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{
"id": 993490036915966100,
"author_id": 483962566977126400,
"author_name": "MarveI",
"timestamp": "07/04/2022 08:14:42",
"content": "AED is an isosceles triangle too",
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"id": 993498384155545700,
"author_id": 805217272087838700,
"author_name": "Mathematics Bot",
"timestamp": "07/04/2022 08:47:53",
"content": "Available help channel!",
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},
{
"id": 993499501358755800,
"author_id": 429527187188875260,
"author_name": "RaresMrc",
"timestamp": "07/04/2022 08:52:19",
"content": "",
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"id": 993499504655474700,
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"author_name": "Mathematics Bot",
"timestamp": "07/04/2022 08:52:20",
"content": "Pinned a message.",
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"id": 993499535454249100,
"author_id": 429527187188875260,
"author_name": "RaresMrc",
"timestamp": "07/04/2022 08:52:27",
"content": "how do you find the number of solutions for f(x) = 1?",
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{
"id": 993499678291263600,
"author_id": 429527187188875260,
"author_name": "RaresMrc",
"timestamp": "07/04/2022 08:53:01",
"content": "if you take 0, 2pi, 4pi, pi/2, 3pi/2, 5pi/2, 7pi/2 these would be 7",
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},
{
"id": 993499710222516200,
"author_id": 429527187188875260,
"author_name": "RaresMrc",
"timestamp": "07/04/2022 08:53:09",
"content": "but how do I know there aren't any others?",
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},
{
"id": 993499793009692800,
"author_id": 429527187188875260,
"author_name": "RaresMrc",
"timestamp": "07/04/2022 08:53:28",
"content": "maybe do f'(x) and study the function?",
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{
"id": 993499907560325200,
"author_id": 429527187188875260,
"author_name": "RaresMrc",
"timestamp": "07/04/2022 08:53:56",
"content": "it's probably a periodic function though so that'd take a bit",
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},
{
"id": 993500054574874800,
"author_id": 429527187188875260,
"author_name": "RaresMrc",
"timestamp": "07/04/2022 08:54:31",
"content": "please ping me if you respond btw",
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},
{
"id": 993502481638228000,
"author_id": 764959481070616600,
"author_name": "Toby",
"timestamp": "07/04/2022 09:04:10",
"content": "I don't agree with your answers, some of these give -1",
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{
"id": 993502514102149100,
"author_id": 429527187188875260,
"author_name": "RaresMrc",
"timestamp": "07/04/2022 09:04:17",
"content": "oh true",
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{
"id": 993502534557769700,
"author_id": 764959481070616600,
"author_name": "Toby",
"timestamp": "07/04/2022 09:04:22",
"content": "sine and cos are both 2pi periodic, so f(x) is also 2pi periodic",
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},
{
"id": 993502537254711400,
"author_id": 429527187188875260,
"author_name": "RaresMrc",
"timestamp": "07/04/2022 09:04:23",
"content": "3pi/2 and 7pi/2",
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},
{
"id": 993502560818307100,
"author_id": 429527187188875260,
"author_name": "RaresMrc",
"timestamp": "07/04/2022 09:04:28",
"content": "mb",
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{
"id": 993502588035141600,
"author_id": 429527187188875260,
"author_name": "RaresMrc",
"timestamp": "07/04/2022 09:04:35",
"content": "ty for correcting me",
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},
{
"id": 993502702371876900,
"author_id": 429527187188875260,
"author_name": "RaresMrc",
"timestamp": "07/04/2022 09:05:02",
"content": "but how do I know I have no solutions except for these?",
"attachments": [],
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{
"id": 993502764028149900,
"author_id": 429527187188875260,
"author_name": "RaresMrc",
"timestamp": "07/04/2022 09:05:17",
"content": "do I just study the monotony of the function as I said earlier or is there a shorter way?",
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{
"id": 993502839122952200,
"author_id": 764959481070616600,
"author_name": "Toby",
"timestamp": "07/04/2022 09:05:35",
"content": "could you sketch your working on how you got 0, pi/2 etc",
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{
"id": 993502990633803800,
"author_id": 429527187188875260,
"author_name": "RaresMrc",
"timestamp": "07/04/2022 09:06:11",
"content": "just thought of where sinx = 0 and cosx = 1 or sinx = 1 and cosx = 0",
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{
"id": 993503922830454800,
"author_id": 189001310937284600,
"author_name": "Tom",
"timestamp": "07/04/2022 09:09:53",
"content": "probably other ways to go about it but you could consider something like sin^5+cos^5 <= sin^2+cos^2 = 1",
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},
{
"id": 993504068691558400,
"author_id": 753979675755151500,
"author_name": "Kitams",
"timestamp": "07/04/2022 09:10:28",
"content": "you know at first i thought you could just simplify the equation",
"attachments": [],
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},
{
"id": 993504198408798300,
"author_id": 753979675755151500,
"author_name": "Kitams",
"timestamp": "07/04/2022 09:10:59",
"content": "x^5 + y^5",
"attachments": [],
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},
{
"id": 993506766967029900,
"author_id": 805217272087838700,
"author_name": "Mathematics Bot",
"timestamp": "07/04/2022 09:21:11",
"content": "@RaresMrc Has your question been resolved?",
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{
"id": 993512832119341000,
"author_id": 764959481070616600,
"author_name": "Toby",
"timestamp": "07/04/2022 09:45:17",
"content": "@RaresMrc $\\sin^5+\\cos^5=1=\\sin^2+\\cos^2$, so $\\sin^2(\\sin^3-1)=cos^2(1-\\cos^3)$. The left is negative, the right is positive. So they can only be equal when they both are zero",
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{
"id": 993512845650182300,
"author_id": 510789298321096700,
"author_name": "TeXit",
"timestamp": "07/04/2022 09:45:20",
"content": "**Toby**",
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"id": 993513479178829800,
"author_id": 429527187188875260,
"author_name": "RaresMrc",
"timestamp": "07/04/2022 09:47:52",
"content": "but that'd mean I'd have 3 solutions in [0, 4pi]",
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{
"id": 993513584011259900,
"author_id": 429527187188875260,
"author_name": "RaresMrc",
"timestamp": "07/04/2022 09:48:17",
"content": "and I already showed you that I have 0, 2pi, 4pi, pi/2, 5pi/2",
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},
{
"id": 993513594476044400,
"author_id": 429527187188875260,
"author_name": "RaresMrc",
"timestamp": "07/04/2022 09:48:19",
"content": "so those are at least 5",
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},
{
"id": 993513959409864700,
"author_id": 429527187188875260,
"author_name": "RaresMrc",
"timestamp": "07/04/2022 09:49:46",
"content": "oh, nvm",
"attachments": [],
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},
{
"id": 993513964493353100,
"author_id": 429527187188875260,
"author_name": "RaresMrc",
"timestamp": "07/04/2022 09:49:47",
"content": "mb",
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},
{
"id": 993513968905769100,
"author_id": 429527187188875260,
"author_name": "RaresMrc",
"timestamp": "07/04/2022 09:49:48",
"content": "mb mb",
"attachments": [],
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},
{
"id": 993513972659662800,
"author_id": 429527187188875260,
"author_name": "RaresMrc",
"timestamp": "07/04/2022 09:49:49",
"content": "I get it",
"attachments": [],
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},
{
"id": 993514042146684900,
"author_id": 429527187188875260,
"author_name": "RaresMrc",
"timestamp": "07/04/2022 09:50:06",
"content": "those're all there",
"attachments": [],
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},
{
"id": 993514055555887200,
"author_id": 764959481070616600,
"author_name": "Toby",
"timestamp": "07/04/2022 09:50:09",
"content": "I count 3 in [0,2pi], so 5 in [0,4pi]",
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{
"id": 993514065412493300,
"author_id": 764959481070616600,
"author_name": "Toby",
"timestamp": "07/04/2022 09:50:11",
"content": "ye",
"attachments": [],
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{
"id": 993514174502150100,
"author_id": 429527187188875260,
"author_name": "RaresMrc",
"timestamp": "07/04/2022 09:50:37",
"content": "ok, ty",
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{
"id": 993514292391444500,
"author_id": 429527187188875260,
"author_name": "RaresMrc",
"timestamp": "07/04/2022 09:51:05",
"content": ".close",
"attachments": [],
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"reference": null
},
{
"id": 993514294236946400,
"author_id": 805217272087838700,
"author_name": "Mathematics Bot",
"timestamp": "07/04/2022 09:51:06",
"content": "Channel closed",
"attachments": [],
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"reference": null
}
] |
help-9
|
4ecd2669d5d64ff5af442f63d00b0170
|
196,966 |
[
{
"id": 993514441725444100,
"author_id": 429527187188875260,
"author_name": "RaresMrc",
"timestamp": "07/04/2022 09:51:41",
"content": "",
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{
"id": 993514465431666800,
"author_id": 429527187188875260,
"author_name": "RaresMrc",
"timestamp": "07/04/2022 09:51:47",
"content": "how do you calculate this?",
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},
{
"id": 993514547442892800,
"author_id": 805217272087838700,
"author_name": "Mathematics Bot",
"timestamp": "07/04/2022 09:52:06",
"content": "Available help channel!",
"attachments": [],
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"reference": null
},
{
"id": 993514547975565400,
"author_id": 764959481070616600,
"author_name": "Toby",
"timestamp": "07/04/2022 09:52:06",
"content": ",calc arctan(1)+arctan(2)+arctan(3)",
"attachments": [],
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"reference": null
},
{
"id": 993514549955264500,
"author_id": 510789298321096700,
"author_name": "TeXit",
"timestamp": "07/04/2022 09:52:07",
"content": "The following error occured while calculating:\n`Error: Undefined function arctan`",
"attachments": [],
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},
{
"id": 993514550500524000,
"author_id": 805217272087838700,
"author_name": "Mathematics Bot",
"timestamp": "07/04/2022 09:52:07",
"content": "Pinned a message.",
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{
"id": 993514576899493900,
"author_id": 764959481070616600,
"author_name": "Toby",
"timestamp": "07/04/2022 09:52:13",
"content": ".close",
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},
{
"id": 993514578505896000,
"author_id": 805217272087838700,
"author_name": "Mathematics Bot",
"timestamp": "07/04/2022 09:52:14",
"content": "Channel closed",
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}
] |
help-9
|
684e82372a6747899df1d46ddb5c0cd5
|
196,967 |
[
{
"id": 993517075094065300,
"author_id": 805217272087838700,
"author_name": "Mathematics Bot",
"timestamp": "07/04/2022 10:02:09",
"content": "Available help channel!",
"attachments": [],
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"reference": null
},
{
"id": 993517981181157400,
"author_id": 445797639892762600,
"author_name": "Aldredz",
"timestamp": "07/04/2022 10:05:45",
"content": "5xΒ³ + 2x - 3 Γ· x - 3\nSynthetic Division\nIm not sure of my answer but I got\n5xΒ² + 15x - 47 + 141/x-3",
"attachments": [],
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},
{
"id": 993517983261524000,
"author_id": 805217272087838700,
"author_name": "Mathematics Bot",
"timestamp": "07/04/2022 10:05:45",
"content": "Pinned a message.",
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{
"id": 993519196220694500,
"author_id": 795717786709000200,
"author_name": "η§ζ°΄",
"timestamp": "07/04/2022 10:10:35",
"content": ",w Apart (5 x^3 + 2 x - 3)/(x - 3)",
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},
{
"id": 993519252051067000,
"author_id": 510789298321096700,
"author_name": "TeXit",
"timestamp": "07/04/2022 10:10:48",
"content": "Results provided by WolframAlpha",
"attachments": [],
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"reference": null
},
{
"id": 993521756910403600,
"author_id": 805217272087838700,
"author_name": "Mathematics Bot",
"timestamp": "07/04/2022 10:20:45",
"content": "@Aldredz Has your question been resolved?",
"attachments": [],
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{
"id": 993521932060348400,
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"author_name": "Mathematics Bot",
"timestamp": "07/04/2022 10:21:27",
"content": "Channel closed",
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}
] |
help-9
|
69e14e4d598b4fff81898ceaecb48a6b
|
196,968 |
[
{
"id": 993525517309448200,
"author_id": 805217272087838700,
"author_name": "Mathematics Bot",
"timestamp": "07/04/2022 10:35:42",
"content": "Available help channel!",
"attachments": [],
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"reference": null
},
{
"id": 993526029270384600,
"author_id": 912061381480702000,
"author_name": "WhyPerson",
"timestamp": "07/04/2022 10:37:44",
"content": "exam consists of 42 questions,\ncomprising 34 questions, each worth 2% of the total examination mark,\nand 8 questions, each worth 4% of the total examination mark. The\nexamination is scheduled to take 3 hours to complete.\n\nAssuming that the time should be allocated in proportion to the\nmarks for each question;\n\nApproximately how long should you spend on answering a\nquestion that is worth 2% of the total marks?\nApproximately how long should you spend on answering a\nquestion that is worth 4% of the total marks?",
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"id": 993526031707283600,
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"author_name": "Mathematics Bot",
"timestamp": "07/04/2022 10:37:44",
"content": "Pinned a message.",
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"id": 993526059821695000,
"author_id": 912061381480702000,
"author_name": "WhyPerson",
"timestamp": "07/04/2022 10:37:51",
"content": "is it just 42/3?",
"attachments": [],
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},
{
"id": 993526316454395900,
"author_id": 689096418585215100,
"author_name": "Yann",
"timestamp": "07/04/2022 10:38:52",
"content": "2% of 3 hours",
"attachments": [],
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},
{
"id": 993526347051847800,
"author_id": 689096418585215100,
"author_name": "Yann",
"timestamp": "07/04/2022 10:38:59",
"content": "and 4 % of 3 hours",
"attachments": [],
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},
{
"id": 993526381109575700,
"author_id": 689096418585215100,
"author_name": "Yann",
"timestamp": "07/04/2022 10:39:08",
"content": "0.02 * 60*3",
"attachments": [],
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},
{
"id": 993526403398123600,
"author_id": 689096418585215100,
"author_name": "Yann",
"timestamp": "07/04/2022 10:39:13",
"content": "and 0.04 * 60 * 3",
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},
{
"id": 993526474088927400,
"author_id": 689096418585215100,
"author_name": "Yann",
"timestamp": "07/04/2022 10:39:30",
"content": "in minutes",
"attachments": [],
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},
{
"id": 993526527281074200,
"author_id": 912061381480702000,
"author_name": "WhyPerson",
"timestamp": "07/04/2022 10:39:42",
"content": "That makes sense thanks Yann",
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},
{
"id": 993530303043866800,
"author_id": 805217272087838700,
"author_name": "Mathematics Bot",
"timestamp": "07/04/2022 10:54:43",
"content": "@WhyPerson Has your question been resolved?",
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"timestamp": "07/04/2022 11:09:43",
"content": "Channel closed",
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}
] |
help-9
|
e7720f703e534ca29b0c2339cc2e08d2
|
196,969 |
[
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"author_name": "Mathematics Bot",
"timestamp": "07/04/2022 11:10:43",
"content": "Available help channel!",
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},
{
"id": 993535508636508200,
"author_id": 912061381480702000,
"author_name": "WhyPerson",
"timestamp": "07/04/2022 11:15:24",
"content": "How many $\\theta$ in radians between $-2\\pi$ and $2\\pi$ satisfy $sin(\\theta) = \\frac{1}{2}$ it is 2 right?",
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"timestamp": "07/04/2022 11:15:24",
"content": "Pinned a message.",
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"timestamp": "07/04/2022 11:15:26",
"content": "**Unknown101**",
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"timestamp": "07/04/2022 11:15:55",
"content": "no",
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"timestamp": "07/04/2022 11:15:59",
"content": "wait",
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"author_name": "WhyPerson",
"timestamp": "07/04/2022 11:16:00",
"content": "it is 4?",
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"author_id": 456226577798135800,
"author_name": "Deleted User",
"timestamp": "07/04/2022 11:16:07",
"content": "yes",
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"id": 993535763801194500,
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"author_name": "WhyPerson",
"timestamp": "07/04/2022 11:16:25",
"content": "makes sense",
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"id": 993535891102511100,
"author_id": 456226577798135800,
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"timestamp": "07/04/2022 11:16:55",
"content": "w",
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"timestamp": "07/04/2022 11:17:02",
"content": "thank you",
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"content": "@WhyPerson Has your question been resolved?",
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"timestamp": "07/04/2022 11:47:02",
"content": "Channel closed",
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}
] |
help-9
|
ff20281481a2448bb4cd670377613542
|
196,970 |
[
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"id": 958472409558687900,
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"author_name": "Mathematics Bot",
"timestamp": "03/29/2022 17:07:09",
"content": "Available help channel!",
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"id": 958474489388212200,
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"author_name": "Avenged7xRL",
"timestamp": "03/29/2022 17:15:31",
"content": "Help anyone?",
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{
"id": 958475843364094000,
"author_id": 485164773647056900,
"author_name": "Gooaaa",
"timestamp": "03/29/2022 17:20:48",
"content": ",w e^lnx",
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},
{
"id": 958475856303521800,
"author_id": 510789298321096700,
"author_name": "TeXit",
"timestamp": "03/29/2022 17:20:51",
"content": "Results provided by WolframAlpha",
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"id": 958475882371088400,
"author_id": 485164773647056900,
"author_name": "Gooaaa",
"timestamp": "03/29/2022 17:20:57",
"content": "use this fact",
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"id": 958476957408956400,
"author_id": 859526158701953000,
"author_name": "Avenged7xRL",
"timestamp": "03/29/2022 17:25:14",
"content": "If thats the case",
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"author_id": 859526158701953000,
"author_name": "Avenged7xRL",
"timestamp": "03/29/2022 17:25:59",
"content": "Wont log(x)log(e) = log(x)",
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"id": 958477193799950500,
"author_id": 859526158701953000,
"author_name": "Avenged7xRL",
"timestamp": "03/29/2022 17:26:10",
"content": "And log (e) = 1 and e isnβt 10",
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},
{
"id": 958478144879349900,
"author_id": 485164773647056900,
"author_name": "Gooaaa",
"timestamp": "03/29/2022 17:29:57",
"content": "https://www.freemathhelp.com/forum/threads/what-is-e-lnx.86986/",
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"id": 958478309031837800,
"author_id": 485164773647056900,
"author_name": "Gooaaa",
"timestamp": "03/29/2022 17:30:36",
"content": "for sinh(lnx) we het ((x-(1/x))/2",
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"id": 958478411100205000,
"author_id": 485164773647056900,
"author_name": "Gooaaa",
"timestamp": "03/29/2022 17:31:00",
"content": "cosh(lnx)=)(x+(1/x))2",
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"author_name": "Avenged7xRL",
"timestamp": "03/29/2022 17:31:15",
"content": "Ok this was helpful",
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"author_id": 859526158701953000,
"author_name": "Avenged7xRL",
"timestamp": "03/29/2022 17:32:45",
"content": "Why is this?",
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"author_id": 485164773647056900,
"author_name": "Gooaaa",
"timestamp": "03/29/2022 17:33:04",
"content": "e^-lnx=1/x",
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"id": 958479195623813200,
"author_id": 859526158701953000,
"author_name": "Avenged7xRL",
"timestamp": "03/29/2022 17:34:07",
"content": "Oh so (e^lnx - e^-lnx)/2",
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"id": 958479303992029200,
"author_id": 485164773647056900,
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"timestamp": "03/29/2022 17:34:33",
"content": "yes",
"attachments": [],
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},
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"id": 958479341874983000,
"author_id": 859526158701953000,
"author_name": "Avenged7xRL",
"timestamp": "03/29/2022 17:34:42",
"content": "And just cause of this fact everything simplifies and you can prove it",
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"id": 958479367225348100,
"author_id": 485164773647056900,
"author_name": "Gooaaa",
"timestamp": "03/29/2022 17:34:48",
"content": "yes",
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"id": 958479370207502300,
"author_id": 859526158701953000,
"author_name": "Avenged7xRL",
"timestamp": "03/29/2022 17:34:49",
"content": "That was neat",
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"id": 958479400200962200,
"author_id": 859526158701953000,
"author_name": "Avenged7xRL",
"timestamp": "03/29/2022 17:34:56",
"content": "Thank you very much",
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},
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"id": 958479835053850800,
"author_id": 859526158701953000,
"author_name": "Avenged7xRL",
"timestamp": "03/29/2022 17:36:40",
"content": "Can you use the same fact for ii too?",
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"id": 958480312072032400,
"author_id": 485164773647056900,
"author_name": "Gooaaa",
"timestamp": "03/29/2022 17:38:34",
"content": "idk how to do 2nd",
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"author_id": 859526158701953000,
"author_name": "Avenged7xRL",
"timestamp": "03/29/2022 17:39:09",
"content": "Nws thanks for the first one",
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"author_name": "Avenged7xRL",
"timestamp": "03/29/2022 17:39:16",
"content": ".close",
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"id": 958480491869253600,
"author_id": 805217272087838700,
"author_name": "Mathematics Bot",
"timestamp": "03/29/2022 17:39:16",
"content": "Channel closed",
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}
] |
help-9
|
e8e214f26dbb43aba431306f927f7e38
|
196,971 |
[
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"timestamp": "07/04/2022 11:59:43",
"content": "Available help channel!",
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"id": 993550629211484300,
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"content": "Pinned a message.",
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"timestamp": "07/04/2022 12:15:38",
"content": "COMPLEX VARIABLES course.",
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"id": 993550851593474200,
"author_id": 281221474604548100,
"author_name": "PoisonedFood",
"timestamp": "07/04/2022 12:16:22",
"content": "In d. How does it get from ln|e^(4+4i)| to ln(4)",
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"id": 993550906891182100,
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"timestamp": "07/04/2022 12:16:35",
"content": "Is it just taking the ln of the Real part?",
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"timestamp": "07/04/2022 12:17:00",
"content": "And how does Arg(β¦)go to i(4-2pi)",
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"timestamp": "07/04/2022 12:17:26",
"content": "@themateo713 here is my new chat",
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"id": 993551698805141600,
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"author_name": "Eric Tao",
"timestamp": "07/04/2022 12:19:44",
"content": "warning: note that ln(ab) = ln(a) + ln(b) isn't always true for complex numbers",
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"id": 993551881475465300,
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"timestamp": "07/04/2022 12:20:27",
"content": "rather, ln(ab) = ln(a) + ln(b) + 2n i pi",
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"timestamp": "07/04/2022 12:32:26",
"content": "@PoisonedFood Has your question been resolved?",
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"id": 993555445933412400,
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"author_name": "Kaynex",
"timestamp": "07/04/2022 12:34:37",
"content": "e^(4 + 4i) = e^(4) e^(4i), by exponential property",
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"id": 993555544080121900,
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"author_name": "Kaynex",
"timestamp": "07/04/2022 12:35:01",
"content": "| | splits over multiplication, so we can just consider the modulus of both parts induvidually",
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"id": 993555608290742300,
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"timestamp": "07/04/2022 12:35:16",
"content": "|e^(ki)| = 1, always.",
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"author_name": "Kaynex",
"timestamp": "07/04/2022 12:36:22",
"content": "So, \n|e^(4 + 4i)|\n= |e^(4)| \\* |e^(4i)|\n= |e^(4)| \\* 1\n= e^(4)",
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"id": 993556087385112700,
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"timestamp": "07/04/2022 12:37:10",
"content": "And of course, we're taking the ln of all that",
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"timestamp": "07/04/2022 12:37:20",
"content": "@PoisonedFood",
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"timestamp": "07/04/2022 12:42:41",
"content": "So how do we get i(4-2pi)?",
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"timestamp": "07/04/2022 12:45:45",
"content": "The line below that explains",
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"author_name": "Eric Tao",
"timestamp": "07/04/2022 12:46:28",
"content": "The principal branch of log uses argument in [-pi, pi) and 4 is not in that interval so we subtract by a full circle (2pi) to get it within that interval",
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"id": 993558476083187800,
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"author_name": "PoisonedFood",
"timestamp": "07/04/2022 12:46:40",
"content": "But why do we choose -2pi and not +2pi?",
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"timestamp": "07/04/2022 12:46:49",
"content": "Ahh okay",
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"author_name": "PoisonedFood",
"timestamp": "07/04/2022 12:47:44",
"content": "Okay on e and f: whatβs the difference between βLogβ and βlogβ",
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},
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"timestamp": "07/04/2022 12:49:21",
"content": "nothing",
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"author_id": 531535537362829300,
"author_name": "Eric Tao",
"timestamp": "07/04/2022 12:49:33",
"content": "ignore the capitalization, prob autocorrect",
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"id": 993559843078160500,
"author_id": 356908116429897700,
"author_name": "Kaynex",
"timestamp": "07/04/2022 12:52:06",
"content": "There are infinitely many logarithms, depending on where you choose the branch cut",
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"author_name": "Kaynex",
"timestamp": "07/04/2022 12:52:47",
"content": "Log(z) is the one whose imaginary part lies in the interval (-pi, pi]",
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"author_name": "Kaynex",
"timestamp": "07/04/2022 12:53:01",
"content": "I never remember that, just looking on wikipedia kek",
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"author_name": "Eric Tao",
"timestamp": "07/04/2022 12:53:36",
"content": "ohh wait yea",
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"author_name": "Kaynex",
"timestamp": "07/04/2022 12:53:53",
"content": "Can put the branch cut above instead, and use a log where im lies in (-3pi/2, pi/2]",
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"id": 993560296042008600,
"author_id": 531535537362829300,
"author_name": "Eric Tao",
"timestamp": "07/04/2022 12:53:54",
"content": "you're right they're using Log here to mean principal branch and log to mean the multifunction",
"attachments": [],
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},
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"id": 993560329449648400,
"author_id": 531535537362829300,
"author_name": "Eric Tao",
"timestamp": "07/04/2022 12:54:01",
"content": "that's so unnecessarily confusing xD",
"attachments": [],
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},
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"id": 993560383333867500,
"author_id": 356908116429897700,
"author_name": "Kaynex",
"timestamp": "07/04/2022 12:54:14",
"content": "Yeah complex logs are pretty glossed over",
"attachments": [],
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},
{
"id": 993560573251944600,
"author_id": 356908116429897700,
"author_name": "Kaynex",
"timestamp": "07/04/2022 12:55:00",
"content": "This is why 1/x has no anti-derivative (over a full circle around the origin), since any log you might use fails on that branch cut",
"attachments": [],
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},
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"id": 993561835632611500,
"author_id": 281221474604548100,
"author_name": "PoisonedFood",
"timestamp": "07/04/2022 13:00:01",
"content": "Okay. Thank you guys.",
"attachments": [],
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},
{
"id": 993566720964964500,
"author_id": 800622149903056900,
"author_name": "Shen",
"timestamp": "07/04/2022 13:19:25",
"content": "Close if youβre done π",
"attachments": [],
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"discriminator": "3553",
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}
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"id": 993567144593871000,
"author_id": 281221474604548100,
"author_name": "PoisonedFood",
"timestamp": "07/04/2022 13:21:06",
"content": "My bad",
"attachments": [],
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},
{
"id": 993567163103314000,
"author_id": 281221474604548100,
"author_name": "PoisonedFood",
"timestamp": "07/04/2022 13:21:11",
"content": ".close",
"attachments": [],
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},
{
"id": 993567164659409000,
"author_id": 805217272087838700,
"author_name": "Mathematics Bot",
"timestamp": "07/04/2022 13:21:11",
"content": "Channel closed",
"attachments": [],
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"reference": null
}
] |
help-9
|
2a8a7cb045964f3c9e2ea5371e7d60ac
|
196,972 |
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{
"id": 993567417630466000,
"author_id": 805217272087838700,
"author_name": "Mathematics Bot",
"timestamp": "07/04/2022 13:22:11",
"content": "Available help channel!",
"attachments": [],
"mentions": [],
"reference": null
},
{
"id": 993567818828222600,
"author_id": 553581172802977800,
"author_name": "Levens",
"timestamp": "07/04/2022 13:23:47",
"content": "Show that $p=\\sum_{i=0}^{n-1} x_{i} t^{i} \\in R[t]$ is a polynomial of degree $(p) \\leq n -1$ and $x=\\left[x_{i-1}\\right] \\in R^{n, 1}$ is the matrix of the coefficients of the polynomial, then it holds\n\n$$\nV_{n} x=\\left[p\\left(\\alpha_{i}\\right)\\right]=\\left[\\begin{array}{c}\np\\left(\\alpha_{1}\\right) \\\\\n\\vdots \\\\\np\\left(\\alpha_{n}\\right)\n\\end{array}\\right]\n$$",
"attachments": [],
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},
{
"id": 993567821017649300,
"author_id": 805217272087838700,
"author_name": "Mathematics Bot",
"timestamp": "07/04/2022 13:23:48",
"content": "Pinned a message.",
"attachments": [],
"mentions": [],
"reference": {
"messageId": 993567818828222600,
"channelId": 486844875632017400,
"guildId": null
}
},
{
"id": 993567835936796700,
"author_id": 510789298321096700,
"author_name": "TeXit",
"timestamp": "07/04/2022 13:23:51",
"content": "**Levens**",
"attachments": [
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"author_id": 805217272087838700,
"author_name": "Mathematics Bot",
"timestamp": "07/04/2022 13:38:47",
"content": "@Levens Has your question been resolved?",
"attachments": [],
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"name": "Levens",
"discriminator": "8384",
"nickname": "Levens",
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{
"id": 993571963756892200,
"author_id": 553581172802977800,
"author_name": "Levens",
"timestamp": "07/04/2022 13:40:15",
"content": "@Helpers",
"attachments": [],
"mentions": [],
"reference": null
},
{
"id": 993573870240022500,
"author_id": 132304137583984640,
"author_name": "Denascite",
"timestamp": "07/04/2022 13:47:50",
"content": "I assume V_n is the vandermonde matrix?",
"attachments": [],
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},
{
"id": 993573905249870000,
"author_id": 553581172802977800,
"author_name": "Levens",
"timestamp": "07/04/2022 13:47:58",
"content": "yep",
"attachments": [],
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},
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"id": 993573910983475200,
"author_id": 132304137583984640,
"author_name": "Denascite",
"timestamp": "07/04/2022 13:48:00",
"content": "write out explicitly what the matrix vector product V_n x is",
"attachments": [],
"mentions": [],
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},
{
"id": 993574057796714600,
"author_id": 132304137583984640,
"author_name": "Denascite",
"timestamp": "07/04/2022 13:48:35",
"content": "first row times x should be enough to see the pattern",
"attachments": [],
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},
{
"id": 993574237107388400,
"author_id": 553581172802977800,
"author_name": "Levens",
"timestamp": "07/04/2022 13:49:17",
"content": "$\\left[\\begin{array}{ccccc}\nx & x^2 & \\ldots & x^n\\\\\n\\alpha_2 & \\alpha^{2}_2 & \\vdots & \\alpha^{n}_2 \\\\\n\\vdots & \\vdots & \\ddots & \\vdots \\\\\n\\alpha_{n} & \\alpha^2_{n} & \\ldots & \\alpha^{n}_{n} \n\\end{array}\\right]$",
"attachments": [],
"mentions": [],
"reference": null
},
{
"id": 993574256090816600,
"author_id": 553581172802977800,
"author_name": "Levens",
"timestamp": "07/04/2022 13:49:22",
"content": "Like that?",
"attachments": [],
"mentions": [],
"reference": null
},
{
"id": 993574309043916800,
"author_id": 132304137583984640,
"author_name": "Denascite",
"timestamp": "07/04/2022 13:49:34",
"content": "why are you taking the determinant",
"attachments": [],
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},
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"id": 993574348944310300,
"author_id": 132304137583984640,
"author_name": "Denascite",
"timestamp": "07/04/2022 13:49:44",
"content": "you just have to multiply a matrix with a vector",
"attachments": [],
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},
{
"id": 993574366795272200,
"author_id": 553581172802977800,
"author_name": "Levens",
"timestamp": "07/04/2022 13:49:48",
"content": "wait sorry cause i did that in adiffeent uestion",
"attachments": [],
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},
{
"id": 993574711382519800,
"author_id": 510789298321096700,
"author_name": "TeXit",
"timestamp": "07/04/2022 13:51:10",
"content": "**Levens**",
"attachments": [
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"id": 993574807251726500,
"author_id": 261933205387477000,
"author_name": "riemann",
"timestamp": "07/04/2022 13:51:33",
"content": "Do the multiplication one row at a time. If you're still stuck do it for n=3, 4",
"attachments": [],
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},
{
"id": 993575045324603500,
"author_id": 553581172802977800,
"author_name": "Levens",
"timestamp": "07/04/2022 13:52:30",
"content": "how does multiplying by x give us the answer?",
"attachments": [],
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},
{
"id": 993575225335758800,
"author_id": 553581172802977800,
"author_name": "Levens",
"timestamp": "07/04/2022 13:53:13",
"content": "is the first row right tho?",
"attachments": [],
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},
{
"id": 993575305857994900,
"author_id": 132304137583984640,
"author_name": "Denascite",
"timestamp": "07/04/2022 13:53:32",
"content": "the first row should be powers of a_1",
"attachments": [],
"mentions": [],
"reference": null
},
{
"id": 993575342352638000,
"author_id": 132304137583984640,
"author_name": "Denascite",
"timestamp": "07/04/2022 13:53:41",
"content": "also the first columns should be ones",
"attachments": [],
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"reference": null
},
{
"id": 993575400762515500,
"author_id": 132304137583984640,
"author_name": "Denascite",
"timestamp": "07/04/2022 13:53:55",
"content": "and the last column should only be a_1^(n-1)",
"attachments": [],
"mentions": [],
"reference": null
},
{
"id": 993576043053056000,
"author_id": 553581172802977800,
"author_name": "Levens",
"timestamp": "07/04/2022 13:56:28",
"content": "$\\left[\\begin{array}{ccccc}\nx & xa_1 & xa^{2}_1 & \\ldots & xa^{n-1}_1\\\\\n1 & \\alpha_2 & \\alpha^{2}_2 & \\vdots & \\alpha^{n-1}_2 \\\\\n\\vdots & \\vdots & \\vdots & \\ddots & \\vdots \\\\\n1 & \\alpha_{n+1} & \\alpha^2_{n+1} & \\ldots & \\alpha^{n-1}_{n} \n\\end{array}\\right]$",
"attachments": [],
"mentions": [],
"reference": null
},
{
"id": 993576170459254900,
"author_id": 132304137583984640,
"author_name": "Denascite",
"timestamp": "07/04/2022 13:56:58",
"content": "what?",
"attachments": [],
"mentions": [],
"reference": null
},
{
"id": 993576283357319200,
"author_id": 132304137583984640,
"author_name": "Denascite",
"timestamp": "07/04/2022 13:57:25",
"content": "$x=(x_0, x_1, \\ldots, x_{n-1})^T$ with $x_i$ being the coefficients of the polynomials",
"attachments": [],
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"reference": null
},
{
"id": 993576297882210300,
"author_id": 510789298321096700,
"author_name": "TeXit",
"timestamp": "07/04/2022 13:57:29",
"content": "**Denascite**",
"attachments": [
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"url": "https://cdn.discordapp.com/attachments/486844875632017408/993576297689268225/132304137583984641.png",
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"id": 993576300621078700,
"author_id": 510789298321096700,
"author_name": "TeXit",
"timestamp": "07/04/2022 13:57:29",
"content": "**Levens**",
"attachments": [
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"url": "https://cdn.discordapp.com/attachments/486844875632017408/993576300742705202/553581172802977812.png",
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"id": 993576521354707100,
"author_id": 553581172802977800,
"author_name": "Levens",
"timestamp": "07/04/2022 13:58:22",
"content": "what does that mean",
"attachments": [],
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},
{
"id": 993576876658401300,
"author_id": 132304137583984640,
"author_name": "Denascite",
"timestamp": "07/04/2022 13:59:47",
"content": "you have the vector $$x = \\begin{pmatrix} x_0 \\\\ x_1 \\\\ \\vdots \\\\ x_{n-1}\\end{pmatrix}$$",
"attachments": [],
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},
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"id": 993576890604470400,
"author_id": 510789298321096700,
"author_name": "TeXit",
"timestamp": "07/04/2022 13:59:50",
"content": "**Denascite**",
"attachments": [
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"id": 993577261057982500,
"author_id": 132304137583984640,
"author_name": "Denascite",
"timestamp": "07/04/2022 14:01:18",
"content": "and the matrix $$\\begin{pmatrix}\n1 & \\alpha_1 & \\alpha_1^2 & \\ldots & \\alpha_1^{n-1}\\\\\n1 & \\alpha_2 & \\alpha^{2}_2 & \\vdots & \\alpha_2^{n-1} \\\\\n\\vdots & \\vdots & \\ddots & \\vdots \\\\\n1 & \\alpha_{n} & \\alpha^2_{n} & \\ldots & \\alpha^{n-1}_{n} \n\\end{pmatrix}$$",
"attachments": [],
"mentions": [],
"reference": null
},
{
"id": 993577274295193700,
"author_id": 510789298321096700,
"author_name": "TeXit",
"timestamp": "07/04/2022 14:01:21",
"content": "**Denascite**",
"attachments": [
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"id": 993577329869738100,
"author_id": 132304137583984640,
"author_name": "Denascite",
"timestamp": "07/04/2022 14:01:35",
"content": "now you just want to multiply those two",
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},
{
"id": 993577355555651600,
"author_id": 553581172802977800,
"author_name": "Levens",
"timestamp": "07/04/2022 14:01:41",
"content": "ooh ok",
"attachments": [],
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},
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"id": 993578022311567400,
"author_id": 553581172802977800,
"author_name": "Levens",
"timestamp": "07/04/2022 14:04:20",
"content": "$\\left[\\begin{array}{ccccc}\nx_0 + x_1\\alpha_1 + x_2\\alpha_1^2 + \\ldots + x_{n-1}\\alpha_1^{n-1}\\\\\nx_0 + x_1\\alpha_2 + x_2\\alpha^{2}_2 + \\dots + x_{n-1}\\alpha_2^{n-1} \\\\\n\\vdots & \\vdots & \\vdots & \\ddots & \\vdots \\\\\nx_0 + x_1\\alpha{n} + x_2\\alpha^2{n} + \\ldots + x_{n-1}\\alpha^{n-1}_{n} \n\\end{array}\\right]$\nLike that?",
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},
{
"id": 993578066603417700,
"author_id": 553581172802977800,
"author_name": "Levens",
"timestamp": "07/04/2022 14:04:30",
"content": "bruh wait sorry",
"attachments": [],
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"reference": null
},
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"id": 993578710827536400,
"author_id": 510789298321096700,
"author_name": "TeXit",
"timestamp": "07/04/2022 14:07:04",
"content": "**Levens**",
"attachments": [
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"author_id": 132304137583984640,
"author_name": "Denascite",
"timestamp": "07/04/2022 14:08:02",
"content": "that is not how matrix vector multiplication works",
"attachments": [],
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},
{
"id": 993579766605168600,
"author_id": 553581172802977800,
"author_name": "Levens",
"timestamp": "07/04/2022 14:11:16",
"content": "what then how does it work",
"attachments": [],
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},
{
"id": 993581403033833600,
"author_id": 132304137583984640,
"author_name": "Denascite",
"timestamp": "07/04/2022 14:17:46",
"content": "$\\begin{pmatrix} a & b \\\\ c & d\\end{pmatrix} \\cdot \\begin{pmatrix} x \\\\ y \\end{pmatrix} = \\begin{pmatrix} ax + by \\\\ cx + dy \\end{pmatrix}$",
"attachments": [],
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},
{
"id": 993581540737032200,
"author_id": 510789298321096700,
"author_name": "TeXit",
"timestamp": "07/04/2022 14:18:19",
"content": "**Denascite**",
"attachments": [
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"id": 993581653966454800,
"author_id": 553581172802977800,
"author_name": "Levens",
"timestamp": "07/04/2022 14:18:46",
"content": "is that not what i did",
"attachments": [],
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},
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"id": 993581833084215300,
"author_id": 132304137583984640,
"author_name": "Denascite",
"timestamp": "07/04/2022 14:19:28",
"content": "no",
"attachments": [],
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},
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"id": 993581872208678900,
"author_id": 132304137583984640,
"author_name": "Denascite",
"timestamp": "07/04/2022 14:19:38",
"content": "maybe you meant it",
"attachments": [],
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},
{
"id": 993581918236967000,
"author_id": 132304137583984640,
"author_name": "Denascite",
"timestamp": "07/04/2022 14:19:49",
"content": "but if you did then you forgot all the pluses",
"attachments": [],
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},
{
"id": 993582492147794000,
"author_id": 553581172802977800,
"author_name": "Levens",
"timestamp": "07/04/2022 14:22:05",
"content": "how do i make them show on latex",
"attachments": [],
"mentions": [],
"reference": null
},
{
"id": 993582642836541600,
"author_id": 132304137583984640,
"author_name": "Denascite",
"timestamp": "07/04/2022 14:22:41",
"content": "oh wait you did type them",
"attachments": [],
"mentions": [],
"reference": null
},
{
"id": 993582654010163300,
"author_id": 132304137583984640,
"author_name": "Denascite",
"timestamp": "07/04/2022 14:22:44",
"content": "huh?",
"attachments": [],
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},
{
"id": 993582677372444800,
"author_id": 132304137583984640,
"author_name": "Denascite",
"timestamp": "07/04/2022 14:22:50",
"content": "did you edit just now?",
"attachments": [],
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},
{
"id": 993582700587917400,
"author_id": 132304137583984640,
"author_name": "Denascite",
"timestamp": "07/04/2022 14:22:55",
"content": "then it's too late for the bot",
"attachments": [],
"mentions": [],
"reference": null
},
{
"id": 993582713107910700,
"author_id": 132304137583984640,
"author_name": "Denascite",
"timestamp": "07/04/2022 14:22:58",
"content": "try again",
"attachments": [],
"mentions": [],
"reference": null
},
{
"id": 993582801431580700,
"author_id": 553581172802977800,
"author_name": "Levens",
"timestamp": "07/04/2022 14:23:19",
"content": "$\\left[\\begin{array}{ccccc}\nx_0 + & x_1\\alpha_1 + & x_2\\alpha1^2 + & \\ldots + & x_{n-1}\\alpha_1^{n-1}\\\\\nx_0 + & x_1\\alpha_2 + & x_2\\alpha^{2}2 + & \\dots + & x{n-1}\\alpha_2^{n-1} \\\\\n\\vdots & \\vdots & \\vdots & \\ddots & \\vdots \\\\\nx_0 + & x_1\\alpha{n} + & x2\\alpha^2{n} + & \\ldots + & x{n-1}\\alpha^{n-1}_{n} \n\\end{array}\\right]$",
