gone wrong",
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"timestamp": "10/30/2022 02:03:49",
"content": "Might help to send the khan academy thing",
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"timestamp": "10/30/2022 02:03:57",
"content": "same result more chance of getting it wrong but makes sense",
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"content": "the squeeze theorem is like",
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"timestamp": "10/30/2022 02:04:35",
"content": "ppl will judge me but",
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"content": "the answer is b",
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"timestamp": "10/30/2022 02:04:39",
"content": "squeeze theorem is esoteric",
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"content": "compared to other whatever fundamental calculus theorems",
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"content": "esoteric?",
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"timestamp": "10/30/2022 02:05:00",
"content": "vague?",
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"timestamp": "10/30/2022 02:05:08",
"content": "its just not as important as others",
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"content": "you will use mean value theorem and extreme value theorem and intermediate value theorem",
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"timestamp": "10/30/2022 02:05:26",
"content": "all the time",
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"content": "ye i dont really see a use case for squeeze",
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"content": "it has a great use",
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"timestamp": "10/30/2022 02:05:46",
"content": "So what’s the not crossing thing?",
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"timestamp": "10/30/2022 02:06:10",
"content": "im guessing this is a limit at 0?",
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"content": "cant cross lines the 2 squeezing lines in the squeeze theorum",
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"content": "in the image you sent",
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"content": "ye but it has color lines that cross",
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"content": "yea but not 'near' 0",
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"content": "it claims its wrong because they cross",
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"content": "well it depends where the limit is",
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"timestamp": "10/30/2022 02:06:49",
"content": "whats the claim",
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"timestamp": "10/30/2022 02:06:53",
"content": "can you show the entire question?",
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"timestamp": "10/30/2022 02:07:04",
"content": "Where does it say anything about crossing?",
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"content": "its 0 the limit",
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"content": "the explination and the question",
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"content": "one has to stay above",
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"content": "on has to stay below",
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"content": "The analysis in that option is between f and h, and f and g",
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"content": "i think i agree with u cat man, i think its just a rule to help you not screw it up",
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"content": "Not between g and h",
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"content": "I mean like when it says the outputs of one function is always below f(x)",
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"timestamp": "10/30/2022 02:09:47",
"content": "this is like a prime example of what i was saying btw",
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"content": "its done right tho",
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"author_name": "💜𝓁𝒶𝓎𝓁𝒶💜",
"timestamp": "10/30/2022 02:10:04",
"content": "That’s something about f and h or about f and g",
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"content": "that you may get to some answer but its not because you used a theorem correctly",
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"timestamp": "10/30/2022 02:10:17",
"content": "oh yeah but its right regardless",
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"content": "squeeze theorem is clearly not satisfied here",
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"content": "so nothing has been shown",
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"timestamp": "10/30/2022 02:10:27",
"content": "ye",
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"timestamp": "10/30/2022 02:11:14",
"content": "wdym",
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"author_id": 618992877846134800,
"author_name": "SnowZillin",
"timestamp": "10/30/2022 02:11:37",
"content": "it wants f to h to always be above f or touching and g to be below or touching",
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"timestamp": "10/30/2022 02:11:59",
"content": "naw but i think i understand it, its just done to prevent some user made mistakes",
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"timestamp": "10/30/2022 02:12:28",
"content": "always works if used correctly",
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"timestamp": "10/30/2022 02:12:54",
"content": "but i think im good ty @jan Niku cat man",
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"timestamp": "10/30/2022 02:13:03",
"content": "Channel closed",
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] | help-9 | 8100cc5007dd4fee9d9020ed30f23f79 |
200,866 | [
{
"id": 1065497560275492900,
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"id": 1065499924415918100,
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"author_name": "PB",
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"content": "Given that point B is (5,7), Point C is (5,1)",
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"author_id": 483962566977126400,
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"timestamp": "01/19/2023 00:17:12",
"content": "yes?",
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"id": 1065500317543825400,
"author_id": 708594064060055600,
"author_name": "PB",
"timestamp": "01/19/2023 00:17:51",
"content": "Then the equation that were created by those two points is x=5",
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"id": 1065500349277941800,
"author_id": 708594064060055600,
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"timestamp": "01/19/2023 00:17:59",
"content": "Am I right",
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"id": 1065500427279421400,
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"timestamp": "01/19/2023 00:18:17",
"content": "Then I have problem",
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"id": 1065500476671524900,
"author_id": 374795910032523260,
"author_name": "SWR",
"timestamp": "01/19/2023 00:18:29",
"content": "\"Then I have _a_ problem\"",
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"id": 1065500573127950300,
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"timestamp": "01/19/2023 00:18:52",
"content": "There’s a triangle called ABC, A is (2,5), B(5,1), C(3,7) and P is a point between lineBC, then given that the orthograph of Vector AP on Vector AB is [(6/25),(-8/25)]. Asks for the coordinate of P",
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"id": 1065500581667541000,
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"author_name": "SWR",
"timestamp": "01/19/2023 00:18:54",
"content": "\"Then the equation that _is_ created by these two points is x=5\"",
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"id": 1065500617457533000,
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"author_name": "PB",
"timestamp": "01/19/2023 00:19:03",
"content": "Thank you",
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"id": 1065500646234656900,
"author_id": 374795910032523260,
"author_name": "SWR",
"timestamp": "01/19/2023 00:19:10",
"content": "(or _was_, either works)",
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"id": 1065500678434345100,
"author_id": 708594064060055600,
"author_name": "PB",
"timestamp": "01/19/2023 00:19:17",
"content": "Here’s the original question",
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"author_name": "PB",
"timestamp": "01/19/2023 00:20:18",
"content": "So I assumed P is (x,y)",
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"timestamp": "01/19/2023 00:21:04",
"content": "Then I put it into the “formula” and i got the blue underlined as the result",
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"id": 1065501324650750000,
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"timestamp": "01/19/2023 00:21:51",
"content": "So that gonna create two overlapping lines",
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"timestamp": "01/19/2023 00:23:20",
"content": "If I could Find the intersection point with lineBC then the question is solved",
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"timestamp": "01/19/2023 00:23:42",
"content": "But the y would be 27/4 which is indifferent to the correct answer",
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"id": 1065501819545067500,
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"author_name": "PB",
"timestamp": "01/19/2023 00:23:49",
"content": "Someone know where’s wrong",
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"author_name": "SWR",
"timestamp": "01/19/2023 00:24:31",
"content": "By orthograph, I believe we americans call it vector projection",
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"timestamp": "01/19/2023 00:24:39",
"content": "Just confirming if I've assumed right",
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"id": 1065503882685448200,
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"timestamp": "01/19/2023 00:32:01",
"content": "Yes ure right",
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"timestamp": "01/19/2023 00:32:22",
"content": "It is called vector projection",
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"author_name": "PB",
"timestamp": "01/19/2023 00:33:48",
"content": "So basically P is the intersection point of x=5 and “L”",
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"id": 1065506218694688800,
"author_id": 374795910032523260,
"author_name": "SWR",
"timestamp": "01/19/2023 00:41:18",
"content": "C is (3, 7), not (5, 7)",
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"timestamp": "01/19/2023 00:48:48",
"content": "@PB Has your question been resolved?",
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"timestamp": "01/19/2023 00:51:09",
"content": "God, you just saved my day",
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"id": 1065508891884015600,
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"timestamp": "01/19/2023 00:51:56",
"content": "good thing you shared the original problem",
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"timestamp": "01/19/2023 01:03:49",
"content": "Channel closed",
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}
] | help-9 | 3688c990bb8e41ffa4b474a970f71744 |
200,867 | [
{
"id": 1065513065317142500,
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"author_name": "Mathematics Bot",
"timestamp": "01/19/2023 01:08:31",
"content": "Available help channel!",
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},
{
"id": 1065514919539261400,
"author_id": 398953173647228900,
"author_name": "BeastCris",
"timestamp": "01/19/2023 01:15:53",
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"timestamp": "01/19/2023 01:15:53",
"content": "Pinned a message.",
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"author_id": 398953173647228900,
"author_name": "BeastCris",
"timestamp": "01/19/2023 01:20:15",
"content": "do i format it like 12/4x+7 = 8/18?",
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"id": 1065516243345486000,
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"timestamp": "01/19/2023 01:21:08",
"content": "and then cross multiply",
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"timestamp": "01/19/2023 01:23:18",
"content": "thank you @SWR",
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"timestamp": "01/19/2023 01:23:47",
"content": "all you, my friend",
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"timestamp": "01/19/2023 01:24:25",
"content": ".close",
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"timestamp": "01/19/2023 01:24:26",
"content": "Channel closed",
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] | help-9 | 2941180706c44e3885806283f0a7f8ec |
200,868 | [
{
"id": 1065521044154228700,
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"timestamp": "01/19/2023 01:40:13",
"content": "Available help channel!",
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{
"id": 1065523043750903800,
"author_id": 361978877146431500,
"author_name": "EsE",
"timestamp": "01/19/2023 01:48:10",
"content": "How do I do c A?",
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"content": "Pinned a message.",
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"author_name": "EsE",
"timestamp": "01/19/2023 01:48:44",
"content": "I need to find out a value of a vertex at 3 -1 and x intercept at 1,0",
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{
"id": 1065523475541930100,
"author_id": 521445300989198340,
"author_name": "WHAT?",
"timestamp": "01/19/2023 01:49:53",
"content": "Do u know vertex form",
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"id": 1065523628994744400,
"author_id": 196447219484852220,
"author_name": "NotABot",
"timestamp": "01/19/2023 01:50:29",
"content": "Do you know how to get a quadratic equation from its two x-intercepts?",
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"id": 1065524607093854200,
"author_id": 361978877146431500,
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"timestamp": "01/19/2023 01:54:22",
"content": "I don’t think so",
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"id": 1065524868071833700,
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"author_name": "NotABot",
"timestamp": "01/19/2023 01:55:25",
"content": "Well let's say f(x) is your quadratic equation, and your vertex occurs at x=n",
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"id": 1065524939978969200,
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"author_name": "NotABot",
"timestamp": "01/19/2023 01:55:42",
"content": "For all values for m, f(n-m) = f(n+m), right?",
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"id": 1065524974275797000,
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"timestamp": "01/19/2023 01:55:50",
"content": "Yes",
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"id": 1065525121676214300,
"author_id": 196447219484852220,
"author_name": "NotABot",
"timestamp": "01/19/2023 01:56:25",
"content": "Oh wait I was explaining how to find a second x intercept",
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"id": 1065525175300403200,
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"author_name": "EsE",
"timestamp": "01/19/2023 01:56:38",
"content": "Oh",
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"id": 1065525200889860100,
"author_id": 361978877146431500,
"author_name": "EsE",
"timestamp": "01/19/2023 01:56:44",
"content": "I need to find a value",
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"id": 1065525209148444700,
"author_id": 361978877146431500,
"author_name": "EsE",
"timestamp": "01/19/2023 01:56:46",
"content": "A",
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"id": 1065525472215183400,
"author_id": 196447219484852220,
"author_name": "NotABot",
"timestamp": "01/19/2023 01:57:49",
"content": "So any quadratic equation that crosses y=0 can be expressed as (nx - i)(mx - j), where i/n and j/m are your x-intercepts (Changes a & b to i & j to prevent confusion)",
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"timestamp": "01/19/2023 01:58:39",
"content": "Ok",
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"id": 1065525866530099200,
"author_id": 196447219484852220,
"author_name": "NotABot",
"timestamp": "01/19/2023 01:59:23",
"content": "Because ax^2 + bx + c will equal 0 when either (nx - i) or (mx - i) equal 0. Make sense?",
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"id": 1065526059128344700,
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"author_name": "EsE",
"timestamp": "01/19/2023 02:00:09",
"content": "Alright",
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"author_name": "NotABot",
"timestamp": "01/19/2023 02:01:09",
"content": "So if you use that and the bit I was talking about above for finding your 2nd x-intercept, you'll be able to find a quadratic equation that shares the x-intercepts and the x value for the vertex of the quadratic equation you'll want",
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"timestamp": "01/19/2023 02:01:51",
"content": "Then all you need to do is change that quadratic equation into one that shares the y value of the vertex as well",
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"timestamp": "01/19/2023 02:04:00",
"content": "Oh I looked up higher on the sheet, yeah looking for a value for `a` is what you'll do in the last step there. I thought it meant `a` as in the fairly common notation `ax^2 + bx + c`",
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"id": 1065527092130893800,
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"timestamp": "01/19/2023 02:04:15",
"content": "Oh",
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"id": 1065527398038241400,
"author_id": 361978877146431500,
"author_name": "EsE",
"timestamp": "01/19/2023 02:05:28",
"content": "So is there a template when solving for A?",
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"author_id": 361978877146431500,
"author_name": "EsE",
"timestamp": "01/19/2023 02:05:35",
"content": "Or formula?",
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"id": 1065527622865518600,
"author_id": 196447219484852220,
"author_name": "NotABot",
"timestamp": "01/19/2023 02:06:21",
"content": "I don't know, I haven't done that kind of math in ages",
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"id": 1065527830336782300,
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"timestamp": "01/19/2023 02:07:11",
"content": "Aw man",
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"id": 1065527880748105700,
"author_id": 196447219484852220,
"author_name": "NotABot",
"timestamp": "01/19/2023 02:07:23",
"content": "But the way I was talking about should work, finding the 2nd intercept and solving for A based on the value of the resulting vertex",
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"id": 1065528008921841700,
"author_id": 196447219484852220,
"author_name": "NotABot",
"timestamp": "01/19/2023 02:07:53",
"content": "Sorry if I explained things in a way that doesn't line up with your current knowledge. Need me to clarify any of that?",
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"id": 1065528180523413500,
"author_id": 361978877146431500,
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"timestamp": "01/19/2023 02:08:34",
"content": "No",
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"id": 1065528262035513500,
"author_id": 361978877146431500,
"author_name": "EsE",
"timestamp": "01/19/2023 02:08:54",
"content": "Just seems more advanced then what I’m currently learning",
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"author_id": 196447219484852220,
"author_name": "NotABot",
"timestamp": "01/19/2023 02:09:25",
"content": "👍 good luck",
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"author_id": 805217272087838700,
"author_name": "Mathematics Bot",
"timestamp": "01/19/2023 02:23:54",
"content": "@EsE Has your question been resolved?",
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"timestamp": "01/19/2023 02:38:54",
"content": "Channel closed",
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] | help-9 | 49ea56263b1147a2b2710fbcbea0b319 |
200,869 | [
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"id": 1065537810901250200,
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"timestamp": "01/19/2023 02:46:50",
"content": "Available help channel!",
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"content": "if $\\log_7{2}=a$ and $\\log_2{3}=b$ then what is $\\log_98{6}$?",
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"content": "**Skill\\_Issue**",
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"timestamp": "01/19/2023 03:31:56",
"content": "the furthest i got was $\\frac{a(1+b)}{a+2}$ and the choices is -1,1,2,3,4",
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"content": "Did you mean $\\log_{98}{6}$?",
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"content": "Was wondering the same",
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"content": ":KEK:",
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"content": "@Skill_Issue",
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"timestamp": "01/19/2023 03:47:14",
"content": "oh yeah",
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"content": "hold on",
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"timestamp": "01/19/2023 03:50:15",
"content": "This is right :checkmark:",
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"timestamp": "01/19/2023 03:50:19",
"content": "what i did was split it into $\\frac{\\log_7{6}}{\\log_7{98}}$",
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"content": "**Skill\\_Issue**",
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"timestamp": "01/19/2023 03:51:42",
"content": "then the $\\log_7{6}$ i turned into $\\log_7{2}+\\log_7{3}$",
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"content": "**Skill\\_Issue**",
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"timestamp": "01/19/2023 03:52:33",
"content": "and thw bottom i made it into $\\log_7{2}+\\log_7{7}+\\log_7{7}$",
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"content": "**Skill\\_Issue**",
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"timestamp": "01/19/2023 03:53:29",
"content": "and since $\\log_7{7}$ is 1 i just made them 1's and $\\log_7{3}$ is ab",
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"content": "**Skill\\_Issue**",
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"timestamp": "01/19/2023 03:53:51",
"content": "inserting a and b and ab's it becomes what i got, did i do anything wrong?",
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"timestamp": "01/19/2023 03:55:35",
"content": "How did you get $\\log_{7}{3}=ab$?",
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"timestamp": "01/19/2023 03:55:44",
"content": "**SWR**",
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"timestamp": "01/19/2023 03:56:11",
"content": "Change of base rule",
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"timestamp": "01/19/2023 03:56:30",
"content": "is this the right answer?",
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"id": 1065555388528873500,
"author_id": 756527780832870500,
"author_name": "eatone_QUBIT",
"timestamp": "01/19/2023 03:56:41",
"content": "oh ig u did the same thing like me",
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"timestamp": "01/19/2023 03:56:57",
"content": "Just wanted them to show their work",
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"timestamp": "01/19/2023 04:00:10",
"content": "$\\log_7{2}×\\log_2{3}=ab$ and using the $\\log_a{b}×\\log_b{c}=\\log_a{c}$ you get $\\log_7{3}=ab$",
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"timestamp": "01/19/2023 04:00:12",
"content": "**Skill\\_Issue**",
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"timestamp": "01/19/2023 04:00:43",
"content": "Cool",
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"author_id": 374795910032523260,
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"timestamp": "01/19/2023 04:00:51",
"content": "Might be worth showing that in your hw",
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"timestamp": "01/19/2023 04:01:01",
"content": "I would get -1 from teacher for omitting a step like that",
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"author_id": 756527780832870500,
"author_name": "eatone_QUBIT",
"timestamp": "01/19/2023 04:01:18",
"content": "damn u r taking this too serious lmao",
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"timestamp": "01/19/2023 04:01:26",
"content": "lmao",
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"author_id": 756527780832870500,
"author_name": "eatone_QUBIT",
"timestamp": "01/19/2023 04:01:37",
"content": "looks like he/she is a professor too",
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"id": 1065556648812367900,
"author_id": 750992393502720000,
"author_name": "Skill_Issue",
"timestamp": "01/19/2023 04:01:42",
"content": "does the question have no answer?",
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"author_id": 709050483335102600,
"author_name": "Hazysleet",
"timestamp": "01/19/2023 04:02:03",
"content": ",w log_{98} 6",
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"timestamp": "01/19/2023 04:02:06",
"content": "Results provided by WolframAlpha",
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"author_id": 750992393502720000,
"author_name": "Skill_Issue",
"timestamp": "01/19/2023 04:02:07",
"content": "not homework, just a question from a book that im wanting to learn",
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"timestamp": "01/19/2023 04:02:39",
"content": "If they come for help, they're gonna get the **best** help",
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"timestamp": "01/19/2023 04:02:53",
"content": "right",
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"timestamp": "01/19/2023 04:02:53",
"content": "You've been on the right track so far",
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"timestamp": "01/19/2023 04:03:49",
"content": "I've tutored for like 10 years. And my teachers drilled into me I had to show my work. I was little showoff and would do the math in my head and they would give me zeros.",
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"author_name": "Skill_Issue",
"timestamp": "01/19/2023 04:05:41",
"content": "should i just close the channel because its like basically finished and there is no answer",
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"id": 1065557709937705000,
"author_id": 709050483335102600,
"author_name": "Hazysleet",
"timestamp": "01/19/2023 04:05:55",
"content": "Seems like it",
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"timestamp": "01/19/2023 04:06:09",
"content": "thx for the help",
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"id": 1065557775041691600,
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"timestamp": "01/19/2023 04:06:10",
"content": ".close",
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"content": "Channel closed",
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] | help-9 | a9869c7558ec4f15bf98adf925318507 |
200,870 | [
{
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"timestamp": "01/19/2023 05:36:45",
"content": "Can f(x) = $f^{-1}(x)$ have solutions other than those lying on y = x, if yes, example?",
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"timestamp": "01/19/2023 05:36:47",
"content": "**Darth Vader**",
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"author_name": "💜𝓁𝒶𝓎𝓁𝒶💜",
"timestamp": "01/19/2023 05:44:53",
"content": "if you look at any point, say, x_1 in f's domain and f(x_1) is not x_1, that means f^(-1)(x_1) will be smth other than f(x_1) (it will be on the opposite side of the line y = x)",
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"content": "@Darth Vader Has your question been resolved?",
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"timestamp": "01/19/2023 05:52:28",
"content": "I don't get it",
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"id": 1065585051871486000,
"author_id": 984319941417251000,
"author_name": "💜𝓁𝒶𝓎𝓁𝒶💜",
"timestamp": "01/19/2023 05:54:33",
"content": "f is an invertible function, you want to determine if there are any x's in f's domain that make f(x) = f^(-1)(x) true outside the ones for which f(x) = x",
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"timestamp": "01/19/2023 05:55:02",
"content": "yes",
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"author_name": "💜𝓁𝒶𝓎𝓁𝒶💜",
"timestamp": "01/19/2023 05:55:11",
"content": "ok sooooo",
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"id": 1065585279211159600,
"author_id": 984319941417251000,
"author_name": "💜𝓁𝒶𝓎𝓁𝒶💜",
"timestamp": "01/19/2023 05:55:28",
"content": "if you send something (say x_1) through f",
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"author_name": "💜𝓁𝒶𝓎𝓁𝒶💜",
"timestamp": "01/19/2023 05:56:23",
"content": "and it doesn't return x_1 (so f(x_1) is not equal to x_1)",
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"author_name": "💜𝓁𝒶𝓎𝓁𝒶💜",
"timestamp": "01/19/2023 05:56:54",
"content": "ok i'm basically just repeating myself i'll draw a little picture instead",
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"author_name": "💜𝓁𝒶𝓎𝓁𝒶💜",
"timestamp": "01/19/2023 05:58:13",
"content": "nvm not drawing it loll",
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"timestamp": "01/19/2023 05:58:14",
"content": "",
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"author_name": "💜𝓁𝒶𝓎𝓁𝒶💜",
"timestamp": "01/19/2023 05:58:29",
"content": "green is the line y = x, red is f, blue is f^(-1)",
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"author_name": "💜𝓁𝒶𝓎𝓁𝒶💜",
"timestamp": "01/19/2023 05:58:43",
"content": "so what i'm saying is",
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"id": 1065586268366450800,
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"author_name": "💜𝓁𝒶𝓎𝓁𝒶💜",
"timestamp": "01/19/2023 05:59:24",
"content": "f(x_1) is going to be one side of y=x, and f^(-1)(x_1) will be on the other",
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{
"id": 1065586622747381900,
"author_id": 984319941417251000,
"author_name": "💜𝓁𝒶𝓎𝓁𝒶💜",
"timestamp": "01/19/2023 06:00:48",
"content": "pink being one \"side\" of y=x",
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"id": 1065587160440373400,
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"author_name": "💜𝓁𝒶𝓎𝓁𝒶💜",
"timestamp": "01/19/2023 06:02:56",
"content": "actually i'm not saying what i'm trying to",
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"id": 1065587421409984500,
"author_id": 913378914318053400,
"author_name": "Darth Vader",
"timestamp": "01/19/2023 06:03:58",
"content": "I'll be back later today can I ping you then",
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{
"id": 1065591486793666600,
"author_id": 984319941417251000,
"author_name": "💜𝓁𝒶𝓎𝓁𝒶💜",
"timestamp": "01/19/2023 06:20:08",
"content": "what i said isn't quite right",
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{
"id": 1065592754186494000,
"author_id": 984319941417251000,
"author_name": "💜𝓁𝒶𝓎𝓁𝒶💜",
"timestamp": "01/19/2023 06:25:10",
"content": "even more thn that i think it is possible to have other solutions actually",
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"id": 1065592810713124900,
"author_id": 984319941417251000,
"author_name": "💜𝓁𝒶𝓎𝓁𝒶💜",
"timestamp": "01/19/2023 06:25:23",
"content": "and what i said might hold for continuous functions or smth",
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"id": 1065593570142199800,
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"author_name": "💜𝓁𝒶𝓎𝓁𝒶💜",
"timestamp": "01/19/2023 06:28:24",
"content": "which means it's totally irrelevant",
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"timestamp": "01/19/2023 06:38:25",
"content": "@Darth Vader Has your question been resolved?",
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"author_id": 1029124463993815000,
"author_name": "stellar",
"timestamp": "01/19/2023 06:48:41",
"content": "whats the problem here",
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"author_name": "💜𝓁𝒶𝓎𝓁𝒶💜",
"timestamp": "01/19/2023 06:49:35",
"content": "just ignore everything i said 🙃",
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"author_id": 805217272087838700,
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"timestamp": "01/19/2023 07:08:25",
"content": "Channel closed",
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] | help-9 | 68e4a43c888f4bd68365e5fed3190e84 |
200,871 | [
{
"id": 1065603891573571600,
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"author_name": "Mathematics Bot",
"timestamp": "01/19/2023 07:09:25",
"content": "Available help channel!",
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},
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"id": 1065605845976621200,
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"timestamp": "01/19/2023 07:17:12",
"content": "Pinned a message.",
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"timestamp": "01/19/2023 07:17:24",
"content": "@Helpers",
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},
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"id": 1065605929208393700,
"author_id": 1022141568737607800,
"author_name": "♡A(lex)♡",
"timestamp": "01/19/2023 07:17:31",
"content": "!15m",
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"id": 1065605930319884400,
"author_id": 805217272087838700,
"author_name": "Mathematics Bot",
"timestamp": "01/19/2023 07:17:31",
"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": 1065606290858049500,
"author_id": 394938706760302600,
"author_name": "heavy",
"timestamp": "01/19/2023 07:18:57",
"content": "quotient rule for differentiation",
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"author_id": 1022141568737607800,
"author_name": "♡A(lex)♡",
"timestamp": "01/19/2023 07:19:34",
"content": "Wouldn't that be missing a 2",
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"id": 1065606462451241100,
"author_id": 1022141568737607800,
"author_name": "♡A(lex)♡",
"timestamp": "01/19/2023 07:19:38",
"content": "In the right term",
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"id": 1065606872293449700,
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"author_name": "heavy",
"timestamp": "01/19/2023 07:21:16",
"content": "not sure what you mean",
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"id": 1065606926215413800,
"author_id": 394938706760302600,
"author_name": "heavy",
"timestamp": "01/19/2023 07:21:29",
"content": "but you can certainly reverse engineer the quotient rule for this",
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"id": 1065607377774198800,
"author_id": 718461587236716500,
"author_name": "NEONPerseus",
"timestamp": "01/19/2023 07:23:16",
"content": "or perhaps split it in two fractions and substitutions?",
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"id": 1065609676647047300,
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"timestamp": "01/19/2023 07:32:24",
"content": "@bl4ze2124265 Has your question been resolved?",
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"timestamp": "01/19/2023 07:36:27",
"content": "Channel closed",
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] | help-9 | 9b429f74e41a4fd7898c886f379d065d |
200,872 | [
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"timestamp": "01/19/2023 07:37:27",
"content": "Available help channel!",
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"id": 1065615590959624300,
"author_id": 837395382111567900,
"author_name": "Tahseenzen",
"timestamp": "01/19/2023 07:55:55",
"content": "Can someone help with this?",
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"timestamp": "01/19/2023 07:55:56",
"content": "Pinned a message.",
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{
"id": 1065616704798982100,
"author_id": 187850624421986300,
"author_name": "Circle",
"timestamp": "01/19/2023 08:00:20",
"content": "ER",
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},
{
"id": 1065616755935952900,
"author_id": 187850624421986300,
"author_name": "Circle",
"timestamp": "01/19/2023 08:00:32",
"content": "im just gonna assume GH passes through mid points again",
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"id": 1065616838073008100,
"author_id": 187850624421986300,
"author_name": "Circle",
"timestamp": "01/19/2023 08:00:52",
"content": "in which case u can treat the thing as a",
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"id": 1065616860395098100,
"author_id": 187850624421986300,
"author_name": "Circle",
"timestamp": "01/19/2023 08:00:57",
"content": "similar triangles",
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"content": "abd uk the ratio of lengths",
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"content": "else idk",
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"content": "idk how to progress on the lengths part",
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"content": "cuz idk any of the lengths",
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"author_name": "blanket",
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"content": "aint that",
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"author_id": 178624944505094140,
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"timestamp": "01/19/2023 08:11:19",
"content": "24?",
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"id": 1065619496846491600,
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"content": "wait",
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"content": "no hold on",
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"content": "@Tahseenzen i think its 72",
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"content": "@Tahseenzen Has your question been resolved?",
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"content": "@Tahseenzen Has your question been resolved?",
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"content": "@Tahseenzen Has your question been resolved?",
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] | help-9 | 6640ea1676f0490aaa4e5e68200856d5 |
200,873 | [
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"author_name": "Pedr0_",
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"content": "I think the problem is in the modeling",
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"content": "Cuz Ive checked the integral already on the calculator",
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"content": "You’ve set up the volume integral incorrectly",
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"content": "Check what you’ve put as the height of each shell again",
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"timestamp": "01/19/2023 11:09:26",
"content": "Thank you 😄",
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"content": ".close",
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] | help-9 | 1c9e05b3262b42e0b5c3105bff84d069 |
200,874 | [
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"id": 1065667106227626000,
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"author_name": "Nattly",
"timestamp": "01/19/2023 11:20:37",
"content": "so this question asks for Rt to be made the subject, but it already kinda is, yet rewritting the expression dosnt say its right, is there something im missing?",
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"content": "discriminant easier",
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"content": "huh?",
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"timestamp": "01/19/2023 11:23:48",
"content": "what test is this?",
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"content": "what",
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"content": "this isnt a test",
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"timestamp": "01/19/2023 11:24:04",
"content": "meme?",
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"content": "what....",
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"author_name": "XGPURustam",
"timestamp": "01/19/2023 11:24:44",
"content": "you didnt understand i mean whitch lesson of math is it",
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"timestamp": "01/19/2023 11:24:59",
"content": "just algabra as far as im aware",
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"timestamp": "01/19/2023 11:25:10",
"content": "oh ok",
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"author_name": "Nattly",
"timestamp": "01/19/2023 11:25:19",
"content": "as i said, it wants Rt to be the subject... but it is...",
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"id": 1065668463093350400,
"author_id": 880146339072188400,
"author_name": "XGPURustam",
"timestamp": "01/19/2023 11:26:00",
"content": "i have always noticed that geometry cooler than algebra",
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"id": 1065668652315197400,
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"author_name": "Nattly",
"timestamp": "01/19/2023 11:26:45",
"content": "@Helpers",
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"id": 1065668789259214800,
"author_id": 724588567451533300,
"author_name": "biharihacker",
"timestamp": "01/19/2023 11:27:18",
"content": "yes",
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"id": 1065668796532142100,
"author_id": 724588567451533300,
"author_name": "biharihacker",
"timestamp": "01/19/2023 11:27:20",
"content": "ask q",
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"id": 1065668833563643900,
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"timestamp": "01/19/2023 11:27:29",
"content": "this",
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"author_id": 880146339072188400,
"author_name": "XGPURustam",
"timestamp": "01/19/2023 11:27:30",
"content": "use photomath until they came",
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"author_name": "Nattly",
"timestamp": "01/19/2023 11:27:43",
"content": "please stop commenting in here",
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"author_id": 880146339072188400,
"author_name": "XGPURustam",
"timestamp": "01/19/2023 11:28:29",
"content": "you are to me?",
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"id": 1065669112119971800,
"author_id": 270678085983141900,
"author_name": "Nattly",
"timestamp": "01/19/2023 11:28:35",
"content": "it wants Rt to be the subject but as far as i can tell its not correct, i believe im wrong somehow",
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"id": 1065669222887346300,
"author_id": 270678085983141900,
"author_name": "Nattly",
"timestamp": "01/19/2023 11:29:01",
"content": "or atleast im missing something",
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"id": 1065669843027763200,
"author_id": 176048095543558140,
"author_name": "tushar",
"timestamp": "01/19/2023 11:31:29",
"content": "get a common denominator on the RHS",
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"id": 1065670037521838100,
"author_id": 220517274845577200,
"author_name": "ramonov",
"timestamp": "01/19/2023 11:32:16",
"content": "you have\n$$\\frac{1}{r_t}$$\nas the subject \\\\\nthey want $r_t$, just $r_t$ not as a denominator of a fraction as the subject. i.e.\n$$r_t = \\text{stuff}$$",
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"id": 1065670050813595800,
"author_id": 510789298321096700,
"author_name": "TeXit",
"timestamp": "01/19/2023 11:32:19",
"content": "**ℝamonov**",
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"id": 1065670226785607800,
"author_id": 270678085983141900,
"author_name": "Nattly",
"timestamp": "01/19/2023 11:33:01",
"content": "wondering, does 1/rt mean its the inverse of rt?",
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"id": 1065670705674453100,
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"author_name": "Nattly",
"timestamp": "01/19/2023 11:34:55",
"content": "also if 1/rt= 1/r1+ 1/r2 + 1/r3\ndoes that mean rt x 1 = 1 x r1 + 1 x r2 +1 x r3?",
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"id": 1065672281642254300,
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"author_name": "Nattly",
"timestamp": "01/19/2023 11:41:11",
"content": "ive seen multiple ways of doing this question but none seem to be working",
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"id": 1065673288673677400,
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"timestamp": "01/19/2023 11:45:11",
"content": "no",
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"id": 1065673378654081000,
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"author_name": "Nattly",
"timestamp": "01/19/2023 11:45:32",
"content": "ye i think one answer seems to be",
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"content": "",
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"id": 1065673451517513700,
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"author_name": "Nattly",
"timestamp": "01/19/2023 11:45:50",
"content": "but... still....",
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"id": 1065674426521231500,
"author_id": 381971715296722940,
"author_name": "ELeonardo",
"timestamp": "01/19/2023 11:49:42",
"content": "Hello, could please show your work? 🤔",
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"author_id": 270678085983141900,
"author_name": "Nattly",
"timestamp": "01/19/2023 11:52:46",
"content": "no real work... just kinda re aranging things as far as im aware",
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"author_id": 381971715296722940,
"author_name": "ELeonardo",
"timestamp": "01/19/2023 11:56:20",
"content": "try adding those fractions until you get a single fraction",
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"author_name": "Nattly",
"timestamp": "01/19/2023 11:57:34",
"content": "eh?",
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"id": 1065677635595804800,
"author_id": 220517274845577200,
"author_name": "ramonov",
"timestamp": "01/19/2023 12:02:27",
"content": "> no real work... just kinda re aranging things as far as im aware\ndo the proper work",
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},
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"id": 1065677689874297000,
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"author_name": "Nattly",
"timestamp": "01/19/2023 12:02:40",
"content": "i dont know how",
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"author_id": 220517274845577200,
"author_name": "ramonov",
"timestamp": "01/19/2023 12:02:50",
"content": "don't just \"move\" things without proper justification",
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"id": 1065677843939467400,
"author_id": 270678085983141900,
"author_name": "Nattly",
"timestamp": "01/19/2023 12:03:17",
"content": "im aware the goal is to turn 1/rt into rt",
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"id": 1065677862545391600,
"author_id": 220517274845577200,
"author_name": "ramonov",
"timestamp": "01/19/2023 12:03:21",
"content": "do you know how to combine fractions through addition?",
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"id": 1065677991381848000,
"author_id": 270678085983141900,
"author_name": "Nattly",
"timestamp": "01/19/2023 12:03:52",
"content": "could you show a reminder?",
"attachments": [],
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"author_id": 220517274845577200,
"author_name": "ramonov",
"timestamp": "01/19/2023 12:03:54",
"content": "e.g would you have an issue simplifying\n$$\\frac12 + \\frac13$$",
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"author_id": 510789298321096700,
"author_name": "TeXit",
"timestamp": "01/19/2023 12:04:10",
"content": "**ℝamonov**",
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"author_name": "Nattly",
"timestamp": "01/19/2023 12:04:59",
"content": "i would imagian that to just be 2/5?",
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"id": 1065678318625632400,
"author_id": 270678085983141900,
"author_name": "Nattly",
"timestamp": "01/19/2023 12:05:10",
"content": "thing is i know that thats wrong",
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"author_name": "Nattly",
"timestamp": "01/19/2023 12:05:35",
"content": "you would have to give them common denominators",
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"id": 1065678505444126700,
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"author_name": "Nattly",
"timestamp": "01/19/2023 12:05:55",
"content": "so 3/6+2/6",
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"author_name": "Nattly",
"timestamp": "01/19/2023 12:06:21",
"content": "but i dont see how to do that with 1/r1+1/r2+1/r3",
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"id": 1065679189618982900,
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"author_name": "ramonov",
"timestamp": "01/19/2023 12:08:38",
"content": "well start with\n1/r_1 + 1/r_2",
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"id": 1065679245369688000,
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"author_name": "ramonov",
"timestamp": "01/19/2023 12:08:51",
"content": "apply the same principle of getting a common denominator",
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"id": 1065679418590232600,
"author_id": 270678085983141900,
"author_name": "Nattly",
"timestamp": "01/19/2023 12:09:32",
"content": "id go with 6 again so... 6/r6+3/r6+2/r6",
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"id": 1065679827799121900,
"author_id": 220517274845577200,
"author_name": "ramonov",
"timestamp": "01/19/2023 12:11:10",
"content": "wdym with 6 again",
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},
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"id": 1065680204070129800,
"author_id": 220517274845577200,
"author_name": "ramonov",
"timestamp": "01/19/2023 12:12:40",
"content": "those 1,2,3 are subscripts",
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"author_name": "ramonov",
"timestamp": "01/19/2023 12:12:59",
"content": "you shouldn't be doing any multiplication with those subscripts",
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"id": 1065680347859255400,
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"author_name": "ramonov",
"timestamp": "01/19/2023 12:13:14",
"content": "the whole expression is a single variable",
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},
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"id": 1065680399361134700,
"author_id": 220517274845577200,
"author_name": "ramonov",
"timestamp": "01/19/2023 12:13:26",
"content": "view them as though they were x,y,z",
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},
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"id": 1065680546409226400,
"author_id": 220517274845577200,
"author_name": "ramonov",
"timestamp": "01/19/2023 12:14:01",
"content": "would you be able to combine\n$$\\frac 1x + \\frac 1y + \\frac 1z$$\ninto a single fraction",
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"id": 1065680559881343000,
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"author_name": "TeXit",
"timestamp": "01/19/2023 12:14:04",
"content": "**ℝamonov**",
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"author_name": "ramonov",
"timestamp": "01/19/2023 12:14:17",
"content": "start with the first two if needed",
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"author_name": "Nattly",
"timestamp": "01/19/2023 12:14:45",
"content": "ah",
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"id": 1065680796733685800,
"author_id": 270678085983141900,
"author_name": "Nattly",
"timestamp": "01/19/2023 12:15:01",
"content": "3/r1 x r2 x r3",
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},
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"id": 1065680923351334900,
"author_id": 220517274845577200,
"author_name": "ramonov",
"timestamp": "01/19/2023 12:15:31",
"content": "how are you getting that, show work",
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},
{
"id": 1065681228885409800,
"author_id": 270678085983141900,
"author_name": "Nattly",
"timestamp": "01/19/2023 12:16:44",
"content": "by multiplying the bottoms together?",
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"id": 1065681289807671300,
"author_id": 270678085983141900,
"author_name": "Nattly",
"timestamp": "01/19/2023 12:16:58",
"content": "what i showed was the working?",
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},
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"id": 1065681418765750300,
"author_id": 220517274845577200,
"author_name": "ramonov",
"timestamp": "01/19/2023 12:17:29",
"content": "show don't tell",
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},
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"id": 1065681525628207200,
"author_id": 220517274845577200,
"author_name": "ramonov",
"timestamp": "01/19/2023 12:17:55",
"content": "apply the same principle as you did to get from\n1/2 + 1/3 to 3/6 + 2/6",
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},
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"id": 1065681660978401400,
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"author_name": "Nattly",
"timestamp": "01/19/2023 12:18:27",
"content": "are you a primary school teacher? XD",
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"id": 1065681682251919400,
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"author_name": "ramonov",
"timestamp": "01/19/2023 12:18:32",
"content": "no",
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"author_name": "Mathematics Bot",
"timestamp": "01/19/2023 12:33:27",
"content": "@Nattly Has your question been resolved?",
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"timestamp": "01/19/2023 12:33:34",
"content": "Channel closed",
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] | help-9 | 3c86cd3e2e0242a694c5576bb03b5488 |
200,875 | [
{
"id": 1065685718397108200,
"author_id": 805217272087838700,
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"timestamp": "01/19/2023 12:34:34",
"content": "Available help channel!",
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"author_name": "spetnaz",
"timestamp": "01/19/2023 12:41:59",
"content": "$\\sin\\left(\\frac{y}{7}\\right)=\\frac{2}{7\\pi}y$",
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"timestamp": "01/19/2023 12:42:00",
"content": "Pinned a message.",
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"timestamp": "01/19/2023 12:42:02",
"content": "**spetnaz**",
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"author_name": "spetnaz",
"timestamp": "01/19/2023 12:42:02",
"content": "How to solve for y?",
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"id": 1065687960206446600,
"author_id": 183668144404037630,
"author_name": "Ann",
"timestamp": "01/19/2023 12:43:29",
"content": ":bleak:",
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"id": 1065687986894803100,
"author_id": 183668144404037630,
"author_name": "Ann",
"timestamp": "01/19/2023 12:43:35",
"content": "you're not going to get any algebraic solution",
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"id": 1065688042221875200,
"author_id": 1064251776238366700,
"author_name": "spetnaz",
"timestamp": "01/19/2023 12:43:48",
"content": "Waaah",
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"id": 1065688078058008600,
"author_id": 183668144404037630,
"author_name": "Ann",
"timestamp": "01/19/2023 12:43:57",
"content": "however you can note that the graphs of y=sin(x) and y=(2/pi)x happen to intersect at precisely 3 easily identifiable points.",
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"id": 1065688079194669200,
"author_id": 348696743388381200,
"author_name": "A Lonely Bean",
"timestamp": "01/19/2023 12:43:57",
"content": "Well",
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},
{
"id": 1065688096169001000,
"author_id": 348696743388381200,
"author_name": "A Lonely Bean",
"timestamp": "01/19/2023 12:44:01",
"content": "There's one thing you could do",
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},
{
"id": 1065688113185300600,
"author_id": 261933205387477000,
"author_name": "riemann",
"timestamp": "01/19/2023 12:44:05",
"content": "do you have another problem you're working that this stems form?",
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"id": 1065688121162858600,
"author_id": 1064251776238366700,
"author_name": "spetnaz",
"timestamp": "01/19/2023 12:44:07",
"content": "I thought I have to do this, because I need to find the intersects",
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},
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"id": 1065688129081712800,
"author_id": 183668144404037630,
"author_name": "Ann",
"timestamp": "01/19/2023 12:44:09",
"content": "which gives you the three possible values for y/7 in your equation",
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"author_name": "spetnaz",
"timestamp": "01/19/2023 12:44:10",
"content": "",
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"author_name": "spetnaz",
"timestamp": "01/19/2023 12:44:12",
"content": "Here it is @riemann",
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"author_name": "spetnaz",
"timestamp": "01/19/2023 12:44:24",
"content": "I believe I need to find the intersections",
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"author_name": "spetnaz",
"timestamp": "01/19/2023 12:44:30",
"content": "Thats why i set equals",
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"id": 1065688341326090200,
"author_id": 348696743388381200,
"author_name": "A Lonely Bean",
"timestamp": "01/19/2023 12:45:00",
"content": "Show that y = 0 is a solution\nShow that RHS < LHS for positive y and RHS > LHS for negative y using calculus",
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"id": 1065688517155500000,
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"author_name": "tushar",
"timestamp": "01/19/2023 12:45:42",
"content": "there are algebraic solutions",
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"timestamp": "01/19/2023 12:45:53",
"content": "Oh wait there are 3 solutions nvm",
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"timestamp": "01/19/2023 12:46:03",
"content": "i meant solution as in method, not solution as in number satisfying the equation @tushar",
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"timestamp": "01/19/2023 12:46:15",
"content": "How can we find the 3 solutions?",
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"id": 1065688669278716000,
"author_id": 176048095543558140,
"author_name": "tushar",
"timestamp": "01/19/2023 12:46:18",
"content": "yep",
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"author_id": 1064251776238366700,
"author_name": "spetnaz",
"timestamp": "01/19/2023 12:46:28",
"content": "Without desmos?",
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"author_id": 348696743388381200,
"author_name": "A Lonely Bean",
"timestamp": "01/19/2023 12:46:35",
"content": "By guessing and checking I think?",
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"id": 1065689512199598200,
"author_id": 176048095543558140,
"author_name": "tushar",
"timestamp": "01/19/2023 12:49:39",
"content": "hmm the equations simplify to sin(pix/2) = x",
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"id": 1065689879528349700,
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"author_name": "tushar",
"timestamp": "01/19/2023 12:51:06",
"content": "so clear that x is between -1 and 1",
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"timestamp": "01/19/2023 13:01:28",
"content": "@spetnaz Has your question been resolved?",
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"timestamp": "01/19/2023 13:16:28",
"content": "Channel closed",
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] | help-9 | b2ee1ab56a79441c9b054a4bf7cf06b5 |
200,876 | [
{
"id": 1036160793793806300,
"author_id": 331558346333224960,
"author_name": "jan Niku",
"timestamp": "10/30/2022 02:13:04",
"content": "its a way to visualize one of the requirements of the theorem",
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"id": 1036160824089251800,
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"timestamp": "10/30/2022 02:13:11",
"content": "odds are you will not use the squeeze theorem very much",
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"id": 1036160850760839200,
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"timestamp": "10/30/2022 02:13:17",
"content": "except if someone contrives a question",
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"timestamp": "10/30/2022 02:13:22",
"content": "to test your understanding of the squeeze theorem",
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"content": "which will probably happen",
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"author_id": 618992877846134800,
"author_name": "SnowZillin",
"timestamp": "10/30/2022 02:13:35",
"content": "how often is it used it anything other then calc 1 tests??",
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"content": "its used a lot in real analysis",
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"id": 1036160997775392800,
"author_id": 331558346333224960,
"author_name": "jan Niku",
"timestamp": "10/30/2022 02:13:52",
"content": "and you know",
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"author_id": 618992877846134800,
"author_name": "SnowZillin",
"timestamp": "10/30/2022 02:13:54",
"content": "what is that",
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{
"id": 1036161020030374000,
"author_id": 331558346333224960,
"author_name": "jan Niku",
"timestamp": "10/30/2022 02:13:58",
"content": "its a great tool for what it does",
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},
{
"id": 1036161039043141600,
"author_id": 331558346333224960,
"author_name": "jan Niku",
"timestamp": "10/30/2022 02:14:02",
"content": "proofs based calculus",
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"author_name": "Mathematics Bot",
"timestamp": "10/30/2022 02:14:03",
"content": "Available help channel!",
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},
{
"id": 1036161103698350100,
"author_id": 331558346333224960,
"author_name": "jan Niku",
"timestamp": "10/30/2022 02:14:18",
"content": "its a great tool for like the problem says",
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"author_name": "Mathematics Bot",
"timestamp": "10/30/2022 02:14:18",
"content": "Pinned a message.",
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"author_id": 331558346333224960,
"author_name": "jan Niku",
"timestamp": "10/30/2022 02:14:24",
"content": "when you cant figure out a limit or dont want to",
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"content": "and the function is easy to bound",
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"timestamp": "10/30/2022 02:14:34",
"content": "something really really oscillatory and weird",
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"id": 1036161190176501800,
"author_id": 331558346333224960,
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"timestamp": "10/30/2022 02:14:38",
"content": "but yea",
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"author_name": "jan Niku",
"timestamp": "10/30/2022 02:14:41",
"content": "other than that 🤷♂️",
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"content": ".close",
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"content": "Channel closed",
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] | help-9 | d5ad2619ef1b472a84c8d8f0b998c2f1 |
200,877 | [
{
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"content": "Available help channel!",
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"content": "I just have no ide how to begin this question",
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"content": "Each year?",
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"content": "That's not part of the definition.",
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"content": "If it was, everything's half-life would be a year!",
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"content": "Idk",
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"author_name": "Castroploiin¹",
"timestamp": "01/19/2023 13:23:00",
"content": "Just \"time it takes for the quantity to halve.\"",
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"author_name": "Einsteinium",
"timestamp": "01/19/2023 13:23:07",
"content": "I ain't no biologist 😭",
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"content": "Ye",
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"content": "(This is chemistry/physics.)",
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"content": "So what do we know about the initial mass?",
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"timestamp": "01/19/2023 13:23:55",
"content": "What does it equal?",
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"author_name": "Einsteinium",
"timestamp": "01/19/2023 13:24:05",
"content": "Initial mass\nWe got no idea",
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"content": "It's in the equation",
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"timestamp": "01/19/2023 13:24:18",
"content": "We know that's it's bene halved in\n\nAt",
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"timestamp": "01/19/2023 13:24:34",
"content": "It doesnt say I think 🤔",
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"content": "It doesn't give you a number.",
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"timestamp": "01/19/2023 13:25:17",
"content": "How do I know the initial amount then",
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"author_id": 1025510803501240300,
"author_name": "Einsteinium",
"timestamp": "01/19/2023 13:25:25",
"content": "Is it always 1 unless told otherwise?",
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"author_id": 1025510803501240300,
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"timestamp": "01/19/2023 13:25:28",
"content": "Like a percentage",
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"author_name": "Castroploiin¹",
"timestamp": "01/19/2023 13:25:40",
"content": "It's... written out",
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"content": "",
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"timestamp": "01/19/2023 13:25:50",
"content": "Sorry im dumb",
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"id": 1065698678611902500,
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"author_name": "Einsteinium",
"timestamp": "01/19/2023 13:26:04",
"content": "What does a0 equal tho",
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"id": 1065698693610737800,
"author_id": 1025510803501240300,
"author_name": "Einsteinium",
"timestamp": "01/19/2023 13:26:08",
"content": "100?",
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"author_id": 446704648485863400,
"author_name": "Castroploiin¹",
"timestamp": "01/19/2023 13:26:10",
"content": "Some number.",
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"author_id": 446704648485863400,
"author_name": "Castroploiin¹",
"timestamp": "01/19/2023 13:26:17",
"content": "A mass in micrograms.",
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"author_name": "Einsteinium",
"timestamp": "01/19/2023 13:26:22",
"content": "How do I find out which number",
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"id": 1065698779610751000,
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"timestamp": "01/19/2023 13:26:28",
"content": "Is IT 2",
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},
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"author_id": 446704648485863400,
"author_name": "Castroploiin¹",
"timestamp": "01/19/2023 13:26:35",
"content": "You don't need to.",
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"author_name": "Castroploiin¹",
"timestamp": "01/19/2023 13:26:55",
"content": "This is the neat thing, any amount of this imaginary substance always has the same half-life.",
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"timestamp": "01/19/2023 13:27:06",
"content": "OHH YEAH DAM",
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"id": 1065698974394228700,
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"timestamp": "01/19/2023 13:27:15",
"content": "Can I put 2 then",
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"author_id": 446704648485863400,
"author_name": "Castroploiin¹",
"timestamp": "01/19/2023 13:27:25",
"content": "Euh sure?",
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"author_id": 1025510803501240300,
"author_name": "Einsteinium",
"timestamp": "01/19/2023 13:27:26",
"content": "So that it's a nice number for later on",
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"id": 1065699038810345600,
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"author_name": "Einsteinium",
"timestamp": "01/19/2023 13:27:30",
"content": "Kk",
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"id": 1065699062529151000,
"author_id": 1025510803501240300,
"author_name": "Einsteinium",
"timestamp": "01/19/2023 13:27:36",