"attachments": [],
"mentions": [],
"reference": null
},
{
"id": 993583359496298500,
"author_id": 132304137583984640,
"author_name": "Denascite",
"timestamp": "07/04/2022 14:25:32",
"content": "there are a lot of &s in there",
"attachments": [],
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},
{
"id": 993583403859464300,
"author_id": 132304137583984640,
"author_name": "Denascite",
"timestamp": "07/04/2022 14:25:43",
"content": "and you are telling latex that you want 5 columns",
"attachments": [],
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"reference": null
},
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"id": 993583403863646200,
"author_id": 553581172802977800,
"author_name": "Levens",
"timestamp": "07/04/2022 14:25:43",
"content": "im tryna make it work",
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"content": "try out \\begin{pmatrix} \\end{pmatrix}",
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"content": "or bmatrix if you want other brackets",
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"timestamp": "07/04/2022 14:26:37",
"content": "**Levens**",
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"content": "is this right now",
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"content": "and what is p(alpha_1 ) ?",
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"content": "that's polynomials right",
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"timestamp": "07/04/2022 14:36:20",
"content": "p is defined here",
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"timestamp": "07/04/2022 14:36:22",
"content": "p is the polynomial with the coefficients x_i",
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"content": "could u give me a link or a formula on how to find p(x)?",
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"timestamp": "07/04/2022 14:44:27",
"content": "how do you evaluate the polynomial $p(t)=x_0+x_1t+x_2t^2+\\ldots x_{n-1}t^{n-1}$",
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"timestamp": "07/04/2022 14:44:29",
"content": "**Denascite**",
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"content": "im not sure.. i need to recap polynomials",
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"content": "how do you evaluate any function",
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"content": "doesn't matter if it's a polynomial or not",
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"content": "equal it to 0?",
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"content": "no",
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"content": "how do you calculate f(4) if f(x)=x^3",
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"content": "oh",
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"content": "plug in for x",
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"content": "so how do you evaluate p(alpha_1) ?",
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"content": "what would it be here",
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"timestamp": "07/04/2022 15:18:55",
"content": "Wherever you see a t, replace it with alpha_1",
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"content": "where was alpha_1 mentioned in that example tho",
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"content": "First row here",
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"content": "Do this but for alpha_1",
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"content": "$\\alpha_1 + \\alpha_1 \\alpha_1 + \\alpha_1 \\alpha_1^2 + \\ldots + \\alpha_1 \\alpha_1^{n-1}$ like this?",
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"content": "**Levens**",
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"content": "x_0, x_1, etc are all fixed",
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"content": "you are just subbing in alpha_1 for t",
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"content": "where is t tho",
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"content": "here",
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"timestamp": "07/04/2022 16:33:58",
"content": "yeah here it would just be $x_0 + x_1\\alpha_1 + x_2\\alpha_1^2 + \\ldots + x_{n-1}\\alpha_1^{n-1}$",
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"content": "**Levens**",
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"timestamp": "07/04/2022 16:35:25",
"content": "and now compare to the first entry",
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"content": "its the same",
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"timestamp": "07/04/2022 16:37:23",
"content": "which means?",
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"content": "idkπ",
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"content": "go back to what we originally wanted to prove",
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"content": "we wanted to prove that when $p=\\sum{i=0}^{n-1} x{i} t^{i} \\in R[t]$ is a polynomial of degree $(p) \\leq n -1$ and $x=\\left[x{i-1}\\right] \\in R^{n, 1}$ is the matrix of the coefficients of the polynomial, then the thing with the vandermonde matrix holds",
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"content": "**Levens**",
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"content": "what does the degree thing mean",
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"timestamp": "07/04/2022 16:50:50",
"content": ",w degree polynomial",
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"timestamp": "07/04/2022 16:50:53",
"content": "Results provided by WolframAlpha",
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"content": "This is degree n in their definition",
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"content": "im a bit lost - where does the word 'degree' come up here",
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"content": "I'm telling you",
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"content": "If you don't trust me, Google it for yourself",
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"content": "wdym?",
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"content": "degree = highest power of the variable",
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"content": "degree 1 = linear",
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"content": "degree 2 = quadratic",
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"content": "degree 3 = cubic",
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"content": "etc",
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"timestamp": "07/04/2022 17:23:33",
"content": "@Levens Has your question been resolved?",
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"timestamp": "07/04/2022 17:26:45",
"content": "ohhh okay",
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] |
help-9
|
4f4d2683ce20456b85f291ea8b87c5e8
|
196,973 |
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"timestamp": "07/04/2022 17:59:30",
"content": "Pinned a message.",
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"author_id": 830200808414118000,
"author_name": "ritualcurse",
"timestamp": "07/04/2022 17:59:34",
"content": "Can someone help me out with this",
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},
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"id": 993637266218041300,
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"timestamp": "07/04/2022 17:59:45",
"content": "I have to transform it",
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"timestamp": "07/04/2022 18:01:16",
"content": "sits..",
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"content": "@ritualcurse Has your question been resolved?",
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"content": "Channel closed",
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] |
help-9
|
bf201cf0d9484ad692d017f75cef5175
|
196,974 |
[
{
"id": 993645454581563500,
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"author_name": "Mathematics Bot",
"timestamp": "07/04/2022 18:32:17",
"content": "Available help channel!",
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},
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"id": 993648680664043500,
"author_id": 300755705034571800,
"author_name": "Rozio",
"timestamp": "07/04/2022 18:45:06",
"content": "@Carl Friederich Gauss idk why it closed",
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"content": "Pinned a message.",
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"author_id": 300755705034571800,
"author_name": "Rozio",
"timestamp": "07/04/2022 18:45:25",
"content": "but yeah so r -> q is 1 1 0 0 no?",
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},
{
"id": 993648771311345800,
"author_id": 300755705034571800,
"author_name": "Rozio",
"timestamp": "07/04/2022 18:45:28",
"content": "for r",
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},
{
"id": 993648812331634800,
"author_id": 300755705034571800,
"author_name": "Rozio",
"timestamp": "07/04/2022 18:45:37",
"content": "like r = 1 1 0 0",
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},
{
"id": 993649479855124500,
"author_id": 678531646106107900,
"author_name": "Carl Friederich Gauss",
"timestamp": "07/04/2022 18:48:17",
"content": "My teacher said to me that the variables should be organized like the alphabet so q goes before r",
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"author_name": "Rozio",
"timestamp": "07/04/2022 18:59:23",
"content": "@Carl Friederich Gauss can u send ur work again please",
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"timestamp": "07/04/2022 19:02:45",
"content": "i see that u wrote not valid as well",
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"author_name": "Rozio",
"timestamp": "07/04/2022 19:02:52",
"content": "how did u determine that for example p -> q",
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"timestamp": "07/04/2022 19:17:52",
"content": "@Rozio Has your question been resolved?",
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"author_name": "Rozio",
"timestamp": "07/04/2022 19:32:36",
"content": "so i plugged it into a calculator",
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"timestamp": "07/04/2022 19:32:57",
"content": "this one is saying its valid lol\\",
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"timestamp": "07/04/2022 20:02:57",
"content": "@Rozio Has your question been resolved?",
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"timestamp": "07/04/2022 20:32:58",
"content": "Channel closed",
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] |
help-9
|
063d70ef0a5044b2bb0d0393c1b110a9
|
196,975 |
[
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"content": "Available help channel!",
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},
{
"id": 993676227049177100,
"author_id": 553581172802977800,
"author_name": "Levens",
"timestamp": "07/04/2022 20:34:34",
"content": "$\\mathcal{I}(A)$ is an ideal of $K[t]$ (see the definition above). In addition, $\\mathcal{I}(A)$ is not trivial,\ni.e. $\\mathcal{I}(A) \\neq \\{0\\}$ and $\\mathal{I}(A) \\neq K[t]$.",
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"timestamp": "07/04/2022 20:34:34",
"content": "Pinned a message.",
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"author_name": "TeXit",
"timestamp": "07/04/2022 20:35:14",
"content": "**Levens**\nCompile Error! Click the :errors: reaction for more information.\n(You may edit your message to recompile.)",
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"content": "@Levens Has your question been resolved?",
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"content": "@Helpers",
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"timestamp": "07/04/2022 21:19:45",
"content": "@Levens Has your question been resolved?",
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"timestamp": "07/04/2022 21:49:45",
"content": "Channel closed",
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] |
help-9
|
2780a871af1e454aa4c003f0a2c3c728
|
196,976 |
[
{
"id": 993780146723110900,
"author_id": 805217272087838700,
"author_name": "Mathematics Bot",
"timestamp": "07/05/2022 03:27:30",
"content": "Available help channel!",
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},
{
"id": 993781095701155800,
"author_id": 351011564544983040,
"author_name": "Potet",
"timestamp": "07/05/2022 03:31:16",
"content": "How do I solve for derivate to In x, in sqrt(In x)?",
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"id": 993781097538265100,
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"timestamp": "07/05/2022 03:31:17",
"content": "Pinned a message.",
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"id": 993781875107704800,
"author_id": 748029603087384700,
"author_name": "Yours truly",
"timestamp": "07/05/2022 03:34:22",
"content": "Do you mean $\\dv{\\sqrt{\\ln(x)}}{x}$",
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"id": 993781982284750800,
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"timestamp": "07/05/2022 03:34:48",
"content": "No, just square root (In x)",
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"id": 993782090338422800,
"author_id": 183668144404037630,
"author_name": "Ann",
"timestamp": "07/05/2022 03:35:13",
"content": "can you show the entire problem exactly as stated",
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"id": 993782115692978300,
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"author_name": "Yours truly",
"timestamp": "07/05/2022 03:35:19",
"content": "Yeah.",
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"id": 993782296505237500,
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"author_name": "Ann",
"timestamp": "07/05/2022 03:36:03",
"content": "that is sqrt(ln(x)).",
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"id": 993782314133880800,
"author_id": 183668144404037630,
"author_name": "Ann",
"timestamp": "07/05/2022 03:36:07",
"content": "but what are you asked to do with it?",
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"id": 993782320249196500,
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"author_name": "Potet",
"timestamp": "07/05/2022 03:36:08",
"content": "The question is to find the derivate",
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{
"id": 993782407197110400,
"author_id": 183668144404037630,
"author_name": "Ann",
"timestamp": "07/05/2022 03:36:29",
"content": "so you are asked for $\\dv{x} \\sqrt{\\ln(x)}...$",
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"id": 993782415615074300,
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"timestamp": "07/05/2022 03:36:31",
"content": "**Ann**",
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"id": 993782433562513400,
"author_id": 183668144404037630,
"author_name": "Ann",
"timestamp": "07/05/2022 03:36:35",
"content": "why mislead us?",
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"id": 993782449924489300,
"author_id": 748029603087384700,
"author_name": "Yours truly",
"timestamp": "07/05/2022 03:36:39",
"content": "Smh.",
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"id": 993782489434832900,
"author_id": 351011564544983040,
"author_name": "Potet",
"timestamp": "07/05/2022 03:36:49",
"content": "I know the half part, but not the other. Which is the derivate to In x",
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"id": 993782496992952300,
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"author_name": "Ann",
"timestamp": "07/05/2022 03:36:50",
"content": "anyway! the derivative of ln(x) is 1/x.",
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"author_name": "Yours truly",
"timestamp": "07/05/2022 03:37:02",
"content": "So you use chain rule.",
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"id": 993782858193850500,
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"author_name": "Potet",
"timestamp": "07/05/2022 03:38:16",
"content": "Iβm working on it, but the half is required derivate of In x, which I donβt know the way to derivate a logarithm.",
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"author_name": "Yours truly",
"timestamp": "07/05/2022 03:38:29",
"content": "Ann just told you.",
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"id": 993782929761255600,
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"author_name": "Potet",
"timestamp": "07/05/2022 03:38:34",
"content": "Iβm not sure why.",
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"id": 993782985952342000,
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"author_name": "Ann",
"timestamp": "07/05/2022 03:38:47",
"content": "do you know the limit definition of the derivative",
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"author_name": "punisher",
"timestamp": "07/05/2022 03:38:51",
"content": "Do you require to do it on a calculator, or sheet?",
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},
{
"id": 993783116902695000,
"author_id": 351011564544983040,
"author_name": "Potet",
"timestamp": "07/05/2022 03:39:18",
"content": "Ops, I forgot to use that. Iβll try:)",
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{
"id": 993783131222061200,
"author_id": 183668144404037630,
"author_name": "Ann",
"timestamp": "07/05/2022 03:39:22",
"content": "it boils down to the limit $\\lim_{t\\to 0} \\frac{\\ln(1+t)}{t} = 1$ (after some algebra that i don't want to write out)",
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"timestamp": "07/05/2022 03:39:29",
"content": "**Ann**",
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"author_name": "Potet",
"timestamp": "07/05/2022 03:39:40",
"content": "No, just by hand.",
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{
"id": 993783297870139400,
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"author_name": "punisher",
"timestamp": "07/05/2022 03:40:01",
"content": "The derivative of a square root is 1/x(1/2) I believe",
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{
"id": 993783380288225300,
"author_id": 980474983115550700,
"author_name": "punisher",
"timestamp": "07/05/2022 03:40:21",
"content": "And the derivative of the ln is what Ann said",
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{
"id": 993783409828700300,
"author_id": 183668144404037630,
"author_name": "Ann",
"timestamp": "07/05/2022 03:40:28",
"content": "no",
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},
{
"id": 993783635520016400,
"author_id": 748029603087384700,
"author_name": "Yours truly",
"timestamp": "07/05/2022 03:41:22",
"content": "> Derivative of a square root\nDoes not even make sense.",
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},
{
"id": 993783659767287900,
"author_id": 980474983115550700,
"author_name": "punisher",
"timestamp": "07/05/2022 03:41:28",
"content": "My bad, (-1/2)",
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"author_name": "punisher",
"timestamp": "07/05/2022 03:41:33",
"content": "What doesnβt?",
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"id": 993783794517688300,
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"author_name": "punisher",
"timestamp": "07/05/2022 03:42:00",
"content": "Iβm just off by a minus sign apparently.",
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},
{
"id": 993783894761550000,
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"author_name": "Potet",
"timestamp": "07/05/2022 03:42:24",
"content": "Ah, I got it.",
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},
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"author_id": 351011564544983040,
"author_name": "Potet",
"timestamp": "07/05/2022 03:42:28",
"content": "Thanks:)",
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},
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"id": 993783942815690800,
"author_id": 980474983115550700,
"author_name": "punisher",
"timestamp": "07/05/2022 03:42:35",
"content": "No worries, have a nice day.",
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},
{
"id": 993783947236474900,
"author_id": 485903210272391200,
"author_name": "dldh06",
"timestamp": "07/05/2022 03:42:36",
"content": "It's more than a minus sign",
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"timestamp": "07/05/2022 03:42:52",
"content": "Either you didnβt read it correctly or I may have written something wrong.",
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},
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"id": 993784061174755300,
"author_id": 485903210272391200,
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"timestamp": "07/05/2022 03:43:03",
"content": "You wrote it wrong",
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},
{
"id": 993784166107852800,
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"author_name": "dldh06",
"timestamp": "07/05/2022 03:43:28",
"content": "-(1/2) is an exponent",
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},
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"id": 993784399214673900,
"author_id": 351011564544983040,
"author_name": "Potet",
"timestamp": "07/05/2022 03:44:24",
"content": ".close",
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},
{
"id": 993784400800124900,
"author_id": 805217272087838700,
"author_name": "Mathematics Bot",
"timestamp": "07/05/2022 03:44:24",
"content": "Channel closed",
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}
] |
help-9
|
e6f5e5f8f0fc406eac3f310c8e0dfec0
|
196,977 |
[
{
"id": 993784640710115300,
"author_id": 980474983115550700,
"author_name": "punisher",
"timestamp": "07/05/2022 03:45:21",
"content": "Then you have read it wrong. I wrote it as such.",
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},
{
"id": 993784653263675400,
"author_id": 805217272087838700,
"author_name": "Mathematics Bot",
"timestamp": "07/05/2022 03:45:24",
"content": "Available help channel!",
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},
{
"id": 993784877600231400,
"author_id": 485903210272391200,
"author_name": "dldh06",
"timestamp": "07/05/2022 03:46:18",
"content": ".No you did not write it as such",
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"id": 993784929638961300,
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"author_name": "dldh06",
"timestamp": "07/05/2022 03:46:30",
"content": ".You did not write it correctly",
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},
{
"id": 993785025059356800,
"author_id": 485903210272391200,
"author_name": "dldh06",
"timestamp": "07/05/2022 03:46:53",
"content": ".There is no exponent symbol used here",
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"id": 993785138871795700,
"author_id": 980474983115550700,
"author_name": "punisher",
"timestamp": "07/05/2022 03:47:20",
"content": "In my country we do not use it. I apologise for the cultural misunderstanding.",
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"id": 993785140662771800,
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"timestamp": "07/05/2022 03:47:21",
"content": "Pinned a message.",
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"id": 993785315959504900,
"author_id": 485903210272391200,
"author_name": "dldh06",
"timestamp": "07/05/2022 03:48:02",
"content": "Then how do you denote exponents?",
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},
{
"id": 993785355763454000,
"author_id": 485903210272391200,
"author_name": "dldh06",
"timestamp": "07/05/2022 03:48:12",
"content": "Like x^2?",
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},
{
"id": 993785417449099400,
"author_id": 485903210272391200,
"author_name": "dldh06",
"timestamp": "07/05/2022 03:48:27",
"content": "Because x2 doesn't mean the same as x^2",
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},
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"id": 993788914571694100,
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"timestamp": "07/05/2022 04:02:20",
"content": "@punisher Has your question been resolved?",
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"timestamp": "07/05/2022 04:17:21",
"content": "Channel closed",
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}
] |
help-9
|
889948d7567d4d42a68e7480e9a44928
|
196,978 |
[
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"timestamp": "07/05/2022 04:48:46",
"content": "Available help channel!",
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},
{
"id": 993805136096927700,
"author_id": 195924636569960450,
"author_name": "Lyuka",
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"content": "",
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"content": "Pinned a message.",
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{
"id": 993805163343118300,
"author_id": 195924636569960450,
"author_name": "Lyuka",
"timestamp": "07/05/2022 05:06:54",
"content": "Let Ξ³ be a circle and let P be a point on the plane inside Ξ³, different from the center. How many are the circumferences of center P tangent to Ξ³?",
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},
{
"id": 993805229017546900,
"author_id": 195924636569960450,
"author_name": "Lyuka",
"timestamp": "07/05/2022 05:07:10",
"content": "How is the answer not 0?",
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},
{
"id": 993809005162004500,
"author_id": 805217272087838700,
"author_name": "Mathematics Bot",
"timestamp": "07/05/2022 05:22:10",
"content": "@Lyuka Has your question been resolved?",
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"id": 993809059486629900,
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"author_name": "Lyuka",
"timestamp": "07/05/2022 05:22:23",
"content": "@Helpers",
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},
{
"id": 993816610336940000,
"author_id": 805217272087838700,
"author_name": "Mathematics Bot",
"timestamp": "07/05/2022 05:52:24",
"content": "@Lyuka Has your question been resolved?",
"attachments": [],
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{
"id": 195924636569960450,
"name": "Lyuka",
"discriminator": "4502",
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"author_id": 795717786709000200,
"author_name": "η§ζ°΄",
"timestamp": "07/05/2022 06:29:35",
"content": "did you draw a graph?",
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"timestamp": "07/05/2022 06:52:22",
"content": "I did but i didnt understand the question properly",
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"timestamp": "07/05/2022 06:54:14",
"content": "I just realized my error",
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"id": 993832258341453800,
"author_id": 195924636569960450,
"author_name": "Lyuka",
"timestamp": "07/05/2022 06:54:34",
"content": "Honestly i would have never thought of this, thank you once again",
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},
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"id": 993832265060724700,
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"author_name": "Lyuka",
"timestamp": "07/05/2022 06:54:36",
"content": ".close",
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},
{
"id": 993832266776195200,
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"timestamp": "07/05/2022 06:54:36",
"content": "Channel closed",
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}
] |
help-9
|
77d43699fd0e4f5fa0e1e1fb86fe3c54
|
196,979 |
[
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"content": "Available help channel!",
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{
"id": 993841111653163100,
"author_id": 898139815525113900,
"author_name": "hello_idont",
"timestamp": "07/05/2022 07:29:45",
"content": "Hi",
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{
"id": 993841114983452700,
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"content": "@hello_idont Has your question been resolved?",
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] |
help-9
|
780bfa38b61642fcae0ce255815c4f20
|
196,980 |
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"content": "Available help channel!",
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},
{
"id": 993888663853355100,
"author_id": 272928139154292740,
"author_name": "Dankus",
"timestamp": "07/05/2022 10:38:43",
"content": "I'm getting confused on a percent question. I have 2 schools. A and B. School A's budget is $3.5 per student. School B's budget per student is $2.5 per student. School A's budget is 40% greater than B's right? Because 2.5 X 1.4 = 3.5? But if I reduce School A's budget by 40% why does it not equal 2.5? 3.5 X .6 = 2.1 not 2.5",
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"content": "Pinned a message.",
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"content": "@Dankus Has your question been resolved?",
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"author_name": "FructosePear",
"timestamp": "07/05/2022 10:56:55",
"content": "because multiplying by 0.6 isnt the reverse of multiplying by 1.4",
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"author_name": "FructosePear",
"timestamp": "07/05/2022 10:57:35",
"content": "so 2.5 x 1.4 = 3.5",
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"id": 993893475135275000,
"author_id": 272928139154292740,
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"timestamp": "07/05/2022 10:57:50",
"content": "Yes divide 3.5 by 1.4 then",
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"id": 993893492784906200,
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"author_name": "FructosePear",
"timestamp": "07/05/2022 10:57:54",
"content": "and if we divide both sides by 1.4 we get 2.5 = 3.5 / 1.4",
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"id": 993893613668937900,
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"author_name": "FructosePear",
"timestamp": "07/05/2022 10:58:23",
"content": "and 3.5/1.4 is not equal to 3.5 x 0.6",
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},
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"id": 993893660972298200,
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"author_name": "Dankus",
"timestamp": "07/05/2022 10:58:34",
"content": "But is it true that school bs budget is 40% less than a?",
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"id": 993893755205726200,
"author_id": 687838064084910100,
"author_name": "FructosePear",
"timestamp": "07/05/2022 10:58:56",
"content": "no",
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"id": 993893877629071500,
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"author_name": "FructosePear",
"timestamp": "07/05/2022 10:59:26",
"content": "it is true that school A's budget is 40% greater than B's though",
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"id": 993893915730124800,
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"author_name": "Dankus",
"timestamp": "07/05/2022 10:59:35",
"content": "Right",
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"id": 993894148639817900,
"author_id": 687838064084910100,
"author_name": "FructosePear",
"timestamp": "07/05/2022 11:00:30",
"content": "if you divide 3.5 by 1.4 you'll get 2.5",
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"id": 993894478794465400,
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"author_name": "Dankus",
"timestamp": "07/05/2022 11:01:49",
"content": "I guess to say how much less bs is would be 2.5 / 3.5 = 71% so school bs budget is 30% less than a's?",
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"id": 993894531013562500,
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"author_name": "FructosePear",
"timestamp": "07/05/2022 11:02:01",
"content": "that is correct",
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"id": 993894572092567700,
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"author_name": "Dankus",
"timestamp": "07/05/2022 11:02:11",
"content": "Ok thank you",
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},
{
"id": 993894645950066800,
"author_id": 272928139154292740,
"author_name": "Dankus",
"timestamp": "07/05/2022 11:02:29",
"content": "I think I see where my thinking was off originally",
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},
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"id": 993894687150723100,
"author_id": 272928139154292740,
"author_name": "Dankus",
"timestamp": "07/05/2022 11:02:39",
"content": "I really appreciate your help",
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},
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"id": 993894717924311200,
"author_id": 687838064084910100,
"author_name": "FructosePear",
"timestamp": "07/05/2022 11:02:46",
"content": "you're welcome \\:)",
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},
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"id": 993894747125076100,
"author_id": 272928139154292740,
"author_name": "Dankus",
"timestamp": "07/05/2022 11:02:53",
"content": "Have a good day",
"attachments": [],
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},
{
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"author_id": 805217272087838700,
"author_name": "Mathematics Bot",
"timestamp": "07/05/2022 11:02:57",
"content": "Channel closed",
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}
] |
help-9
|
0d5ec13770dd49d8bb633699f528363e
|
196,981 |
[
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"timestamp": "03/29/2022 20:27:01",
"content": "Available help channel!",
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},
{
"id": 958523888013287600,
"author_id": 773744785945002000,
"author_name": "! mike",
"timestamp": "03/29/2022 20:31:43",
"content": "please helpp",
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"content": "Pinned a message.",
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"id": 958525159134871700,
"author_id": 773744785945002000,
"author_name": "! mike",
"timestamp": "03/29/2022 20:36:46",
"content": ".close",
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}
] |
help-9
|
ef94ece33d824ad180d29f5386aa4b59
|
196,982 |
[
{
"id": 993902924495335400,
"author_id": 805217272087838700,
"author_name": "Mathematics Bot",
"timestamp": "07/05/2022 11:35:23",
"content": "Available help channel!",
"attachments": [],
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"reference": null
},
{
"id": 993904568964485200,
"author_id": 798181429996421100,
"author_name": "stargazer206",
"timestamp": "07/05/2022 11:41:55",
"content": "hello im trying to learn mathematical induction on my own and im stuck on this part, it's too complicated any help is appreciated",
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},
{
"id": 993904571304915000,
"author_id": 805217272087838700,
"author_name": "Mathematics Bot",
"timestamp": "07/05/2022 11:41:55",
"content": "Pinned a message.",
"attachments": [],
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"channelId": 486844875632017400,
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"author_id": 798181429996421100,
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"timestamp": "07/05/2022 11:42:48",
"content": "i need the basic step to start solving",
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"author_name": "stargazer206",
"timestamp": "07/05/2022 11:42:55",
"content": "which is hard to get",
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},
{
"id": 993904887924539500,
"author_id": 189001310937284600,
"author_name": "Tom",
"timestamp": "07/05/2022 11:43:11",
"content": "to start you show it's true for n=1",
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},
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"author_id": 189001310937284600,
"author_name": "Tom",
"timestamp": "07/05/2022 11:43:37",
"content": "then you assume that it's true for n=k and use that to show it would be true for n=k+1",
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},
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"timestamp": "07/05/2022 11:44:19",
"content": "i tried for n=1",
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},
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"author_id": 798181429996421100,
"author_name": "stargazer206",
"timestamp": "07/05/2022 11:44:25",
"content": "it didn't work",
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},
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"id": 993905295338246300,
"author_id": 189001310937284600,
"author_name": "Tom",
"timestamp": "07/05/2022 11:44:48",
"content": "so left hand side would be $1^2 = 1$ right?",
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},
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"id": 993905305236811800,
"author_id": 510789298321096700,
"author_name": "TeXit",
"timestamp": "07/05/2022 11:44:50",
"content": "**Tom**",
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"author_name": "stargazer206",
"timestamp": "07/05/2022 11:45:02",
"content": "yes",
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},
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"id": 993905434735939600,
"author_id": 189001310937284600,
"author_name": "Tom",
"timestamp": "07/05/2022 11:45:21",
"content": "then right hand side would be $(-1)^{1-1} \\cdot \\frac{1 \\cdot 2}{2}$",
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},
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"id": 993905446144450700,
"author_id": 510789298321096700,
"author_name": "TeXit",
"timestamp": "07/05/2022 11:45:24",
"content": "**Tom**",
"attachments": [
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"id": 993905609210613900,
"author_id": 189001310937284600,
"author_name": "Tom",
"timestamp": "07/05/2022 11:46:03",
"content": "$(-1)^0 = 1$ and $\\frac{1 \\cdot 2}{2} = 1$ so that should be 1 as well right?",
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},
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"author_id": 510789298321096700,
"author_name": "TeXit",
"timestamp": "07/05/2022 11:46:06",
"content": "**Tom**",
"attachments": [
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"author_id": 798181429996421100,
"author_name": "stargazer206",
"timestamp": "07/05/2022 11:46:14",
"content": "yess",
"attachments": [],
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},
{
"id": 993905924471263400,
"author_id": 798181429996421100,
"author_name": "stargazer206",
"timestamp": "07/05/2022 11:47:18",
"content": "i did it wrong in the beginning because i added the (-1) to /2",
"attachments": [],
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},
{
"id": 993905940287995900,
"author_id": 798181429996421100,
"author_name": "stargazer206",
"timestamp": "07/05/2022 11:47:22",
"content": "which is wrong",
"attachments": [],
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},
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"id": 993906162158289000,
"author_id": 798181429996421100,
"author_name": "stargazer206",
"timestamp": "07/05/2022 11:48:14",
"content": "$(-1) {2}",
"attachments": [],
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},
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"id": 993906223189594200,
"author_id": 798181429996421100,
"author_name": "stargazer206",
"timestamp": "07/05/2022 11:48:29",
"content": "how do i carry on from here?",
"attachments": [],
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},
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"id": 993906722664100000,
"author_id": 189001310937284600,
"author_name": "Tom",
"timestamp": "07/05/2022 11:50:28",
"content": "you assume that it's true for n=k, so",
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"id": 993906792855785500,
"author_id": 189001310937284600,
"author_name": "Tom",
"timestamp": "07/05/2022 11:50:45",
"content": "$\\sum_{i=1}^k (-1)^{i-1} \\cdot i^2 = (-1)^{k-1} \\cdot \\frac{k(k+1)}{2}$",
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"id": 993906803681263700,
"author_id": 510789298321096700,
"author_name": "TeXit",
"timestamp": "07/05/2022 11:50:47",
"content": "**Tom**",
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"author_name": "Tom",
"timestamp": "07/05/2022 11:51:47",
"content": "then using that you want to show that it's true for k+1, so\n$\\sum_{i=1}^{k+1} (-1)^{i-1} \\cdot i^2 = (-1)^{k} \\cdot \\frac{(k+2)(k+1)}{2}$",
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"author_name": "TeXit",
"timestamp": "07/05/2022 11:51:50",
"content": "**Tom**",
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"author_name": "stargazer206",
"timestamp": "07/05/2022 11:52:06",
"content": "oh okay",
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},
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"id": 993907147748409300,
"author_id": 798181429996421100,
"author_name": "stargazer206",
"timestamp": "07/05/2022 11:52:09",
"content": "and that's it?",
"attachments": [],
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},
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"id": 993907179037937800,
"author_id": 189001310937284600,
"author_name": "Tom",
"timestamp": "07/05/2022 11:52:17",
"content": "yes",
"attachments": [],
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},
{
"id": 993907222453170300,
"author_id": 189001310937284600,
"author_name": "Tom",
"timestamp": "07/05/2022 11:52:27",
"content": "the idea is that you know it's true for n=1",
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},
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"id": 993907261992874100,
"author_id": 189001310937284600,
"author_name": "Tom",
"timestamp": "07/05/2022 11:52:37",
"content": "and if it's true for an n it's also true for the next n",
"attachments": [],
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},
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"id": 993907377730506800,
"author_id": 798181429996421100,
"author_name": "stargazer206",
"timestamp": "07/05/2022 11:53:04",
"content": "so (-1)^k . (k+2) (k+1) over 2 is the final answer",
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},
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"id": 993907406310477800,
"author_id": 798181429996421100,
"author_name": "stargazer206",
"timestamp": "07/05/2022 11:53:11",
"content": "yes",
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"timestamp": "07/05/2022 11:53:29",
"content": "awesome!",
"attachments": [],
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"id": 993907600838099000,
"author_id": 189001310937284600,
"author_name": "Tom",
"timestamp": "07/05/2022 11:53:57",
"content": "the answer would be you working through it to show it's true",
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},
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"id": 993907649735315500,
"author_id": 798181429996421100,
"author_name": "stargazer206",
"timestamp": "07/05/2022 11:54:09",
"content": "okayy",
"attachments": [],
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},
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"id": 993907865171542000,
"author_id": 189001310937284600,
"author_name": "Tom",
"timestamp": "07/05/2022 11:55:00",
"content": "you'd still need to actually show that this is true using the previous equation",
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},
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"id": 993907928555864200,
"author_id": 798181429996421100,
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"timestamp": "07/05/2022 11:55:16",
"content": "noted!",
"attachments": [],
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},
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"id": 993907983031480300,
"author_id": 798181429996421100,
"author_name": "stargazer206",
"timestamp": "07/05/2022 11:55:29",
"content": "and we're done?",
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"id": 993908160408600600,
"author_id": 189001310937284600,
"author_name": "Tom",
"timestamp": "07/05/2022 11:56:11",
"content": "yes",
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"author_id": 798181429996421100,
"author_name": "stargazer206",
"timestamp": "07/05/2022 11:56:45",
"content": "thank you so much Tom I highly appreciate your help!",
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},
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"author_id": 798181429996421100,
"author_name": "stargazer206",
"timestamp": "07/05/2022 11:59:26",
"content": ".close",
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},
{
"id": 993908979254169700,
"author_id": 805217272087838700,
"author_name": "Mathematics Bot",
"timestamp": "07/05/2022 11:59:26",
"content": "Channel closed",
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}
] |
help-9
|
e539fb40932a44a6a497035ea373fe0f
|
196,983 |
[
{
"id": 993909233118625900,
"author_id": 805217272087838700,
"author_name": "Mathematics Bot",
"timestamp": "07/05/2022 12:00:27",
"content": "Available help channel!",
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},
{
"id": 993910020867633200,
"author_id": 293487460615192600,
"author_name": "what?",
"timestamp": "07/05/2022 12:03:34",
"content": "I",
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"timestamp": "07/05/2022 12:03:35",
"content": "Pinned a message.",
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{
"id": 993910204297138200,
"author_id": 293487460615192600,
"author_name": "what?",
"timestamp": "07/05/2022 12:04:18",
"content": "In example 3, how did they achieve the value 242x?",
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"id": 993910712130875500,
"author_id": 183668144404037630,
"author_name": "Ann",
"timestamp": "07/05/2022 12:06:19",
"content": "the 242x at the beginning is out of place ngl",
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},
{
"id": 993910824475304100,
"author_id": 293487460615192600,
"author_name": "what?",
"timestamp": "07/05/2022 12:06:46",
"content": "Is it just a typo?",
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"id": 993912630731350000,
"author_id": 183668144404037630,
"author_name": "Ann",
"timestamp": "07/05/2022 12:13:57",
"content": "kind of?",
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"id": 993912667645423600,
"author_id": 183668144404037630,
"author_name": "Ann",
"timestamp": "07/05/2022 12:14:05",
"content": "like, it's a typographical screwup, but somewhat bigger than a typo.",
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},
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"id": 993913669169729500,
"author_id": 755831671588126700,
"author_name": "RepliedPencil",
"timestamp": "07/05/2022 12:18:04",
"content": "Well no because -c/a here is sum of roots three at a time, which actually correspond to -80.666..... \n=> c/3 = 80.666...\n=> c = 242\nWhat Ann said could be the issue, as they wrote the solution of c, 242 by mistake, instead of c in the beginning of the example's answer",
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"id": 993914581623779500,
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"author_name": "what?",
"timestamp": "07/05/2022 12:21:42",
"content": "Thank you :)!",
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},
{