"content": "OK so",
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},
{
"id": 1065699130753699800,
"author_id": 446704648485863400,
"author_name": "Castroploiin¹",
"timestamp": "01/19/2023 13:27:52",
"content": "All we care about is what A_t equals in terms of A_0, or your A_0 = 2.",
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"id": 1065699150047490000,
"author_id": 1025510803501240300,
"author_name": "Einsteinium",
"timestamp": "01/19/2023 13:27:57",
"content": "1 = 2(e(whatever bullshit))",
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"author_name": "Castroploiin¹",
"timestamp": "01/19/2023 13:28:03",
"content": "Yep.",
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"id": 1065699204531503200,
"author_id": 446704648485863400,
"author_name": "Castroploiin¹",
"timestamp": "01/19/2023 13:28:10",
"content": "So can you rearrange for t?",
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"id": 1065699237758771300,
"author_id": 1025510803501240300,
"author_name": "Einsteinium",
"timestamp": "01/19/2023 13:28:18",
"content": "YEA",
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},
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"id": 1065699240950640800,
"author_id": 1025510803501240300,
"author_name": "Einsteinium",
"timestamp": "01/19/2023 13:28:18",
"content": "Wait",
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},
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"id": 1065699247900606500,
"author_id": 1025510803501240300,
"author_name": "Einsteinium",
"timestamp": "01/19/2023 13:28:20",
"content": "OK so",
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},
{
"id": 1065699306172068000,
"author_id": 1025510803501240300,
"author_name": "Einsteinium",
"timestamp": "01/19/2023 13:28:34",
"content": "Divide by 2",
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},
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"id": 1065699317043707900,
"author_id": 1025510803501240300,
"author_name": "Einsteinium",
"timestamp": "01/19/2023 13:28:36",
"content": "On both side",
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"author_name": "Einsteinium",
"timestamp": "01/19/2023 13:28:38",
"content": "I thinm",
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"timestamp": "01/19/2023 13:28:53",
"content": "So then 1/2 = e(bullshit)",
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"id": 1065699415446261800,
"author_id": 1025510803501240300,
"author_name": "Einsteinium",
"timestamp": "01/19/2023 13:29:00",
"content": "THEN idk what to do next 😭",
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"timestamp": "01/19/2023 13:29:11",
"content": "What's the inverse of e^x?",
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"content": "Xe",
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"content": "Maybe",
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"content": "X x E",
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"timestamp": "01/19/2023 13:30:12",
"content": "I mean something for which e^(something) = x.",
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"content": "f^-1(x) if f(x) = e^x",
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"timestamp": "01/19/2023 13:31:11",
"content": "Ah fk",
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"timestamp": "01/19/2023 13:31:18",
"content": "Wait u want me to put it into a log right",
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"timestamp": "01/19/2023 13:31:29",
"content": "Yeaaaah, with what base?",
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"timestamp": "01/19/2023 13:31:46",
"content": "Base 10",
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"timestamp": "01/19/2023 13:31:52",
"content": "Because",
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"content": "Ye",
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"timestamp": "01/19/2023 13:32:29",
"content": "I mean that works, but there's a number which makes this easier to work with as a base.",
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"timestamp": "01/19/2023 13:33:13",
"content": "On your calculator you'd have two logs, \"log_10\" and \"?\"",
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"timestamp": "01/19/2023 13:33:28",
"content": "Lemme see",
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"timestamp": "01/19/2023 13:33:30",
"content": "On my calc",
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"content": "BASE E @Castroploiin¹",
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"timestamp": "01/19/2023 13:33:46",
"content": "Or otherwise",
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"content": "Ln",
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"content": "Yes.",
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"content": "Do you see why base e might make your answer a little cleaner?",
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"content": "YE",
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"timestamp": "01/19/2023 13:34:48",
"content": "1sec",
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"timestamp": "01/19/2023 13:34:58",
"content": "Base e of e is just",
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"timestamp": "01/19/2023 13:35:25",
"content": "1",
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"author_id": 446704648485863400,
"author_name": "Castroploiin¹",
"timestamp": "01/19/2023 13:35:41",
"content": "So taking the ln of both sides, you get...?",
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"timestamp": "01/19/2023 13:35:44",
"content": "SO IT DISAPPEARS YOO",
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"timestamp": "01/19/2023 13:36:21",
"content": "1/2 = - (something number)t",
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"author_name": "Castroploiin¹",
"timestamp": "01/19/2023 13:36:45",
"content": "We need to take the natural log of *both sides*.",
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"timestamp": "01/19/2023 13:37:00",
"content": "Oh yeah I forgot to add it in",
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"timestamp": "01/19/2023 13:37:08",
"content": "It's log e 1divided by 2",
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"timestamp": "01/19/2023 13:37:25",
"content": "BUT THE RIGHT SIDE HAS NO LOGS YES",
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"timestamp": "01/19/2023 13:37:29",
"content": "I think",
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"author_name": "Castroploiin¹",
"timestamp": "01/19/2023 13:37:35",
"content": "So, what is t equal to then?",
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"timestamp": "01/19/2023 13:38:17",
"content": "T = loge1/2 / (- weird number)",
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"timestamp": "01/19/2023 13:38:42",
"content": "Sorry forgot log still exists",
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"timestamp": "01/19/2023 13:39:12",
"content": "ln(1/2) = -0.003t\n-ln(2)/-0.003 = t\n=> t = ln(2)/0.003 ~ 231 s",
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"author_name": "Castroploiin¹",
"timestamp": "01/19/2023 13:39:31",
"content": "You see how ln(1/2) = -ln(2), yeah?",
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"timestamp": "01/19/2023 13:40:10",
"content": "Not rlly",
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"author_name": "Einsteinium",
"timestamp": "01/19/2023 13:40:32",
"content": "U found Perpendicular Bisectors of ln 1/2",
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"timestamp": "01/19/2023 13:40:45",
"content": "Do you know the rule, log(a^b) = blog(a)?",
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"timestamp": "01/19/2023 13:40:54",
"content": "OHH SHIT YEA",
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"timestamp": "01/19/2023 13:41:02",
"content": "I do",
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"author_name": "Castroploiin¹",
"timestamp": "01/19/2023 13:41:07",
"content": "Put in appropriate numbers for a and b.",
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"timestamp": "01/19/2023 13:41:14",
"content": "You get this.",
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"author_name": "Einsteinium",
"timestamp": "01/19/2023 13:41:40",
"content": "Ln1/2^?",
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"author_name": "Einsteinium",
"timestamp": "01/19/2023 13:41:46",
"content": "Which power tho",
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"timestamp": "01/19/2023 13:42:11",
"content": "1/2 = 2^(?)",
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"timestamp": "01/19/2023 13:42:41",
"content": "-1",
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"author_name": "Einsteinium",
"timestamp": "01/19/2023 13:42:43",
"content": "Maybe",
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"author_name": "Castroploiin¹",
"timestamp": "01/19/2023 13:43:25",
"content": "2^(-1) = ?",
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"timestamp": "01/19/2023 13:43:32",
"content": "1/2",
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"author_name": "Castroploiin¹",
"timestamp": "01/19/2023 13:43:57",
"content": "So ln(1/2) = ln(2^(-1)) = -1*ln(2)",
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"timestamp": "01/19/2023 13:44:11",
"content": "Ohh I see",
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"author_id": 1025510803501240300,
"author_name": "Einsteinium",
"timestamp": "01/19/2023 13:44:37",
"content": "So then u divide by weird number",
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"id": 1065703367743131800,
"author_id": 1025510803501240300,
"author_name": "Einsteinium",
"timestamp": "01/19/2023 13:44:42",
"content": "Then shove it in calculator?",
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"timestamp": "01/19/2023 13:44:46",
"content": "THEN BOOOM",
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"timestamp": "01/19/2023 13:46:26",
"content": "Yes.",
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"timestamp": "01/19/2023 13:59:46",
"content": "@Einsteinium Has your question been resolved?",
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"timestamp": "01/19/2023 14:01:07",
"content": "Yes",
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"content": "Channel closed",
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] | help-9 | 5af0d2955ffb45eea7bb0c0185ede285 |
200,878 | [
{
"id": 1065714109439557800,
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"author_name": "Mathematics Bot",
"timestamp": "01/19/2023 14:27:23",
"content": "Available help channel!",
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"id": 1065716516126982300,
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"timestamp": "01/19/2023 14:36:57",
"content": "$f'(x) = \\begin {cases}\n0 & x = 0 \\\\\n4x^3(2+\\sin\\frac{1}{x})-x^2\\cos\\frac{1}{x}), x \\neq 0\n\\end{cases} \\newline$\nhow do i prove that f is not monotonic in proximity of 0",
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"content": "Pinned a message.",
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"id": 1065716840648671400,
"author_id": 165914200332304400,
"author_name": "Steakanator",
"timestamp": "01/19/2023 14:38:14",
"content": ">0 \\text{for} x = 0 \\\n0 & x=0 would look cleaner",
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"author_id": 328662734008746000,
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"content": "Take a derivative and show it changes sign around 0",
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"timestamp": "01/19/2023 14:38:32",
"content": "Cuz then it would be increasing and decreasing (so clearly not monotonic)",
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"id": 1065716958407954600,
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"timestamp": "01/19/2023 14:38:42",
"content": "**ta**",
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"timestamp": "01/19/2023 14:38:57",
"content": "but i already did",
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"id": 1065717044324094100,
"author_id": 646060251594096600,
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"content": "how do i show it changes sign",
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"author_name": "Geopchad",
"timestamp": "01/19/2023 14:39:13",
"content": "Find two points where one is positive and the other is negative",
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"content": "in proximity means for any point close to 0",
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"id": 1065717248121127000,
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"timestamp": "01/19/2023 14:39:52",
"content": "like epsilon close",
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"author_name": "Geopchad",
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"content": "Prescribe any epsilon ball around 0",
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"timestamp": "01/19/2023 14:40:14",
"content": "And find two points where derivative has different sign",
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"timestamp": "01/19/2023 14:40:28",
"content": "( maybe try things like epsilon^2 and -epsilon^2 for example)",
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"timestamp": "01/19/2023 14:40:33",
"content": "Also can you send the original function",
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"timestamp": "01/19/2023 14:40:52",
"content": "sure",
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"id": 1065717508121833500,
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"timestamp": "01/19/2023 14:40:54",
"content": "wait a sec",
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"timestamp": "01/19/2023 14:41:35",
"content": "$f(x) = \\begin {cases}\n0 & x = 0 \\\\\nx^4(2+\\sin\\frac{1}{x}) & x \\neq 0\n\\end{cases}$",
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"id": 1065717731955069000,
"author_id": 510789298321096700,
"author_name": "TeXit",
"timestamp": "01/19/2023 14:41:47",
"content": "**ta**",
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"timestamp": "01/19/2023 14:41:54",
"content": "Beautiful tex",
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"id": 1065717818651320300,
"author_id": 646060251594096600,
"author_name": "ta",
"timestamp": "01/19/2023 14:42:08",
"content": "🥹 ik",
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"timestamp": "01/19/2023 14:42:42",
"content": "Okay for x = epsilon and - epsilon it’s pisitive",
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"timestamp": "01/19/2023 14:42:43",
"content": "i hope i calculated derivative correctly",
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"timestamp": "01/19/2023 14:42:47",
"content": "But at x = 0 it’s just 0",
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"timestamp": "01/19/2023 14:42:53",
"content": "So can’t be monotonic",
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"author_name": "Geopchad",
"timestamp": "01/19/2023 14:43:11",
"content": "(Follows from sin(x) >= -1 and x^4 > 0 for x not 0",
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"timestamp": "01/19/2023 14:43:42",
"content": "Montonic would be f(y) >= f(x) for all y >= x or vice versa, but clearly that’s not the case",
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"id": 1065718399554048100,
"author_id": 646060251594096600,
"author_name": "ta",
"timestamp": "01/19/2023 14:44:26",
"content": "for -eps its positive?",
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"id": 1065718454377775200,
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"author_name": "ta",
"timestamp": "01/19/2023 14:44:39",
"content": "nvm it is",
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"author_name": "Geopchad",
"timestamp": "01/19/2023 14:44:59",
"content": "So we have finished the question",
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"id": 1065718561181548500,
"author_id": 646060251594096600,
"author_name": "ta",
"timestamp": "01/19/2023 14:45:05",
"content": "no",
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"id": 1065718584581554300,
"author_id": 328662734008746000,
"author_name": "Geopchad",
"timestamp": "01/19/2023 14:45:10",
"content": "What else?",
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},
{
"id": 1065718623760560300,
"author_id": 646060251594096600,
"author_name": "ta",
"timestamp": "01/19/2023 14:45:19",
"content": "i formulated the conditions of the question in a wrong way",
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"id": 1065718839909830700,
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"author_name": "ta",
"timestamp": "01/19/2023 14:46:11",
"content": "translated from my native language it would be \"show that f isnt monotonic in any left hand or right hand proximity of 0\"",
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"id": 1065718893588516900,
"author_id": 328662734008746000,
"author_name": "Geopchad",
"timestamp": "01/19/2023 14:46:24",
"content": "Ah",
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},
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"id": 1065718981731831800,
"author_id": 646060251594096600,
"author_name": "ta",
"timestamp": "01/19/2023 14:46:45",
"content": "so -eps < x, y < 0",
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},
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"author_id": 328662734008746000,
"author_name": "Geopchad",
"timestamp": "01/19/2023 14:47:21",
"content": "Looks monotonic to me",
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"timestamp": "01/19/2023 14:48:05",
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"id": 1065719399002149000,
"author_id": 646060251594096600,
"author_name": "ta",
"timestamp": "01/19/2023 14:48:24",
"content": "why is desmos freaking out",
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"id": 1065719464760463400,
"author_id": 328662734008746000,
"author_name": "Geopchad",
"timestamp": "01/19/2023 14:48:40",
"content": "I think you gave me the wrong function",
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},
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"id": 1065719516736270500,
"author_id": 328662734008746000,
"author_name": "Geopchad",
"timestamp": "01/19/2023 14:48:52",
"content": "Was it x^3 instead of to the 4th?",
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"id": 1065719601956139000,
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"author_name": "ta",
"timestamp": "01/19/2023 14:49:13",
"content": "no it was x^4",
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"id": 1065719622420136100,
"author_id": 328662734008746000,
"author_name": "Geopchad",
"timestamp": "01/19/2023 14:49:18",
"content": "Hmmm",
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"id": 1065719639256092700,
"author_id": 646060251594096600,
"author_name": "ta",
"timestamp": "01/19/2023 14:49:22",
"content": "i zoomed in",
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},
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"author_id": 328662734008746000,
"author_name": "Geopchad",
"timestamp": "01/19/2023 14:49:24",
"content": "Idk why I’m getting a different graph",
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"id": 1065719651667034200,
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"author_name": "ta",
"timestamp": "01/19/2023 14:49:25",
"content": "on the screenshot",
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"id": 1065719697762427000,
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"timestamp": "01/19/2023 14:49:36",
"content": "look at x and y values",
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"author_id": 328662734008746000,
"author_name": "Geopchad",
"timestamp": "01/19/2023 14:49:48",
"content": "Might be a mobile thing",
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},
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"id": 1065719769157865500,
"author_id": 646060251594096600,
"author_name": "ta",
"timestamp": "01/19/2023 14:49:53",
"content": "im just wondering why are there these little dots",
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"id": 1065719804989800600,
"author_id": 328662734008746000,
"author_name": "Geopchad",
"timestamp": "01/19/2023 14:50:01",
"content": "Those are the functions zeroes",
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"id": 1065719856944648200,
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"author_name": "Geopchad",
"timestamp": "01/19/2023 14:50:14",
"content": "Which doesn’t make any sense as it should only have one zero at x = 0",
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},
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"id": 1065719863659724900,
"author_id": 646060251594096600,
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"timestamp": "01/19/2023 14:50:15",
"content": "but its positive for x->0",
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"id": 1065719909188907100,
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"timestamp": "01/19/2023 14:50:26",
"content": "yeah exactly",
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"id": 1065719973789573200,
"author_id": 646060251594096600,
"author_name": "ta",
"timestamp": "01/19/2023 14:50:41",
"content": "desmos bug",
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"id": 1065720061152743600,
"author_id": 646060251594096600,
"author_name": "ta",
"timestamp": "01/19/2023 14:51:02",
"content": "maybe these are maxima/minima",
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"id": 1065720242862567600,
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"timestamp": "01/19/2023 14:51:46",
"content": "they are",
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"id": 1065720243361693800,
"author_id": 328662734008746000,
"author_name": "Geopchad",
"timestamp": "01/19/2023 14:51:46",
"content": "Ah u right",
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"id": 1065720280284139600,
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"timestamp": "01/19/2023 14:51:54",
"content": "but the problem is that i need to show that",
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"author_id": 328662734008746000,
"author_name": "Geopchad",
"timestamp": "01/19/2023 14:52:01",
"content": "But it still has 0s outside of x = 0",
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"id": 1065720347539812500,
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"timestamp": "01/19/2023 14:52:10",
"content": "Oh u plotted the derivative",
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"id": 1065720357123784700,
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"timestamp": "01/19/2023 14:52:13",
"content": "its the derivative",
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"id": 1065720364920996000,
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"timestamp": "01/19/2023 14:52:15",
"content": "yeah",
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"id": 1065720411507138700,
"author_id": 646060251594096600,
"author_name": "ta",
"timestamp": "01/19/2023 14:52:26",
"content": "to show that these points were maxima and minima",
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"id": 1065720531820748900,
"author_id": 646060251594096600,
"author_name": "ta",
"timestamp": "01/19/2023 14:52:54",
"content": "do u know how",
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"id": 1065720773689483400,
"author_id": 646060251594096600,
"author_name": "ta",
"timestamp": "01/19/2023 14:53:52",
"content": "im thinking of calculating $\\lim_{x\\to 0} f'(x)$",
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"id": 1065720805482307600,
"author_id": 510789298321096700,
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"timestamp": "01/19/2023 14:54:00",
"content": "**ta**",
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"timestamp": "01/19/2023 14:54:16",
"content": "but idk how since its $0 \\cdot \\infty$",
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"timestamp": "01/19/2023 14:54:18",
"content": "**ta**",
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"id": 1065721238179295400,
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"author_name": "ta",
"timestamp": "01/19/2023 14:55:43",
"content": "nah its useless",
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"id": 1065722261035823200,
"author_id": 646060251594096600,
"author_name": "ta",
"timestamp": "01/19/2023 14:59:47",
"content": "its not even 0 times inf",
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{
"id": 1065722336604590100,
"author_id": 646060251594096600,
"author_name": "ta",
"timestamp": "01/19/2023 15:00:05",
"content": "my dumb ass thought sin(1/x) = inf",
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"id": 1065726113634070500,
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"timestamp": "01/19/2023 15:15:05",
"content": "@ta Has your question been resolved?",
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"timestamp": "01/19/2023 15:30:06",
"content": "Channel closed",
"attachments": [],
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}
] | help-9 | c9299f0bdd3949dfbeb1b4b27f532e5e |
200,879 | [
{
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"author_name": "Mathematics Bot",
"timestamp": "01/19/2023 15:31:06",
"content": "Available help channel!",
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},
{
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"content": "Pinned a message.",
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"id": 1065730395821322400,
"author_id": 402114534552371200,
"author_name": "hotemogirl",
"timestamp": "01/19/2023 15:32:06",
"content": "Can someone write the formula with values from question A and B",
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{
"id": 1065731153719468200,
"author_id": 370444508644769800,
"author_name": "DootDooter",
"timestamp": "01/19/2023 15:35:07",
"content": "https://d138zd1ktt9iqe.cloudfront.net/media/seo_landing_files/sneha-b-volume-of-triangular-prism-9-1603978985.png",
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"author_name": "DootDooter",
"timestamp": "01/19/2023 15:35:21",
"content": "You can use this for the parts that are triangular prisms",
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},
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"id": 1065731301249912800,
"author_id": 370444508644769800,
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"timestamp": "01/19/2023 15:35:42",
"content": "For the cube-like parts you would just do base x height x width.",
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"id": 1065731527750717600,
"author_id": 370444508644769800,
"author_name": "DootDooter",
"timestamp": "01/19/2023 15:36:36",
"content": "So, for the each whole shape you can just break each one down into triangle/cube-like parts, compute the volumes of the pieces and add the individual volumes of the pieces you got together at the end.",
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"timestamp": "01/19/2023 15:37:02",
"content": "For A?",
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"id": 1065731774749089800,
"author_id": 402114534552371200,
"author_name": "hotemogirl",
"timestamp": "01/19/2023 15:37:35",
"content": "or is this only for the questions with 4 values",
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"timestamp": "01/19/2023 15:41:58",
"content": "For (a) I think somebody posted a paralleliped volume formula you can use? I don't think you can use the approach I mentioned for that one actually.",
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"timestamp": "01/19/2023 15:42:14",
"content": "Lemme track down that image from earlier. :thonk:",
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"content": "Ah damn the image they gave you was for something else.",
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"content": "Ah wait, I think paralleliped volume is just base area times height.",
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"content": "That should work for (a), (c) and (f).",
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"timestamp": "01/19/2023 15:49:44",
"content": "Well, assuming those are actually parallelipeds.",
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"author_name": "hotemogirl",
"timestamp": "01/19/2023 15:50:23",
"content": "could u do A and B with the formula and put the values in im a bit confused please",
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"content": "is A 1/2 5x17x3?",
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"author_name": "DootDooter",
"timestamp": "01/19/2023 15:53:59",
"content": "I am not going to do the problems for you.",
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"timestamp": "01/19/2023 15:56:01",
"content": "I’m still confused though",
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"author_name": "DootDooter",
"timestamp": "01/19/2023 15:57:09",
"content": "I think maybe the other shapes are trapezoid prisms?",
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"timestamp": "01/19/2023 15:57:34",
"content": "I’m not sure, I was sick for a week in shcool so idk the formulas",
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"timestamp": "01/19/2023 15:57:41",
"content": "https://d138zd1ktt9iqe.cloudfront.net/media/seo_landing_files/vishakha-volume-of-trapezoidal-prism-seo-02-1-1622196574.png",
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"timestamp": "01/19/2023 15:57:59",
"content": "I could be wrong about this. I have not done geometry in a very long time.",
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"content": "I would recommend double checking your book or course notes if you have any to be sure.",
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"content": "I got notes but it’s only for certain shapes and its only for area not volume",
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"content": "Is this for B?",
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"timestamp": "01/19/2023 16:01:44",
"content": "Sorry trying to find a good picture of the paralleliped ones.",
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"author_name": "DootDooter",
"timestamp": "01/19/2023 16:02:48",
"content": "Yeah, I was thinking the ones that are not (a), (c) and (f) are meant to be rectangular prisms? I could be wrong though.",
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"author_name": "hotemogirl",
"timestamp": "01/19/2023 16:03:39",
"content": "yea it looks like the shape and got 4 values so I’m guessing so",
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"author_name": "hotemogirl",
"timestamp": "01/19/2023 16:03:52",
"content": "and what do u think for a c and f",
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"timestamp": "01/19/2023 16:04:58",
"content": "https://www.technologyuk.net/mathematics/geometry/images/geometry_0163.gif",
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"timestamp": "01/19/2023 16:05:17",
"content": "Pretty sure it's this",
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"timestamp": "01/19/2023 16:05:34",
"content": "They give you enough info to work out the area of the base.",
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"timestamp": "01/19/2023 16:06:18",
"content": "I'd still double check this too though. I have not done geometry in years.",
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"timestamp": "01/19/2023 16:06:40",
"content": "wdym base area x h",
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"author_id": 402114534552371200,
"author_name": "hotemogirl",
"timestamp": "01/19/2023 16:06:44",
"content": "17x3x5?",
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"author_name": "hotemogirl",
"timestamp": "01/19/2023 16:06:52",
"content": "for A",
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"author_name": "DootDooter",
"timestamp": "01/19/2023 16:07:27",
"content": "Do you see how to find the base area of the figure in (a)?",
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"author_name": "DootDooter",
"timestamp": "01/19/2023 16:07:47",
"content": "For this pic they show you which surface the base is in red.",
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"author_name": "hotemogirl",
"timestamp": "01/19/2023 16:08:28",
"content": "yea I thought you’d work it out as 17x3 for A to get base area",
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"author_name": "DootDooter",
"timestamp": "01/19/2023 16:08:57",
"content": "Yep, that's what I'd do too. Then multiply by the height to get the total volume.",
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"author_name": "hotemogirl",
"timestamp": "01/19/2023 16:10:10",
"content": "yea that’s what I thought cool cool thank you 🙏",
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"timestamp": "01/19/2023 16:10:28",
"content": "Double check this with your professor to be sure of course.",
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"timestamp": "01/19/2023 16:10:34",
"content": "I will thank you",
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"timestamp": "01/19/2023 16:25:34",
"content": "@hotemogirl Has your question been resolved?",
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"content": "Channel closed",
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] | help-9 | 4424ad62e749491baa3b6486e8320e2a |
200,880 | [
{
"id": 1065748991876288600,
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"timestamp": "01/19/2023 16:55:13",
"content": "How do I know the answer 12 not 4?",
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"content": "Pinned a message.",
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"timestamp": "01/19/2023 16:55:26",
"content": "What",
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"id": 1065751388778401800,
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"timestamp": "01/19/2023 16:55:31",
"content": "Oh ok",
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"timestamp": "01/19/2023 16:56:41",
"content": "4 is the value they gave you in the question",
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"timestamp": "01/19/2023 16:56:46",
"content": "Lol",
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"content": "They gave you (4,0)",
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"content": "I need to learn to read lol",
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"timestamp": "01/19/2023 16:57:09",
"content": "Thank you",
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"id": 1065751827368399100,
"author_id": 489473096730935300,
"author_name": "Rainyzack81",
"timestamp": "01/19/2023 16:57:16",
"content": "For the help",
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"author_name": "chartbit",
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"content": "The whole time I was reading q8 like it was q9 :kekw:",
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"content": "Started even looking through the book for the whole question 8 lol, so you're not the only one :catGiggle:",
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"content": "@Rainyzack81 Has your question been resolved?",
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"content": "Channel closed",
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] | help-9 | 3c3312e1e0ce4c4ba21a0eaa52c825c3 |
200,881 | [
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"content": "Can someone guide me through the process of finding (-4e^-x) using u sub? I keep getting the same answer",
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"content": "Do you have to integrate that?",
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"id": 1065764325194743900,
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"timestamp": "01/19/2023 17:46:56",
"content": "Show your work",
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"id": 1065765755427246200,
"author_id": 450753049603080200,
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"timestamp": "01/19/2023 17:52:37",
"content": "Def having a brain fart or something",
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"id": 1065765796120379400,
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"timestamp": "01/19/2023 17:52:46",
"content": "Pic loading",
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"timestamp": "01/19/2023 17:53:37",
"content": "Anyway im integrating it inside a def integral to find volume using washer method",
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"content": "Mh ok, are you sure du = 1?",
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"timestamp": "01/19/2023 17:54:46",
"content": "Not at all",
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"id": 1065766324124520400,
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"content": "-1",
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"id": 1065766341967106200,
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"author_name": "Nonna",
"timestamp": "01/19/2023 17:54:56",
"content": ":catthumbsup:",
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"id": 1065766378591748200,
"author_id": 573905759134548000,
"author_name": "Nonna",
"timestamp": "01/19/2023 17:55:05",
"content": "So how can you fix that?",
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"author_name": "Mukby",
"timestamp": "01/19/2023 17:55:32",
"content": "Mult right side by -1 and divide other side of integral by -1?",
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"timestamp": "01/19/2023 17:56:21",
"content": "(You forgor to write the differential, it's important to put it when you are doing usub, or you might forget what you are integrating with respect to)",
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"timestamp": "01/19/2023 17:56:47",
"content": "Right dx right",
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"author_id": 450753049603080200,
"author_name": "Mukby",
"timestamp": "01/19/2023 17:57:04",
"content": "Hol up picture loading",
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},
{
"id": 1065766884722610200,
"author_id": 450753049603080200,
"author_name": "Mukby",
"timestamp": "01/19/2023 17:57:06",
"content": "",
"attachments": [
{
"id": 1065766884198334500,
"url": "https://cdn.discordapp.com/attachments/486844875632017408/1065766884198334474/2BADF75A-05E6-4EFB-96E3-796BB37F14A1.jpg",
"fileName": "2BADF75A-05E6-4EFB-96E3-796BB37F14A1.jpg",
"fileSizeBytes": 4379042
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},
{
"id": 1065767067392954500,
"author_id": 450753049603080200,
"author_name": "Mukby",
"timestamp": "01/19/2023 17:57:49",
"content": "Didnt put a dx but answer is right?",
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},
{
"id": 1065767121319116800,
"author_id": 573905759134548000,
"author_name": "Nonna",
"timestamp": "01/19/2023 17:58:02",
"content": "Yes that's correct",
"attachments": [],
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},
{
"id": 1065767149865533600,
"author_id": 450753049603080200,
"author_name": "Mukby",
"timestamp": "01/19/2023 17:58:09",
"content": "Noice",
"attachments": [],
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},
{
"id": 1065767261417246800,
"author_id": 450753049603080200,
"author_name": "Mukby",
"timestamp": "01/19/2023 17:58:36",
"content": "I sent it before u noticed the diff was missing",
"attachments": [],
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"reference": null
},
{
"id": 1065767371949744100,
"author_id": 573905759134548000,
"author_name": "Nonna",
"timestamp": "01/19/2023 17:59:02",
"content": "u = -x\n__ du __ = -1\n**dx**\n\nSo\n\n-du = dx",
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},
{
"id": 1065767399653118000,
"author_id": 573905759134548000,
"author_name": "Nonna",
"timestamp": "01/19/2023 17:59:09",
"content": "and then you can substitute dx with -du",
"attachments": [],
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},
{
"id": 1065767448382542000,
"author_id": 573905759134548000,
"author_name": "Nonna",
"timestamp": "01/19/2023 17:59:20",
"content": "It's nice to work with differentials",
"attachments": [],
"mentions": [],
"reference": null
},
{
"id": 1065767489507700900,
"author_id": 573905759134548000,
"author_name": "Nonna",
"timestamp": "01/19/2023 17:59:30",
"content": ":catthumbsup:",
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},
{
"id": 1065767587394371600,
"author_id": 450753049603080200,
"author_name": "Mukby",
"timestamp": "01/19/2023 17:59:53",
"content": "Yus 👍",
"attachments": [],
"mentions": [],
"reference": null
},
{
"id": 1065767598626705500,
"author_id": 450753049603080200,
"author_name": "Mukby",
"timestamp": "01/19/2023 17:59:56",
"content": "Ty",
"attachments": [],
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"reference": null
},
{
"id": 1065767644382384300,
"author_id": 573905759134548000,
"author_name": "Nonna",
"timestamp": "01/19/2023 18:00:07",
"content": "Yw!",
"attachments": [],
"mentions": [],
"reference": null
},
{
"id": 1065771374536294400,
"author_id": 805217272087838700,
"author_name": "Mathematics Bot",
"timestamp": "01/19/2023 18:14:56",
"content": "@Mukby Has your question been resolved?",
"attachments": [],
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{
"id": 450753049603080200,
"name": "Mukby",
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"nickname": "Mukby",
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},
{
"id": 1065771404508795000,
"author_id": 805217272087838700,
"author_name": "Mathematics Bot",
"timestamp": "01/19/2023 18:15:03",
"content": "Channel closed",
"attachments": [],
"mentions": [],
"reference": null
}
] | help-9 | 3b7b3f3c3a3a433e825d21782e85096f |
200,882 | [
{
"id": 1065780177587675100,
"author_id": 805217272087838700,
"author_name": "Mathematics Bot",
"timestamp": "01/19/2023 18:49:55",
"content": "Available help channel!",
"attachments": [],
"mentions": [],
"reference": null
},
{
"id": 1065784041351168100,
"author_id": 805217272087838700,
"author_name": "Mathematics Bot",
"timestamp": "01/19/2023 19:05:16",
"content": "Pinned a message.",
"attachments": [],
"mentions": [],
"reference": {
"messageId": 1065784038780043300,
"channelId": 486844875632017400,
"guildId": null
}
},
{
"id": 1065784114692767900,
"author_id": 1011300066264354800,
"author_name": "spicygreenpeppers",
"timestamp": "01/19/2023 19:05:34",
"content": "the top is a semicircle with radius 24",
"attachments": [],
"mentions": [],
"reference": null
},
{
"id": 1065784189850501100,
"author_id": 1011300066264354800,
"author_name": "spicygreenpeppers",
"timestamp": "01/19/2023 19:05:52",
"content": "so $\\pi \\cdot r^2 \\cdot \\frac{1}{2}$",
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"reference": null
},
{
"id": 1065784200885698600,
"author_id": 510789298321096700,
"author_name": "TeXit",
"timestamp": "01/19/2023 19:05:54",
"content": "**spicygreenpeppers**",
"attachments": [
{
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"url": "https://cdn.discordapp.com/attachments/486844875632017408/1065784200717938758/1011300066264354826.png",
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"fileSizeBytes": 6130
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},
{
"id": 1065784201468727300,
"author_id": 788085606483361800,
"author_name": "chartbit",
"timestamp": "01/19/2023 19:05:54",
"content": "How comes your friend can't ask here?",
"attachments": [],
"mentions": [],
"reference": null
},
{
"id": 1065784252022652900,
"author_id": 1060375293308710900,
"author_name": "Evanixia",
"timestamp": "01/19/2023 19:06:06",
"content": "She asked me for help",
"attachments": [],
"mentions": [
{
"id": 788085606483361800,
"name": "chartbit",
"discriminator": "3171",
"nickname": "chartbit",
"isBot": false
}
],
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},
{
"id": 1065784266367193200,
"author_id": 1011300066264354800,
"author_name": "spicygreenpeppers",
"timestamp": "01/19/2023 19:06:10",
"content": "the bottom is a triangle with base 48 and height 64",
"attachments": [],
"mentions": [],
"reference": null
},
{
"id": 1065784306716389500,
"author_id": 1060375293308710900,
"author_name": "Evanixia",
"timestamp": "01/19/2023 19:06:20",
"content": "I said idk what to do in this question",
"attachments": [],
"mentions": [],
"reference": null
},
{
"id": 1065784361477230600,
"author_id": 1060375293308710900,
"author_name": "Evanixia",
"timestamp": "01/19/2023 19:06:33",
"content": "Mhm",
"attachments": [],
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},
{
"id": 1065784374471180400,
"author_id": 788085606483361800,
"author_name": "chartbit",
"timestamp": "01/19/2023 19:06:36",
"content": "Also I suggest strongly you delete the original picture and crop it slightly",
"attachments": [],
"mentions": [
{
"id": 1060375293308710900,
"name": "Evanixia",
"discriminator": "2901",
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},
{
"id": 1065784374815113200,
"author_id": 1011300066264354800,
"author_name": "spicygreenpeppers",
"timestamp": "01/19/2023 19:06:36",
"content": "it looks intimidating, but it's just two simple shapes' areas added together",
"attachments": [],
"mentions": [],
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},
{
"id": 1065784398676508800,
"author_id": 1011300066264354800,
"author_name": "spicygreenpeppers",
"timestamp": "01/19/2023 19:06:41",
"content": "find out the semicircle, find out the triangle, add them up",
"attachments": [],
"mentions": [],
"reference": null
},
{
"id": 1065784501231440000,
"author_id": 805217272087838700,
"author_name": "Mathematics Bot",
"timestamp": "01/19/2023 19:07:06",
"content": "Channel closed",
"attachments": [],
"mentions": [],
"reference": null
}
] | help-9 | cfd27d8d19d542f3b038ebe0427908e7 |
200,883 | [
{
"id": 1065784627056349200,
"author_id": 788085606483361800,
"author_name": "chartbit",
"timestamp": "01/19/2023 19:07:36",
"content": "You'll need to post this in another channel though",
"attachments": [],
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{
"id": 1060375293308710900,
"name": "Evanixia",
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{
"id": 1065784644739534800,
"author_id": 1060375293308710900,
"author_name": "Evanixia",
"timestamp": "01/19/2023 19:07:40",
"content": "Agh",
"attachments": [],
"mentions": [],
"reference": null
},
{
"id": 1065784647176421400,
"author_id": 788085606483361800,
"author_name": "chartbit",
"timestamp": "01/19/2023 19:07:41",
"content": "But yea fixed",
"attachments": [],
"mentions": [],
"reference": null
},
{
"id": 1065784787656249300,
"author_id": 1060375293308710900,
"author_name": "Evanixia",
"timestamp": "01/19/2023 19:08:14",
"content": "How to close",
"attachments": [],
"mentions": [],
"reference": null
},
{
"id": 1065784815560970400,
"author_id": 1060375293308710900,
"author_name": "Evanixia",
"timestamp": "01/19/2023 19:08:21",
"content": ".close",
"attachments": [],
"mentions": [],
"reference": null
},
{
"id": 1065784875329798300,
"author_id": 788085606483361800,
"author_name": "chartbit",
"timestamp": "01/19/2023 19:08:35",
"content": "This one is already closed by deleting the original picture",
"attachments": [],
"mentions": [
{
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"name": "Mathematics Bot",
"discriminator": "0196",
"nickname": "Bot",
"isBot": true
}
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"reference": null
},
{
"id": 1065784894896209900,
"author_id": 1060375293308710900,
"author_name": "Evanixia",
"timestamp": "01/19/2023 19:08:40",
"content": "Oh oki",
"attachments": [],
"mentions": [],
"reference": null
},
{
"id": 1065784928857501700,
"author_id": 788085606483361800,
"author_name": "chartbit",
"timestamp": "01/19/2023 19:08:48",
"content": "Just go back to math help available and take a new one",
"attachments": [],
"mentions": [],
"reference": null
},
{
"id": 1065784936734408700,
"author_id": 1060375293308710900,
"author_name": "Evanixia",
"timestamp": "01/19/2023 19:08:50",
"content": "So I need new one?",
"attachments": [],
"mentions": [],
"reference": null
},
{
"id": 1065784948541370400,
"author_id": 1060375293308710900,
"author_name": "Evanixia",
"timestamp": "01/19/2023 19:08:53",
"content": "Okii",
"attachments": [],
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},
{
"id": 1065784953578733600,
"author_id": 1060375293308710900,
"author_name": "Evanixia",
"timestamp": "01/19/2023 19:08:54",
"content": "Ty",
"attachments": [],
"mentions": [],
"reference": null
},
{
"id": 1065786570180919300,
"author_id": 805217272087838700,
"author_name": "Mathematics Bot",
"timestamp": "01/19/2023 19:15:19",
"content": "Available help channel!",
"attachments": [],
"mentions": [],
"reference": null
},
{
"id": 1065786833008607400,
"author_id": 928230192164511700,
"author_name": "Angie♥",
"timestamp": "01/19/2023 19:16:22",
"content": "",
"attachments": [
{
"id": 1065786832794689500,
"url": "https://cdn.discordapp.com/attachments/486844875632017408/1065786832794689597/IMG_7261.png",
"fileName": "IMG_7261.png",
"fileSizeBytes": 684627
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},
{
"id": 1065786834526949400,
"author_id": 805217272087838700,
"author_name": "Mathematics Bot",
"timestamp": "01/19/2023 19:16:22",
"content": "Pinned a message.",
"attachments": [],
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{
"id": 1065786953674526700,
"author_id": 1011300066264354800,
"author_name": "spicygreenpeppers",
"timestamp": "01/19/2023 19:16:51",
"content": "the variable t represents the number of hours",
"attachments": [],
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},
{
"id": 1065786984255201300,
"author_id": 1011300066264354800,
"author_name": "spicygreenpeppers",
"timestamp": "01/19/2023 19:16:58",
"content": "so if you want to rent it for 4 hours, just put 4 instead of t",
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},
{
"id": 1065787057143828600,
"author_id": 1011300066264354800,
"author_name": "spicygreenpeppers",
"timestamp": "01/19/2023 19:17:15",
"content": "and find out your answer by working out (50x4)+1200",
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},
{
"id": 1065787655540981900,
"author_id": 928230192164511700,
"author_name": "Angie♥",
"timestamp": "01/19/2023 19:19:38",
"content": "50x6)+1200",
"attachments": [],
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},
{
"id": 1065787690714406900,
"author_id": 928230192164511700,
"author_name": "Angie♥",
"timestamp": "01/19/2023 19:19:46",
"content": "for b",
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},
{
"id": 1065789521586835500,
"author_id": 928230192164511700,
"author_name": "Angie♥",
"timestamp": "01/19/2023 19:27:03",
"content": ".close",
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"reference": null
},
{
"id": 1065789524728348700,
"author_id": 805217272087838700,
"author_name": "Mathematics Bot",
"timestamp": "01/19/2023 19:27:04",
"content": "Channel closed",
"attachments": [],
"mentions": [],
"reference": null
}
] | help-9 | 2dc08349d2814cf59d685395282c702d |
200,884 | [
{
"id": 1065794189054451800,
"author_id": 805217272087838700,
"author_name": "Mathematics Bot",
"timestamp": "01/19/2023 19:45:36",
"content": "Available help channel!",
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"mentions": [],
"reference": null
},
{
"id": 1065795100191490000,
"author_id": 687497805958217700,
"author_name": "Willow",
"timestamp": "01/19/2023 19:49:13",
"content": "https://discord.com/channels/268882317391429632/903430333888884736/1065688858852868106",
"attachments": [],
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},
{
"id": 1065795102204764300,
"author_id": 805217272087838700,
"author_name": "Mathematics Bot",
"timestamp": "01/19/2023 19:49:13",
"content": "Pinned a message.",
"attachments": [],
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"messageId": 1065795100191490000,
"channelId": 486844875632017400,
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}
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{
"id": 1065795175990972400,
"author_id": 687497805958217700,
"author_name": "Willow",
"timestamp": "01/19/2023 19:49:31",
"content": "I don't know the difference:",
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"reference": null
},
{
"id": 1065795180655038600,
"author_id": 687497805958217700,
"author_name": "Willow",
"timestamp": "01/19/2023 19:49:32",
"content": "https://onlinemschool.com/math/library/multiplication_formulas/sum3/",
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},
{
"id": 1065797069354307600,
"author_id": 485903210272391200,
"author_name": "dldh06",
"timestamp": "01/19/2023 19:57:02",
"content": "Sum of two cubes is factoring. Cube of sum, the link you posted, is expanding",
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},
{
"id": 1065797390340206600,
"author_id": 687497805958217700,
"author_name": "Willow",
"timestamp": "01/19/2023 19:58:19",
"content": "I don't see a link on this.",
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"id": 1065797408950321200,
"author_id": 687497805958217700,
"author_name": "Willow",
"timestamp": "01/19/2023 19:58:23",
"content": "Would you happen to have one?",
"attachments": [],
"mentions": [],
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},
{
"id": 1065797515057836000,
"author_id": 485903210272391200,
"author_name": "dldh06",
"timestamp": "01/19/2023 19:58:49",
"content": "This link was what I was referring to",
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{
"id": 1065797572704338000,
"author_id": 687497805958217700,
"author_name": "Willow",
"timestamp": "01/19/2023 19:59:02",
"content": "I mean regarding the factoring",
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},
{
"id": 1065797630749311000,
"author_id": 687497805958217700,
"author_name": "Willow",
"timestamp": "01/19/2023 19:59:16",
"content": "you mentioned that link describes expanding",
"attachments": [],
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"reference": null
},
{
"id": 1065797842234507300,
"author_id": 485903210272391200,
"author_name": "dldh06",
"timestamp": "01/19/2023 20:00:07",
"content": "You can look it up",
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},
{
"id": 1065798108329558100,
"author_id": 687497805958217700,
"author_name": "Willow",
"timestamp": "01/19/2023 20:01:10",
"content": "Ramonov, I'm not sure what you were referring to here.",
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},
{
"id": 1065798353344012400,
"author_id": 485903210272391200,
"author_name": "dldh06",
"timestamp": "01/19/2023 20:02:09",
"content": "This is what ramonov was saying\n> do you know the factorisation for the sum of two cubes?\nAs I mentioned, sum of two cubes is a factoring method",
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},
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"id": 1065801884331413500,
"author_id": 805217272087838700,
"author_name": "Mathematics Bot",
"timestamp": "01/19/2023 20:16:10",
"content": "@Willow Has your question been resolved?",
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{
"id": 1065801963003990000,
"author_id": 687497805958217700,
"author_name": "Willow",
"timestamp": "01/19/2023 20:16:29",
"content": "@Helpers",
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},
{
"id": 1065802175294492800,
"author_id": 485903210272391200,
"author_name": "dldh06",
"timestamp": "01/19/2023 20:17:20",
"content": "I gave you what you asked, what are you confused about?",
"attachments": [],
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},
{
"id": 1065802564836266000,
"author_id": 687497805958217700,
"author_name": "Willow",
"timestamp": "01/19/2023 20:18:53",
"content": "I don't understand what you're saying",
"attachments": [],
"mentions": [],
"reference": null
},
{
"id": 1065802572528615600,
"author_id": 687497805958217700,
"author_name": "Willow",
"timestamp": "01/19/2023 20:18:54",
"content": "but it's ok, I can wait",
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"content": "You linked this, because you were stuck on what ramonov stated. What was stated was you needed to apply sum of two cubes",
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"content": "Sum of two cubes is a factoring method",
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"content": "This link is not sum of two cubes, but cube of sums, like the link stated. Cube of sums if an expansion method",
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"timestamp": "01/19/2023 20:28:13",
"content": "I tried to search for the \"sum of two cubes\" and links like the one I shared are what I found",
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"timestamp": "01/19/2023 20:28:41",
"content": "so, i haven't had luck looking this up",
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"timestamp": "01/19/2023 20:29:13",
"content": "but again, it's ok. i can wait.",
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"timestamp": "01/19/2023 20:38:34",
"content": "One of the first links I looked up\nhttps://www.cuemath.com/sum-of-cubes-formula/",
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"timestamp": "01/19/2023 20:39:53",
"content": "This is the exact same material in the link I posted.",
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"timestamp": "01/19/2023 20:40:01",
"content": "No it's not",
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"timestamp": "01/19/2023 20:40:37",
"content": "That is expansion",
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"timestamp": "01/19/2023 20:40:41",
"content": "Look at it",
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"timestamp": "01/19/2023 20:41:20",
"content": "Does that look like this?",
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"timestamp": "01/19/2023 20:41:33",
"content": "the second line",
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"timestamp": "01/19/2023 20:41:52",
"content": "Still not the same",
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"author_name": "Willow",
"timestamp": "01/19/2023 20:42:01",
"content": "at any rate, how does this relate to the cube root of my initial question?",
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"timestamp": "01/19/2023 20:56:18",
"content": "@Helpers",
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"author_id": 1049903022051962900,
"author_name": "ari.",
"timestamp": "01/19/2023 21:05:02",
"content": "hello, how can i help? whats the qs?",
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"timestamp": "01/19/2023 21:05:41",
"content": "https://discord.com/channels/268882317391429632/486844875632017408/1065795100191490098",
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"timestamp": "01/19/2023 21:06:49",
"content": "the original question is here though:",
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"timestamp": "01/19/2023 21:06:49",
"content": "https://discord.com/channels/268882317391429632/903463353417072641/1065601246804840469",
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"timestamp": "01/19/2023 21:08:06",
"content": "oh sorry, couldnt help with that 😿",
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"timestamp": "01/19/2023 21:08:31",
"content": "no worries",
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"timestamp": "01/19/2023 21:08:42",
"content": "hopefully, someone can explain this clearly a bit later",
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"timestamp": "01/19/2023 21:20:57",
"content": "@Willow",
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"timestamp": "01/19/2023 21:21:05",
"content": "I'm adding the image back for context",
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"timestamp": "01/19/2023 21:21:16",
"content": "Can you explain your question to me?",
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"timestamp": "01/19/2023 21:26:10",
"content": "i'm inquiring about rationalizing the numerator and what's happening with that cube root",
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"timestamp": "01/19/2023 21:30:16",
"content": "rationalizing this numerator?",
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"timestamp": "01/19/2023 21:37:49",
"content": "yes, correct",
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"timestamp": "01/19/2023 21:41:18",
"content": "I see this explanation was given",
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"timestamp": "01/19/2023 21:41:29",
"content": "Did it make sense or were you still lost somewhere?",
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"timestamp": "01/19/2023 21:42:04",
"content": "yes, I don't completely understand this.",
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"timestamp": "01/19/2023 21:42:28",
"content": "if possible, i think it would be helpful to step through each change here",
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"timestamp": "01/19/2023 21:43:20",
"content": "someone else helping me actually just gave me what seems to be a *very* helpful link regarding what's happening here:",
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"timestamp": "01/19/2023 21:43:31",
"content": "https://en.wikipedia.org/wiki/Nth_root",
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"timestamp": "01/19/2023 21:43:44",
"content": "this:",
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"timestamp": "01/19/2023 21:43:47",
"content": "",
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"timestamp": "01/19/2023 21:44:03",
"content": "this seems to be EXACTLY what I needed",
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"timestamp": "01/19/2023 21:44:15",
"content": "Yeah that looks like it",
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"timestamp": "01/19/2023 21:44:19",
"content": "the signs are different though which is confusing a bit",
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"timestamp": "01/19/2023 21:44:27",
"content": "num and den switched, but pretty much right",
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"timestamp": "01/19/2023 21:44:30",
"content": "but i still think it is the difference of cubes",
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"timestamp": "01/19/2023 21:44:55",
"content": "sum of cubes and difference of cubes doesn't really make a difference thankfully",
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"id": 1065824253531926700,
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"timestamp": "01/19/2023 21:45:04",
"content": "so, that means this is what is happening:",
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"timestamp": "01/19/2023 21:45:04",
"content": "$\\lim_{x \\to 1}\\frac{\\sqrt[3]{x}-1}{2x-2} = \\frac{(\\sqrt[3]{x}-1) \\cdot (\\sqrt[3]{x^2} - \\sqrt[3]{x*(1)} + (1)^2)}{(2x-2) \\cdot (\\sqrt[3]{x^2} - \\sqrt[3]{x*(1)} + (1)^2)}$",
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"timestamp": "01/19/2023 21:45:07",
"content": "**Willow**",
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"timestamp": "01/19/2023 21:45:20",
"content": "It's not like quadratics, where you can't take negative square roots",
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"timestamp": "01/19/2023 21:45:59",
"content": "correct?",
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"timestamp": "01/19/2023 21:46:03",
"content": "yes exactly this",
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"timestamp": "01/19/2023 21:46:26",
"content": "but there is a discrepancy between my work and the picture",
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"timestamp": "01/19/2023 21:46:29",
"content": "the negative sign",
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"timestamp": "01/19/2023 21:47:26",
"content": "Lemme take a look",
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"timestamp": "01/19/2023 21:47:35",
"content": "i'll highlight it for you",
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"timestamp": "01/19/2023 21:48:35",
"content": "VS",
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"timestamp": "01/19/2023 21:50:47",
"content": "Ah I see the issue",
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"timestamp": "01/19/2023 21:51:21",
"content": "These should be -1, not 1",
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"timestamp": "01/19/2023 21:54:36",
"content": "why?",
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"timestamp": "01/19/2023 21:54:38",
"content": "the formula is:\n\n$a^3 - b^3 = (a-b)(a^2-ab+b^2)$",
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"timestamp": "01/19/2023 21:54:40",
"content": "**Willow**",
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"timestamp": "01/19/2023 21:55:43",
"content": "wait, let me read your post above",
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"timestamp": "01/19/2023 21:56:08",
"content": "Just distribute the multiplication on the right to check and verify",
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"timestamp": "01/19/2023 21:56:57",
"content": "Oh, you know what, I have this in my notes.",
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"timestamp": "01/19/2023 21:56:58",
"content": "$a^3 \\pm b^3 = (a \\pm b)(a^2 \\mp ab + b^2)$",
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"timestamp": "01/19/2023 21:57:00",
"content": "**Mr. Gamer**",
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"timestamp": "01/19/2023 21:57:11",
"content": "I think I was mimicing the wiki link",
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"timestamp": "01/19/2023 21:57:27",
"content": "This is indeed the correct formula",
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"timestamp": "01/19/2023 21:57:46",
"content": "see here:",
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"content": "",
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"timestamp": "01/19/2023 21:58:07",
"content": "Is the wiki link wrong, then?",
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"timestamp": "01/19/2023 21:58:10",
"content": "no",
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"timestamp": "01/19/2023 21:58:18",
"content": "It's doing sum of cubes in that image",
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"timestamp": "01/19/2023 21:58:48",
"content": "i thought you said they don't make a difference:",
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"timestamp": "01/19/2023 21:58:48",
"content": "https://discord.com/channels/268882317391429632/486844875632017408/1065824217444126730",
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"timestamp": "01/19/2023 21:59:09",
"content": "Let me clarify that a bit",
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"timestamp": "01/19/2023 22:00:00",
"content": "I meant that if you knew the formula for a³+b³, then you could find the formula for a³-b³ simply by using the a³+b³ formula but replacing b with -b",
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"timestamp": "01/19/2023 22:03:27",
"content": "difference of cubes\n\n$a^3 - b^3 = (a - b) (a^2 + ab + b^2)$\n\nsum of cubes\n\n$a^3 + b^3 = (a + b) (a^2 - ab + b^2)$",
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"timestamp": "01/19/2023 22:03:29",
"content": "yes?",
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"timestamp": "01/19/2023 22:03:39",
"content": "yes",
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"timestamp": "01/19/2023 22:03:59",
"content": "Same as what you wrote here",
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"timestamp": "01/19/2023 22:04:03",
"content": "**Willow**",
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"timestamp": "01/19/2023 22:04:17",
"content": "I didn't write that.",
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"timestamp": "01/19/2023 22:04:23",
"content": "Oh",
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"timestamp": "01/19/2023 22:04:28",
"content": "Same is mr gamer wrote there",
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"timestamp": "01/19/2023 22:12:41",
"content": "ok, that makes a bit more sense now",
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"timestamp": "01/19/2023 22:12:49",
"content": "so, how does this simplify?",
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"timestamp": "01/19/2023 22:12:50",
"content": "$\\sqrt[3]{x}-1 = (\\sqrt[3]{x}-1) \\cdot (\\sqrt[3]{x^2} + \\sqrt[3]{x*(1)} + (1)^2)$",
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"timestamp": "01/19/2023 22:12:52",
"content": "**Willow**",
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"timestamp": "01/19/2023 22:13:30",
"content": "That, in isolation, does not simplify",
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"timestamp": "01/19/2023 22:13:42",
"content": "actually...",
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"timestamp": "01/19/2023 22:13:45",
"content": "It's incorrect",
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"timestamp": "01/19/2023 22:13:48",
"content": "or evaluate, I mean",
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"timestamp": "01/19/2023 22:14:01",
"content": "$x-1 = (\\sqrt[3]{x}-1) \\cdot (\\sqrt[3]{x^2} + \\sqrt[3]{x*(1)} + (1)^2)$",
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"timestamp": "01/19/2023 22:14:03",
"content": "**SWR**",
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"timestamp": "01/19/2023 22:14:54",