"id": 993914898016899200,
"author_id": 293487460615192600,
"author_name": "what?",
"timestamp": "07/05/2022 12:22:57",
"content": "I think I probably need to do some more research into factorizing quartics",
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},
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"timestamp": "07/05/2022 12:37:58",
"content": "@what? Has your question been resolved?",
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"timestamp": "07/05/2022 12:39:59",
"content": "Channel closed",
"attachments": [],
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}
] |
help-9
|
5260294e76d54cb49eb4fc1a8d15e3cd
|
196,984 |
[
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"id": 993919434785833100,
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"timestamp": "07/05/2022 12:40:59",
"content": "Available help channel!",
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},
{
"id": 993921752918925400,
"author_id": 615703104004030500,
"author_name": "TallKoala",
"timestamp": "07/05/2022 12:50:12",
"content": "I can't figure out what I'm doing wrong with this linear algebra problem",
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"content": "Pinned a message.",
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"timestamp": "07/05/2022 12:52:21",
"content": "Help",
"attachments": [],
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"reference": null
},
{
"id": 993922307510779900,
"author_id": 598960698525089900,
"author_name": "Grant",
"timestamp": "07/05/2022 12:52:24",
"content": "!",
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},
{
"id": 993922319091253200,
"author_id": 598960698525089900,
"author_name": "Grant",
"timestamp": "07/05/2022 12:52:27",
"content": "Plz",
"attachments": [],
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},
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"author_id": 615703104004030500,
"author_name": "TallKoala",
"timestamp": "07/05/2022 12:52:44",
"content": "I'm already in this channel @Grant",
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"timestamp": "07/05/2022 12:53:04",
"content": "#βhow-to-get-help @Grant",
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"timestamp": "07/05/2022 12:53:06",
"content": "Oh",
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"timestamp": "07/05/2022 12:53:25",
"content": "I can't figure out what I'm doing wrong with this linear algebra problem",
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"content": "@TallKoala Has your question been resolved?",
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"timestamp": "07/05/2022 13:17:06",
"content": "is what you showed your work or the solution?",
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"content": "My work",
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"timestamp": "07/05/2022 13:21:03",
"content": "I guess P^-1 and P should be swapped here",
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"timestamp": "07/05/2022 13:23:39",
"content": "As in P should be \n$\\begin{pmatrix}\n0&1\\\\\n1&-1\\end{pmatrix}\n$",
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"timestamp": "07/05/2022 13:23:41",
"content": "**Drake**",
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"timestamp": "07/05/2022 13:24:54",
"content": "I donβt see how that would be possible with how they are describing P as composed of v1 and v2",
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"timestamp": "07/05/2022 13:37:44",
"content": "there's a typo in the question. It should be",
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"timestamp": "07/05/2022 13:37:45",
"content": "$A - \\lambda I$ and not plus",
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"id": 993933729837891700,
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"timestamp": "07/05/2022 13:37:47",
"content": "**riemann**",
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"timestamp": "07/05/2022 13:38:21",
"content": "https://www.math.utah.edu/~yplee/teaching/2270f14/Jordan_Form.pdf",
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"timestamp": "07/05/2022 13:54:54",
"content": "@TallKoala Has your question been resolved?",
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"timestamp": "07/05/2022 14:00:07",
"content": "Omg. Thank you. π€¦ββοΈ",
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"content": "Channel closed",
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] |
help-9
|
0c6abef43a7c4ac7aba01599c5a0d2c6
|
196,985 |
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"timestamp": "07/05/2022 14:06:44",
"content": "Available help channel!",
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"author_name": "Kharis",
"timestamp": "07/05/2022 14:18:02",
"content": "Does anyone have a good video or website explaining the similar methods to do question 6?",
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"content": "Pinned a message.",
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"author_name": "dldh06",
"timestamp": "07/05/2022 14:18:26",
"content": "Look up completing the square",
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"content": "I tried asking my teacher but he just give us the answer and not actually explain it π",
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"content": "@Kharis Has your question been resolved?",
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"content": "Channel closed",
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] |
help-9
|
a7991e3914534f2f86f94ca6dedfe138
|
196,986 |
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"content": "Hi",
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"content": "@hello_idont Has your question been resolved?",
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help-9
|
d01b46464f2b42e2aaaa879418d260db
|
196,987 |
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"author_name": "Mathematics Bot",
"timestamp": "07/05/2022 16:06:08",
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"author_id": 181569083416772600,
"author_name": "Evilebob",
"timestamp": "07/05/2022 16:41:11",
"content": "I'm hoping to find help forming an equation to a problem. This is for a programming project for a personal motor device. \nI have x units of power going to the motor and I want to put in a safety if the motor cycle reaches 90-95%.\nSo If motor duty is 90 or higher then the x units of power becomes the previous value px that went to the motor subtracted by one\nNow if motor duty is going above 90 on the next run, then I need to decrease the x units of power in ratio to the current duty cycle up to 95% where at 95% I want to deduct up to 90% of the potential x value. Lets say the potential x value is 3000.",
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"timestamp": "07/05/2022 16:41:11",
"content": "Pinned a message.",
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"author_id": 307070375735459840,
"author_name": "abs_0",
"timestamp": "07/05/2022 16:44:03",
"content": "What is βmotor dutyβ",
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"author_id": 484702191156985860,
"author_name": "themateo713",
"timestamp": "07/05/2022 16:44:19",
"content": "percentage of maximum speed/power I guess",
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"id": 993980791505829900,
"author_id": 484702191156985860,
"author_name": "themateo713",
"timestamp": "07/05/2022 16:44:47",
"content": "\"decrease the x units of power in ratio to the current duty cycle up to 95% where at 95% I want to deduct up to 90% of the potential x value\" is the part I struggle to understand",
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"author_name": "Evilebob",
"timestamp": "07/05/2022 16:45:31",
"content": "\"percentage of maximum speed/power I guess\" about as close as any of us understand it yes... motor will shut down higher than 95%",
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"author_name": "themateo713",
"timestamp": "07/05/2022 16:45:31",
"content": "is it (if motor duty > 95%) then (reduce input x such that motor duty = 90%) ?",
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"author_name": "Evilebob",
"timestamp": "07/05/2022 16:46:48",
"content": "So at 90% I'm only deducting the previous value sent to the motor -1\nat 92% I need to deduct way more because -1 wasn't enough\nat 94% I need to be deducting near my limit because duty still is climbing",
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"author_name": "themateo713",
"timestamp": "07/05/2022 16:47:40",
"content": "so by the time you reach 95%, you say \"emergency ! feed nothing to make sure it doesn't go up anymore\" ?",
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"author_name": "Evilebob",
"timestamp": "07/05/2022 16:48:33",
"content": "yeah... so bunch of equations happen and create a value of x going to the motor... \"send x power to motor\"\nthe purpose of this equation is the intercept that call if duty is higher than norms as a safety measure.",
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"author_name": "Evilebob",
"timestamp": "07/05/2022 16:50:17",
"content": "3000 is an example... x could be any positive number",
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"author_name": "themateo713",
"timestamp": "07/05/2022 16:50:46",
"content": "so for example, if you were at 94% and feed it x=3000, next measure is 95%, what x do you want to feed",
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"author_name": "Evilebob",
"timestamp": "07/05/2022 16:54:18",
"content": "so by your example, x going into this function is at 3000 but the duty cycle is at 94% meaning the previous subtractions of x were not enough. If I started subtracting by 1 at 90% and increased that value by every increase of duty % then I would suspect that new x would be getting nearish to zero since I'm trying to avoid getting to 95",
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"author_name": "Evilebob",
"timestamp": "07/05/2022 16:55:38",
"content": "calling x after the equation is probably wrong... the value of subtraction would be y or something. y is output of this equation of how much to subtract from x before x is pushed to the motor.",
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"author_name": "Evilebob",
"timestamp": "07/05/2022 16:57:14",
"content": "Lets say in your example that the max value the motor can take is 5000 or more to illustrate that by this cycle we have already run the equation a few times and subtracted from x",
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"author_name": "themateo713",
"timestamp": "07/05/2022 16:57:55",
"content": "regarding your question, are we trying to find a formula that's basically (new power to feed)(current power, percentage) that works well, right ?",
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"author_name": "Evilebob",
"timestamp": "07/05/2022 16:58:45",
"content": "yeah that's looking right",
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"author_name": "Evilebob",
"timestamp": "07/05/2022 17:01:40",
"content": "At 90% when this triggers I don't want to make any sudden adjustments since it could \"throw the rider\" so that's why it's just the previous value minus 1. Hopefully that alone would lower duty beyond next iterations but then again that's why the formula adds a bit more safety buffer",
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"author_name": "hello_idont",
"timestamp": "07/05/2022 17:02:22",
"content": "No",
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"author_id": 898139815525113900,
"author_name": "hello_idont",
"timestamp": "07/05/2022 17:02:23",
"content": "@Helpers",
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"id": 993985219931676700,
"author_id": 898139815525113900,
"author_name": "hello_idont",
"timestamp": "07/05/2022 17:02:23",
"content": "No",
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"author_name": "themateo713",
"timestamp": "07/05/2022 17:05:45",
"content": "ngl I feel like it's hard to find a solution just like that because the constraints aren't really clear/specified. How smooth must the changes be to be kind to rider, but how rough should they be to still do their job ? It's hard to know without being more precise about the requirements. Also not having a clue about the relationship between the duty and the power makes it really obscure",
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{
"id": 993987859319103600,
"author_id": 181569083416772600,
"author_name": "Evilebob",
"timestamp": "07/05/2022 17:12:53",
"content": "Yeah, I get that some parts are a bit obscure... even for me in the real world application I have to revert back to logs of the actions to see if they matched the expectations. A bit of trial and error mixed with physics and math I guess?\nI think you have the rough outline of the formula going though but as I'm thinking about it there are a few parts I'm not visualizing yet. \nlets say current power is 5000 or as percentage 100%\nWe enter the formula when duty cycle reaches 90%\npower to motor after formula 4999 or = < 1% power cutback\nNext cycle power to motor is 4999 or 99.somethingpercent\nDuty cycle climbed again.. now 91% \nSo 90-95% a 5% range... if at 5% I want to remove up to 80% of max power",
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"id": 993988212638896300,
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"author_name": "Evilebob",
"timestamp": "07/05/2022 17:14:17",
"content": "tbh I made up 80%... I can always adjust the max deduction percentage after real world tests if it was extreme enough",
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"id": 993989088694779900,
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"author_name": "Evilebob",
"timestamp": "07/05/2022 17:17:46",
"content": "are there any constraints that would make this cleaner that I could add to this?",
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"timestamp": "07/05/2022 17:18:44",
"content": "you can always try various types of reductions and see what works best, and try to adjust based on your intuitive understanding of things. Usually that's how things go",
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"content": "what I'm saying, from my perspective, is that it's such an abstract thing to control that setting some better defined requirements to try to meet would be beneficial, like what causes the rider to throw etc",
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"content": "Well if the motor does actually reach 95 then it's a shutoff which will of course throw a rider. \nSudden shift in power would do the same. \nThere's quite a few equations that happen already which determine factors such as terrain, current speeds, etc.... so this comes in as a very very last measure just in case we are trying to push more power into the motor beyond safe riding limits and adjust that power gently so as not to jar the rider off balance.",
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"content": "I guess as a simple model, you try to make it decrease linearly. Like putting it on a line that reaches 0 at 95%. Then for practical purposes you look at the current speed at which the duty is increasing to see where on that line to look, and because it's likely an under-approximation you make the line reach 0 halfway before 95% to give yourself a margin. Or something like that",
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"author_name": "Evilebob",
"timestamp": "07/05/2022 17:27:58",
"content": "what does that equation look like?",
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"timestamp": "07/05/2022 17:31:48",
"content": "x2 = max(0, x1 * (1 - 2|p1 - p0| / (95% - p1))) I guess",
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"timestamp": "07/05/2022 17:32:09",
"content": "where p1 = latest power read, p0 = previous read, x1 = power sent at p1",
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"author_name": "Evilebob",
"timestamp": "07/05/2022 17:36:32",
"content": "okay that helps and I think I can simplify the problem further... hopefully this helps...\ndutyadjust= currentduty-90. (dutyadjust would now be 0-5%)\npercentageadjust = !!!this is definitely wrong!!! = 80%* dutyadjust\n(current power, percentageadjust) = (new power to feed)",
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"author_name": "Evilebob",
"timestamp": "07/05/2022 17:37:40",
"content": "that last part isn't complete... it would be like... current power = currentpower - (currentpower * percentageadjust)",
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"timestamp": "07/05/2022 17:38:49",
"content": "percentageadjust is where I need the value of 80 if dutyadjust 5% and value of 1% if dutyadjust 0",
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"author_name": "Mathematics Bot",
"timestamp": "07/05/2022 17:53:49",
"content": "@Evilebob Has your question been resolved?",
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"timestamp": "07/05/2022 17:58:01",
"content": "Channel closed",
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}
] |
help-9
|
0383fda6424d4384b9f6b259692ac0b7
|
196,988 |
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"author_id": 805217272087838700,
"author_name": "Mathematics Bot",
"timestamp": "07/05/2022 17:59:01",
"content": "Available help channel!",
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"id": 994003767924097000,
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"author_name": "Talon",
"timestamp": "07/05/2022 18:16:05",
"content": "Is this a proper way to define a sample space of an experiment with infinite coin tosses?\n$S={c:c=c_1,c_2,..., \\text{where } c_i\\epsilon{H,T}}$",
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"timestamp": "07/05/2022 18:16:06",
"content": "Pinned a message.",
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"author_name": "TeXit",
"timestamp": "07/05/2022 18:16:08",
"content": "**CuriousTalon**",
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"content": "$S={c:c=c_1,c_2,..., \\text{where } c_i\\epsilon{H,T}}$",
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"timestamp": "07/05/2022 18:16:19",
"content": "**CuriousTalon**",
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"timestamp": "07/05/2022 18:16:31",
"content": "$\\in$",
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"author_id": 510789298321096700,
"author_name": "TeXit",
"timestamp": "07/05/2022 18:16:34",
"content": "**riemann**",
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"timestamp": "07/05/2022 18:16:50",
"content": "huh I literally got it working in the testing channel",
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"author_name": "riemann",
"timestamp": "07/05/2022 18:17:01",
"content": "$\\epsilon,\\ \\in$",
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"timestamp": "07/05/2022 18:17:03",
"content": "**riemann**",
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"author_name": "riemann",
"timestamp": "07/05/2022 18:17:09",
"content": "it works, just not pretty",
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"id": 994004082597572700,
"author_id": 966575640612593700,
"author_name": "Talon",
"timestamp": "07/05/2022 18:17:20",
"content": "what would the \"pretty\" way be",
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},
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"id": 994004170174632000,
"author_id": 261933205387477000,
"author_name": "riemann",
"timestamp": "07/05/2022 18:17:41",
"content": ".",
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"id": 994004259400061000,
"author_id": 966575640612593700,
"author_name": "Talon",
"timestamp": "07/05/2022 18:18:03",
"content": "ah",
"attachments": [],
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"id": 994004299170463900,
"author_id": 966575640612593700,
"author_name": "Talon",
"timestamp": "07/05/2022 18:18:12",
"content": "the rest is fine?",
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"id": 994004457455112300,
"author_id": 261933205387477000,
"author_name": "riemann",
"timestamp": "07/05/2022 18:18:50",
"content": "Chapter 2\nhttps://www.colorado.edu/amath/sites/default/files/attached-files/billingsley.pdf",
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"timestamp": "07/05/2022 18:20:14",
"content": "Your specific question is eqn 2.15",
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"timestamp": "07/05/2022 18:21:09",
"content": "thanks",
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"timestamp": "07/05/2022 18:36:09",
"content": "@Talon Has your question been resolved?",
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"timestamp": "07/05/2022 18:36:15",
"content": "Channel closed",
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}
] |
help-9
|
03d9f8c540954f6995ce605046493cc8
|
196,989 |
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"timestamp": "07/05/2022 22:40:00",
"content": "Available help channel!",
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"content": "Pinned a message.",
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"id": 994072111779938400,
"author_id": 825620400154083300,
"author_name": "Lerena",
"timestamp": "07/05/2022 22:47:40",
"content": "Not really sure what to do",
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"id": 994072414227013600,
"author_id": 356908116429897700,
"author_name": "Kaynex",
"timestamp": "07/05/2022 22:48:52",
"content": "Would you be able to write this polynomial if the roots were 2 and 3?",
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"id": 994072507701280900,
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"author_name": "Lerena",
"timestamp": "07/05/2022 22:49:14",
"content": "yeah",
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"author_name": "Kaynex",
"timestamp": "07/05/2022 22:49:21",
"content": "Okay sick. Same thing here",
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"id": 994072619252986000,
"author_id": 356908116429897700,
"author_name": "Kaynex",
"timestamp": "07/05/2022 22:49:41",
"content": "*except*, if the coefficients are integers, then we have to add more roots",
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"id": 994072686764499100,
"author_id": 356908116429897700,
"author_name": "Kaynex",
"timestamp": "07/05/2022 22:49:57",
"content": "The extra roots are -2 - 3i\nAnd 1 - β5",
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"id": 994072716967673900,
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"author_name": "Lerena",
"timestamp": "07/05/2022 22:50:04",
"content": "yep",
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"id": 994072771967590400,
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"author_name": "Lerena",
"timestamp": "07/05/2022 22:50:17",
"content": "i understand that",
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"id": 994073010090815600,
"author_id": 356908116429897700,
"author_name": "Kaynex",
"timestamp": "07/05/2022 22:51:14",
"content": "Okay, so you have all of the roots now.",
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"author_name": "Kaynex",
"timestamp": "07/05/2022 22:51:41",
"content": "And, you can write a polynomial using its roots, so that's the way to go",
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"id": 994073193574834200,
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"author_name": "Lerena",
"timestamp": "07/05/2022 22:51:58",
"content": "how would i write it",
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"id": 994073205297918100,
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"author_name": "Lerena",
"timestamp": "07/05/2022 22:52:01",
"content": "when the roots are like this lol",
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"id": 994073260851462300,
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"author_name": "Lerena",
"timestamp": "07/05/2022 22:52:14",
"content": "(x-(2+3i)",
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"id": 994073263389020300,
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"author_name": "Lerena",
"timestamp": "07/05/2022 22:52:14",
"content": "idk",
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"author_name": "Kaynex",
"timestamp": "07/05/2022 22:52:54",
"content": "Yeah exactly. That's going to include the root 2 + 3i",
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"id": 994073479995469800,
"author_id": 356908116429897700,
"author_name": "Kaynex",
"timestamp": "07/05/2022 22:53:06",
"content": "Well, wait, we don't have that root",
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"id": 994073528838127600,
"author_id": 356908116429897700,
"author_name": "Kaynex",
"timestamp": "07/05/2022 22:53:18",
"content": "But for the ones we DO have",
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"id": 994074626932092900,
"author_id": 825620400154083300,
"author_name": "Lerena",
"timestamp": "07/05/2022 22:57:40",
"content": "wdym?",
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"id": 994074693353091200,
"author_id": 825620400154083300,
"author_name": "Lerena",
"timestamp": "07/05/2022 22:57:55",
"content": "1+sqrt 5?",
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{
"id": 994074712403619800,
"author_id": 825620400154083300,
"author_name": "Lerena",
"timestamp": "07/05/2022 22:58:00",
"content": "im not sure what u mean",
"attachments": [],
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"author_id": 356908116429897700,
"author_name": "Kaynex",
"timestamp": "07/05/2022 23:02:51",
"content": "(x - 2) includes 2 as a root",
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},
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"id": 994076049195401300,
"author_id": 356908116429897700,
"author_name": "Kaynex",
"timestamp": "07/05/2022 23:03:19",
"content": "(x - π) includes π as a root",
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},
{
"id": 994076112688791600,
"author_id": 825620400154083300,
"author_name": "Lerena",
"timestamp": "07/05/2022 23:03:34",
"content": "yes",
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"id": 994076146977210500,
"author_id": 825620400154083300,
"author_name": "Lerena",
"timestamp": "07/05/2022 23:03:42",
"content": "but how would we write that",
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"id": 994076162177372200,
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"author_name": "Lerena",
"timestamp": "07/05/2022 23:03:46",
"content": "when the roots are -2+3i",
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"id": 994076179055255700,
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"author_name": "Lerena",
"timestamp": "07/05/2022 23:03:50",
"content": "1+ sqrt 5",
"attachments": [],
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},
{
"id": 994076186051367000,
"author_id": 825620400154083300,
"author_name": "Lerena",
"timestamp": "07/05/2022 23:03:51",
"content": "and the other 2 roots",
"attachments": [],
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{
"id": 994076214887190500,
"author_id": 825620400154083300,
"author_name": "Lerena",
"timestamp": "07/05/2022 23:03:58",
"content": "like i dont get how to write those as roots",
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{
"id": 994076227780489200,
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"author_name": "Lerena",
"timestamp": "07/05/2022 23:04:01",
"content": "i understand with integers",
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{
"id": 994076274328862800,
"author_id": 825620400154083300,
"author_name": "Lerena",
"timestamp": "07/05/2022 23:04:12",
"content": "just roots with multiple terms are a bit confusing",
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"id": 994077814833811600,
"author_id": 896625754383724500,
"author_name": "lirmirit",
"timestamp": "07/05/2022 23:10:20",
"content": "Replace π with -2+3i and 1+sqrt 5",
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{
"id": 994078233148534800,
"author_id": 825620400154083300,
"author_name": "Lerena",
"timestamp": "07/05/2022 23:11:59",
"content": "should i write this",
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},
{
"id": 994078240102695000,
"author_id": 825620400154083300,
"author_name": "Lerena",
"timestamp": "07/05/2022 23:12:01",
"content": "with all 4 roots",
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},
{
"id": 994078252912099300,
"author_id": 825620400154083300,
"author_name": "Lerena",
"timestamp": "07/05/2022 23:12:04",
"content": "or just the 2 we were given",
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},
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"id": 994078386320318600,
"author_id": 825620400154083300,
"author_name": "Lerena",
"timestamp": "07/05/2022 23:12:36",
"content": "ugh when i do this i get a bunch of imaginary terms",
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},
{
"id": 994080194182779000,
"author_id": 825620400154083300,
"author_name": "Lerena",
"timestamp": "07/05/2022 23:19:47",
"content": "nvm",
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},
{
"id": 994080197194297500,
"author_id": 825620400154083300,
"author_name": "Lerena",
"timestamp": "07/05/2022 23:19:48",
"content": ".close",
"attachments": [],
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},
{
"id": 994080199002030200,
"author_id": 805217272087838700,
"author_name": "Mathematics Bot",
"timestamp": "07/05/2022 23:19:48",
"content": "Channel closed",
"attachments": [],
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"reference": null
}
] |
help-9
|
45b8d48965ab44d49bcd808572d98212
|
196,990 |
[
{
"id": 994084900862972000,
"author_id": 805217272087838700,
"author_name": "Mathematics Bot",
"timestamp": "07/05/2022 23:38:29",
"content": "Available help channel!",
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},
{
"id": 994113326286110700,
"author_id": 819818586965016600,
"author_name": "JunβΎ",
"timestamp": "07/06/2022 01:31:26",
"content": "Is this a causal relationship?",
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"timestamp": "07/06/2022 01:31:27",
"content": "Pinned a message.",
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"id": 994113663021629400,
"author_id": 819818586965016600,
"author_name": "JunβΎ",
"timestamp": "07/06/2022 01:32:47",
"content": "I say yes because the price of the petrol enables the amount of people who buy it",
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},
{
"id": 994113755891896300,
"author_id": 819818586965016600,
"author_name": "JunβΎ",
"timestamp": "07/06/2022 01:33:09",
"content": "My book says no so Iβm a bit confused",
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},
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"id": 994117531801501800,
"author_id": 805217272087838700,
"author_name": "Mathematics Bot",
"timestamp": "07/06/2022 01:48:09",
"content": "@JunβΎ Has your question been resolved?",
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"id": 994120168127082500,
"author_id": 356908116429897700,
"author_name": "Kaynex",
"timestamp": "07/06/2022 01:58:37",
"content": "Gas has unlimited demand. They can charge anything for it, and it will sell as well as it does.",
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"id": 994120267972489200,
"author_id": 356908116429897700,
"author_name": "Kaynex",
"timestamp": "07/06/2022 01:59:01",
"content": "But I don't know if the book is going that way",
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},
{
"id": 994120864859689000,
"author_id": 141791176540946430,
"author_name": "frownyfrog",
"timestamp": "07/06/2022 02:01:24",
"content": "\"Gas doesn't have fixed demand. You can always price out a certain customer by raising the price\"",
"attachments": [],
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},
{
"id": 994120904961433700,
"author_id": 141791176540946430,
"author_name": "frownyfrog",
"timestamp": "07/06/2022 02:01:33",
"content": "makes at least as much sense imo",
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},
{
"id": 994121287892992000,
"author_id": 733586866003116000,
"author_name": "Andrea276",
"timestamp": "07/06/2022 02:03:04",
"content": "The price of petrol should change only based on the amount of petrol available and on the demand, although that seems intuitively true",
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},
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"id": 994121307467829200,
"author_id": 805217272087838700,
"author_name": "Mathematics Bot",
"timestamp": "07/06/2022 02:03:09",
"content": "Channel closed",
"attachments": [],
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"reference": null
}
] |
help-9
|
298bf275c3cb45c99e79f71a66602505
|
196,991 |
[
{
"id": 994121560275296300,
"author_id": 805217272087838700,
"author_name": "Mathematics Bot",
"timestamp": "07/06/2022 02:04:09",
"content": "Available help channel!",
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},
{
"id": 994131222936682600,
"author_id": 782468629312307200,
"author_name": "-.-",
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"content": "Pinned a message.",
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"id": 994131253139869700,
"author_id": 782468629312307200,
"author_name": "-.-",
"timestamp": "07/06/2022 02:42:40",
"content": "ik how to do part a but\nhow do i do part (b)?",
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"id": 994131328457003000,
"author_id": 782468629312307200,
"author_name": "-.-",
"timestamp": "07/06/2022 02:42:58",
"content": "am i supposed to let AC = smth?",
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"author_id": 307877392603676700,
"author_name": "ToxicFantasies",
"timestamp": "07/06/2022 02:46:57",
"content": "You can try using what you've proved in part (a). What do you know about similar triangles?",
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"id": 994132423451365400,
"author_id": 782468629312307200,
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"timestamp": "07/06/2022 02:47:19",
"content": "hmm",
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{
"id": 994132457991446500,
"author_id": 782468629312307200,
"author_name": "-.-",
"timestamp": "07/06/2022 02:47:28",
"content": "that theyre similar?",
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"id": 994132532008321000,
"author_id": 782468629312307200,
"author_name": "-.-",
"timestamp": "07/06/2022 02:47:45",
"content": "jk",
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{
"id": 994132546373832800,
"author_id": 782468629312307200,
"author_name": "-.-",
"timestamp": "07/06/2022 02:47:49",
"content": "wait let me think",
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},
{
"id": 994132659007664300,
"author_id": 307877392603676700,
"author_name": "ToxicFantasies",
"timestamp": "07/06/2022 02:48:15",
"content": "Think about their properties, take your time",
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"id": 994132801433637000,
"author_id": 782468629312307200,
"author_name": "-.-",
"timestamp": "07/06/2022 02:48:49",
"content": "they have the same ratios? π
",
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"author_id": 307877392603676700,
"author_name": "ToxicFantasies",
"timestamp": "07/06/2022 02:48:57",
"content": "Yup!",
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"id": 994133076814876700,
"author_id": 307877392603676700,
"author_name": "ToxicFantasies",
"timestamp": "07/06/2022 02:49:55",
"content": "Now look at the equation they want you to show, you want to find some ratios that relate to the length of AC",
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"id": 994133157941104800,
"author_id": 782468629312307200,
"author_name": "-.-",
"timestamp": "07/06/2022 02:50:14",
"content": "Do i let AC = 1/2 ?........",
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"id": 994133388040601600,
"author_id": 307877392603676700,
"author_name": "ToxicFantasies",
"timestamp": "07/06/2022 02:51:09",
"content": "Nah, don't think about the actual values of the ratios",
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{
"id": 994133469514960900,
"author_id": 782468629312307200,
"author_name": "-.-",
"timestamp": "07/06/2022 02:51:29",
"content": "Ohh",
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},
{
"id": 994133527052439700,
"author_id": 782468629312307200,
"author_name": "-.-",
"timestamp": "07/06/2022 02:51:42",
"content": "ohhhh",
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},
{
"id": 994133647496069200,
"author_id": 782468629312307200,
"author_name": "-.-",
"timestamp": "07/06/2022 02:52:11",
"content": "BC / AC = AC / CD",
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"id": 994133742752903300,
"author_id": 307877392603676700,
"author_name": "ToxicFantasies",
"timestamp": "07/06/2022 02:52:34",
"content": "Yup! And you can manipulate that to show (b)",
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"id": 994133772419203200,
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"author_name": "-.-",
"timestamp": "07/06/2022 02:52:41",
"content": "ayeee nice",
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},
{
"id": 994133790828015600,
"author_id": 782468629312307200,
"author_name": "-.-",
"timestamp": "07/06/2022 02:52:45",
"content": "I get it now",
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},
{
"id": 994133814664253400,
"author_id": 782468629312307200,
"author_name": "-.-",
"timestamp": "07/06/2022 02:52:51",
"content": "thanks a lot!!!",
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},
{
"id": 994133855273492500,
"author_id": 782468629312307200,
"author_name": "-.-",
"timestamp": "07/06/2022 02:53:01",
"content": "really appreciate it!",
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{
"id": 994134034064085000,
"author_id": 782468629312307200,
"author_name": "-.-",
"timestamp": "07/06/2022 02:53:43",
"content": "hope you have an amazing day and week and life ahead",
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"id": 994134058038722600,
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"content": ".close",
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"id": 994134062379827200,
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"timestamp": "07/06/2022 02:53:50",
"content": "Channel closed",
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] |
help-9
|
84d7ece56fcb46469fd3133ee6f74240
|
196,992 |
[
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"timestamp": "03/21/2022 15:16:34",
"content": "Available help channel!",
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"id": 955549322370511000,
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"author_id": 261952052077395970,
"author_name": "Tarehjerne",
"timestamp": "03/21/2022 15:34:44",
"content": "Does it say $y=sin(x)-\\sqrt{3}cos(x), x\\epsilon \\mathbf{R}$",
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"id": 955550055400607900,
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"timestamp": "03/21/2022 15:34:46",
"content": "**Tarehjerne**",
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"author_name": "Tarehjerne",
"timestamp": "03/21/2022 15:37:45",
"content": "So, to find the lowest number, you must consider the derivative. You want to find where the derivative is zero",
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"timestamp": "03/21/2022 15:38:04",
"content": "After that we work out if its the highest or smallest number",
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"id": 955550937471131900,
"author_id": 261952052077395970,
"author_name": "Tarehjerne",
"timestamp": "03/21/2022 15:38:16",
"content": "you haven't ever looked at derivatives?",
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"id": 955550981066719400,
"author_id": 261952052077395970,
"author_name": "Tarehjerne",
"timestamp": "03/21/2022 15:38:27",
"content": "How are you at trig frunctions?",
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"id": 955550992718500000,
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"author_name": "Tarehjerne",
"timestamp": "03/21/2022 15:38:29",
"content": "ok good",
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"id": 955551093113385000,
"author_id": 261952052077395970,
"author_name": "Tarehjerne",
"timestamp": "03/21/2022 15:38:53",
"content": "its odd giving these tasks if you havent looked at derivatives, but there are other ways to do it i guess",
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"id": 955551276140208100,
"author_id": 529668257339408400,
"author_name": "Mr.Darkside",
"timestamp": "03/21/2022 15:39:37",
"content": "One way would be to graph it ig",
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"id": 955551330766827500,
"author_id": 261952052077395970,
"author_name": "Tarehjerne",
"timestamp": "03/21/2022 15:39:50",
"content": "no, thats dumb",
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"author_name": "Tarehjerne",
"timestamp": "03/21/2022 15:41:41",
"content": "@orangev You can do it logically by looking at the function",
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"author_name": "Tarehjerne",
"timestamp": "03/21/2022 15:42:20",
"content": "We want to be somewhere where the sin(x) is the smallest possible value and the cos(x) is as large as possible",
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"timestamp": "03/21/2022 15:45:04",
"content": "you still here @orangev ?",
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"timestamp": "03/21/2022 15:45:27",
"content": "yes lets think then, where is sin(x) smallest",
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"author_name": "Tarehjerne",
"timestamp": "03/21/2022 15:46:35",
"content": "Where is sin(x) smallest?",
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"author_id": 261952052077395970,
"author_name": "Tarehjerne",
"timestamp": "03/21/2022 15:47:28",
"content": "it'd be at 3pi/2",
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"id": 955553268669505700,
"author_id": 261952052077395970,
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"timestamp": "03/21/2022 15:47:32",
"content": "there sin(x) is -1",
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"id": 955553338441736200,
"author_id": 261952052077395970,
"author_name": "Tarehjerne",
"timestamp": "03/21/2022 15:47:49",
"content": "where is cos(x) largest?",
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"id": 955553358838644700,
"author_id": 261952052077395970,
"author_name": "Tarehjerne",
"timestamp": "03/21/2022 15:47:54",
"content": "at 0",
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"author_id": 261952052077395970,
"author_name": "Tarehjerne",
"timestamp": "03/21/2022 15:47:58",
"content": "there its 1",
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"author_name": "Tarehjerne",
"timestamp": "03/21/2022 15:48:42",
"content": "so we know that we want to be somewhere between 3pi/2 and 0 (we won't but lets think)",
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"timestamp": "03/21/2022 15:50:20",
"content": "its kinda hard to solve without the derivatives, but here it is",
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"timestamp": "03/21/2022 15:50:32",
"content": "",
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"author_name": "Tarehjerne",
"timestamp": "03/21/2022 15:50:36",
"content": "this is your function",
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},
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"id": 955554101226254300,
"author_id": 261952052077395970,
"author_name": "Tarehjerne",
"timestamp": "03/21/2022 15:50:51",
"content": "notice its a wave, so there are indefinietly many low points",
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"id": 955554133149118600,
"author_id": 261952052077395970,
"author_name": "Tarehjerne",
"timestamp": "03/21/2022 15:50:58",
"content": "here we have a high point, and a low point",
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"id": 955554259452166300,
"author_id": 261952052077395970,
"author_name": "Tarehjerne",
"timestamp": "03/21/2022 15:51:28",
"content": "we want our low point, naturally",
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"id": 955554624310476800,
"author_id": 261952052077395970,
"author_name": "Tarehjerne",
"timestamp": "03/21/2022 15:52:55",
"content": "If we write up our sin and cosine values we can look at where we want to be between 3pi/2 and 0",
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"timestamp": "03/21/2022 15:53:29",
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"id": 955554943148900500,
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"author_name": "Tarehjerne",
"timestamp": "03/21/2022 15:54:11",
"content": "you still here?",
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"author_id": 261952052077395970,
"author_name": "Tarehjerne",
"timestamp": "03/21/2022 15:54:35",
"content": "right, so if you put a negative on the pi/6 the sin becomes -1/2",
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"author_id": 261952052077395970,
"author_name": "Tarehjerne",
"timestamp": "03/21/2022 15:54:38",
"content": "instead of 1/2",
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},
{
"id": 955555066851504300,
"author_id": 261952052077395970,
"author_name": "Tarehjerne",
"timestamp": "03/21/2022 15:54:41",
"content": "reason being:",
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"author_name": "Tarehjerne",
"timestamp": "03/21/2022 15:55:10",
"content": "a is pi/6",
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"id": 955555208560246800,
"author_id": 261952052077395970,
"author_name": "Tarehjerne",
"timestamp": "03/21/2022 15:55:15",
"content": "b is -pi/6",
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},
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"id": 955555350025756800,
"author_id": 261952052077395970,
"author_name": "Tarehjerne",
"timestamp": "03/21/2022 15:55:48",
"content": "notice, that cos(x) is still fairly large here as well",
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},
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"id": 955555466442833900,
"author_id": 261952052077395970,
"author_name": "Tarehjerne",
"timestamp": "03/21/2022 15:56:16",
"content": "cos(x) is more powerful because of its multiplier sqrt(3)",
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},
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"id": 955555621627908100,
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"author_name": "Tarehjerne",
"timestamp": "03/21/2022 15:56:53",
"content": "thats why we are leaning more towards a stronger cos than a stronger sin",
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"id": 955555761394704400,
"author_id": 261952052077395970,
"author_name": "Tarehjerne",
"timestamp": "03/21/2022 15:57:26",
"content": "So our angle where our function is smallest is actually -pi/6",
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"id": 955555850645303300,
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"author_name": "Tarehjerne",