"content": "how? i thought we just went over this?",
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"timestamp": "01/19/2023 22:15:19",
"content": "$(\\sqrt[3]{x})^3-1 = (\\sqrt[3]{x}-1) \\cdot (\\sqrt[3]{x^2} + \\sqrt[3]{x*(1)} + (1)^2)$",
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"timestamp": "01/19/2023 22:15:21",
"content": "**SWR**",
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"timestamp": "01/19/2023 22:16:40",
"content": "i don't think so, is it?",
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"timestamp": "01/19/2023 22:16:45",
"content": "Not sure if this picture explains it",
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"timestamp": "01/19/2023 22:16:49",
"content": "i'm just evaluating the numerator separately",
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"timestamp": "01/19/2023 22:17:05",
"content": "If you're unsure, just try multiplying out the rhs",
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"timestamp": "01/19/2023 22:17:52",
"content": "I copied the wiki link",
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"timestamp": "01/19/2023 22:18:48",
"content": "unless you're just referring to the cube notation?",
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"timestamp": "01/19/2023 22:19:02",
"content": "I'm lost.",
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"author_name": "SWR",
"timestamp": "01/19/2023 22:19:09",
"content": "Which exact equation are you unsure about?",
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"author_name": "Willow",
"timestamp": "01/19/2023 22:19:29",
"content": "ok, let's go back",
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"author_name": "Willow",
"timestamp": "01/19/2023 22:19:37",
"content": "my last question was here:",
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"author_name": "Willow",
"timestamp": "01/19/2023 22:19:38",
"content": "https://discord.com/channels/268882317391429632/486844875632017408/1065831243930943548",
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"timestamp": "01/19/2023 22:20:03",
"content": "Right",
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"timestamp": "01/19/2023 22:20:15",
"content": "so, the question is:",
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"author_id": 374795910032523260,
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"timestamp": "01/19/2023 22:20:18",
"content": "The left and right sides are not equal",
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"id": 1065833140934951000,
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"author_name": "Willow",
"timestamp": "01/19/2023 22:20:23",
"content": "how does $(\\sqrt[3]{x}-1) \\cdot (\\sqrt[3]{x^2} + \\sqrt[3]{x*(1)} + (1)^2)$ evaluate",
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"timestamp": "01/19/2023 22:20:25",
"content": "**Willow**",
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"timestamp": "01/19/2023 22:20:49",
"content": ",w simplify (cbrt(x)-1)(cbrt(x^2)+cbrt(x)+1)",
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"timestamp": "01/19/2023 22:21:16",
"content": "Results provided by WolframAlpha",
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"timestamp": "01/19/2023 22:22:54",
"content": "i'm getting lost again",
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"author_name": "Willow",
"timestamp": "01/19/2023 22:23:07",
"content": "ok, let's stop and baby walk",
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"timestamp": "01/19/2023 22:23:50",
"content": "you ask the questions, I'll try best to answer",
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"timestamp": "01/19/2023 22:24:02",
"content": "step 1. Assess $\\sqrt[3]{x}-1$",
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"timestamp": "01/19/2023 22:24:05",
"content": "**Willow**",
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"timestamp": "01/19/2023 22:24:19",
"content": "cannot be simplified",
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"author_id": 374795910032523260,
"author_name": "SWR",
"timestamp": "01/19/2023 22:24:28",
"content": "(not the way you are trying to)",
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"id": 1065834234046062600,
"author_id": 687497805958217700,
"author_name": "Willow",
"timestamp": "01/19/2023 22:24:43",
"content": "wait, you can just interrupt me if I am incorrect some place",
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"id": 1065834315071631500,
"author_id": 374795910032523260,
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"timestamp": "01/19/2023 22:25:02",
"content": "🤐",
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"id": 1065834328921231400,
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"author_name": "Willow",
"timestamp": "01/19/2023 22:25:06",
"content": "step 2. realize that difference of cubes will be used here",
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"author_name": "Willow",
"timestamp": "01/19/2023 22:25:53",
"content": "step 3. look in notes and find formula which is $a^3 - b^3 = (a - b) (a^2 + ab + b^2)$",
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"timestamp": "01/19/2023 22:25:55",
"content": "**Willow**",
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"timestamp": "01/19/2023 22:26:52",
"content": "step 4. plug $\\sqrt[3]{x}-1$ into formula",
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"timestamp": "01/19/2023 22:26:54",
"content": "**Willow**",
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"author_name": "Willow",
"timestamp": "01/19/2023 22:27:29",
"content": "step 5. confirm the formula's accuracy after inputting $\\sqrt[3]{x}-1$",
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"timestamp": "01/19/2023 22:27:31",
"content": "**Willow**",
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"timestamp": "01/19/2023 22:28:00",
"content": "question here",
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"id": 1065835350141964400,
"author_id": 687497805958217700,
"author_name": "Willow",
"timestamp": "01/19/2023 22:29:09",
"content": "yes?",
"attachments": [],
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"id": 1065835366805930100,
"author_id": 374795910032523260,
"author_name": "SWR",
"timestamp": "01/19/2023 22:29:13",
"content": "How are you \"plugging it in\"?",
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"id": 1065835388062662800,
"author_id": 374795910032523260,
"author_name": "SWR",
"timestamp": "01/19/2023 22:29:18",
"content": "what is going where?",
"attachments": [],
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"id": 1065835442173399000,
"author_id": 374795910032523260,
"author_name": "SWR",
"timestamp": "01/19/2023 22:29:31",
"content": "Like what will _a_ and _b_ be?",
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"author_name": "Willow",
"timestamp": "01/19/2023 22:30:07",
"content": "a = x, b = 1",
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"id": 1065835643009253400,
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"timestamp": "01/19/2023 22:30:19",
"content": "ah here is the mistake",
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"id": 1065835762723061800,
"author_id": 374795910032523260,
"author_name": "SWR",
"timestamp": "01/19/2023 22:30:48",
"content": "It should be $a=\\sqrt[3]{x}$",
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"author_name": "TeXit",
"timestamp": "01/19/2023 22:30:59",
"content": "**SWR**",
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"id": 1065835840640659500,
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"author_name": "Willow",
"timestamp": "01/19/2023 22:31:06",
"content": "how?",
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"id": 1065835872915824600,
"author_id": 687497805958217700,
"author_name": "Willow",
"timestamp": "01/19/2023 22:31:14",
"content": "only x is squared in the wiki link",
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"id": 1065835939487817900,
"author_id": 374795910032523260,
"author_name": "SWR",
"timestamp": "01/19/2023 22:31:30",
"content": "Let's say you chose a=x",
"attachments": [],
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"id": 1065835967606427600,
"author_id": 374795910032523260,
"author_name": "SWR",
"timestamp": "01/19/2023 22:31:36",
"content": "Then what will a² and a³ be?",
"attachments": [],
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"author_id": 687497805958217700,
"author_name": "Willow",
"timestamp": "01/19/2023 22:32:58",
"content": "there is no $a^3$ here besides the initial given function",
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"id": 1065836318216704100,
"author_id": 510789298321096700,
"author_name": "TeXit",
"timestamp": "01/19/2023 22:33:00",
"content": "**Willow**",
"attachments": [
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"author_name": "SWR",
"timestamp": "01/19/2023 22:33:18",
"content": "There is no a³ in here?",
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"id": 1065836478111957000,
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"author_name": "Willow",
"timestamp": "01/19/2023 22:33:38",
"content": "> besides the *initial* given function",
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"id": 1065836620537934000,
"author_id": 687497805958217700,
"author_name": "Willow",
"timestamp": "01/19/2023 22:34:12",
"content": "meaning a cube isn't applied in solving the problem",
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"author_name": "Willow",
"timestamp": "01/19/2023 22:34:19",
"content": "but hmm, I think I see your point",
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"id": 1065836709968883700,
"author_id": 687497805958217700,
"author_name": "Willow",
"timestamp": "01/19/2023 22:34:33",
"content": "so, what rule am i misunderstanding here?",
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"id": 1065836791963340900,
"author_id": 687497805958217700,
"author_name": "Willow",
"timestamp": "01/19/2023 22:34:53",
"content": "i don't wish to dwell on this that long if at all possible",
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"id": 1065836827904331900,
"author_id": 687497805958217700,
"author_name": "Willow",
"timestamp": "01/19/2023 22:35:02",
"content": "i have too much other hw",
"attachments": [],
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"id": 1065836885030735900,
"author_id": 687497805958217700,
"author_name": "Willow",
"timestamp": "01/19/2023 22:35:15",
"content": "and got another F today in Calculus on the quiz",
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"id": 1065836893801025700,
"author_id": 687497805958217700,
"author_name": "Willow",
"timestamp": "01/19/2023 22:35:17",
"content": "so depressing",
"attachments": [],
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"id": 1065836896703500400,
"author_id": 374795910032523260,
"author_name": "SWR",
"timestamp": "01/19/2023 22:35:18",
"content": "This formula is for difference of cubes",
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"id": 1065836913568776300,
"author_id": 374795910032523260,
"author_name": "SWR",
"timestamp": "01/19/2023 22:35:22",
"content": "But you have a cube root",
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"id": 1065837050563149800,
"author_id": 374795910032523260,
"author_name": "SWR",
"timestamp": "01/19/2023 22:35:55",
"content": "But x³ is to x as x is ∛x",
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"id": 1065837098369814500,
"author_id": 374795910032523260,
"author_name": "SWR",
"timestamp": "01/19/2023 22:36:06",
"content": "So you can use difference of cubes formula",
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"id": 1065837151926882300,
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"author_name": "SWR",
"timestamp": "01/19/2023 22:36:19",
"content": "but you're using a³=x, which is the cubed form of a=∛x",
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"id": 1065837515287830500,
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"author_name": "Willow",
"timestamp": "01/19/2023 22:37:45",
"content": "ok, what should it be?",
"attachments": [],
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"id": 1065837683445858300,
"author_id": 374795910032523260,
"author_name": "SWR",
"timestamp": "01/19/2023 22:38:26",
"content": "what should what be?",
"attachments": [],
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"author_name": "Willow",
"timestamp": "01/19/2023 22:40:54",
"content": "you just mean step. 4 should use $a = \\sqrt[3]{x}, b = -1$ , yes?",
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"id": 1065838313723924500,
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"author_name": "TeXit",
"timestamp": "01/19/2023 22:40:56",
"content": "**Willow**",
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"timestamp": "01/19/2023 22:41:16",
"content": "yes",
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"id": 1065838407101714600,
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"timestamp": "01/19/2023 22:41:18",
"content": "exactly that",
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"timestamp": "01/19/2023 22:41:25",
"content": "ok, I'll continue from there",
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"timestamp": "01/19/2023 22:42:04",
"content": "step 4. plug $\\sqrt[3]{x}-1$ into formula\n\n$a=\\sqrt[3]{x}, b = 1$",
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"timestamp": "01/19/2023 22:44:03",
"content": "b=1",
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"author_name": "TeXit",
"timestamp": "01/19/2023 22:45:09",
"content": "**Willow**",
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"id": 1065839674351956000,
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"author_name": "Willow",
"timestamp": "01/19/2023 22:46:20",
"content": "so, when squaring $\\sqrt[3]{x}$, only `x` is squared?",
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"timestamp": "01/19/2023 22:46:22",
"content": "**Willow**",
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"timestamp": "01/19/2023 22:47:03",
"content": "so, $\\sqrt[3]{x^2}$ and not this $(\\sqrt[3]{x})^2$",
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"id": 1065839971199619100,
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"timestamp": "01/19/2023 22:47:31",
"content": "${\\sqrt[3]{x}}^2=\\sqrt[3]{x^2}$",
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"timestamp": "01/19/2023 22:47:36",
"content": "**Willow**",
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"timestamp": "01/19/2023 22:47:43",
"content": "**SWR**",
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"author_name": "Willow",
"timestamp": "01/19/2023 22:48:01",
"content": "you mean both notations are correct?",
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"timestamp": "01/19/2023 22:49:40",
"content": "yup",
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"timestamp": "01/19/2023 22:49:50",
"content": "ok",
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"id": 1065840678627721200,
"author_id": 374795910032523260,
"author_name": "SWR",
"timestamp": "01/19/2023 22:50:20",
"content": ",w cbrt(x^2)-cbrt(x)^2",
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"timestamp": "01/19/2023 22:50:47",
"content": "Results provided by WolframAlpha",
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"timestamp": "01/19/2023 22:53:56",
"content": "step 5. confirm the formula's accuracy after inputting $\\sqrt[3]{x}-1$\n\nhere is the formula with `a` and `b` plugged in:\n\n$(\\sqrt[3]{x}-1) \\cdot (\\sqrt[3]{x^2} + \\sqrt[3]{x*(1)} + (1)^2)$",
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"timestamp": "01/19/2023 22:54:25",
"content": "**Willow**",
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"timestamp": "01/19/2023 22:56:03",
"content": "step 6. multiply this entire formula:\n\n$(\\sqrt[3]{x}-1) \\cdot (\\sqrt[3]{x^2} + \\sqrt[3]{x*(1)} + (1)^2)$\n\nby $\\sqrt[3]{x}-1$",
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"timestamp": "01/19/2023 22:56:05",
"content": "**Willow**",
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"timestamp": "01/19/2023 22:57:23",
"content": "This doesn't seem right..",
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"author_name": "Willow",
"timestamp": "01/19/2023 22:58:04",
"content": "ok, let's discuss it",
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"content": "Sure",
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"content": "So here is your original limit",
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"content": "the teacher is mulitplying here as indicated by the dot",
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"content": "yeah",
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"content": "Sorry got pulled away",
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"content": "Okay, so any number multiplied by 1 is the same number (obviously)",
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"content": "Also, any number divided by itself (except 0) is 1",
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"content": "Next, we know $\\frac{a}{b}\\cdot\\frac{c}{d}=\\frac{a\\cdot c}{b \\cdot d}$",
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"content": "**SWR**",
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"content": "wait",
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"content": "what happened to the first half of the Difference of Cubes formula?",
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"content": "it just disappeared",
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"content": "It was here all along",
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"content": "We're including the second half now to actually make it a difference of cubes",
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"timestamp": "01/19/2023 23:06:37",
"content": "After the series of steps, we end up here",
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"timestamp": "01/19/2023 23:06:42",
"content": "Which is the difference of cubes formula",
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"content": "the right part is just a continuation of the left?",
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"content": "Not sure what you mean here",
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"content": "i thought you calculate the difference of cubes and THEN, multiply that entire new formula by the numerator",
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"content": "but what you're doing here is just extending it",
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"timestamp": "01/19/2023 23:09:03",
"content": "or factoring it",
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"content": "If I understand you correctly, yes",
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"content": "Here's the whole thing",
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"content": "Does it make sense?",
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"content": "how does the numerator become `x - 1` ?",
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"content": "Difference of cubes formula",
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"content": "ok, i think i understand (hopefully) enough to pass the test",
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] | help-9 | d2cece138a02419dbd42025086f99231 |
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] | help-9 | 5302928ba17d49cdbaad8b6bba9e8d5f |
200,886 | [
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"content": "is a valid proof, let y = x, y is then not greater than x so therefore the statement is false?",
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"content": "I'm assuming that's supposed to be \"there exists an x such that for all y, y is greater than x\"?",
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"content": "I mean",
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"content": "yes",
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"content": "domain is reals",
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"content": "I guess?",
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"content": "Yeah",
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"content": "That works",
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"content": "Is there a better way to structure it?",
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"content": "You can state this as contra example and say that the statement is false",
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"content": "If y = x, then y = x lol",
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"content": ".close",
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] | help-9 | 52cfc6890b7a44649904a675d9b3da91 |
200,887 | [
{
"id": 1036193366922248200,
"author_id": 805217272087838700,
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"timestamp": "10/30/2022 04:22:30",
"content": "Available help channel!",
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"id": 1036195514414288900,
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"timestamp": "10/30/2022 04:31:02",
"content": "yo",
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"timestamp": "10/30/2022 04:31:23",
"content": "is there any way to integrate this (ignore the upper and lower bounds)",
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"content": "ive used symbolab and it cant do it",
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"timestamp": "10/30/2022 04:31:42",
"content": "and i used wolfram alpha and it gives me a complex number",
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"content": "i dont really need the actual integral i can just graph the function",
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"timestamp": "10/30/2022 04:32:09",
"content": "because all im trying to do is find the upper bound so that the volume = some number",
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"author_name": "Maximus Laurie",
"timestamp": "10/30/2022 04:35:49",
"content": "Hi, can I see the phrasing of the original question!",
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"content": "?",
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"author_name": "Maximus Laurie",
"timestamp": "10/30/2022 04:36:47",
"content": "Some integrals cannot be integrated by analytic methods, however it is difficult to tell just by looking at the form of the integrand",
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"author_name": "Maximus Laurie",
"timestamp": "10/30/2022 04:37:24",
"content": "that said, there may be an analytic way to find an upper bound. The question I want to know is, how good does the upper bound have to be?",
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"timestamp": "10/30/2022 04:38:17",
"content": "it just says find where the standard drink would be on the glass lol",
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"timestamp": "10/30/2022 04:38:29",
"content": "the function i just sent you finds the volume of the glass",
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"author_name": "Maximus Laurie",
"timestamp": "10/30/2022 04:41:20",
"content": "so by upper bound, do you mean the domain of integration, or do you mean a highest value the integral can have",
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"content": "no",
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"timestamp": "10/30/2022 04:42:34",
"content": "thank you for your help",
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"timestamp": "10/30/2022 04:57:35",
"content": "@gmail.com Has your question been resolved?",
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"timestamp": "10/30/2022 05:12:35",
"content": "Channel closed",
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] | help-9 | 6b6ff5d39a48473b98bb63cdad6ef8fc |
200,888 | [
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"content": "@dottables Has your question been resolved?",
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] | help-9 | c30d192c014340b7bc956d6eb8af4d97 |
200,889 | [
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"author_id": 716679417203523600,
"author_name": "akagi",
"timestamp": "01/20/2023 00:55:27",
"content": "how to get this?",
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"id": 1065872216161517600,
"author_id": 220517274845577200,
"author_name": "ramonov",
"timestamp": "01/20/2023 00:55:39",
"content": "sohcahtoa",
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"id": 1065872242464018600,
"author_id": 716679417203523600,
"author_name": "akagi",
"timestamp": "01/20/2023 00:55:45",
"content": "what",
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"id": 1065872273774481400,
"author_id": 851170607755558900,
"author_name": "ℕαv",
"timestamp": "01/20/2023 00:55:53",
"content": "trig",
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"id": 1065872330678620200,
"author_id": 716679417203523600,
"author_name": "akagi",
"timestamp": "01/20/2023 00:56:06",
"content": "yeah triangle trigonometry",
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"id": 1065872378812452900,
"author_id": 716679417203523600,
"author_name": "akagi",
"timestamp": "01/20/2023 00:56:18",
"content": "how do i apply sohcahtoa",
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"id": 1065872379349307400,
"author_id": 220517274845577200,
"author_name": "ramonov",
"timestamp": "01/20/2023 00:56:18",
"content": "> sohcahtoa\nis the mnemonic for what sin,cos,tan do in a right triangle",
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"id": 1065872393819664400,
"author_id": 851170607755558900,
"author_name": "ℕαv",
"timestamp": "01/20/2023 00:56:21",
"content": "so you need to use the hypotenuse that's for sure",
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"id": 1065872433212559400,
"author_id": 851170607755558900,
"author_name": "ℕαv",
"timestamp": "01/20/2023 00:56:31",
"content": "after that you can pretty much choose any other side",
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"id": 1065872584207499300,
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"author_name": "ramonov",
"timestamp": "01/20/2023 00:57:07",
"content": "you can consult that and\nbased on the angle you want to use,\nrelative position of what's given\nrelative position of what you want to find\nset up your equation",
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"id": 1065873142062526500,
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"author_name": "akagi",
"timestamp": "01/20/2023 00:59:20",
"content": "so how exactly can i get the measure of side c?",
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"id": 1065873185666506800,
"author_id": 716679417203523600,
"author_name": "akagi",
"timestamp": "01/20/2023 00:59:30",
"content": "in step by step",
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},
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"id": 1065873266650132500,
"author_id": 220517274845577200,
"author_name": "ramonov",
"timestamp": "01/20/2023 00:59:49",
"content": "have you looked up sohcahtoa",
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"id": 1065873311969583100,
"author_id": 716679417203523600,
"author_name": "akagi",
"timestamp": "01/20/2023 01:00:00",
"content": "yes",
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"id": 1065873346169950200,
"author_id": 220517274845577200,
"author_name": "ramonov",
"timestamp": "01/20/2023 01:00:08",
"content": "> based on the angle you want to use,\nwhich angle do you want to use",
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},
{
"id": 1065873811850920100,
"author_id": 716679417203523600,
"author_name": "akagi",
"timestamp": "01/20/2023 01:01:59",
"content": "the one here preferably",
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"id": 1065874001060188300,
"author_id": 220517274845577200,
"author_name": "ramonov",
"timestamp": "01/20/2023 01:02:44",
"content": "i want you to explicitly state which one",
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"id": 1065874122988605400,
"author_id": 220517274845577200,
"author_name": "ramonov",
"timestamp": "01/20/2023 01:03:13",
"content": "using understandable notation",
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"author_name": "Mathematics Bot",
"timestamp": "01/20/2023 01:16:59",
"content": "@akagi Has your question been resolved?",
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"timestamp": "01/20/2023 01:32:00",
"content": "Channel closed",
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] | help-9 | d8ada1b39965406c80cbd1d6b1775e6c |
200,890 | [
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"content": "Available help channel!",
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"id": 1065901630232469600,
"author_id": 283204823820664830,
"author_name": "ok yes",
"timestamp": "01/20/2023 02:52:32",
"content": "hi is there a more efficient way of doing this nonhomogenous equation without having to do product rule three times?",
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"content": "Pinned a message.",
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"content": "@ok yes Has your question been resolved?",
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"content": "notability",
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"author_id": 722683408190406700,
"author_name": "waterr beam",
"timestamp": "01/20/2023 03:21:34",
"content": "free?",
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"id": 1065908957236965400,
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"timestamp": "01/20/2023 03:21:39",
"content": "no",
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"id": 1065908976086163500,
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"author_name": "waterr beam",
"timestamp": "01/20/2023 03:21:43",
"content": ":sully:",
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"id": 1065909075302428700,
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"timestamp": "01/20/2023 03:22:07",
"content": "education is expensive :bhappy:",
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"timestamp": "01/20/2023 03:52:07",
"content": "@ok yes Has your question been resolved?",
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"timestamp": "01/20/2023 03:57:45",
"content": "i mean i solved it but is there an easier method",
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"author_name": "DerpZ",
"timestamp": "01/20/2023 04:43:28",
"content": "didnt read fully but",
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"id": 1065929556520878100,
"author_id": 196556976866459650,
"author_name": "DerpZ",
"timestamp": "01/20/2023 04:43:30",
"content": "id integrate",
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"id": 1065929580503892000,
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"author_name": "DerpZ",
"timestamp": "01/20/2023 04:43:36",
"content": "charge your ipad lol",
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"id": 1065930261302353900,
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"timestamp": "01/20/2023 04:46:18",
"content": "wait",
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"timestamp": "01/20/2023 04:47:35",
"content": "thats even more painful",
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"content": "@ok yes Has your question been resolved?",
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"content": "@ok yes Has your question been resolved?",
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] | help-9 | ffc63c48f58f422f8c5e81e54b620bc9 |
200,891 | [
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"content": "while here not",
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"content": "why is that",
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"content": "whats the bit before this",
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"id": 1066007509627838500,
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"content": "or is there none",
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"author_id": 182179228840755200,
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"content": "basically they're taking the left limit but not saying so",
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"content": "i mean why didnt we do this here too",
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"content": "why didnt we take from the left and right",
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"timestamp": "01/20/2023 09:58:00",
"content": "like here",
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"content": "that is what i am saying",
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"content": "oh actually scratch that",
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"content": "they say it above",
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"author_name": "iCaird",
"timestamp": "01/20/2023 10:00:39",
"content": "> Therefore |x| = -x in the neighbourhood of x = -2",
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"timestamp": "01/20/2023 10:02:13",
"content": "because -2 is not the point at which the absolute value |x| has its discontinuity, which is zero",
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"timestamp": "01/20/2023 10:02:38",
"content": "whereas in the other example the limit is x -> -6 and that *is* the point at which |x+6| has its discontinuity",
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"timestamp": "01/20/2023 10:05:48",
"content": "@iCaird please explain in anoteher way i wanna understand it",
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"content": "idk whats discontinuity",
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"content": "https://www.desmos.com/calculator/2eaigfzk55",
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"content": "just look at these graphs",
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"content": "x=-2 is not where the sharp corner is one blue so we dont need to worry",
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"content": "but -6 is where the \"jump\" is on red so we need to consider whats happening each side",
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"content": "@Acer. Has your question been resolved?",
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] | help-9 | 0264e91bb8414cadbd52f91b64bcca96 |
200,892 | [
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"content": "I found this question in my homework and I couldn't find a way to solve it",
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"content": "Hello, draw segments from M and N to the center C of the circle",
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"content": "Ok thank you very much",
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"content": ".close",
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] | help-9 | 4b6850f0c757471b9de803d8b32704b2 |
200,893 | [
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"content": "average growth rate of what, and over which time span?",
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"content": "from 2001 to 2021",
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"content": "and of both? i guess im new to this",
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"content": "do you have the instructions somewhere?",
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"id": 1066032661476430000,
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"content": "hold up need to translate the task",
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"id": 1066032689829912700,
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"timestamp": "01/20/2023 11:33:19",
"content": "even if they are in Danish or Norwegian or Swedish",
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"timestamp": "01/20/2023 11:33:25",
"content": "post the original first",
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"id": 1066032956185002100,
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"timestamp": "01/20/2023 11:34:22",
"content": "a retail chain sells goods in both physical stores in, for example, shopping centers and through online shopping. The graphs show the turnover development for the two sales methods. Find the average growing color in sales for both store sales and online sales",
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"content": "theres in norwegian as well",
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"content": ",rccw",
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"timestamp": "01/20/2023 11:40:03",
"content": "does that help",
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"content": "or",
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"content": "?",
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"timestamp": "01/20/2023 11:43:38",
"content": "uh huh...",
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"timestamp": "01/20/2023 11:43:51",
"content": "okay, so over the entire timespan depicted, then.",
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"timestamp": "01/20/2023 11:44:22",
"content": "write down the sales volume (in millions of NOK) in 2001 and in 2021, for both categories of sales",
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"id": 1066036259128103000,
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"timestamp": "01/20/2023 11:47:30",
"content": "so 2001: 18 million 2021: 13 million",
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"content": "physical store",
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"timestamp": "01/20/2023 11:48:18",
"content": "2001: 5 million 2021: 42 million",
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"author_id": 490928916207370240,
"author_name": "jesper",
"timestamp": "01/20/2023 11:48:20",
"content": "online",
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"id": 1066036672204132500,
"author_id": 490928916207370240,
"author_name": "jesper",
"timestamp": "01/20/2023 11:49:08",
"content": "what after this",
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"id": 1066036882082898000,
"author_id": 183668144404037630,
"author_name": "Ann",
"timestamp": "01/20/2023 11:49:58",
"content": "how much did physical store sales change over the 20 years?",
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},
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"id": 1066037638395596900,
"author_id": 490928916207370240,
"author_name": "jesper",
"timestamp": "01/20/2023 11:52:59",
"content": "changed by 5 million",
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},
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"id": 1066037668972081200,
"author_id": 490928916207370240,
"author_name": "jesper",
"timestamp": "01/20/2023 11:53:06",
"content": "or -5 million",
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},
{
"id": 1066037742401765400,
"author_id": 490928916207370240,
"author_name": "jesper",
"timestamp": "01/20/2023 11:53:23",
"content": "not sure which one thats correct",
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},
{
"id": 1066037945397694600,
"author_id": 490928916207370240,
"author_name": "jesper",
"timestamp": "01/20/2023 11:54:12",
"content": "and online changed with 37",
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},
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"id": 1066037974422278300,
"author_id": 490928916207370240,
"author_name": "jesper",
"timestamp": "01/20/2023 11:54:19",
"content": "million",
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},
{
"id": 1066038197496336500,
"author_id": 490928916207370240,
"author_name": "jesper",
"timestamp": "01/20/2023 11:55:12",
"content": "then do i just divide this by the ammount of years (20) ?",
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"id": 1066038358180106200,
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"author_name": "jesper",
"timestamp": "01/20/2023 11:55:50",
"content": "5/20 = 0.25 which makes the growth rate -0.25?",
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},
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"id": 1066042134001619000,
"author_id": 805217272087838700,
"author_name": "Mathematics Bot",
"timestamp": "01/20/2023 12:10:50",
"content": "@jesper Has your question been resolved?",
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"id": 1066042559304061000,
"author_id": 183668144404037630,
"author_name": "Ann",
"timestamp": "01/20/2023 12:12:32",
"content": "yes, -0.25 million NOK/year",
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},
{
"id": 1066042592762003600,
"author_id": 183668144404037630,
"author_name": "Ann",
"timestamp": "01/20/2023 12:12:40",
"content": "or -250k NOK/year",
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"reference": null
},
{
"id": 1066042758663520300,
"author_id": 490928916207370240,
"author_name": "jesper",
"timestamp": "01/20/2023 12:13:19",
"content": "understood, thank you",
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"id": 1066050208959561900,
"author_id": 490928916207370240,
"author_name": "jesper",
"timestamp": "01/20/2023 12:42:56",
"content": ".close",
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},
{
"id": 1066050211996258300,
"author_id": 805217272087838700,
"author_name": "Mathematics Bot",
"timestamp": "01/20/2023 12:42:56",
"content": "Channel closed",
"attachments": [],
"mentions": [],
"reference": null
}
] | help-9 | f7fbb612fde14e34b50f1e1b83855a4a |
200,894 | [
{
"id": 1066050463885168600,
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"timestamp": "01/20/2023 12:43:56",
"content": "Available help channel!",
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},
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"id": 1066050601240232100,
"author_id": 264776565001420800,
"author_name": "Riley",
"timestamp": "01/20/2023 12:44:29",
"content": "",
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"content": "Pinned a message.",
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"id": 1066051425710395500,
"author_id": 859166603114315800,
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"timestamp": "01/20/2023 12:47:46",
"content": "h = fg^(-1)",
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"id": 1066051580664762500,
"author_id": 264776565001420800,
"author_name": "Riley",
"timestamp": "01/20/2023 12:48:23",
"content": "What's this",
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"timestamp": "01/20/2023 12:48:34",
"content": "h = fg^(-1)",
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{
"id": 1066051673052684300,
"author_id": 707998648637849700,
"author_name": "AliveUser",
"timestamp": "01/20/2023 12:48:45",
"content": "inverse function??",
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"id": 1066051851377713300,
"author_id": 485164773647056900,
"author_name": "Gooaaa",
"timestamp": "01/20/2023 12:49:27",
"content": "It's h=fg^(-1)",
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"id": 1066051977219420200,
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"author_name": "AliveUser",
"timestamp": "01/20/2023 12:49:57",
"content": "Again you wrote the same thing!",
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},
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"id": 1066052003752579100,
"author_id": 756407624626470900,
"author_name": "Welf",
"timestamp": "01/20/2023 12:50:03",
"content": "I see",
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"content": ".close",
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"id": 1066052364743741400,
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"timestamp": "01/20/2023 12:51:30",
"content": "Channel closed",
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}
] | help-9 | 864c6f061d6b43a7a1c15ff03d093ba5 |
200,895 | [
{
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"content": "Available help channel!",
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},
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"id": 1066053433674698800,
"author_id": 644278811294302300,
"author_name": "Hmz",
"timestamp": "01/20/2023 12:55:44",
"content": "How can I show that a group action is doubly transitive ?",
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"id": 1066054447211479000,
"author_id": 644278811294302300,
"author_name": "Hmz",
"timestamp": "01/20/2023 12:59:46",
"content": "I want to show that the action of SL(E) on the projective space P(E) defined by $u.\\overline{x} = \\overline{u(x)}, with \\overline{x} \\in P(E)$ is doubly transitive",
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"timestamp": "01/20/2023 12:59:48",
"content": "**Hmz**",
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"timestamp": "01/20/2023 13:01:47",
"content": "You might want to try #abstract-algebra",
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"content": "I can't speak there",
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"id": 1066056161146720300,
"author_id": 788085606483361800,
"author_name": "chartbit",
"timestamp": "01/20/2023 13:06:35",
"content": "Go to #get-advanced-access and self-assign the advanced roles if you'd like access to it :catthumbsup:",
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"timestamp": "01/20/2023 13:07:34",
"content": "ok thx",
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"timestamp": "01/20/2023 13:08:49",
"content": "Channel closed",
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}
] | help-9 | 9c0b3c087be84f8c8f03b01630b2f940 |
200,896 | [
{
"id": 1066056977119199200,
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"content": "Available help channel!",
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},
{
"id": 1066057960159182800,
"author_id": 225495948208373760,
"author_name": "Cuzl.",
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"content": "ln(x) = 1",
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"id": 1066057962273112200,
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"content": "Pinned a message.",
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"author_id": 225495948208373760,
"author_name": "Cuzl.",
"timestamp": "01/20/2023 13:13:46",
"content": "or whatever",
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},
{
"id": 1066057996544786600,
"author_id": 225495948208373760,
"author_name": "Cuzl.",
"timestamp": "01/20/2023 13:13:52",
"content": "ln(x) = anything",
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},
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"id": 1066058020032876700,
"author_id": 225495948208373760,
"author_name": "Cuzl.",
"timestamp": "01/20/2023 13:13:58",
"content": "how do we get ride of ln.",
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},
{
"id": 1066058058012307500,
"author_id": 225495948208373760,
"author_name": "Cuzl.",
"timestamp": "01/20/2023 13:14:07",
"content": "I know that we have to use e",
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"id": 1066058077889114100,
"author_id": 225495948208373760,
"author_name": "Cuzl.",
"timestamp": "01/20/2023 13:14:12",
"content": "but how",
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},
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"id": 1066058234437316700,
"author_id": 756407624626470900,
"author_name": "Welf",
"timestamp": "01/20/2023 13:14:49",
"content": "well",
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},
{
"id": 1066058251336163500,
"author_id": 718461587236716500,
"author_name": "NEONPerseus",
"timestamp": "01/20/2023 13:14:53",
"content": "e to this power e to that power",
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},
{
"id": 1066058386204012700,
"author_id": 718461587236716500,
"author_name": "NEONPerseus",
"timestamp": "01/20/2023 13:15:25",
"content": "$\\ln x = y \\implies e^{\\ln x} = e^y \\implies x = e^y$",
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},
{
"id": 1066058386703134800,
"author_id": 318024849333288960,
"author_name": "Mortta",
"timestamp": "01/20/2023 13:15:25",
"content": "make everything a power of e",
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},
{
"id": 1066058395267907600,
"author_id": 510789298321096700,
"author_name": "TeXit",
"timestamp": "01/20/2023 13:15:27",
"content": "**NEONPerseus**",
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"id": 1066058460887789700,
"author_id": 225495948208373760,
"author_name": "Cuzl.",
"timestamp": "01/20/2023 13:15:43",
"content": "oh",
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},
{
"id": 1066058484229083100,
"author_id": 718461587236716500,
"author_name": "NEONPerseus",
"timestamp": "01/20/2023 13:15:49",
"content": "Hence, e to this power, e to that power",
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},
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"id": 1066058548649398300,
"author_id": 225495948208373760,
"author_name": "Cuzl.",
"timestamp": "01/20/2023 13:16:04",
"content": "so the answer is",
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"id": 1066058585504751700,
"author_id": 225495948208373760,
"author_name": "Cuzl.",
"timestamp": "01/20/2023 13:16:13",
"content": "x = e to the power -1",
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"id": 1066058589875216500,
"author_id": 225495948208373760,
"author_name": "Cuzl.",
"timestamp": "01/20/2023 13:16:14",
"content": "which is",
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},
{
"id": 1066058600054792200,
"author_id": 225495948208373760,
"author_name": "Cuzl.",
"timestamp": "01/20/2023 13:16:16",
"content": "x = 1/e",
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},
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"id": 1066058610825760900,
"author_id": 225495948208373760,
"author_name": "Cuzl.",
"timestamp": "01/20/2023 13:16:19",
"content": "thanks.",
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},
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"id": 1066058646443806700,
"author_id": 718461587236716500,
"author_name": "NEONPerseus",
"timestamp": "01/20/2023 13:16:27",
"content": "Uh",
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},
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"id": 1066058693940101100,
"author_id": 225495948208373760,
"author_name": "Cuzl.",
"timestamp": "01/20/2023 13:16:39",
"content": "no? 😨",
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},
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"id": 1066058777314480300,
"author_id": 718461587236716500,
"author_name": "NEONPerseus",
"timestamp": "01/20/2023 13:16:58",
"content": "$ln x = 1 \\implies x = e$",
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},
{
"id": 1066058786491596900,
"author_id": 510789298321096700,
"author_name": "TeXit",
"timestamp": "01/20/2023 13:17:01",
"content": "**NEONPerseus**",
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"id": 1066058819907629000,
"author_id": 225495948208373760,
"author_name": "Cuzl.",
"timestamp": "01/20/2023 13:17:09",
"content": "i meant -1",
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},
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"id": 1066058826123579500,
"author_id": 225495948208373760,
"author_name": "Cuzl.",
"timestamp": "01/20/2023 13:17:10",
"content": "not 1.",
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},
{
"id": 1066058832939339900,
"author_id": 225495948208373760,
"author_name": "Cuzl.",
"timestamp": "01/20/2023 13:17:12",
"content": "my bad",
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},
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"id": 1066058850362474600,
"author_id": 718461587236716500,
"author_name": "NEONPerseus",
"timestamp": "01/20/2023 13:17:16",
"content": "Ah then you're good",
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},
{
"id": 1066058870654521500,
"author_id": 225495948208373760,
"author_name": "Cuzl.",
"timestamp": "01/20/2023 13:17:21",
"content": "https://tenor.com/view/heart-ritsu-tainaka-k-on-anime-gif-8871041",
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},
{
"id": 1066058903873405000,
"author_id": 225495948208373760,
"author_name": "Cuzl.",
"timestamp": "01/20/2023 13:17:29",
"content": ".close",
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},
{
"id": 1066058907077845000,
"author_id": 805217272087838700,
"author_name": "Mathematics Bot",
"timestamp": "01/20/2023 13:17:29",
"content": "Channel closed",
"attachments": [],
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}
] | help-9 | 4187180c47fe43f2826531e02611bf53 |
200,897 | [
{
"id": 1066062024460738600,
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"author_name": "Mathematics Bot",
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"content": "Available help channel!",
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},
{
"id": 1066062064101105800,
"author_id": 1048823396781273100,
"author_name": "hibyehibye",
"timestamp": "01/20/2023 13:30:02",
"content": "$\\exists x (x-0 \\implies x-1)$",
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"author_name": "Mathematics Bot",
"timestamp": "01/20/2023 13:30:03",
"content": "Pinned a message.",
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"timestamp": "01/20/2023 13:30:19",
"content": "**hibyehibye**",
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"author_id": 1048823396781273100,
"author_name": "hibyehibye",
"timestamp": "01/20/2023 13:30:38",
"content": "could someone explain what the bit inside the parenthesis means in english?",
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"author_id": 1048823396781273100,
"author_name": "hibyehibye",
"timestamp": "01/20/2023 13:30:50",
"content": "Like I dont get what x implies x-1 means logically",
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"author_name": "hibyehibye",
"timestamp": "01/20/2023 13:30:53",
"content": "Domain is reals",
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"author_name": "Denascite",
"timestamp": "01/20/2023 13:30:54",
"content": "it's bullshit",
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"content": "what",
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"id": 1066062325146194000,
"author_id": 132304137583984640,
"author_name": "Denascite",
"timestamp": "01/20/2023 13:31:04",
"content": "is that the correct original statement?",
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"author_name": "hibyehibye",
"timestamp": "01/20/2023 13:31:14",
"content": "I need to prove/disprove it",
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"author_name": "Denascite",
"timestamp": "01/20/2023 13:31:18",
"content": "\"implies\" is between two statements",
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"author_id": 132304137583984640,
"author_name": "Denascite",
"timestamp": "01/20/2023 13:31:22",
"content": "x-0 and x-1 are not statements",
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"content": "oh",
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"timestamp": "01/20/2023 13:31:36",
"content": "i mean if x then x-1",
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"author_name": "Denascite",
"timestamp": "01/20/2023 13:31:41",
"content": "then x-1 what",
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"author_name": "hibyehibye",
"timestamp": "01/20/2023 13:32:01",
"content": "idk isnt that how you say the $\\implies$ operator in english",
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"author_name": "TeXit",
"timestamp": "01/20/2023 13:32:04",
"content": "**hibyehibye**",
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"author_name": "Denascite",
"timestamp": "01/20/2023 13:32:13",
"content": "well yes but you have to put it between statement",
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"id": 1066062632555122700,
"author_id": 132304137583984640,
"author_name": "Denascite",
"timestamp": "01/20/2023 13:32:18",
"content": "x isn't a statement, it's a number",
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"id": 1066062682320552100,
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"author_name": "Denascite",
"timestamp": "01/20/2023 13:32:29",
"content": "\"if 2 then 1\"",
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"author_name": "hibyehibye",
"timestamp": "01/20/2023 13:32:31",
"content": "Theres exists an x such that if x then x-1",
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"author_name": "Denascite",
"timestamp": "01/20/2023 13:32:40",
"content": "that makes no sense",
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"author_name": "hibyehibye",
"timestamp": "01/20/2023 13:32:57",
"content": "yeah thats my confusion",
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"id": 1066062825073684500,
"author_id": 1048823396781273100,
"author_name": "hibyehibye",
"timestamp": "01/20/2023 13:33:03",
"content": "i dont understand the statement",
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"id": 1066062848503058600,
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"author_name": "chartbit",
"timestamp": "01/20/2023 13:33:09",
"content": "Do you mean \"if x [has some property], then x-1 [has the same property]\"?",
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"author_name": "Denascite",
"timestamp": "01/20/2023 13:33:15",
"content": "can you show a picture of the original problem",
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"author_name": "hibyehibye",
"timestamp": "01/20/2023 13:33:22",
"content": "That is the problem",
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"author_name": "hibyehibye",
"timestamp": "01/20/2023 13:33:25",
"content": "word for word",
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"author_id": 1048823396781273100,
"author_name": "hibyehibye",
"timestamp": "01/20/2023 13:33:51",
"content": "“Identify each of the statements as true or false. Domain of discourse is all real numbers”",
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},
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"id": 1066063177370046600,
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"author_name": "Denascite",
"timestamp": "01/20/2023 13:34:27",
"content": "there are 2 options, either you messed up or the instructor messed up",
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"id": 1066063212145016800,
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"author_name": "Denascite",
"timestamp": "01/20/2023 13:34:36",
"content": "we can easily see which is the case if you just give us an image",
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"id": 1066063277710377100,
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"author_name": "hibyehibye",
"timestamp": "01/20/2023 13:34:51",
"content": "urm in on my phone so its hard to get an image",
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"author_name": "hibyehibye",
"timestamp": "01/20/2023 13:35:02",
"content": "but it is quite literally this statement",
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"id": 1066063333993758700,
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"author_name": "Denascite",
"timestamp": "01/20/2023 13:35:05",
"content": "which phone doesn't have a camera",
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},
{
"id": 1066063363697807400,
"author_id": 132304137583984640,
"author_name": "Denascite",
"timestamp": "01/20/2023 13:35:12",
"content": "or cant take screenshots",
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"id": 1066063478844031100,
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"author_name": "Denascite",
"timestamp": "01/20/2023 13:35:39",
"content": "huh",
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"id": 1066063520669642900,
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"author_name": "Denascite",
"timestamp": "01/20/2023 13:35:49",
"content": "who cares",
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"author_name": "chartbit",
"timestamp": "01/20/2023 13:35:58",
"content": "Is it on a piece of paper, or like on your phone?",
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"id": 1066063557445304300,
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"author_name": "Denascite",
"timestamp": "01/20/2023 13:35:58",
"content": "you are already on your phone typing",
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"id": 1066063667021488100,
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"author_name": "hibyehibye",
"timestamp": "01/20/2023 13:36:24",
"content": "thats the whole question",
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"author_name": "chartbit",
"timestamp": "01/20/2023 13:36:39",
"content": "Looks like an equals sign to me I think?",
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"id": 1066063759006773200,
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"author_name": "Denascite",
"timestamp": "01/20/2023 13:36:46",
"content": "well the whole question is more than that cause it also has to include (among other things) the quote from above",
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"timestamp": "01/20/2023 13:36:53",
"content": "this is the bit above",
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"author_name": "hibyehibye",
"timestamp": "01/20/2023 13:37:04",
"content": "Again word for word",
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"id": 1066063847259127900,
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"author_name": "chartbit",
"timestamp": "01/20/2023 13:37:07",
"content": "Unless it's my eyes? :glassescat: Like underneath it looks like there's a line",
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"author_name": "hibyehibye",
"timestamp": "01/20/2023 13:37:14",
"content": "its a minus I think??",
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"author_name": "hibyehibye",
"timestamp": "01/20/2023 13:37:33",
"content": "maybe its meant to be an equals?",
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"id": 1066063964997431300,
"author_id": 132304137583984640,
"author_name": "Denascite",
"timestamp": "01/20/2023 13:37:35",
"content": "test $x-0 \\to \\rightarrow x-1$",
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"timestamp": "01/20/2023 13:37:37",
"content": "**Denascite**",
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"timestamp": "01/20/2023 13:37:45",
"content": "it's too high for a minus",
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"timestamp": "01/20/2023 13:37:49",
"content": "Yeah that's what I meant",
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"content": "huh",
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"id": 1066064079883620400,
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"timestamp": "01/20/2023 13:38:03",
"content": "Ur",
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"author_name": "hibyehibye",
"timestamp": "01/20/2023 13:38:07",
"content": "I guess ill ask my prof",
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"author_name": "chartbit",
"timestamp": "01/20/2023 13:38:13",
"content": "(was typing out a comment on Denascite's post that it shouldn't matter r.e. weirdness but accidentally put my statement on the picture as a reply when I saw the pic)",
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"timestamp": "01/20/2023 13:38:24",
"content": "ic",
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"timestamp": "01/20/2023 13:38:32",
"content": "x=0 would make more sense than x-0",
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"timestamp": "01/20/2023 13:38:42",
"content": "tysm ill ask tonight what its meant to be",
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"timestamp": "01/20/2023 13:38:43",
"content": "and now it is in fact a statement",
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"content": "yea that would make sense",
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"timestamp": "01/20/2023 13:39:05",
"content": "theres also a latex version",
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"id": 1066064364228071600,
"author_id": 1048823396781273100,
"author_name": "hibyehibye",
"timestamp": "01/20/2023 13:39:10",
"content": "which is just a -",
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"author_id": 1048823396781273100,
"author_name": "hibyehibye",
"timestamp": "01/20/2023 13:39:18",
"content": "bec i can see the code",
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"id": 1066064449150136300,
"author_id": 1048823396781273100,
"author_name": "hibyehibye",
"timestamp": "01/20/2023 13:39:31",
"content": "but maybe it was a misinput",
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"id": 1066064478678044800,
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"timestamp": "01/20/2023 13:39:38",
"content": "probably",
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"timestamp": "01/20/2023 13:39:55",
"content": "alr ill ask tonight tysm @Denascite and @chartbit",
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"content": ".close",
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"id": 1066064587285340300,
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"timestamp": "01/20/2023 13:40:04",
"content": "Channel closed",
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}
] | help-9 | e575ccd9310e4322814695a39da8d4f0 |
200,898 | [
{
"id": 1036212610896506900,
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"author_name": "Mathematics Bot",
"timestamp": "10/30/2022 05:38:58",
"content": "Available help channel!",
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},
{
"id": 1036213381692133400,
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"timestamp": "10/30/2022 05:42:02",
"content": "how",
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"timestamp": "10/30/2022 05:42:02",
"content": "Pinned a message.",
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"author_id": 483962566977126400,
"author_name": "MarveI",
"timestamp": "10/30/2022 05:44:44",
"content": "How to do it? or how is 2 + 5i a zero of the polynomial?",
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"timestamp": "10/30/2022 05:44:50",
"content": "how what?",
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"author_name": "splooze",
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"content": "what are the 3 zeros",
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"content": "do you know how to factor a cubic polynomials?",
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"content": "in this case no",
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"content": "https://www.youtube.com/watch?v=rnAKWPM-YBc&t=467s",
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"timestamp": "10/30/2022 05:48:05",
"content": "watching that rn haha",
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"content": "oh ok good",
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"timestamp": "10/30/2022 05:48:11",
"content": "soi just take the two biggest terms",
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"timestamp": "10/30/2022 05:48:15",
"content": "from each pair",
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"timestamp": "10/30/2022 05:48:21",
"content": "and it should ideally give me two groups",
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"content": "what...",
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"content": "oh factor by grouping",
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"content": "that's what my man did",
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"timestamp": "10/30/2022 05:48:41",
"content": "yeah that won't work here",
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"timestamp": "10/30/2022 05:48:42",
"content": "yes",
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"timestamp": "10/30/2022 05:48:47",
"content": "didn't think so",
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"author_name": "splooze",
"timestamp": "10/30/2022 05:48:55",
"content": "that's the one method i was familiar with and that didn't work lmao",
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"timestamp": "10/30/2022 05:49:21",
"content": "there is another one in the video",
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"timestamp": "10/30/2022 05:49:48",
"content": "is there an example in this vid",
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"timestamp": "10/30/2022 05:49:51",
"content": "without grouping",
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"author_name": "splooze",
"timestamp": "10/30/2022 05:50:23",
"content": "ah yea got it",
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"timestamp": "10/30/2022 05:52:24",
"content": "@MarveI are you suggesting synthetic division",
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"timestamp": "10/30/2022 05:52:29",
"content": "yes",
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"timestamp": "10/30/2022 05:52:43",
"content": "have you tried it on my question",
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"timestamp": "10/30/2022 05:52:58",
"content": "synthetic division was never taught in my school",
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"timestamp": "10/30/2022 05:53:06",
"content": "so i don't know if they want us to solve it a different way",
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"timestamp": "10/30/2022 05:53:07",
"content": "or",