"timestamp": "03/21/2022 15:57:48",
"content": "if you try plug that into your formula, you get a number close to two",
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"id": 955555909160013800,
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"author_name": "Tarehjerne",
"timestamp": "03/21/2022 15:58:02",
"content": "change that by any slight amount it starts to go up",
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"id": 955556011392004200,
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"author_name": "Tarehjerne",
"timestamp": "03/21/2022 15:58:26",
"content": "its a bad way, but you didnt want to do derivatives, and solving it any other way is 20x more complicated than derivatives",
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"id": 955556150496092300,
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"author_name": "Tarehjerne",
"timestamp": "03/21/2022 15:58:59",
"content": "the next lowest point is exactly 2pi away",
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"author_name": "Tarehjerne",
"timestamp": "03/21/2022 15:59:28",
"content": "so your answer is n (n= natural number {1,2,3,4...}*2pi - pi/6",
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"id": 955556563022667800,
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"author_name": "Tarehjerne",
"timestamp": "03/21/2022 16:00:38",
"content": "the much much faster way is to take the derivative",
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},
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"id": 955556601597657100,
"author_id": 261952052077395970,
"author_name": "Tarehjerne",
"timestamp": "03/21/2022 16:00:47",
"content": "and then work out which one is the lowest value",
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"id": 955556992540344300,
"author_id": 261952052077395970,
"author_name": "Tarehjerne",
"timestamp": "03/21/2022 16:02:20",
"content": "i have found that if you get too logical with maths its wrong in the sense of showing work",
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},
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"id": 955560556855722000,
"author_id": 805217272087838700,
"author_name": "Mathematics Bot",
"timestamp": "03/21/2022 16:16:30",
"content": "@orangev Has your question been resolved?",
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{
"id": 955560647909863400,
"author_id": 732368034039201800,
"author_name": "bussy",
"timestamp": "03/21/2022 16:16:51",
"content": "hey is it okay if your in 7th grade?",
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},
{
"id": 955561312665088100,
"author_id": 732368034039201800,
"author_name": "bussy",
"timestamp": "03/21/2022 16:19:30",
"content": "im 14, but im not sure if yall help with easier questions like this, it seems like you solve big problems, is that okay?",
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},
{
"id": 955563519376494600,
"author_id": 141791176540946430,
"author_name": "frownyfrog",
"timestamp": "03/21/2022 16:28:16",
"content": "yeah i think so",
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},
{
"id": 955565020169793500,
"author_id": 805217272087838700,
"author_name": "Mathematics Bot",
"timestamp": "03/21/2022 16:34:14",
"content": "Channel closed",
"attachments": [],
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"reference": null
}
] |
help-9
|
2a11d84cfa754647b749e791df2ebf28
|
196,993 |
[
{
"id": 958526415903551600,
"author_id": 805217272087838700,
"author_name": "Mathematics Bot",
"timestamp": "03/29/2022 20:41:46",
"content": "Available help channel!",
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},
{
"id": 958527721477144600,
"author_id": 888040109390311400,
"author_name": "speed",
"timestamp": "03/29/2022 20:46:57",
"content": "The distance between (2, -1) and (3,y) is 1. Find the value of y. ??",
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"id": 958527723536523300,
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"content": "Pinned a message.",
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"id": 958528204522528800,
"author_id": 220517274845577200,
"author_name": "ramonov",
"timestamp": "03/29/2022 20:48:52",
"content": "what have you tried?",
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},
{
"id": 958528256779358200,
"author_id": 503928755341885440,
"author_name": "π₯β€β’AK_ΓPα΅α΅α΅β",
"timestamp": "03/29/2022 20:49:05",
"content": "β[(-1 β 2)^2 + (y β 3)^2] = 1\n\nequate this may get you the answer",
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"id": 958529684344307700,
"author_id": 521326998195273700,
"author_name": "shreksdad",
"timestamp": "03/29/2022 20:54:45",
"content": "What the guy above said, use the distance formula",
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"id": 958529756901572600,
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"timestamp": "03/29/2022 20:55:02",
"content": "oh ok",
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},
{
"id": 958529774123360300,
"author_id": 888040109390311400,
"author_name": "speed",
"timestamp": "03/29/2022 20:55:06",
"content": "thanks !",
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},
{
"id": 958533549760315400,
"author_id": 805217272087838700,
"author_name": "Mathematics Bot",
"timestamp": "03/29/2022 21:10:06",
"content": "@speed Has your question been resolved?",
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"timestamp": "03/29/2022 21:25:07",
"content": "Channel closed",
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}
] |
help-9
|
bef07e87e43642c8a996bea16e010d23
|
196,994 |
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"timestamp": "07/06/2022 02:54:50",
"content": "Available help channel!",
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{
"id": 994135491811221500,
"author_id": 613891196233842700,
"author_name": "xlz",
"timestamp": "07/06/2022 02:59:31",
"content": "how do you write a double summation but skip when i = j",
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"content": "Pinned a message.",
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"id": 994135503332987000,
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"timestamp": "07/06/2022 02:59:34",
"content": "and both start at 1",
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"id": 994136480190578700,
"author_id": 244390699431100400,
"author_name": "Frosst",
"timestamp": "07/06/2022 03:03:27",
"content": "Couldnβt you minus that case",
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"id": 994136677457084500,
"author_id": 244390699431100400,
"author_name": "Frosst",
"timestamp": "07/06/2022 03:04:14",
"content": "So youβd have a minus sum at the end with just 1 summation and put i and j as the same variable",
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},
{
"id": 994137173563539500,
"author_id": 244390699431100400,
"author_name": "Frosst",
"timestamp": "07/06/2022 03:06:12",
"content": "Say you had $\\sum_{i=1}^{10}\\sum_{j=1}^{10} (i+j) - \\sum_{i=1}^{10} (i + i)$",
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},
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"id": 994137183973810200,
"author_id": 510789298321096700,
"author_name": "TeXit",
"timestamp": "07/06/2022 03:06:14",
"content": "**Frosst**",
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"author_id": 244390699431100400,
"author_name": "Frosst",
"timestamp": "07/06/2022 03:06:31",
"content": "Does this work?",
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"timestamp": "07/06/2022 03:14:34",
"content": "@xlz Has your question been resolved?",
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"timestamp": "07/06/2022 03:29:34",
"content": "Channel closed",
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"reference": null
}
] |
help-9
|
db4cb9ac544c4daabbec654ec65139ee
|
196,995 |
[
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"timestamp": "07/06/2022 03:30:34",
"content": "Available help channel!",
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"timestamp": "07/06/2022 04:20:26",
"content": "How many times does y change sign",
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"id": 994156079997005800,
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"timestamp": "07/06/2022 04:21:19",
"content": "3",
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"timestamp": "07/06/2022 04:21:48",
"content": "Use the intermediate value theorem",
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"timestamp": "07/06/2022 04:22:17",
"content": "There you go",
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"timestamp": "07/06/2022 04:22:41",
"content": "ty",
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"id": 994156431588729000,
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"timestamp": "07/06/2022 04:22:43",
"content": ".close",
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}
] |
help-9
|
b51b622cd7de4eb2bacfd86c46853ab3
|
196,996 |
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},
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"content": "Pinned a message.",
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"author_name": "Ann",
"timestamp": "07/06/2022 04:42:30",
"content": "any progress thus far?",
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"timestamp": "07/06/2022 04:44:48",
"content": "So far",
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"author_name": "Fin",
"timestamp": "07/06/2022 04:44:57",
"content": "I know it probably has something to do",
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"author_name": "Fin",
"timestamp": "07/06/2022 04:45:24",
"content": "with turning points and whether its an odd or even function",
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"author_name": "Ann",
"timestamp": "07/06/2022 04:46:12",
"content": "its oddness or evenness _as a function_ is kind of irrelevant here, because this function is neither.",
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"author_name": "Ann",
"timestamp": "07/06/2022 04:46:31",
"content": "you are right on turning points. can you tell me how many of them are visible in the graph?",
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"content": "3",
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"timestamp": "07/06/2022 04:46:53",
"content": "I believe",
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"timestamp": "07/06/2022 04:47:09",
"content": "that's right",
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"timestamp": "07/06/2022 04:47:14",
"content": "and what does this tell you about the degree?",
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"author_name": "Fin",
"timestamp": "07/06/2022 04:47:42",
"content": "its one less then the maxmium number of turning points",
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"author_name": "Ann",
"timestamp": "07/06/2022 04:48:03",
"content": "...i think your wording got a little slippery there.",
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"timestamp": "07/06/2022 04:48:07",
"content": "it's the other way around",
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"timestamp": "07/06/2022 04:48:15",
"content": "the max possible number of turning points is the degree minus 1.",
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"author_name": "Ann",
"timestamp": "07/06/2022 04:48:34",
"content": "so the degree is _at least_ the number of turning points + 1.",
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"timestamp": "07/06/2022 04:49:09",
"content": "in our case, the degree must be at least 4.",
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"author_name": "Ann",
"timestamp": "07/06/2022 04:49:19",
"content": "that is not all - we aren't quite done here yet - but do you follow thus far?",
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"author_name": "Fin",
"timestamp": "07/06/2022 04:49:30",
"content": "Wait give me a second",
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"author_name": "Fin",
"timestamp": "07/06/2022 04:49:34",
"content": "I was looking through my notes",
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"timestamp": "07/06/2022 04:49:38",
"content": "and thats waht it said",
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"author_name": "Fin",
"timestamp": "07/06/2022 04:49:41",
"content": "let me replay the lesson",
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"author_name": "Fin",
"timestamp": "07/06/2022 04:50:11",
"content": "yea see",
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"timestamp": "07/06/2022 04:51:15",
"content": "yeah, so it's you who switched things around.",
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"timestamp": "07/06/2022 04:51:38",
"content": "No",
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"author_name": "Fin",
"timestamp": "07/06/2022 04:51:41",
"content": "That's the video",
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"author_name": "Fin",
"timestamp": "07/06/2022 04:51:47",
"content": "Look",
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"id": 994163784929263600,
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"author_name": "Ann",
"timestamp": "07/06/2022 04:51:56",
"content": "> The maximum number of turning points is one less than the degree of the function.",
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"timestamp": "07/06/2022 04:51:59",
"content": "that is exactly what i said too.",
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"timestamp": "07/06/2022 04:52:05",
"content": "right here.",
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"timestamp": "07/06/2022 04:52:19",
"content": "but you said\n\"The degree is one less than the maximum number of turning points.\"\nand that's switching shit around",
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"author_name": "Fin",
"timestamp": "07/06/2022 04:53:00",
"content": "Yea I know",
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"author_name": "Fin",
"timestamp": "07/06/2022 04:53:06",
"content": "Im just telling you im confused",
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"timestamp": "07/06/2022 04:53:11",
"content": "because the dude in the video",
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"content": "i can see the video just fine.",
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"timestamp": "07/06/2022 04:53:53",
"content": "i am saying",
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"timestamp": "07/06/2022 04:53:59",
"content": "THE VIDEO is correct.",
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"content": "YOU are not correct. YOU switched things around when you should not have.",
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"timestamp": "07/06/2022 04:54:26",
"content": "Oh",
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"id": 994164561450115100,
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"content": "ok",
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"id": 994164921333973000,
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"author_name": "Fin",
"timestamp": "07/06/2022 04:56:27",
"content": ".close",
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"timestamp": "07/06/2022 04:56:28",
"content": "Channel closed",
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] |
help-9
|
0f8d5feff40241808a3d431d1ab9eae9
|
196,997 |
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"timestamp": "07/06/2022 06:09:36",
"content": "Available help channel!",
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"id": 994201392443035600,
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"author_name": "ghostkiller8804",
"timestamp": "07/06/2022 07:21:23",
"content": "btw you need to calculate A",
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"content": "Pinned a message.",
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"timestamp": "07/06/2022 07:22:07",
"content": "how do I write this mathematically",
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"timestamp": "07/06/2022 07:23:18",
"content": "I know that my calculations are correct but I don't know how to write them down properly",
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"timestamp": "07/06/2022 07:38:18",
"content": "@ghostkiller8804 Has your question been resolved?",
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"content": "@Helpers",
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"timestamp": "07/06/2022 07:49:44",
"content": ".close",
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"id": 994208528967401500,
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help-9
|
afd2b95c8c7346009000288da387b169
|
196,998 |
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"timestamp": "07/06/2022 07:50:45",
"content": "Available help channel!",
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{
"id": 994217841425391600,
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"content": "Pinned a message.",
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"timestamp": "07/06/2022 08:27:04",
"content": "Please help with (c)(i), (c)(ii) and (d)",
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"timestamp": "07/06/2022 08:42:04",
"content": "@Yolk Has your question been resolved?",
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"id": 994222556469010600,
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"timestamp": "07/06/2022 08:45:29",
"content": "@Helpers please help",
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},
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"id": 994222924791816300,
"author_id": 264901235834880000,
"author_name": "Modus",
"timestamp": "07/06/2022 08:46:57",
"content": "for c(i) u can draw a right triangle",
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"timestamp": "07/06/2022 08:47:12",
"content": "including point (-1,-1) (u have \"x\" dot here or smth)",
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"timestamp": "07/06/2022 08:47:17",
"content": "yeah",
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"id": 994223050218287200,
"author_id": 264901235834880000,
"author_name": "Modus",
"timestamp": "07/06/2022 08:47:26",
"content": "then use SOH",
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"id": 994223070355144800,
"author_id": 387501841803378700,
"author_name": "Yolk",
"timestamp": "07/06/2022 08:47:31",
"content": "mhm",
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"id": 994223085433659500,
"author_id": 387501841803378700,
"author_name": "Yolk",
"timestamp": "07/06/2022 08:47:35",
"content": "AX/AC",
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"id": 994223119831158900,
"author_id": 264901235834880000,
"author_name": "Modus",
"timestamp": "07/06/2022 08:47:43",
"content": "yes",
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"timestamp": "07/06/2022 08:47:48",
"content": "okay thank you",
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"id": 994223179214110700,
"author_id": 387501841803378700,
"author_name": "Yolk",
"timestamp": "07/06/2022 08:47:57",
"content": "do you have any idea about (ii) and (d)?",
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"id": 994223266128474100,
"author_id": 264901235834880000,
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"timestamp": "07/06/2022 08:48:18",
"content": "for c(ii) u can firstly find cos(ABX)",
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"id": 994223319870083100,
"author_id": 264901235834880000,
"author_name": "Modus",
"timestamp": "07/06/2022 08:48:31",
"content": "then notice that ABC = 180 - ABX",
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"id": 994223390627991600,
"author_id": 264901235834880000,
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"timestamp": "07/06/2022 08:48:48",
"content": "cuz they're supplementary",
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"id": 994223504780185600,
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"timestamp": "07/06/2022 08:49:15",
"content": "indeed cos(ABC) = cos(180 - ABX) = -cos(ABX)",
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"content": "ohhhhhhh",
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"content": "i see it now",
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"author_name": "Modus",
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"content": "for (d) I guess easiest option is to use formula for the area of the triangle with sine between two sides",
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"author_id": 387501841803378700,
"author_name": "Yolk",
"timestamp": "07/06/2022 08:50:57",
"content": "the 1/2 ab sin included angle one?",
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"timestamp": "07/06/2022 08:51:08",
"content": "basically, area of ABC = 1/2 * AB * AC * sin <BAC",
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"content": "I guess you can proceed from here, u can find area using well known formula 1/2 * b * h",
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"content": "yes",
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"timestamp": "07/06/2022 08:53:12",
"content": "thank you very much",
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"content": "i understand it now",
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"content": ".close",
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"content": "Channel closed",
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}
] |
help-9
|
993a54143df645bb84b7f12924a33d05
|
196,999 |
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"content": "Where would be the typo there ?",
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"id": 994233690622275600,
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"content": "there do not appear to be any typos there",
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"content": "i too am curious where you think the typo is @sushi",
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"timestamp": "07/06/2022 09:30:01",
"content": "The solution for a simplifies the statement Β¬(βxβy(x<y β¨ y<x))",
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"content": "they did not",
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"timestamp": "07/06/2022 09:30:55",
"content": "they made that step",
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"id": 994234004440092700,
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"content": "twice in one line",
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"author_name": "Tsuwako",
"timestamp": "07/06/2022 09:37:04",
"content": "They used the fact that the statement \"Β¬(βx P(x))\" is equivalent to \"βx Β¬P(x)\". That's why the negative symbol is drawn to the expression within the parentheses",
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"content": "I believe they meant to write (2l+1)Β² = 4lΒ²+4l+1 = 2(2lΒ²+2l) + 1 = 2k+1 with k=2lΒ²+2l as an integer to show explicitely that (2l+1)Β² is odd",
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"timestamp": "07/06/2022 09:50:06",
"content": "Yes, the statements \"nΒ² is even -> n is even\" and \"n is odd -> nΒ² is odd\" are equivalent",
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"timestamp": "07/06/2022 09:50:38",
"content": "This whole part was meant to prove the second statement so it means that the first one is also true by contraposition",
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"timestamp": "07/06/2022 09:53:47",
"content": "That's because \"P -> Q\" and \"Β¬Q -> Β¬P\" are equivalent",
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}
] |
help-9
|
1d72eb33cb4b468b9283ca5011addaa4
|
197,000 |
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"content": "Can someone check what I did wrong for 6.c",
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"content": "Um, how did you get a 7 in step 4 ?",
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"content": "That seems out of place to me",
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"content": "Step 4 should be 3(x+1)^2 = 2",
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"content": "@Kharis Has your question been resolved?",
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"timestamp": "07/06/2022 10:51:16",
"content": "Oops It was suppose to be one",
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"timestamp": "07/06/2022 10:51:25",
"content": "Thank you so much!",
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] |
help-9
|
49ca39e44a6e40aab8f8a838b9f92e24
|
197,001 |
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"content": "-1 @Kharis",
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"content": "i just woke up like an hour ago lol my brain is not yet fully functioning",
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"content": "donβt know how I copy -1 to a 7",
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"content": "Pinned a message.",
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help-9
|
93453307396940119fb6f0b7fdbca5d5
|
197,002 |
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"id": 994323855684407300,
"author_id": 878798685264285700,
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"content": "For questions 3 and 4 can anyone lend a hand to me these statements look essentially identical but one is false and the other is true Iβm not sure why",
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"timestamp": "07/06/2022 15:29:13",
"content": "6 is false because for x = 0, x^2 - x is not greater than 0",
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"content": "I havenβt even got to 6 Iβm confused about 3 and 4",
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"content": "Oh sorry lmao I was reading the 3rd and fourth lines",
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"id": 994324406660772000,
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"content": "lets define a=n+m",
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"id": 994324481986281500,
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"content": "3 | a means that a/3 has no rest",
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"id": 994324527133765600,
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"timestamp": "07/06/2022 15:30:40",
"content": "so a must be a multiple of 3",
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"id": 994324553457217500,
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"timestamp": "07/06/2022 15:30:47",
"content": "yes",
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"id": 994324573497598100,
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"content": "given any number n in N",
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"content": "you could add 0 1 or 2 to it",
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"timestamp": "07/06/2022 15:31:09",
"content": "so it becomes a multiple of 3",
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"id": 994324655689191600,
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"content": "for example",
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"content": "n=19",
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"content": "add 2",
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"content": "19+2=21",
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"content": "Yes so why would both statements not be true",
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"content": "21/3 has no rest",
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"timestamp": "07/06/2022 15:31:39",
"content": "they are not true?",
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"timestamp": "07/06/2022 15:31:47",
"content": "The first is false",
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"timestamp": "07/06/2022 15:31:50",
"content": "The second is true",
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"timestamp": "07/06/2022 15:31:55",
"content": "oh sry",
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"content": "i see now",
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"content": "i switched it around",
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"content": "i said:\ngiven any n, we always find m such that 3 | n+m",
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"timestamp": "07/06/2022 15:32:21",
"content": "this is true",
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"timestamp": "07/06/2022 15:32:26",
"content": "but we want to know:",
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"timestamp": "07/06/2022 15:33:03",
"content": "there exists an m such that for all n: 3 | n+m",
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"id": 994325248386273400,
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"timestamp": "07/06/2022 15:33:32",
"content": "lets pick 2 different n",
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"content": "1 and 2",
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"timestamp": "07/06/2022 15:33:59",
"content": "this statement claims that there is an m such that\n1+m and 2+m are multiples of 3",
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"timestamp": "07/06/2022 15:34:03",
"content": "which can't be true",
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"timestamp": "07/06/2022 15:35:47",
"content": "Can m not change",
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"timestamp": "07/06/2022 15:35:50",
"content": "Itβs fixed",
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"timestamp": "07/06/2022 15:37:25",
"content": "CAuse for any value of n wouldnβt there be a m that could make it divisible",
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"timestamp": "07/06/2022 15:37:49",
"content": "like if n is 5 m can be 1",
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"id": 994326339928740000,
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"timestamp": "07/06/2022 15:37:53",
"content": "or no?",
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"timestamp": "07/06/2022 15:44:14",
"content": "@Helpers",
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"id": 994329606863737000,
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"author_name": "JSwift",
"timestamp": "07/06/2022 15:50:52",
"content": "I feel like you can prove the original statement and the negation both correct ?",
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"author_name": "Mathematics Bot",
"timestamp": "07/06/2022 16:05:52",
"content": "@JSwift Has your question been resolved?",
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"timestamp": "07/06/2022 16:37:10",
"content": "@JSwift Has your question been resolved?",
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"author_name": "DootDooter",
"timestamp": "07/06/2022 17:17:34",
"content": "Do you know division algorithm?",
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"timestamp": "07/06/2022 17:23:37",
"content": "Martin is saying consider n=1 and n=2. (3) causes the two cases m+n=m+1 and m+n=m+2 to both be divisible by 3, this is impossible by division algorithm. The m isn't changing, Martin is just considering two different choices of n.",
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"timestamp": "07/06/2022 17:23:51",
"content": "You don't explicitly need division algorithm I guess.",
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"timestamp": "07/06/2022 17:24:22",
"content": "It's not hard to show a contradiction follows from 3|m+1 and 3|m+2 without it.",
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"timestamp": "07/06/2022 17:25:31",
"content": "This would be impossible.",
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"timestamp": "07/06/2022 17:26:07",
"content": "Unless you're assuming some other contradiction somewhere, which you shouldn't be.",
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"timestamp": "07/06/2022 17:46:07",
"content": "@JSwift Has your question been resolved?",
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"timestamp": "07/06/2022 17:58:11",
"content": "How does 3 and 4 differ",
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"author_name": "DootDooter",
"timestamp": "07/06/2022 17:58:24",
"content": "Different quantifier order",
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"author_name": "DootDooter",
"timestamp": "07/06/2022 17:59:39",
"content": "\"There exists ... for all ...\" vs \"for all ... there exists ...\"",
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"timestamp": "07/06/2022 17:59:48",
"content": "They are not the same or equivalent ofc",
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"author_name": "JSwift",
"timestamp": "07/06/2022 18:17:36",
"content": "But is saying βthere exists an integer n for m for all nβ different than βan m for all nβ in this context",
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"author_name": "DootDooter",
"timestamp": "07/06/2022 18:17:56",
"content": "\"is saying\"",
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"id": 994366648666566800,
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"author_name": "DootDooter",
"timestamp": "07/06/2022 18:18:03",
"content": "Which thing are you talking about?",
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"author_name": "DootDooter",
"timestamp": "07/06/2022 18:18:46",
"content": "We are talking about two different statements. So, do you mean (3) or (4)?",
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"timestamp": "07/06/2022 18:18:59",
"content": "Yeah",
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"timestamp": "07/06/2022 18:19:08",
"content": "...",
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"timestamp": "07/06/2022 18:19:22",
"content": "Here",
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"author_name": "DootDooter",
"timestamp": "07/06/2022 18:19:34",
"content": "Are you talking about (3) or are you talking about (4)?",
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"id": 994367126695583700,
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"timestamp": "07/06/2022 18:19:57",
"content": "I was talking about the difference between the 2",
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"id": 994367155548209300,
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"timestamp": "07/06/2022 18:20:04",
"content": "Quantifier",
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"id": 994367168261144700,
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"timestamp": "07/06/2022 18:20:07",
"content": "In that context",
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"id": 994367327283990500,
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"author_name": "DootDooter",
"timestamp": "07/06/2022 18:20:45",
"content": "(3) says \"**there exists** a natural number m such that **for any** natural number n, 3|n+m.",
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"id": 994367550366433400,
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"timestamp": "07/06/2022 18:21:38",
"content": "(4) says \"**for any** natural number n, **there exists** a natural number m such that 3|n+m\"",
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"id": 994367663985922200,
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"author_name": "DootDooter",
"timestamp": "07/06/2022 18:22:05",
"content": "We can't just switch \"there exists\" and \"for any\", switching quantifier order is a pretty common logical fallacy.",
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"timestamp": "07/06/2022 18:23:11",
"content": "But n+m are just arbitrary natural numbers",
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"timestamp": "07/06/2022 18:23:19",
"content": "No they aren't..",
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"id": 994368021088972900,
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"timestamp": "07/06/2022 18:23:30",
"content": "But there order doesnβt matter",
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"id": 994368029867659300,
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"timestamp": "07/06/2022 18:23:32",
"content": "Does it?",
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"id": 994368042073079800,
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"timestamp": "07/06/2022 18:23:35",
"content": "In the context",
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"id": 994368083705725000,
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"timestamp": "07/06/2022 18:23:45",
"content": "a+b = b+a",
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"author_name": "DootDooter",
"timestamp": "07/06/2022 18:23:50",
"content": "Addition commutes, but that's not the issue here.",
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"id": 994368155587711200,
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"timestamp": "07/06/2022 18:24:02",
"content": "Logical quantifiers don't commute",
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"id": 994368343953915900,
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"timestamp": "07/06/2022 18:24:47",
"content": "\"For every person x, there exists a person y such that y is the mother of x.\" You see how this is naively true right?",
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"id": 994368493459886100,
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"timestamp": "07/06/2022 18:25:23",
"content": "\"There exists a person x such that for every person y, y is the mother of x.\"",
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"id": 994368531464462500,
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"author_name": "DootDooter",
"timestamp": "07/06/2022 18:25:32",
"content": "You see how this one is false right?",
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"author_name": "DootDooter",
"timestamp": "07/06/2022 18:25:50",
"content": "There's no single person who has every other person as their mother yeah?",
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"timestamp": "07/06/2022 18:26:23",
"content": "Yeah I see that",
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"id": 994368790848618500,
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"timestamp": "07/06/2022 18:26:34",
"content": "But doesnβt this expression seem different with addition",
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"timestamp": "07/06/2022 18:26:37",
"content": "At least it does for me",
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"timestamp": "07/06/2022 18:26:39",
"content": "Idk why",
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"timestamp": "07/06/2022 18:26:59",
"content": "Nope. Just because addition commutes doesn't mean the quantifiers commute.",
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"timestamp": "07/06/2022 18:29:03",
"content": "I see it like this there exists a man for all women and there exists a woman for all man",
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"timestamp": "07/06/2022 18:29:20",
"content": "Ya know",
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"timestamp": "07/06/2022 18:29:25",
"content": "Nope",
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"timestamp": "07/06/2022 18:29:28",
"content": "They are logically identical no?",
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"timestamp": "07/06/2022 18:29:54",
"content": "Not really.",
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"timestamp": "07/06/2022 18:30:06",
"content": "First of all this is super vague.",
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"timestamp": "07/06/2022 18:30:21",
"content": "But like, lets say we have a collection of 3 men and 2 women..",
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"timestamp": "07/06/2022 18:30:26",
"content": "But isnβt the other example Iβm just in 3 extremely vague",
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"author_name": "aguaman",
"timestamp": "07/06/2022 18:30:29",
"content": "https://tenor.com/view/capybara-melon-watermelon-muncher-the-ferocious-muncher-gif-23667477",
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"timestamp": "07/06/2022 18:30:34",
"content": "wait wrong channel sorry",
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"content": "If we're just pairing men and women then for any women we can pair them with one man but not vice versa unless we pair two or more men to one woman.",
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"content": "Everything in (3) is about as rigorous as we can expect to get logically.",
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"content": "I think what's happening is you're mixing up three different ordering issues.",
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"content": "The variables we use in each quantifier matters.",
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"content": "The ordering in which we write n+m **in this case** doesn't really matter.",
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"content": "(Because, like you mentioned, + is commutative.)",
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"content": "So are both true both false one true one false and why",
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"content": "Cause thatβs whatβs trippinβ me up",
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"content": "(3) is false",
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"content": "(4) is true",
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"content": "Assume (3) were true.",
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"content": "Then, consider the cases n=1 and n=2. (3) says we can find an m where 3|m+n for any n we want.",
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"content": "So when n=1 thus tells us 3|m+1",
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"content": "But when n=2 this tells us 3|m+2.",
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"content": "Do you see how 3 can't divide both m+1 and m+2?",
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"timestamp": "07/06/2022 18:38:37",
"content": "If m is fixed then yes",
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"content": "Why would you think m isn't fixed?",
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"content": "The statement in (3) says there exists an m, it doesn't tell us which or how many. Just that at least one natural number m works.",
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"content": "When we refer to m here in the proof we're basically saying \"give me one of those m's\"",
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"content": "Oh",
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"content": "We've picked out ONE of the m's that (3) tells us exists.",
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"content": "We could have used a different letter for it if that confuses you?",
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"content": "But we're right now assuming we have one such m that we've decided to call m",
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"content": "So is it saying for example that m which could be letβs say 5 + any number would always be divisible",
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"timestamp": "07/06/2022 18:41:40",
"content": "Which is obviously not true",
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"content": "What?",
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"content": "Like there exists a number",
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"content": "M",
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"content": "Which we would find",
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"content": "No think about what you said.",
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"content": "\"It's it\"",
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"timestamp": "07/06/2022 18:42:25",
"content": "Assuming you mean \"is it\"",
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"content": "I still don't know what \"it\" is to you?",
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"timestamp": "07/06/2022 18:42:36",
"content": "Ah sorry I think it corrected",
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"timestamp": "07/06/2022 18:42:49",
"content": "That still doesn't fix the ambiguity.",
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"content": "What is \"it\" to you?",
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"content": "Is it",
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"timestamp": "07/06/2022 18:43:06",
"content": "The question",
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"timestamp": "07/06/2022 18:43:09",
"content": "The statement",
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"content": "(3)",
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"content": "I see",
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"timestamp": "07/06/2022 18:43:46",
"content": "Well we don't really know if m is 5+some number",
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"content": "What if m is 1?",
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"content": "Well yeah Iβm just listing a random example",
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"content": "But m could be true in theory",
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"timestamp": "07/06/2022 18:44:13",
"content": "Then m isn't a sum of 5 and any other numbers",
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"timestamp": "07/06/2022 18:44:14",
"content": "If we found one",
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"timestamp": "07/06/2022 18:44:18",
"content": "That fit?",
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"timestamp": "07/06/2022 18:44:19",
"content": "m can't be true",
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"timestamp": "07/06/2022 18:44:26",
"content": "m is a number",
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"timestamp": "07/06/2022 18:44:31",
"content": "Well yes itβs incorrect",
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"content": "It's not true or false",
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"content": "How can a number be incorrect?",
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"content": "You mean (3) is incorrect?",
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"content": "M = 5 would not satisfy",
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"content": "that statement",
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"content": "so it would be incorrect?",
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"content": "Mmm",
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"content": "Yeah m=5 will fail to satisfy (3)",
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"timestamp": "07/06/2022 18:46:08",
"content": "But what if some other number does?",
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"timestamp": "07/06/2022 18:46:18",