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"timestamp": "10/30/2022 05:59:47",
"content": "Should work",
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"author_name": "MarveI",
"timestamp": "10/30/2022 05:59:56",
"content": "Im in the toilet rn, cant try it",
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"timestamp": "10/30/2022 06:01:23",
"content": "i don't see how it works",
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"author_name": "splooze",
"timestamp": "10/30/2022 06:01:46",
"content": "because the question's asking you to use the 2 + 5i somehow",
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"author_name": "splooze",
"timestamp": "10/30/2022 06:02:03",
"content": "synthetic division with a complex number seems out of my depth",
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"author_name": "splooze",
"timestamp": "10/30/2022 06:02:08",
"content": "do you know how to do it?",
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"timestamp": "10/30/2022 06:02:40",
"content": "you must be pretty small :laugh_cry:",
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"timestamp": "10/30/2022 06:03:00",
"content": "wdym....",
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"author_name": "splooze",
"timestamp": "10/30/2022 06:03:09",
"content": "you said you're in a toilet",
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"id": 1036218712790945800,
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"author_name": "MarveI",
"timestamp": "10/30/2022 06:03:13",
"content": "oh",
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"id": 1036218715345272800,
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"author_name": "MarveI",
"timestamp": "10/30/2022 06:03:13",
"content": "bro",
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"id": 1036218717392085000,
"author_id": 483962566977126400,
"author_name": "MarveI",
"timestamp": "10/30/2022 06:03:14",
"content": "ok",
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"id": 1036218724555952100,
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"author_name": "splooze",
"timestamp": "10/30/2022 06:03:15",
"content": "usually you're on a toilet",
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"author_name": "MarveI",
"timestamp": "10/30/2022 06:03:16",
"content": "im out",
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"id": 1036218727508758500,
"author_id": 483962566977126400,
"author_name": "MarveI",
"timestamp": "10/30/2022 06:03:16",
"content": "bye",
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"author_name": "MarveI",
"timestamp": "10/30/2022 06:03:30",
"content": "i meant like the bathroom",
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"timestamp": "10/30/2022 06:03:33",
"content": "i see",
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"timestamp": "10/30/2022 06:03:46",
"content": "we call it toilet in my country for some reason 😄",
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"author_name": "MarveI",
"timestamp": "10/30/2022 06:03:56",
"content": "but yeah",
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"content": "ok",
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"timestamp": "10/30/2022 06:03:58",
"content": "it",
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"timestamp": "10/30/2022 06:03:59",
"content": "works",
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"id": 1036218909944193000,
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"author_name": "MarveI",
"timestamp": "10/30/2022 06:04:00",
"content": "i think",
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"id": 1036218916529254400,
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"author_name": "MarveI",
"timestamp": "10/30/2022 06:04:01",
"content": "hopefully",
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"id": 1036218918865481700,
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"author_name": "MarveI",
"timestamp": "10/30/2022 06:04:02",
"content": "just",
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"id": 1036218921168150700,
"author_id": 483962566977126400,
"author_name": "MarveI",
"timestamp": "10/30/2022 06:04:02",
"content": "try",
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"id": 1036219175183589400,
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"timestamp": "10/30/2022 06:05:03",
"content": "4 is a zero",
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"id": 1036219216988221400,
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"author_name": "splooze",
"timestamp": "10/30/2022 06:05:13",
"content": "so i guess i can do synthetic division with 4",
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"id": 1036219800323625100,
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"timestamp": "10/30/2022 06:07:32",
"content": "i'm onto smth here",
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"id": 1036220035657629700,
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"timestamp": "10/30/2022 06:08:28",
"content": "got it",
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"timestamp": "10/30/2022 06:23:28",
"content": "@splooze Has your question been resolved?",
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"timestamp": "10/30/2022 06:30:54",
"content": "Channel closed",
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}
] | help-9 | 6f3e1f1111e544268ff6b4e93d8090cb |
200,899 | [
{
"id": 1066064839778250900,
"author_id": 805217272087838700,
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"timestamp": "01/20/2023 13:41:04",
"content": "Available help channel!",
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},
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"author_name": "duday",
"timestamp": "01/20/2023 13:44:54",
"content": "Hey can someone help me simplify 49a(8)b(4)/56a(7)b(10)",
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"id": 1066065811183243300,
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"timestamp": "01/20/2023 13:44:55",
"content": "Pinned a message.",
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"author_id": 781855224948195300,
"author_name": "duday",
"timestamp": "01/20/2023 13:45:17",
"content": "the numbers in the brackets are squared numbers",
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},
{
"id": 1066065925683544000,
"author_id": 781855224948195300,
"author_name": "duday",
"timestamp": "01/20/2023 13:45:23",
"content": "just dont know how to type them in",
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},
{
"id": 1066066137734975600,
"author_id": 217089972933623800,
"author_name": "maximo",
"timestamp": "01/20/2023 13:46:13",
"content": "$\\frac{49a^8b^4}{56a^7b^{10}}$",
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},
{
"id": 1066066148883439600,
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"author_name": "TeXit",
"timestamp": "01/20/2023 13:46:16",
"content": "**maximo**",
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"timestamp": "01/20/2023 13:46:20",
"content": "does this look right?",
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"id": 1066066258858090500,
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"author_name": "duday",
"timestamp": "01/20/2023 13:46:42",
"content": "yep!",
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"author_name": "duday",
"timestamp": "01/20/2023 13:47:02",
"content": "7a/8b(6) is what im thinking",
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"id": 1066066355108991000,
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"author_name": "duday",
"timestamp": "01/20/2023 13:47:05",
"content": "but im very unsure",
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},
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"id": 1066066402118738000,
"author_id": 217089972933623800,
"author_name": "maximo",
"timestamp": "01/20/2023 13:47:16",
"content": "looks good",
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},
{
"id": 1066066433504710700,
"author_id": 781855224948195300,
"author_name": "duday",
"timestamp": "01/20/2023 13:47:24",
"content": "oh",
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},
{
"id": 1066066456539844600,
"author_id": 781855224948195300,
"author_name": "duday",
"timestamp": "01/20/2023 13:47:29",
"content": "alr thanks!",
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},
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"id": 1066066490031341600,
"author_id": 781855224948195300,
"author_name": "duday",
"timestamp": "01/20/2023 13:47:37",
"content": ".close",
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},
{
"id": 1066066492745060500,
"author_id": 805217272087838700,
"author_name": "Mathematics Bot",
"timestamp": "01/20/2023 13:47:38",
"content": "Channel closed",
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}
] | help-9 | 0c5074e8a8cb4fe2a274fe1e79a6c678 |
200,900 | [
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"timestamp": "01/20/2023 13:54:58",
"content": "Available help channel!",
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"reference": null
},
{
"id": 1066070102581186600,
"author_id": 1036675196976898200,
"author_name": "lvg",
"timestamp": "01/20/2023 14:01:59",
"content": "Hey could somoene confirm if everything, I did was correct?",
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"timestamp": "01/20/2023 14:01:59",
"content": "Pinned a message.",
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"content": "@lvg Has your question been resolved?",
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"content": ".close",
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] | help-9 | 945ccb078212401684bd5c5a76291c0f |
200,901 | [
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"content": "is\nx = sqrt(12-x)\n\nthe correct solution to\nx^2+x-12=0",
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"content": "it's not a solution",
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"content": ",w calculate (sqrt(12-x))^2 + sqrt(12-x) - 12",
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"content": "Results provided by WolframAlpha",
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"content": "why not test solutions yourself?",
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"content": "I think you're asking whether it's equivalent form, but it's not",
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"content": "all in all, how can it be a solution for x if it has x in it",
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"content": "you have to be careful doing sqrt( . ) both sides",
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"content": "btw it's not a way to solve this anyway",
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"content": "well it could be x = 2sqrt(3)-sqrt(x) aswell right",
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"content": ":hmmCat:",
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"author_name": "Jigglyproff",
"timestamp": "01/20/2023 14:39:11",
"content": "one does not simply distribute a root over subtraction",
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"timestamp": "01/20/2023 14:39:39",
"content": "i don't know what's happening :DIESOFCRINGE:",
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"timestamp": "01/20/2023 14:40:17",
"content": "here $x^2+x-12=0$, if you take a root on both sides you get\n$\\sqrt{x^2+x-12}=0$",
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"timestamp": "01/20/2023 14:40:20",
"content": "**Jigglyproff**",
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"content": "i only took a root to get rid of x^2 so i could set it 'x ='",
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"timestamp": "01/20/2023 14:42:13",
"content": "well, you can not 'only' take a root of some terms, you have to take the root of everything\n\nso taking the root here does not really help",
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"timestamp": "01/20/2023 14:42:24",
"content": "i took a root of everything though",
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"timestamp": "01/20/2023 14:42:36",
"content": "are you sure",
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"content": "yeah i think",
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"timestamp": "01/20/2023 14:42:50",
"content": "x = sqrt(12-x)",
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"timestamp": "01/20/2023 14:43:07",
"content": "and you can't take a square root of both sides unless you're sure they're both positive (or zero)",
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"timestamp": "01/20/2023 14:43:08",
"content": "how did you come from $\\sqrt{x^2+x-12}=0$ to $x = \\sqrt{12-x}$",
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"timestamp": "01/20/2023 14:43:10",
"content": "**Jigglyproff**",
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"timestamp": "01/20/2023 14:43:29",
"content": "**What the hell am I doing here?**",
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"timestamp": "01/20/2023 14:43:39",
"content": "x^2+x-12=0 was the problem",
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"timestamp": "01/20/2023 14:43:49",
"content": "sure",
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"timestamp": "01/20/2023 14:43:54",
"content": "this is destroying my brain",
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"timestamp": "01/20/2023 14:46:04",
"content": "well again, that doesn't really answer it\\\\\nyou could rewrite it as $x^2=12-x$ and take a root, but\\\\\n$x=\\sqrt{12-x}$ does give you nothing on the solution, you want x to be one side and a number on the other",
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"timestamp": "01/20/2023 14:46:07",
"content": "**Jigglyproff**",
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"timestamp": "01/20/2023 14:46:45",
"content": "https://www.khanacademy.org/test-prep/sat/x0a8c2e5f:untitled-652/x0a8c2e5f:passport-to-advanced-math-lessons-by-skill/a/gtp--sat-math--article--solving-quadratic-equations--lesson",
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"timestamp": "01/20/2023 14:46:49",
"content": "this might help you",
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"author_name": "Joca9",
"timestamp": "01/20/2023 14:48:38",
"content": "i'm just going to wait for whenever i get the quiz back and see what the teacher says but thanks for the help",
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"timestamp": "01/20/2023 15:03:38",
"content": "@Joca9 Has your question been resolved?",
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"timestamp": "01/20/2023 15:05:04",
"content": "Channel closed",
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}
] | help-9 | 6f7ddfde7b11498abda449bef2b72530 |
200,902 | [
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"id": 1066092608184660000,
"author_id": 719768601174999000,
"author_name": "Ritualz",
"timestamp": "01/20/2023 15:31:24",
"content": "is this correct",
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"content": "Pinned a message.",
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"timestamp": "01/20/2023 15:31:30",
"content": "i know its 1 or 2",
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"id": 1066093423720923100,
"author_id": 374795910032523260,
"author_name": "SWR",
"timestamp": "01/20/2023 15:34:39",
"content": "What made you decide it was 1 or 2?",
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"id": 1066094494207975600,
"author_id": 719768601174999000,
"author_name": "Ritualz",
"timestamp": "01/20/2023 15:38:54",
"content": "its 2",
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"id": 1066094498431639600,
"author_id": 719768601174999000,
"author_name": "Ritualz",
"timestamp": "01/20/2023 15:38:55",
"content": ".",
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"id": 1066094504580501600,
"author_id": 719768601174999000,
"author_name": "Ritualz",
"timestamp": "01/20/2023 15:38:56",
"content": "Lol",
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"id": 1066095181998334100,
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"timestamp": "01/20/2023 15:41:38",
"content": "How do you figure?",
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"content": "@Ritualz Has your question been resolved?",
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200,903 | [
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200,904 | [
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] | help-9 | 3a5fc010bbb840a9be4c7b90972008fd |
200,905 | [
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"timestamp": "01/20/2023 16:22:42",
"content": ".CLOSE",
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"timestamp": "01/20/2023 18:00:53",
"content": "trying to prove b^(r+s) = b^r * b^s for rational numbers r and s",
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"id": 1066130274452246700,
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"content": "they use in this solution that",
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"id": 1066130289149083800,
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"content": "show theorem 1.21 and the entire problem",
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"content": "ok",
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"author_id": 299357465236078600,
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"timestamp": "01/20/2023 18:01:39",
"content": "theorem 1.21 is just the existence of a unique positive real root",
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"content": "i dont get how he pulls 1/nw out of the exponent",
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"content": "even though he says he is using \"integer exponent rules\"",
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"content": "like we havet yet proved that rule works for real numbers",
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"content": "this is exactly the problem",
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"content": "b>1",
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"timestamp": "01/20/2023 18:17:49",
"content": "@Epsilon Has your question been resolved?",
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"author_name": "Kefir101Awesome",
"timestamp": "01/20/2023 18:25:03",
"content": "so youre basically asking how can b^((mw+vn)/nw)) is equal to b^(mw+vn)^(1/nw)?",
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"author_name": "Kefir101Awesome",
"timestamp": "01/20/2023 18:25:47",
"content": "you havent proved yet that (b^a)^c = b^(ac)?",
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"content": "Well we haven’t proved it’s true for reals",
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"content": "It’s easy to prove for integers ofc",
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"timestamp": "01/20/2023 18:26:21",
"content": "what level of math is this",
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"timestamp": "01/20/2023 18:26:25",
"content": "I thoguth it would be the same proof",
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"timestamp": "01/20/2023 18:26:26",
"content": "Analysis",
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"author_id": 484888077760725000,
"author_name": "Kefir101Awesome",
"timestamp": "01/20/2023 18:26:29",
"content": "real analysis?",
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"author_id": 299357465236078600,
"author_name": "Epsilon",
"timestamp": "01/20/2023 18:26:35",
"content": "Yea",
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"id": 1066136788655165600,
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"author_name": "Epsilon",
"timestamp": "01/20/2023 18:26:58",
"content": "Can’t induct on reals",
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"id": 1066136880913059800,
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"author_name": "Kefir101Awesome",
"timestamp": "01/20/2023 18:27:20",
"content": "I never took real analysis so I guess I can't help you",
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"id": 1066136929239842800,
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"author_name": "Epsilon",
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"content": "Np lol",
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"timestamp": "01/20/2023 18:27:48",
"content": "why do you think its for reals though",
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"author_name": "Kefir101Awesome",
"timestamp": "01/20/2023 18:28:00",
"content": "why cant you take m,w,v,n to be integers",
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"id": 1066137087490928600,
"author_id": 484888077760725000,
"author_name": "Kefir101Awesome",
"timestamp": "01/20/2023 18:28:09",
"content": "so that their quotient, sum, and product are all integers too",
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"id": 1066137437480431600,
"author_id": 299357465236078600,
"author_name": "Epsilon",
"timestamp": "01/20/2023 18:29:32",
"content": "Quotient of int is not int",
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"id": 1066137482221060100,
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"timestamp": "01/20/2023 18:29:43",
"content": "1/n is real",
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"timestamp": "01/20/2023 18:30:31",
"content": "it could be if a % b is 0",
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"timestamp": "01/20/2023 18:30:48",
"content": "Yea but it doesn’t have to be",
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"timestamp": "01/20/2023 19:00:48",
"content": "@Epsilon Has your question been resolved?",
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"timestamp": "01/20/2023 19:30:49",
"content": "Channel closed",
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] | help-9 | 660e8442c1414a8bbcd18fb023043b80 |
200,906 | [
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"timestamp": "01/20/2023 19:41:52",
"content": "Available help channel!",
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"timestamp": "01/20/2023 19:44:00",
"content": "Did you mean 10^(-6)",
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"id": 1066156415128981500,
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"content": "Is this right wrong screenshots",
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"content": "Channel closed",
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}
] | help-9 | 7d0ba0845664439d90c00165da3412be |
200,907 | [
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"id": 1066158891399925900,
"author_id": 607385391766437900,
"author_name": "heli0",
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"content": "im having trouble finding the co-vertices of this hyperbola equation?",
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"content": "i need help",
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"content": "occupied channel buddy",
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"author_name": "biggboy",
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"content": "!help",
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"author_id": 805217272087838700,
"author_name": "Mathematics Bot",
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"content": "Please read #❓how-to-get-help",
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"id": 1066159270141378600,
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"content": "im having trouble find the co-vertices of this hyperbola equation",
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"content": "@heli0 Has your question been resolved?",
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"timestamp": "01/20/2023 20:52:42",
"content": "@heli0 Has your question been resolved?",
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"timestamp": "01/20/2023 21:09:51",
"content": "I dont understand this. how can you find the angle if its a straight line?",
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"timestamp": "01/20/2023 21:38:15",
"content": "usually the angle is between the vector and the +x axis",
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"timestamp": "01/20/2023 21:38:39",
"content": "@heli0",
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"timestamp": "01/20/2023 21:38:57",
"content": "they give you the formula too T-T",
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"id": 1066185132605710500,
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"timestamp": "01/20/2023 21:39:04",
"content": "Ø=arctan(x/y)",
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"author_name": "heli0",
"timestamp": "01/20/2023 21:40:26",
"content": "yeah thats what i did 18.4 right?",
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"id": 1066185498554544300,
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"author_name": "heli0",
"timestamp": "01/20/2023 21:40:31",
"content": "it says incorrect",
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"id": 1066185529214914700,
"author_id": 444537905919164400,
"author_name": "Scythe",
"timestamp": "01/20/2023 21:40:38",
"content": "they might want it in radians",
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},
{
"id": 1066185553323757700,
"author_id": 444537905919164400,
"author_name": "Scythe",
"timestamp": "01/20/2023 21:40:44",
"content": "and 18.4º is wrong?",
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"id": 1066185568758800500,
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"author_name": "heli0",
"timestamp": "01/20/2023 21:40:48",
"content": "yeah",
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"id": 1066185593383559200,
"author_id": 444537905919164400,
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"timestamp": "01/20/2023 21:40:54",
"content": "like, look at the vector",
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{
"id": 1066185602598445200,
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"author_name": "Scythe",
"timestamp": "01/20/2023 21:40:56",
"content": "ofc it's wrong lmao",
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"id": 1066185697972731900,
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"timestamp": "01/20/2023 21:41:19",
"content": "whoops arctan(y/x) not x/y as per the formula",
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"id": 1066185849504530600,
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"author_name": "heli0",
"timestamp": "01/20/2023 21:41:55",
"content": "well i did the formula and its wrong so idk what to do",
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{
"id": 1066185912205193200,
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"timestamp": "01/20/2023 21:42:10",
"content": "wait a second",
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{
"id": 1066185936808984700,
"author_id": 444537905919164400,
"author_name": "Scythe",
"timestamp": "01/20/2023 21:42:16",
"content": "the drawn vector is not <6,2> lol",
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"id": 1066186008338628600,
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"timestamp": "01/20/2023 21:42:33",
"content": "I got 18.4º for <6,2>, but that vector is not <6,2>",
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"id": 1066186041293283500,
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"timestamp": "01/20/2023 21:42:41",
"content": "i cant with american schools this shit is so scuffed lmao",
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"id": 1066186074801569900,
"author_id": 444537905919164400,
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"timestamp": "01/20/2023 21:42:49",
"content": "that's <2,6>",
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"id": 1066186101112459300,
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"timestamp": "01/20/2023 21:42:55",
"content": ";-;",
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{
"id": 1066186177805303900,
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"timestamp": "01/20/2023 21:43:13",
"content": "71.6",
"attachments": [],
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},
{
"id": 1066186184558129300,
"author_id": 444537905919164400,
"author_name": "Scythe",
"timestamp": "01/20/2023 21:43:15",
"content": "71.56º",
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},
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"id": 1066186188383338600,
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"timestamp": "01/20/2023 21:43:16",
"content": "yup",
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"id": 1066186684733063200,
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"author_name": "heli0",
"timestamp": "01/20/2023 21:45:14",
"content": "same for this one",
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"author_name": "heli0",
"timestamp": "01/20/2023 21:45:51",
"content": "i did tan^-1(5/-4) = -51.34 +180 = 128.7",
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"author_name": "Scythe",
"timestamp": "01/20/2023 21:46:54",
"content": "the angle is indicated here",
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"timestamp": "01/20/2023 21:46:57",
"content": "you can see the green arc",
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"id": 1066187141463425200,
"author_id": 444537905919164400,
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"timestamp": "01/20/2023 21:47:03",
"content": "take 180-(+x angle)",
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"id": 1066187155057148000,
"author_id": 444537905919164400,
"author_name": "Scythe",
"timestamp": "01/20/2023 21:47:06",
"content": "so 180-128.7",
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"id": 1066187184480194700,
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"author_name": "heli0",
"timestamp": "01/20/2023 21:47:13",
"content": "oh ok",
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"id": 1066187197407035400,
"author_id": 444537905919164400,
"author_name": "Scythe",
"timestamp": "01/20/2023 21:47:16",
"content": "my fault, sorry",
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"id": 1066187232844730400,
"author_id": 444537905919164400,
"author_name": "Scythe",
"timestamp": "01/20/2023 21:47:25",
"content": "I said it was because it's always +x, not because it was indicated",
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"id": 1066187301421600900,
"author_id": 444537905919164400,
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"timestamp": "01/20/2023 21:47:41",
"content": "lol they specifically warn you about the negative angle too",
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"author_name": "heli0",
"timestamp": "01/20/2023 21:48:16",
"content": "thanks for the help 🙂",
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"author_id": 444537905919164400,
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"timestamp": "01/20/2023 21:48:33",
"content": "np!",
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"id": 1066190245982392400,
"author_id": 560122149126275100,
"author_name": "Civil Service Pigeon",
"timestamp": "01/20/2023 21:59:23",
"content": ".close",
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"id": 1066190249077780500,
"author_id": 805217272087838700,
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"timestamp": "01/20/2023 21:59:24",
"content": "Channel closed",
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] | help-9 | c59a8358ed804c7982ed25d3448c1294 |
200,908 | [
{
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"id": 1066199559031758800,
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"author_name": "!monke",
"timestamp": "01/20/2023 22:36:23",
"content": "Anyone know a thing or two about quantum geometry and black holes I need it for a math project",
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},
{
"id": 1066199562596913200,
"author_id": 805217272087838700,
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"content": "This seems like a topic question which is better suited for a channel like math-discussion.",
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"content": "@!monke Has your question been resolved?",
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] | help-9 | 4772da907e3044a0b4c13b2ae6ba2f50 |
200,909 | [
{
"id": 1036225931079069700,
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"content": "Available help channel!",
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"id": 1036226633725644800,
"author_id": 556204234354196500,
"author_name": "koche",
"timestamp": "10/30/2022 06:34:41",
"content": "hi, i'm having trouble understanding what does c* mean and how do we get c/x instead of (e^c)/x in the middle part, can anyone explain?",
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"author_id": 299974051127099400,
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"timestamp": "10/30/2022 06:39:34",
"content": "$c = e^{c^*}$",
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"id": 1036227869887709200,
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"timestamp": "10/30/2022 06:39:36",
"content": "**Zanarcane**",
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"author_name": "koche",
"timestamp": "10/30/2022 06:41:37",
"content": "so since both c and e^c are just constants it doesn't matter which one we take and it's just written like that for simplicity?",
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"timestamp": "10/30/2022 06:42:00",
"content": "Yeah",
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"id": 1036228507275100200,
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"author_name": "koche",
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"content": "i see",
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"timestamp": "10/30/2022 06:42:09",
"content": "thank you",
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"author_id": 299974051127099400,
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"timestamp": "10/30/2022 06:42:13",
"content": "Np",
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"timestamp": "10/30/2022 06:43:37",
"content": ".close",
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] | help-9 | d5ebb92a90f249f4b2543a8e2890f62b |
200,910 | [
{
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"timestamp": "01/20/2023 22:59:19",
"content": "Available help channel!",
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"content": "Need help continuing off of proof",
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"author_name": "! matthewzz",
"timestamp": "01/20/2023 23:53:43",
"content": "that sqrt of prime number is irrational",
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"content": "sqrt of a prime number is irrational",
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"content": "it can't be prime",
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"id": 1066219177729331200,
"author_id": 1046637327734288400,
"author_name": "! matthewzz",
"timestamp": "01/20/2023 23:54:21",
"content": "oops sry",
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"id": 1066219321258414200,
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"author_name": "monikanicity",
"timestamp": "01/20/2023 23:54:55",
"content": "What do you have so far?",
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"id": 1066219610753474600,
"author_id": 742629776300310500,
"author_name": "Void Walker",
"timestamp": "01/20/2023 23:56:04",
"content": "I believe the standard $\\sqrt{2}$ proof works in general for all primes.",
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"id": 1066219619976753300,
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"timestamp": "01/20/2023 23:56:06",
"content": "**Void Walker**",
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"timestamp": "01/20/2023 23:57:27",
"content": "So far I have",
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"id": 1066220013901578400,
"author_id": 1046637327734288400,
"author_name": "! matthewzz",
"timestamp": "01/20/2023 23:57:40",
"content": "Suppose $\\sqrt{p}$ is rational",
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"id": 1066220022797709400,
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"author_name": "TeXit",
"timestamp": "01/20/2023 23:57:42",
"content": "**! matthewzz**",
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"author_name": "! matthewzz",
"timestamp": "01/20/2023 23:58:30",
"content": "then $\\sqrt{p} = \\frac{a}{b}$ s.t. a,b $\\in \\mathbb{Z}$; gcd(a,b) = 1; b $\\neq$ 0",
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"id": 1066220233989312500,
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"timestamp": "01/20/2023 23:58:33",
"content": "**! matthewzz**",
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"author_name": "! matthewzz",
"timestamp": "01/20/2023 23:59:17",
"content": "then $p = \\frac{a^2}{b^2}$ and $b^2 * p = a^2$",
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"id": 1066220429984936000,
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"timestamp": "01/20/2023 23:59:19",
"content": "**! matthewzz**",
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"author_name": "! matthewzz",
"timestamp": "01/21/2023 00:00:51",
"content": "This means p divides $a^2$ since $b^2 = \\frac{a^2}{p}$, and since p is prime, p | a.",
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"id": 1066220825621049500,
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"timestamp": "01/21/2023 00:00:54",
"content": "**! matthewzz**",
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"id": 1066220871993262200,
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"timestamp": "01/21/2023 00:01:05",
"content": "yes",
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"id": 1066220910828322800,
"author_id": 1046637327734288400,
"author_name": "! matthewzz",
"timestamp": "01/21/2023 00:01:14",
"content": "How do we show that p divides b now?",
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"author_name": "! matthewzz",
"timestamp": "01/21/2023 00:03:04",
"content": "@Wither @monikanicity",
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"id": 1066221440828973000,
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"author_name": "Wither",
"timestamp": "01/21/2023 00:03:20",
"content": "I have a similar proof ig",
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"id": 1066221457480360000,
"author_id": 1010435537586372600,
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"timestamp": "01/21/2023 00:03:24",
"content": "if that matches",
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"id": 1066221474580545700,
"author_id": 1010435537586372600,
"author_name": "Wither",
"timestamp": "01/21/2023 00:03:28",
"content": "we good",
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"id": 1066221567048175600,
"author_id": 1046637327734288400,
"author_name": "! matthewzz",
"timestamp": "01/21/2023 00:03:51",
"content": "?",
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"id": 1066221777027600500,
"author_id": 1010435537586372600,
"author_name": "Wither",
"timestamp": "01/21/2023 00:04:41",
"content": "let p belong to Z",
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},
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"id": 1066221865036677100,
"author_id": 1010435537586372600,
"author_name": "Wither",
"timestamp": "01/21/2023 00:05:02",
"content": "$P (x) = x^2 - p$",
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},
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"id": 1066221873890861000,
"author_id": 742629776300310500,
"author_name": "Void Walker",
"timestamp": "01/21/2023 00:05:04",
"content": "$p,a,b \\in \\mathbb{Z}$",
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},
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"id": 1066221909508902900,
"author_id": 510789298321096700,
"author_name": "TeXit",
"timestamp": "01/21/2023 00:05:12",
"content": "**Void Walker**",
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"timestamp": "01/21/2023 00:05:13",
"content": "**Wither**",
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"author_id": 1010435537586372600,
"author_name": "Wither",
"timestamp": "01/21/2023 00:05:45",
"content": "from difference of squares",
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"id": 1066222199943483400,
"author_id": 1046637327734288400,
"author_name": "! matthewzz",
"timestamp": "01/21/2023 00:06:21",
"content": "?",
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"id": 1066222274929234000,
"author_id": 1010435537586372600,
"author_name": "Wither",
"timestamp": "01/21/2023 00:06:39",
"content": "$x^2 - p = (x + \\sqrt p) (x - \\sqrt p)$",
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},
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"id": 1066222316129894500,
"author_id": 260118674306760700,
"author_name": "monikanicity",
"timestamp": "01/21/2023 00:06:49",
"content": "what",
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},
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"content": "**Wither**",
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"content": "this",
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"timestamp": "01/21/2023 00:07:31",
"content": "Yes, exactly, what are you doing? Please elaborate...",
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"timestamp": "01/21/2023 00:07:46",
"content": "so",
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"timestamp": "01/21/2023 00:07:51",
"content": "because p is prime",
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"author_id": 485903210272391200,
"author_name": "dldh06",
"timestamp": "01/21/2023 00:07:53",
"content": "From the power of google https://proofwiki.org/wiki/Square_Root_of_Prime_is_Irrational#:~:text=3%20Proof%202-,Theorem,a%20prime%20number%20is%20irrational.",
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"timestamp": "01/21/2023 00:08:08",
"content": "$\\sqrt p$ is not an integer",
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"content": "**Wither**",
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"timestamp": "01/21/2023 00:08:28",
"content": "im confused why you can subsittute a = pk",
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"author_name": "! matthewzz",
"timestamp": "01/21/2023 00:08:57",
"content": "https://math.stackexchange.com/questions/979211/the-square-root-of-a-prime-number-is-irrational",
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"timestamp": "01/21/2023 00:09:32",
"content": "$a^2$ divides p",
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"id": 1066223073486966900,
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"timestamp": "01/21/2023 00:09:50",
"content": "oh wait",
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"timestamp": "01/21/2023 00:09:56",
"content": "no offense but could you leave it to the other pplll",
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"timestamp": "01/21/2023 00:10:05",
"content": "I could but",
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"author_id": 1010435537586372600,
"author_name": "Wither",
"timestamp": "01/21/2023 00:10:10",
"content": "I just want to get into it",
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"timestamp": "01/21/2023 00:10:20",
"content": "maybe not here",
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"timestamp": "01/21/2023 00:10:29",
"content": "maybe",
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"timestamp": "01/21/2023 00:10:54",
"content": "from the proof i linked",
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"author_name": "! matthewzz",
"timestamp": "01/21/2023 00:10:58",
"content": "once you know p divides a",
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"timestamp": "01/21/2023 00:11:03",
"content": "we can substitute a = pk",
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"timestamp": "01/21/2023 00:11:05",
"content": "so p divides a right",
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"timestamp": "01/21/2023 00:11:05",
"content": "why is that",
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"content": "ya",
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"timestamp": "01/21/2023 00:11:18",
"content": "definition of divides",
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"timestamp": "01/21/2023 00:11:28",
"content": "k is p/a",
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"author_name": "! matthewzz",
"timestamp": "01/21/2023 00:11:35",
"content": "is k an integer?",
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"timestamp": "01/21/2023 00:11:43",
"content": "yes, by the definition of divides",
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"timestamp": "01/21/2023 00:11:48",
"content": "ahh ok",
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"timestamp": "01/21/2023 00:11:50",
"content": "p/a is an integer",
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"timestamp": "01/21/2023 00:12:38",
"content": "ah",
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"author_name": "! matthewzz",
"timestamp": "01/21/2023 00:12:54",
"content": "then once we have",
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"timestamp": "01/21/2023 00:13:04",
"content": "$b^2p = p^2k^2$",
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"timestamp": "01/21/2023 00:13:06",
"content": "**! matthewzz**",
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"author_name": "! matthewzz",
"timestamp": "01/21/2023 00:13:17",
"content": "we know that p divides b^2",
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"author_id": 1046637327734288400,
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"timestamp": "01/21/2023 00:13:30",
"content": "and by same rational as a^2",
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"timestamp": "01/21/2023 00:13:34",
"content": "we know that p divides b",
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"timestamp": "01/21/2023 00:13:35",
"content": "right?",
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"content": "yeah",
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"timestamp": "01/21/2023 00:16:09",
"content": ".cloes",
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"author_id": 1046637327734288400,
"author_name": "! matthewzz",
"timestamp": "01/21/2023 00:20:50",
"content": ".close",
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{
"id": 1066225846530089000,
"author_id": 805217272087838700,
"author_name": "Mathematics Bot",
"timestamp": "01/21/2023 00:20:51",
"content": "Channel closed",
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] | help-9 | c819a3b265ec47968cd8229457ac800a |
200,911 | [
{
"id": 1066226099245285400,
"author_id": 805217272087838700,
"author_name": "Mathematics Bot",
"timestamp": "01/21/2023 00:21:51",
"content": "Available help channel!",
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},
{
"id": 1066229945946357800,
"author_id": 935756663674257400,
"author_name": "^ENFT.Nate",
"timestamp": "01/21/2023 00:37:08",
"content": "Having trouble figuring out how to evaluate this limit, i know it is something to do with the limit def of a derivative I just dont know where to begin",
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"timestamp": "01/21/2023 00:37:09",
"content": "Pinned a message.",
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"timestamp": "01/21/2023 00:42:49",
"content": "@Helpers",
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"id": 1066231981605658600,
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"author_name": "DerpZ",
"timestamp": "01/21/2023 00:45:14",
"content": "ok are you allowed to use lhopital",
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"author_name": "Mathematics Bot",
"timestamp": "01/21/2023 00:45:58",
"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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"timestamp": "01/21/2023 00:57:50",
"content": "@^ENFT.Nate Has your question been resolved?",
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"timestamp": "01/21/2023 00:58:02",
"content": ".close",
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"id": 1066235206996082700,
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"content": "Channel closed",
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] | help-9 | 11b79f396f3e4945b634143fbc06a82c |
200,912 | [
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"timestamp": "01/21/2023 00:59:03",
"content": "Available help channel!",
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},
{
"id": 1066245044350222500,
"author_id": 1046637327734288400,
"author_name": "! matthewzz",
"timestamp": "01/21/2023 01:37:08",
"content": "Show sup(C) = $\\alpha + \\beta$ where $\\alpha = sup(A)$ and $\\beta = sup(B)$ and C = {a+b | \\forall a \\in A, b \\in B}",
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"timestamp": "01/21/2023 01:37:08",
"content": "Pinned a message.",
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"author_id": 1046637327734288400,
"author_name": "! matthewzz",
"timestamp": "01/21/2023 01:37:19",
"content": "where A,B $\\subset \\mathbb{R}$",
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"timestamp": "01/21/2023 01:37:21",
"content": "**! matthewzz**",
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"timestamp": "01/21/2023 01:37:33",
"content": "My hint was",
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"author_name": "! matthewzz",
"timestamp": "01/21/2023 01:37:34",
"content": "Hint: For γ < α + β, let ϵ = α + β − γ. Is\nα − ϵ/2 an upper bound for A? Is β − ϵ/2 an upper bound for B?",
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"timestamp": "01/21/2023 01:37:34",
"content": "You can use characterization",
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"timestamp": "01/21/2023 01:37:48",
"content": "?",
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"timestamp": "01/21/2023 01:38:01",
"content": "Let sup(A)=a and sup(B)=b",
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"timestamp": "01/21/2023 01:38:59",
"content": "thats technically the actual problem ^",
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"author_name": "TeXit",
"timestamp": "01/21/2023 01:39:54",
"content": "**! matthewzz**\nCompile Error! Click the :errors: reaction for more information.\n(You may edit your message to recompile.)",
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"content": "then use the defⁿ of sup that: $u \\in \\mathbb{R}$ is said to be supremum of a set $S \\subset \\mathbb{R}$ iff $\\\\$\na. $u \\ge x \\forall x \\in \\mathbb{S},$ and $\\\\$\nb. $\\forall \\epsilon >0, \\exists y \\in \\mathbb{S}$ s.t. $y > u - \\epsilon$",
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"timestamp": "01/21/2023 01:40:03",
"content": "**n11**",
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"timestamp": "01/21/2023 01:40:50",
"content": "you'll get four equations in this order, add 1,3 and 2,4",
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"timestamp": "01/21/2023 01:41:21",
"content": "do you know how to use the hint?",
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"timestamp": "01/21/2023 01:42:02",
"content": "hmmmmm",
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"timestamp": "01/21/2023 01:43:24",
"content": "Contradiction huh",
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"timestamp": "01/21/2023 01:44:23",
"content": "I think your hint is more or less just based on this lol",
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"author_name": "n11",
"timestamp": "01/21/2023 01:44:41",
"content": "proving it an upper bound will be easy, just straight forward definitions",
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"timestamp": "01/21/2023 01:45:12",
"content": "for supremum you can take epsilon/2 for each part, which upon adding will give epsilon forall epsilon more than zero",
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"timestamp": "01/21/2023 01:52:21",
"content": "can you try to explain it more carefully",
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"timestamp": "01/21/2023 02:01:26",
"content": ".close",
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"author_id": 805217272087838700,
"author_name": "Mathematics Bot",
"timestamp": "01/21/2023 02:01:26",
"content": "Channel closed",
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] | help-9 | cf5106f181e34d9292aa27861548ccc7 |
200,913 | [
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"author_name": "Mathematics Bot",
"timestamp": "01/21/2023 02:02:27",
"content": "Available help channel!",
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"author_id": 1046637327734288400,
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"timestamp": "01/21/2023 02:04:55",
"content": "that",
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"author_name": "! matthewzz",
"timestamp": "01/21/2023 02:05:30",
"content": "If x $\\neq 0$ and y $\\neq 0$ then xy $\\neq 0$",
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"timestamp": "01/21/2023 02:05:32",
"content": "**! matthewzz**",
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"content": "How do i prove this with field axioms",
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"timestamp": "01/21/2023 02:06:19",
"content": "so far i was using if x !=0, then $x(x^{-1}) = (x^{-1}) x = 1$",
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"content": "**! matthewzz**",
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"content": "$x(x^{-1}) = y(y^{-1}) = 1$",
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"content": "**! matthewzz**",
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"timestamp": "01/21/2023 02:07:16",
"content": "then",
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"timestamp": "01/21/2023 02:07:28",
"content": "$x(x^{-1})y = y$",
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"author_id": 1046637327734288400,
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"timestamp": "01/21/2023 02:07:34",
"content": "then",
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"author_id": 1046637327734288400,
"author_name": "! matthewzz",
"timestamp": "01/21/2023 02:07:45",
"content": "$x(x^{-1})y(y^{-1}) = 1$",
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"timestamp": "01/21/2023 02:07:47",
"content": "**! matthewzz**",
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"author_name": "! matthewzz",
"timestamp": "01/21/2023 02:07:53",
"content": "is that the correct route?",
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"author_name": "riemann",
"timestamp": "01/21/2023 02:08:08",
"content": "do you have an axiom that says anything about the multiplication of two numbers",
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"timestamp": "01/21/2023 02:08:18",
"content": "**! matthewzz**",
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"content": "wdym",
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"timestamp": "01/21/2023 02:08:41",
"content": "show all your field axioms",
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"timestamp": "01/21/2023 02:08:42",
"content": "its closed under multiplication",
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"timestamp": "01/21/2023 02:08:48",
"content": "Field axioms. For all real numbers x,y,z, we have\nAdditive axioms:\nx+y is real (closure)\nx+y=y+x (commutativity)\n(x+y)+z = x+(y+z) (associativity)\nx+0 = 0+x = x (identity)\nx + (-x) = (-x) + x = 0 (inverse)\nMultiplicative axioms:\nxy is real (closure)\nxy=yx (commutativity)\n(xy)z = x(yz) (associativity)\nx1 = 1x = x (identity)\nif x !=0, then x(x-1) = (x-1) x = 1 (inverse)\nDistributive laws: x(y+z) = xy + xz and (y+z)x = yx + zx.",
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"id": 1066253123636707300,
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"timestamp": "01/21/2023 02:09:14",
"content": "damn just 5",
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"author_id": 1046637327734288400,
"author_name": "! matthewzz",
"timestamp": "01/21/2023 02:09:34",
"content": "oops",
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"author_name": "! matthewzz",
"timestamp": "01/21/2023 02:09:45",
"content": "sorry i thought you meant the ones relating to multiplciation",
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"timestamp": "01/21/2023 02:11:35",
"content": "yea i think this is right",
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"timestamp": "01/21/2023 02:11:51",
"content": "then we group",
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"author_name": "! matthewzz",
"timestamp": "01/21/2023 02:12:04",
"content": "$xy(x^{-1})(y^{-1}) = 1$",
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"timestamp": "01/21/2023 02:12:06",
"content": "**! matthewzz**",
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"timestamp": "01/21/2023 02:12:15",
"content": "$xy(xy)^-1= 1$",
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"author_name": "TeXit",
"timestamp": "01/21/2023 02:12:25",
"content": "**! matthewzz**",
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"timestamp": "01/21/2023 02:12:37",
"content": "but from here can we conclude that xy != 0? @riemann",
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"timestamp": "01/21/2023 02:12:51",
"content": "this axiom: if x !=0, then x(x-1) = (x-1) x = 1 (inverse)",
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"author_name": "! matthewzz",
"timestamp": "01/21/2023 02:12:59",
"content": "is not iff",
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"id": 1066254080370016300,
"author_id": 1046637327734288400,
"author_name": "! matthewzz",
"timestamp": "01/21/2023 02:13:02",
"content": "its only left to right",
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"id": 1066254234007384000,
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"author_name": "riemann",
"timestamp": "01/21/2023 02:13:39",
"content": "where's the right to left statement here?",
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"timestamp": "01/21/2023 02:14:02",
"content": "wdym",
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"author_name": "riemann",
"timestamp": "01/21/2023 02:14:18",
"content": "where's the iff statement",
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"author_name": "! matthewzz",
"timestamp": "01/21/2023 02:14:28",
"content": "im not say there is",
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"timestamp": "01/21/2023 02:14:37",
"content": "im saying we need to conclude that xy != 0",
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"author_name": "! matthewzz",
"timestamp": "01/21/2023 02:14:50",
"content": "and how do we get from this^^ to xy != 0",
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"timestamp": "01/21/2023 02:15:58",
"content": "then prove that if a number has an inverse, it must not be zero",
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"author_id": 1046637327734288400,
"author_name": "! matthewzz",
"timestamp": "01/21/2023 02:17:01",
"content": "how?",
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"author_name": "! matthewzz",
"timestamp": "01/21/2023 02:17:19",
"content": "do we know that because the inverse property only applies to nonzero numbers?",
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"timestamp": "01/21/2023 02:25:11",
"content": "Suppose xy=0, arrive at a contradiction",
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"timestamp": "01/21/2023 02:25:33",
"content": "Your inverse should be outside the parentheses",
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"author_name": "! matthewzz",
"timestamp": "01/21/2023 02:27:34",
"content": "you mean x(x^-1) = 0 ?",
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"timestamp": "01/21/2023 02:27:56",
"content": "Yes",
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"timestamp": "01/21/2023 02:28:09",
"content": "ah right",
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"id": 1066257904497348700,
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"author_name": "! matthewzz",
"timestamp": "01/21/2023 02:28:14",
"content": "since x != 0",
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"timestamp": "01/21/2023 02:28:21",
"content": "we arrive at the contradiction x = 0",
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"author_id": 1046637327734288400,
"author_name": "! matthewzz",
"timestamp": "01/21/2023 02:28:25",
"content": "so it has to have an inverse",
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"author_name": "! matthewzz",
"timestamp": "01/21/2023 02:28:37",
"content": "could you help me with my last problem?",
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"content": "Nah",
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"timestamp": "01/21/2023 02:29:13",
"content": "oh shit",
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"author_id": 1046637327734288400,
"author_name": "! matthewzz",
"timestamp": "01/21/2023 02:29:16",
"content": "sry",
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"author_id": 1046637327734288400,
"author_name": "! matthewzz",
"timestamp": "01/21/2023 02:29:18",
"content": "nvm",
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"timestamp": "01/21/2023 02:29:49",
"content": ".clos",
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"timestamp": "01/21/2023 02:30:09",
"content": ".close",
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] | help-9 | a81ac2d8e55443bbb182c3997ba6abd4 |
200,914 | [
{
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"author_id": 805217272087838700,
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"timestamp": "01/21/2023 02:31:10",
"content": "Available help channel!",
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"author_name": "deathmorf",
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"content": "hi",
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"id": 1066269898055102500,
"author_id": 805217272087838700,
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"timestamp": "01/21/2023 03:16:48",
"content": "Ask your question",
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"id": 1066273621686898700,
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"content": "http://dontasktoask.com",
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"timestamp": "01/21/2023 03:35:48",
"content": "@deathmorf Has your question been resolved?",
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"content": "Channel closed",
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] | help-9 | e1fe721349534ea7ac7a14df68d80a51 |
200,915 | [
{
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"timestamp": "01/21/2023 03:51:49",
"content": "Available help channel!",
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"id": 1066288712876556300,
"author_id": 1045016845910032500,
"author_name": "Pierre de Fermat",
"timestamp": "01/21/2023 04:30:39",
"content": "Hello, I was given this figure in math class and was asked to determine the equations of the trajectory at the center of point O.\n\nThe only method I have in mind is to use the tools in physics.\nExcept that we are in math.\nSo it's not clear to me.\nIf someone could help me.(please).",
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"content": "Pinned a message.",
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"content": ",rotate",
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"timestamp": "01/21/2023 04:46:04",
"content": "@Pierre de Fermat Has your question been resolved?",
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"id": 1066292863324934100,
"author_id": 646026076950233100,
"author_name": "mreow",
"timestamp": "01/21/2023 04:47:09",
"content": "could you be a little more specific?",
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"author_id": 646026076950233100,
"author_name": "mreow",
"timestamp": "01/21/2023 04:47:22",
"content": "trajectory of what and what does O represent here",
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"id": 1066295349448290300,
"author_id": 1045016845910032500,
"author_name": "Pierre de Fermat",
"timestamp": "01/21/2023 04:57:02",
"content": "We want to determine the trajectory of this scale, at the point of center 0",
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"id": 1066299212926554100,
"author_id": 294136651804835840,
"author_name": "Silfer",
"timestamp": "01/21/2023 05:12:23",
"content": "Well, what would then question be if not something that involves physics ?",
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"id": 1066299708953337900,
"author_id": 1045016845910032500,
"author_name": "Pierre de Fermat",
"timestamp": "01/21/2023 05:14:21",
"content": "So yes physics is present, Inevitably, but I ask if we could not do it with pure math, with trigonometry for example.",
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"timestamp": "01/21/2023 05:44:21",
"content": "@Pierre de Fermat Has your question been resolved?",
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"author_name": "Pierre de Fermat",
"timestamp": "01/21/2023 06:43:56",
"content": "I found by the second low of Newton:\n$y(t)=-\\frac12\\cdot gt^2-v_0 t+h$ is that correct?",
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"id": 1066322263785341000,
"author_id": 510789298321096700,
"author_name": "TeXit",
"timestamp": "01/21/2023 06:43:58",
"content": "**Pierre de Fermat**",
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"author_id": 1045016845910032500,
"author_name": "Pierre de Fermat",
"timestamp": "01/21/2023 06:44:53",
"content": "So $x(t)=0$ because the movement is only on the $y$ axis.",
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"author_id": 510789298321096700,
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"timestamp": "01/21/2023 06:45:33",
"content": "**Pierre de Fermat**",
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"timestamp": "01/21/2023 07:44:54",
"content": "@Pierre de Fermat Has your question been resolved?",
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] | help-9 | 541b6da9018d46fe979b30269390d43b |
200,916 | [
{
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"author_name": "Mathematics Bot",
"timestamp": "01/21/2023 08:45:54",
"content": "Available help channel!",
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},
{
"id": 1066353944571416700,
"author_id": 332561465405866000,
"author_name": "Kepe",
"timestamp": "01/21/2023 08:49:52",
"content": "Given $f(1) = 2$, $f'(1) = 1$ and $f''(1) = 1$, $P(1, 2)$ can't be an extremum, right?\n\nMy book says that it could be an edge extremum, but in that case, $f'(1)$ wouldn't be defined, would it? It could only be a one-sided limit and that shouldn't be sufficient for a derivative",
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"content": "Pinned a message.",
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{
"id": 1066354907474567200,
"author_id": 984319941417251000,
"author_name": "💜𝓁𝒶𝓎𝓁𝒶💜",
"timestamp": "01/21/2023 08:53:41",
"content": "what's an edge extremum?",
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"id": 1066355613405298800,
"author_id": 332561465405866000,
"author_name": "Kepe",
"timestamp": "01/21/2023 08:56:30",
"content": "If f(x) = x^2 is defined on the domain [-2, 3], then P(-2, 4) is an edge extremum point, just like P(3, 9)",
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"author_name": "💜𝓁𝒶𝓎𝓁𝒶💜",
"timestamp": "01/21/2023 08:57:01",
"content": "idk what the book is saying then :c",
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"id": 1066355860135223400,
"author_id": 332561465405866000,
"author_name": "Kepe",
"timestamp": "01/21/2023 08:57:28",
"content": "It should be wrong, the derivative can't just be a one-sided limit, right?",
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"timestamp": "01/21/2023 09:12:29",
"content": "@Kepe Has your question been resolved?",
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"content": "Channel closed",
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] | help-9 | 81eef177465945e3a222fa2b609ba059 |
200,917 | [
{
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"timestamp": "01/21/2023 09:28:30",
"content": "Available help channel!",
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"id": 1066367101679439900,
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"content": "Pinned a message.",
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"author_id": 849961886874730500,
"author_name": "SA2017",
"timestamp": "01/21/2023 09:42:13",
"content": "doesnt this series converge to 0?",
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{
"id": 1066367429019701200,
"author_id": 788085606483361800,
"author_name": "chartbit",
"timestamp": "01/21/2023 09:43:27",
"content": "The *sequence* it's made up of converges to zero, sure, but not the *series*",
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{
"id": 1066367606031929300,
"author_id": 788085606483361800,
"author_name": "chartbit",
"timestamp": "01/21/2023 09:44:09",
"content": "Remember, of course, that for a series to converge, it's necessary to have the sequence it's made up of go to zero, but the converse isn't true (as per here!)",
"attachments": [],
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{
"id": 1066367613208379500,
"author_id": 849961886874730500,