"content": "Then we would prove itβs existence",
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"timestamp": "07/06/2022 18:46:19",
"content": "Right",
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"content": "The claim is that at least one m works such that blah blah ...",
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"timestamp": "07/06/2022 18:46:45",
"content": "So to disprove (3) we need to show NO m's have the property in (3).",
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"timestamp": "07/06/2022 18:47:09",
"content": "Yes okay",
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"timestamp": "07/06/2022 18:47:12",
"content": "It would be like me claiming some dogs are nice to you",
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"timestamp": "07/06/2022 18:47:29",
"content": "And you asking me why, and me saying, \"well my dog is nice so all others must be nice too\"",
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"content": "You see?",
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"timestamp": "07/06/2022 18:48:20",
"content": "Yeah I get that",
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"content": "We need to rule out every single natural number m having the property.",
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"content": "In particular yeah m=5 should fail",
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"timestamp": "07/06/2022 18:49:03",
"content": "It just doesn't prove much for us",
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"timestamp": "07/06/2022 18:49:46",
"content": "So yeah to clarify the statement essentially is saying that there exists a natural number such that that natural number + all natural numbers is divisible by 3?",
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"timestamp": "07/06/2022 18:50:05",
"content": "Yeah roughly speaking.",
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"timestamp": "07/06/2022 18:51:42",
"content": "Okay so then weβd just prove the negation true than",
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"content": "Yeah you could do that",
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"content": ".",
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"content": "That's what I was doing here",
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"timestamp": "07/06/2022 18:52:42",
"content": "And what martin was basically trying to explain to you.",
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"id": 994375372017770600,
"author_id": 878798685264285700,
"author_name": "JSwift",
"timestamp": "07/06/2022 18:52:43",
"content": "For all m E N there exists n E N, 3(does not divide)n+m",
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"id": 994375487184965800,
"author_id": 878798685264285700,
"author_name": "JSwift",
"timestamp": "07/06/2022 18:53:10",
"content": "Is this the negation?",
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"id": 994375520068317200,
"author_id": 370444508644769800,
"author_name": "DootDooter",
"timestamp": "07/06/2022 18:53:18",
"content": "Yep",
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"id": 994375556906877000,
"author_id": 370444508644769800,
"author_name": "DootDooter",
"timestamp": "07/06/2022 18:53:27",
"content": "But you don't need to go that far",
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"id": 994375604235415800,
"author_id": 370444508644769800,
"author_name": "DootDooter",
"timestamp": "07/06/2022 18:53:38",
"content": "You could just prove NOT (the stmt of (3))",
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"id": 994375706626764900,
"author_id": 370444508644769800,
"author_name": "DootDooter",
"timestamp": "07/06/2022 18:54:03",
"content": "Rather than shuffling around negations using quantifier equivalences.",
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"id": 994375810238664700,
"author_id": 370444508644769800,
"author_name": "DootDooter",
"timestamp": "07/06/2022 18:54:27",
"content": "A contradiction proof is pretty easy in this case.",
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"id": 994375911791136900,
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"author_name": "DootDooter",
"timestamp": "07/06/2022 18:54:51",
"content": "Assume (3) is true, show that a contradiction follows. Conclude that NOT (3) must be true.",
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"id": 994376015474331800,
"author_id": 370444508644769800,
"author_name": "DootDooter",
"timestamp": "07/06/2022 18:55:16",
"content": "Or in other words that (3) is false.",
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"id": 994376185620480100,
"author_id": 878798685264285700,
"author_name": "JSwift",
"timestamp": "07/06/2022 18:55:57",
"content": "I havenβt even got that far in my class Iβm a 3 classes in and weβve just done logic and direct but that seems easy enough I suppose",
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"author_name": "JSwift",
"timestamp": "07/06/2022 18:56:31",
"content": "Iβve just been taught if the statement is false prove negation",
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"id": 994376480282915000,
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"author_name": "DootDooter",
"timestamp": "07/06/2022 18:57:07",
"content": "Hmm :thonk:",
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"author_id": 370444508644769800,
"author_name": "DootDooter",
"timestamp": "07/06/2022 18:57:23",
"content": "I mean more strictly if you have P, the negation is ~P.",
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},
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"id": 994376611833061500,
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"author_name": "DootDooter",
"timestamp": "07/06/2022 18:57:38",
"content": "Like, there's a bunch of equivalent forms probably",
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},
{
"id": 994376781035491500,
"author_id": 370444508644769800,
"author_name": "DootDooter",
"timestamp": "07/06/2022 18:58:19",
"content": "But idk, it depends what tools you have to work with.",
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"id": 994377122900623400,
"author_id": 370444508644769800,
"author_name": "DootDooter",
"timestamp": "07/06/2022 18:59:40",
"content": "How you wanna go about proving this.",
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},
{
"id": 994377280413507700,
"author_id": 878798685264285700,
"author_name": "JSwift",
"timestamp": "07/06/2022 19:00:18",
"content": "I can try to prove negation true",
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},
{
"id": 994377333714726900,
"author_id": 878798685264285700,
"author_name": "JSwift",
"timestamp": "07/06/2022 19:00:30",
"content": "Is that alright?",
"attachments": [],
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},
{
"id": 994379220836942000,
"author_id": 878798685264285700,
"author_name": "JSwift",
"timestamp": "07/06/2022 19:08:00",
"content": "Or no?",
"attachments": [],
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},
{
"id": 994409421390221400,
"author_id": 805217272087838700,
"author_name": "Mathematics Bot",
"timestamp": "07/06/2022 21:08:01",
"content": "@JSwift Has your question been resolved?",
"attachments": [],
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"id": 994410751622127600,
"author_id": 878798685264285700,
"author_name": "JSwift",
"timestamp": "07/06/2022 21:13:18",
"content": ".close",
"attachments": [],
"mentions": [],
"reference": null
},
{
"id": 994410753492787200,
"author_id": 805217272087838700,
"author_name": "Mathematics Bot",
"timestamp": "07/06/2022 21:13:18",
"content": "Channel closed",
"attachments": [],
"mentions": [],
"reference": null
}
] |
help-9
|
98cdaccbb0e14fb790f5cad4719a56d7
|
197,003 |
[
{
"id": 994411005914394600,
"author_id": 805217272087838700,
"author_name": "Mathematics Bot",
"timestamp": "07/06/2022 21:14:19",
"content": "Available help channel!",
"attachments": [],
"mentions": [],
"reference": null
},
{
"id": 994414966876684400,
"author_id": 209300311091838980,
"author_name": "Peacemaker II",
"timestamp": "07/06/2022 21:30:03",
"content": "how do I prove that the standard deviation is equal to sqrt(npq)",
"attachments": [],
"mentions": [],
"reference": null
},
{
"id": 994414968822845400,
"author_id": 805217272087838700,
"author_name": "Mathematics Bot",
"timestamp": "07/06/2022 21:30:03",
"content": "Pinned a message.",
"attachments": [],
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"messageId": 994414966876684400,
"channelId": 486844875632017400,
"guildId": null
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{
"id": 994418742568157300,
"author_id": 805217272087838700,
"author_name": "Mathematics Bot",
"timestamp": "07/06/2022 21:45:03",
"content": "@Peacemaker II Has your question been resolved?",
"attachments": [],
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{
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"name": "Peacemaker II",
"discriminator": "5950",
"nickname": "Peacemaker II",
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},
{
"id": 994421632649150500,
"author_id": 894078972944584700,
"author_name": "john82625",
"timestamp": "07/06/2022 21:56:32",
"content": "https://math.stackexchange.com/questions/1951842/prove-standard-deviation-sqrtnpq",
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},
{
"id": 994421772453695600,
"author_id": 209300311091838980,
"author_name": "Peacemaker II",
"timestamp": "07/06/2022 21:57:06",
"content": "thanks",
"attachments": [],
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},
{
"id": 994421806326890500,
"author_id": 209300311091838980,
"author_name": "Peacemaker II",
"timestamp": "07/06/2022 21:57:14",
"content": "yeah I could've just googled it",
"attachments": [],
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"reference": null
},
{
"id": 994421853470855200,
"author_id": 209300311091838980,
"author_name": "Peacemaker II",
"timestamp": "07/06/2022 21:57:25",
"content": "maybe I'll try deriving it myself first before looking at that",
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},
{
"id": 994421873062461600,
"author_id": 209300311091838980,
"author_name": "Peacemaker II",
"timestamp": "07/06/2022 21:57:30",
"content": ".close",
"attachments": [],
"mentions": [],
"reference": null
},
{
"id": 994421874765332500,
"author_id": 805217272087838700,
"author_name": "Mathematics Bot",
"timestamp": "07/06/2022 21:57:30",
"content": "Channel closed",
"attachments": [],
"mentions": [],
"reference": null
}
] |
help-9
|
cd8bc1244d624ee998c1fbc676c8f812
|
197,004 |
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{
"id": 958537578276081700,
"author_id": 805217272087838700,
"author_name": "Mathematics Bot",
"timestamp": "03/29/2022 21:26:07",
"content": "Available help channel!",
"attachments": [],
"mentions": [],
"reference": null
},
{
"id": 958539802922340400,
"author_id": 819818586965016600,
"author_name": "JunβΎ",
"timestamp": "03/29/2022 21:34:57",
"content": "I need help with this question",
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"timestamp": "03/29/2022 21:34:58",
"content": "Pinned a message.",
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"author_id": 598041720583618600,
"author_name": "Disorganized",
"timestamp": "03/29/2022 21:36:07",
"content": "ok, any ideas where you might start?",
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"author_name": "JunβΎ",
"timestamp": "03/29/2022 21:36:18",
"content": "Mm..",
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{
"id": 958540353634447500,
"author_id": 819818586965016600,
"author_name": "JunβΎ",
"timestamp": "03/29/2022 21:37:09",
"content": "Well maybe I can solve the second equation for y and put it in the first equation",
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"id": 958540387021111300,
"author_id": 598041720583618600,
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"timestamp": "03/29/2022 21:37:17",
"content": "very good",
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{
"id": 958540464590573700,
"author_id": 598041720583618600,
"author_name": "Disorganized",
"timestamp": "03/29/2022 21:37:35",
"content": "then what would the equation be",
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{
"id": 958540639635652700,
"author_id": 819818586965016600,
"author_name": "JunβΎ",
"timestamp": "03/29/2022 21:38:17",
"content": "Ok let me do that first",
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{
"id": 958540922415616100,
"author_id": 819818586965016600,
"author_name": "JunβΎ",
"timestamp": "03/29/2022 21:39:24",
"content": "So I rearranged the second equation and solved for y which got me:y=-3x-4",
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"id": 958541095829123200,
"author_id": 819818586965016600,
"author_name": "JunβΎ",
"timestamp": "03/29/2022 21:40:06",
"content": "Now what would I do with the y value?",
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{
"id": 958541245771296900,
"author_id": 220517274845577200,
"author_name": "ramonov",
"timestamp": "03/29/2022 21:40:41",
"content": "> Well maybe I can solve the second equation for y **and put it in the first equation**",
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},
{
"id": 958541310556508200,
"author_id": 819818586965016600,
"author_name": "JunβΎ",
"timestamp": "03/29/2022 21:40:57",
"content": "But thereβs no y value",
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"id": 958541361517322200,
"author_id": 819818586965016600,
"author_name": "JunβΎ",
"timestamp": "03/29/2022 21:41:09",
"content": "Do I set it βequalβ to each other?",
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"id": 958541466848858100,
"author_id": 220517274845577200,
"author_name": "ramonov",
"timestamp": "03/29/2022 21:41:34",
"content": "replace P(x) with your y and/or -3x-4",
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"id": 958541519873278000,
"author_id": 819818586965016600,
"author_name": "JunβΎ",
"timestamp": "03/29/2022 21:41:47",
"content": "Ok",
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"id": 958541691294462100,
"author_id": 819818586965016600,
"author_name": "JunβΎ",
"timestamp": "03/29/2022 21:42:28",
"content": "So I did this",
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"timestamp": "03/29/2022 21:42:50",
"content": "a *function* is a special relationship between the *input* and the *output*",
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"author_name": "Disorganized",
"timestamp": "03/29/2022 21:43:10",
"content": "so you can always reinterpret f(x) or p(x) or whatever as y",
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"id": 958541901852717000,
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"author_name": "JunβΎ",
"timestamp": "03/29/2022 21:43:18",
"content": "Oh yh true",
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"id": 958541914402070700,
"author_id": 598041720583618600,
"author_name": "Disorganized",
"timestamp": "03/29/2022 21:43:21",
"content": "...for single variable functions",
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"id": 958541945012105300,
"author_id": 819818586965016600,
"author_name": "JunβΎ",
"timestamp": "03/29/2022 21:43:28",
"content": "Ok",
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"id": 958541960577179600,
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"author_name": "Disorganized",
"timestamp": "03/29/2022 21:43:32",
"content": "fine so far ^",
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"id": 958542000452436000,
"author_id": 598041720583618600,
"author_name": "Disorganized",
"timestamp": "03/29/2022 21:43:41",
"content": "now what",
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"id": 958542087102554100,
"author_id": 819818586965016600,
"author_name": "JunβΎ",
"timestamp": "03/29/2022 21:44:02",
"content": "Mm..",
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"id": 958542218279399600,
"author_id": 598041720583618600,
"author_name": "Disorganized",
"timestamp": "03/29/2022 21:44:33",
"content": "what should this look like when you are finding roots?",
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"author_id": 819818586965016600,
"author_name": "JunβΎ",
"timestamp": "03/29/2022 21:44:54",
"content": "So I rearrange it and solve the polynomial ?",
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"id": 958542332402233300,
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"timestamp": "03/29/2022 21:45:00",
"content": "yes",
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"author_name": "JunβΎ",
"timestamp": "03/29/2022 21:45:06",
"content": "Ok sure",
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"id": 958542849308229600,
"author_id": 819818586965016600,
"author_name": "JunβΎ",
"timestamp": "03/29/2022 21:47:04",
"content": "So I wrote it as a product of its factors",
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"timestamp": "03/29/2022 21:47:17",
"content": "Which means x=-1 and -3",
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"id": 958542946481877000,
"author_id": 598041720583618600,
"author_name": "Disorganized",
"timestamp": "03/29/2022 21:47:27",
"content": "good job, not fully factored",
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},
{
"id": 958543038819479600,
"author_id": 819818586965016600,
"author_name": "JunβΎ",
"timestamp": "03/29/2022 21:47:49",
"content": "Whatβs not done?",
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},
{
"id": 958543111078961200,
"author_id": 598041720583618600,
"author_name": "Disorganized",
"timestamp": "03/29/2022 21:48:06",
"content": "$(x+1)^2 (x+3)$",
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},
{
"id": 958543121745084400,
"author_id": 510789298321096700,
"author_name": "TeXit",
"timestamp": "03/29/2022 21:48:09",
"content": "**Disorganized**",
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"timestamp": "03/29/2022 21:48:20",
"content": "but I mean they just want the roots so...",
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"id": 958543227034693800,
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"author_name": "JunβΎ",
"timestamp": "03/29/2022 21:48:34",
"content": "Yh so thatβs why I just left it like that",
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"id": 958543481041739800,
"author_id": 598041720583618600,
"author_name": "Disorganized",
"timestamp": "03/29/2022 21:49:34",
"content": "now what?",
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"id": 958543576336326700,
"author_id": 819818586965016600,
"author_name": "JunβΎ",
"timestamp": "03/29/2022 21:49:57",
"content": "I can use the second equation and plug in the values for y",
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},
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"id": 958543690756944000,
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"author_name": "Disorganized",
"timestamp": "03/29/2022 21:50:24",
"content": "either equation will work. Do you mean you want to use the linear equation, since it is simpler?",
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"timestamp": "03/29/2022 21:50:30",
"content": "Yes",
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"id": 958543745366773800,
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"timestamp": "03/29/2022 21:50:37",
"content": "sounds good",
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"author_name": "JunβΎ",
"timestamp": "03/29/2022 21:50:48",
"content": "π",
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"id": 958543943937708000,
"author_id": 598041720583618600,
"author_name": "Disorganized",
"timestamp": "03/29/2022 21:51:25",
"content": "btw, did you use Rational Root Theorem when you decided to test x=-1, or was that just a hunch?",
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"id": 958544077073318000,
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"author_name": "JunβΎ",
"timestamp": "03/29/2022 21:51:56",
"content": "Yh rational root theorem",
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"author_name": "Disorganized",
"timestamp": "03/29/2022 21:52:08",
"content": "π",
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{
"id": 958544288227147800,
"author_id": 598041720583618600,
"author_name": "Disorganized",
"timestamp": "03/29/2022 21:52:47",
"content": "Descartes' is underrated too, when you have a lot of choices",
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"author_id": 819818586965016600,
"author_name": "JunβΎ",
"timestamp": "03/29/2022 21:52:58",
"content": "I donβt know what that is",
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"id": 958544396113051600,
"author_id": 598041720583618600,
"author_name": "Disorganized",
"timestamp": "03/29/2022 21:53:12",
"content": "Descarte's Rules of Signs",
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"id": 958544520692236300,
"author_id": 819818586965016600,
"author_name": "JunβΎ",
"timestamp": "03/29/2022 21:53:42",
"content": "I got my points so would you mind telling me what that is?",
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"author_id": 819818586965016600,
"author_name": "JunβΎ",
"timestamp": "03/29/2022 21:54:01",
"content": "I searched it up and Iβm not so familiar with it",
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"id": 958544677865390100,
"author_id": 598041720583618600,
"author_name": "Disorganized",
"timestamp": "03/29/2022 21:54:20",
"content": "It's a test for how many positive or negative rational root solutions there can be for a polynomial equation",
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"id": 958544717614813200,
"author_id": 598041720583618600,
"author_name": "Disorganized",
"timestamp": "03/29/2022 21:54:29",
"content": "it's used along with RRT",
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"id": 958544739571990500,
"author_id": 819818586965016600,
"author_name": "JunβΎ",
"timestamp": "03/29/2022 21:54:34",
"content": "Oh wow",
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},
{
"id": 958544757586534400,
"author_id": 598041720583618600,
"author_name": "Disorganized",
"timestamp": "03/29/2022 21:54:39",
"content": "but not all teachers try to teach it",
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"id": 958544780764278800,
"author_id": 819818586965016600,
"author_name": "JunβΎ",
"timestamp": "03/29/2022 21:54:44",
"content": "Why?",
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"id": 958544782236459100,
"author_id": 598041720583618600,
"author_name": "Disorganized",
"timestamp": "03/29/2022 21:54:44",
"content": "it's easy.",
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"id": 958544820417220700,
"author_id": 598041720583618600,
"author_name": "Disorganized",
"timestamp": "03/29/2022 21:54:54",
"content": "oh, b.c. kids are awful sometimes",
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"id": 958544858639925200,
"author_id": 819818586965016600,
"author_name": "JunβΎ",
"timestamp": "03/29/2022 21:55:03",
"content": "Bruh lol true",
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"id": 958544904647229600,
"author_id": 819818586965016600,
"author_name": "JunβΎ",
"timestamp": "03/29/2022 21:55:14",
"content": "Is it worth learning it",
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},
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"id": 958544942060421200,
"author_id": 598041720583618600,
"author_name": "Disorganized",
"timestamp": "03/29/2022 21:55:23",
"content": "I think so",
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"id": 958544980404764700,
"author_id": 598041720583618600,
"author_name": "Disorganized",
"timestamp": "03/29/2022 21:55:32",
"content": "really easy",
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},
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"id": 958545066534772900,
"author_id": 819818586965016600,
"author_name": "JunβΎ",
"timestamp": "03/29/2022 21:55:52",
"content": "Ok",
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},
{
"id": 958545112261070800,
"author_id": 819818586965016600,
"author_name": "JunβΎ",
"timestamp": "03/29/2022 21:56:03",
"content": "Why can I see complex numbers here?",
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"timestamp": "03/29/2022 21:56:12",
"content": "you just count the number of times the terms alternate in sign; that's the number of possible + rational roots. Also, decrement this amount by 2 until you hit zero or a negative number",
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"id": 958545199364186100,
"author_id": 598041720583618600,
"author_name": "Disorganized",
"timestamp": "03/29/2022 21:56:24",
"content": "all those outcomes are possible",
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"id": 958545201591386100,
"author_id": 819818586965016600,
"author_name": "JunβΎ",
"timestamp": "03/29/2022 21:56:24",
"content": "Oh ok",
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{
"id": 958545419732942800,
"author_id": 598041720583618600,
"author_name": "Disorganized",
"timestamp": "03/29/2022 21:57:16",
"content": "negate all the odd terms and count the sign changes and do the same thing; that's the number of possible negative rational roots",
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"author_name": "JunβΎ",
"timestamp": "03/29/2022 21:57:49",
"content": "Ok I see",
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"id": 958545557582921900,
"author_id": 598041720583618600,
"author_name": "Disorganized",
"timestamp": "03/29/2022 21:57:49",
"content": "obviously, complex numbers always come in complex-conjugate pairs",
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"id": 958545673937113200,
"author_id": 819818586965016600,
"author_name": "JunβΎ",
"timestamp": "03/29/2022 21:58:17",
"content": "But how are they included in this? Like whatβs their use here?",
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"id": 958545723736076400,
"author_id": 598041720583618600,
"author_name": "Disorganized",
"timestamp": "03/29/2022 21:58:29",
"content": "the complex numbers?",
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"id": 958545757974184100,
"author_id": 819818586965016600,
"author_name": "JunβΎ",
"timestamp": "03/29/2022 21:58:37",
"content": "Yes",
"attachments": [],
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},
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"id": 958545833320652800,
"author_id": 598041720583618600,
"author_name": "Disorganized",
"timestamp": "03/29/2022 21:58:55",
"content": "this particular polynomial was degree 3 and had 3 real roots",
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"id": 958545863070875600,
"author_id": 819818586965016600,
"author_name": "JunβΎ",
"timestamp": "03/29/2022 21:59:02",
"content": "Yes",
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"id": 958545895044051000,
"author_id": 598041720583618600,
"author_name": "Disorganized",
"timestamp": "03/29/2022 21:59:10",
"content": "it could have had at most 2 complex roots",
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},
{
"id": 958545989373943800,
"author_id": 598041720583618600,
"author_name": "Disorganized",
"timestamp": "03/29/2022 21:59:32",
"content": "(only knowing that it was degree 3)",
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},
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"id": 958546034403979300,
"author_id": 819818586965016600,
"author_name": "JunβΎ",
"timestamp": "03/29/2022 21:59:43",
"content": "Oh",
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"id": 958546099189215200,
"author_id": 598041720583618600,
"author_name": "Disorganized",
"timestamp": "03/29/2022 21:59:58",
"content": "notice in the table that they decremented by 2",
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},
{
"id": 958546143204217000,
"author_id": 598041720583618600,
"author_name": "Disorganized",
"timestamp": "03/29/2022 22:00:09",
"content": "until they hit 0",
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},
{
"id": 958546187630293000,
"author_id": 301752011962056700,
"author_name": "RudyTheButler",
"timestamp": "03/29/2022 22:00:20",
"content": "Hello I was wondering how I would solve this:",
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"author_name": "JunβΎ",
"timestamp": "03/29/2022 22:00:23",
"content": "Yh I see that",
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"author_name": "Disorganized",
"timestamp": "03/29/2022 22:00:41",
"content": "wait, man",
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"author_id": 598041720583618600,
"author_name": "Disorganized",
"timestamp": "03/29/2022 22:01:31",
"content": "anyway. You have your x and y coordinates now?",
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{
"id": 958546505332047900,
"author_id": 819818586965016600,
"author_name": "JunβΎ",
"timestamp": "03/29/2022 22:01:35",
"content": "Yes",
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"id": 958546518611226800,
"author_id": 598041720583618600,
"author_name": "Disorganized",
"timestamp": "03/29/2022 22:01:38",
"content": "you're done!",
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},
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"id": 958546534146916500,
"author_id": 819818586965016600,
"author_name": "JunβΎ",
"timestamp": "03/29/2022 22:01:42",
"content": "Yep",
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{
"id": 958546546092277800,
"author_id": 819818586965016600,
"author_name": "JunβΎ",
"timestamp": "03/29/2022 22:01:45",
"content": "Thanks",
"attachments": [],
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},
{
"id": 958546548583694500,
"author_id": 598041720583618600,
"author_name": "Disorganized",
"timestamp": "03/29/2022 22:01:46",
"content": "congrats",
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"id": 958546560935932000,
"author_id": 598041720583618600,
"author_name": "Disorganized",
"timestamp": "03/29/2022 22:01:49",
"content": "yup",
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"id": 958546633358979200,
"author_id": 598041720583618600,
"author_name": "Disorganized",
"timestamp": "03/29/2022 22:02:06",
"content": "`.close`",
"attachments": [],
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},
{
"id": 958546648630440100,
"author_id": 819818586965016600,
"author_name": "JunβΎ",
"timestamp": "03/29/2022 22:02:09",
"content": "Yep",
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"id": 958546676803579900,
"author_id": 819818586965016600,
"author_name": "JunβΎ",
"timestamp": "03/29/2022 22:02:16",
"content": ".close",
"attachments": [],
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},
{
"id": 958546678468710400,
"author_id": 805217272087838700,
"author_name": "Mathematics Bot",
"timestamp": "03/29/2022 22:02:17",
"content": "Channel closed",
"attachments": [],
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}
] |
help-9
|
b49d005f8e7e4b1b9b7146a64530cf46
|
197,005 |
[
{
"id": 994421982332465200,
"author_id": 894078972944584700,
"author_name": "john82625",
"timestamp": "07/06/2022 21:57:56",
"content": "Your welcome",
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},
{
"id": 994422128730448000,
"author_id": 805217272087838700,
"author_name": "Mathematics Bot",
"timestamp": "07/06/2022 21:58:30",
"content": "Available help channel!",
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},
{
"id": 994422835965591600,
"author_id": 617029525007761400,
"author_name": "ren",
"timestamp": "07/06/2022 22:01:19",
"content": "Hi! I'm trying to prepare for my college entrance exams. I just wanna ask if there's an efficient way of solving this? The answer is D btw",
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"timestamp": "07/06/2022 22:01:20",
"content": "Pinned a message.",
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{
"id": 994423464310096000,
"author_id": 852256521986768900,
"author_name": ".,..",
"timestamp": "07/06/2022 22:03:49",
"content": "calculator",
"attachments": [],
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},
{
"id": 994423532970852400,
"author_id": 878798685264285700,
"author_name": "JSwift",
"timestamp": "07/06/2022 22:04:05",
"content": "^",
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{
"id": 994423565376049300,
"author_id": 878798685264285700,
"author_name": "JSwift",
"timestamp": "07/06/2022 22:04:13",
"content": "Just type all those numbers multiplied",
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},
{
"id": 994423642538647700,
"author_id": 878798685264285700,
"author_name": "JSwift",
"timestamp": "07/06/2022 22:04:31",
"content": "Then do those fractions to decimals is prob whatβd Iβd do",
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},
{
"id": 994423882431860700,
"author_id": 617029525007761400,
"author_name": "ren",
"timestamp": "07/06/2022 22:05:29",
"content": "I don't think we are allowed to use calculator during the exams",
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},
{
"id": 994424256542806100,
"author_id": 852256521986768900,
"author_name": ".,..",
"timestamp": "07/06/2022 22:06:58",
"content": "you should be",
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},
{
"id": 994424259801796700,
"author_id": 894078972944584700,
"author_name": "john82625",
"timestamp": "07/06/2022 22:06:59",
"content": "Would be hard to not use calculator",
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},
{
"id": 994424286515318800,
"author_id": 183668144404037630,
"author_name": "Ann",
"timestamp": "07/06/2022 22:07:05",
"content": "especially given that we are asked for the APPROXIMATE value",
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},
{
"id": 994424310041153700,
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"timestamp": "07/06/2022 22:07:11",
"content": "You can round then multiply",
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"id": 994424323781697700,
"author_id": 878798685264285700,
"author_name": "JSwift",
"timestamp": "07/06/2022 22:07:14",
"content": "The fractions",
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"id": 994424326717722800,
"author_id": 183668144404037630,
"author_name": "Ann",
"timestamp": "07/06/2022 22:07:15",
"content": "i think calculating the exact value is not the point",
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"timestamp": "07/06/2022 22:09:35",
"content": "Youβd do something like this",
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"id": 994424982790754300,
"author_id": 878798685264285700,
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"timestamp": "07/06/2022 22:09:51",
"content": "Without calc",
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"id": 994425800994590800,
"author_id": 617029525007761400,
"author_name": "ren",
"timestamp": "07/06/2022 22:13:06",
"content": "Ohhh yeah wait so the given can become like this?\n\n(1/5)(3/5)(4/5)(9/10)(1/4)",
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"timestamp": "07/06/2022 22:13:15",
"content": "sure but also maybe reduce the fraction as much as you can",
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"author_name": "Ann",
"timestamp": "07/06/2022 22:13:18",
"content": "first factor is 1/2 tho",
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"id": 994425910193299600,
"author_id": 617029525007761400,
"author_name": "ren",
"timestamp": "07/06/2022 22:13:32",
"content": "Ohh shoot i didnt notice lmao",
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"id": 994425913133498400,
"author_id": 878798685264285700,
"author_name": "JSwift",
"timestamp": "07/06/2022 22:13:33",
"content": "Yes yes that fraction will reduce all the way to 27/625",
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"id": 994425959539286100,
"author_id": 617029525007761400,
"author_name": "ren",
"timestamp": "07/06/2022 22:13:44",
"content": "Nice thats pretty cool",
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"id": 994425968095674400,
"author_id": 617029525007761400,
"author_name": "ren",
"timestamp": "07/06/2022 22:13:46",
"content": "thanks!",
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"id": 994426071451713500,
"author_id": 878798685264285700,
"author_name": "JSwift",
"timestamp": "07/06/2022 22:14:10",
"content": "no prob π",
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"author_name": "ren",
"timestamp": "07/06/2022 22:16:30",
"content": ".close",
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"timestamp": "07/06/2022 22:16:31",
"content": "Channel closed",
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}
] |
help-9
|
c34c5cf07b0446a18aca10075a520c30
|
197,006 |
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"timestamp": "07/06/2022 22:17:31",
"content": "Available help channel!",
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"id": 994435491179008000,
"author_id": 497822179610722300,
"author_name": "Snwpsh_7014",
"timestamp": "07/06/2022 22:51:36",
"content": "hello, I'm trying to get the inverse function of f(x)= x^2-4x+3 algebraically, but while i am in the process of isolating for y, I am not sure where to go next. Can I get some advice on where I am going wrong or what I should do to go on the correct path?",
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"content": "Pinned a message.",
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"author_name": "HeadShotCem",
"timestamp": "07/06/2022 22:54:26",
"content": "youβre stuck at x-3=y^2-4y cuz thereβs more than one y to deal with in the RHS, right?",
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"author_name": "Snwpsh_7014",
"timestamp": "07/06/2022 22:54:33",
"content": "yes",
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"author_id": 277133612812468220,
"author_name": "HeadShotCem",
"timestamp": "07/06/2022 22:54:34",
"content": "to avoid this, what can we do at the beginning?",
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"author_id": 497822179610722300,
"author_name": "Snwpsh_7014",
"timestamp": "07/06/2022 22:54:48",
"content": "factor it?",
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"author_id": 277133612812468220,
"author_name": "HeadShotCem",
"timestamp": "07/06/2022 22:54:56",
"content": "π",
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"id": 994436452597387400,
"author_id": 497822179610722300,
"author_name": "Snwpsh_7014",
"timestamp": "07/06/2022 22:55:26",
"content": "thanks! may i come again if i need more help?",
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"id": 994436486269239400,
"author_id": 277133612812468220,
"author_name": "HeadShotCem",
"timestamp": "07/06/2022 22:55:34",
"content": "feel free to ^^",
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"author_id": 497822179610722300,
"author_name": "Snwpsh_7014",
"timestamp": "07/06/2022 22:55:44",
"content": "thank you",
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},
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"id": 994436542930096100,
"author_id": 277133612812468220,
"author_name": "HeadShotCem",
"timestamp": "07/06/2022 22:55:47",
"content": "yw",
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"author_name": "HeadShotCem",
"timestamp": "07/06/2022 22:55:50",
"content": ".close?",
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"timestamp": "07/06/2022 22:55:54",
"content": "sure",
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help-9
|
44b48017eb034a03930390bd3f3a3c9b
|
197,007 |
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"content": "Available help channel!",
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"author_id": 874351379177685000,
"author_name": "α΅α΅β‘",
"timestamp": "07/06/2022 23:20:06",
"content": "How do you tell if a radian value such as the one in the picture provided is on the horizontal/vertical axis?",
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"content": "@α΅α΅β‘ Has your question been resolved?",
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"author_name": "Ann",
"timestamp": "07/06/2022 23:37:20",
"content": "what does that even _mean_?",
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"author_id": 874351379177685000,
"author_name": "α΅α΅β‘",
"timestamp": "07/06/2022 23:37:44",
"content": "I don't know tbh",
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"author_name": "α΅α΅β‘",
"timestamp": "07/06/2022 23:37:50",
"content": "That's why I'm asking π",
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"id": 994447182054830200,
"author_id": 183668144404037630,
"author_name": "Ann",
"timestamp": "07/06/2022 23:38:04",
"content": "so you're asking a question but not even you yourself know what you're asking",
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"id": 994447189642313700,
"author_id": 183668144404037630,
"author_name": "Ann",
"timestamp": "07/06/2022 23:38:05",
"content": "okay...",
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"id": 994447243027423400,
"author_id": 183668144404037630,
"author_name": "Ann",
"timestamp": "07/06/2022 23:38:18",
"content": "did this question come from reading something in your textbook?",
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"id": 994447289928134700,
"author_id": 874351379177685000,
"author_name": "α΅α΅β‘",
"timestamp": "07/06/2022 23:38:29",
"content": "I understand what I'm asking, I don't understand how to find what I'm looking for",
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"author_id": 874351379177685000,
"author_name": "α΅α΅β‘",
"timestamp": "07/06/2022 23:38:30",
"content": "No",
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"id": 994447339135705100,
"author_id": 874351379177685000,
"author_name": "α΅α΅β‘",
"timestamp": "07/06/2022 23:38:41",
"content": "It's practice my teacher posted",
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},
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"id": 994447444601475100,
"author_id": 183668144404037630,
"author_name": "Ann",
"timestamp": "07/06/2022 23:39:06",
"content": "show the practice",
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},
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"id": 994447577611247600,
"author_id": 183668144404037630,
"author_name": "Ann",
"timestamp": "07/06/2022 23:39:38",
"content": "...",
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"author_id": 183668144404037630,
"author_name": "Ann",
"timestamp": "07/06/2022 23:39:41",
"content": ":thonk:",
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"id": 994447599648120800,
"author_id": 183668144404037630,
"author_name": "Ann",
"timestamp": "07/06/2022 23:39:43",
"content": "what the hell",
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"id": 994447611509604500,
"author_id": 183668144404037630,
"author_name": "Ann",
"timestamp": "07/06/2022 23:39:46",
"content": "did they mean like",
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"id": 994447657743421600,
"author_id": 183668144404037630,
"author_name": "Ann",
"timestamp": "07/06/2022 23:39:57",
"content": "angles whose unit circle points lie on the x-axis???",
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"id": 994447690849071100,
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"timestamp": "07/06/2022 23:40:05",
"content": "if so then those would be integer multiples of pi",
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"author_name": "α΅α΅β‘",
"timestamp": "07/06/2022 23:40:46",
"content": "Alright, thanks",
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"timestamp": "07/06/2022 23:41:14",
"content": ".close",
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] |
help-9
|
599efc26349746dd88ac06863ac20275
|
197,008 |
[
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"id": 994458332314214500,
"author_id": 261933205387477000,
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"timestamp": "07/07/2022 00:22:57",
"content": "Find a closed formula for the sum of first n squares from your notes/book",
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"content": "https://www.cuemath.com/algebra/sum-of-squares/",
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"content": "@Eightpeach Has your question been resolved?",
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"content": "Channel closed",
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help-9
|
a0e82e99526c4f2fb059f676bec65c45
|
197,009 |
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"timestamp": "07/07/2022 01:07:46",
"content": "firstly I will differentiate it wrt to X then with y??",
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"content": "just plug into the formula\nhttps://phys.libretexts.org/Bookshelves/Thermodynamics_and_Statistical_Mechanics/Book%3A_Heat_and_Thermodynamics_(Tatum)/02%3A_Partial_Derivatives/2.06%3A_Euler's_Theorem_for_Homogeneous_Functions",
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"timestamp": "07/07/2022 01:11:31",
"content": "Ok thanks",
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"content": ".close",
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help-9
|
7eadc2b03d194ce999d56e49a2e4d171
|
197,010 |
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"id": 994472270036742300,
"author_id": 719355286606839800,
"author_name": "Tiene",
"timestamp": "07/07/2022 01:17:45",
"content": "Hey, so what is a 2 sphere exactly? How does a two dimensional sphere fit into a 3D space?",
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},
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"id": 994472272201011200,
"author_id": 805217272087838700,
"author_name": "Mathematics Bot",
"timestamp": "07/07/2022 01:17:46",
"content": "Pinned a message.",
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{
"id": 994472493207257200,
"author_id": 261933205387477000,
"author_name": "riemann",
"timestamp": "07/07/2022 01:18:38",
"content": "https://topospaces.subwiki.org/wiki/2-sphere",
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},
{
"id": 994472767451836500,
"author_id": 719355286606839800,
"author_name": "Tiene",
"timestamp": "07/07/2022 01:19:44",
"content": "yeah but how is a sphere 2d",
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},
{
"id": 994472785470566400,
"author_id": 719355286606839800,
"author_name": "Tiene",
"timestamp": "07/07/2022 01:19:48",
"content": "isn't that just a circle",
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},
{
"id": 994472967448825900,
"author_id": 261933205387477000,
"author_name": "riemann",
"timestamp": "07/07/2022 01:20:31",
"content": "a circle is a 1 sphere",
"attachments": [],
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},
{
"id": 994473079453528200,
"author_id": 261933205387477000,
"author_name": "riemann",
"timestamp": "07/07/2022 01:20:58",
"content": "https://topospaces.subwiki.org/wiki/Circle",
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},
{
"id": 994473092300681200,
"author_id": 261933205387477000,
"author_name": "riemann",
"timestamp": "07/07/2022 01:21:01",
"content": "compare their definitions",
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"timestamp": "07/07/2022 01:34:48",