"author_name": "SA2017",
"timestamp": "01/21/2023 09:44:11",
"content": "im a bit confused on the differences of the definitions of converge and diverge",
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"id": 1066367725401800800,
"author_id": 788085606483361800,
"author_name": "chartbit",
"timestamp": "01/21/2023 09:44:37",
"content": "Alight, let's take a sequence for now, by itself",
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"id": 1066367858961043500,
"author_id": 788085606483361800,
"author_name": "chartbit",
"timestamp": "01/21/2023 09:45:09",
"content": "A sequence converges to a limit if \"as you go on, your sequence gets closer to a limit\"",
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"id": 1066367861712490600,
"author_id": 362794394887127040,
"author_name": "numbpy",
"timestamp": "01/21/2023 09:45:10",
"content": "Do you know convergence of a sequence?",
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"id": 1066367949230841900,
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"timestamp": "01/21/2023 09:45:31",
"content": "More precisely, your epsilon-n definition",
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"id": 1066367952812769300,
"author_id": 849961886874730500,
"author_name": "SA2017",
"timestamp": "01/21/2023 09:45:32",
"content": "does that limit have to be a real ?",
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"timestamp": "01/21/2023 09:45:37",
"content": "ok",
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"timestamp": "01/21/2023 09:45:40",
"content": "funny u say that",
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"timestamp": "01/21/2023 09:45:44",
"content": "im doing that now lol",
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"content": "Well yes, for a sequence of real numbers, you need the limit to be a real number",
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"content": "Anyways, being divergent is basically not converging to any real number as a limit, for whatever reason",
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"content": "[e.g. blowing up to ♾️, alternating between two terms like (-1)^n, etc]",
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"content": "i see",
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"content": "reason i was confused here was because as n gets larger, 1/n tends to a real number ie 0 hence converges",
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"content": "Now, series convergence and divergence is basically the same but you consider the sequence of partial sums $s_{n} = \\sum_{k=1}^{n} a_{k}$",
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"content": "ie the limit being 0",
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"content": "**chartbit**",
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"content": "The sequence does grow very very slowly, but it increases without bounds",
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"content": "Oh would you fancy that, I made the same mistake they did just there :kekw:",
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"content": "lmao",
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"content": "That should be $\\sum_{n=1}^{\\infty} \\frac{1}{n}$",
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"content": "**chartbit**",
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"content": "lmao",
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"content": "yh",
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"content": "ok if the series converges the sequence definitely converges to 0",
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"content": "however the converse is not true",
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"content": "like if sum an converges then an converges to 0",
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"content": "ye",
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"content": "also",
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"timestamp": "01/21/2023 09:51:42",
"content": "to prove a sequence converges, do we always use the e -N proof, and if we wanna prove that the sequece diverges, do we always use the e - M proof?",
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"content": "one nice way to see this diverges is to note that",
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"content": "for divergence you can just",
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"content": "negate convergence",
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"content": "p series converges iff p > 1",
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"content": "Welll think of it a little bit like differentiation, you do some things from first principles, but for the most part you just use things you know, if that answers your question?",
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"content": "ye",
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"content": "but like",
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"timestamp": "01/21/2023 09:54:06",
"content": "if a question asks to prove if a sequence converges",
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"content": "So like a lot of the time you might e.g. use the sandwich theorem 🥪 to prove some sequence converges, or the algebra of limits",
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"content": "do we do e - N or M - N",
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"content": "sandwich theorem meaning squeeze theorem?",
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"content": "eps-N proof",
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"content": "ok",
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"content": "for divergence you negate or you can use your one",
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"content": "Wait what's the M - N def?",
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"content": "like",
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"content": "given M > 0 show that the series > M",
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"content": "its for divergence",
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"content": "cauchy condensation test there is that",
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"content": "this",
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"timestamp": "01/21/2023 09:55:54",
"content": "Oh that's divergence to infinity, be careful",
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"timestamp": "01/21/2023 09:56:21",
"content": "oh",
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"timestamp": "01/21/2023 09:56:23",
"content": "You can diverge but not diverge to -♾️ or +♾️",
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"content": "diverge literally means not convergent fyi",
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"timestamp": "01/21/2023 09:56:41",
"content": "See before (-1)^n diverges but doesn't blow up",
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"timestamp": "01/21/2023 09:56:57",
"content": "is this only true if n tends to infinity?",
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"content": "er",
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"timestamp": "01/21/2023 09:57:30",
"content": "like using the eps - N defn",
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"content": "read definition",
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"timestamp": "01/21/2023 09:57:36",
"content": "I mean, it doesn't really make too much sense to talk about a limit of a sequence if you don't go off to infinity",
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"content": "lim n to inf is just notation",
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"content": "ye",
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"content": "when you write lim n to inf of a_n = L",
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"content": "you're saying for all eps > 0 blah blah",
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"content": "blah blah blah",
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"content": "yeah basically",
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"timestamp": "01/21/2023 09:58:28",
"content": "(im on mobile so)",
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"content": "For all $\\varepsilon >0$, you can find some $n_{\\epsilon} \\in \\bN$ such that for any $n\\geq n_{\\epsilon}$, you have $|a_{n} - L| < \\varepsilon$",
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"content": "**chartbit**",
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"content": "I know the pain of mobile typesetting, absolutely not fun one bit :thonkHang:",
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"content": "i swear i should like",
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"content": "setup a command",
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"content": "but oh well",
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"content": "its probably easier to say \"recall the definition\"",
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"timestamp": "01/21/2023 10:01:27",
"content": "The people who actually have those preamble setups, I really should do that honestly",
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"content": "[mind you, the only times I tried to update my preamble it got rejected, because turns out, commands I thought weren't defined and I used the long method of writing out were :thonkHang:]",
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"timestamp": "01/21/2023 10:02:34",
"content": "Well at least they check the LaTeX for you",
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"content": "which is nice",
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"timestamp": "01/21/2023 10:09:42",
"content": "looks good",
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"timestamp": "01/21/2023 10:23:13",
"content": "@SA2017 Has your question been resolved?",
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"timestamp": "01/21/2023 10:29:46",
"content": "@chartbit when a question asks u to give the e - N or M - N proof, will u have to use ur intuition to realise firstly if its converging or diverging?",
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"timestamp": "01/21/2023 10:30:13",
"content": "ie u kinda need to know before hand whether its converging or diverging before u can choose whether to do an eps - N proof or an M - N proof",
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"timestamp": "01/21/2023 10:34:03",
"content": "Hmmm, depends on the situation I think",
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"timestamp": "01/21/2023 10:35:01",
"content": "For diverging to infinity it should ideally be quite clear whether it does, from where you can do the proof with that M-N definition",
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"content": "However, depending on the question they may not *need* you to prove it via the actual strict definitions [see here]",
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"content": "But anyways, if they give you a sequence and tell you to prove it converges to a limit via the strict definition, you'd do it that way, actually let me take a look at the paper you have",
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"timestamp": "01/21/2023 10:37:18",
"content": "okok",
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"timestamp": "01/21/2023 10:37:34",
"content": "but i see ur point",
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"timestamp": "01/21/2023 10:38:15",
"content": "For example, see 5c for a sandwich theorem type question [which they hint at you to do]",
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"timestamp": "01/21/2023 10:38:28",
"content": "5b also tells you to use a theorem too",
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"timestamp": "01/21/2023 10:38:38",
"content": "ye i noticed that",
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"timestamp": "01/21/2023 10:38:53",
"content": "i dont think ill have to do this in the exam then by the looks of it",
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"timestamp": "01/21/2023 10:39:01",
"content": "but its good to just in case",
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"timestamp": "01/21/2023 10:39:31",
"content": "I think definitely remember the definitions of course, and the theorems",
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"timestamp": "01/21/2023 10:39:40",
"content": "remember",
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"timestamp": "01/21/2023 10:39:45",
"content": "hehehhe SUIIIII",
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"timestamp": "01/21/2023 10:39:46",
"content": "[and try and understand the proofs for them, overall I think they're decent]",
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"timestamp": "01/21/2023 10:39:57",
"content": "https://tenor.com/view/laughing-okay-bud-hilarious-funny-gif-15869195",
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"timestamp": "01/21/2023 10:40:17",
"content": "lmao",
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"timestamp": "01/21/2023 10:40:52",
"content": "You gotta make sure you smash this one then, like you're set if you play your cards right!",
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"timestamp": "01/21/2023 10:41:02",
"content": "very true",
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"timestamp": "01/21/2023 10:41:51",
"content": "Like overall it looks pretty nice as a paper, there are some open book exams where they aren't necessarily that nice, but I think with this one you should be fine :happyCat:",
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"timestamp": "01/21/2023 10:42:12",
"content": "next year we do real analysis 2",
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"timestamp": "01/21/2023 10:42:17",
"content": "if this is real analysis 1",
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"timestamp": "01/21/2023 10:42:19",
"content": "lord have mercy",
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"timestamp": "01/21/2023 10:43:08",
"content": "Real analysis 2 :catlove: hope there's metric spaces in there",
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"timestamp": "01/21/2023 10:43:22",
"content": "...actually why am I hoping when it's not my module :kekw:",
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"timestamp": "01/21/2023 10:44:12",
"content": "next semester, which starts in 2 weeks, we do vector calc, linear algbera, classical dynamics",
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"timestamp": "01/21/2023 10:44:15",
"content": "and python...",
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"timestamp": "01/21/2023 10:44:21",
"content": "thats 100% coursework",
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"timestamp": "01/21/2023 10:44:24",
"content": "💀",
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"timestamp": "01/21/2023 10:45:44",
"content": "Wait the next semester is just coursework or the Python module?",
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"timestamp": "01/21/2023 10:45:59",
"content": "If the former then 🕊️",
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"timestamp": "01/21/2023 10:46:28",
"content": "Linalg :catlove:",
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"timestamp": "01/21/2023 10:46:37",
"content": "Dynamics :inTheTrash:",
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"timestamp": "01/21/2023 10:52:39",
"content": "the python module is the ones thats 100% cw",
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"timestamp": "01/21/2023 10:52:48",
"content": "the rest modules r exam",
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"timestamp": "01/21/2023 10:52:59",
"content": "vector calc is apparently hard",
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"timestamp": "01/21/2023 10:53:02",
"content": "Ah fairs, makes more sense",
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"timestamp": "01/21/2023 10:53:11",
"content": "https://tenor.com/view/yes-gif-23634406",
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"timestamp": "01/21/2023 10:53:26",
"content": "That is the common consensus amongst many, across different years, universities, yea you get the picture",
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"timestamp": "01/21/2023 10:55:34",
"content": "thats the content for vector calc",
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"timestamp": "01/21/2023 10:55:36",
"content": "for my module",
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"timestamp": "01/21/2023 10:57:28",
"content": "Yeaaa seems pretty standard for multivariate calc I think",
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"timestamp": "01/21/2023 10:57:47",
"content": "Stuff like Green's/Stokes and all",
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"timestamp": "01/21/2023 10:57:59",
"content": "stokes?",
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"timestamp": "01/21/2023 10:58:03",
"content": "ben stokes theorem",
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"timestamp": "01/21/2023 10:58:03",
"content": "lol",
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"id": 1066386250434629600,
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"timestamp": "01/21/2023 10:58:14",
"content": "does it involve cricket at all :kekw:",
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"timestamp": "01/21/2023 10:58:29",
"content": "sry for the cringe",
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"timestamp": "01/21/2023 10:59:49",
"content": ":catThimc:",
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"timestamp": "01/21/2023 11:01:10",
"content": "Can't even remember the last time I did anything more than working out partial derivatives and just simple double integrals tbh :catThimc:",
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"timestamp": "01/21/2023 11:03:52",
"content": "are M - N proofs for divergent similar to epsilon - N proofs for convergent?",
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"timestamp": "01/21/2023 11:03:58",
"content": "cant find any videos for M - N proofs",
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"timestamp": "01/21/2023 11:04:37",
"content": "Yea they're analogous to the epsilon-N proofs really",
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"timestamp": "01/21/2023 11:05:10",
"content": "[in fact, some people decide that you can \"converge to infinity\", at which point any sequence has a convergent subsequence :monkey:]",
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"timestamp": "01/21/2023 11:06:05",
"content": "[For bounded sequences that is true [that there is a convergent subsequence], there is a famous proof for that]",
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"timestamp": "01/21/2023 11:06:57",
"content": "Anyways, the process for both are pretty similar, if you get how to show something converges to a finite limit, then you should have virtually no problem in showing it would diverge to + or - ♾️",
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"timestamp": "01/21/2023 11:18:30",
"content": "trying to do this proof",
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"timestamp": "01/21/2023 11:18:35",
"content": "how do i make n the subject here?",
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"id": 1066392151941980300,
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"author_name": "chartbit",
"timestamp": "01/21/2023 11:21:41",
"content": "You could e.g. complete the square for it?",
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"timestamp": "01/21/2023 11:22:06",
"content": "kl",
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"timestamp": "01/21/2023 11:22:13",
"content": "i feel like all these proofs r so pointless",
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"timestamp": "01/21/2023 11:22:15",
"content": "idk why",
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"timestamp": "01/21/2023 11:22:21",
"content": "likw what does it show lol",
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"author_id": 849961886874730500,
"author_name": "SA2017",
"timestamp": "01/21/2023 11:22:27",
"content": "i get it proves the limit is correct but",
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"id": 1066392357207023600,
"author_id": 849961886874730500,
"author_name": "SA2017",
"timestamp": "01/21/2023 11:22:30",
"content": "how",
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"id": 1066392463771713700,
"author_id": 788085606483361800,
"author_name": "chartbit",
"timestamp": "01/21/2023 11:22:55",
"content": "Because you destroyed them with facts and logic :catThimc:",
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"id": 1066392750859227300,
"author_id": 849961886874730500,
"author_name": "SA2017",
"timestamp": "01/21/2023 11:24:04",
"content": "cough l hopitals rule cough cough",
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"id": 1066392835865194600,
"author_id": 788085606483361800,
"author_name": "chartbit",
"timestamp": "01/21/2023 11:24:24",
"content": "Well, you've made a definition of the limit, and then shown that you meet that definition I guess(?) For me I quite prefer the proofs of theorems that make life easier (e.g. functions are continuous if and only if they map convergent sequences to convergent sequences etc)",
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"id": 1066392942027231400,
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"author_name": "chartbit",
"timestamp": "01/21/2023 11:24:50",
"content": "Those ones are the nice ones because you get to actually save time and not have to do all the work further down the line",
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"timestamp": "01/21/2023 11:28:00",
"content": "hows this?",
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"content": "https://tenor.com/view/perfection-perfect-flawless-ultimate-spotless-gif-13993155",
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"timestamp": "01/21/2023 11:30:41",
"content": "LESGOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOO",
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"content": "SUIIIIIIIIIIIIIIIIIIIIIIIIIIII",
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"id": 1066394510394921000,
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"timestamp": "01/21/2023 11:31:03",
"content": "also is mehdi alright?",
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"author_id": 849961886874730500,
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"timestamp": "01/21/2023 11:31:09",
"content": "hasnt been here for the last2 days",
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"author_id": 788085606483361800,
"author_name": "chartbit",
"timestamp": "01/21/2023 11:32:05",
"content": "Oh yeah he literally hasn't been, no posts for the two days 😟",
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"id": 1066394852050346200,
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"author_name": "chartbit",
"timestamp": "01/21/2023 11:32:25",
"content": "Maybe he's busy I'm guessing, hopefully he's all good of course!",
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"id": 1066395745353212000,
"author_id": 485164773647056900,
"author_name": "Gooaaa",
"timestamp": "01/21/2023 11:35:58",
"content": ":poggers:",
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"timestamp": "01/21/2023 11:55:19",
"content": ".close",
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"id": 1066400619381932200,
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"timestamp": "01/21/2023 11:55:20",
"content": "Channel closed",
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] | help-9 | 8ff7eb6e607d464881324cc8975418cf |
200,918 | [
{
"id": 1066405562205614200,
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"author_name": "Mathematics Bot",
"timestamp": "01/21/2023 12:14:58",
"content": "Available help channel!",
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"id": 1066406732017975300,
"author_id": 296282005812019200,
"author_name": "Wrld",
"timestamp": "01/21/2023 12:19:37",
"content": "This is regarding probability and I dont understand a concept from the book.\n\nSo according to the first sentence A and B are independent if the occurence of A does not affect the occurence of B and vice versa. Doesn't this \"vice versa\" imply mutual independency and not regular independency?\n\nFor instance, lets call A = {2} and C = S (which is the sample space = {1,2,3,4,5,6}). Yes, whether or not A happens, it won't affect the outcome of C. But can this be really said for the other way around (i.e. vice versa)? Isn't every event dependent on the sample space? If the sample space doesn't happen, then the experiment hasn't been made which ultimately means that A won't happen. But if the sample space happens it means that A could possibly happen.",
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"content": "Pinned a message.",
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"id": 1066407258323419100,
"author_id": 154343039878299650,
"author_name": "Fέliχ",
"timestamp": "01/21/2023 12:21:43",
"content": "You must always assume that the experiments are made",
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},
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"id": 1066407352988881000,
"author_id": 154343039878299650,
"author_name": "Fέliχ",
"timestamp": "01/21/2023 12:22:05",
"content": "So having information about the experiment being made doesn't affect the information of having a 2, because you knew the experiment would happen anyway",
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},
{
"id": 1066407756854214700,
"author_id": 154343039878299650,
"author_name": "Fέliχ",
"timestamp": "01/21/2023 12:23:42",
"content": "And if you ask why, then remember the probability axioms",
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"id": 1066407769005105300,
"author_id": 154343039878299650,
"author_name": "Fέliχ",
"timestamp": "01/21/2023 12:23:45",
"content": "One of them is that P(S) = 1",
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"author_name": "Fέliχ",
"timestamp": "01/21/2023 12:27:17",
"content": "@Wrld",
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"timestamp": "01/21/2023 12:29:29",
"content": "okay i understand ty",
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"timestamp": "01/21/2023 12:44:29",
"content": "@Wrld Has your question been resolved?",
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"content": "Channel closed",
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}
] | help-9 | 2784c5b679ba4e9889a4598d1a6da07d |
200,919 | [
{
"id": 1066417018519162900,
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"author_name": "Mathematics Bot",
"timestamp": "01/21/2023 13:00:30",
"content": "Available help channel!",
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},
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"id": 1066417923033411600,
"author_id": 880114036711243800,
"author_name": "Cend",
"timestamp": "01/21/2023 13:04:05",
"content": "i am assuming that c is 33° due to angles in the same segment being equal, but i am struggling to find the other values",
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"content": "Pinned a message.",
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"id": 1066421680869744800,
"author_id": 693531172059217900,
"author_name": "phoestaclies",
"timestamp": "01/21/2023 13:19:01",
"content": "if u have c u can resolve this easily",
"attachments": [],
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},
{
"id": 1066422022013456400,
"author_id": 693531172059217900,
"author_name": "phoestaclies",
"timestamp": "01/21/2023 13:20:23",
"content": "we know that the sum of angle in a triangle are 180, so let the point in the center be O the the angle YOX is equal to 180-55",
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},
{
"id": 1066422188133064800,
"author_id": 693531172059217900,
"author_name": "phoestaclies",
"timestamp": "01/21/2023 13:21:02",
"content": "so we have also the angle WOX which is equal to 180 minus the angle YOX",
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},
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"id": 1066422201617744100,
"author_id": 693531172059217900,
"author_name": "phoestaclies",
"timestamp": "01/21/2023 13:21:06",
"content": "and so on",
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},
{
"id": 1066422507269267500,
"author_id": 154343039878299650,
"author_name": "Fέliχ",
"timestamp": "01/21/2023 13:22:18",
"content": "You cannot assume that c is 33 degrees",
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"id": 1066422653042299000,
"author_id": 693531172059217900,
"author_name": "phoestaclies",
"timestamp": "01/21/2023 13:22:53",
"content": "yes i don't understand how u can have c",
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"id": 1066422693710266500,
"author_id": 154343039878299650,
"author_name": "Fέliχ",
"timestamp": "01/21/2023 13:23:03",
"content": "If that was true you would also have b",
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{
"id": 1066422714711163000,
"author_id": 154343039878299650,
"author_name": "Fέliχ",
"timestamp": "01/21/2023 13:23:08",
"content": "Right away",
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},
{
"id": 1066422942222794900,
"author_id": 154343039878299650,
"author_name": "Fέliχ",
"timestamp": "01/21/2023 13:24:02",
"content": "By doing that you assume that WZ and XY are parallel and you have no reasons to believe so @Cend",
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"timestamp": "01/21/2023 13:29:02",
"content": "@Cend Has your question been resolved?",
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"id": 1066424873297125500,
"author_id": 951190447185875000,
"author_name": "MathIsAlwaysRight",
"timestamp": "01/21/2023 13:31:43",
"content": "You can model 4 equations with 4 unknows D: Sounds like nightmare, but it's possible solutions. You know that 33+80+a+b=180, because it's a triangle. Do this for all other triangles and you will get 4 equations.",
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"author_id": 951190447185875000,
"author_name": "MathIsAlwaysRight",
"timestamp": "01/21/2023 13:33:06",
"content": "Here is the triangle I showed the equation for",
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"author_name": "Cend",
"timestamp": "01/21/2023 13:33:53",
"content": "would this give the value for a or b?",
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"author_id": 951190447185875000,
"author_name": "MathIsAlwaysRight",
"timestamp": "01/21/2023 13:34:19",
"content": "It gives just an equation. You need more equations to solve the whole problem.",
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"author_name": "MathIsAlwaysRight",
"timestamp": "01/21/2023 13:36:08",
"content": "a+b+80+33=180, a+c+80+22=180, b+d+33+45=180, c+d+45+22=180 are all the equations you need",
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},
{
"id": 1066426221677772800,
"author_id": 720578124190056400,
"author_name": "~elise~",
"timestamp": "01/21/2023 13:37:04",
"content": "a+b=67. c+d = 113. b+d = 102. c+a = 78 a+b+c+d=180",
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"id": 1066426601878863900,
"author_id": 880114036711243800,
"author_name": "Cend",
"timestamp": "01/21/2023 13:38:35",
"content": "oh i see now",
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"timestamp": "01/21/2023 13:38:58",
"content": "Great :) Elise simplified those equations for you, now just solve them",
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"id": 1066427257293373400,
"author_id": 880114036711243800,
"author_name": "Cend",
"timestamp": "01/21/2023 13:41:11",
"content": "alright",
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},
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"id": 1066427346007113700,
"author_id": 880114036711243800,
"author_name": "Cend",
"timestamp": "01/21/2023 13:41:32",
"content": "thanks guys, have a good day 👍",
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"id": 1066427369151287400,
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"timestamp": "01/21/2023 13:41:38",
"content": ".close",
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"timestamp": "01/21/2023 13:41:38",
"content": "Channel closed",
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] | help-9 | 5551b1f7ff58457aaaeafdb83185b0bd |
200,920 | [
{
"id": 1036229165206208600,
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"author_name": "Mathematics Bot",
"timestamp": "10/30/2022 06:44:45",
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"id": 1036231281610076300,
"author_id": 213073438221271040,
"author_name": "Clase",
"timestamp": "10/30/2022 06:53:09",
"content": "So I haven't done integrals in quite a while, and I figured the two equations are equal",
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"timestamp": "10/30/2022 06:53:10",
"content": "Pinned a message.",
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"timestamp": "10/30/2022 06:54:06",
"content": "However, when I put `x=1` into the equation, I get a negative number - which should be impossible\nAnd indeed, the result is supposed to be `1/120` (I'm getting `-1/460`). I'm assuming my development of the integral is wrong somehow. Would anybody care to explain what's wrong with my second equation?",
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"timestamp": "10/30/2022 06:56:20",
"content": "Hey where is dx?",
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"timestamp": "10/30/2022 06:56:43",
"content": "There's supposed to be a dx at the end, I just copied it off a website.",
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"timestamp": "10/30/2022 06:56:49",
"content": "Ok",
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"author_name": "𝓐𝓡𝓝𝓐𝓑 𝓟𝓐𝓛",
"timestamp": "10/30/2022 06:57:29",
"content": "Wait",
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"timestamp": "10/30/2022 07:05:20",
"content": "Aren't you supposed to plug in 1 and then plug in 0 and substract the first one with the second one",
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"timestamp": "10/30/2022 07:05:28",
"content": "Fundamental theorem of calculus",
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"timestamp": "10/30/2022 07:05:48",
"content": "What's the point of subtracting by 0 though?",
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"timestamp": "10/30/2022 07:06:11",
"content": "Oh there are no constant terms",
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"timestamp": "10/30/2022 07:06:16",
"content": "Well shit",
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"timestamp": "10/30/2022 07:06:29",
"content": "Ok wait let me try something",
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"timestamp": "10/30/2022 07:09:14",
"content": "I think you forgot the +c",
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"timestamp": "10/30/2022 07:10:25",
"content": "It is finite integration",
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"timestamp": "10/30/2022 07:10:28",
"content": "Doesn't have an effect on the outcome",
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"timestamp": "10/30/2022 07:10:33",
"content": "Precisely",
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"timestamp": "10/30/2022 07:10:56",
"content": "Doesn't make a difference",
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"timestamp": "10/30/2022 07:11:00",
"content": "I mean if it isn't that I don't what it is",
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"timestamp": "10/30/2022 07:11:10",
"content": "You integrated correctly",
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"timestamp": "10/30/2022 07:11:55",
"content": "Perhaps I just calculated wrong.",
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"timestamp": "10/30/2022 07:11:59",
"content": "Let me triple check",
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"author_name": "𝓐𝓡𝓝𝓐𝓑 𝓟𝓐𝓛",
"timestamp": "10/30/2022 07:12:07",
"content": "$\\frac{1}{6}-\\frac{1}{5}+\\frac{1}{24}$",
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"timestamp": "10/30/2022 07:12:10",
"content": "**𝓐𝓡𝓝𝓐𝓑 𝓟𝓐𝓛**",
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"content": "...",
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"timestamp": "10/30/2022 07:12:17",
"content": "Yep",
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"timestamp": "10/30/2022 07:12:24",
"content": "I wrote down 32 instead of 24",
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"timestamp": "10/30/2022 07:12:28",
"content": "Lol. Cheers fellas",
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"timestamp": "10/30/2022 07:12:32",
"content": "bruuuh",
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"author_name": "𝓐𝓡𝓝𝓐𝓑 𝓟𝓐𝓛",
"timestamp": "10/30/2022 07:12:38",
"content": ",w solve 1/6-1/5+1/24",
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"timestamp": "10/30/2022 07:12:43",
"content": "Results provided by WolframAlpha",
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"timestamp": "10/30/2022 07:12:49",
"content": "wtf how are u student with 14",
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"timestamp": "10/30/2022 07:13:10",
"content": "Hehehe Actually I am studying for an exam",
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"timestamp": "10/30/2022 07:13:16",
"content": "Called JEE",
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"author_name": "𝓐𝓡𝓝𝓐𝓑 𝓟𝓐𝓛",
"timestamp": "10/30/2022 07:13:34",
"content": "I am a 9 grader Actually",
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"timestamp": "10/30/2022 07:13:38",
"content": "oh",
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"timestamp": "10/30/2022 07:13:41",
"content": "Yupp",
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"timestamp": "10/30/2022 07:13:44",
"content": "Oh you're indian good luck bro is it the jee advanced?",
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"timestamp": "10/30/2022 07:14:00",
"content": "Yupp but also JEE mains",
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"timestamp": "10/30/2022 07:14:10",
"content": "I am aiming for IIT",
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"timestamp": "10/30/2022 07:14:23",
"content": "what do u want",
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"id": 1036236630090064000,
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"timestamp": "10/30/2022 07:14:24",
"content": "to study",
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"author_name": "𝓐𝓡𝓝𝓐𝓑 𝓟𝓐𝓛",
"timestamp": "10/30/2022 07:14:27",
"content": "Thaks btw",
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"timestamp": "10/30/2022 07:14:41",
"content": "Computer science",
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"timestamp": "10/30/2022 07:14:47",
"content": "do u know something about it",
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"author_name": "Senku",
"timestamp": "10/30/2022 07:14:47",
"content": "Yeah I tried some of the physics questions on the advanced it's brutal",
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"timestamp": "10/30/2022 07:14:47",
"content": "alrd",
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"timestamp": "10/30/2022 07:15:06",
"content": "Yupp it is too brutal for mee 😂",
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"timestamp": "10/30/2022 07:15:17",
"content": "physic is disgusting",
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"timestamp": "10/30/2022 07:15:37",
"content": "But I love physics more than anything ☠️",
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"timestamp": "10/30/2022 07:15:45",
"content": "damn 😮",
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"timestamp": "10/30/2022 07:15:47",
"content": "Don't worry you can do anything with enough preparation",
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"timestamp": "10/30/2022 07:16:18",
"content": "Yupp I have more 4 years left but I have to be consistent thanks bro 🫂",
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"author_name": "𝓐𝓡𝓝𝓐𝓑 𝓟𝓐𝓛",
"timestamp": "10/30/2022 07:16:30",
"content": ",w plot x^2 + {y -3/4(x^2)^(1/3)}^2 = 1",
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"timestamp": "10/30/2022 07:16:33",
"content": "Results provided by WolframAlpha",
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"id": 1036237273106231300,
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"timestamp": "10/30/2022 07:16:58",
"content": "bro u know so complex stuff",
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"timestamp": "10/30/2022 07:17:00",
"content": "in 9th grade",
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"timestamp": "10/30/2022 07:17:02",
"content": "thats insane",
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"timestamp": "10/30/2022 07:17:14",
"content": "That's what she said",
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"timestamp": "10/30/2022 07:17:14",
"content": "Wow I didn't know you could graph a heart",
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"timestamp": "10/30/2022 07:17:24",
"content": "is everyone like that",
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"id": 1036237388973867000,
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"timestamp": "10/30/2022 07:17:25",
"content": "in india",
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},
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"id": 1036237402999631900,
"author_id": 232392180474314750,
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"timestamp": "10/30/2022 07:17:29",
"content": "💀",
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},
{
"id": 1036237405939843200,
"author_id": 518716603928543200,
"author_name": "𝓐𝓡𝓝𝓐𝓑 𝓟𝓐𝓛",
"timestamp": "10/30/2022 07:17:29",
"content": "Yeah I have Google it 😂",
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"id": 1036237440458956800,
"author_id": 518716603928543200,
"author_name": "𝓐𝓡𝓝𝓐𝓑 𝓟𝓐𝓛",
"timestamp": "10/30/2022 07:17:38",
"content": "No",
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"id": 1036237490211799000,
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"author_name": "Senku",
"timestamp": "10/30/2022 07:17:50",
"content": "That's what you gotta do to pass the JEE advanced",
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"timestamp": "10/30/2022 07:18:07",
"content": "It's one of the hardest exams in the world",
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},
{
"id": 1036237610961600500,
"author_id": 518716603928543200,
"author_name": "𝓐𝓡𝓝𝓐𝓑 𝓟𝓐𝓛",
"timestamp": "10/30/2022 07:18:18",
"content": "If you exclude me then other are getting introduce to Cartesian system now",
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"id": 1036237658625691800,
"author_id": 232392180474314750,
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"timestamp": "10/30/2022 07:18:30",
"content": "😮",
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"id": 1036237690431090700,
"author_id": 518716603928543200,
"author_name": "𝓐𝓡𝓝𝓐𝓑 𝓟𝓐𝓛",
"timestamp": "10/30/2022 07:18:37",
"content": "2nd hardest",
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"id": 1036237770538106900,
"author_id": 432321730753855500,
"author_name": "Senku",
"timestamp": "10/30/2022 07:18:56",
"content": "After what?",
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},
{
"id": 1036237847495200800,
"author_id": 518716603928543200,
"author_name": "𝓐𝓡𝓝𝓐𝓑 𝓟𝓐𝓛",
"timestamp": "10/30/2022 07:19:15",
"content": "Gaokao a Chinese exam",
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},
{
"id": 1036238068623097900,
"author_id": 432321730753855500,
"author_name": "Senku",
"timestamp": "10/30/2022 07:20:07",
"content": "Oh yeah but the gaokao isn't just math",
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},
{
"id": 1036238115888701400,
"author_id": 432321730753855500,
"author_name": "Senku",
"timestamp": "10/30/2022 07:20:19",
"content": "They also do languages",
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},
{
"id": 1036238225582346200,
"author_id": 518716603928543200,
"author_name": "𝓐𝓡𝓝𝓐𝓑 𝓟𝓐𝓛",
"timestamp": "10/30/2022 07:20:45",
"content": "Yupp if you are talking about maths and other science stuff then JEE is the hardest",
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"id": 1036238434941022200,
"author_id": 432321730753855500,
"author_name": "Senku",
"timestamp": "10/30/2022 07:21:35",
"content": "Yeah I gotta go good luck to you in 4 years!",
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{
"id": 1036238508207124500,
"author_id": 518716603928543200,
"author_name": "𝓐𝓡𝓝𝓐𝓑 𝓟𝓐𝓛",
"timestamp": "10/30/2022 07:21:52",
"content": "Thank you bro and gool luck for your future too 🫂",
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"id": 1036239276041568300,
"author_id": 213073438221271040,
"author_name": "Clase",
"timestamp": "10/30/2022 07:24:55",
"content": "I'll go out on a limb and assume you guys are done :P",
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"id": 1036239285797519400,
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"author_name": "Clase",
"timestamp": "10/30/2022 07:24:58",
"content": ".close",
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"timestamp": "10/30/2022 07:24:58",
"content": "Channel closed",
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] | help-9 | 719bfc40e476476bbbb9d5e9cd7af895 |
200,921 | [
{
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"id": 1066429662470885400,
"author_id": 731345746326192100,
"author_name": "ResetNew19",
"timestamp": "01/21/2023 13:50:44",
"content": "Area of a sector. Formula is A=1/2thetar^2. I just need to know how to switch the equation around to find the radius, as well as theta",
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"timestamp": "01/21/2023 13:54:18",
"content": "If you meant this, you can do following manipulations",
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"timestamp": "01/21/2023 13:54:27",
"content": "*When theta is in radiants",
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"id": 1066431005591879800,
"author_id": 951190447185875000,
"author_name": "MathIsAlwaysRight",
"timestamp": "01/21/2023 13:56:05",
"content": "Do you understand all the steps?",
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"id": 1066431109325390000,
"author_id": 731345746326192100,
"author_name": "ResetNew19",
"timestamp": "01/21/2023 13:56:29",
"content": "Give me a sec to look over it",
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},
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"id": 1066431125867741300,
"author_id": 600510288067952600,
"author_name": "GarlicBredFries",
"timestamp": "01/21/2023 13:56:33",
"content": "please do not just give answers",
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"timestamp": "01/21/2023 13:57:30",
"content": "I deleted the formula for theta. You will have to find it yourself :)",
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"timestamp": "01/21/2023 13:57:51",
"content": "It shouldn't be that hard if you look at the radius example",
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"id": 1066431948794363900,
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"author_name": "ResetNew19",
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"content": "is it 2a/r^2=theta?",
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"content": "Exactly! Great job",
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"timestamp": "01/21/2023 14:00:08",
"content": "Thank you!!!",
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{
"id": 1066432297882108000,
"author_id": 307914411648090100,
"author_name": "Stephen",
"timestamp": "01/21/2023 14:01:13",
"content": "Raijinmaru",
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"id": 1066432556809072800,
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"author_name": "ResetNew19",
"timestamp": "01/21/2023 14:02:14",
"content": "So you can also use this if theta is in degree measurement. You will just have to convert at the end?",
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"id": 1066434739042533500,
"author_id": 704213466193592300,
"author_name": "McMystix",
"timestamp": "01/21/2023 14:10:55",
"content": "no",
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"id": 1066434766586511500,
"author_id": 704213466193592300,
"author_name": "McMystix",
"timestamp": "01/21/2023 14:11:01",
"content": "rad only",
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"id": 1066435922507337900,
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"author_name": "ResetNew19",
"timestamp": "01/21/2023 14:15:37",
"content": "Ok I get it thank you for all the help!!",
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"timestamp": "01/21/2023 14:30:37",
"content": "@ResetNew19 Has your question been resolved?",
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"author_name": "Mathematics Bot",
"timestamp": "01/21/2023 14:43:16",
"content": "Channel closed",
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}
] | help-9 | 5e8f492cb4f84d90b8e7d505ad032d58 |
200,922 | [
{
"id": 1066444851752751100,
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"timestamp": "01/21/2023 14:51:06",
"content": "Available help channel!",
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{
"id": 1066445027770904700,
"author_id": 313298495417221100,
"author_name": "avidrunner",
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"id": 1066445030019051800,
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"timestamp": "01/21/2023 14:51:48",
"content": "Pinned a message.",
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"author_id": 313298495417221100,
"author_name": "avidrunner",
"timestamp": "01/21/2023 14:52:11",
"content": "Trying to prove this identity, but I lost a sec(theta) somewhere",
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"id": 1066446123679633400,
"author_id": 313298495417221100,
"author_name": "avidrunner",
"timestamp": "01/21/2023 14:56:09",
"content": "Oh..",
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},
{
"id": 1066446158311993300,
"author_id": 313298495417221100,
"author_name": "avidrunner",
"timestamp": "01/21/2023 14:56:17",
"content": "I messed up with denominator",
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"id": 1066446204134760600,
"author_id": 313298495417221100,
"author_name": "avidrunner",
"timestamp": "01/21/2023 14:56:28",
"content": "Should be cos^2(theta)",
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"id": 1066446998737272800,
"author_id": 313298495417221100,
"author_name": "avidrunner",
"timestamp": "01/21/2023 14:59:38",
"content": "Solved it",
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"id": 1066447059290439800,
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"author_name": "avidrunner",
"timestamp": "01/21/2023 14:59:52",
"content": ".close",
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"id": 1066447062469709800,
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"author_name": "Mathematics Bot",
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"content": "Channel closed",
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] | help-9 | 771466e2f9c8443b9e9d205bedd5b3e7 |
200,923 | [
{
"id": 1066447559637348400,
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"timestamp": "01/21/2023 15:01:51",
"content": "Available help channel!",
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},
{
"id": 1066447721667502100,
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"author_name": "TheWigles",
"timestamp": "01/21/2023 15:02:30",
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"content": "Pinned a message.",
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"id": 1066447757411373000,
"author_id": 796320020963262500,
"author_name": "TheWigles",
"timestamp": "01/21/2023 15:02:39",
"content": "8th grade math, congruent triangles",
"attachments": [],
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},
{
"id": 1066447782367465600,
"author_id": 796320020963262500,
"author_name": "TheWigles",
"timestamp": "01/21/2023 15:02:44",
"content": "@Helpers",
"attachments": [],
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},
{
"id": 1066447861937615000,
"author_id": 1062114268922790000,
"author_name": "flag",
"timestamp": "01/21/2023 15:03:03",
"content": "What do you need help with",
"attachments": [],
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},
{
"id": 1066447903561883800,
"author_id": 796320020963262500,
"author_name": "TheWigles",
"timestamp": "01/21/2023 15:03:13",
"content": "this one",
"attachments": [],
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},
{
"id": 1066448106398433400,
"author_id": 796320020963262500,
"author_name": "TheWigles",
"timestamp": "01/21/2023 15:04:02",
"content": "I have to determine if the given triangles are congruent by SSS (side side side), SAS (side angle side), etc",
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{
"id": 1066448127915212800,
"author_id": 796320020963262500,
"author_name": "TheWigles",
"timestamp": "01/21/2023 15:04:07",
"content": "every number",
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},
{
"id": 1066448184802558200,
"author_id": 630849659660927100,
"author_name": "SPS",
"timestamp": "01/21/2023 15:04:20",
"content": "yeah but what do you not know?",
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},
{
"id": 1066448238074409100,
"author_id": 796320020963262500,
"author_name": "TheWigles",
"timestamp": "01/21/2023 15:04:33",
"content": "idk how to determine them",
"attachments": [],
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"reference": null
},
{
"id": 1066448302016561200,
"author_id": 630849659660927100,
"author_name": "SPS",
"timestamp": "01/21/2023 15:04:48",
"content": "you know what the acronyms stand for right?",
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},
{
"id": 1066448323042607200,
"author_id": 796320020963262500,
"author_name": "TheWigles",
"timestamp": "01/21/2023 15:04:53",
"content": "yep",
"attachments": [],
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},
{
"id": 1066448443939225700,
"author_id": 630849659660927100,
"author_name": "SPS",
"timestamp": "01/21/2023 15:05:22",
"content": "Alr so for the first one",
"attachments": [],
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},
{
"id": 1066448468157141000,
"author_id": 796320020963262500,
"author_name": "TheWigles",
"timestamp": "01/21/2023 15:05:28",
"content": "I'm just confused on what to look for in the triangle to be able to determine which it is congruent with",
"attachments": [],
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"reference": null
},
{
"id": 1066448600407740400,
"author_id": 630849659660927100,
"author_name": "SPS",
"timestamp": "01/21/2023 15:05:59",
"content": "so for the first one",
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},
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"id": 1066448673921323100,
"author_id": 630849659660927100,
"author_name": "SPS",
"timestamp": "01/21/2023 15:06:17",
"content": "it gives us that there is one pair of congruent angles and one pair of congruent sides",
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"id": 1066448836165374000,
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"author_name": "SPS",
"timestamp": "01/21/2023 15:06:56",
"content": "if you know the vertical angle theorem",
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"id": 1066448904259911800,
"author_id": 630849659660927100,
"author_name": "SPS",
"timestamp": "01/21/2023 15:07:12",
"content": "then you chouble be able to conclude that those angles are congruent as well",
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"id": 1066448928284876800,
"author_id": 630849659660927100,
"author_name": "SPS",
"timestamp": "01/21/2023 15:07:18",
"content": "so we have ASA",
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"id": 1066449053874925600,
"author_id": 796320020963262500,
"author_name": "TheWigles",
"timestamp": "01/21/2023 15:07:48",
"content": "oh",
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"id": 1066449127866642600,
"author_id": 796320020963262500,
"author_name": "TheWigles",
"timestamp": "01/21/2023 15:08:05",
"content": "do u have um any notes abt this topic?",
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"id": 1066449155981058000,
"author_id": 796320020963262500,
"author_name": "TheWigles",
"timestamp": "01/21/2023 15:08:12",
"content": "ty for explaining btw",
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"id": 1066449223459033200,
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"author_name": "TheWigles",
"timestamp": "01/21/2023 15:08:28",
"content": "I was absent during the day and I don't have any friends so I can't ask for notes",
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"timestamp": "01/21/2023 15:23:28",
"content": "@TheWigles Has your question been resolved?",
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"timestamp": "01/21/2023 15:26:41",
"content": "Channel closed",
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] | help-9 | 2b16b0f18a394f1f90249e90c8349dd2 |
200,924 | [
{
"id": 1066454061559316600,
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"author_name": "Mathematics Bot",
"timestamp": "01/21/2023 15:27:42",
"content": "Available help channel!",
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},
{
"id": 1066454374831882400,
"author_id": 998702837934596200,
"author_name": "user23",
"timestamp": "01/21/2023 15:28:56",
"content": "if x+1/2x=3\nwhat is the value of 4x^2+1/x^2",
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},
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"id": 1066454376908075000,
"author_id": 805217272087838700,
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"timestamp": "01/21/2023 15:28:57",
"content": "Pinned a message.",
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"author_id": 845183482782679000,
"author_name": "ÆNex",
"timestamp": "01/21/2023 15:29:39",
"content": "Hello, How can I help?",
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},
{
"id": 1066454646480183400,
"author_id": 752737032694005900,
"author_name": "barometer",
"timestamp": "01/21/2023 15:30:01",
"content": "!help",
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"name": "ÆNex",
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"nickname": "ÆNex",
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{
"id": 1066454647549743400,
"author_id": 805217272087838700,
"author_name": "Mathematics Bot",
"timestamp": "01/21/2023 15:30:01",
"content": "Please read #❓how-to-get-help",
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},
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"id": 1066454753799839700,
"author_id": 752737032694005900,
"author_name": "barometer",
"timestamp": "01/21/2023 15:30:27",
"content": "> Show your work, and if possible, explain where you are stuck.",
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"id": 1066455047963168900,
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"author_name": "user23",
"timestamp": "01/21/2023 15:31:37",
"content": "i am kinda stuck on where to start",
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"author_name": "user23",
"timestamp": "01/21/2023 15:31:58",
"content": "i think they meant how can they help me lol",
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"author_id": 845183482782679000,
"author_name": "ÆNex",
"timestamp": "01/21/2023 15:32:06",
"content": "yeah",
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"id": 1066455196173086800,
"author_id": 752737032694005900,
"author_name": "barometer",
"timestamp": "01/21/2023 15:32:12",
"content": "you're right 😭",
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"author_id": 845183482782679000,
"author_name": "ÆNex",
"timestamp": "01/21/2023 15:32:22",
"content": "LoL",
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"author_name": "user23",
"timestamp": "01/21/2023 15:33:16",
"content": "i tried to whole square it and i got that x^2+1/4x^2=8 but its not what i wanted",
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"id": 1066455707798474900,
"author_id": 518716603928543200,
"author_name": "𝓐𝓡𝓝𝓐𝓑 𝓟𝓐𝓛",
"timestamp": "01/21/2023 15:34:14",
"content": "Remember \n$x+\\frac{1}{2x}=\\frac{2x²+1}{2x}$",
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"id": 1066455717587988500,
"author_id": 510789298321096700,
"author_name": "TeXit",
"timestamp": "01/21/2023 15:34:16",
"content": "**Arnab**",
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"author_id": 518716603928543200,
"author_name": "𝓐𝓡𝓝𝓐𝓑 𝓟𝓐𝓛",
"timestamp": "01/21/2023 15:35:20",
"content": "Then $2x+\\frac{1}{x}=3×6$",
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"id": 1066456041233064100,
"author_id": 510789298321096700,
"author_name": "TeXit",
"timestamp": "01/21/2023 15:35:34",
"content": "**Arnab**",
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"author_name": "𝓐𝓡𝓝𝓐𝓑 𝓟𝓐𝓛",
"timestamp": "01/21/2023 15:36:37",
"content": "Cause $\\frac{2x²+1}{x}=\\frac{2x²}{x}+\\frac{1}{x}$",
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"id": 1066456314122883200,
"author_id": 510789298321096700,
"author_name": "TeXit",
"timestamp": "01/21/2023 15:36:39",
"content": "**Arnab**",
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"author_id": 518716603928543200,
"author_name": "𝓐𝓡𝓝𝓐𝓑 𝓟𝓐𝓛",
"timestamp": "01/21/2023 15:36:47",
"content": "Got it?@user23",
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"author_id": 518716603928543200,
"author_name": "𝓐𝓡𝓝𝓐𝓑 𝓟𝓐𝓛",
"timestamp": "01/21/2023 15:36:55",
"content": "You have this approach",
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"id": 1066456703949881300,
"author_id": 998702837934596200,
"author_name": "user23",
"timestamp": "01/21/2023 15:38:12",
"content": "i think i know how to do it now",
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"id": 1066456739500789800,
"author_id": 518716603928543200,
"author_name": "𝓐𝓡𝓝𝓐𝓑 𝓟𝓐𝓛",
"timestamp": "01/21/2023 15:38:20",
"content": "Great",
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"id": 1066456780755959800,
"author_id": 518716603928543200,
"author_name": "𝓐𝓡𝓝𝓐𝓑 𝓟𝓐𝓛",
"timestamp": "01/21/2023 15:38:30",
"content": "Just square it",
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"author_name": "𝓐𝓡𝓝𝓐𝓑 𝓟𝓐𝓛",
"timestamp": "01/21/2023 15:38:46",
"content": "You will get 4x²+1/x² which you need the most",
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"id": 1066456948779778300,
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"author_name": "user23",
"timestamp": "01/21/2023 15:39:10",
"content": "ty",
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},
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"id": 1066456956342128600,
"author_id": 998702837934596200,
"author_name": "user23",
"timestamp": "01/21/2023 15:39:12",
"content": ".close",
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"id": 1066456959366209500,
"author_id": 805217272087838700,
"author_name": "Mathematics Bot",
"timestamp": "01/21/2023 15:39:12",
"content": "Channel closed",
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}
] | help-9 | c61914715db047ffa51ceba33ae147fb |
200,925 | [
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"id": 1066461723562881200,
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"author_name": "Mathematics Bot",
"timestamp": "01/21/2023 15:58:08",
"content": "Available help channel!",
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},
{
"id": 1066461983295164500,
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"author_name": "bluefire",
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"timestamp": "01/21/2023 15:59:11",
"content": "Pinned a message.",
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"id": 1066462044120956900,
"author_id": 725008982519054300,
"author_name": "bluefire",
"timestamp": "01/21/2023 15:59:25",
"content": "How would I solve this problem?",
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{
"id": 1066462108549660800,
"author_id": 725008982519054300,
"author_name": "bluefire",
"timestamp": "01/21/2023 15:59:40",
"content": "I understand the first step is finding the base case(n=1) and plugging it in which is 4",
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"id": 1066462186421100500,
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"author_name": "bluefire",
"timestamp": "01/21/2023 15:59:59",
"content": "that checks out to be an integer",
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"id": 1066462226380230700,
"author_id": 725008982519054300,
"author_name": "bluefire",
"timestamp": "01/21/2023 16:00:08",
"content": "step 2 would be to set n=k",
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"id": 1066462301441499400,
"author_id": 725008982519054300,
"author_name": "bluefire",
"timestamp": "01/21/2023 16:00:26",
"content": "making it (9^k + 24k + 15)/48 for a fixed integer k >= 1",
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"id": 1066462383813439600,
"author_id": 725008982519054300,
"author_name": "bluefire",
"timestamp": "01/21/2023 16:00:46",
"content": "step 3 would be to set n = k + 1",
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"id": 1066462501652410500,
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"author_name": "bluefire",
"timestamp": "01/21/2023 16:01:14",
"content": "making it (9^(k+1) + 24(k + 1) + 15)/48",
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"id": 1066462544664998000,
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"author_name": "bluefire",
"timestamp": "01/21/2023 16:01:24",
"content": "Now how would I prove this is an integer?",
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"id": 1066462636507676700,
"author_id": 217089972933623800,
"author_name": "maximo",
"timestamp": "01/21/2023 16:01:46",
"content": "show that it is divisible by 48",
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"id": 1066462750303326300,
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"author_name": "bluefire",
"timestamp": "01/21/2023 16:02:13",
"content": "Ok",
"attachments": [],
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"id": 1066462794330935400,
"author_id": 217089972933623800,
"author_name": "maximo",
"timestamp": "01/21/2023 16:02:24",
"content": "meaning show the numerator is divisible by 48",
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"id": 1066463023792934900,
"author_id": 375373128202977300,
"author_name": "RPNATOR",
"timestamp": "01/21/2023 16:03:18",
"content": "break this down into 8.9^k+24+(9^k+24k+15)",
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"timestamp": "01/21/2023 16:03:40",
"content": "the part within the brackets is obviously divisible by 48 through the inductive hypothesis",
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"id": 1066463210699501600,
"author_id": 375373128202977300,
"author_name": "RPNATOR",
"timestamp": "01/21/2023 16:04:03",
"content": "so now all that remains is to show that 8.9^k+24 is a multiple of 48",
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"id": 1066463301187420300,
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"author_name": "bluefire",
"timestamp": "01/21/2023 16:04:24",
"content": "8.9?",
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"id": 1066463325904449700,
"author_id": 217089972933623800,
"author_name": "maximo",
"timestamp": "01/21/2023 16:04:30",
"content": "8*9",
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"id": 1066463460029894800,
"author_id": 375373128202977300,
"author_name": "RPNATOR",
"timestamp": "01/21/2023 16:05:02",
"content": "9^(k+1) can be written as 9.9^k ( 9 times 9^k )",
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"id": 1066463534428471300,
"author_id": 725008982519054300,
"author_name": "bluefire",
"timestamp": "01/21/2023 16:05:20",
"content": "Ok yeah I agree",
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"id": 1066463558617006100,
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"author_name": "RPNATOR",
"timestamp": "01/21/2023 16:05:26",
"content": "just break the 9 in front to 8+1",
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"id": 1066463561280389100,
"author_id": 375373128202977300,
"author_name": "RPNATOR",
"timestamp": "01/21/2023 16:05:26",
"content": "ye",
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"id": 1066463589554192500,
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"author_name": "bluefire",
"timestamp": "01/21/2023 16:05:33",
"content": "Ok",
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"timestamp": "01/21/2023 16:06:05",
"content": "alternative you are to show that 8.9^k on dividing by 48 gives you a remainder of 24",
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"timestamp": "01/21/2023 16:08:02",
"content": "you can apply induction again if you want to, along with a bit of congruency\n8.9^k = 24 mod 48 (assume)\n8.9^(k+1) = 8.9.9^k= 9.24 mod 48= 24 mod 48 again",
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"id": 1066464287452844000,
"author_id": 725008982519054300,
"author_name": "bluefire",
"timestamp": "01/21/2023 16:08:20",
"content": "ok",
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"id": 1066464351550193800,
"author_id": 375373128202977300,
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"timestamp": "01/21/2023 16:08:35",
"content": "if you want there are intuitive explanations for this as well, it's just that congruency helps formalize stuff much better",
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"id": 1066464395166765000,
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"author_name": "RPNATOR",
"timestamp": "01/21/2023 16:08:45",
"content": "so that completes your proof",
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"timestamp": "01/21/2023 16:08:58",
"content": "Ok thanks",
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},
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"id": 1066464487441453000,
"author_id": 375373128202977300,
"author_name": "RPNATOR",
"timestamp": "01/21/2023 16:09:07",
"content": "cool",
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"id": 1066464516512174200,
"author_id": 725008982519054300,
"author_name": "bluefire",
"timestamp": "01/21/2023 16:09:14",
"content": ".close",
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"id": 1066464519376883700,
"author_id": 805217272087838700,
"author_name": "Mathematics Bot",
"timestamp": "01/21/2023 16:09:15",
"content": "Channel closed",
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}
] | help-9 | 9b0fb9cf718545cd88d629b36f72a98e |
200,926 | [
{
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"timestamp": "01/21/2023 16:10:15",
"content": "Available help channel!",
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},
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"timestamp": "01/21/2023 16:27:36",
"content": "i am trying to solve this one",
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},
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"id": 1066469192481648800,
"author_id": 1061917325470728200,
"author_name": "Klaus v3",
"timestamp": "01/21/2023 16:27:49",
"content": "confused how to calculate this",
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},
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"id": 1066469279869972500,
"author_id": 1061917325470728200,
"author_name": "Klaus v3",
"timestamp": "01/21/2023 16:28:10",
"content": "did i partially solve it?",
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"id": 1066469455019909200,
"author_id": 1061917325470728200,
"author_name": "Klaus v3",
"timestamp": "01/21/2023 16:28:52",
"content": "it says V is a vector space",
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"id": 1066469475194523600,
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"author_name": "Klaus v3",
"timestamp": "01/21/2023 16:28:56",
"content": "u1 u2 is the basis",
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"timestamp": "01/21/2023 16:29:02",
"content": "and calculate",
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"timestamp": "01/21/2023 16:29:36",
"content": "x1 x2 are numbers i assume",
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"author_id": 132304137583984640,
"author_name": "Denascite",
"timestamp": "01/21/2023 16:30:46",
"content": "you could rearrange to get (something)\\*u_1 + (something) \\* u_2",
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"author_name": "Klaus v3",
"timestamp": "01/21/2023 16:31:00",
"content": "herausheben?",
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"id": 1066469992033435600,
"author_id": 132304137583984640,
"author_name": "Denascite",
"timestamp": "01/21/2023 16:31:00",
"content": "but that's as far as you can go",
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"timestamp": "01/21/2023 16:31:11",
"content": "ah so i did it right?",
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"author_name": "Klaus v3",
"timestamp": "01/21/2023 16:33:15",
"content": "@Denascitebtw can you check this",
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"author_id": 1010570867169820800,
"author_name": "Tomasss",
"timestamp": "01/21/2023 16:33:19",
"content": "Hi everyone, I need a help please. I'm trying to demonstrate why when you do -1 * both sides of inequality you have to change the direction of inequality. I started from this \n0<=a and 0<=b => 0<=a*b\nAnd I used (a<=b => a+c<=b+c) -a*b as c and it changes to -a*b<=a*b-a*b and after some steps it goes into -a*b<=0. Is this right? because axioms says it with opposite number but I used more than one number.",
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"author_name": "Klaus v3",
"timestamp": "01/21/2023 16:33:25",
"content": "here i am trying to proof that b) is lineare Abbildung",
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"timestamp": "01/21/2023 16:33:44",
"content": "copy and paste this into an empty help channel pls",
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"author_name": "Klaus v3",
"timestamp": "01/21/2023 16:33:48",
"content": "this one is occupied",
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"author_name": "Tomasss",
"timestamp": "01/21/2023 16:33:56",
"content": "Ok sorry",
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},
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"id": 1066472069140860900,
"author_id": 334482942506041340,
"author_name": "Zybikron",
"timestamp": "01/21/2023 16:39:15",
"content": "pretty sure that proof of f(u)+f(v) = f(u+v) doesn't work",
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},
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"id": 1066474474079269000,
"author_id": 805217272087838700,
"author_name": "Mathematics Bot",
"timestamp": "01/21/2023 16:48:48",
"content": "@Klaus v3 Has your question been resolved?",
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"timestamp": "01/21/2023 17:03:49",
"content": "Channel closed",
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}
] | help-9 | e4436bcfbc764c1d99d6e3cbd5f40343 |
200,927 | [
{
"id": 1066478307425652700,
"author_id": 132304137583984640,
"author_name": "Denascite",
"timestamp": "01/21/2023 17:04:02",
"content": ".reopen",
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},
{
"id": 1066478325721202800,
"author_id": 132304137583984640,
"author_name": "Denascite",
"timestamp": "01/21/2023 17:04:07",
"content": ".reopen",
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},
{
"id": 1066478332557918200,
"author_id": 805217272087838700,
"author_name": "Mathematics Bot",
"timestamp": "01/21/2023 17:04:08",
"content": "✅",
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},
{
"id": 1066478384219173000,
"author_id": 132304137583984640,
"author_name": "Denascite",
"timestamp": "01/21/2023 17:04:21",
"content": "spoiler the function isn't linear",
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},
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"id": 1066478409955409900,
"author_id": 132304137583984640,
"author_name": "Denascite",
"timestamp": "01/21/2023 17:04:27",
"content": "you didn't plug f(u+v) in correctly",
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},
{
"id": 1066478507263283200,
"author_id": 132304137583984640,
"author_name": "Denascite",
"timestamp": "01/21/2023 17:04:50",
"content": "the first coordinate would be (u1+v1)(u2+v2)",
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"id": 1066478642521178200,
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"timestamp": "01/21/2023 17:05:22",
"content": "@Klaus v3",
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"author_name": "Denascite",
"timestamp": "01/21/2023 17:06:02",
"content": "similarly for f(lambda v) it would be (lambda v1)*(lambda v2)",
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"author_name": "Klaus v3",
"timestamp": "01/21/2023 17:10:37",
"content": "😭",
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"id": 1066479970001621000,
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"author_name": "Klaus v3",
"timestamp": "01/21/2023 17:10:39",
"content": "what",
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"id": 1066480027690082400,
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"author_name": "Klaus v3",
"timestamp": "01/21/2023 17:10:52",
"content": "b isn't linear?",
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"timestamp": "01/21/2023 17:13:46",
"content": "pls show how you proof if it's a lineare Abbildung or not",
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"timestamp": "01/21/2023 17:13:49",
"content": "@Denascite",
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"timestamp": "01/21/2023 17:13:57",
"content": "this is important",
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"author_name": "Klaus v3",
"timestamp": "01/21/2023 17:15:46",
"content": "i was trying to proof it the same way as on the slides",
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"id": 1066481326443745400,
"author_id": 1061917325470728200,
"author_name": "Klaus v3",
"timestamp": "01/21/2023 17:16:02",
"content": "why doesn'T it work in our case?",
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"author_name": "Klaus v3",
"timestamp": "01/21/2023 17:16:44",
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"author_name": "Klaus v3",
"timestamp": "01/21/2023 17:16:46",
"content": "these are the 2 conditions",
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"author_name": "Mathematics Bot",
"timestamp": "01/21/2023 17:31:46",
"content": "@Klaus v3 Has your question been resolved?",
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"author_id": 132304137583984640,
"author_name": "Denascite",
"timestamp": "01/21/2023 17:43:49",
"content": "let u=(1,1). calculate 2f(u) and f(2u)",
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"id": 1066488374866739300,
"author_id": 132304137583984640,
"author_name": "Denascite",
"timestamp": "01/21/2023 17:44:02",
"content": "or let u=(1,1) and v=(2,2). calculate f(u+v) and f(u)+f(v)",
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"timestamp": "01/21/2023 18:02:07",
"content": "@Klaus v3 Has your question been resolved?",
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"timestamp": "01/21/2023 18:32:07",
"content": "Channel closed",
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}
] | help-9 | 1ede47d2e130428e96f22ac07ac61b3e |
200,928 | [
{
"id": 1066500725405913200,
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"author_name": "Mathematics Bot",
"timestamp": "01/21/2023 18:33:07",
"content": "Available help channel!",
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},
{
"id": 1066501233344516100,
"author_id": 849961886874730500,
"author_name": "SA2017",
"timestamp": "01/21/2023 18:35:08",
"content": "@chartbit sry to ping",
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"id": 1066501235424903200,
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"timestamp": "01/21/2023 18:35:09",
"content": "Pinned a message.",
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"id": 1066501251501666400,
"author_id": 849961886874730500,
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"timestamp": "01/21/2023 18:35:12",
"content": "u know what we did earlier",
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"id": 1066501278445875200,
"author_id": 849961886874730500,
"author_name": "SA2017",
"timestamp": "01/21/2023 18:35:19",
"content": "with e and M - N proofs",
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},
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"id": 1066501441432326100,
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"timestamp": "01/21/2023 18:36:07",
"content": "were we using the sandwich theorem here?",
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"id": 1066502402850701400,
"author_id": 788085606483361800,
"author_name": "chartbit",
"timestamp": "01/21/2023 18:39:47",
"content": "Hmmmm, well yes and no :catGiggle:\nFor this one there's a similar theorem where you can prove that if you have, say, $a_{n} \\geq b_{n}$ and $b_{n} \\to \\infty$ then $a_{n} \\to \\infty$ (it really isn't too hard to show)",
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"id": 1066502414682824800,
"author_id": 510789298321096700,
"author_name": "TeXit",
"timestamp": "01/21/2023 18:39:50",
"content": "**chartbit**",
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"timestamp": "01/21/2023 18:40:21",
"content": "what the hekk",
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},
{
"id": 1066502574213177500,
"author_id": 849961886874730500,
"author_name": "SA2017",
"timestamp": "01/21/2023 18:40:28",
"content": "cat giggle 6269372193792139037",
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},
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"id": 1066502587186167800,
"author_id": 849961886874730500,
"author_name": "SA2017",
"timestamp": "01/21/2023 18:40:31",
"content": ":kekw:",
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"timestamp": "01/21/2023 18:40:31",
"content": "Nice cat giggle",
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"content": "Of course we \"already know\" that $\\frac{\\sqrt{n}}{2}$ diverges to $\\infty$, so we could have been done there, but we wanted a $M - N$ proof so did it explicitly",
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"content": "ye i see",
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"content": "Funny thing is I didn't intend to use $\\LaTeX$ then changed my way midway so then forgot to remove the cat emote :kekw:",
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"timestamp": "01/21/2023 18:47:51",
"content": "how did they get 4/n here?",
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"content": "$3n - 2 > n$ implies that $\\frac{1}{n} > \\frac{1}{3n - 2}$",
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"content": "**chartbit**",
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"timestamp": "01/21/2023 18:51:15",
"content": "how can 3n -2 > n?",
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"timestamp": "01/21/2023 18:51:17",
"content": "if n is 1",
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"timestamp": "01/21/2023 18:51:20",
"content": "1> 1",
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"timestamp": "01/21/2023 18:51:23",
"content": "doesnt make sense",
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"id": 1066505596406345700,
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"author_name": "chartbit",
"timestamp": "01/21/2023 18:52:28",
"content": "Should have been a nonstrict inequality tbf, or they should have stated \"for all n>=2\" or something",
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"timestamp": "01/21/2023 18:53:14",
"content": "Remember how I stressed so much to make sure you make it clear that if you pick a \"minimum\" for an inequality to hold, you must state it?",
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"timestamp": "01/21/2023 18:53:24",
"content": "yh lmao",
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"timestamp": "01/21/2023 18:53:51",
"content": "Yep don't be like these jokemans :catThimc:",
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"id": 1066506295714267300,
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"timestamp": "01/21/2023 18:55:15",
"content": "my LNs r ass",
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"timestamp": "01/21/2023 18:55:20",
"content": "lecture notes",
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"timestamp": "01/21/2023 19:03:43",
"content": "could we not have just kept it as 4/ (3n-2)?",
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"id": 1066508463653519500,
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"timestamp": "01/21/2023 19:03:52",
"content": "instead of changing it to 2 + 4/n",
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"timestamp": "01/21/2023 19:06:07",
"content": "Well, you could have tbh, as you know it goes to zero anyway, but I think they wanted to use something you're \"familiar\" with, if you get me?",
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"content": "ye ok ok",
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"content": "chartbit seems like we have an intruder",
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"content": "https://tenor.com/view/kazookid-wait-a-minute-who-are-you-wait-a-minute-who-are-you-gif-8850963",
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"content": "Where are you even getting that from(?)",
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"content": "sigh",
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"id": 1066511750859608000,
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"timestamp": "01/21/2023 19:16:56",
"content": "...anyways, back to where we were...",
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"timestamp": "01/21/2023 19:28:41",
"content": "@SA2017 Has your question been resolved?",
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] | help-9 | edee57ce71964f2f94e52249517e9d31 |
200,929 | [
{
"id": 1066539471081853000,
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"timestamp": "01/21/2023 21:07:05",
"content": "Available help channel!",
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{
"id": 1066541920186286100,
"author_id": 402545906718605300,
"author_name": "Jash",
"timestamp": "01/21/2023 21:16:49",
"content": "how can i rationalize 1/[ cbrt(3)-1 ]",
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"author_name": "ramonov",
"timestamp": "01/21/2023 21:22:38",
"content": "the denominator can be rationalised by considering the factorisation for a difference of two cubes",
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"id": 1066543713465155600,
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"timestamp": "01/21/2023 21:23:56",
"content": "What is that",
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"id": 1066543789449167000,
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"timestamp": "01/21/2023 21:24:14",
"content": "try looking it up",
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"author_name": "Jash",
"timestamp": "01/21/2023 21:26:10",
"content": "i got a³-b³=(a-b)(a²+ab+b²)",
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"timestamp": "01/21/2023 21:26:27",
"content": "yeh use that",
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"author_name": "ramonov",
"timestamp": "01/21/2023 21:26:58",
"content": "knowing that what could you do to your fraction that would result in a rational denominator",
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"id": 1066544716046409900,
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"timestamp": "01/21/2023 21:27:55",
"content": "i think it would result in cbrt(3)³-1³",
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"timestamp": "01/21/2023 21:28:26",
"content": "not quite what I was asking",
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"timestamp": "01/21/2023 21:28:48",
"content": "Multiply it by a²+ab+b²",
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"timestamp": "01/21/2023 21:29:16",
"content": "you multiply numerator and denominator by that",
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"timestamp": "01/21/2023 21:29:54",
"content": "Ye",
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"timestamp": "01/21/2023 21:31:04",
"content": "so i make substitution that a=cbrt(3) and b=1",
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"timestamp": "01/21/2023 21:41:36",
"content": ".close",
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] | help-9 | 9be9395881a542eb94471bd9bb3f717e |
200,930 | [
{
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{
"id": 1066576681118220400,
"author_id": 743681516197904500,
"author_name": "Кураптор",
"timestamp": "01/21/2023 23:34:56",
"content": "If 𝑓(𝑥) is a linear function such that 𝑓(2) = 8, and 𝑓(11) = 35, what is the value of 𝑓(0)?",
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"content": "Pinned a message.",
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"id": 1066578770905026600,
"author_id": 761095788960284700,
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"timestamp": "01/21/2023 23:43:15",
"content": "y=mx+c",
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},
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"id": 1066578816723603500,
"author_id": 761095788960284700,
"author_name": "fantastic mr. fox",
"timestamp": "01/21/2023 23:43:25",
"content": "you have 2 equation find m and c",
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"timestamp": "01/21/2023 23:49:57",
"content": "@Кураптор Has your question been resolved?",
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"timestamp": "01/21/2023 23:50:03",
"content": "Channel closed",
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}
] | help-9 | 1a16f2e3d6c24943bd12cd122f5f62c4 |
200,931 | [
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"timestamp": "10/30/2022 07:31:18",
"content": "how can i prove that the root thing evaluates to 1 at minimum and can't go below 1?",
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"timestamp": "10/30/2022 07:31:45",
"content": "i was thinking about limits but im not sure how to prove it",
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"id": 1036241080762511500,
"author_id": 984319941417251000,
"author_name": "💜𝓁𝒶𝓎𝓁𝒶💜",
"timestamp": "10/30/2022 07:32:06",
"content": "The inside is always >1",
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"author_name": "💜𝓁𝒶𝓎𝓁𝒶💜",
"timestamp": "10/30/2022 07:32:43",
"content": "Induction be the easiest way",
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"timestamp": "10/30/2022 07:32:43",
"content": "this may be of use",
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"author_name": "Milky Ware",
"timestamp": "10/30/2022 07:34:30",
"content": "thank you! ill try to prove it by induction. the first step is a0=2022 right? Then for an and generalize for an+1",
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"id": 1036241775502835700,
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"author_name": "xHqrry",
"timestamp": "10/30/2022 07:34:51",
"content": "for (b) maybe try to express the equation in terms of a(n) - a(n+1) = something or anything similar to that",
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"id": 1036241852724162600,
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"author_name": "💜𝓁𝒶𝓎𝓁𝒶💜",
"timestamp": "10/30/2022 07:35:10",
"content": "It mostly just comes down to (3*a_n^2 - 1)/2 is greater than 1 if a_n > 1",
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"author_name": "Milky Ware",
"timestamp": "10/30/2022 07:36:49",
"content": "can i do `a(n)/a(n+1) > 1 `?",
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"timestamp": "10/30/2022 07:38:07",
"content": "if that works, you can do that as well",
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"timestamp": "10/30/2022 07:38:20",
"content": "thanks",
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},
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"id": 1036242765710905300,
"author_id": 794866187996495900,
"author_name": "xHqrry",
"timestamp": "10/30/2022 07:38:47",
"content": "actually, yea i think a_n/a_n+1 is easier",
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"timestamp": "10/30/2022 07:53:20",
"content": "@Milky Ware Has your question been resolved?",
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"content": ".close",
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"content": "Channel closed",
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] | help-9 | 1066477348764cef978ca3d5819d95ff |
200,932 | [
{
"id": 1066593273516409000,
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"author_name": "Mathematics Bot",
"timestamp": "01/22/2023 00:40:52",
"content": "Available help channel!",
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},
{
"id": 1066593581374128100,
"author_id": 175989134421131260,
"author_name": "Marco.",
"timestamp": "01/22/2023 00:42:06",
"content": "What is the inverse of a vector of 1s?",
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},
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"id": 1066593583387381800,
"author_id": 805217272087838700,
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"author_id": 175989134421131260,
"author_name": "Marco.",
"timestamp": "01/22/2023 00:42:35",
"content": "bold 1 is a vector of n ones, what is bold 1' in that case?",
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},
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"id": 1066594970015891500,
"author_id": 261933205387477000,
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"content": "what kind of inverse",
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"timestamp": "01/22/2023 00:57:36",
"content": "@Marco. Has your question been resolved?",
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"timestamp": "01/22/2023 01:10:00",
"content": "my bad, I mixed up the signs",
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"timestamp": "01/22/2023 01:10:06",
"content": "its just transposed",
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"id": 1066601089413165000,
"author_id": 261933205387477000,
"author_name": "riemann",
"timestamp": "01/22/2023 01:11:56",
"content": "Row vectors become column and vice versa",
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"content": "Channel closed",
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}
] | help-9 | 0c1bcb3fb4cf4e3ab1503ccbc7ae9ef2 |
200,933 | [
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"timestamp": "01/22/2023 01:43:49",
"content": "what i have so far:",
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"content": "what's your goal here?",
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"timestamp": "01/22/2023 01:49:51",
"content": "sorry about the delay",
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"timestamp": "01/22/2023 01:49:55",
"content": "dumb imgur!",
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"timestamp": "01/22/2023 01:51:11",
"content": "i see that the image you've sent for #33 already contains the solution. is that what you are trying to reproduce?",
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"timestamp": "01/22/2023 01:52:20",
"content": "I don't understand how they got the final solution from where I am so far",
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"timestamp": "01/22/2023 01:52:43",
"content": "there must be steps omitted (again)",
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"id": 1066611375629144000,
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"author_name": "Ann",
"timestamp": "01/22/2023 01:52:48",
"content": "so you do not understand how to go from $\\frac32 x^{-1/2} + \\frac12 x^{-3/2}$ to $\\frac{3x+1}{2x^{3/2}}$?",
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"id": 1066611453165043700,
"author_id": 510789298321096700,
"author_name": "TeXit",
"timestamp": "01/22/2023 01:53:07",
"content": "**Ann**",
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"timestamp": "01/22/2023 01:53:13",
"content": "yes, exactly",
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"id": 1066611677031841800,
"author_id": 183668144404037630,
"author_name": "Ann",
"timestamp": "01/22/2023 01:54:00",
"content": "$\\frac{3}{2x^{1/2}} + \\frac{1}{2x^{3/2}} = \\frac{3x}{2x^{1/2} \\cdot x} + \\frac{1}{2x^{3/2}}$",
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"timestamp": "01/22/2023 01:54:02",
"content": "**Ann**",
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"id": 1066611941231054800,
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"timestamp": "01/22/2023 01:55:03",
"content": "ah, they multiplied by `x`",
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"id": 1066611958385737900,
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"timestamp": "01/22/2023 01:55:07",
"content": "ok, let me try that",
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"id": 1066614132062830600,
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"timestamp": "01/22/2023 02:03:45",
"content": "ok, i understand now",
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"id": 1066614135527321600,
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"timestamp": "01/22/2023 02:03:46",
"content": "ty",
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"id": 1066614476863979500,
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"author_name": "Willow",
"timestamp": "01/22/2023 02:05:08",
"content": ".close",
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"id": 1066614479531552800,
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"author_name": "Mathematics Bot",
"timestamp": "01/22/2023 02:05:08",
"content": "Channel closed",
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}
] | help-9 | 6528555fe7f94da893058391b6459fd6 |
200,934 | [
{
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"timestamp": "01/22/2023 02:24:12",
"content": "Available help channel!",
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"id": 1066624376444821500,
"author_id": 408833365404287000,
"author_name": "Hydro",
"timestamp": "01/22/2023 02:44:28",
"content": "How can I interpret this",
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"content": "Pinned a message.",
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"id": 1066624469919072300,
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"author_name": "Hydro",
"timestamp": "01/22/2023 02:44:50",
"content": "As in how can I go about solving it with given k, x and n values.",
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"id": 1066624511807606800,
"author_id": 408833365404287000,
"author_name": "Hydro",
"timestamp": "01/22/2023 02:45:00",
"content": "Treat me as a layman preferably.",
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"id": 1066624574386606100,
"author_id": 218476117101772800,
"author_name": "Sooshon",
"timestamp": "01/22/2023 02:45:15",
"content": "what are the given k, x, and n values?",
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"id": 1066624733531095000,
"author_id": 408833365404287000,
"author_name": "Hydro",
"timestamp": "01/22/2023 02:45:53",
"content": "Well they're very large but if you want them its",
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"id": 1066624776120057900,
"author_id": 984319941417251000,
"author_name": "💜𝓁𝒶𝓎𝓁𝒶💜",
"timestamp": "01/22/2023 02:46:03",
"content": "no one would do that by hand",
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"id": 1066624833376485400,
"author_id": 408833365404287000,
"author_name": "Hydro",
"timestamp": "01/22/2023 02:46:17",
"content": "Oh hang on ive gotta brb",
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},
{
"id": 1066624933217697800,
"author_id": 218476117101772800,
"author_name": "Sooshon",
"timestamp": "01/22/2023 02:46:41",
"content": "are you familiar with the notations?",
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"id": 1066624972824522800,
"author_id": 218476117101772800,
"author_name": "Sooshon",
"timestamp": "01/22/2023 02:46:50",
"content": "https://en.wikipedia.org/wiki/Binomial_coefficient",
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"id": 1066625698887909400,
"author_id": 408833365404287000,
"author_name": "Hydro",
"timestamp": "01/22/2023 02:49:43",
"content": "Not really. Do you think you could breify describe them?",
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"id": 1066626040354582500,
"author_id": 218476117101772800,
"author_name": "Sooshon",
"timestamp": "01/22/2023 02:51:04",
"content": "I don't really remember this stuff too well unfortunately, but you can read up on the binomial coefficient one on the wiki anyway",
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"author_name": "Sooshon",
"timestamp": "01/22/2023 02:51:40",
"content": "if you don't know where to start this at all, you're gonna have to read up on it in your book etc because it's not something trivial to explain over 20 seconds in a chat",
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"timestamp": "01/22/2023 02:51:53",
"content": "yeah alright",
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"author_id": 408833365404287000,
"author_name": "Hydro",
"timestamp": "01/22/2023 02:52:03",
"content": "I'm very surprised that this is the only way to solve my problem",
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"author_name": "Hydro",
"timestamp": "01/22/2023 02:53:18",
"content": "Honestly do you just wanna confirm if this really is the only way to solve my problem because it doesnt seem likely",
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"author_name": "Hydro",
"timestamp": "01/22/2023 02:54:17",
"content": "Hey frowny. Don't worry, im not doubting your method I'm just very surprised is all.",
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"timestamp": "01/22/2023 02:54:29",
"content": "i specifically said it's not an attempt to solve your problem",
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"id": 1066626936207573000,
"author_id": 408833365404287000,
"author_name": "Hydro",
"timestamp": "01/22/2023 02:54:38",
"content": "I know, its the formula I should use right?",
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"author_id": 408833365404287000,
"author_name": "Hydro",
"timestamp": "01/22/2023 02:54:55",
"content": "I can't figure out how to use it though is all.",
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"author_name": "Hydro",
"timestamp": "01/22/2023 02:56:03",
"content": "and I'm just shocked that such a seemingly simple question requires stirling numbers and stuff. Like the birthday paradox seems more complex yet it just uses way simpler math.",
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"id": 1066627433316487300,
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"author_name": "frownyfrog",
"timestamp": "01/22/2023 02:56:37",
"content": "a computer would refuse to calculate it with the numbers you showed",
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"id": 1066627479365759000,
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"timestamp": "01/22/2023 02:56:48",
"content": "hm",
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"id": 1066627529185689600,
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"timestamp": "01/22/2023 02:56:59",
"content": "probably",
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"author_name": "Hydro",
"timestamp": "01/22/2023 02:57:28",
"content": "So is there no way to figure out the value or approximate it?",
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"author_name": "Mathematics Bot",
"timestamp": "01/22/2023 03:12:28",
"content": "@Hydro Has your question been resolved?",
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"timestamp": "01/22/2023 03:27:28",
"content": "Channel closed",
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] | help-9 | f5930ca65bbd4f6cb1bf48da06c4bc2f |
200,935 | [
{
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"timestamp": "01/22/2023 04:35:20",
"content": "Available help channel!",
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"id": 1066655574512635900,
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"timestamp": "01/22/2023 04:48:26",
"content": "Can someone explain how to do arctan questions",
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"timestamp": "01/22/2023 04:50:23",
"content": "The tangent of which angle between -pi/2 and pi/2 is -1/sqrt(3)?",
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"content": "That's the part I'm struggling with",
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"author_name": "DemonicThunder",
"timestamp": "01/22/2023 04:50:50",
"content": "Do you know why is say from -pi/2 to pi/2?",
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"timestamp": "01/22/2023 04:51:09",
"content": "Yes, because after that it'd be undefined?",
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"author_name": "DemonicThunder",
"timestamp": "01/22/2023 04:51:35",
"content": "Do you remember the values of trigonometric functions for 0, pi/6, pi/4, pi/3 and pi/2?",
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"timestamp": "01/22/2023 04:51:51",
"content": "Yes, the range of arctan is defined from -pi/2 to pi/2",
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"timestamp": "01/22/2023 04:51:56",
"content": "If I take a peek... can't fully remember them",
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"author_name": "DemonicThunder",
"timestamp": "01/22/2023 04:52:12",
"content": "May I ask what grade are you in currently?",
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"id": 1066656685038514200,
"author_id": 576665017785647100,
"author_name": "lbjam",
"timestamp": "01/22/2023 04:52:51",
"content": "I'm year 12 so grade 11?",
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"author_name": "DemonicThunder",
"timestamp": "01/22/2023 04:53:03",
"content": "Fair enough",
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"id": 1066656763832705000,
"author_id": 409372165033689100,
"author_name": "DemonicThunder",
"timestamp": "01/22/2023 04:53:10",
"content": "How much trig have you done?",
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"author_name": "DemonicThunder",
"timestamp": "01/22/2023 04:53:28",
"content": "Do you know which trig function has what sign in different quadrants?",
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"timestamp": "01/22/2023 04:53:34",
"content": "My teacher just covered all of them really quickly",
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"timestamp": "01/22/2023 04:53:52",
"content": "Okay so",
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"timestamp": "01/22/2023 04:53:59",
"content": "Sign?",
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"timestamp": "01/22/2023 04:54:12",
"content": "tan(pi/6) gives +1/sqrt(3)",
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"timestamp": "01/22/2023 04:54:18",
"content": "Positive or negative",
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"timestamp": "01/22/2023 04:54:19",
"content": "Yep i got that",
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"timestamp": "01/22/2023 04:54:26",
"content": "Yeah",
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"author_name": "DemonicThunder",
"timestamp": "01/22/2023 04:54:38",
"content": "Yes, but since you have been asked for -1/sqrt(3)",
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"timestamp": "01/22/2023 04:54:46",
"content": "Your answer will be -pi/6",
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"timestamp": "01/22/2023 04:54:47",
"content": "it's in quadrant 4",
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"timestamp": "01/22/2023 04:54:51",
"content": "Correct",
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"timestamp": "01/22/2023 04:55:08",
"content": "That's the part that I don't get😅",
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"timestamp": "01/22/2023 04:55:19",
"content": "I get it for arcsin and arccos but for some reason, I can't get arctan",
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"timestamp": "01/22/2023 04:55:22",
"content": "tan(-pi/6) is?",
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"timestamp": "01/22/2023 04:55:58",
"content": "-1/sqrt(3)",
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"author_id": 409372165033689100,
"author_name": "DemonicThunder",
"timestamp": "01/22/2023 04:56:13",
"content": "So arctan(-1/sqrt(3)) should be?",
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"timestamp": "01/22/2023 04:56:31",
"content": "(-pi/6)",
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"timestamp": "01/22/2023 04:56:34",
"content": "Correct",
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"id": 1066657648554025000,
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"author_name": "DemonicThunder",
"timestamp": "01/22/2023 04:56:40",
"content": "It is just that",
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"author_id": 409372165033689100,
"author_name": "DemonicThunder",
"timestamp": "01/22/2023 04:56:50",
"content": "The inverse trig functions give you an angle",
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"timestamp": "01/22/2023 04:57:05",
"content": "Always think what angle gives what value in such problems",
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"timestamp": "01/22/2023 04:57:24",
"content": "You need to know the domains and ranges of inverse trig functions",
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"timestamp": "01/22/2023 04:57:36",
"content": "I understood everything other than the part of where you got -pi/6",
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"author_id": 409372165033689100,
"author_name": "DemonicThunder",
"timestamp": "01/22/2023 04:57:52",
"content": "-pi/6 is angle correct?",
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"id": 1066657966440325100,
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"timestamp": "01/22/2023 04:57:56",
"content": "Yes",
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"author_name": "DemonicThunder",
"timestamp": "01/22/2023 04:58:16",
"content": "And the tangent of that angle is -1/sqrt(3), agreed?",
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"timestamp": "01/22/2023 04:58:23",
"content": "Yes",
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"author_name": "DemonicThunder",
"timestamp": "01/22/2023 04:59:06",
"content": "So, arctan(-1/sqrt(3)) asks you, \"The tangent of what angle in -pi/2 to pi/2 is -1/sqrt(3)?\"",
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"timestamp": "01/22/2023 04:59:13",
"content": "So your answer should be?",
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"timestamp": "01/22/2023 05:00:37",
"content": "-pi/6. I understand that that's the correct answer, but I don't understand the process of how you do it. Do you just manually calculate the values in quadrant 4 (do sin/cos for each angle in q4) or is there some other way of getting the correct answer quickly?",
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"timestamp": "01/22/2023 05:01:10",
"content": "You need to remember what trig function gives you what value for 0, pi/6, pi/4, pi/3, and pi/2",
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"timestamp": "01/22/2023 05:01:36",
"content": "Apart from that, you need to know tan(-x) = -tan(x)",
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"timestamp": "01/22/2023 05:01:57",
"content": "Like, I remember tan(pi/6) = 1/sqrt(3)",
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"timestamp": "01/22/2023 05:02:06",
"content": "So tan(-pi/6) = -1/sqrt(3)",
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"timestamp": "01/22/2023 05:02:13",
"content": "Ahh so it's just memorizing. I thought that it's only for sin and cos.",
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"timestamp": "01/22/2023 05:02:24",
"content": "Means arctan(-1/sqrt(3)) = -pi/6",
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"timestamp": "01/22/2023 05:02:34",
"content": "Ah, okay. Do it for tan too",
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"timestamp": "01/22/2023 05:02:39",
"content": "Sine, cosine, and tangent",
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"timestamp": "01/22/2023 05:02:52",
"content": "The other three are the reciprocals of these so they are not a problem",
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"timestamp": "01/22/2023 05:02:59",
"content": "Got it. Thanks for clearing things up!",
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"timestamp": "01/22/2023 05:03:09",
"content": "You're welcome, glad it helped",
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},
{
"id": 1066659296403791900,
"author_id": 409372165033689100,
"author_name": "DemonicThunder",
"timestamp": "01/22/2023 05:03:13",
"content": "And remember",
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},
{
"id": 1066659333263343700,
"author_id": 409372165033689100,
"author_name": "DemonicThunder",
"timestamp": "01/22/2023 05:03:22",
"content": "tan(x) = sin(x)/cos(x)",
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},
{
"id": 1066659400502227000,
"author_id": 576665017785647100,
"author_name": "lbjam",
"timestamp": "01/22/2023 05:03:38",
"content": "👍",
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},
{
"id": 1066659418172817400,
"author_id": 576665017785647100,
"author_name": "lbjam",
"timestamp": "01/22/2023 05:03:42",
"content": "Thanks again!",
"attachments": [],
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"reference": null
},
{
"id": 1066659482060476400,
"author_id": 409372165033689100,
"author_name": "DemonicThunder",
"timestamp": "01/22/2023 05:03:58",
"content": "You're welcome",
"attachments": [],
"mentions": [],
"reference": null
},
{
"id": 1066659648775651300,
"author_id": 576665017785647100,
"author_name": "lbjam",
"timestamp": "01/22/2023 05:04:37",
"content": ".close",
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},
{
"id": 1066659652630216700,
"author_id": 805217272087838700,
"author_name": "Mathematics Bot",
"timestamp": "01/22/2023 05:04:38",
"content": "Channel closed",
"attachments": [],
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}
] | help-9 | e0699497ec8a4c4eb2b2c7bc886c2e7b |
200,936 | [
{
"id": 1066659903764181000,
"author_id": 805217272087838700,
"author_name": "Mathematics Bot",
"timestamp": "01/22/2023 05:05:38",
"content": "Available help channel!",
"attachments": [],
"mentions": [],
"reference": null
},
{
"id": 1066660821087813600,
"author_id": 322738097265573900,
"author_name": "F3rrucc10",
"timestamp": "01/22/2023 05:09:17",
"content": "hi, I'm doing an example exercise fo my math book but i don't understand a step",
"attachments": [],
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},
{
"id": 1066660823646339100,
"author_id": 805217272087838700,
"author_name": "Mathematics Bot",
"timestamp": "01/22/2023 05:09:17",
"content": "Pinned a message.",
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"channelId": 486844875632017400,
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"author_name": "F3rrucc10",
"timestamp": "01/22/2023 05:09:33",
"content": "",
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"id": 1066660913152790500,
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"author_name": "F3rrucc10",
"timestamp": "01/22/2023 05:09:39",
"content": "This is the disequation",
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},
{
"id": 1066660974003765200,
"author_id": 322738097265573900,
"author_name": "F3rrucc10",
"timestamp": "01/22/2023 05:09:53",
"content": "i put log2(4x) = y",
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},
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"id": 1066661113409835000,
"author_id": 322738097265573900,
"author_name": "F3rrucc10",
"timestamp": "01/22/2023 05:10:27",
"content": "and became:\n\ny < 3 + 4/y",
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},
{
"id": 1066661157953359900,
"author_id": 702491873021001900,
"author_name": "sloppymope",
"timestamp": "01/22/2023 05:10:37",
"content": "That’s right",
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},
{
"id": 1066661343308030100,
"author_id": 322738097265573900,
"author_name": "F3rrucc10",
"timestamp": "01/22/2023 05:11:21",
"content": "after i put everyting in one side and became:",
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{
"id": 1066661377227378800,
"author_id": 623609325805371500,
"author_name": "thomas.",
"timestamp": "01/22/2023 05:11:29",
"content": "right",
"attachments": [],
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},
{
"id": 1066661439223386100,
"author_id": 623609325805371500,
"author_name": "thomas.",
"timestamp": "01/22/2023 05:11:44",
"content": "i assume the calculations r ok",
"attachments": [],
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},
{
"id": 1066661450409594900,
"author_id": 702491873021001900,
"author_name": "sloppymope",
"timestamp": "01/22/2023 05:11:47",
"content": "It’s plus 3y",
"attachments": [],
"mentions": [],
"reference": null
},
{
"id": 1066661475176955900,
"author_id": 702491873021001900,
"author_name": "sloppymope",
"timestamp": "01/22/2023 05:11:53",
"content": "Oh nvm",
"attachments": [],
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},
{
"id": 1066661495041171500,
"author_id": 702491873021001900,
"author_name": "sloppymope",
"timestamp": "01/22/2023 05:11:58",
"content": "You put on a diff side",
"attachments": [],
"mentions": [],
"reference": null
},
{
"id": 1066661510685929600,
"author_id": 702491873021001900,
"author_name": "sloppymope",
"timestamp": "01/22/2023 05:12:01",
"content": "Ok so it’s fine",
"attachments": [],
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"reference": null
},
{
"id": 1066661582039416800,
"author_id": 322738097265573900,
"author_name": "F3rrucc10",
"timestamp": "01/22/2023 05:12:18",
"content": "now my book put this like next step",
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},
{
"id": 1066661604277620900,
"author_id": 322738097265573900,
"author_name": "F3rrucc10",
"timestamp": "01/22/2023 05:12:24",
"content": "but i don't undesrtand it",
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"reference": null
},
{
"id": 1066661685890383900,
"author_id": 623609325805371500,
"author_name": "thomas.",
"timestamp": "01/22/2023 05:12:43",
"content": "are you by any chance Italian?",
"attachments": [],
"mentions": [],
"reference": null
},
{
"id": 1066661713543430100,
"author_id": 702491873021001900,
"author_name": "sloppymope",
"timestamp": "01/22/2023 05:12:50",
"content": "no lol",
"attachments": [],
"mentions": [],
"reference": null
},
{
"id": 1066661765376651300,
"author_id": 322738097265573900,
"author_name": "F3rrucc10",
"timestamp": "01/22/2023 05:13:02",
"content": "yes",
"attachments": [],
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},
{
"id": 1066661815892856800,
"author_id": 623609325805371500,
"author_name": "thomas.",
"timestamp": "01/22/2023 05:13:14",
"content": "Devi studiare il segno",
"attachments": [],
"mentions": [],
"reference": null
},
{
"id": 1066661929302642700,
"author_id": 623609325805371500,
"author_name": "thomas.",
"timestamp": "01/22/2023 05:13:41",
"content": "fai numeratore ≥ 0 e denominatore > 0",
"attachments": [],
"mentions": [],
"reference": null
},
{
"id": 1066662104960077800,
"author_id": 322738097265573900,
"author_name": "F3rrucc10",
"timestamp": "01/22/2023 05:14:23",
"content": "y^2 - 3y - 4 ≥ 0\ny > 0",
"attachments": [],
"mentions": [],
"reference": null
},
{
"id": 1066662109410250800,
"author_id": 322738097265573900,
"author_name": "F3rrucc10",
"timestamp": "01/22/2023 05:14:24",
"content": "?",
"attachments": [],
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"reference": null
},
{
"id": 1066662124820103200,
"author_id": 623609325805371500,
"author_name": "thomas.",
"timestamp": "01/22/2023 05:14:28",
"content": "yes",
"attachments": [],
"mentions": [],
"reference": null
},
{
"id": 1066662220076953600,
"author_id": 623609325805371500,
"author_name": "thomas.",
"timestamp": "01/22/2023 05:14:50",
"content": "mind that it's not a system",
"attachments": [],
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},
{
"id": 1066662297457672300,
"author_id": 623609325805371500,
"author_name": "thomas.",
"timestamp": "01/22/2023 05:15:09",
"content": "you'll find two intervals",
"attachments": [],
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},
{
"id": 1066662380597166100,
"author_id": 322738097265573900,
"author_name": "F3rrucc10",
"timestamp": "01/22/2023 05:15:29",
"content": "okk",
"attachments": [],
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},
{
"id": 1066662414424227800,
"author_id": 623609325805371500,
"author_name": "thomas.",
"timestamp": "01/22/2023 05:15:37",
"content": "",
"attachments": [
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"id": 1066662914704019600,
"author_id": 322738097265573900,
"author_name": "F3rrucc10",
"timestamp": "01/22/2023 05:17:36",
"content": "nel numeratore gli intervalli sono y1=4 e y2=-1??",
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},
{
"id": 1066663228060487800,
"author_id": 322738097265573900,
"author_name": "F3rrucc10",
"timestamp": "01/22/2023 05:18:51",
"content": "quindi tipo -1<y<4 ?",
"attachments": [],
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},
{
"id": 1066663322163884000,
"author_id": 623609325805371500,
"author_name": "thomas.",
"timestamp": "01/22/2023 05:19:13",
"content": "-4 e 1 comunque",
"attachments": [],
"mentions": [],
"reference": null
},
{
"id": 1066663454368334000,
"author_id": 623609325805371500,
"author_name": "thomas.",
"timestamp": "01/22/2023 05:19:45",
"content": "somma = -3, prodotto = -4",
"attachments": [],
"mentions": [],
"reference": null
},
{
"id": 1066663470252163200,
"author_id": 322738097265573900,
"author_name": "F3rrucc10",
"timestamp": "01/22/2023 05:19:48",
"content": "perché -4?",
"attachments": [],
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"reference": null
},
{
"id": 1066663984947798100,
"author_id": 623609325805371500,
"author_name": "thomas.",
"timestamp": "01/22/2023 05:21:51",
"content": "y^2 - 3y - 4 \n\ndevi trovare due numeri che la loro somma sia -3 e il prodotto sia -4",
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},
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"id": 1066664093282476200,
"author_id": 623609325805371500,
"author_name": "thomas.",
"timestamp": "01/22/2023 05:22:17",
"content": "-4 e +1 quindi",
"attachments": [],
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},
{
"id": 1066664163868422100,
"author_id": 623609325805371500,
"author_name": "thomas.",
"timestamp": "01/22/2023 05:22:34",
"content": "(x-4)(x+1)",
"attachments": [],
"mentions": [],
"reference": null
},
{
"id": 1066664231933587600,
"author_id": 322738097265573900,
"author_name": "F3rrucc10",
"timestamp": "01/22/2023 05:22:50",
"content": "Io avevo fatto in questo modo",
"attachments": [
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{
"id": 1066664295292743700,
"author_id": 623609325805371500,
"author_name": "thomas.",
"timestamp": "01/22/2023 05:23:05",
"content": "è ok va bene anche così",
"attachments": [],
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},
{
"id": 1066664392650932200,
"author_id": 623609325805371500,
"author_name": "thomas.",
"timestamp": "01/22/2023 05:23:28",
"content": "adesso hai le soluzioni dell'equazione",
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},
{
"id": 1066664453581582300,
"author_id": 623609325805371500,
"author_name": "thomas.",
"timestamp": "01/22/2023 05:23:43",
"content": "pensa a come è fatta la parabola",
"attachments": [],
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"reference": null
},
{
"id": 1066664559500341200,
"author_id": 623609325805371500,
"author_name": "thomas.",
"timestamp": "01/22/2023 05:24:08",
"content": "",
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{
"id": 1066664652257378300,
"author_id": 623609325805371500,
"author_name": "thomas.",
"timestamp": "01/22/2023 05:24:30",
"content": "B = -4, A = 1",
"attachments": [],
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},
{
"id": 1066664661732315300,
"author_id": 322738097265573900,
"author_name": "F3rrucc10",
"timestamp": "01/22/2023 05:24:33",
"content": "quindi compreso tra -1 e 4",
"attachments": [],
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},
{
"id": 1066664928989163600,
"author_id": 623609325805371500,
"author_name": "thomas.",
"timestamp": "01/22/2023 05:25:36",
"content": "cosa succede quando è compreso?",
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},
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"id": 1066664979299831800,
"author_id": 623609325805371500,
"author_name": "thomas.",
"timestamp": "01/22/2023 05:25:48",
"content": "in che parte del piano di trova la funzione?",
"attachments": [],
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"reference": null
},
{
"id": 1066665253670223900,
"author_id": 322738097265573900,
"author_name": "F3rrucc10",
"timestamp": "01/22/2023 05:26:54",
"content": "nella parte che hai evidenziato in verde",
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},
{
"id": 1066665370489987100,
"author_id": 623609325805371500,
"author_name": "thomas.",
"timestamp": "01/22/2023 05:27:22",
"content": "quello è l'intervallo, tu devi dire quando la funzione è positiva (o nulla)",
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"reference": null
},
{
"id": 1066665897424588800,
"author_id": 623609325805371500,
"author_name": "thomas.",
"timestamp": "01/22/2023 05:29:27",
"content": "in generale le parabole ax^2 + bx +c seguono tutte questo schema:\n\n+ - +\n\ncon a>0",
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},
{
"id": 1066666025011122300,
"author_id": 322738097265573900,
"author_name": "F3rrucc10",
"timestamp": "01/22/2023 05:29:58",
"content": "postiva per y<-1 e y>4?",
"attachments": [],
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},
{
"id": 1066666034335064200,
"author_id": 623609325805371500,
"author_name": "thomas.",
"timestamp": "01/22/2023 05:30:00",
"content": "sono positive sul lato esterno delle soluzioni mentre sono negative all'interno",
"attachments": [],
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"reference": null
},
{
"id": 1066666051347173500,
"author_id": 623609325805371500,
"author_name": "thomas.",
"timestamp": "01/22/2023 05:30:04",
"content": "esatto",
"attachments": [],
"mentions": [],
"reference": null
},
{
"id": 1066669801289810000,
"author_id": 805217272087838700,
"author_name": "Mathematics Bot",
"timestamp": "01/22/2023 05:44:58",
"content": "@F3rrucc10 Has your question been resolved?",
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"id": 1066673578155724800,
"author_id": 805217272087838700,
"author_name": "Mathematics Bot",
"timestamp": "01/22/2023 05:59:58",
"content": "Channel closed",
"attachments": [],
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}
] | help-9 | 153f96b5b4ab4c8dabe17643819e1a62 |
200,937 | [
{
"id": 1066673830220795900,
"author_id": 805217272087838700,
"author_name": "Mathematics Bot",
"timestamp": "01/22/2023 06:00:58",
"content": "Available help channel!",
"attachments": [],
"mentions": [],
"reference": null
},
{
"id": 1066675361871581200,
"author_id": 805217272087838700,
"author_name": "Mathematics Bot",
"timestamp": "01/22/2023 06:07:04",
"content": "Pinned a message.",
"attachments": [],
"mentions": [],
"reference": {
"messageId": 1066675359745052700,
"channelId": 486844875632017400,
"guildId": null
}
},
{
"id": 1066675430230335500,
"author_id": 805217272087838700,
"author_name": "Mathematics Bot",
"timestamp": "01/22/2023 06:07:20",
"content": "Channel closed",
"attachments": [],
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}
] | help-9 | 14b66119e72047309a68f68638a9c595 |
200,938 | [
{
"id": 1066679393872777200,
"author_id": 805217272087838700,
"author_name": "Mathematics Bot",
"timestamp": "01/22/2023 06:23:05",
"content": "Available help channel!",
"attachments": [],
"mentions": [],
"reference": null
},
{
"id": 1066683291857588200,
"author_id": 979013156984729600,
"author_name": "Rahim",
"timestamp": "01/22/2023 06:38:34",
"content": "can someone tell me if my solution is correct or totally wrong",
"attachments": [],
"mentions": [],
"reference": null
},
{
"id": 1066683293484982400,
"author_id": 805217272087838700,
"author_name": "Mathematics Bot",
"timestamp": "01/22/2023 06:38:35",
"content": "Pinned a message.",
"attachments": [],
"mentions": [],
"reference": {
"messageId": 1066683291857588200,
"channelId": 486844875632017400,
"guildId": null
}
},
{
"id": 1066683475865907200,
"author_id": 183668144404037630,
"author_name": "Ann",
"timestamp": "01/22/2023 06:39:18",
"content": "image on its way?",
"attachments": [],
"mentions": [],
"reference": null
},
{
"id": 1066683498284466300,
"author_id": 979013156984729600,
"author_name": "Rahim",
"timestamp": "01/22/2023 06:39:24",
"content": "yes",
"attachments": [],
"mentions": [],
"reference": null
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"content": "one sec",
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"content": "Also is there a fast way of finding RRF of a matrix. Gaussian elimination seems very tedious",
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"content": "@Rahim Has your question been resolved?",
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"content": "you're saying that a set of vectors which contains zero vector is linearly independent?",
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"content": "v1 = (1, 0, 0) and v2 = (-1, 0, 0) aren't linearly independent either",
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"content": "Hmm",
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"content": "What should I do then",
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"content": "revisit the definition of basis and linear dependence/independence",
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"content": "How do I define the basis B tho",
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"content": "just like any other basis",
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"content": "basis is a set of linearly independent vectors",
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"timestamp": "01/22/2023 08:10:19",
"content": "What if we define B=(u2,u3…..un) where uj is a vector with -1 in position 1 and 1 in position j and everything else 0",
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"content": "I haven't checked it, but there's a much more intuitive answer",
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"content": "you seem to be just not understanding the definition of linear independence based on your argument about linear independence of the set you proposed, so you really should revisit that first",
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"content": "Idk if intuition and linear algebra go together",
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"content": "None of this shit clicks for me",
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"timestamp": "01/22/2023 08:14:43",
"content": "Isn’t linear independent that the solution to a1v1+a2v2+…..anVn=0 a non trivial solution",
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"timestamp": "01/22/2023 08:15:57",
"content": "that's linearly dependent",
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"timestamp": "01/22/2023 08:18:30",
"content": "Ah yes you’re correct",
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"timestamp": "01/22/2023 08:19:59",
"content": "Ok so B is a basis of V if each vector in V can be written as a linear combination of the vectors in B in exactly one way",
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"timestamp": "01/22/2023 08:21:11",
"content": "yes, though that's far less useful property in this problem than simply linear independence",
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"timestamp": "01/22/2023 08:22:21",
"content": "now try to construct one vector in R^3 such that it's components add up to 0 and it's not a zero vector",
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"content": "this can be easily done by combination of 1 and -1",
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"timestamp": "01/22/2023 08:23:16",
"content": "So (1,-1,0)^t",
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"timestamp": "01/22/2023 08:25:09",
"content": "now try to do the same but for the second vector such that first and second vector are linearly independent",
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"timestamp": "01/22/2023 08:26:49",
"content": "Hmm",
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"content": "(1,0,-1)^t and (0,1,-1)^t",
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"content": "So essentially we are just moving the 0 into the different axis",
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"content": "the (0, 1, -1) variant is better because you can easily track where the 0's are located and where the 1 and -1 are",
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"content": "you essentially made circular shift of all coordinates",
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"timestamp": "01/22/2023 08:28:40",
"content": "Ok yeah",
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"content": "Don’t we need 3 vectors tho for R^3",
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"timestamp": "01/22/2023 08:29:17",
"content": "no, you're asked about a basis for a subspace and not the space itself",
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"content": "since the subspace is described using one constraint equation it's dimension is 1 less of the space",
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"content": "so if V is n-dimensional the subspace is n-1 dimensional, hence the basis contains n-1 vectors for that subspace",
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"timestamp": "01/22/2023 08:30:52",
"content": "Ah yes that was a theorem in the lecture",
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"timestamp": "01/22/2023 08:31:36",
"content": "Ok so how are we generalising this to R^n",
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"timestamp": "01/22/2023 08:32:13",
"content": "by just repeating the shift over and over again and checking that indeed such vectors are linearly independent",
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"content": "the only trick there is what does the last vector looks like",
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"timestamp": "01/22/2023 08:32:41",
"content": "but it's clear what it is after you do the special case for R^3 and R^4",
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"content": "So are we saying the vectors with 1 in poisition n and -1 in position n+1 and 0 else where",
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"content": "So for R^4 we get v1=(1,-1,0,0) v2=(0,1,-1,0) v3=(0,0,1,-1)",
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"content": "yes",
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"timestamp": "01/22/2023 08:36:15",
"content": "though i'd use letter k or something else because n stands for dimension",
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"timestamp": "01/22/2023 08:36:32",
"content": "How would we write that formally",
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"timestamp": "01/22/2023 08:36:35",
"content": "Or is that fine",
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"content": "Just using k",
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"content": "you can just write a few (1, -1, 0, ..., 0); (0, 1, -1, 0, ..., 0); (0, 0, 1, -1, 0, ..., 0) and that's clear enough",
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"timestamp": "01/22/2023 08:37:42",
"content": "but I'd also include what the last one looks like in this set",
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"timestamp": "01/22/2023 08:39:00",
"content": "Ok and then it is quite simple to show linear independence right ?",
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"timestamp": "01/22/2023 08:39:29",
"content": "Since the only solution is the trivial one",
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"timestamp": "01/22/2023 08:40:16",
"content": "yes, there's many ways you can do that",
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"content": "I’m guessing I can’t right that it is obvious? Lol",
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"content": "Cuz we’d get something like a(1)+b(0)+…= 0",
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"timestamp": "01/22/2023 08:43:25",
"content": "Wait that doesn’t make sense idk",
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"content": "well showing linear independence is the same as solving a system of linear equations, you can probably construct a matrix of these vectors and figure out what it's kernel looks like (it'll be the vector full of ones, which matches our expectation because that's what the sum of components equal 0 means)",
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"timestamp": "01/22/2023 08:44:25",
"content": "What the 😭",
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"timestamp": "01/22/2023 08:46:19",
"content": "or, well, I guess if you construct it differently it'll be a rectangular matrix in which case the null space would be trivial - the zero vector",
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"timestamp": "01/22/2023 08:46:27",
"content": "that would mean they're linearly independent",
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"timestamp": "01/22/2023 08:48:08",
"content": "Bruh",
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"timestamp": "01/22/2023 08:48:21",