"content": "@Tiene Has your question been resolved?",
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"timestamp": "07/07/2022 01:35:46",
"content": "Channel closed",
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}
] |
help-9
|
6a26b6ab1cac446ca608ae077f1b7c69
|
197,011 |
[
{
"id": 994477058245800100,
"author_id": 805217272087838700,
"author_name": "Mathematics Bot",
"timestamp": "07/07/2022 01:36:47",
"content": "Available help channel!",
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},
{
"id": 994488204252172300,
"author_id": 560241701612945400,
"author_name": "HellO",
"timestamp": "07/07/2022 02:21:04",
"content": "Hi! can someone very quickly tell me how to find the reflection of plane on a plane?",
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},
{
"id": 994488206714212400,
"author_id": 805217272087838700,
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"content": "Pinned a message.",
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{
"id": 994488345918971900,
"author_id": 560241701612945400,
"author_name": "HellO",
"timestamp": "07/07/2022 02:21:38",
"content": "so i have plane 1: r . (1,2,3) = 5\nplane 2: r . (3,4,5) = 1\ni wanna find plane 3 which is plane 1 reflected on plane 2",
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},
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"id": 994488543349063700,
"author_id": 183668144404037630,
"author_name": "Ann",
"timestamp": "07/07/2022 02:22:25",
"content": "find a point (any point) that lies on both",
"attachments": [],
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},
{
"id": 994488613561700500,
"author_id": 183668144404037630,
"author_name": "Ann",
"timestamp": "07/07/2022 02:22:42",
"content": "then reflect plane 1's normal vector in plane 2",
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},
{
"id": 994488721216897000,
"author_id": 560241701612945400,
"author_name": "HellO",
"timestamp": "07/07/2022 02:23:07",
"content": "oh wait i think i forgot to specify that theyre non parallel",
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},
{
"id": 994488765450047500,
"author_id": 560241701612945400,
"author_name": "HellO",
"timestamp": "07/07/2022 02:23:18",
"content": "or does that work for non parallel vectors as well?",
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},
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"id": 994489048620085400,
"author_id": 560241701612945400,
"author_name": "HellO",
"timestamp": "07/07/2022 02:24:25",
"content": "can this be the point where plane 1 and plane 2 intersects at?",
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"id": 994489970196750300,
"author_id": 183668144404037630,
"author_name": "Ann",
"timestamp": "07/07/2022 02:28:05",
"content": "they intersect along a line",
"attachments": [],
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},
{
"id": 994490103797928100,
"author_id": 560241701612945400,
"author_name": "HellO",
"timestamp": "07/07/2022 02:28:37",
"content": "oh right",
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},
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"id": 994490157241729000,
"author_id": 560241701612945400,
"author_name": "HellO",
"timestamp": "07/07/2022 02:28:50",
"content": "so to get the equation of the line i need a point and the direction vector",
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},
{
"id": 994490212510093300,
"author_id": 560241701612945400,
"author_name": "HellO",
"timestamp": "07/07/2022 02:29:03",
"content": "or can i get both rightaway after equating p1 and p2?",
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},
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"author_id": 805217272087838700,
"author_name": "Mathematics Bot",
"timestamp": "07/07/2022 02:44:03",
"content": "@HellO Has your question been resolved?",
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"id": 994499195664867300,
"author_id": 560241701612945400,
"author_name": "HellO",
"timestamp": "07/07/2022 03:04:45",
"content": "@Helpers",
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},
{
"id": 994499589296111700,
"author_id": 183668144404037630,
"author_name": "Ann",
"timestamp": "07/07/2022 03:06:18",
"content": "you don't need the entire line...",
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"id": 994499636041633800,
"author_id": 560241701612945400,
"author_name": "HellO",
"timestamp": "07/07/2022 03:06:30",
"content": "err",
"attachments": [],
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},
{
"id": 994499665884098600,
"author_id": 560241701612945400,
"author_name": "HellO",
"timestamp": "07/07/2022 03:06:37",
"content": "just the direction vector?",
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},
{
"id": 994499731059396600,
"author_id": 560241701612945400,
"author_name": "HellO",
"timestamp": "07/07/2022 03:06:52",
"content": "sorry im rly bad at this",
"attachments": [],
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},
{
"id": 994499753977065500,
"author_id": 183668144404037630,
"author_name": "Ann",
"timestamp": "07/07/2022 03:06:58",
"content": "no, just a point on it",
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},
{
"id": 994499767658873000,
"author_id": 183668144404037630,
"author_name": "Ann",
"timestamp": "07/07/2022 03:07:01",
"content": "as i said before",
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},
{
"id": 994499827670974600,
"author_id": 560241701612945400,
"author_name": "HellO",
"timestamp": "07/07/2022 03:07:15",
"content": "how do i find that thou",
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},
{
"id": 994506637782032400,
"author_id": 560241701612945400,
"author_name": "HellO",
"timestamp": "07/07/2022 03:34:19",
"content": "With the two vector plane equations im given",
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},
{
"id": 994511629444206700,
"author_id": 183668144404037630,
"author_name": "Ann",
"timestamp": "07/07/2022 03:54:09",
"content": "write them out as equations",
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},
{
"id": 994511641695752200,
"author_id": 183668144404037630,
"author_name": "Ann",
"timestamp": "07/07/2022 03:54:12",
"content": "find at least one solution",
"attachments": [],
"mentions": [],
"reference": null
},
{
"id": 994511709173715000,
"author_id": 183668144404037630,
"author_name": "Ann",
"timestamp": "07/07/2022 03:54:28",
"content": "you can solve the system and find them all and then just pick your favorite one",
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},
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"author_id": 805217272087838700,
"author_name": "Mathematics Bot",
"timestamp": "07/07/2022 04:04:28",
"content": "@HellO Has your question been resolved?",
"attachments": [],
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"id": 994514279233507300,
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"author_name": "HellO",
"timestamp": "07/07/2022 04:04:41",
"content": "okay, ill try",
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},
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"author_name": "Mathematics Bot",
"timestamp": "07/07/2022 04:04:42",
"content": "Channel closed",
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}
] |
help-9
|
ea142e9c17734596b25aa266666e6452
|
197,012 |
[
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"timestamp": "07/07/2022 04:42:04",
"content": "Available help channel!",
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},
{
"id": 994530663409668100,
"author_id": 254152365156859900,
"author_name": "razzy",
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"timestamp": "07/07/2022 05:10:18",
"content": "am i doing it right because im not sure it said it is rotated around the line y = -2",
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"timestamp": "07/07/2022 05:25:18",
"content": "@razzy Has your question been resolved?",
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"content": "@razzy Has your question been resolved?",
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}
] |
help-9
|
e5b0b2f494e643d6820a463fb285736f
|
197,013 |
[
{
"id": 994551146486169700,
"author_id": 805217272087838700,
"author_name": "Mathematics Bot",
"timestamp": "07/07/2022 06:31:11",
"content": "Available help channel!",
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},
{
"id": 994557781094957200,
"author_id": 909218746801979400,
"author_name": "xzino",
"timestamp": "07/07/2022 06:57:33",
"content": "Find the values of n <=7 for which n ! + 1 is a perfect square \nany hints on how to proof this using induction ?",
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"id": 994558254048886800,
"author_id": 764959481070616600,
"author_name": "Toby",
"timestamp": "07/07/2022 06:59:25",
"content": "unless I'm misinterpreting something, there's only 8 cases. And you are asked to check something is true or false in these cases. So why do you want to use induction?",
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"id": 994560005808324600,
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"author_name": "xzino",
"timestamp": "07/07/2022 07:06:23",
"content": "it's because this question is from a book in a section about induction",
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"id": 994561173473206300,
"author_id": 764959481070616600,
"author_name": "Toby",
"timestamp": "07/07/2022 07:11:01",
"content": "well I don't see how this relates to induction. sorry. the way I would to do it would be:\n0!+1=2 not square\n1!+1=2 not square\n...\n7!+1=... square",
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"id": 994562304404373600,
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"author_name": "MarveI",
"timestamp": "07/07/2022 07:15:31",
"content": "0! is 1 no?",
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"timestamp": "07/07/2022 07:15:36",
"content": "oh yeah mb",
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"id": 994562421630959600,
"author_id": 764959481070616600,
"author_name": "Toby",
"timestamp": "07/07/2022 07:15:59",
"content": "fixed",
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"id": 994563781306892400,
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"timestamp": "07/07/2022 07:21:23",
"content": "@xzino Has your question been resolved?",
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"author_name": "xzino",
"timestamp": "07/07/2022 07:25:12",
"content": "Thanks, I guess there is no other way to prove it",
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"timestamp": "07/07/2022 07:25:26",
"content": "Channel closed",
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}
] |
help-9
|
aadf05cb498b4135ae9342e10df6db26
|
197,014 |
[
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"timestamp": "07/07/2022 07:26:26",
"content": "Available help channel!",
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},
{
"id": 994569793581633500,
"author_id": 240225041353146370,
"author_name": "bobbyt",
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"id": 994569819301085300,
"author_id": 240225041353146370,
"author_name": "bobbyt",
"timestamp": "07/07/2022 07:45:23",
"content": "hey i forgot how to do these questions",
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{
"id": 994569842843717800,
"author_id": 240225041353146370,
"author_name": "bobbyt",
"timestamp": "07/07/2022 07:45:28",
"content": "is the correct answer B?",
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"id": 994569910023880700,
"author_id": 240225041353146370,
"author_name": "bobbyt",
"timestamp": "07/07/2022 07:45:44",
"content": "because any number (m) divided by itself is 1",
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"id": 994570154744754200,
"author_id": 764959481070616600,
"author_name": "Toby",
"timestamp": "07/07/2022 07:46:43",
"content": "no it's not b",
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"id": 994570214605848600,
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"timestamp": "07/07/2022 07:46:57",
"content": "i see",
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"id": 994570249242411100,
"author_id": 764959481070616600,
"author_name": "Toby",
"timestamp": "07/07/2022 07:47:05",
"content": "(note also that log_9(1)=0)",
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"timestamp": "07/07/2022 07:47:36",
"content": "change of base rule eh",
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"content": "yup",
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"timestamp": "07/07/2022 07:49:08",
"content": "what is b in my case tho?",
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"content": "ohhhhhhhh",
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"timestamp": "07/07/2022 07:49:37",
"content": "the assignment on the right is my equation. lol",
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"timestamp": "07/07/2022 07:51:57",
"content": "wait",
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"timestamp": "07/07/2022 07:52:01",
"content": "these two equations on the right",
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"timestamp": "07/07/2022 07:52:06",
"content": "have the same base :/",
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"timestamp": "07/07/2022 07:52:10",
"content": "mine do not",
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"timestamp": "07/07/2022 07:52:44",
"content": "not quite, you want to convert the top thing (log_9(m)) to base of the bottom (I assume it's e here? or 10? but it doesn't matter for notation)",
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"content": "alternatively, you can divide both sides by log_b(x) here and arrive at the same conclusion with clever substitutions",
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"timestamp": "07/07/2022 07:54:55",
"content": "what is log_b tho",
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"content": "just log",
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"timestamp": "07/07/2022 07:55:22",
"content": "log without a base written",
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"timestamp": "07/07/2022 07:55:32",
"content": "then wouldn't log_a be 9?",
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"timestamp": "07/07/2022 07:55:44",
"content": "huh?",
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"timestamp": "07/07/2022 07:55:52",
"content": "you mean a=9?",
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"timestamp": "07/07/2022 07:55:56",
"content": "yes",
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"timestamp": "07/07/2022 07:56:01",
"content": "yeah, then yes",
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"timestamp": "07/07/2022 07:58:02",
"content": "but do the log's cancel out ?",
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"timestamp": "07/07/2022 07:58:15",
"content": "log_b / log_b = 1?",
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"timestamp": "07/07/2022 07:58:17",
"content": "or no",
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"timestamp": "07/07/2022 07:59:34",
"content": "this gives $\\log_9(m)=\\frac{\\log(m)}{\\log(9)}$",
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"author_name": "TeXit",
"timestamp": "07/07/2022 07:59:51",
"content": "**Toby**",
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"timestamp": "07/07/2022 08:11:49",
"content": "how can i rewrite this as a logarithm",
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"timestamp": "07/07/2022 08:13:38",
"content": "do u know how?",
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"author_name": "Toby",
"timestamp": "07/07/2022 08:14:01",
"content": "take logs of both sides?",
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"timestamp": "07/07/2022 08:14:23",
"content": "ah i see",
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"author_name": "Joy Light",
"timestamp": "07/07/2022 08:14:59",
"content": "do you still need help?",
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"timestamp": "07/07/2022 08:15:08",
"content": "im at the step of",
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"timestamp": "07/07/2022 08:15:29",
"content": "10^-(t/12)=0.44444444444444",
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"author_name": "Joy Light",
"timestamp": "07/07/2022 08:17:57",
"content": "i multiply 0.44444444444444 to 22,500 and have 10,000",
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"timestamp": "07/07/2022 08:18:31",
"content": "thats not a logarithm",
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"timestamp": "07/07/2022 08:18:36",
"content": "right now i'm thinking",
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"timestamp": "07/07/2022 08:18:42",
"content": "12log(4/9)",
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"timestamp": "07/07/2022 08:18:46",
"content": "but",
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"author_name": "Joy Light",
"timestamp": "07/07/2022 08:18:47",
"content": "10 to the fourth power = 10,000",
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"timestamp": "07/07/2022 08:18:52",
"content": "that gives a negative answer",
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"timestamp": "07/07/2022 08:19:00",
"content": "what",
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"timestamp": "07/07/2022 08:19:11",
"content": "10^4 = 10,000",
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"timestamp": "07/07/2022 08:19:18",
"content": "thats completely irrelevant",
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"timestamp": "07/07/2022 08:19:38",
"content": "i can't express that as a model",
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"id": 994578494854017000,
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"timestamp": "07/07/2022 08:19:51",
"content": ",calc 12log(4/9)",
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"timestamp": "07/07/2022 08:19:51",
"content": "Result:\n```\n-9.7311625945959\n```",
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"author_name": "Joy Light",
"timestamp": "07/07/2022 08:19:59",
"content": "i'm thinking log base 10 10,000 = 4",
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"timestamp": "07/07/2022 08:20:11",
"content": "thats not the answer",
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"timestamp": "07/07/2022 08:20:32",
"content": "sorry",
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"id": 994578698625888300,
"author_id": 240225041353146370,
"author_name": "bobbyt",
"timestamp": "07/07/2022 08:20:40",
"content": ",calc 12 * log(4/9)",
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"timestamp": "07/07/2022 08:20:40",
"content": "Result:\n```\n-9.7311625945959\n```",
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},
{
"id": 994578708356669600,
"author_id": 240225041353146370,
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"timestamp": "07/07/2022 08:20:42",
"content": "wtf",
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"id": 994578717672231000,
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"timestamp": "07/07/2022 08:20:44",
"content": "is wrong with this",
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{
"id": 994578777453641700,
"author_id": 240225041353146370,
"author_name": "bobbyt",
"timestamp": "07/07/2022 08:20:58",
"content": ",calc log(4/9) * 12",
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"timestamp": "07/07/2022 08:20:59",
"content": "Result:\n```\n-9.7311625945959\n```",
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},
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"id": 994578797766660100,
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"timestamp": "07/07/2022 08:21:03",
"content": ":???????????????\n|",
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"timestamp": "07/07/2022 08:21:28",
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"timestamp": "07/07/2022 08:21:37",
"content": "why is this giving me a different answer than texit",
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"id": 994579105305608200,
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"timestamp": "07/07/2022 08:22:17",
"content": "ugh this quiz is so frustrating i got 2 answers wrong for the most pedantic reasons",
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"timestamp": "07/07/2022 08:22:52",
"content": "wtf",
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"timestamp": "07/07/2022 08:23:09",
"content": "why would any sane person move the 12 inside the log",
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"timestamp": "07/07/2022 08:23:26",
"content": "i didn't",
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"timestamp": "07/07/2022 08:23:29",
"content": "i know",
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"id": 994579426983563400,
"author_id": 764959481070616600,
"author_name": "Toby",
"timestamp": "07/07/2022 08:23:33",
"content": "but why does it want you to",
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"id": 994579465122361300,
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"timestamp": "07/07/2022 08:23:42",
"content": "texit?",
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"timestamp": "07/07/2022 08:23:57",
"content": "i didn't know that it wants me to do that",
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"timestamp": "07/07/2022 08:24:05",
"content": "i don't know what it would look like",
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"timestamp": "07/07/2022 08:24:06",
"content": "no, here ^",
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"timestamp": "07/07/2022 08:24:24",
"content": "i believe 4.226 is the correct answer though",
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"author_id": 764959481070616600,
"author_name": "Toby",
"timestamp": "07/07/2022 08:24:24",
"content": "oh wait, i misunderstood everything you said, hold up",
"attachments": [],
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},
{
"id": 994579729778745300,
"author_id": 764959481070616600,
"author_name": "Toby",
"timestamp": "07/07/2022 08:24:45",
"content": ",calc log(e)",
"attachments": [],
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},
{
"id": 994579731968176300,
"author_id": 510789298321096700,
"author_name": "TeXit",
"timestamp": "07/07/2022 08:24:46",
"content": "Result:\n```\n1\n```",
"attachments": [],
"mentions": [],
"reference": null
},
{
"id": 994579764952170600,
"author_id": 764959481070616600,
"author_name": "Toby",
"timestamp": "07/07/2022 08:24:54",
"content": "the bot uses log base e, you are using log base 10",
"attachments": [],
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},
{
"id": 994579804814856200,
"author_id": 764959481070616600,
"author_name": "Toby",
"timestamp": "07/07/2022 08:25:03",
"content": "you are probably correct",
"attachments": [],
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},
{
"id": 994579813065031800,
"author_id": 240225041353146370,
"author_name": "bobbyt",
"timestamp": "07/07/2022 08:25:05",
"content": "thats what i thought but that is stupid",
"attachments": [],
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},
{
"id": 994579896963706900,
"author_id": 764959481070616600,
"author_name": "Toby",
"timestamp": "07/07/2022 08:25:25",
"content": "e is the natural base Β―\\_(γ)_/Β―",
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},
{
"id": 994579927204626600,
"author_id": 240225041353146370,
"author_name": "bobbyt",
"timestamp": "07/07/2022 08:25:33",
"content": "expressed as ln",
"attachments": [],
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{
"id": 994579931092758700,
"author_id": 764959481070616600,
"author_name": "Toby",
"timestamp": "07/07/2022 08:25:33",
"content": ",calc log_10(10)",
"attachments": [],
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},
{
"id": 994579933303148700,
"author_id": 510789298321096700,
"author_name": "TeXit",
"timestamp": "07/07/2022 08:25:34",
"content": "The following error occured while calculating:\n`Error: Undefined function log_10`",
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},
{
"id": 994579958666104800,
"author_id": 240225041353146370,
"author_name": "bobbyt",
"timestamp": "07/07/2022 08:25:40",
"content": "that too",
"attachments": [],
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"nickname": "Toby",
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},
{
"id": 994579960620650500,
"author_id": 240225041353146370,
"author_name": "bobbyt",
"timestamp": "07/07/2022 08:25:41",
"content": "lmfao",
"attachments": [],
"mentions": [],
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},
{
"id": 994579988152058000,
"author_id": 764959481070616600,
"author_name": "Toby",
"timestamp": "07/07/2022 08:25:47",
"content": "not to people who do maths :p",
"attachments": [],
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"nickname": "bobbyt",
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},
{
"id": 994580029352710100,
"author_id": 764959481070616600,
"author_name": "Toby",
"timestamp": "07/07/2022 08:25:57",
"content": ",calc log(10,10)",
"attachments": [],
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},
{
"id": 994580031080763500,
"author_id": 510789298321096700,
"author_name": "TeXit",
"timestamp": "07/07/2022 08:25:57",
"content": "Result:\n```\n1\n```",
"attachments": [],
"mentions": [],
"reference": null
},
{
"id": 994580056632471700,
"author_id": 764959481070616600,
"author_name": "Toby",
"timestamp": "07/07/2022 08:26:03",
"content": ",calc log(100,10)",
"attachments": [],
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},
{
"id": 994580085694812200,
"author_id": 510789298321096700,
"author_name": "TeXit",
"timestamp": "07/07/2022 08:26:10",
"content": "Result:\n```\n2\n```",
"attachments": [],
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},
{
"id": 994580134961098800,
"author_id": 240225041353146370,
"author_name": "bobbyt",
"timestamp": "07/07/2022 08:26:22",
"content": "this is patrick bateman vibes",
"attachments": [],
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}
],
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},
{
"id": 994580158902182000,
"author_id": 764959481070616600,
"author_name": "Toby",
"timestamp": "07/07/2022 08:26:28",
"content": ",calc 12*log(4/9,10)",
"attachments": [],
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},
{
"id": 994580160684752900,
"author_id": 510789298321096700,
"author_name": "TeXit",
"timestamp": "07/07/2022 08:26:28",
"content": "Result:\n```\n-4.2261902173364\n```",
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},
{
"id": 994580310207496200,
"author_id": 240225041353146370,
"author_name": "bobbyt",
"timestamp": "07/07/2022 08:27:04",
"content": "but why is it a negative?",
"attachments": [],
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{
"id": 994580345343180900,
"author_id": 764959481070616600,
"author_name": "Toby",
"timestamp": "07/07/2022 08:27:12",
"content": "because 4/9<1",
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},
{
"id": 994580356239982600,
"author_id": 240225041353146370,
"author_name": "bobbyt",
"timestamp": "07/07/2022 08:27:15",
"content": "don't think i can express it as a negative",
"attachments": [],
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},
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"id": 994580400993218700,
"author_id": 240225041353146370,
"author_name": "bobbyt",
"timestamp": "07/07/2022 08:27:26",
"content": "",
"attachments": [
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"id": 994580404566757400,
"author_id": 240225041353146370,
"author_name": "bobbyt",
"timestamp": "07/07/2022 08:27:26",
"content": "like",
"attachments": [],
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},
{
"id": 994580431204786300,
"author_id": 240225041353146370,
"author_name": "bobbyt",
"timestamp": "07/07/2022 08:27:33",
"content": "i don't think it's expecting a negative answer",
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},
{
"id": 994580582875009000,
"author_id": 240225041353146370,
"author_name": "bobbyt",
"timestamp": "07/07/2022 08:28:09",
"content": "do i do",
"attachments": [],
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},
{
"id": 994580627309477900,
"author_id": 240225041353146370,
"author_name": "bobbyt",
"timestamp": "07/07/2022 08:28:19",
"content": "negative 12 * log(4/9) ?",
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},
{
"id": 994580649597997200,
"author_id": 764959481070616600,
"author_name": "Toby",
"timestamp": "07/07/2022 08:28:25",
"content": "yes",
"attachments": [],
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},
{
"id": 994580690911895600,
"author_id": 240225041353146370,
"author_name": "bobbyt",
"timestamp": "07/07/2022 08:28:35",
"content": "because the whole fraction is negative",
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},
{
"id": 994580711006802000,
"author_id": 240225041353146370,
"author_name": "bobbyt",
"timestamp": "07/07/2022 08:28:39",
"content": "?",
"attachments": [],
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},
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"id": 994581095507038200,
"author_id": 764959481070616600,
"author_name": "Toby",
"timestamp": "07/07/2022 08:30:11",
"content": "\\begin{align*}10000&=22500\\cdot 10^{-t/12}\\\\\\log(4/9)&=\\frac{-t}{12}\\log(10)\\\\ -12\\log(4/9)&=t\\end{align*}",
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"id": 994581197852246000,
"author_id": 510789298321096700,
"author_name": "TeXit",
"timestamp": "07/07/2022 08:30:35",
"content": "**Toby**",
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"id": 994581220103041200,
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"timestamp": "07/07/2022 08:30:41",
"content": "this is the full working ^",
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{
"id": 994582159354511400,
"author_id": 240225041353146370,
"author_name": "bobbyt",
"timestamp": "07/07/2022 08:34:25",
"content": "appreciate",
"attachments": [],
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{
"id": 994585935108915300,
"author_id": 805217272087838700,
"author_name": "Mathematics Bot",
"timestamp": "07/07/2022 08:49:25",
"content": "@bobbyt Has your question been resolved?",
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"id": 994585946752303200,
"author_id": 805217272087838700,
"author_name": "Mathematics Bot",
"timestamp": "07/07/2022 08:49:28",
"content": "Channel closed",
"attachments": [],
"mentions": [],
"reference": null
}
] |
help-9
|
ef2846ef8cb44509bd9ef18cb4c7ebf2
|
197,015 |
[
{
"id": 958546722857054200,
"author_id": 598041720583618600,
"author_name": "Disorganized",
"timestamp": "03/29/2022 22:02:27",
"content": "repost",
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{
"id": 958546741421031600,
"author_id": 598041720583618600,
"author_name": "Disorganized",
"timestamp": "03/29/2022 22:02:32",
"content": "so you can claim",
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},
{
"id": 958546857854922900,
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"author_name": "RudyTheButler",
"timestamp": "03/29/2022 22:02:59",
"content": "",
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"timestamp": "03/29/2022 22:03:17",
"content": "Available help channel!",
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{
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"author_id": 301752011962056700,
"author_name": "RudyTheButler",
"timestamp": "03/29/2022 22:03:55",
"content": "Hello can someone explain how I can solve this one?:",
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"timestamp": "03/29/2022 22:03:56",
"content": "Pinned a message.",
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"author_name": "RudyTheButler",
"timestamp": "03/29/2022 22:05:07",
"content": "@Disorganized",
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"author_name": "RudyTheButler",
"timestamp": "03/29/2022 22:05:50",
"content": "Thank you for the help",
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},
{
"id": 958547576871874600,
"author_id": 598041720583618600,
"author_name": "Disorganized",
"timestamp": "03/29/2022 22:05:51",
"content": "yuck.",
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},
{
"id": 958547630793830400,
"author_id": 598041720583618600,
"author_name": "Disorganized",
"timestamp": "03/29/2022 22:06:04",
"content": "I don't think this has an integer or even a rational solution",
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},
{
"id": 958547674607534100,
"author_id": 598041720583618600,
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"timestamp": "03/29/2022 22:06:14",
"content": "another way of writing this is",
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},
{
"id": 958547773756690600,
"author_id": 598041720583618600,
"author_name": "Disorganized",
"timestamp": "03/29/2022 22:06:38",
"content": "$2^{2+a} = 3^{1+b}$",
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},
{
"id": 958547785077125100,
"author_id": 510789298321096700,
"author_name": "TeXit",
"timestamp": "03/29/2022 22:06:40",
"content": "**Disorganized**",
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"timestamp": "03/29/2022 22:07:04",
"content": "Hmmm...",
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},
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"id": 958547904501518300,
"author_id": 598041720583618600,
"author_name": "Disorganized",
"timestamp": "03/29/2022 22:07:09",
"content": "that is, a power of 2 equal to a power of 3",
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},
{
"id": 958547950894723200,
"author_id": 598041720583618600,
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"timestamp": "03/29/2022 22:07:20",
"content": "(being unprecise)",
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},
{
"id": 958548002929279100,
"author_id": 598041720583618600,
"author_name": "Disorganized",
"timestamp": "03/29/2022 22:07:32",
"content": "and using \"power\" loosely",
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},
{
"id": 958548055995588600,
"author_id": 598041720583618600,
"author_name": "Disorganized",
"timestamp": "03/29/2022 22:07:45",
"content": "oh",
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},
{
"id": 958548079722786800,
"author_id": 598041720583618600,
"author_name": "Disorganized",
"timestamp": "03/29/2022 22:07:51",
"content": "no, nevermind",
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},
{
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"author_id": 301752011962056700,
"author_name": "RudyTheButler",
"timestamp": "03/29/2022 22:08:27",
"content": "Umm..",
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},
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"timestamp": "03/29/2022 22:08:34",
"content": "thinking",
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},
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"author_id": 301752011962056700,
"author_name": "RudyTheButler",
"timestamp": "03/29/2022 22:09:01",
"content": "Same it has been a real doozie",
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"id": 958549921416478700,
"author_id": 598041720583618600,
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"timestamp": "03/29/2022 22:15:10",
"content": "Stuck here",
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},
{
"id": 958550028153139200,
"author_id": 598041720583618600,
"author_name": "Disorganized",
"timestamp": "03/29/2022 22:15:35",
"content": "Since I have x inside of two differently-based logarithms",
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"id": 958550068519125000,
"author_id": 598041720583618600,
"author_name": "Disorganized",
"timestamp": "03/29/2022 22:15:45",
"content": "We can find a numerical solution",
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},
{
"id": 958550197946970100,
"author_id": 598041720583618600,
"author_name": "Disorganized",
"timestamp": "03/29/2022 22:16:16",
"content": "we would need to find where",
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},
{
"id": 958550224245235700,
"author_id": 301752011962056700,
"author_name": "RudyTheButler",
"timestamp": "03/29/2022 22:16:22",
"content": "hmmm",
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},
{
"id": 958550350086959200,
"author_id": 598041720583618600,
"author_name": "Disorganized",
"timestamp": "03/29/2022 22:16:52",
"content": "$y=\\log_2{3} + \\log_2{x}$",
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},
{
"id": 958550352679018500,
"author_id": 301752011962056700,
"author_name": "RudyTheButler",
"timestamp": "03/29/2022 22:16:53",
"content": "Yeah it looks like factoring is not an option anymore",
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"timestamp": "03/29/2022 22:16:54",
"content": "**Disorganized**",
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"timestamp": "03/29/2022 22:16:59",
"content": "intersects",
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"author_name": "Disorganized",
"timestamp": "03/29/2022 22:17:39",
"content": "$y=2(\\log_3{2} + \\log_3{x})$",
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},
{
"id": 958550558170570800,
"author_id": 510789298321096700,
"author_name": "TeXit",
"timestamp": "03/29/2022 22:17:42",
"content": "**Disorganized**",
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"author_name": "RudyTheButler",
"timestamp": "03/29/2022 22:18:29",
"content": "Hmmm",
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"id": 958550792552472700,
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"author_name": "RudyTheButler",
"timestamp": "03/29/2022 22:18:37",
"content": "So this is as far as it gets it seems",
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},
{
"id": 958551305733951500,
"author_id": 598041720583618600,
"author_name": "Disorganized",
"timestamp": "03/29/2022 22:20:40",
"content": "I wonder if change-of-base will help?",
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{
"id": 958551415595339900,
"author_id": 301752011962056700,
"author_name": "RudyTheButler",
"timestamp": "03/29/2022 22:21:06",
"content": "That seems to be like one of the only options left",
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},
{
"id": 958551439456735400,
"author_id": 598041720583618600,
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"timestamp": "03/29/2022 22:21:12",
"content": "yes",
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},
{
"id": 958551473548046300,
"author_id": 598041720583618600,
"author_name": "Disorganized",
"timestamp": "03/29/2022 22:21:20",
"content": "it will make this work",
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},
{
"id": 958551508104904700,
"author_id": 598041720583618600,
"author_name": "Disorganized",
"timestamp": "03/29/2022 22:21:28",
"content": "change of base:",
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},
{
"id": 958551721796309000,
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"author_name": "Disorganized",
"timestamp": "03/29/2022 22:22:19",
"content": "$\\log_b{x}=\\frac{\\log{x}}{\\log{b}}$",
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},
{
"id": 958551734622507000,
"author_id": 510789298321096700,
"author_name": "TeXit",
"timestamp": "03/29/2022 22:22:22",
"content": "**Disorganized**",
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"author_name": "RudyTheButler",
"timestamp": "03/29/2022 22:24:45",
"content": "Okay how will that affect this though.. hmm I am curious",
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},
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"id": 958552573349073000,
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"author_name": "Disorganized",
"timestamp": "03/29/2022 22:25:42",
"content": "",
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{
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{
"id": 958552658518605800,
"author_id": 598041720583618600,
"author_name": "Disorganized",
"timestamp": "03/29/2022 22:26:02",
"content": "interpret`log` as log-base-10 in this writeup",
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},
{
"id": 958552696690995300,
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"author_name": "Disorganized",
"timestamp": "03/29/2022 22:26:11",
"content": "the base is arbitrary as long as you are consistent",
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"id": 958552735790284800,
"author_id": 598041720583618600,
"author_name": "Disorganized",
"timestamp": "03/29/2022 22:26:21",
"content": "I use that base in the last step",
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},
{
"id": 958552806044860400,
"author_id": 598041720583618600,
"author_name": "Disorganized",
"timestamp": "03/29/2022 22:26:38",
"content": "`RHS` = \"right-hand-side\"",
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},
{
"id": 958552944058445800,
"author_id": 598041720583618600,
"author_name": "Disorganized",
"timestamp": "03/29/2022 22:27:10",
"content": "I used almost every law of logarithms here",
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},
{
"id": 958553016485687300,
"author_id": 301752011962056700,
"author_name": "RudyTheButler",
"timestamp": "03/29/2022 22:27:28",
"content": "That is insane!",
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},
{
"id": 958553079958102000,
"author_id": 301752011962056700,
"author_name": "RudyTheButler",
"timestamp": "03/29/2022 22:27:43",
"content": "Wow thank you so much!",
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},
{
"id": 958553236116209700,
"author_id": 598041720583618600,
"author_name": "Disorganized",
"timestamp": "03/29/2022 22:28:20",
"content": "any questions?",
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},
{
"id": 958553393092235300,
"author_id": 301752011962056700,
"author_name": "RudyTheButler",
"timestamp": "03/29/2022 22:28:57",
"content": "Hmmm, it seems that symbol lab claims that there is 2 solutions though",
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},
{
"id": 958553482145706000,
"author_id": 301752011962056700,
"author_name": "RudyTheButler",
"timestamp": "03/29/2022 22:29:19",
"content": "Also I am not sure if the square root is correct",
"attachments": [],
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},
{
"id": 958553538512953300,
"author_id": 598041720583618600,
"author_name": "Disorganized",
"timestamp": "03/29/2022 22:29:32",
"content": "square root?",
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},
{
"id": 958553655160737800,
"author_id": 301752011962056700,
"author_name": "RudyTheButler",
"timestamp": "03/29/2022 22:30:00",
"content": "Yes, symbol lab claims that:",
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"id": 958553730905702400,
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"author_name": "RudyTheButler",
"timestamp": "03/29/2022 22:30:18",
"content": "But I may have inputted it incorrectly:",
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"id": 958553840884543600,
"author_id": 598041720583618600,
"author_name": "Disorganized",
"timestamp": "03/29/2022 22:30:44",
"content": "where's the coefficient of 2 on the RHS?",
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},
{
"id": 958553878520029200,
"author_id": 598041720583618600,
"author_name": "Disorganized",
"timestamp": "03/29/2022 22:30:53",
"content": "oh wait",
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},
{
"id": 958553954508238800,
"author_id": 598041720583618600,
"author_name": "Disorganized",
"timestamp": "03/29/2022 22:31:11",
"content": "nvermnd",
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"reference": null
},
{
"id": 958554060393447400,
"author_id": 598041720583618600,
"author_name": "Disorganized",
"timestamp": "03/29/2022 22:31:37",
"content": "I might have started with the wrong thing",
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},
{
"id": 958554068622655600,
"author_id": 598041720583618600,
"author_name": "Disorganized",
"timestamp": "03/29/2022 22:31:39",
"content": "one sec",
"attachments": [],
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},
{
"id": 958554254740697100,
"author_id": 301752011962056700,
"author_name": "RudyTheButler",
"timestamp": "03/29/2022 22:32:23",
"content": "okay",
"attachments": [],
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},
{
"id": 958556060615053300,
"author_id": 598041720583618600,
"author_name": "Disorganized",
"timestamp": "03/29/2022 22:39:33",
"content": "got it",
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},
{
"id": 958556128793481200,
"author_id": 301752011962056700,
"author_name": "RudyTheButler",
"timestamp": "03/29/2022 22:39:50",
"content": "Awesome!",
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},
{
"id": 958556285807235100,
"author_id": 301752011962056700,
"author_name": "RudyTheButler",
"timestamp": "03/29/2022 22:40:27",
"content": "hmm",
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},
{
"id": 958556395270185000,
"author_id": 598041720583618600,
"author_name": "Disorganized",
"timestamp": "03/29/2022 22:40:53",
"content": "",
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"id": 958556515965501400,
"author_id": 301752011962056700,
"author_name": "RudyTheButler",
"timestamp": "03/29/2022 22:41:22",
"content": "Okay I am just tracing through your steps",
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},
{
"id": 958556854630367200,
"author_id": 301752011962056700,
"author_name": "RudyTheButler",
"timestamp": "03/29/2022 22:42:43",
"content": "Oh you used a different rule to start with it seems",
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},
{
"id": 958557101066715100,
"author_id": 598041720583618600,
"author_name": "Disorganized",
"timestamp": "03/29/2022 22:43:42",
"content": "notice that their answer retains log-base-3",
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},
{
"id": 958557213713109000,
"author_id": 301752011962056700,
"author_name": "RudyTheButler",
"timestamp": "03/29/2022 22:44:08",
"content": "hmm yes",
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},
{
"id": 958557488666529800,
"author_id": 301752011962056700,
"author_name": "RudyTheButler",
"timestamp": "03/29/2022 22:45:14",
"content": "Hmmm I think I am understanding it a little more now",
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},
{
"id": 958557573697642600,
"author_id": 301752011962056700,
"author_name": "RudyTheButler",
"timestamp": "03/29/2022 22:45:34",
"content": "Alright I think I got it!",
"attachments": [],
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},
{
"id": 958557650675716100,
"author_id": 598041720583618600,
"author_name": "Disorganized",
"timestamp": "03/29/2022 22:45:53",
"content": "are the answers the same?",
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},
{
"id": 958557672377053200,
"author_id": 598041720583618600,
"author_name": "Disorganized",
"timestamp": "03/29/2022 22:45:58",
"content": "I haven't checked yet",
"attachments": [],
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"reference": null
},
{
"id": 958557717612621800,
"author_id": 598041720583618600,
"author_name": "Disorganized",
"timestamp": "03/29/2022 22:46:09",
"content": "algebraically or otherwise",
"attachments": [],
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},
{
"id": 958557767189270500,
"author_id": 598041720583618600,
"author_name": "Disorganized",
"timestamp": "03/29/2022 22:46:20",
"content": "I'm pretty confident.",
"attachments": [],
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},
{
"id": 958557777234636800,
"author_id": 301752011962056700,
"author_name": "RudyTheButler",
"timestamp": "03/29/2022 22:46:23",
"content": "Well symbol lab does say this:",
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"id": 958557977739161700,
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"author_name": "Disorganized",
"timestamp": "03/29/2022 22:47:11",
"content": "is that 3 supposed to be a factor of the denominator?",
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},
{
"id": 958558017207541800,
"author_id": 598041720583618600,
"author_name": "Disorganized",
"timestamp": "03/29/2022 22:47:20",
"content": "it's not under the fraction bar",
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},
{
"id": 958558082919723000,
"author_id": 301752011962056700,
"author_name": "RudyTheButler",
"timestamp": "03/29/2022 22:47:36",
"content": "that is correct",
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},
{
"id": 958558156634587100,
"author_id": 301752011962056700,
"author_name": "RudyTheButler",
"timestamp": "03/29/2022 22:47:53",
"content": "It is not under the fraction bar",
"attachments": [],
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},
{
"id": 958558264235270100,
"author_id": 598041720583618600,
"author_name": "Disorganized",
"timestamp": "03/29/2022 22:48:19",
"content": "ok, well it's still a factor of the denominator, I guess",
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},
{
"id": 958558318413119500,
"author_id": 598041720583618600,
"author_name": "Disorganized",
"timestamp": "03/29/2022 22:48:32",
"content": "I'll check the positive case",
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},
{
"id": 958558373324914700,
"author_id": 301752011962056700,
"author_name": "RudyTheButler",
"timestamp": "03/29/2022 22:48:45",
"content": "It may be the same",
"attachments": [],
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},
{
"id": 958558658516627500,
"author_id": 598041720583618600,
"author_name": "Disorganized",
"timestamp": "03/29/2022 22:49:53",
"content": "so the positive answer that I got is approximately",
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},
{
"id": 958558720281948300,
"author_id": 598041720583618600,
"author_name": "Disorganized",
"timestamp": "03/29/2022 22:50:08",
"content": "2.414602465",
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},
{
"id": 958558838695542800,
"author_id": 301752011962056700,
"author_name": "RudyTheButler",
"timestamp": "03/29/2022 22:50:36",
"content": "Hmmm",
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},
{
"id": 958558917997264900,
"author_id": 301752011962056700,
"author_name": "RudyTheButler",
"timestamp": "03/29/2022 22:50:55",
"content": "I will check that with my calculator",
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},
{
"id": 958559986626216000,
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"author_name": "RudyTheButler",
"timestamp": "03/29/2022 22:55:09",
"content": "Okay interestingly enough I am getting a \"Nonreal Answers\" error",
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},
{
"id": 958560106809794600,
"author_id": 301752011962056700,
"author_name": "RudyTheButler",
"timestamp": "03/29/2022 22:55:38",
"content": "Though I am pretty sure I entered everything exactly as written",
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},
{
"id": 958560130058817500,
"author_id": 598041720583618600,
"author_name": "Disorganized",
"timestamp": "03/29/2022 22:55:44",
"content": "yeah, I'm not getting the same values but I keep getting different answers for their work b.c. I'm trying to jam it into my scientific and it's hard",
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},
{
"id": 958560181090926600,
"author_id": 598041720583618600,
"author_name": "Disorganized",
"timestamp": "03/29/2022 22:55:56",
"content": "I'ma try wolfram so I know I got the same thing",
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},
{
"id": 958560236032102400,
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"author_name": "RudyTheButler",
"timestamp": "03/29/2022 22:56:09",
"content": "Okay sounds good that may work better",
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},
{
"id": 958561591366918100,
"author_id": 598041720583618600,
"author_name": "Disorganized",
"timestamp": "03/29/2022 23:01:32",
"content": "ok so their positive root is imaginary",
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},
{
"id": 958561715983880200,
"author_id": 598041720583618600,
"author_name": "Disorganized",
"timestamp": "03/29/2022 23:02:02",
"content": "meaning I messed something up either in my algebra or more likely my crunching\\",
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{
"id": 958562014907727900,
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"author_name": "RudyTheButler",
"timestamp": "03/29/2022 23:03:13",
"content": "Ohhh I see",
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},
{
"id": 958562064014639100,
"author_id": 301752011962056700,
"author_name": "RudyTheButler",
"timestamp": "03/29/2022 23:03:25",
"content": "I wonder how they came up with the imaginary number",
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},
{
"id": 958562297071165400,
"author_id": 598041720583618600,
"author_name": "Disorganized",
"timestamp": "03/29/2022 23:04:20",
"content": "negative argument for the square root",
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},
{
"id": 958562338179543200,
"author_id": 598041720583618600,
"author_name": "Disorganized",
"timestamp": "03/29/2022 23:04:30",
"content": "mine is positive for some reason",
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},
{
"id": 958562358366699500,
"author_id": 598041720583618600,
"author_name": "Disorganized",
"timestamp": "03/29/2022 23:04:35",
"content": "I must have messed up",
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},
{
"id": 958562595512651800,
"author_id": 301752011962056700,
"author_name": "RudyTheButler",
"timestamp": "03/29/2022 23:05:32",
"content": "It may have been a negative that did not get factored somewhere yeah..",
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},
{
"id": 958562691390251000,
"author_id": 301752011962056700,
"author_name": "RudyTheButler",
"timestamp": "03/29/2022 23:05:54",
"content": "I feel like what you did though makes sense though",
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},
{
"id": 958562786437374000,
"author_id": 301752011962056700,
"author_name": "RudyTheButler",
"timestamp": "03/29/2022 23:06:17",
"content": "Although, it is hard to wrap my head around it",
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},
{
"id": 958563049160208500,
"author_id": 301752011962056700,
"author_name": "RudyTheButler",
"timestamp": "03/29/2022 23:07:20",
"content": "By the way thank you for helping me so far. This gives me enough to figure out what a viable process should be in the least",
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"timestamp": "03/29/2022 23:08:40",
"content": "ok, let me try this now",
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"timestamp": "03/29/2022 23:08:48",
"content": "one term is different by a factor of 2",
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"content": "Hmm",
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"timestamp": "03/29/2022 23:11:41",
"content": "well...I just got a different wrong answer",
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"timestamp": "03/29/2022 23:11:46",
"content": "what class is this for?",
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"timestamp": "03/29/2022 23:11:57",
"content": "This is actually for a history of math course lol",
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"timestamp": "03/29/2022 23:12:09",
"content": "oh, I ducked out of that one",
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"timestamp": "03/29/2022 23:12:15",
"content": "teacher was a real chode",
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"timestamp": "03/29/2022 23:12:31",
"content": "he would brag at the start of every meeting about how many decimal places of pi he could compute",
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"timestamp": "03/29/2022 23:12:45",
"content": "Oh wow that is absolutely terrible",
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"timestamp": "03/29/2022 23:12:55",
"content": "lol",
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"author_name": "RudyTheButler",
"timestamp": "03/29/2022 23:14:41",
"content": "Well, considering that this is a history of math course it would not surprise me that there are these \"unsolved\" mysteries out there",
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"timestamp": "03/29/2022 23:14:54",
"content": "This one that we are doing may just be one of them",
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"author_name": "RudyTheButler",
"timestamp": "03/29/2022 23:15:10",
"content": "But I honestly do no know",
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"id": 958565093883396200,
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"timestamp": "03/29/2022 23:15:27",
"content": "no...there's a rule we aren't using",
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"author_name": "Disorganized",
"timestamp": "03/29/2022 23:15:42",
"content": "that has to do with computing complex inputs of logarithms",
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"timestamp": "03/29/2022 23:15:52",
"content": "something we are supposed to be mindful of",
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"timestamp": "03/29/2022 23:16:05",
"content": "I didn't finish complex analysis",
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"timestamp": "03/29/2022 23:17:38",
"content": "Right, I honestly did not get to that either",
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"timestamp": "03/29/2022 23:18:41",
"content": "these solutions look real to me",
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"timestamp": "03/29/2022 23:18:55",
"content": "Haha right",
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"timestamp": "03/29/2022 23:19:01",
"content": "in fact, this positive answer is approximately what I just got",
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"timestamp": "03/29/2022 23:20:53",
"content": "$x=\\pm \\sqrt{10^{\\frac{2\\left(\\log{2}\\right)^2 - \\left(\\log{3}\\right)^2}{\\log{3}-\\log{2}}}}$",
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"timestamp": "03/29/2022 23:21:15",
"content": "dude...",
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"id": 958566557804548100,
"author_id": 598041720583618600,
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"timestamp": "03/29/2022 23:21:16",
"content": "the 3",
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"id": 958566568437113000,
"author_id": 598041720583618600,
"author_name": "Disorganized",
"timestamp": "03/29/2022 23:21:19",
"content": "it's a base",
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"id": 958566586376142800,
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"timestamp": "03/29/2022 23:21:23",
"content": "like the 10 here",
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"timestamp": "03/29/2022 23:21:32",
"content": "bro lol that is so weird!",
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"author_name": "TeXit",
"timestamp": "03/29/2022 23:21:44",
"content": "**Disorganized**",
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"timestamp": "03/29/2022 23:21:57",
"content": "Haha nice",
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"id": 958566771357548500,
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"timestamp": "03/29/2022 23:22:07",
"content": "this is assuming that log is base 10",
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"id": 958566821060051100,
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"timestamp": "03/29/2022 23:22:19",
"content": "if log were base e, the base would be e",
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"id": 958566854916440200,
"author_id": 598041720583618600,
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"timestamp": "03/29/2022 23:22:27",
"content": "instead of 10 here",
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{
"id": 958566887548145700,
"author_id": 598041720583618600,
"author_name": "Disorganized",
"timestamp": "03/29/2022 23:22:35",
"content": "get what I'm saying?",
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"author_name": "RudyTheButler",
"timestamp": "03/29/2022 23:23:42",
"content": "Yeah that makes sense",
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"author_name": "RudyTheButler",
"timestamp": "03/29/2022 23:23:56",
"content": "It is just how these online editors display this information of bases",
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"author_name": "RudyTheButler",
"timestamp": "03/29/2022 23:24:19",
"content": "So if we review your method...",
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"timestamp": "03/29/2022 23:24:23",
"content": "I think..",
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"author_name": "RudyTheButler",
"timestamp": "03/29/2022 23:24:49",
"content": "I think you are correct!",
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"timestamp": "03/29/2022 23:25:08",
"content": "This one specifically",
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"timestamp": "03/29/2022 23:25:36",
"content": "Do you agree?",
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{
"id": 958567763423678500,
"author_id": 598041720583618600,
"author_name": "Disorganized",
"timestamp": "03/29/2022 23:26:04",
"content": "here it is in base e (same answer)",
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"timestamp": "03/29/2022 23:26:16",
"content": "plus-and-minus",
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"id": 958568010791149600,
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"author_name": "Disorganized",
"timestamp": "03/29/2022 23:27:03",
"content": "yeah this is the one from the writeup I did that you like best",
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"author_name": "Disorganized",
"timestamp": "03/29/2022 23:27:16",
"content": "the latex is me converting to base-10 instead of base-e",
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"id": 958568104693223400,
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"author_name": "Disorganized",
"timestamp": "03/29/2022 23:27:25",
"content": "it is ARBITRARY which base you use in change-of-base",
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"timestamp": "03/29/2022 23:27:37",
"content": "it's just convenient to use a base that calculators can crunch",
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"author_name": "RudyTheButler",
"timestamp": "03/29/2022 23:27:45",
"content": "Right, it was not specified in the assignment",
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"author_name": "RudyTheButler",
"timestamp": "03/29/2022 23:28:24",
"content": "Awesome, I think that may resolve this problem. Thanks a lot man. Do you think I should be aware of anything else?",
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"id": 958568379709550600,
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"timestamp": "03/29/2022 23:28:31",
"content": "no",
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"id": 958568392229523500,
"author_id": 598041720583618600,
"author_name": "Disorganized",
"timestamp": "03/29/2022 23:28:34",
"content": "except",
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},
{
"id": 958568470176473200,
"author_id": 598041720583618600,
"author_name": "Disorganized",
"timestamp": "03/29/2022 23:28:52",
"content": "don't go into teaching, and insist on programming courses in your college curriculum",
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"id": 958568493672960000,
"author_id": 598041720583618600,
"author_name": "Disorganized",
"timestamp": "03/29/2022 23:28:58",
"content": "applied math programming",
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"id": 958568568306401300,
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"author_name": "RudyTheButler",
"timestamp": "03/29/2022 23:29:16",
"content": "Ahh I see",
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"id": 958568656458121200,
"author_id": 301752011962056700,
"author_name": "RudyTheButler",
"timestamp": "03/29/2022 23:29:37",
"content": "Do you think programming would be more favorable?",
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{
"id": 958568744907595900,
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"author_name": "RudyTheButler",
"timestamp": "03/29/2022 23:29:58",
"content": "I am doing a couple of programming assignments actually lol",
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"id": 958568968195563500,
"author_id": 598041720583618600,
"author_name": "Disorganized",
"timestamp": "03/29/2022 23:30:51",
"content": "that just depends on what you want to do",
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"id": 958569065406926800,
"author_id": 598041720583618600,
"author_name": "Disorganized",
"timestamp": "03/29/2022 23:31:14",
"content": "you will find work pretty easily if you are a very flexible programmer",
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{
"id": 958569138383646700,
"author_id": 598041720583618600,
"author_name": "Disorganized",
"timestamp": "03/29/2022 23:31:31",
"content": "well-rounded",
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},
{
"id": 958569203416313900,
"author_id": 598041720583618600,
"author_name": "Disorganized",
"timestamp": "03/29/2022 23:31:47",
"content": "who knows how to write complete programs",
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{
"id": 958569266842591200,
"author_id": 598041720583618600,
"author_name": "Disorganized",
"timestamp": "03/29/2022 23:32:02",
"content": "what are you in now?",
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"id": 958569303186215000,
"author_id": 301752011962056700,
"author_name": "RudyTheButler",
"timestamp": "03/29/2022 23:32:11",
"content": "Computer Science lol",
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"id": 958569356017668200,
"author_id": 598041720583618600,
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"timestamp": "03/29/2022 23:32:23",
"content": "ok, you're fine",
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{
"id": 958569550415269900,
"author_id": 598041720583618600,
"author_name": "Disorganized",
"timestamp": "03/29/2022 23:33:10",
"content": "if you decide you want to do GIS and shit like that, you can take graduate-level courses in numerical methods, optimization theory, etc",
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"author_name": "RudyTheButler",
"timestamp": "03/29/2022 23:33:54",
"content": "You mean for databases and artificial intelligence?",
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"id": 958569873095671800,
"author_id": 598041720583618600,
"author_name": "Disorganized",
"timestamp": "03/29/2022 23:34:27",
"content": "Geographic Information Systems",
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},
{
"id": 958569918138310700,
"author_id": 598041720583618600,
"author_name": "Disorganized",
"timestamp": "03/29/2022 23:34:37",
"content": "Google Maps, ArcGIS",
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},
{
"id": 958569934865190900,
"author_id": 598041720583618600,
"author_name": "Disorganized",
"timestamp": "03/29/2022 23:34:41",
"content": "NASA",
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},
{
"id": 958570048803442700,
"author_id": 598041720583618600,
"author_name": "Disorganized",
"timestamp": "03/29/2022 23:35:09",
"content": "Naval command",
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},
{
"id": 958570120844824600,
"author_id": 598041720583618600,
"author_name": "Disorganized",
"timestamp": "03/29/2022 23:35:26",
"content": "comp sci is a route there too",
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},
{
"id": 958570259424624600,
"author_id": 598041720583618600,
"author_name": "Disorganized",
"timestamp": "03/29/2022 23:35:59",
"content": "that's all",
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"id": 958570408314032100,
"author_id": 301752011962056700,
"author_name": "RudyTheButler",
"timestamp": "03/29/2022 23:36:34",
"content": "Yeah there is are a lot of options",
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"id": 958570580934795300,
"author_id": 301752011962056700,
"author_name": "RudyTheButler",
"timestamp": "03/29/2022 23:37:15",
"content": "Are you CS?",
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},
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"id": 958570751554912300,
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"author_name": "RudyTheButler",
"timestamp": "03/29/2022 23:37:56",
"content": "I presume all the math courses would had you studying for your phd lol",
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"author_name": "RudyTheButler",
"timestamp": "03/29/2022 23:40:20",
"content": "Well anyway, good luck in what you do man! Cheers! @Disorganized",
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] |
help-9
|
c435cf0c7b0d4dc6a927e4221d487e24
|
197,016 |
[
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"timestamp": "07/07/2022 10:20:22",
"content": "Available help channel!",
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},
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"id": 994612032898875500,
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"content": "u sub then trig sub",
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"id": 994616047049113600,
"author_id": 264901235834880000,
"author_name": "Modus",
"timestamp": "07/07/2022 10:49:04",
"content": "think about substitution that will make it of form 1/sqrt(1-u^2)",
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"id": 994616086332985300,
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"timestamp": "07/07/2022 10:49:14",
"content": "it's close to arcsin",
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"timestamp": "07/07/2022 10:49:30",
"content": "hello",
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"id": 994616182793572400,
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"author_name": "Sparky",
"timestamp": "07/07/2022 10:49:37",
"content": "new to server",
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},
{
"id": 994616194491490300,
"author_id": 989645494374498400,
"author_name": "Sparky",
"timestamp": "07/07/2022 10:49:39",
"content": "can i ask for help here",
"attachments": [],
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},
{
"id": 994616204947894300,
"author_id": 783190731589943300,
"author_name": "Madden",
"timestamp": "07/07/2022 10:49:42",
"content": "are you regular helper here?",
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},
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"id": 994616232374456300,
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"author_name": "Madden",
"timestamp": "07/07/2022 10:49:48",
"content": "ye I think (also new)",
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"author_name": "dldh06",
"timestamp": "07/07/2022 10:50:03",
"content": "#βhow-to-get-help",
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"author_name": "Sparky",
"timestamp": "07/07/2022 10:50:08",
"content": "k thanks",
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},
{
"id": 994616587988508800,
"author_id": 264901235834880000,
"author_name": "Modus",
"timestamp": "07/07/2022 10:51:13",
"content": "not really, you have a question?",
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"timestamp": "07/07/2022 10:51:51",
"content": "nah",
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"timestamp": "07/07/2022 10:56:52",
"content": "@Aditya Patel Has your question been resolved?",
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"timestamp": "07/07/2022 11:03:53",
"content": "First factoring out sth so that we get the 1/sqrt(1-...) and then do u sub as Modus has already said",
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"timestamp": "07/07/2022 11:11:52",
"content": "Channel closed",
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}
] |
help-9
|
efc01f5df77e44e89f87e731a18ec7f4
|
197,017 |
[
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"id": 994626945725763700,
"author_id": 456226577798135800,
"author_name": "Deleted User",
"timestamp": "07/07/2022 11:32:23",
"content": "simplify $\\frac{log_a{x}\\cdot log_b{x}}{log_a{x}+log_b{x}}$",
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"content": "@Deleted User Has your question been resolved?",
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"timestamp": "07/07/2022 11:47:34",
"content": "@Helpers",
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"id": 994632262127734900,
"author_id": 347122115071442940,
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"timestamp": "07/07/2022 11:53:30",
"content": "Are you familiar with the change of base formula",
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"timestamp": "07/07/2022 11:54:59",
"content": "$log_a{x} = \\frac{log_b{x}}/{log_b{a}}$",
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"id": 994632646061731800,
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"timestamp": "07/07/2022 11:55:02",
"content": "**Syrenate**",
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"content": "oop",
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"id": 994632685223944200,
"author_id": 347122115071442940,
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"timestamp": "07/07/2022 11:55:11",
"content": "$log_a{x} = \\frac{log_b{x}}{log_b{a}}$",
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"timestamp": "07/07/2022 11:55:15",
"content": "**Syrenate**",
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"timestamp": "07/07/2022 12:06:12",
"content": "I did think about this but I'm not sure whether the base in the numerator and the denominator will be the same after you apply it",
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"timestamp": "07/07/2022 12:06:19",
"content": "does it not matter",
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"timestamp": "07/07/2022 12:06:30",
"content": "as long as they're all the same base it doesnt matter",
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"timestamp": "07/07/2022 12:07:24",
"content": "so can you just assume whatever you want",
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"timestamp": "07/07/2022 12:07:37",
"content": "as long as they are same of course",
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"timestamp": "07/07/2022 12:08:35",
"content": "yeah",
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"timestamp": "07/07/2022 12:08:56",
"content": "i chose 'a' in my solution but I suppose either would simplify to roughly the same",
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"timestamp": "07/07/2022 12:09:06",
"content": "you're welcome to try both though, as far as im aware",
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"timestamp": "07/07/2022 12:10:40",
"content": "I got my answer\n$\\log_{ab}{x}$",
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"timestamp": "07/07/2022 12:11:05",
"content": "thank you",
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"content": ".close",
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] |
help-9
|
3955882b7bbb4c1a9cb36afc622ef3e2
|
197,018 |
[
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"author_id": 701043425029652600,
"author_name": "Night WΓΈlf",
"timestamp": "07/07/2022 12:21:18",
"content": "$$sin(45+A)sin(45-A)= 1/2cos(2A)$$",
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"timestamp": "07/07/2022 12:21:21",
"content": "**Night WΓΈlf**",
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"author_name": "Night WΓΈlf",
"timestamp": "07/07/2022 12:21:28",
"content": "Guys any idea how to approach this proof?",
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"timestamp": "07/07/2022 12:36:28",
"content": "@Night WΓΈlf Has your question been resolved?",
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"content": "Channel closed",
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}
] |
help-9
|
7434487f35a342c59fc1db22e100ed2e
|
197,019 |
[
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"id": 994658160361091100,
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"author_name": "Mathematics Bot",
"timestamp": "07/07/2022 13:36:25",
"content": "Available help channel!",
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},
{
"id": 994658822377447600,
"author_id": 933067480929300500,
"author_name": "percn",
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"content": "Pinned a message.",
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"author_id": 933067480929300500,
"author_name": "percn",
"timestamp": "07/07/2022 13:39:14",
"content": "Can someone show me how to solve",
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},
{
"id": 994658917449744500,
"author_id": 264901235834880000,
"author_name": "Modus",
"timestamp": "07/07/2022 13:39:25",
"content": "u know definition of the derivative?",
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},
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"id": 994659015328018600,
"author_id": 933067480929300500,
"author_name": "percn",
"timestamp": "07/07/2022 13:39:49",
"content": "Not rlly",
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},
{
"id": 994659227220050000,
"author_id": 264901235834880000,
"author_name": "Modus",
"timestamp": "07/07/2022 13:40:39",
"content": "$$f'(x)=\\lim_{h \\to 0} \\frac{f(x+h)-f(x)}{h}$$",
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},
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"id": 994659239891042300,
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"timestamp": "07/07/2022 13:40:42",
"content": "**Modus**",
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"timestamp": "07/07/2022 13:40:54",
"content": "Okay yes ive seen that",
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"timestamp": "07/07/2022 13:41:13",
"content": "basically u need to solve that limit, usually it's about getting rid of \"h\"",
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"timestamp": "07/07/2022 13:41:41",
"content": "try with your c(x) = x^3",
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"timestamp": "07/07/2022 13:41:47",
"content": "Okay",
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"author_name": "Madden",
"timestamp": "07/07/2022 13:41:55",
"content": "def of derivative π",
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"timestamp": "07/07/2022 13:44:19",
"content": "@Modus can you start it off?",
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"timestamp": "07/07/2022 13:45:30",
"content": "Do you know what does c(x+h) mean?",
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"timestamp": "07/07/2022 13:45:40",
"content": "Maybe? Idk",
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"timestamp": "07/07/2022 13:46:31",
"content": "it means you're calculating value of the function for argument x + h, so basically you substitute \"x+h\" instead of \"x\" into c(x)",
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"timestamp": "07/07/2022 13:46:49",
"content": "like if c(x) was x^2 then c(x+h) would be (x+h)^2",
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"timestamp": "07/07/2022 13:46:59",
"content": "so if c(x) = x^3 then c(x+h) is...?",
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"timestamp": "07/07/2022 13:47:23",
"content": "Well yes i know that but not how everything is setup its the first time ive seen this equation",
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"timestamp": "07/07/2022 13:47:54",
"content": "F (x + h)^3 - f(x)^3",
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"timestamp": "07/07/2022 13:47:56",
"content": "?",
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"timestamp": "07/07/2022 13:48:15",
"content": "nope, c(x) = x^3",
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"timestamp": "07/07/2022 13:48:39",
"content": "it's c(x+h) - c(x) then",
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"timestamp": "07/07/2022 13:48:46",
"content": "so (x+h)^3 - x^3",
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"timestamp": "07/07/2022 13:48:49",
"content": "in the numerator",
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"timestamp": "07/07/2022 13:48:55",
"content": "What i just wrote",
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"timestamp": "07/07/2022 13:49:13",
"content": "But i kept the fβs",
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"timestamp": "07/07/2022 13:49:20",
"content": "idk, you've cubed whole function which is wrong",
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"timestamp": "07/07/2022 13:49:44",
"content": "So for now, you have:",
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"timestamp": "07/07/2022 13:50:17",
"content": "$$c'(x)=\\lim_{h \\to 0} \\frac{c(x+h)-c(x)}{h}=\\lim_{h\\ to 0} \\frac{(x+h)^3-x^3}{h}$$",
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"timestamp": "07/07/2022 13:50:19",
"content": "**Modus**",
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"timestamp": "07/07/2022 13:51:00",
"content": "don't write \"c\" if you substitue",
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"timestamp": "07/07/2022 13:51:04",
"content": "Okay",
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"timestamp": "07/07/2022 13:51:14",
"content": "if c(x) = x^3 then c(x+h) = (x+h)^3",
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"timestamp": "07/07/2022 13:51:22",
"content": "we write (x+h)^3 not c(x+h)^3",
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"timestamp": "07/07/2022 13:51:31",
"content": "because it isn't the same",
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"timestamp": "07/07/2022 13:51:31",
"content": "Alright",
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"timestamp": "07/07/2022 13:51:36",
"content": "you need to be careful here",
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"timestamp": "07/07/2022 13:51:49",
"content": "What comes next",
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"timestamp": "07/07/2022 13:52:19",
"content": "now you need to solve the limit, try to eliminate \"h\" from the denominator because you have 0/0 form",
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"timestamp": "07/07/2022 13:53:08",
"content": "hint: use a^3 - b^3 formula",
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"timestamp": "07/07/2022 13:55:51",
"content": "Need a refresher on that formula",
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"timestamp": "07/07/2022 13:56:26",
"content": "That eliminates h?",
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"timestamp": "07/07/2022 13:56:33",
"content": "yes",
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"timestamp": "07/07/2022 13:56:43",
"content": "How so",
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"timestamp": "07/07/2022 13:56:48",
"content": "in your case: a = x + h, b = x",
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"timestamp": "07/07/2022 13:57:04",
"content": "try to do this following formula I've sent",
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"timestamp": "07/07/2022 13:59:45",
"content": "Iβve completely messed it up",
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"timestamp": "07/07/2022 14:00:41",
"content": "you did it in the denominator",
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"timestamp": "07/07/2022 14:00:43",
"content": "why?",
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"timestamp": "07/07/2022 14:00:49",
"content": "there you have \"h\" only",
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"timestamp": "07/07/2022 14:01:10",
"content": "I dont know",
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"timestamp": "07/07/2022 14:01:20",
"content": "by \"this eliminates h\" I meant after that we will be able to get rid of \"h\" (cancel it out)",
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"timestamp": "07/07/2022 14:01:33",
"content": "do this, but in the numerator",
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"timestamp": "07/07/2022 14:01:41",
"content": "Are the numbers correct?",
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"timestamp": "07/07/2022 14:02:18",
"content": "multiplication here",
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"timestamp": "07/07/2022 14:02:30",
"content": "and why h(x)?, just x * h",
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"timestamp": "07/07/2022 14:02:39",
"content": "rest looks quite good",
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"timestamp": "07/07/2022 14:04:19",
"content": "Doesnβt a equal x + h",
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"content": "Thatβs why i had it as a plus and not multiply",
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"content": "@Modus",
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"timestamp": "07/07/2022 14:08:04",
"content": "bro",
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"timestamp": "07/07/2022 14:08:19",
"content": "why have you stayed with (x+h)^3 - x^3 ?",
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"timestamp": "07/07/2022 14:08:47",
"content": "I dont know?",
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"timestamp": "07/07/2022 14:08:54",
"content": "Wdym",
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"timestamp": "07/07/2022 14:10:59",
"content": "look",
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"timestamp": "07/07/2022 14:11:24",
"content": "$$(x+h)^{3}-x^{3}=(x+h-x)((x+h)^{2}+xh+x^{2})$$",
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"timestamp": "07/07/2022 14:11:26",
"content": "**Modus**",
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"timestamp": "07/07/2022 14:11:42",
"content": "so you plug the RHS instead of LHS in the numerator",
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"timestamp": "07/07/2022 14:11:59",
"content": "Oh",
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"content": "I see now it was a^3-b^3 so that makes sense",
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"content": "So this should cancel out h now?",
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"content": "@Modus",
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"timestamp": "07/07/2022 14:16:04",
"content": "yes",
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"timestamp": "07/07/2022 14:16:10",
"content": "because x + h - x = h",
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"timestamp": "07/07/2022 14:16:31",
"content": "now you can plug h = 0 into this expression and calculate",
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"content": "@Modus",
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"timestamp": "07/07/2022 14:18:29",
"content": "a sorry",
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"timestamp": "07/07/2022 14:18:42",
"content": "middle term in the 2nd bracket should be x(x+h)",
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"timestamp": "07/07/2022 14:19:08",
"content": "because a = x + h, b = x",
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"timestamp": "07/07/2022 14:19:12",
"content": "Where?",
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"timestamp": "07/07/2022 14:19:29",
"content": "On the x * h term?",
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"content": "yes",
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"timestamp": "07/07/2022 14:21:16",
"content": "yea, 3x^2 is valid",
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"timestamp": "07/07/2022 14:21:28",
"content": "Ok. What is next?",
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"timestamp": "07/07/2022 14:21:45",
"content": "that's all for the 1st example",
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"timestamp": "07/07/2022 14:21:51",
"content": "derivative of x^3 is 3x^2",
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"timestamp": "07/07/2022 14:22:57",
"content": "Ok i want to try for square root of x",
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"timestamp": "07/07/2022 14:23:18",
"content": "Is it any different process",
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"timestamp": "07/07/2022 14:24:07",
"content": "a bit different if it comes to cancelling out \"h\"",
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"timestamp": "07/07/2022 14:24:28",
"content": "for this one, you should multiply by conjugate of the numerator",
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"timestamp": "07/07/2022 14:25:03",
"content": "process similar to the process of removing irrationality from the denominator",
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"timestamp": "07/07/2022 14:25:11",
"content": "of rational expression",
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"timestamp": "07/07/2022 14:25:19",
"content": "Do i start like this?",
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"timestamp": "07/07/2022 14:25:34",
"content": "yes but",
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"timestamp": "07/07/2022 14:26:31",
"content": "and you should write limes before the expression until you don't calculate it",
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"timestamp": "07/07/2022 14:26:32",
"content": "like",
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"timestamp": "07/07/2022 14:26:50",
"content": "$$f'(x)=\\lim_{h \\to 0} \\frac{\\sqrt{x+h}-\\sqrt{x}}{h}$$",
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"timestamp": "07/07/2022 14:26:53",
"content": "**Modus**",
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"timestamp": "07/07/2022 14:29:49",
"content": "Do i do a-b again?",
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"timestamp": "07/07/2022 14:30:16",
"content": "not really",
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"timestamp": "07/07/2022 14:30:21",
"content": "it wouldn't work",
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"timestamp": "07/07/2022 14:31:06",
"content": "You should multiply the numerator and the denominator by conjugate:\n$$[...] \\cdot \\frac{\\sqrt{x+h}+\\sqrt{x}}{\\sqrt{x+h}+\\sqrt{x}}$$",
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"timestamp": "07/07/2022 14:31:09",
"content": "**Modus**",
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"timestamp": "07/07/2022 14:31:31",
"content": "then use formula (a-b)(a+b) = a^2 - b^2 in the numerator",
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"timestamp": "07/07/2022 14:33:25",
"content": "Like this?",
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"timestamp": "07/07/2022 14:33:48",
"content": "be careful with the brackets",
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"timestamp": "07/07/2022 14:35:05",
"content": "Okay I fixed them where do I go next",
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"timestamp": "07/07/2022 14:36:30",
"content": "use (a-b)(a+b) = a^2 - b^2\nwhere:\na = sqrt(x+h)\nb = sqrt(x)",
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"timestamp": "07/07/2022 14:38:24",
"content": "This right @Modus",
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"timestamp": "07/07/2022 14:38:35",
"content": "yes",
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"timestamp": "07/07/2022 14:38:40",
"content": "proceed",
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"timestamp": "07/07/2022 14:39:14",
"content": "Not sure how to",
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"timestamp": "07/07/2022 14:40:29",
"content": "?",
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"timestamp": "07/07/2022 14:40:41",
"content": "Do i get rid of denominator",
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"timestamp": "07/07/2022 14:42:41",
"content": "I mean numerator",
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"timestamp": "07/07/2022 14:43:07",
"content": "what is sqrt(5) ^ 2",
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"timestamp": "07/07/2022 14:43:36",
"content": "Iβm not sure?",
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"timestamp": "07/07/2022 14:43:49",
"content": "$$(\\sqrt{a})^{2}=a$$",
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"timestamp": "07/07/2022 14:43:52",
"content": "**Modus**",
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"timestamp": "07/07/2022 14:44:07",
"content": "(for a >= 0)",
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"timestamp": "07/07/2022 14:44:20",
"content": "So a = 0",
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"timestamp": "07/07/2022 14:44:24",
"content": "I mean",
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"timestamp": "07/07/2022 14:44:30",
"content": "you can simplify your numerator",
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"timestamp": "07/07/2022 14:44:55",
"content": "Yes by taking away a because it equals 0",
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"timestamp": "07/07/2022 14:45:04",
"content": "ehh, it was an example",
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"timestamp": "07/07/2022 14:45:23",
"content": "$$(\\sqrt{x})^2=x$$",
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"timestamp": "07/07/2022 14:45:29",
"content": "same with sqrt(x+h)",
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"timestamp": "07/07/2022 14:45:35",
"content": "**Modus**",
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"timestamp": "07/07/2022 14:45:52",
"content": "I'm a bit lost",
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"content": "I see that but what comes after",
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"timestamp": "07/07/2022 14:46:55",
"content": "you see what will you get in the numerator?",
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"timestamp": "07/07/2022 14:47:22",
"content": "Yes",
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"id": 994676065454784600,
"author_id": 264901235834880000,
"author_name": "Modus",
"timestamp": "07/07/2022 14:47:34",
"content": "tell me",
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"id": 994676153652609000,