"content": "Ok and how do we show the the basis spans V",
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"timestamp": "01/22/2023 08:48:26",
"content": "the equation $\\alpha v_1 + \\beta v_2 + \\gamma v_3 + ... + \\mu v_n = 0$ just means take the columns of the matrix $\\begin{pmatrix} v_1 & v_2 & v_3 & ... & v_n \\end{pmatrix}$ with coefficients $(\\alpha , \\beta , \\gamma , ..., \\mu )$ and that's the same thing as multiplying this matrix by this vector and solving for the zero vector",
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"timestamp": "01/22/2023 08:48:29",
"content": "**Transparent\\_Elemental**",
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"content": "~~it doesn't~~",
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"content": "~~there's only n-1 linearly independent vectors and that's 1 less than needed to span n-dimensional space~~",
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"content": "Isn’t V also n-1",
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"timestamp": "01/22/2023 08:49:51",
"content": "nvm I though V was a space which wasn't a subspace",
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"content": "well it's enough to show that B spans V given that all the vectors in B are linearly independent and belong to subspace",
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"content": "i. e. satisfy the equation that the sum of all components is 0",
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"content": "Is that a theorem",
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"content": "I was thinking of arguing by the dimensions so then we get Lin B having n-1 dimensions same as V so Lin(B)=V",
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"content": "well that argument isn't necessarily true because you can pick a subspace where the sum of components is not 0, but, say, 5",
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"content": "that'll be a n-1 dimensional subspace yet it's different from V",
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"content": "it's like rotating a plane in 3D space, a plane spanned by 2 vectors is a 2-dimensional subspace, yet planes rotated differently are intuitively different",
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"content": "now that I'm realizing that the sum of components equal to 5 isn't a subspace at all, but you get the idea",
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"content": "Hmm",
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"content": "Can we prove it directly from the definition ?",
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"content": "So any vector in V can be written as a linear combination of the vectors in B",
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"timestamp": "01/22/2023 08:58:01",
"content": "yes, you can start with the special case R^2 or R^3",
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"content": "Isn’t it trivial?",
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"content": "If every vector in V satisfies the equation v1+v2+….=0",
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"content": "And all the vectors in B also satisfy it",
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"content": "well I should've said that any vector in V should be uniquely described by linear combination of vectors in B, but I think that follows from the fact that B is a basis because the related theorem uses the fact that you've got two linear combinations of the basis vectors",
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"timestamp": "01/22/2023 09:03:08",
"content": "so you'd need to first show that B is a set of linearly independent vectors",
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"timestamp": "01/22/2023 09:06:17",
"content": "the problem currently is that in linear algebra there's far too many ways to prove same thing, so you should just pick something, e. g. it's not so bad to prove that the kernel of the matrix is trivial because in fact the matrix turns out quite nice",
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"timestamp": "01/22/2023 09:07:07",
"content": "1's on the main diagonal, -1's on the nearby diagonal and 0's everywhere else, which simplifies calculations",
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"content": "I can’t even remember what the kernel is from last year",
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"content": "I guess I need to revisit all of this",
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"author_name": "Rahim",
"timestamp": "01/22/2023 09:07:42",
"content": "Do you have a way for developing the intuition for linear algebra",
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"content": "It seems like I only learn methods and not understand it",
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"timestamp": "01/22/2023 09:10:16",
"content": "I guess it's just a matter of using the appropriate definitions enough times, looking at what they mean in low dimension and learning what matrix multiplication really means because there's at least 3 different useful perspectives you can look at it",
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"content": "e. g. a kernel of A is a set of solutions x to the equation Ax=0, if A is a 1x3 matrix and x is therefore a 3x1 vector the equation describes dot product of vector A and x and that's equal to zero",
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"timestamp": "01/22/2023 09:11:38",
"content": "that's fairly intuitive that there's a whole plane of orthogonal vectors that satisfy this",
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"timestamp": "01/22/2023 09:12:34",
"content": "so in some sense kernel is an orthogonal space to the vectors in A",
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"timestamp": "01/22/2023 09:14:45",
"content": "matrix-vector multipilcation Ax can be viewed as taking linear combinations of columns of A with weights which are written in components of vector x (you can see this by just doing the multiplication the usual way)",
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"timestamp": "01/22/2023 09:15:03",
"content": "or it can be seen as taking dot products of row vectors of A with vector x",
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"timestamp": "01/22/2023 09:15:40",
"content": "and again dot product equal 0 implies something about orthogonality",
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"timestamp": "01/22/2023 09:16:54",
"content": "@Moderators",
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"timestamp": "01/22/2023 09:30:53",
"content": "the definition of linear independence is nothing more than solving this system for weights alpha $\\\\\\\\ \\alpha_1v_1 + \\alpha_2v_2 + \\alpha_3v_3 = \\vec{0} \\iff \\begin{pmatrix} | & | & | \\\\ v_1 & v_2 & v_3 \\\\ | & | & | \\end{pmatrix}\\begin{pmatrix}\\alpha_1 \\\\ \\alpha_2 \\\\ \\alpha_3 \\end{pmatrix} = \\begin{pmatrix} 0 \\\\ 0 \\\\ 0 \\end{pmatrix}$",
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"timestamp": "01/22/2023 09:31:25",
"content": "**Transparent\\_Elemental**",
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"timestamp": "01/22/2023 10:07:52",
"content": "@Rahim Has your question been resolved?",
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"content": "Channel closed",
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] | help-9 | f6be94b77c874f1b9c27078b355238cc |
200,939 | [
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"timestamp": "01/22/2023 10:51:10",
"content": "Available help channel!",
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"timestamp": "01/22/2023 10:52:21",
"content": "Hi. The problem: ABC triangle. AB=26, BC=28, AC=30, AD height of triangle. \" I \" center of inscribed triangle, find the radius of the inscribed triangle. A few things to make the question harder: shouldn't use trigonometry ( sin, cos, arcsin etc)",
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"content": "the red segment (which was supposed to be straight, but I had trouble drawing it). I know the center of the circle is the intersection of the angles' bisectors. Tried representing that.",
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"content": "Try finding the area of the triangle from the radius",
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"content": "And from Base times height/2",
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"content": "Then you can set them equal to each other and solve for the radius",
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"timestamp": "01/22/2023 10:56:58",
"content": "I see. I will try. should I close this and reopen if I don't manage? or I can hold the chat hostage a bit until I see what I can do",
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"content": "I've been looking at this problem for a few hours, I think I am not using the length of AC and that I is equally distant to the 3 sides of ABC.",
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"content": "but I don't know how to make use of them...",
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"timestamp": "01/22/2023 10:58:07",
"content": "Let me find an online pic",
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"timestamp": "01/22/2023 10:58:15",
"content": "Look at it tbis way",
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"timestamp": "01/22/2023 10:58:21",
"content": "if it helps, at a) I found the Area of triangle",
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"content": "b) distance between B and AC",
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"timestamp": "01/22/2023 10:58:35",
"content": "so i know these (and they might help)",
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"timestamp": "01/22/2023 10:58:58",
"content": "Here",
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"timestamp": "01/22/2023 10:59:02",
"content": "Let me find a better image",
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"timestamp": "01/22/2023 10:59:29",
"content": "Look at it from this pov",
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"content": "Solve for each of the triangles that are with the blue sides",
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"content": "Like the first one is br/2",
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"timestamp": "01/22/2023 11:00:39",
"content": "Apply that to ur problem",
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"timestamp": "01/22/2023 11:01:03",
"content": "oh, you're right. br+cr+ar/2= area of triangle.",
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"timestamp": "01/22/2023 11:01:17",
"content": "Yeah now you can plug in those values",
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"timestamp": "01/22/2023 11:01:24",
"content": "Set that equal to the area",
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"timestamp": "01/22/2023 11:01:25",
"content": "(b+c+a)r/2= 336 and then",
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"timestamp": "01/22/2023 11:01:26",
"content": "And solve for r",
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"timestamp": "01/22/2023 11:01:35",
"content": "you're quite right, thank you very much.",
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"timestamp": "01/22/2023 11:01:38",
"content": "Np",
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"timestamp": "01/22/2023 11:02:19",
"content": "brilliant idea. I'm a univ student, and tried explaining this to a 7th grader (and failed). good to know, let me write it down and I will close the help asap",
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"timestamp": "01/22/2023 11:02:35",
"content": "What",
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"content": "You tried explaining this to a 7th grader",
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"timestamp": "01/22/2023 11:02:52",
"content": "yea, I tried to solve it with him (sort of tutoring)",
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"author_name": "Wild Rage",
"timestamp": "01/22/2023 11:03:02",
"content": "but I couldn't find a solution",
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"id": 1066749874638434400,
"author_id": 605044221010772000,
"author_name": "Trumpet Bot",
"timestamp": "01/22/2023 11:03:09",
"content": "Some 7th graders are really smart",
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"author_name": "Wild Rage",
"timestamp": "01/22/2023 11:04:15",
"content": "Done, I'll wrap it up. Have a nice day, and thanks again for the brilliant idea.",
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"id": 1066750205145403500,
"author_id": 605044221010772000,
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"timestamp": "01/22/2023 11:04:28",
"content": "Np",
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"author_name": "Wild Rage",
"timestamp": "01/22/2023 11:04:31",
"content": ".close",
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"author_id": 805217272087838700,
"author_name": "Mathematics Bot",
"timestamp": "01/22/2023 11:04:32",
"content": "Channel closed",
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}
] | help-9 | 9ad2bb8c5bcf4549a3658c193b2eadbc |
200,940 | [
{
"id": 1066750475954835600,
"author_id": 805217272087838700,
"author_name": "Mathematics Bot",
"timestamp": "01/22/2023 11:05:32",
"content": "Available help channel!",
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"id": 1066750891153174700,
"author_id": 490928916207370240,
"author_name": "jesper",
"timestamp": "01/22/2023 11:07:11",
"content": "**A steel wire is 40 cm long. It is divided into two pieces, which are used to make two squares.\n\na. Let x be the side of one square. What then is the side of the second square?\n\nb. Show that the combined area of the two squares is A(x) = 2x^2 - 20x + 100.\n\nc. Draw the graph of A in a coordinate system.\n\nd. Determine the smallest value the total area can have.**",
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"timestamp": "01/22/2023 11:07:12",
"content": "Pinned a message.",
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"author_id": 490928916207370240,
"author_name": "jesper",
"timestamp": "01/22/2023 11:07:56",
"content": "need help with pretty much everything, might understand a little tho once i get a push",
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"timestamp": "01/22/2023 11:10:35",
"content": "easy",
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"author_id": 987071591169011700,
"author_name": "kiritoholy",
"timestamp": "01/22/2023 11:10:46",
"content": "let the steel wire be lenght l",
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},
{
"id": 1066751810825633800,
"author_id": 987071591169011700,
"author_name": "kiritoholy",
"timestamp": "01/22/2023 11:10:50",
"content": "l=40cm",
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},
{
"id": 1066751826361319400,
"author_id": 490928916207370240,
"author_name": "jesper",
"timestamp": "01/22/2023 11:10:54",
"content": "alright",
"attachments": [],
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},
{
"id": 1066751858053488600,
"author_id": 987071591169011700,
"author_name": "kiritoholy",
"timestamp": "01/22/2023 11:11:02",
"content": "as you know square",
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},
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"author_id": 987071591169011700,
"author_name": "kiritoholy",
"timestamp": "01/22/2023 11:11:10",
"content": "has all sides equal",
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},
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"id": 1066751919462285300,
"author_id": 490928916207370240,
"author_name": "jesper",
"timestamp": "01/22/2023 11:11:16",
"content": "yes",
"attachments": [],
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},
{
"id": 1066751941608218600,
"author_id": 987071591169011700,
"author_name": "kiritoholy",
"timestamp": "01/22/2023 11:11:22",
"content": "divide the wire into two",
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},
{
"id": 1066751949287981000,
"author_id": 987071591169011700,
"author_name": "kiritoholy",
"timestamp": "01/22/2023 11:11:24",
"content": "parts",
"attachments": [],
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},
{
"id": 1066751966509813900,
"author_id": 987071591169011700,
"author_name": "kiritoholy",
"timestamp": "01/22/2023 11:11:28",
"content": "40/2",
"attachments": [],
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},
{
"id": 1066751974646763600,
"author_id": 490928916207370240,
"author_name": "jesper",
"timestamp": "01/22/2023 11:11:30",
"content": "right",
"attachments": [],
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},
{
"id": 1066751981433135100,
"author_id": 987071591169011700,
"author_name": "kiritoholy",
"timestamp": "01/22/2023 11:11:31",
"content": "===20",
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{
"id": 1066752031202758700,
"author_id": 987071591169011700,
"author_name": "kiritoholy",
"timestamp": "01/22/2023 11:11:43",
"content": "now this is used to make the square",
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},
{
"id": 1066752064203526100,
"author_id": 490928916207370240,
"author_name": "jesper",
"timestamp": "01/22/2023 11:11:51",
"content": "/4?",
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"id": 1066752067735134300,
"author_id": 987071591169011700,
"author_name": "kiritoholy",
"timestamp": "01/22/2023 11:11:52",
"content": "the perimeter of square",
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"author_id": 987071591169011700,
"author_name": "kiritoholy",
"timestamp": "01/22/2023 11:11:59",
"content": "is 4x",
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"author_id": 987071591169011700,
"author_name": "kiritoholy",
"timestamp": "01/22/2023 11:12:05",
"content": "so 4x=20",
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"id": 1066752137134100500,
"author_id": 987071591169011700,
"author_name": "kiritoholy",
"timestamp": "01/22/2023 11:12:08",
"content": "x=5",
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"author_id": 987071591169011700,
"author_name": "kiritoholy",
"timestamp": "01/22/2023 11:12:14",
"content": "yes",
"attachments": [],
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"author_name": "jesper",
"timestamp": "01/22/2023 11:12:15",
"content": "right okay",
"attachments": [],
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"id": 1066752300703555600,
"author_id": 987071591169011700,
"author_name": "kiritoholy",
"timestamp": "01/22/2023 11:12:47",
"content": "as the wire is equally divides so the second square is also of same side",
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"author_id": 771757790397071400,
"author_name": "Wild Rage",
"timestamp": "01/22/2023 11:13:17",
"content": "kirito check b. actually the 2 pieces that form the 2 squares are not equal probably. you need to express the length of 2nd square based on side of 1st.",
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"id": 1066752517330976900,
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"author_name": "jesper",
"timestamp": "01/22/2023 11:13:39",
"content": "ill give you the answers if that helps you help me",
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"id": 1066752569503912000,
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"author_name": "jesper",
"timestamp": "01/22/2023 11:13:51",
"content": "i have the answers just need to show how i did it",
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"author_id": 987071591169011700,
"author_name": "kiritoholy",
"timestamp": "01/22/2023 11:15:05",
"content": "yes you are right buddy",
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"id": 1066752884475187200,
"author_id": 987071591169011700,
"author_name": "kiritoholy",
"timestamp": "01/22/2023 11:15:06",
"content": "i thought wire is evenly divided",
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"id": 1066753096144932900,
"author_id": 490928916207370240,
"author_name": "jesper",
"timestamp": "01/22/2023 11:15:57",
"content": "**Area of square 1: 2x \nArea of square 2: (10 - x)^2 = 100 - 20x + x^2**",
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"author_name": "kiritoholy",
"timestamp": "01/22/2023 11:16:16",
"content": "ohh",
"attachments": [],
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},
{
"id": 1066753369164759000,
"author_id": 987071591169011700,
"author_name": "kiritoholy",
"timestamp": "01/22/2023 11:17:02",
"content": "you need to do reverse process to see the method they used",
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"id": 1066753424651206800,
"author_id": 490928916207370240,
"author_name": "jesper",
"timestamp": "01/22/2023 11:17:15",
"content": "no idea how to do that",
"attachments": [],
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"id": 1066753463670800400,
"author_id": 987071591169011700,
"author_name": "kiritoholy",
"timestamp": "01/22/2023 11:17:25",
"content": "no problem.",
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"author_id": 987071591169011700,
"author_name": "kiritoholy",
"timestamp": "01/22/2023 11:17:30",
"content": "i am telling",
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"author_id": 987071591169011700,
"author_name": "kiritoholy",
"timestamp": "01/22/2023 11:17:51",
"content": "first take the area of square 1 be a1",
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"author_name": "jesper",
"timestamp": "01/22/2023 11:17:58",
"content": "sure",
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{
"id": 1066753917553229800,
"author_id": 987071591169011700,
"author_name": "kiritoholy",
"timestamp": "01/22/2023 11:19:13",
"content": "find",
"attachments": [],
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},
{
"id": 1066753923014201500,
"author_id": 987071591169011700,
"author_name": "kiritoholy",
"timestamp": "01/22/2023 11:19:14",
"content": "side",
"attachments": [],
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},
{
"id": 1066753943541141500,
"author_id": 987071591169011700,
"author_name": "kiritoholy",
"timestamp": "01/22/2023 11:19:19",
"content": "of first square",
"attachments": [],
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},
{
"id": 1066753991775637600,
"author_id": 987071591169011700,
"author_name": "kiritoholy",
"timestamp": "01/22/2023 11:19:30",
"content": "let s be the side",
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},
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"id": 1066754032733016200,
"author_id": 987071591169011700,
"author_name": "kiritoholy",
"timestamp": "01/22/2023 11:19:40",
"content": "s^2 = 2x",
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"author_id": 987071591169011700,
"author_name": "kiritoholy",
"timestamp": "01/22/2023 11:19:55",
"content": "s=sqrt(2x)",
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"id": 1066754116547784700,
"author_id": 987071591169011700,
"author_name": "kiritoholy",
"timestamp": "01/22/2023 11:20:00",
"content": "this is the side",
"attachments": [],
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},
{
"id": 1066754154040668200,
"author_id": 987071591169011700,
"author_name": "kiritoholy",
"timestamp": "01/22/2023 11:20:09",
"content": "of the first square",
"attachments": [],
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"id": 1066754180536090600,
"author_id": 490928916207370240,
"author_name": "jesper",
"timestamp": "01/22/2023 11:20:15",
"content": "one side?",
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"id": 1066754181622415400,
"author_id": 987071591169011700,
"author_name": "kiritoholy",
"timestamp": "01/22/2023 11:20:16",
"content": "now multiply it by 4",
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"author_name": "kiritoholy",
"timestamp": "01/22/2023 11:20:23",
"content": "yes",
"attachments": [],
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"id": 1066754234999115800,
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"author_name": "jesper",
"timestamp": "01/22/2023 11:20:28",
"content": "wait why is it ^2",
"attachments": [],
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"id": 1066754247502336000,
"author_id": 490928916207370240,
"author_name": "jesper",
"timestamp": "01/22/2023 11:20:31",
"content": "if its only 1 side",
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"id": 1066754308676255900,
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"author_name": "kiritoholy",
"timestamp": "01/22/2023 11:20:46",
"content": "area =s^2",
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"id": 1066754363894280300,
"author_id": 987071591169011700,
"author_name": "kiritoholy",
"timestamp": "01/22/2023 11:20:59",
"content": "s stands for side",
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},
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"id": 1066754382256947300,
"author_id": 490928916207370240,
"author_name": "jesper",
"timestamp": "01/22/2023 11:21:04",
"content": "oh alright",
"attachments": [],
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"id": 1066754440809414800,
"author_id": 987071591169011700,
"author_name": "kiritoholy",
"timestamp": "01/22/2023 11:21:18",
"content": "s=sqrt(2x)",
"attachments": [],
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},
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"id": 1066754471734030500,
"author_id": 987071591169011700,
"author_name": "kiritoholy",
"timestamp": "01/22/2023 11:21:25",
"content": "multiply s by 4",
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},
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"id": 1066754703221870700,
"author_id": 490928916207370240,
"author_name": "jesper",
"timestamp": "01/22/2023 11:22:20",
"content": "is it just multiplying both sides by 4?",
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"id": 1066754718820479000,
"author_id": 987071591169011700,
"author_name": "kiritoholy",
"timestamp": "01/22/2023 11:22:24",
"content": "so length that is used to create the squre 1 is 4*sqrt(2x)",
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"timestamp": "01/22/2023 11:22:43",
"content": "nope",
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"id": 1066754816048648200,
"author_id": 490928916207370240,
"author_name": "jesper",
"timestamp": "01/22/2023 11:22:47",
"content": "oh",
"attachments": [],
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},
{
"id": 1066754838131654800,
"author_id": 987071591169011700,
"author_name": "kiritoholy",
"timestamp": "01/22/2023 11:22:52",
"content": "we are doing reverse process",
"attachments": [],
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},
{
"id": 1066754962559860700,
"author_id": 987071591169011700,
"author_name": "kiritoholy",
"timestamp": "01/22/2023 11:23:22",
"content": "just to understand what are length of wire should they tak e",
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},
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"id": 1066755042243248300,
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"author_name": "jesper",
"timestamp": "01/22/2023 11:23:41",
"content": "right okay",
"attachments": [],
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},
{
"id": 1066755053999886300,
"author_id": 987071591169011700,
"author_name": "kiritoholy",
"timestamp": "01/22/2023 11:23:44",
"content": "so this process",
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"id": 1066755067333595100,
"author_id": 987071591169011700,
"author_name": "kiritoholy",
"timestamp": "01/22/2023 11:23:47",
"content": "checks",
"attachments": [],
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},
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"author_id": 987071591169011700,
"author_name": "kiritoholy",
"timestamp": "01/22/2023 11:23:49",
"content": "that",
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},
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"id": 1066755105480773600,
"author_id": 987071591169011700,
"author_name": "kiritoholy",
"timestamp": "01/22/2023 11:23:56",
"content": "the wire is not evenly cutt",
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},
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"id": 1066755176507125800,
"author_id": 490928916207370240,
"author_name": "jesper",
"timestamp": "01/22/2023 11:24:13",
"content": "understood",
"attachments": [],
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"id": 1066755490396258400,
"author_id": 987071591169011700,
"author_name": "kiritoholy",
"timestamp": "01/22/2023 11:25:28",
"content": "now we need to find the the length of the wire",
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"id": 1066755527712981000,
"author_id": 987071591169011700,
"author_name": "kiritoholy",
"timestamp": "01/22/2023 11:25:37",
"content": "lemme create diagram",
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"author_name": "kiritoholy",
"timestamp": "01/22/2023 11:25:42",
"content": "to better explain it",
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"id": 1066755577042190500,
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"author_name": "jesper",
"timestamp": "01/22/2023 11:25:48",
"content": "go ahead yeah will probably be better",
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"id": 1066756413289922700,
"author_id": 987071591169011700,
"author_name": "kiritoholy",
"timestamp": "01/22/2023 11:29:08",
"content": "see this",
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"id": 1066756445518954500,
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"id": 1066756522215997600,
"author_id": 987071591169011700,
"author_name": "kiritoholy",
"timestamp": "01/22/2023 11:29:34",
"content": "so the red square has side x/4",
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"id": 1066756547646066700,
"author_id": 490928916207370240,
"author_name": "jesper",
"timestamp": "01/22/2023 11:29:40",
"content": "okay",
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},
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"id": 1066756879201611800,
"author_id": 987071591169011700,
"author_name": "kiritoholy",
"timestamp": "01/22/2023 11:30:59",
"content": "creating diagram",
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{
"id": 1066756891620933600,
"author_id": 490928916207370240,
"author_name": "jesper",
"timestamp": "01/22/2023 11:31:02",
"content": "i understand the top line not quite the bottom one tho",
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},
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"id": 1066756902186389500,
"author_id": 490928916207370240,
"author_name": "jesper",
"timestamp": "01/22/2023 11:31:04",
"content": "ah alright",
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},
{
"id": 1066756902433861800,
"author_id": 987071591169011700,
"author_name": "kiritoholy",
"timestamp": "01/22/2023 11:31:04",
"content": "wait a bit",
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"id": 1066756925334765700,
"author_id": 490928916207370240,
"author_name": "jesper",
"timestamp": "01/22/2023 11:31:10",
"content": "yeah take your time",
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"id": 1066757880453267600,
"author_id": 987071591169011700,
"author_name": "kiritoholy",
"timestamp": "01/22/2023 11:34:58",
"content": "is this right?",
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"timestamp": "01/22/2023 11:35:03",
"content": "",
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"id": 1066757930092871700,
"author_id": 490928916207370240,
"author_name": "jesper",
"timestamp": "01/22/2023 11:35:09",
"content": "holy lord",
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},
{
"id": 1066758018206814200,
"author_id": 987071591169011700,
"author_name": "kiritoholy",
"timestamp": "01/22/2023 11:35:30",
"content": "now we can combine these",
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},
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"id": 1066758055762600000,
"author_id": 490928916207370240,
"author_name": "jesper",
"timestamp": "01/22/2023 11:35:39",
"content": "yeah right",
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"id": 1066758190286508200,
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"timestamp": "01/22/2023 11:36:11",
"content": "dude",
"attachments": [],
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{
"id": 1066758216844849300,
"author_id": 987071591169011700,
"author_name": "kiritoholy",
"timestamp": "01/22/2023 11:36:18",
"content": "i got the answer of a",
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"id": 1066758257517019100,
"author_id": 490928916207370240,
"author_name": "jesper",
"timestamp": "01/22/2023 11:36:28",
"content": "huh",
"attachments": [],
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},
{
"id": 1066758376794628200,
"author_id": 490928916207370240,
"author_name": "jesper",
"timestamp": "01/22/2023 11:36:56",
"content": "oh right",
"attachments": [],
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},
{
"id": 1066758462941429900,
"author_id": 490928916207370240,
"author_name": "jesper",
"timestamp": "01/22/2023 11:37:16",
"content": "still confused on the math you did on the diagram",
"attachments": [],
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},
{
"id": 1066758508114088200,
"author_id": 490928916207370240,
"author_name": "jesper",
"timestamp": "01/22/2023 11:37:27",
"content": "oh wait np",
"attachments": [],
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},
{
"id": 1066758527332389000,
"author_id": 490928916207370240,
"author_name": "jesper",
"timestamp": "01/22/2023 11:37:32",
"content": "i think i understand",
"attachments": [],
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},
{
"id": 1066758580767826000,
"author_id": 987071591169011700,
"author_name": "kiritoholy",
"timestamp": "01/22/2023 11:37:45",
"content": "ohh",
"attachments": [],
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},
{
"id": 1066758590016278700,
"author_id": 490928916207370240,
"author_name": "jesper",
"timestamp": "01/22/2023 11:37:47",
"content": "so the length x is being taken of the wire",
"attachments": [],
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},
{
"id": 1066758606999015600,
"author_id": 490928916207370240,
"author_name": "jesper",
"timestamp": "01/22/2023 11:37:51",
"content": "then its divided into 4",
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},
{
"id": 1066758611361091700,
"author_id": 987071591169011700,
"author_name": "kiritoholy",
"timestamp": "01/22/2023 11:37:52",
"content": "yes",
"attachments": [],
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},
{
"id": 1066758623138697300,
"author_id": 490928916207370240,
"author_name": "jesper",
"timestamp": "01/22/2023 11:37:55",
"content": "to take all sides",
"attachments": [],
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},
{
"id": 1066758637147660400,
"author_id": 987071591169011700,
"author_name": "kiritoholy",
"timestamp": "01/22/2023 11:37:58",
"content": "but wait",
"attachments": [],
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},
{
"id": 1066758681380786200,
"author_id": 490928916207370240,
"author_name": "jesper",
"timestamp": "01/22/2023 11:38:09",
"content": "then the remaining part of the wire is 40-x then divide by 4!",
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{
"id": 1066758684161622000,
"author_id": 987071591169011700,
"author_name": "kiritoholy",
"timestamp": "01/22/2023 11:38:09",
"content": "i have to take another variable",
"attachments": [],
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},
{
"id": 1066758689559674900,
"author_id": 490928916207370240,
"author_name": "jesper",
"timestamp": "01/22/2023 11:38:11",
"content": "?*",
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},
{
"id": 1066758692659273700,
"author_id": 987071591169011700,
"author_name": "kiritoholy",
"timestamp": "01/22/2023 11:38:11",
"content": "like z",
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},
{
"id": 1066758696736129200,
"author_id": 490928916207370240,
"author_name": "jesper",
"timestamp": "01/22/2023 11:38:12",
"content": "oh",
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},
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"id": 1066758713454641300,
"author_id": 490928916207370240,
"author_name": "jesper",
"timestamp": "01/22/2023 11:38:16",
"content": "alright",
"attachments": [],
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},
{
"id": 1066758726058520600,
"author_id": 987071591169011700,
"author_name": "kiritoholy",
"timestamp": "01/22/2023 11:38:19",
"content": "because in a) its asking if the side of square is taken be x",
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},
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"id": 1066758883890188400,
"author_id": 987071591169011700,
"author_name": "kiritoholy",
"timestamp": "01/22/2023 11:38:57",
"content": "so u understand",
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},
{
"id": 1066758893906178200,
"author_id": 987071591169011700,
"author_name": "kiritoholy",
"timestamp": "01/22/2023 11:38:59",
"content": "or not",
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},
{
"id": 1066759012315570300,
"author_id": 490928916207370240,
"author_name": "jesper",
"timestamp": "01/22/2023 11:39:27",
"content": "didnt quite understand that part",
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},
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"id": 1066759072654835700,
"author_id": 987071591169011700,
"author_name": "kiritoholy",
"timestamp": "01/22/2023 11:39:42",
"content": "ok lemme send you full solution",
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},
{
"id": 1066759097866797200,
"author_id": 490928916207370240,
"author_name": "jesper",
"timestamp": "01/22/2023 11:39:48",
"content": "yes please",
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},
{
"id": 1066761237343518700,
"author_id": 987071591169011700,
"author_name": "kiritoholy",
"timestamp": "01/22/2023 11:48:18",
"content": "here",
"attachments": [],
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},
{
"id": 1066761249288888400,
"author_id": 987071591169011700,
"author_name": "kiritoholy",
"timestamp": "01/22/2023 11:48:21",
"content": "see this",
"attachments": [],
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},
{
"id": 1066761315307225200,
"author_id": 987071591169011700,
"author_name": "kiritoholy",
"timestamp": "01/22/2023 11:48:37",
"content": "the solution of a",
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},
{
"id": 1066761371708039200,
"author_id": 987071591169011700,
"author_name": "kiritoholy",
"timestamp": "01/22/2023 11:48:50",
"content": "after this you know x=a/4",
"attachments": [],
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},
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"id": 1066761607797022700,
"author_id": 987071591169011700,
"author_name": "kiritoholy",
"timestamp": "01/22/2023 11:49:46",
"content": "",
"attachments": [
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{
"id": 1066762160836976800,
"author_id": 490928916207370240,
"author_name": "jesper",
"timestamp": "01/22/2023 11:51:58",
"content": "whats the difference between that and the one you sent earlier",
"attachments": [],
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},
{
"id": 1066762178792804500,
"author_id": 490928916207370240,
"author_name": "jesper",
"timestamp": "01/22/2023 11:52:02",
"content": "why cant you use x?",
"attachments": [],
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},
{
"id": 1066762302411509800,
"author_id": 490928916207370240,
"author_name": "jesper",
"timestamp": "01/22/2023 11:52:32",
"content": "oh right",
"attachments": [],
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},
{
"id": 1066762391771152400,
"author_id": 490928916207370240,
"author_name": "jesper",
"timestamp": "01/22/2023 11:52:53",
"content": "but can you explain why it needs to be a/4",
"attachments": [],
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},
{
"id": 1066762417364811900,
"author_id": 490928916207370240,
"author_name": "jesper",
"timestamp": "01/22/2023 11:52:59",
"content": "what does it change",
"attachments": [],
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},
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"id": 1066766193790288000,
"author_id": 805217272087838700,
"author_name": "Mathematics Bot",
"timestamp": "01/22/2023 12:08:00",
"content": "@jesper Has your question been resolved?",
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"id": 1066766752794550400,
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"timestamp": "01/22/2023 12:10:13",
"content": "@Helpers",
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{
"id": 1066771136215523500,
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"timestamp": "01/22/2023 12:27:38",
"content": "@Helpers",
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"id": 1066773603598729200,
"author_id": 490928916207370240,
"author_name": "jesper",
"timestamp": "01/22/2023 12:37:26",
"content": ".close",
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},
{
"id": 1066773606572499100,
"author_id": 805217272087838700,
"author_name": "Mathematics Bot",
"timestamp": "01/22/2023 12:37:27",
"content": "Channel closed",
"attachments": [],
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}
] | help-9 | e097353b9578466da8cd39e3d69975d0 |
200,941 | [
{
"id": 1066773858696310900,
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"timestamp": "01/22/2023 12:38:27",
"content": "Available help channel!",
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"id": 1066774110505545900,
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"timestamp": "01/22/2023 12:39:28",
"content": "Pinned a message.",
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"id": 1066774224993259500,
"author_id": 308167389579706400,
"author_name": "Shift",
"timestamp": "01/22/2023 12:39:54",
"content": "How am I suppose to solve this",
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{
"id": 1066774346011521000,
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"author_name": "Shift",
"timestamp": "01/22/2023 12:40:23",
"content": "How do I start?",
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"author_id": 805217272087838700,
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"content": "@Shift Has your question been resolved?",
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"id": 1066780816199401500,
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"content": "@Helpers",
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"content": "@Shift Has your question been resolved?",
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"content": "@Helpers",
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"content": "@Helpers",
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{
"id": 1066798120253542500,
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"timestamp": "01/22/2023 14:14:52",
"content": "@Helpers 🙏 help",
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{
"id": 1066804287742681200,
"author_id": 1059704692571127900,
"author_name": "BR.BAKHTI",
"timestamp": "01/22/2023 14:39:22",
"content": "help me",
"attachments": [
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"timestamp": "01/22/2023 15:14:52",
"content": "@Shift Has your question been resolved?",
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"author_id": 1066827809823142000,
"author_name": "stéphane",
"timestamp": "01/22/2023 16:37:20",
"content": "/Hello. Someone wondered about the harmonic series. One way to understand that she diverges is to draw a picture. It is compared to the area between the abscissa axis and the curve with equation $y=\\frac1x$. Since this area is of the order of $logX$ and $\\lim logX=+\\infty$, the harmonic series diverges. It is to be checked but it should work by starting by making a drawing.",
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{
"id": 1066833987579941000,
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"author_name": "TeXit",
"timestamp": "01/22/2023 16:37:23",
"content": "**stéphane**",
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"timestamp": "01/22/2023 17:17:20",
"content": "@Shift Has your question been resolved?",
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"id": 1066847353685954600,
"author_id": 182179228840755200,
"author_name": "iCaird",
"timestamp": "01/22/2023 17:30:30",
"content": "#❓how-to-get-help",
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"timestamp": "01/22/2023 19:17:20",
"content": "Channel closed",
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}
] | help-9 | 002371b3cdfa457593d5ece97fbcd723 |
200,942 | [
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"timestamp": "10/30/2022 08:05:36",
"content": "Available help channel!",
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"id": 1036252721491222500,
"author_id": 1014406960134754300,
"author_name": "Polaris",
"timestamp": "10/30/2022 08:18:21",
"content": "Where am I making a mistake ?? same integration but different methods getting an extra -1/4 somehow",
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"timestamp": "10/30/2022 08:18:22",
"content": "Pinned a message.",
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"id": 1036253321159266400,
"author_id": 348696743388381200,
"author_name": "A Lonely Bean",
"timestamp": "10/30/2022 08:20:44",
"content": "C is just a constant",
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"author_id": 348696743388381200,
"author_name": "A Lonely Bean",
"timestamp": "10/30/2022 08:20:50",
"content": "And so is -1/4 + C",
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"id": 1036253360816410600,
"author_id": 348696743388381200,
"author_name": "A Lonely Bean",
"timestamp": "10/30/2022 08:20:53",
"content": "There's nothing wrong",
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"author_id": 1014406960134754300,
"author_name": "Polaris",
"timestamp": "10/30/2022 08:29:40",
"content": "Ohh like that... oke got it thx",
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"author_id": 1014406960134754300,
"author_name": "Polaris",
"timestamp": "10/30/2022 08:29:47",
"content": ".close",
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"author_id": 805217272087838700,
"author_name": "Mathematics Bot",
"timestamp": "10/30/2022 08:29:48",
"content": "Channel closed",
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}
] | help-9 | 774e4d9210f64e20a91df990e6e201a8 |
200,943 | [
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"timestamp": "01/22/2023 19:18:21",
"content": "Available help channel!",
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},
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"id": 1066875426565267600,
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"author_name": "Stroheim",
"timestamp": "01/22/2023 19:22:31",
"content": "Hi, i know that FB = 10, and i wrote the following assuming AF = X and FD = Y but i don't know what else i can do, nor how to use the condition that MC = 7",
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"timestamp": "01/22/2023 19:37:31",
"content": "@Stroheim Has your question been resolved?",
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"content": ".close",
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"timestamp": "01/22/2023 19:48:06",
"content": "Channel closed",
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}
] | help-9 | 0f57ad620a754701b3d8c35317321e90 |
200,944 | [
{
"id": 1066882235464175600,
"author_id": 805217272087838700,
"author_name": "Mathematics Bot",
"timestamp": "01/22/2023 19:49:06",
"content": "Available help channel!",
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},
{
"id": 1066884460362080400,
"author_id": 304017277815357440,
"author_name": "Zeffy",
"timestamp": "01/22/2023 19:57:57",
"content": "how would I solve for F?",
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"content": "Pinned a message.",
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"id": 1066884519845703700,
"author_id": 304017277815357440,
"author_name": "Zeffy",
"timestamp": "01/22/2023 19:58:11",
"content": "i tried doing -2 = 4cos(x)\nthen i divided by 4 and go -1/2 = cos(x)",
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},
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"id": 1066884548463440000,
"author_id": 304017277815357440,
"author_name": "Zeffy",
"timestamp": "01/22/2023 19:58:18",
"content": "got*",
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"id": 1066885757328961500,
"author_id": 696748240758112300,
"author_name": "everg",
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"id": 1066886888218185900,
"author_id": 304017277815357440,
"author_name": "Zeffy",
"timestamp": "01/22/2023 20:07:35",
"content": "i dont get it",
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},
{
"id": 1066886898703941800,
"author_id": 304017277815357440,
"author_name": "Zeffy",
"timestamp": "01/22/2023 20:07:38",
"content": "did i pull a stupid",
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},
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"id": 1066887024591769600,
"author_id": 304017277815357440,
"author_name": "Zeffy",
"timestamp": "01/22/2023 20:08:08",
"content": "i picked 4pi/3 which is bottom left and 2pi/3 which is top left",
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},
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"id": 1066887745009627100,
"author_id": 696748240758112300,
"author_name": "everg",
"timestamp": "01/22/2023 20:11:00",
"content": "its good",
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},
{
"id": 1066887833140342800,
"author_id": 304017277815357440,
"author_name": "Zeffy",
"timestamp": "01/22/2023 20:11:21",
"content": "but it keeps giving me an error 😢",
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{
"id": 1066888012237123600,
"author_id": 696748240758112300,
"author_name": "everg",
"timestamp": "01/22/2023 20:12:03",
"content": "twy to invert the answers xD",
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},
{
"id": 1066888051361583200,
"author_id": 304017277815357440,
"author_name": "Zeffy",
"timestamp": "01/22/2023 20:12:13",
"content": "oki",
"attachments": [],
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"reference": null
},
{
"id": 1066888135402864600,
"author_id": 304017277815357440,
"author_name": "Zeffy",
"timestamp": "01/22/2023 20:12:33",
"content": "o nvm i see why its wrng",
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},
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"id": 1066888170005864400,
"author_id": 304017277815357440,
"author_name": "Zeffy",
"timestamp": "01/22/2023 20:12:41",
"content": "its because i need to do the negative version also",
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"author_name": "Mathematics Bot",
"timestamp": "01/22/2023 20:27:41",
"content": "@Zeffy Has your question been resolved?",
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"author_name": "Mathematics Bot",
"timestamp": "01/22/2023 20:42:42",
"content": "Channel closed",
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}
] | help-9 | 56e937266fa6442f8e0fc37d57d705e2 |
200,945 | [
{
"id": 1066895974213107800,
"author_id": 805217272087838700,
"author_name": "Mathematics Bot",
"timestamp": "01/22/2023 20:43:42",
"content": "Available help channel!",
"attachments": [],
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"reference": null
},
{
"id": 1066896809680711800,
"author_id": 619976004986732500,
"author_name": "明多夢",
"timestamp": "01/22/2023 20:47:01",
"content": "express the following satisfying the given conditions as an interval |x-8| < 8.",
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"id": 1066896811693965300,
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"timestamp": "01/22/2023 20:47:01",
"content": "Pinned a message.",
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"id": 1066897017558814700,
"author_id": 619976004986732500,
"author_name": "明多夢",
"timestamp": "01/22/2023 20:47:50",
"content": "(-INF, 0) U (0, INF), whats wrong with thsi answer?",
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},
{
"id": 1066897067668160600,
"author_id": 349354952961032200,
"author_name": "Umbraleviathan",
"timestamp": "01/22/2023 20:48:02",
"content": "You neglected the 8",
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},
{
"id": 1066897110097731700,
"author_id": 349354952961032200,
"author_name": "Umbraleviathan",
"timestamp": "01/22/2023 20:48:13",
"content": "$$|k| < a \\implies -a < k < a$$",
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{
"id": 1066897114669531100,
"author_id": 619976004986732500,
"author_name": "明多夢",
"timestamp": "01/22/2023 20:48:14",
"content": "OH god, lol",
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},
{
"id": 1066897119413272600,
"author_id": 510789298321096700,
"author_name": "TeXit",
"timestamp": "01/22/2023 20:48:15",
"content": "**$e^{\\\\text{Umbraleviathan}}$**",
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"id": 1066897167584862300,
"author_id": 619976004986732500,
"author_name": "明多夢",
"timestamp": "01/22/2023 20:48:26",
"content": "just realized I read it backwards",
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{
"id": 1066897185268043800,
"author_id": 619976004986732500,
"author_name": "明多夢",
"timestamp": "01/22/2023 20:48:30",
"content": "thanks",
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},
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"id": 1066897366520700900,
"author_id": 619976004986732500,
"author_name": "明多夢",
"timestamp": "01/22/2023 20:49:14",
"content": ".close",
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"id": 1066897369037283300,
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"author_name": "Mathematics Bot",
"timestamp": "01/22/2023 20:49:14",
"content": "Channel closed",
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}
] | help-9 | c5101241d7e744bd8e1d8d1918973b3d |
200,946 | [
{
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"timestamp": "01/22/2023 21:16:09",
"content": "Available help channel!",
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},
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"id": 1066904267807539300,
"author_id": 811472956332572700,
"author_name": "roam",
"timestamp": "01/22/2023 21:16:39",
"content": "can someone help me with this question",
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"timestamp": "01/22/2023 21:16:40",
"content": "Pinned a message.",
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"id": 1066904591003820200,
"author_id": 196556976866459650,
"author_name": "DerpZ",
"timestamp": "01/22/2023 21:17:56",
"content": "!status",
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"id": 1066904592043999400,
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"author_name": "Mathematics Bot",
"timestamp": "01/22/2023 21:17:56",
"content": "```\nWhat step are you on?\n1. I don't know where to begin\n2. I have begun but got stuck midway\n3. I got an answer but I'm told it's wrong\n4. I got an answer and would like my work checked\n5. I have a question about someone else's worked solution\n6. None of the above\n```",
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"id": 1066905315850850300,
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"author_name": "roam",
"timestamp": "01/22/2023 21:20:49",
"content": "don’t know where to begin",
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"id": 1066905360117530600,
"author_id": 196556976866459650,
"author_name": "DerpZ",
"timestamp": "01/22/2023 21:20:59",
"content": "draw a diagram",
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"id": 1066905454921388200,
"author_id": 196556976866459650,
"author_name": "DerpZ",
"timestamp": "01/22/2023 21:21:22",
"content": "hint: it will look like a triangle",
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"id": 1066906870092152800,
"author_id": 811472956332572700,
"author_name": "roam",
"timestamp": "01/22/2023 21:27:00",
"content": "something like this I assume?",
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"id": 1066907438466486300,
"author_id": 196556976866459650,
"author_name": "DerpZ",
"timestamp": "01/22/2023 21:29:15",
"content": "yup",
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{
"id": 1066907497518092300,
"author_id": 196556976866459650,
"author_name": "DerpZ",
"timestamp": "01/22/2023 21:29:29",
"content": "now draw the triangle for her friend",
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},
{
"id": 1066907533547159700,
"author_id": 196556976866459650,
"author_name": "DerpZ",
"timestamp": "01/22/2023 21:29:38",
"content": "the triangles are similar triangles",
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"id": 1066907993553248300,
"author_id": 811472956332572700,
"author_name": "roam",
"timestamp": "01/22/2023 21:31:27",
"content": "how would I draw one, I don’t really have enough information",
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"id": 1066908052894257300,
"author_id": 196556976866459650,
"author_name": "DerpZ",
"timestamp": "01/22/2023 21:31:42",
"content": "her friend's shadow is 1 foot shorter than hers",
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"id": 1066908138495819900,
"author_id": 196556976866459650,
"author_name": "DerpZ",
"timestamp": "01/22/2023 21:32:02",
"content": "you can, by letting her friend's height be x",
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"id": 1066908142484607100,
"author_id": 196556976866459650,
"author_name": "DerpZ",
"timestamp": "01/22/2023 21:32:03",
"content": "or something",
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},
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"id": 1066908635457933300,
"author_id": 811472956332572700,
"author_name": "roam",
"timestamp": "01/22/2023 21:34:00",
"content": "how does that help me figure out the height though",
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"id": 1066908671877054500,
"author_id": 196556976866459650,
"author_name": "DerpZ",
"timestamp": "01/22/2023 21:34:09",
"content": "similar triangles",
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"timestamp": "01/22/2023 21:37:41",
"content": "",
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"id": 1066909613338927200,
"author_id": 811472956332572700,
"author_name": "roam",
"timestamp": "01/22/2023 21:37:54",
"content": "there’s the second one",
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},
{
"id": 1066909647010807900,
"author_id": 811472956332572700,
"author_name": "roam",
"timestamp": "01/22/2023 21:38:02",
"content": "not sure what I should do now",
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"author_name": "DerpZ",
"timestamp": "01/22/2023 21:40:49",
"content": "similar triangles",
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"author_name": "roam",
"timestamp": "01/22/2023 21:41:29",
"content": "okay so what should I do now?",
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"timestamp": "01/22/2023 21:41:44",
"content": "ok do you know trigonometry",
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"content": "no",
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"author_name": "DerpZ",
"timestamp": "01/22/2023 21:52:32",
"content": "sorry I'm going to go now so helper ping if ur still stuck after 15mins",
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"timestamp": "01/22/2023 21:52:34",
"content": "but the hint here is",
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"timestamp": "01/22/2023 21:52:54",
"content": "the ratio of x to 6 is the same as the ratio in the first triangle you drew",
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"author_name": "roam",
"timestamp": "01/22/2023 21:53:12",
"content": "okay thanks for the help",
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"id": 1066916645005709400,
"author_id": 811472956332572700,
"author_name": "roam",
"timestamp": "01/22/2023 22:05:50",
"content": "@Helpers working on this, not sure what to do",
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},
{
"id": 1066916866469150800,
"author_id": 374795910032523260,
"author_name": "SWR",
"timestamp": "01/22/2023 22:06:43",
"content": "similar triangles",
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"id": 1066916992914821200,
"author_id": 374795910032523260,
"author_name": "SWR",
"timestamp": "01/22/2023 22:07:13",
"content": "If you have this problem, then you should have notes on them somewhere",
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"id": 1066917016277094500,
"author_id": 374795910032523260,
"author_name": "SWR",
"timestamp": "01/22/2023 22:07:19",
"content": "I assume this is for geometry",
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"id": 1066917065446916100,
"author_id": 811472956332572700,
"author_name": "roam",
"timestamp": "01/22/2023 22:07:30",
"content": "yeah it is",
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"id": 1066917105909379200,
"author_id": 811472956332572700,
"author_name": "roam",
"timestamp": "01/22/2023 22:07:40",
"content": "and I don’t have notes because my teacher has been sick",
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"id": 1066917294711775400,
"author_id": 374795910032523260,
"author_name": "SWR",
"timestamp": "01/22/2023 22:08:25",
"content": "https://www.cuemath.com/geometry/similar-triangles/",
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"timestamp": "01/22/2023 22:09:04",
"content": "thanks I’ll take a look",
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"timestamp": "01/22/2023 22:24:05",
"content": "@roam Has your question been resolved?",
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"timestamp": "01/22/2023 22:39:06",
"content": "Channel closed",
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] | help-9 | f7a394c978f04dc18a4d6fda1596cf4a |
200,947 | [
{
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"content": "Available help channel!",
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"id": 1066925665099710600,
"author_id": 229666616957337600,
"author_name": "Aurora",
"timestamp": "01/22/2023 22:41:41",
"content": "I need help with vector math. In this scenario, there is a line with a fulcrum at the center and two angled vectors on either side, creating torque. The vectors remain at the same absolute angle (in this case, 45 degrees), meaning that as the line rotates due to the torque, the amount of torque present will also change, and thus the effect of that torque on angular velocity. I need a way to calculate the rotational velocity over time with this feedback loop in mind",
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"content": "@Aurora Has your question been resolved?",
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] | help-9 | 9acfdcbd82704b5f9f14e25106b3ff9c |
200,948 | [
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"timestamp": "01/22/2023 23:59:25",
"content": "Available help channel!",
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{
"id": 1066945595295682600,
"author_id": 309857272522342400,
"author_name": "zura",
"timestamp": "01/23/2023 00:00:52",
"content": "can someone help me find 4 my brain is off rn",
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"id": 1066945838275887100,
"author_id": 605044221010772000,
"author_name": "Trumpet Bot",
"timestamp": "01/23/2023 00:01:50",
"content": "You know what 7 is and the angles of a triangle at to 180",
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"id": 1066946096523382900,
"author_id": 309857272522342400,
"author_name": "zura",
"timestamp": "01/23/2023 00:02:52",
"content": "so 118?",
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},
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"id": 1066946375490744300,
"author_id": 1003857269802401900,
"author_name": "starlight",
"timestamp": "01/23/2023 00:03:58",
"content": "a triangle has 3 angles",
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"id": 1066946696203993100,
"author_id": 309857272522342400,
"author_name": "zura",
"timestamp": "01/23/2023 00:05:15",
"content": "62?",
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"id": 1066946850755711000,
"author_id": 309857272522342400,
"author_name": "zura",
"timestamp": "01/23/2023 00:05:52",
"content": "but im pretty sure i tried that and it was wrong",
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"id": 1066947040996773900,
"author_id": 605044221010772000,
"author_name": "Trumpet Bot",
"timestamp": "01/23/2023 00:06:37",
"content": "Addition",
"attachments": [],
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{
"id": 1066947126669606900,
"author_id": 605044221010772000,
"author_name": "Trumpet Bot",
"timestamp": "01/23/2023 00:06:57",
"content": "What’s 62+67",
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{
"id": 1066947167996096500,
"author_id": 309857272522342400,
"author_name": "zura",
"timestamp": "01/23/2023 00:07:07",
"content": "129",
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{
"id": 1066947185419243500,
"author_id": 485903210272391200,
"author_name": "dldh06",
"timestamp": "01/23/2023 00:07:11",
"content": "Here's another way to approach the problem, notice how 62, angle 4, and angle 5 are on a straight line",
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"id": 1066947227613941800,
"author_id": 485903210272391200,
"author_name": "dldh06",
"timestamp": "01/23/2023 00:07:21",
"content": "What's the measure of a straight line?",
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{
"id": 1066947361928126500,
"author_id": 309857272522342400,
"author_name": "zura",
"timestamp": "01/23/2023 00:07:54",
"content": "180",
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"id": 1066947383532986500,
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"author_name": "zura",
"timestamp": "01/23/2023 00:07:59",
"content": "i think i got it now",
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"id": 1066947637397438500,
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"author_name": "zura",
"timestamp": "01/23/2023 00:08:59",
"content": "got it",
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"author_name": "dldh06",
"timestamp": "01/23/2023 00:09:21",
"content": "`.close` if you are done",
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"id": 1066947749616037900,
"author_id": 309857272522342400,
"author_name": "zura",
"timestamp": "01/23/2023 00:09:26",
"content": ".close",
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},
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"author_name": "Mathematics Bot",
"timestamp": "01/23/2023 00:09:27",
"content": "Channel closed",
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] | help-9 | f0d21df319364421b90b31b7560b77be |
200,949 | [
{
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"id": 1066948537239228500,
"author_id": 885812980468572200,
"author_name": "Eunike",
"timestamp": "01/23/2023 00:12:34",
"content": "May i know why the answer is 0,8621 but the z score is -1.09 it doesn't match isn't it?",
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"author_name": "dldh06",
"timestamp": "01/23/2023 00:13:52",
"content": "You use the z table",
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"id": 1066948878982721700,
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"author_name": "Eunike",
"timestamp": "01/23/2023 00:13:55",
"content": "If 1.09 = 0.8621 is correct\nBut why\n-1.09 can be 0.8621 too?",
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"id": 1066948886427611100,
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"timestamp": "01/23/2023 00:13:57",
"content": "Yes",
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"author_name": "dldh06",
"timestamp": "01/23/2023 00:14:12",
"content": "That z score relates to a z table value",
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"id": 1066949088270110800,
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"author_name": "dldh06",
"timestamp": "01/23/2023 00:14:45",
"content": "That table value relates to the area under the normal distribution curve",
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"id": 1066949457284976800,
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"timestamp": "01/23/2023 00:16:13",
"content": "-1.09 relates to 0.1379, the area from the left end of the curve to the z score. You wanted the other part of the curve",
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"author_name": "Eunike",
"timestamp": "01/23/2023 00:16:13",
"content": "But in this table it show me different value",
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"author_name": "dldh06",
"timestamp": "01/23/2023 00:16:27",
"content": "So you do 1 - 0.1379",
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"author_name": "Eunike",
"timestamp": "01/23/2023 00:16:45",
"content": "Oh should i?",
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"timestamp": "01/23/2023 00:17:19",
"content": "I think just match it in the z table",
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"timestamp": "01/23/2023 00:17:52",
"content": "Not drawn to scale, but that black area is 0.1379, you're looking for the blue shaded",
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"timestamp": "01/23/2023 00:18:05",
"content": "To find that, you do 1 - 0.1379",
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"author_name": "Eunike",
"timestamp": "01/23/2023 00:18:22",
"content": "🤔🤔how it can be",
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"author_name": "dldh06",
"timestamp": "01/23/2023 00:18:51",
"content": "Because it says \"at least\" so you want the area greater than that z score",
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"timestamp": "01/23/2023 00:19:13",
"content": "Which is the blue",
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"author_id": 885812980468572200,
"author_name": "Eunike",
"timestamp": "01/23/2023 00:19:19",
"content": "How about equal to 25?",
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"author_id": 885812980468572200,
"author_name": "Eunike",
"timestamp": "01/23/2023 00:19:26",
"content": "Is it should be the same?",
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"id": 1066950335333146600,
"author_id": 485903210272391200,
"author_name": "dldh06",
"timestamp": "01/23/2023 00:19:42",
"content": "No what if questions",
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"author_name": "dldh06",
"timestamp": "01/23/2023 00:20:01",
"content": "The question stated at least 25 people, that is the blue area",
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"timestamp": "01/23/2023 00:20:17",
"content": "So you find the black area first, subtract it from 1",
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"author_id": 485903210272391200,
"author_name": "dldh06",
"timestamp": "01/23/2023 00:20:21",
"content": "To get the blue",
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"author_id": 885812980468572200,
"author_name": "Eunike",
"timestamp": "01/23/2023 00:20:29",
"content": "Okay , if i have another question",
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"author_id": 885812980468572200,
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"content": "equal to 25 people",
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"author_id": 885812980468572200,
"author_name": "Eunike",
"timestamp": "01/23/2023 00:21:04",
"content": "Is it show me the same result?",
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"id": 1066950793833492500,
"author_id": 885812980468572200,
"author_name": "Eunike",
"timestamp": "01/23/2023 00:21:32",
"content": "Or it has different formula and way to solve this problem?",
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"id": 1066950956463440000,
"author_id": 485903210272391200,
"author_name": "dldh06",
"timestamp": "01/23/2023 00:22:11",
"content": "Don't remember probability well enough to help you there",
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"author_id": 885812980468572200,
"author_name": "Eunike",
"timestamp": "01/23/2023 00:22:51",
"content": "Wait , may i know , why 0,1379 at the left side of -1.09?",
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"timestamp": "01/23/2023 00:23:21",
"content": "Because that's how the z table works",
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"content": "It's the area under the curve starting from the left",
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"timestamp": "01/23/2023 00:25:38",
"content": "Oh okay thanks",
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"author_id": 885812980468572200,
"author_name": "Eunike",
"timestamp": "01/23/2023 00:25:52",
"content": ".close",
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"content": "Channel closed",
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] | help-9 | afc7dea8ea6346438cd313228f6a4367 |
200,950 | [
{
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"content": "why is this wrong?",
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"id": 1066967321098330100,
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"author_name": "tatpoj",
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"content": "What was the original form?",
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"content": "what is the original question",
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"content": "@DantonBlack Has your question been resolved?",
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] | help-9 | ddc40fa66fbf4c6cbaca6fd91670bca6 |
200,951 | [
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"content": "Available help channel!",
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"content": "ping me plz",
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"content": "@DantonBlack Has your question been resolved?",
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] | help-9 | 6524c70a07c04c4aabacdf3fe943588e |
200,952 | [
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"content": "Available help channel!",
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"id": 1066983878767685600,
"author_id": 346451029966979100,
"author_name": "Mingus",
"timestamp": "01/23/2023 02:33:00",
"content": "so this might be me being really dumb rn but this is a thing i learned a long time ago and now i need to do it again, i feel like im doing this very wrong but idk i just need someone to help tell me what im doing wrong and how to actually do it",
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"content": "Pinned a message.",
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"content": "@Mingus Has your question been resolved?",
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"content": "@Helpers",
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"author_id": 329749386315956200,
"author_name": "Sneaky",
"timestamp": "01/23/2023 02:48:51",
"content": "a) is good",
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"author_name": "eatone_QUBIT",
"timestamp": "01/23/2023 02:48:53",
"content": "ok let me try",
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"content": "b) is good",
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"content": "c) is not.",
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"content": "yes",
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"author_name": "Sneaky",
"timestamp": "01/23/2023 02:50:27",
"content": "For c), consider peter and alice as one person",
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"timestamp": "01/23/2023 02:50:36",
"content": "i.e. there are 5! possible arrangements",
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"timestamp": "01/23/2023 02:50:45",
"content": "then multiply that by 2 for swapping peter and alice",
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"timestamp": "01/23/2023 02:51:06",
"content": "ok hold on",
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"author_name": "Mingus",
"timestamp": "01/23/2023 02:51:52",
"content": "but that would mean there are 120 combinations of peter and alice but 24 combinations of the other 4?",
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"id": 1066988692259995600,
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"timestamp": "01/23/2023 02:52:07",
"content": "or 240 combinations after you multiplied by 2",
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"timestamp": "01/23/2023 02:52:31",
"content": "The latter",
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"timestamp": "01/23/2023 02:53:09",
"content": "that seems like a lot of combinations for 2 people to be swapped in compared to 4 people only having 24 i dont think i understand",
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"timestamp": "01/23/2023 02:55:17",
"content": "Here's a visual representation. there are 5!=120 ways to arrange this, considering Peter and alice as a unit, you can't move them away from each other? And for each of those ways, you can get another arrangement by swapping peter and alice around. Thus, 120*2=240",
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"timestamp": "01/23/2023 02:56:07",
"content": "ok so 240 would be the total number of combinations, no need for the 4p4 thing i had there originally?",
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"timestamp": "01/23/2023 02:56:19",
"content": "Yeah.",
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"timestamp": "01/23/2023 02:57:38",
"content": "ok i dont really understand but as long as it's right thats enough lol this is only question 2 of 11. Thank you",
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"timestamp": "01/23/2023 02:57:50",
"content": "how do i close this thingy",
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"timestamp": "01/23/2023 02:59:12",
"content": "I can help you Mingus.",
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"timestamp": "01/23/2023 03:04:53",
"content": ".close",
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] | help-9 | 562b937bcbb649e999c576aae844d14e |
200,953 | [
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"timestamp": "10/21/2022 18:59:19",
"content": "So this is totally wrong right",
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"id": 1033152591393198100,
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"timestamp": "10/21/2022 18:59:32",
"content": "But I'm having troubling formulating exactly why this is wrong",
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"id": 1033152880284282900,
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"timestamp": "10/21/2022 19:00:41",
"content": "you can't split the product unless both are positive",
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"timestamp": "10/21/2022 19:01:03",
"content": "Ahh",
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"timestamp": "10/21/2022 19:01:21",
"content": "Yeah that makes sense",
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"author_name": "GarlicBredFries",
"timestamp": "10/21/2022 19:01:23",
"content": "oh thats a funny one",
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"id": 1033153109180039200,
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"timestamp": "10/21/2022 19:01:36",
"content": "Could make a whole lot of other weird stuff if you could haha",
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"id": 1033153113240121300,
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"timestamp": "10/21/2022 19:01:37",
"content": "or maybe it's okay if they're the same sign i forget",
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"timestamp": "10/21/2022 19:01:48",
"content": "no it has to be positive",
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"content": "Hmm",
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"timestamp": "10/21/2022 19:01:57",
"content": "That sounds wrong",
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"author_id": 600510288067952600,
"author_name": "GarlicBredFries",
"timestamp": "10/21/2022 19:02:44",
"content": "or at least if written in polar form doesnt go past 2pi?",
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"id": 1033153413493567500,
"author_id": 600510288067952600,
"author_name": "GarlicBredFries",
"timestamp": "10/21/2022 19:02:48",
"content": "i think that sounds right",
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"author_id": 394938706760302600,
"author_name": "heavy",
"timestamp": "10/21/2022 19:03:23",
"content": "Yeah they definitely both have to be positive",
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"id": 1033153659221053400,
"author_id": 394938706760302600,
"author_name": "heavy",
"timestamp": "10/21/2022 19:03:47",
"content": "Last step is the wrong power",
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"id": 1033153664484913200,
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"timestamp": "10/21/2022 19:03:48",
"content": "Woops",
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"timestamp": "10/21/2022 19:18:48",
"content": "@heavy Has your question been resolved?",
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"timestamp": "10/21/2022 19:19:02",
"content": "Channel closed",
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}
] | help-9 | 07b1c1632da0432c883eb944dd14fb38 |
200,954 | [
{
"id": 1036265830113095800,
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"content": "Available help channel!",
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"content": "@ProGamer Has your question been resolved?",
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"timestamp": "10/30/2022 09:26:42",
"content": "@Helpers",
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"author_name": "Duhon",
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"content": "not sure we can read this even",
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"content": "we can't read the question",
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"author_name": "gamingarren",
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"content": "Try and post a translation of the question if you can",
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"content": "There is English translation",
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"content": "@ProGamer Has your question been resolved?",
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"content": "@ProGamer Has your question been resolved?",
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"content": "@ProGamer Has your question been resolved?",
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"author_name": "djuji",
"timestamp": "10/30/2022 14:23:02",
"content": "Where are you stuck exactly? Don't know where to place the angles or?",
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"content": "Channel closed",
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}
] | help-9 | e5d3ed5dc1a049ca91220ac02840eb75 |
200,955 | [
{
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"content": "Available help channel!",
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"id": 1066992802619199500,
"author_id": 274196262759301120,
"author_name": "taemed",
"timestamp": "01/23/2023 03:08:27",
"content": "What type of statistical analysis would be suitable for this data, if any?",
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"content": "@taemed Has your question been resolved?",
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] | help-9 | 1f3e2796dca14dc0a14bb3f1870bea63 |
200,956 | [
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"content": "Factor completely remember to look first for the common factor",
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"author_name": "putridplanet",
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"content": "I’m stuck",
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"author_name": "Quasar",
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"content": "What are you stuck at, the quadratic factoring?",
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"author_name": "Quasar",
"timestamp": "01/23/2023 04:31:53",
"content": "Maybe find pairs like px and qy such that pq = -60",
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"content": "?",
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"author_name": "Quasar",
"timestamp": "01/23/2023 04:33:10",
"content": "Well, what would you do next",
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"id": 1067014147268694000,
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"author_name": "putridplanet",
"timestamp": "01/23/2023 04:33:16",
"content": "I don’t know",
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"author_name": "Quasar",
"timestamp": "01/23/2023 04:33:17",
"content": "Im asking you to split the middle term",
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"timestamp": "01/23/2023 04:33:22",
"content": "Try to, atleast",
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"author_name": "putridplanet",
"timestamp": "01/23/2023 04:33:43",
"content": "Nothing multiplies into 11",
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"id": 1067014284338532500,
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"author_name": "Quasar",
"timestamp": "01/23/2023 04:33:49",
"content": "No",
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"id": 1067014308703244300,
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"timestamp": "01/23/2023 04:33:55",
"content": "Something that adds into 11",
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"id": 1067014322229882900,
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"author_name": "Quasar",
"timestamp": "01/23/2023 04:33:58",
"content": "And multiplies into -60",
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"id": 1067014360729399300,
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"author_name": "putridplanet",
"timestamp": "01/23/2023 04:34:07",
"content": "Why -60 ?",
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"id": 1067014401674199000,
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"author_name": "Quasar",
"timestamp": "01/23/2023 04:34:17",
"content": "12*(-5)",
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"id": 1067014433102123100,
"author_id": 758350848115212300,
"author_name": "Quasar",
"timestamp": "01/23/2023 04:34:25",
"content": "That last term is -5y",
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"id": 1067014435278966800,
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"author_name": "putridplanet",
"timestamp": "01/23/2023 04:34:25",
"content": "Oh I see",
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"id": 1067014530170888200,
"author_id": 758350848115212300,
"author_name": "Quasar",
"timestamp": "01/23/2023 04:34:48",
"content": "Yup so one of the terms would be negative and one positive",
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"id": 1067014556204937200,
"author_id": 858293468710174700,
"author_name": "putridplanet",
"timestamp": "01/23/2023 04:34:54",
"content": "-6 and 5",
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"id": 1067014575259652100,
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"author_name": "Quasar",
"timestamp": "01/23/2023 04:34:58",
"content": "No",
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"id": 1067014587783860200,
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"author_name": "Quasar",
"timestamp": "01/23/2023 04:35:01",
"content": "-6+5",
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},
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"id": 1067014593211269200,
"author_id": 758350848115212300,
"author_name": "Quasar",
"timestamp": "01/23/2023 04:35:03",
"content": "=-1",
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},
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"id": 1067014604074520600,
"author_id": 758350848115212300,
"author_name": "Quasar",
"timestamp": "01/23/2023 04:35:05",
"content": "Not 11",
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"id": 1067014633975726100,
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"author_name": "Quasar",
"timestamp": "01/23/2023 04:35:12",
"content": "And also",
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"id": 1067014639726121000,
"author_id": 858293468710174700,
"author_name": "putridplanet",
"timestamp": "01/23/2023 04:35:14",
"content": "Ok 6 and 5 sorry I’m tired",
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"id": 1067014656436219900,
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"author_name": "Quasar",
"timestamp": "01/23/2023 04:35:18",
"content": "Nah",
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"id": 1067014690976301200,
"author_id": 758350848115212300,
"author_name": "Quasar",
"timestamp": "01/23/2023 04:35:26",
"content": "They dont multipy to -60",
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"id": 1067014817396830200,
"author_id": 858293468710174700,
"author_name": "putridplanet",
"timestamp": "01/23/2023 04:35:56",
"content": "-4 and 15",
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},
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"id": 1067014861873238000,
"author_id": 758350848115212300,
"author_name": "Quasar",
"timestamp": "01/23/2023 04:36:07",
"content": "Yup nice!",
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"id": 1067014893397626900,
"author_id": 858293468710174700,
"author_name": "putridplanet",
"timestamp": "01/23/2023 04:36:14",
"content": "Ok what do I do with it",
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"id": 1067014917246419000,
"author_id": 758350848115212300,
"author_name": "Quasar",
"timestamp": "01/23/2023 04:36:20",
"content": "So you split that thing",
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"id": 1067014921373614100,
"author_id": 758350848115212300,
"author_name": "Quasar",
"timestamp": "01/23/2023 04:36:21",
"content": "Here",
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},
{
"id": 1067014929430892500,
"author_id": 758350848115212300,
"author_name": "Quasar",
"timestamp": "01/23/2023 04:36:23",
"content": "Ill show you",
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},
{
"id": 1067014964231032800,
"author_id": 758350848115212300,
"author_name": "Quasar",
"timestamp": "01/23/2023 04:36:31",
"content": "That 11yx could be written as",
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"id": 1067015130971381800,
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"author_name": "Quasar",
"timestamp": "01/23/2023 04:37:11",
"content": "$4x^2 (12x^2 y + 11yx - 5y)\\\\\\\\\n4x^2(12x^2 y -4yx+15yx - 5y)$",
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"timestamp": "01/23/2023 04:37:13",
"content": "**Quasar**",
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"timestamp": "01/23/2023 04:37:47",
"content": "You see its just the same, we just broke that term in between",
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"timestamp": "01/23/2023 04:37:55",
"content": "Ok then we split them into two groups ?",
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"content": "Do you know splitting the middle term",
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"content": "?",
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"timestamp": "01/23/2023 04:38:17",
"content": "Now I do",
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"timestamp": "01/23/2023 04:38:36",
"content": "Hmm so next would be to find something common between the first two and the last two",
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"timestamp": "01/23/2023 04:38:38",
"content": "like so",
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"timestamp": "01/23/2023 04:40:10",
"content": "Actually uh",
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"content": "You could've",
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"timestamp": "01/23/2023 04:40:18",
"content": "Put that y out as well",
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"timestamp": "01/23/2023 04:40:45",
"content": "$4x^2 y(12x^2 + 11x - 5)\\\\\\\\\n4x^2y(12x^2 -4x+15x - 5)$",
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"timestamp": "01/23/2023 04:40:48",
"content": "**Quasar**",
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"timestamp": "01/23/2023 04:41:10",
"content": "You get it?",
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"timestamp": "01/23/2023 04:41:33",
"content": "Yeah",
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"timestamp": "01/23/2023 04:41:52",
"content": "Yup",
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"author_name": "putridplanet",
"timestamp": "01/23/2023 04:41:57",
"content": "So do we combine like terms",
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"timestamp": "01/23/2023 04:42:08",
"content": "So next, you take some more common things out, here I'll show",
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"timestamp": "01/23/2023 04:42:34",
"content": "$4x^2 y(12x^2 + 11x - 5)\\\\\\\\\n4x^2y(12x^2 -4x+15x - 5)\\\\\\\\\n4x^2y(4x(3x-1) + 5(3x-1))$",
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"timestamp": "01/23/2023 04:42:37",
"content": "**Quasar**",
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"timestamp": "01/23/2023 04:43:53",
"content": "So \n(4x+5) (3x-1)",
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"timestamp": "01/23/2023 04:44:14",
"content": "Yep",
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"timestamp": "01/23/2023 04:44:20",
"content": ":sotrue:",
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"author_name": "Quasar",
"timestamp": "01/23/2023 04:44:21",
"content": "And dont forget that 4x^2y outside",
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"author_name": "putridplanet",
"timestamp": "01/23/2023 04:45:03",
"content": "And that’s as far as it goes ?",
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"content": "Yup that's it, completely factorised",
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"timestamp": "01/23/2023 04:47:07",
"content": "You could up it a notch but",
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"timestamp": "01/23/2023 04:47:19",
"content": "Thats not really needed and is just nothing to be worried of",
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"timestamp": "01/23/2023 04:48:33",
"content": "Ok I’m also stuck on these three",
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"timestamp": "01/23/2023 04:49:50",
"content": "Well uh there's continuously something wrong going on there",
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"content": "Here",
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"timestamp": "01/23/2023 04:50:10",
"content": "$a^2 + b^2 \\neq (a+b)^2$",
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"timestamp": "01/23/2023 04:50:12",
"content": "**Quasar**",
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"author_name": "putridplanet",
"timestamp": "01/23/2023 04:51:31",
"content": "8x^2(2+27)",
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"timestamp": "01/23/2023 04:51:45",
"content": "8x^2 as common",
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"author_name": "Quasar",
"timestamp": "01/23/2023 04:51:53",
"content": "You dont see any \"x\" in the second term do you",
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"timestamp": "01/23/2023 04:51:58",
"content": "No",
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"timestamp": "01/23/2023 04:52:36",
"content": "And how do you even get 27",
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"timestamp": "01/23/2023 04:55:24",
"content": "54 divided by 2",
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"author_name": "putridplanet",
"timestamp": "01/23/2023 04:55:33",
"content": "Sorry I’m tired",
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"timestamp": "01/23/2023 04:55:37",
"content": "If youre taking out 8 common",
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"timestamp": "01/23/2023 04:55:41",
"content": "Then why do you divide by 2",
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"content": "You should divide by 8",
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"timestamp": "01/23/2023 04:55:50",
"content": "2(8x^3+27)",
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"author_name": "putridplanet",
"timestamp": "01/23/2023 04:55:58",
"content": "I’m sleep deprived rn",
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"id": 1067019874192339100,
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"timestamp": "01/23/2023 04:56:02",
"content": "Better",
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"author_id": 758350848115212300,
"author_name": "Quasar",
"timestamp": "01/23/2023 04:56:10",
"content": "Why're you doing this then",
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"author_name": "putridplanet",
"timestamp": "01/23/2023 04:56:42",
"content": "I procrastinated",
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"timestamp": "01/23/2023 04:56:47",
"content": "Ah, I see",
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"timestamp": "01/23/2023 04:56:52",
"content": "Im actually doing the same rn",
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"timestamp": "01/23/2023 04:56:54",
"content": "Haha",
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"author_name": "putridplanet",
"timestamp": "01/23/2023 04:57:31",
"content": "I don’t see how you could factor further",
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"timestamp": "01/23/2023 04:57:34",
"content": "From there",
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"content": "(x+2) (8x^3+27)",
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"timestamp": "01/23/2023 04:58:17",
"content": "No no no",
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"content": "You cant factor more than that",
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"timestamp": "01/23/2023 04:58:40",
"content": "Ok so that’s the answer ?",
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"timestamp": "01/23/2023 04:59:33",
"content": "Yup",
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"timestamp": "01/23/2023 04:59:41",
"content": "And do the next one then.",
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"timestamp": "01/23/2023 05:00:06",
"content": "1(x^2 +81)",
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"author_name": "Quasar",
"timestamp": "01/23/2023 05:00:44",
"content": "It just cant be factored further, thats what we can say",
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"author_name": "putridplanet",
"timestamp": "01/23/2023 05:00:55",
"content": "So it’s prime ?",
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"timestamp": "01/23/2023 05:01:07",
"content": "Bringing that 1 out isnt gonna make a difference",
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"timestamp": "01/23/2023 05:01:20",
"content": "It may or may not be prime, but the expression can't be factored",
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"author_name": "putridplanet",
"timestamp": "01/23/2023 05:01:43",
"content": "The last one can’t be factored further as well right ?",
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"id": 1067021385714647000,
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"timestamp": "01/23/2023 05:02:02",
"content": "It can",
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"timestamp": "01/23/2023 05:02:03",
"content": "try",
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"author_name": "putridplanet",
"timestamp": "01/23/2023 05:03:49",
"content": "3x^2(3) -5(5)",
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"timestamp": "01/23/2023 05:05:34",
"content": ".",
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"timestamp": "01/23/2023 05:06:03",
"content": "No",
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"timestamp": "01/23/2023 05:06:20",
"content": "Try to bring it in this form",
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"timestamp": "01/23/2023 05:06:53",
"content": "**Quasar**",
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"id": 1067022652914532400,
"author_id": 872095482208481400,
"author_name": "Hira",
"timestamp": "01/23/2023 05:07:04",
"content": "It has SOTC or im tripping",
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"author_name": "putridplanet",
"timestamp": "01/23/2023 05:07:31",
"content": "x^2(9-25)",
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"author_name": "Quasar",
"timestamp": "01/23/2023 05:07:31",
"content": "Whats that?",
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"id": 1067022819680075800,
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"author_name": "Quasar",
"timestamp": "01/23/2023 05:07:44",
"content": "Bruh",
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"id": 1067023036185858000,
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"author_name": "Quasar",
"timestamp": "01/23/2023 05:08:36",
"content": "$9x^2-25=(3x)^2-5^2$",
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},
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"id": 1067023044528328800,
"author_id": 510789298321096700,
"author_name": "TeXit",
"timestamp": "01/23/2023 05:08:38",
"content": "**Quasar**",
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"timestamp": "01/23/2023 05:08:51",
"content": "Hmmm",
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"author_name": "putridplanet",
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"content": "I didn’t know you could do that",
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"id": 1067023206453616600,
"author_id": 858293468710174700,
"author_name": "putridplanet",
"timestamp": "01/23/2023 05:09:16",
"content": "Why the parenthesis around the 3x ?",
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"id": 1067023701121441800,
"author_id": 758350848115212300,
"author_name": "Quasar",
"timestamp": "01/23/2023 05:11:14",
"content": "Whole squared",
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},
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"id": 1067024322226573300,
"author_id": 858293468710174700,
"author_name": "putridplanet",
"timestamp": "01/23/2023 05:13:42",
"content": "What do you do after that ?",
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"timestamp": "01/23/2023 05:15:16",
"content": "Thatd make it $(3x-5)(3x+5)$",
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"timestamp": "01/23/2023 05:15:54",
"content": "**Quasar**",
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"timestamp": "01/23/2023 05:16:17",
"content": "Ohhhhhhh",
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"timestamp": "01/23/2023 05:31:17",
"content": "@putridplanet Has your question been resolved?",
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"timestamp": "01/23/2023 05:46:18",
"content": "Channel closed",
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}
] | help-9 | 7dabc46b1a3f445b94d36fd170f44198 |
200,957 | [
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},
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"id": 1067033658835345400,
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"content": ".close",
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"content": "Channel closed",
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}
] | help-9 | dcf0093b4c4a457793b5d5d3cc19ba65 |
200,958 | [
{
"id": 1067042478450016300,
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"content": "Available help channel!",
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},
{
"id": 1067051476100325400,
"author_id": 868073526937129000,
"author_name": "syesgdjohnny(ReTraY 100%)",
"timestamp": "01/23/2023 07:01:36",
"content": "how computer calculate nth root?",
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},
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"id": 1067051478465925100,
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"content": "Pinned a message.",
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"id": 1067052292525785200,
"author_id": 348696743388381200,
"author_name": "A Lonely Bean",
"timestamp": "01/23/2023 07:04:51",
"content": "Probably logarithms or just Taylor approximations",
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"author_name": "syesgdjohnny(ReTraY 100%)",
"timestamp": "01/23/2023 07:08:00",
"content": "https://en.wikipedia.org/wiki/Nth_root i find this",
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"timestamp": "01/23/2023 07:23:00",
"content": "@syesgdjohnny(ReTraY 100%) Has your question been resolved?",
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"content": "Channel closed",
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}
] | help-9 | 4f3317d0252c419eba2120a6aa8ed445 |
200,959 | [
{
"id": 1067060891062911100,
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"author_name": "Mathematics Bot",
"timestamp": "01/23/2023 07:39:01",
"content": "Available help channel!",
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},
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"id": 1067060948579393500,
"author_id": 340048758018408450,
"author_name": "sirius",
"timestamp": "01/23/2023 07:39:15",
"content": "Wait for this question, are both B and D correct? Or is it just D? Other websites say it's only D but not B. I chose B because it follows the rule of Similarity. The angle of ACB is also as congruent as the other angle DFE. Thank you!",
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"content": "Pinned a message.",
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"author_name": "Shockshwat",
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"content": "I think B is more appropriate",
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"timestamp": "01/23/2023 07:48:17",
"content": "hmm why tho",
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"content": "I agree for B, but why is D not part",
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"author_name": "sirius",
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"content": "Isn't that corresponding angles are always congruent?",
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"author_id": 593770484446003200,
"author_name": "Shockshwat",
"timestamp": "01/23/2023 07:48:56",
"content": "Can you link where it says D is the correct answer?",
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"timestamp": "01/23/2023 07:49:51",
"content": "It's not actually a source HAHA",
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"id": 1067063634401972200,
"author_id": 340048758018408450,
"author_name": "sirius",
"timestamp": "01/23/2023 07:49:55",
"content": "It's from an AI chatbot",
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"author_id": 593770484446003200,
"author_name": "Shockshwat",
"timestamp": "01/23/2023 07:50:01",
"content": ":catBruh:",
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"id": 1067063691348017200,
"author_id": 340048758018408450,
"author_name": "sirius",
"timestamp": "01/23/2023 07:50:09",
"content": "I am just making sure if the info is u know consistent",
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"id": 1067063716497084400,
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"author_name": "Shockshwat",
"timestamp": "01/23/2023 07:50:15",
"content": "bro why would you use a AI chatbot",
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"id": 1067063792506257500,
"author_id": 340048758018408450,
"author_name": "sirius",
"timestamp": "01/23/2023 07:50:33",
"content": "as a last resort I guess if I couldn't really find an answer HAHA",
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"id": 1067063814589255700,
"author_id": 593770484446003200,
"author_name": "Shockshwat",
"timestamp": "01/23/2023 07:50:38",
"content": "it can always be incorrect specially about mathematics",
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"id": 1067063898836062300,
"author_id": 593770484446003200,
"author_name": "Shockshwat",
"timestamp": "01/23/2023 07:50:58",
"content": "the most advanced chatGPT doesnt even convert units to put formulas to",
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},
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"id": 1067064011629281400,
"author_id": 593770484446003200,
"author_name": "Shockshwat",
"timestamp": "01/23/2023 07:51:25",
"content": "rather than a chatbot wolfram alpha is much better to use",
"attachments": [],
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},
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"id": 1067064045162741800,
"author_id": 340048758018408450,
"author_name": "sirius",
"timestamp": "01/23/2023 07:51:33",
"content": "yo ikr 💀",
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"id": 1067064085834911700,
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"author_name": "sirius",
"timestamp": "01/23/2023 07:51:43",
"content": "really???",
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"id": 1067064112137379800,
"author_id": 340048758018408450,
"author_name": "sirius",
"timestamp": "01/23/2023 07:51:49",
"content": "is it more accurate?",
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},
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"id": 1067064115174060000,
"author_id": 593770484446003200,
"author_name": "Shockshwat",
"timestamp": "01/23/2023 07:51:50",
"content": "ofcourse",
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"id": 1067064264331894800,
"author_id": 593770484446003200,
"author_name": "Shockshwat",
"timestamp": "01/23/2023 07:52:25",
"content": "difference of accuracy of wolfram alpha than chatgpt is huge",
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},
{
"id": 1067064373115367400,
"author_id": 593770484446003200,
"author_name": "Shockshwat",
"timestamp": "01/23/2023 07:52:51",
"content": "you can also use wolphrame alpha in the server by using `,w`",
"attachments": [],
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},
{
"id": 1067064446964478100,
"author_id": 593770484446003200,
"author_name": "Shockshwat",
"timestamp": "01/23/2023 07:53:09",
"content": ",w y = x^2 + 5x - 6",
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},
{
"id": 1067064463007699000,
"author_id": 510789298321096700,
"author_name": "TeXit",
"timestamp": "01/23/2023 07:53:13",
"content": "Results provided by WolframAlpha",
"attachments": [],
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},
{
"id": 1067064478602104800,
"author_id": 593770484446003200,
"author_name": "Shockshwat",
"timestamp": "01/23/2023 07:53:16",
"content": "see",
"attachments": [],
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},
{
"id": 1067064551671083000,
"author_id": 340048758018408450,
"author_name": "sirius",
"timestamp": "01/23/2023 07:53:34",
"content": "I didn't know u can actually use a bot AHAH",
"attachments": [],
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},
{
"id": 1067064584088858600,
"author_id": 593770484446003200,
"author_name": "Shockshwat",
"timestamp": "01/23/2023 07:53:41",
"content": "ok",
"attachments": [],
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},
{
"id": 1067064615269322800,
"author_id": 340048758018408450,
"author_name": "sirius",
"timestamp": "01/23/2023 07:53:49",
"content": "anyway, so it's B only?",
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},
{
"id": 1067064713009188900,
"author_id": 593770484446003200,
"author_name": "Shockshwat",
"timestamp": "01/23/2023 07:54:12",
"content": "yep",
"attachments": [],
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},
{
"id": 1067064960666050600,
"author_id": 340048758018408450,
"author_name": "sirius",
"timestamp": "01/23/2023 07:55:11",
"content": "ayt ty!",
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},
{
"id": 1067064971210531000,
"author_id": 340048758018408450,
"author_name": "sirius",
"timestamp": "01/23/2023 07:55:14",
"content": ".close",
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},
{
"id": 1067064974368841700,
"author_id": 805217272087838700,
"author_name": "Mathematics Bot",
"timestamp": "01/23/2023 07:55:14",
"content": "Channel closed",
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}
] | help-9 | 3e03ddb86a4e4256bec1843b58188f6c |
200,960 | [
{
"id": 1067071981607977000,
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"timestamp": "01/23/2023 08:23:05",
"content": "Available help channel!",
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},
{
"id": 1067075173716598800,
"author_id": 717430182561972200,
"author_name": "celine",
"timestamp": "01/23/2023 08:35:46",
"content": "this is the final answer but i have nooo idea how to solve",
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"content": "Pinned a message.",
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"author_id": 1003857269802401900,
"author_name": "starlight",
"timestamp": "01/23/2023 08:36:58",
"content": "do you notice anything between the ratio of the sides 6, 3.6 and 10,6? and can you figure out what angle KHL is based on vertical angles?",
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"id": 1067075580262105200,
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"author_name": "celine",
"timestamp": "01/23/2023 08:37:23",
"content": "hmm",
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"author_name": "celine",
"timestamp": "01/23/2023 08:37:35",
"content": "theres H in the middle??",
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"author_name": "celine",
"timestamp": "01/23/2023 08:38:05",
"content": "im not sure",
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"author_id": 485903210272391200,
"author_name": "dldh06",
"timestamp": "01/23/2023 08:39:28",
"content": "The hint is, they are similar shapes",
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"author_name": "celine",
"timestamp": "01/23/2023 08:39:35",
"content": "oh right",
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"author_id": 717430182561972200,
"author_name": "celine",
"timestamp": "01/23/2023 08:39:39",
"content": "theyre both triangles",
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"id": 1067076417319342200,
"author_id": 1003857269802401900,
"author_name": "starlight",
"timestamp": "01/23/2023 08:40:43",
"content": "by \"similar\" it means they are proportional",
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"id": 1067076450118799400,
"author_id": 1003857269802401900,
"author_name": "starlight",
"timestamp": "01/23/2023 08:40:51",
"content": "not that they are the same shape",
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"id": 1067076617874178000,
"author_id": 1003857269802401900,
"author_name": "starlight",
"timestamp": "01/23/2023 08:41:31",
"content": "what that would mean is that the angles of the triangle would be congruent to the corresponding angles of a similar triangle",
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"id": 1067076807620296800,
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"author_name": "starlight",
"timestamp": "01/23/2023 08:42:16",
"content": "not congruent, but similar no?",
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"id": 1067076892634661000,
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"author_name": "celine",
"timestamp": "01/23/2023 08:42:36",
"content": "yess",
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"id": 1067076941468926000,
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"author_name": "celine",
"timestamp": "01/23/2023 08:42:48",
"content": "but how does rhat help with finding x",
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"author_id": 485903210272391200,
"author_name": "dldh06",
"timestamp": "01/23/2023 08:43:09",
"content": "It's cause you confused me by saying \"similar\"",
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"author_name": "dldh06",
"timestamp": "01/23/2023 08:43:45",
"content": "Angles in similar shapes don't change, only the side lengths are different",
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"id": 1067077244117328000,
"author_id": 717430182561972200,
"author_name": "celine",
"timestamp": "01/23/2023 08:44:00",
"content": "OHH",
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},
{
"id": 1067077256758968300,
"author_id": 717430182561972200,
"author_name": "celine",
"timestamp": "01/23/2023 08:44:03",
"content": "OKOK",
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"id": 1067077274970640400,
"author_id": 717430182561972200,
"author_name": "celine",
"timestamp": "01/23/2023 08:44:07",
"content": "so how do we get 33?",
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},
{
"id": 1067077355840999600,
"author_id": 485903210272391200,
"author_name": "dldh06",
"timestamp": "01/23/2023 08:44:26",
"content": "What's the sum of angles in a triangle?",
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},
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"id": 1067077378238582800,
"author_id": 717430182561972200,
"author_name": "celine",
"timestamp": "01/23/2023 08:44:32",
"content": "180",
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},
{
"id": 1067077503153340400,
"author_id": 485903210272391200,
"author_name": "dldh06",
"timestamp": "01/23/2023 08:45:02",
"content": "You can make an equation based on that",
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"id": 1067077586980704400,
"author_id": 717430182561972200,
"author_name": "celine",
"timestamp": "01/23/2023 08:45:22",
"content": "soo do we use the degrees inside or the numbers outside",
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},
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"id": 1067077680140386300,
"author_id": 485903210272391200,
"author_name": "dldh06",
"timestamp": "01/23/2023 08:45:44",
"content": "Why would you use the numbers outside?",
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},
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"id": 1067077703972438100,
"author_id": 485903210272391200,
"author_name": "dldh06",
"timestamp": "01/23/2023 08:45:49",
"content": "Those are side lengths",
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"id": 1067077726332264600,
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"author_name": "celine",
"timestamp": "01/23/2023 08:45:55",
"content": "oh okay",
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"id": 1067077730920841200,
"author_id": 717430182561972200,
"author_name": "celine",
"timestamp": "01/23/2023 08:45:56",
"content": "so",
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},
{
"id": 1067077768619245600,
"author_id": 717430182561972200,
"author_name": "celine",
"timestamp": "01/23/2023 08:46:05",
"content": "wait let me try an equation",
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},
{
"id": 1067077795185950700,
"author_id": 717430182561972200,
"author_name": "celine",
"timestamp": "01/23/2023 08:46:11",
"content": "give me a min",
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},
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"id": 1067077884272988200,
"author_id": 485903210272391200,
"author_name": "dldh06",
"timestamp": "01/23/2023 08:46:32",
"content": "Like this is the biggest hint",
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},
{
"id": 1067078101365964900,
"author_id": 717430182561972200,
"author_name": "celine",
"timestamp": "01/23/2023 08:47:24",
"content": "180",
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},
{
"id": 1067078145804611600,
"author_id": 717430182561972200,
"author_name": "celine",
"timestamp": "01/23/2023 08:47:35",
"content": "im dumb sorry 😭",
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},
{
"id": 1067078193154097200,
"author_id": 717430182561972200,
"author_name": "celine",
"timestamp": "01/23/2023 08:47:46",
"content": "i came up with 42x+105=180",
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},
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"id": 1067078842172330000,
"author_id": 717430182561972200,
"author_name": "celine",
"timestamp": "01/23/2023 08:50:21",
"content": "OMDSSS",
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},
{
"id": 1067078845808791600,
"author_id": 717430182561972200,
"author_name": "celine",
"timestamp": "01/23/2023 08:50:22",
"content": "NVM",
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},
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"id": 1067078858144235600,
"author_id": 717430182561972200,
"author_name": "celine",
"timestamp": "01/23/2023 08:50:25",
"content": "I DOUND IT OUT",
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},
{
"id": 1067078896807326000,
"author_id": 717430182561972200,
"author_name": "celine",
"timestamp": "01/23/2023 08:50:34",
"content": "42+105+x=180",
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},
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"id": 1067078911789367300,
"author_id": 717430182561972200,
"author_name": "celine",
"timestamp": "01/23/2023 08:50:37",
"content": "WHICH IS 33",
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},
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"id": 1067078937747923100,
"author_id": 717430182561972200,
"author_name": "celine",
"timestamp": "01/23/2023 08:50:44",
"content": "thats so easy",
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},
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"id": 1067078959604432900,
"author_id": 717430182561972200,
"author_name": "celine",
"timestamp": "01/23/2023 08:50:49",
"content": "thank uuuu 😁😁",
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},
{
"id": 1067078980689199100,
"author_id": 717430182561972200,
"author_name": "celine",
"timestamp": "01/23/2023 08:50:54",
"content": ".close",
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{
"id": 1067078983256113300,
"author_id": 805217272087838700,
"author_name": "Mathematics Bot",
"timestamp": "01/23/2023 08:50:54",
"content": "Channel closed",
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}
] | help-9 | 8ebf095968b445348507a8bfec2445c0 |
200,961 | [
{
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"timestamp": "01/23/2023 08:51:55",
"content": "Available help channel!",
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"id": 1067080993929965600,
"author_id": 979508041483427800,
"author_name": "alcithoe",
"timestamp": "01/23/2023 08:58:54",
"content": "If $1_{\\{|Y_n| > \\varepsilon \\} } \\to 0$ P-a.s. for $n \\to \\infty$, how can we conclude that $0 \\leq \\limsup_{n \\to \\infty} |Y_n| < \\varepsilon$ P-a.s.?",
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"content": "Pinned a message.",
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"timestamp": "01/23/2023 08:59:56",
"content": "**alcithoe**",
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"content": "@alcithoe Has your question been resolved?",
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"content": "@alcithoe Has your question been resolved?",
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"content": ".close",
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"id": 1067092386548813800,
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"content": "Channel closed",
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] | help-9 | 79f0cfbe67be4945a6dea040773a9b34 |
200,962 | [
{
"id": 1067092638618095600,
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"timestamp": "01/23/2023 09:45:10",
"content": "Available help channel!",
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"id": 1067100086695362700,
"author_id": 747263971660398600,
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"timestamp": "01/23/2023 10:14:46",
"content": "A public health researcher examines the medical records of a group of 937 men who died in 1999 and discovers that 210 of the men died from causes related to heart disease. Moreover, 312 of the 937 men had at least one parent who suffered from heart disease, and of these 312 men, 102 died from causes related to heart disease. Suppose A is the event where a selected man from this group died of causes related to heart diseased, and B is the event where at least one parent suffered from heart disease.\n\nConstruct a venn diagram to represent the given scenario.\n\nA is the 210 or 102?",
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"content": "Pinned a message.",
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"content": "@Reiko Has your question been resolved?",
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] | help-9 | c874dde9e7dc495088eb4e0f0b9fec3e |
200,963 | [
{
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"content": "Available help channel!",
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"author_id": 282651244374523900,
"author_name": "MattNyte",
"timestamp": "01/23/2023 10:49:09",
"content": "Can someone please help me understand why my answer is incorrect? Correct answer from book is in red",
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"content": "Pinned a message.",
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"author_id": 394938706760302600,
"author_name": "heavy",
"timestamp": "01/23/2023 10:50:48",
"content": "area of the rectangle is not x",
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"id": 1067109163223748600,
"author_id": 394938706760302600,
"author_name": "heavy",
"timestamp": "01/23/2023 10:50:50",
"content": "its pi/2",
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"id": 1067109312419340300,
"author_id": 394938706760302600,
"author_name": "heavy",
"timestamp": "01/23/2023 10:51:26",
"content": "area of the half \"circle\" is wrong too",
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"author_id": 282651244374523900,
"author_name": "MattNyte",
"timestamp": "01/23/2023 10:51:46",
"content": "Isn't area based on location of x? So at x = pi/2 then x would be pi/2.",
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"timestamp": "01/23/2023 10:51:55",
"content": "How come",
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"timestamp": "01/23/2023 10:53:39",
"content": "the area is constant",
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"timestamp": "01/23/2023 10:53:41",
"content": "and its not a circle",
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"author_id": 394938706760302600,
"author_name": "heavy",
"timestamp": "01/23/2023 10:53:47",
"content": "so you cant use a circle formula",
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"author_name": "MattNyte",
"timestamp": "01/23/2023 10:57:54",
"content": "Dang it I don't fully understand",
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"timestamp": "01/23/2023 11:00:08",
"content": "",
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"timestamp": "01/23/2023 11:00:16",
"content": "the red line looks like an ellipse",
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"id": 1067111542077792400,
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"timestamp": "01/23/2023 11:00:17",
"content": "but its not",
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"id": 1067111780784021500,
"author_id": 394938706760302600,
"author_name": "heavy",
"timestamp": "01/23/2023 11:01:14",
"content": "and its definitely not a circle",
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"timestamp": "01/23/2023 11:03:44",
"content": "Sure then would",
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"timestamp": "01/23/2023 11:04:02",
"content": "So it doesn't use this disc method?",
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},
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"author_name": "MattNyte",
"timestamp": "01/23/2023 11:17:43",
"content": "@Helpers HI I was wondering if someone can help me",
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},
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"id": 1067115951868346400,
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"timestamp": "01/23/2023 11:18:03",
"content": "I got the wrong answer and not sure why",
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"author_name": "MattNyte",
"timestamp": "01/23/2023 11:18:20",
"content": "Someone pointed that the areas are wrong but I am not sure why",
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},
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"id": 1067118498624581600,
"author_id": 894941576885862500,
"author_name": "Amine_AAH",
"timestamp": "01/23/2023 11:27:56",
"content": "whats the question tho ( i can't clearly see the sentences)",
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"id": 1067119069251260400,
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"author_name": "Amine_AAH",
"timestamp": "01/23/2023 11:30:12",
"content": "@MattNyte",
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"author_id": 282651244374523900,
"author_name": "MattNyte",
"timestamp": "01/23/2023 11:31:22",
"content": "Sorry",
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},
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"id": 1067119479756169200,
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"content": "",
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"timestamp": "01/23/2023 11:35:13",
"content": "@Amine_AAH",
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"author_id": 354899211617042400,
"author_name": "lewis_f04",
"timestamp": "01/23/2023 11:38:22",
"content": "Why are you integrating x?",
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},
{
"id": 1067121252310974600,
"author_id": 354899211617042400,
"author_name": "lewis_f04",
"timestamp": "01/23/2023 11:38:52",
"content": "You should just find the area of the rectangle using b x h",
"attachments": [],
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},
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"id": 1067121418107633800,
"author_id": 894941576885862500,
"author_name": "Amine_AAH",
"timestamp": "01/23/2023 11:39:32",
"content": "the volume he is searching is the volume of a cylinder minus the volume created by your y=sqrt(cos(x)) right... ?",
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"id": 1067121803434139600,
"author_id": 282651244374523900,
"author_name": "MattNyte",
"timestamp": "01/23/2023 11:41:04",
"content": "Isn't it a rectangular prism volume minus volume of y = sqrt(cosx) right?",
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"timestamp": "01/23/2023 11:42:27",
"content": "Oh wait",
"attachments": [],
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},
{
"id": 1067122181840060400,
"author_id": 282651244374523900,
"author_name": "MattNyte",
"timestamp": "01/23/2023 11:42:34",
"content": "It is a cylinder...",
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},
{
"id": 1067122214148767900,
"author_id": 282651244374523900,
"author_name": "MattNyte",
"timestamp": "01/23/2023 11:42:42",
"content": "If rotated around x axis",
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},
{
"id": 1067122225209155600,
"author_id": 282651244374523900,
"author_name": "MattNyte",
"timestamp": "01/23/2023 11:42:44",
"content": "Shit",
"attachments": [],
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},
{
"id": 1067122265608687600,
"author_id": 894941576885862500,
"author_name": "Amine_AAH",
"timestamp": "01/23/2023 11:42:54",
"content": "u see",
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},
{
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"author_id": 282651244374523900,
"author_name": "MattNyte",
"timestamp": "01/23/2023 11:43:43",
"content": "So first volume is integral of pi * 1^2 right?",
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},
{
"id": 1067122536975958100,
"author_id": 282651244374523900,
"author_name": "MattNyte",
"timestamp": "01/23/2023 11:43:58",
"content": "Cause 1 is radius",
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},
{
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"author_id": 894941576885862500,
"author_name": "Amine_AAH",
"timestamp": "01/23/2023 11:44:12",
"content": "its $int_0^{\\pi}1^2 dx$",
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},
{
"id": 1067122622866915300,
"author_id": 894941576885862500,
"author_name": "Amine_AAH",
"timestamp": "01/23/2023 11:44:19",
"content": "oh wait",
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},
{
"id": 1067122768136634500,
"author_id": 894941576885862500,
"author_name": "Amine_AAH",
"timestamp": "01/23/2023 11:44:54",
"content": "its $\\int_0^{\\pi}1^2 dx$",
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},
{
"id": 1067122833752346600,
"author_id": 894941576885862500,
"author_name": "Amine_AAH",
"timestamp": "01/23/2023 11:45:09",
"content": "shit",
"attachments": [],
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},
{
"id": 1067122910818476200,
"author_id": 894941576885862500,
"author_name": "Amine_AAH",
"timestamp": "01/23/2023 11:45:28",
"content": "its $\\int_0^{\\frac{\\pi}{2}}1^2 dx$",
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},
{
"id": 1067122922050822100,
"author_id": 510789298321096700,
"author_name": "TeXit",
"timestamp": "01/23/2023 11:45:30",
"content": "**SAKUUN**",
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"author_name": "Amine_AAH",
"timestamp": "01/23/2023 11:47:14",
"content": "$V=2\\pi\\left(\\int_0^{\\dfrac{\\pi}{2}}\\left(1-\\cos(x)\\right)dx\\right)$",
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},
{
"id": 1067123368396079100,
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"author_name": "TeXit",
"timestamp": "01/23/2023 11:47:17",
"content": "**SAKUUN**",
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"timestamp": "01/23/2023 11:47:22",
"content": "Omg I got the right answe",
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},
{
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"author_id": 282651244374523900,
"author_name": "MattNyte",
"timestamp": "01/23/2023 11:47:24",
"content": "Woooh",
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},
{
"id": 1067123428575944700,
"author_id": 894941576885862500,
"author_name": "Amine_AAH",
"timestamp": "01/23/2023 11:47:31",
"content": "👏🏼",
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},
{
"id": 1067123450365366500,
"author_id": 282651244374523900,
"author_name": "MattNyte",
"timestamp": "01/23/2023 11:47:36",
"content": "Ty so much!",
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},
{
"id": 1067123477959676000,
"author_id": 894941576885862500,
"author_name": "Amine_AAH",
"timestamp": "01/23/2023 11:47:43",
"content": "glad i could help",
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},
{
"id": 1067123527225966700,
"author_id": 282651244374523900,
"author_name": "MattNyte",
"timestamp": "01/23/2023 11:47:55",
"content": ".close",
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},
{
"id": 1067123531260891300,
"author_id": 805217272087838700,
"author_name": "Mathematics Bot",
"timestamp": "01/23/2023 11:47:56",
"content": "Channel closed",
"attachments": [],
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}
] | help-9 | 8053a8194fab434194b057e4c7bbbdf4 |
200,964 | [
{
"id": 1067124093419274200,
"author_id": 805217272087838700,
"author_name": "Mathematics Bot",
"timestamp": "01/23/2023 11:50:10",
"content": "Available help channel!",
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},
{
"id": 1067124183856853000,
"author_id": 805217272087838700,
"author_name": "Mathematics Bot",
"timestamp": "01/23/2023 11:50:31",
"content": "Pinned a message.",
"attachments": [],
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"channelId": 486844875632017400,
"guildId": null
}
},
{
"id": 1067124349234065400,
"author_id": 279217052521201660,
"author_name": "tobi.",
"timestamp": "01/23/2023 11:51:11",
"content": ",w 5500*565e",
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},
{
"id": 1067124366665596900,
"author_id": 510789298321096700,
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"timestamp": "01/23/2023 11:51:15",
"content": "Results provided by WolframAlpha",
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},
{
"id": 1067124402401067100,
"author_id": 912969666295627800,
"author_name": "n11",
"timestamp": "01/23/2023 11:51:23",
"content": "why do you want to know",
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},
{
"id": 1067124463432372200,
"author_id": 912969666295627800,
"author_name": "n11",
"timestamp": "01/23/2023 11:51:38",
"content": "whats the question",
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"reference": null
},
{
"id": 1067124539705790500,
"author_id": 912969666295627800,
"author_name": "n11",
"timestamp": "01/23/2023 11:51:56",
"content": "just \"find 5500*565e\"?",
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},
{
"id": 1067124569644732500,
"author_id": 183668144404037630,
"author_name": "Ann",
"timestamp": "01/23/2023 11:52:03",
"content": "... ???",
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},
{
"id": 1067124587034325000,
"author_id": 183668144404037630,
"author_name": "Ann",
"timestamp": "01/23/2023 11:52:07",
"content": "@JackWinston are you in an exam right now?",
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"id": 1067124714214006900,
"author_id": 912969666295627800,
"author_name": "n11",
"timestamp": "01/23/2023 11:52:38",
"content": "thats what someone in an exam would say",
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},
{
"id": 1067124754106044500,
"author_id": 183668144404037630,
"author_name": "Ann",
"timestamp": "01/23/2023 11:52:47",
"content": "we do not allow cheating on exams.",
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},
{
"id": 1067124950923747300,
"author_id": 183668144404037630,
"author_name": "Ann",
"timestamp": "01/23/2023 11:53:34",
"content": "note also that responding \"yes\" to the question of \"are you in an exam right now\", EVEN AS A JOKE, is grounds for a ban.",
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},
{
"id": 1067125241047961700,
"author_id": 102705166754549760,
"author_name": "ShiN",
"timestamp": "01/23/2023 11:54:43",
"content": "bonk",
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"reference": null
},
{
"id": 1067125477711552500,
"author_id": 102705166754549760,
"author_name": "ShiN",
"timestamp": "01/23/2023 11:55:40",
"content": ".close",
"attachments": [],
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"reference": null
},
{
"id": 1067125480362348700,
"author_id": 805217272087838700,
"author_name": "Mathematics Bot",
"timestamp": "01/23/2023 11:55:40",
"content": "Channel closed",
"attachments": [],
"mentions": [],
"reference": null
}
] | help-9 | 96f8ae3e02e14f36968d73ef8780c4db |
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