"author_id": 933067480929300500,
"author_name": "percn",
"timestamp": "07/07/2022 14:47:55",
"content": "X+h - x",
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},
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"id": 994676206958031000,
"author_id": 264901235834880000,
"author_name": "Modus",
"timestamp": "07/07/2022 14:48:07",
"content": "which is...?",
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"id": 994676298335146100,
"author_id": 933067480929300500,
"author_name": "percn",
"timestamp": "07/07/2022 14:48:29",
"content": "Not sure",
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"id": 994676456573644800,
"author_id": 264901235834880000,
"author_name": "Modus",
"timestamp": "07/07/2022 14:49:07",
"content": "look at the previous example :v",
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"id": 994676543907446800,
"author_id": 264901235834880000,
"author_name": "Modus",
"timestamp": "07/07/2022 14:49:28",
"content": "or tell me what is x - x",
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"id": 994676596915044500,
"author_id": 933067480929300500,
"author_name": "percn",
"timestamp": "07/07/2022 14:49:40",
"content": "Oh it's h?",
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"timestamp": "07/07/2022 14:49:44",
"content": "yes",
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"id": 994676627059515400,
"author_id": 264901235834880000,
"author_name": "Modus",
"timestamp": "07/07/2022 14:49:48",
"content": "!!!",
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"author_id": 933067480929300500,
"author_name": "percn",
"timestamp": "07/07/2022 14:49:57",
"content": "Sorry bruh my brains is slow rn",
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"author_id": 264901235834880000,
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"timestamp": "07/07/2022 14:50:15",
"content": "now you can cancel out h and calculate the limit",
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"timestamp": "07/07/2022 14:51:44",
"content": "",
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"timestamp": "07/07/2022 14:52:22",
"content": "it's",
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"author_name": "Modus",
"timestamp": "07/07/2022 14:52:43",
"content": "$$\\lim_{h \\to 0} \\frac{1}{\\sqrt{x+h}+\\sqrt{x}}$$",
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"author_name": "TeXit",
"timestamp": "07/07/2022 14:52:45",
"content": "**Modus**",
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"timestamp": "07/07/2022 14:53:00",
"content": "Whers 1 from",
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"id": 994677553082159100,
"author_id": 264901235834880000,
"author_name": "Modus",
"timestamp": "07/07/2022 14:53:28",
"content": "you cancel \"h\" so in fact you divide the numerator and the denominator by h, right?",
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"timestamp": "07/07/2022 14:53:37",
"content": "Yes",
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"id": 994677614302208100,
"author_id": 264901235834880000,
"author_name": "Modus",
"timestamp": "07/07/2022 14:53:43",
"content": "what is h/h",
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"id": 994677635059822600,
"author_id": 933067480929300500,
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"timestamp": "07/07/2022 14:53:48",
"content": "1",
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"id": 994677663774023800,
"author_id": 264901235834880000,
"author_name": "Modus",
"timestamp": "07/07/2022 14:53:55",
"content": "so you have the answer",
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"id": 994677758598856800,
"author_id": 264901235834880000,
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"timestamp": "07/07/2022 14:54:17",
"content": "this is why it's 1/[...]",
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"id": 994677797589094500,
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"author_name": "percn",
"timestamp": "07/07/2022 14:54:27",
"content": "Yeah",
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"author_id": 933067480929300500,
"author_name": "percn",
"timestamp": "07/07/2022 14:54:36",
"content": "Do i sub in 0 for h next?",
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"id": 994678015076356100,
"author_id": 261933205387477000,
"author_name": "riemann",
"timestamp": "07/07/2022 14:55:19",
"content": "yes",
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"author_id": 933067480929300500,
"author_name": "percn",
"timestamp": "07/07/2022 14:56:09",
"content": "Is that final answer?",
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"timestamp": "07/07/2022 14:56:20",
"content": "1/2rootx",
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"id": 994678605584019500,
"author_id": 264901235834880000,
"author_name": "Modus",
"timestamp": "07/07/2022 14:57:39",
"content": "yes",
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"id": 994678682134249500,
"author_id": 933067480929300500,
"author_name": "percn",
"timestamp": "07/07/2022 14:57:58",
"content": "Alright thank you",
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"id": 994678751600316400,
"author_id": 933067480929300500,
"author_name": "percn",
"timestamp": "07/07/2022 14:58:14",
"content": "Gonna closw this",
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"id": 994678779811221500,
"author_id": 933067480929300500,
"author_name": "percn",
"timestamp": "07/07/2022 14:58:21",
"content": ".close",
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},
{
"id": 994678781379883000,
"author_id": 805217272087838700,
"author_name": "Mathematics Bot",
"timestamp": "07/07/2022 14:58:21",
"content": "Channel closed",
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}
] |
help-9
|
678f5647084545d8b9cc05fe87661985
|
197,020 |
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"author_name": "Mathematics Bot",
"timestamp": "07/07/2022 14:59:21",
"content": "Available help channel!",
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"timestamp": "07/07/2022 15:19:05",
"content": "What's next",
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"timestamp": "07/07/2022 15:20:17",
"content": "It's [d(x+h)-d(x)]/h",
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"timestamp": "07/07/2022 15:20:56",
"content": "Past that ive subbed e into it",
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"content": "e^(x+h) I think",
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"timestamp": "07/07/2022 15:21:37",
"content": "That's not what it was like for the last one",
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"timestamp": "07/07/2022 15:22:16",
"content": "probably because the last one wasn't an exponential function ?",
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"timestamp": "07/07/2022 15:22:30",
"content": "Yeah",
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"timestamp": "07/07/2022 15:22:42",
"content": "For x^3",
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"timestamp": "07/07/2022 15:23:38",
"content": "I dont think (x+h) turns into exponent tho",
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"content": "f(x+h) basically means that you replace every x with a (x+h)",
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"timestamp": "07/07/2022 15:24:33",
"content": "What does that look like in this question",
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"content": "@Modus",
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"content": ".",
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"timestamp": "07/07/2022 15:30:26",
"content": "@Kohlemaennchen",
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"timestamp": "07/07/2022 15:31:33",
"content": "You need to include the -e^x in te second one",
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"timestamp": "07/07/2022 15:32:02",
"content": "Ok then what is next step?",
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"content": "It's [d(x+h)-d(x)]/h",
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"content": "Why do you include d",
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"content": "[e^(x+h)-e^x]/h",
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"content": "Yes i have that",
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"timestamp": "07/07/2022 15:33:27",
"content": "Then factor out e^x",
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"timestamp": "07/07/2022 15:33:27",
"content": "Is that the starting equation?",
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"content": "Yes",
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"timestamp": "07/07/2022 15:34:04",
"content": "How is e^x factored out",
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"timestamp": "07/07/2022 15:34:09",
"content": "And it is the third last equation",
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"timestamp": "07/07/2022 15:34:33",
"content": "What",
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"timestamp": "07/07/2022 15:34:42",
"content": "e^(x+h) = e^x β’ e^h",
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"timestamp": "07/07/2022 15:35:15",
"content": "Like we need two more steps",
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"timestamp": "07/07/2022 15:36:02",
"content": "So the numerator is e^x β’ e^h - e^x",
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"content": "β
",
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"content": ".",
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"timestamp": "07/07/2022 15:37:08",
"content": "So e^h / h ?",
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"author_id": 774739847608139800,
"author_name": "Kohlemaennchen",
"timestamp": "07/07/2022 15:37:18",
"content": "No",
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"id": 994688682026086400,
"author_id": 933067480929300500,
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"timestamp": "07/07/2022 15:37:42",
"content": "What",
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"author_name": "Kohlemaennchen",
"timestamp": "07/07/2022 15:38:04",
"content": "e^x β’ [e^h-1]/h",
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"id": 994688966878036000,
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"author_name": "Kohlemaennchen",
"timestamp": "07/07/2022 15:38:50",
"content": "Is this clear?",
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"timestamp": "07/07/2022 15:39:14",
"content": "Yes",
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"timestamp": "07/07/2022 15:39:33",
"content": "β
",
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"author_id": 933067480929300500,
"author_name": "percn",
"timestamp": "07/07/2022 15:39:53",
"content": "Am i able to get rid of denominator?",
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"timestamp": "07/07/2022 15:41:37",
"content": "Or what comes next",
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"author_name": "Kohlemaennchen",
"timestamp": "07/07/2022 15:42:15",
"content": "So now we got a problem. The limit [e^h-1]/h is not so easy to proof. Either way we go, we basically need to recall definitions at some point",
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"timestamp": "07/07/2022 15:42:52",
"content": "Hmm okay?",
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"author_name": "Kohlemaennchen",
"timestamp": "07/07/2022 15:42:58",
"content": "You know there are many ways to go, but I advice this one:",
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"author_name": "Kohlemaennchen",
"timestamp": "07/07/2022 15:43:27",
"content": "write 1 as e^0 and e^h as e^(0+h)",
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"content": "",
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"author_name": "Kohlemaennchen",
"timestamp": "07/07/2022 15:46:16",
"content": "Exaktly. Everything but e^x is basically f\"(0)",
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"author_name": "percn",
"timestamp": "07/07/2022 15:46:37",
"content": "Wdym?",
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"author_name": "Kohlemaennchen",
"timestamp": "07/07/2022 15:47:25",
"content": "Look at the first Line and set x= 0",
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"author_name": "percn",
"timestamp": "07/07/2022 15:47:55",
"content": "I see",
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"author_name": "percn",
"timestamp": "07/07/2022 15:48:03",
"content": "So what do I change",
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"author_name": "Kohlemaennchen",
"timestamp": "07/07/2022 15:48:25",
"content": "f\"(x) = e^x * f\"(0)",
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"timestamp": "07/07/2022 15:49:40",
"content": "",
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"timestamp": "07/07/2022 15:50:09",
"content": "@Kohlemaennchen",
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"timestamp": "07/07/2022 15:50:12",
"content": "Like so?",
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"author_name": "Kohlemaennchen",
"timestamp": "07/07/2022 15:51:31",
"content": "Just f\"(0)* e^x",
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"author_name": "Modus",
"timestamp": "07/07/2022 15:51:49",
"content": "I'd rather recommend proving:\n$$\\lim_{h \\to 0} \\frac{e^h-1}{h}=1$$\nusing definition of e.",
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"timestamp": "07/07/2022 15:52:13",
"content": "Where did I go wrong",
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"author_name": "TeXit",
"timestamp": "07/07/2022 15:52:16",
"content": "**Modus**",
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"author_name": "Kohlemaennchen",
"timestamp": "07/07/2022 15:53:15",
"content": "You can do that as well, I was refering to another known defintion of e. But yours might be better.",
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"timestamp": "07/07/2022 15:53:40",
"content": "but it's interesting I've never seen that before :d",
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"author_name": "Kohlemaennchen",
"timestamp": "07/07/2022 15:53:43",
"content": "Do you want to take over?",
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"author_name": "percn",
"timestamp": "07/07/2022 15:53:45",
"content": "How far do I go back?",
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"timestamp": "07/07/2022 15:55:03",
"content": "@Modus u there",
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"timestamp": "07/07/2022 15:57:42",
"content": "$$\\lim_{h \\to 0} \\frac{e^h-1}{h}=1$$\nLet $u=e^{h}-1 \\iff h = \\ln (u+1)$.\nObviously if $h \\to 0$ then $u \\to 0$ as well.\nTherefore:\n$$\\lim_{u \\to 0} \\frac{u}{\\ln (u+1)}=\\lim_{u \\to 0} \\frac{1}{\\frac{1}{u} \\ln (u+1)}$$\nUsing property:\n$$c\\log_{a}b=\\log_{a}b^{c}$$\nwe have:\n$$\\lim_{u \\to 0} \\frac{1}{\\ln (u+1)^{\\frac{1}{u}}}=\\frac{1}{\\ln e}=1$$",
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"timestamp": "07/07/2022 15:58:03",
"content": "U can use this and you're done, that's only my tip",
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"author_name": "percn",
"timestamp": "07/07/2022 15:58:15",
"content": "Is that from restarting?",
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"id": 994694015742120000,
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"author_name": "percn",
"timestamp": "07/07/2022 15:58:53",
"content": "Iβm confused man",
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"author_name": "Kohlemaennchen",
"timestamp": "07/07/2022 15:59:23",
"content": "You need to delete the last line",
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"timestamp": "07/07/2022 16:00:08",
"content": "Then?",
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"timestamp": "07/07/2022 16:01:09",
"content": "**Modus**",
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"timestamp": "07/07/2022 16:02:30",
"content": "",
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"timestamp": "07/07/2022 16:02:32",
"content": "Lost",
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"author_name": "percn",
"timestamp": "07/07/2022 16:03:25",
"content": "@Kohlemaennchen",
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"timestamp": "07/07/2022 16:05:45",
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"author_name": "Kohlemaennchen",
"timestamp": "07/07/2022 16:06:35",
"content": "e^x * Lim h goes to 0 (e^h-1)/h",
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"author_name": "Kohlemaennchen",
"timestamp": "07/07/2022 16:07:00",
"content": "Then write this",
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"author_name": "Kohlemaennchen",
"timestamp": "07/07/2022 16:07:30",
"content": "And lastly write f'(x) = e^x *1",
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"timestamp": "07/07/2022 16:16:35",
"content": "Uh",
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"timestamp": "07/07/2022 16:18:52",
"content": "Man write what",
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"timestamp": "07/07/2022 16:19:05",
"content": "Can you show me please",
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"timestamp": "07/07/2022 16:19:11",
"content": "@Kohlemaennchen",
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"timestamp": "07/07/2022 16:19:29",
"content": "beautiful",
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"timestamp": "07/07/2022 16:19:48",
"content": "?",
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"timestamp": "07/07/2022 16:20:33",
"content": "where in kohl's work did you get lost?",
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"timestamp": "07/07/2022 16:22:17",
"content": "@riemann @Kohlemaennchen",
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"author_name": "riemann",
"timestamp": "07/07/2022 16:24:10",
"content": "couple things wrong. 1. you don't need the inserted equal sign on your line 2 between the limit and the fraction. 2. your f'(x) magically became e'(x) and lost e^x on your last line",
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"timestamp": "07/07/2022 16:24:41",
"content": "Yeah is it supposed to be f x or e x",
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"timestamp": "07/07/2022 16:25:00",
"content": "Or d x",
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"timestamp": "07/07/2022 16:25:58",
"content": "f'(x) stays f'(x)",
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"timestamp": "07/07/2022 16:26:01",
"content": "",
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"timestamp": "07/07/2022 16:27:05",
"content": "great",
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"timestamp": "07/07/2022 16:27:38",
"content": "Whatβs next?",
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"timestamp": "07/07/2022 16:28:34",
"content": "go back here",
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"timestamp": "07/07/2022 16:29:30",
"content": "And?",
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"content": "@Modus",
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"timestamp": "07/07/2022 16:32:20",
"content": "Sorry, but someone has to do this: f'(x) = e^x.",
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"content": "read the next line",
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"content": ".",
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"timestamp": "07/07/2022 16:32:37",
"content": "I'm always happy to come back online and be pinged 3 times π‘",
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"timestamp": "07/07/2022 16:32:57",
"content": "Because all 3 of you are saying different steps to doπ",
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"content": "Thatβs why Iβm going in circles",
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"content": "Thing is I guess you don't understand the concept, finding (e^x)' by definition isn't that easy, you had problems with x^3, so I'd recommend you to practice doing simpler examples.",
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"timestamp": "07/07/2022 16:35:31",
"content": "I want to finish the question",
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"content": "Answer is above, look carefully.",
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"timestamp": "07/07/2022 16:39:04",
"content": "Nah, after Modus took over we did not go in different directions.",
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"timestamp": "07/07/2022 16:39:22",
"content": "U guys really arenβt clear then",
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"timestamp": "07/07/2022 16:40:27",
"content": "None of you can write it out ?",
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"timestamp": "07/07/2022 16:40:55",
"content": "we're not here to do work for you",
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"timestamp": "07/07/2022 16:42:32",
"content": "plus, modus already proved this for you so",
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"timestamp": "07/07/2022 16:42:33",
"content": "Well, it's already written out. You're just having difficulties to write it on your own.",
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"timestamp": "07/07/2022 16:42:56",
"content": "Because im confused at how it works",
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"timestamp": "07/07/2022 16:43:00",
"content": "you did the mistake in 2. again",
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"timestamp": "07/07/2022 16:43:03",
"content": "If you can help me understand",
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"content": "You're in 11th grate?",
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"timestamp": "07/07/2022 16:43:52",
"content": "Is this supposed to be written?",
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"timestamp": "07/07/2022 16:43:59",
"content": "Nah",
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"content": "I wrote out what modus put",
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"timestamp": "07/07/2022 16:45:09",
"content": "Where?",
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"timestamp": "07/07/2022 16:45:34",
"content": "Here",
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"timestamp": "07/07/2022 16:46:00",
"content": "yes you did. but you also made the same mistake again",
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"timestamp": "07/07/2022 16:46:14",
"content": "e^x got lost",
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"timestamp": "07/07/2022 16:46:26",
"content": "Why does modus drop e^x",
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"timestamp": "07/07/2022 16:46:44",
"content": "modus never had it in the first place because that isn't part of the limit",
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"timestamp": "07/07/2022 16:47:11",
"content": "you're supposed to factor out e^x from the limit since the limit doesn't depend on x",
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"timestamp": "07/07/2022 16:47:37",
"content": "Ok where do i do that",
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"timestamp": "07/07/2022 16:48:01",
"content": "use rule 1 here\nhttps://tutorial.math.lamar.edu/classes/calci/limitsproperties.aspx",
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"timestamp": "07/07/2022 16:48:05",
"content": "Not Sure. But doesn't he skip so many steps that the proof becomes invalid?",
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"content": "are you talking about modus?",
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"timestamp": "07/07/2022 16:49:25",
"content": "this is perfectly rigorous",
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"timestamp": "07/07/2022 16:49:55",
"content": "I mean this",
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"timestamp": "07/07/2022 16:50:15",
"content": "What did I skip",
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"timestamp": "07/07/2022 16:50:22",
"content": "well yea it's almost all invalid as it stands",
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"content": "All invalid but its all Tobias work",
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"timestamp": "07/07/2022 16:51:08",
"content": "where is that tobias work?",
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"timestamp": "07/07/2022 16:51:20",
"content": "The first 3 lines",
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"timestamp": "07/07/2022 16:51:30",
"content": "The First 3 steps",
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"timestamp": "07/07/2022 16:51:33",
"content": "Then the last 3 is modus",
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"timestamp": "07/07/2022 16:51:59",
"content": "Together they create this",
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"timestamp": "07/07/2022 16:52:46",
"content": "nah. you just stitched what they said together incorrectly",
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"timestamp": "07/07/2022 16:53:01",
"content": "Okay how can i correct it?",
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"content": ".",
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"content": ".",
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"timestamp": "07/07/2022 16:54:56",
"content": "also you changed to u but left the limit variable as h.",
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"content": "you're just making algebra mistakes",
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"timestamp": "07/07/2022 16:56:07",
"content": "(or l'hop btw, idk if anyone's mentioned it, but it's pretty easy if you're fine with it)",
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"timestamp": "07/07/2022 16:56:17",
"content": "`a * (b-c)` is not equal to `a * b - c`",
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"timestamp": "07/07/2022 16:56:59",
"content": "Anyways, I go to bed now Good Luck riemann. It'd be great if we could once play chess",
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"timestamp": "07/07/2022 16:57:32",
"content": "thing is we're looking for the derivative of e^x and l' Hospital requires using it, so it isn't a good way I guess",
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"timestamp": "07/07/2022 16:57:47",
"content": "Yep true",
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"timestamp": "07/07/2022 16:57:55",
"content": "same mistake again",
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"timestamp": "07/07/2022 16:57:56",
"content": "Overlooked that π€¦ββοΈ",
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"timestamp": "07/07/2022 16:58:44",
"content": "I didnβt change to u",
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"content": "Itβs all h",
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"content": "you should because what you have is confusing",
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"content": "you use h for two separate variables",
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"timestamp": "07/07/2022 16:59:53",
"content": "is this a speedrun to you?",
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"timestamp": "07/07/2022 17:00:30",
"content": "U said i have basic Algebra mistakes as if its correct but a few things are written wrong",
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"timestamp": "07/07/2022 17:01:02",
"content": "Now ur telling me to switch variables",
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"content": "@Modus ??",
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"timestamp": "07/07/2022 17:01:13",
"content": "this is wrong. it's not equal to 1",
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"content": "Itβs copied from what modus put",
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"content": "if you read what modus wrote, it's correct.",
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"content": "Read it more carefully",
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"timestamp": "07/07/2022 17:01:43",
"content": "you used it incorrectly",
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"content": "You should try to understand the reason behind what he showed, and that should make it more obvious",
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"content": "it's like if you had `f = a * b` and i tell you `b = 5` and you put `f = a * b = 5`",
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"content": "review the basics\nhttps://www.cuemath.com/algebra/basic-of-algebra/",
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"content": "Iβm fine with basics thanks",
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"content": "This is my second derivative question ever",
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"content": "You should probably start with others",
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"content": "Clearly you're not",
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"content": "Lol copied modus",
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"content": "Writing",
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"content": "No you didn't",
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"content": "Copied wrong because your basics are lacking",
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"content": "See",
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"content": "You didn't realise there's no e^x in what modus put",
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"content": "Yeah i didnβt have e^x and rie kept telling me to put it in",
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"content": "you realize you did this right?",
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"content": "that part was correct",
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"timestamp": "07/07/2022 17:06:45",
"content": "modus was not claiming the derivative of e^x to be 1",
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"content": "They were claiming the limit (they showed), which is part of that expression for the derivative, to be 1",
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"content": "They didn't do all of the work for you",
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"timestamp": "07/07/2022 17:09:16",
"content": "Did most of it though",
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"timestamp": "07/07/2022 17:11:23",
"content": "You basically copied exactly what they put even down to the reversible equality (but missed a 1/u in the denominator of the second-to-last limit)",
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"content": "So sure I guess, but you should try to actually understand what they were saying",
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"timestamp": "07/07/2022 17:11:57",
"content": "Care to explain?",
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"content": "What part?",
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"content": ".",
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"content": "The substitution is just algebra that need not really be explained",
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"timestamp": "07/07/2022 17:13:15",
"content": "Is that how i find the derivative of that from start to finish?",
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"timestamp": "07/07/2022 17:13:16",
"content": "You do have to understand why (1+u)^(1/u) = e as u -> 0 though",
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"timestamp": "07/07/2022 17:13:21",
"content": "No",
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"timestamp": "07/07/2022 17:13:33",
"content": "Why no?",
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"timestamp": "07/07/2022 17:13:48",
"content": "Because it's not the limit you were actually working with",
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"timestamp": "07/07/2022 17:14:00",
"content": "There is an e^x missing",
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"timestamp": "07/07/2022 17:14:04",
"content": "Man",
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"timestamp": "07/07/2022 17:14:05",
"content": "Anyway",
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"author_name": "dk.dkn",
"timestamp": "07/07/2022 17:14:22",
"content": "Why is (1+u)^(1/u) = e as u -> 0?",
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"id": 994713188316758100,
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"timestamp": "07/07/2022 17:15:04",
"content": "No idea",
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"id": 994713241018187900,
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"timestamp": "07/07/2022 17:15:17",
"content": "let n = 1/u",
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"timestamp": "07/07/2022 17:15:42",
"content": "Then as u -> 0 (from the positive direction) n -> infinity",
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"timestamp": "07/07/2022 17:16:04",
"content": "We then have (1 + 1/n)^n as n -> infinity",
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"timestamp": "07/07/2022 17:16:17",
"content": "Do you recognise this limit now?",
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"timestamp": "07/07/2022 17:16:50",
"content": "Iβm high af i give up bro Iβm gonna call my tutor",
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"timestamp": "07/07/2022 17:17:45",
"content": "Not a bad idea",
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"timestamp": "07/07/2022 17:17:57",
"content": ".close",
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"timestamp": "07/07/2022 17:17:57",
"content": "Channel closed",
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}
] |
help-9
|
80e589ca6e034ffea06750c6595ce932
|
197,021 |
[
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"author_name": "Mathematics Bot",
"timestamp": "07/07/2022 17:18:57",
"content": "Available help channel!",
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{
"id": 994715281358344400,
"author_id": 766352996714938400,
"author_name": "mns",
"timestamp": "07/07/2022 17:23:23",
"content": "let z be a complex number, then the nth root is z^1/n = |z|^1/n * exp(i (arg(z)/n + 2kpi/n)) right?",
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"id": 994715282381742200,
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"timestamp": "07/07/2022 17:23:24",
"content": "then the principal root is when k = 0",
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"id": 994715283874922600,
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"content": "?",
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"timestamp": "07/07/2022 17:23:24",
"content": "Pinned a message.",
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"timestamp": "07/07/2022 17:31:34",
"content": "@mns Yea",
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"id": 994717619091427300,
"author_id": 766352996714938400,
"author_name": "mns",
"timestamp": "07/07/2022 17:32:41",
"content": "c0 is not the same for me",
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"timestamp": "07/07/2022 17:32:56",
"content": "so we have |z0| = 8",
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"timestamp": "07/07/2022 17:33:45",
"content": "theta_0 = tan^-1(-1) = -pi/4",
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"id": 994717994380972000,
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"author_name": "mns",
"timestamp": "07/07/2022 17:34:10",
"content": "so z0 = 8exp(i pi/4)",
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"id": 994718086689210500,
"author_id": 766352996714938400,
"author_name": "mns",
"timestamp": "07/07/2022 17:34:32",
"content": "then z0^1/3 = 2exp(i -pi/12 + 2kpi/3)",
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"id": 994718149423415400,
"author_id": 766352996714938400,
"author_name": "mns",
"timestamp": "07/07/2022 17:34:47",
"content": "for k = 0 we have 2exp(i -pi/12)",
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"id": 994718260530516000,
"author_id": 766352996714938400,
"author_name": "mns",
"timestamp": "07/07/2022 17:35:14",
"content": "then the principal root is given by 2(cos(-pi/12) + isin(-pi/12)) which is different from sqrt(2)(1+i)",
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"id": 994718298610610300,
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"author_name": "mns",
"timestamp": "07/07/2022 17:35:23",
"content": "what's wrong here'",
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"author_name": "Mathematics Bot",
"timestamp": "07/07/2022 17:50:23",
"content": "@mns Has your question been resolved?",
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"author_id": 884904554037141600,
"author_name": "dk.dkn",
"timestamp": "07/07/2022 18:20:27",
"content": "This angle is wrong",
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"id": 994729932246757500,
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"author_name": "dk.dkn",
"timestamp": "07/07/2022 18:21:37",
"content": "Itβs generally not a good idea to try to work out angles in this way",
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"timestamp": "07/07/2022 18:31:37",
"content": "@mns Has your question been resolved?",
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"id": 994733275962675200,
"author_id": 766352996714938400,
"author_name": "mns",
"timestamp": "07/07/2022 18:34:54",
"content": "how so?",
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},
{
"id": 994734485356687400,
"author_id": 884904554037141600,
"author_name": "dk.dkn",
"timestamp": "07/07/2022 18:39:42",
"content": "Think about the parity (even/odd) of the real and imaginary parts and decide if your argument seems reasonable",
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"author_name": "dk.dkn",
"timestamp": "07/07/2022 18:42:00",
"content": "Youβre off by -pi, and itβs basically to do with the range of arctan",
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},
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"id": 994735095942500400,
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"author_name": "mns",
"timestamp": "07/07/2022 18:42:08",
"content": "oh I see",
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},
{
"id": 994735143417815000,
"author_id": 884904554037141600,
"author_name": "dk.dkn",
"timestamp": "07/07/2022 18:42:19",
"content": "Itβs usually best to just imagine a right-angled triangle and make the necessary adjustments",
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"timestamp": "07/07/2022 18:43:15",
"content": "what do you mean?",
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},
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"author_id": 805217272087838700,
"author_name": "Mathematics Bot",
"timestamp": "07/07/2022 19:43:15",
"content": "@mns Has your question been resolved?",
"attachments": [],
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"timestamp": "07/07/2022 19:45:55",
"content": "Channel closed",
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}
] |
help-9
|
b8e795d251fb468ca9e851c66e5c2693
|
197,022 |
[
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"author_name": "Mathematics Bot",
"timestamp": "07/07/2022 20:50:25",
"content": "Available help channel!",
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},
{
"id": 994769358268154000,
"author_id": 841135943397539800,
"author_name": "Aaxrl",
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"content": "",
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"content": "Pinned a message.",
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"author_name": "Aaxrl",
"timestamp": "07/07/2022 20:59:24",
"content": "Is this the answer if I were to put it in signal radical form?",
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"author_id": 533543009774731260,
"author_name": "2 3 5 7",
"timestamp": "07/07/2022 21:00:30",
"content": "Yes",
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},
{
"id": 994770238346379300,
"author_id": 841135943397539800,
"author_name": "Aaxrl",
"timestamp": "07/07/2022 21:01:46",
"content": "Are you sure? I donβt want to go to a test and put the wrong answer-",
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{
"id": 994774014419534000,
"author_id": 805217272087838700,
"author_name": "Mathematics Bot",
"timestamp": "07/07/2022 21:16:47",
"content": "@Aaxrl Has your question been resolved?",
"attachments": [],
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"name": "Aaxrl",
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"id": 994779763279413200,
"author_id": 573905759134548000,
"author_name": "Nonna",
"timestamp": "07/07/2022 21:39:37",
"content": "Yes that's correct",
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},
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"id": 994780302964695000,
"author_id": 573905759134548000,
"author_name": "Nonna",
"timestamp": "07/07/2022 21:41:46",
"content": "@Aaxrl",
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"author_id": 841135943397539800,
"author_name": "Aaxrl",
"timestamp": "07/07/2022 21:41:57",
"content": "Okay thank you",
"attachments": [],
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"reference": null
},
{
"id": 994780369679306800,
"author_id": 841135943397539800,
"author_name": "Aaxrl",
"timestamp": "07/07/2022 21:42:02",
"content": ".close",
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},
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"id": 994780371612868600,
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"timestamp": "07/07/2022 21:42:02",
"content": "Channel closed",
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}
] |
help-9
|
58fb134476814380a353c9de94079549
|
197,023 |
[
{
"id": 994796442466140300,
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"author_name": "Mathematics Bot",
"timestamp": "07/07/2022 22:45:54",
"content": "Available help channel!",
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"reference": null
},
{
"id": 994798708023623700,
"author_id": 846597162149871600,
"author_name": "Jettπ₯",
"timestamp": "07/07/2022 22:54:54",
"content": "@Mathematics Bot",
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"content": "Pinned a message.",
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"id": 994798746393129100,
"author_id": 846597162149871600,
"author_name": "Jettπ₯",
"timestamp": "07/07/2022 22:55:03",
"content": "Could you help me",
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},
{
"id": 994798846909612000,
"author_id": 846597162149871600,
"author_name": "Jettπ₯",
"timestamp": "07/07/2022 22:55:27",
"content": "Please",
"attachments": [],
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},
{
"id": 994799065831317600,
"author_id": 846597162149871600,
"author_name": "Jettπ₯",
"timestamp": "07/07/2022 22:56:19",
"content": "SOMEONE I NEED HELP",
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},
{
"id": 994801629096329300,
"author_id": 884745462446448600,
"author_name": "jade π¦₯",
"timestamp": "07/07/2022 23:06:30",
"content": "",
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"timestamp": "07/07/2022 23:11:31",
"content": "@Jettπ₯ Has your question been resolved?",
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"timestamp": "07/07/2022 23:26:31",
"content": "Channel closed",
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}
] |
help-9
|
b939f4b3d83048cb8bedff14674733f0
|
197,024 |
[
{
"id": 994830189563486200,
"author_id": 805217272087838700,
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"timestamp": "07/08/2022 01:00:00",
"content": "Available help channel!",
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},
{
"id": 994837392521429100,
"author_id": 456226577798135800,
"author_name": "Deleted User",
"timestamp": "07/08/2022 01:28:37",
"content": "hi there",
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},
{
"id": 994837394568269800,
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"author_id": 456226577798135800,
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"timestamp": "07/08/2022 01:28:40",
"content": "for this question",
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},
{
"id": 994837408300404700,
"author_id": 456226577798135800,
"author_name": "Deleted User",
"timestamp": "07/08/2022 01:28:41",
"content": "https://gyazo.com/96aa016b80451a575677b5c0fc33cff8?token=0ab8a69130359395fa59a6901ce2fac9",
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"author_id": 456226577798135800,
"author_name": "Deleted User",
"timestamp": "07/08/2022 01:28:50",
"content": "how come a karnaugh table doesn't help?",
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{
"id": 994837494149427200,
"author_id": 456226577798135800,
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"timestamp": "07/08/2022 01:29:01",
"content": "i tried doing it and ended up with 97%",
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"id": 994837534469263500,
"author_id": 456226577798135800,
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"timestamp": "07/08/2022 01:29:11",
"content": "answer is 0.0479",
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},
{
"id": 994837997818228700,
"author_id": 183668144404037630,
"author_name": "Ann",
"timestamp": "07/08/2022 01:31:01",
"content": "what is a karnaugh table?",
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"timestamp": "07/08/2022 01:37:46",
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"content": "@Deleted User Has your question been resolved?",
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"id": 994844624373944400,
"author_id": 356908116429897700,
"author_name": "Kaynex",
"timestamp": "07/08/2022 01:57:21",
"content": "Hehe FU. Hehe.",
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},
{
"id": 994844781333188700,
"author_id": 356908116429897700,
"author_name": "Kaynex",
"timestamp": "07/08/2022 01:57:59",
"content": "I don't see where these values come from though?",
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"id": 994845015530541000,
"author_id": 456226577798135800,
"author_name": "Deleted User",
"timestamp": "07/08/2022 01:58:55",
"content": "that table does not relate to the question",
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},
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"id": 994845046983630800,
"author_id": 456226577798135800,
"author_name": "Deleted User",
"timestamp": "07/08/2022 01:59:02",
"content": "it's just showing what a karnaugh table is",
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"timestamp": "07/08/2022 01:59:18",
"content": "i did a similar one for the question i sent however i ended up with the wrong answer",
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"content": "@Deleted User Has your question been resolved?",
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"content": "@Deleted User Has your question been resolved?",
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] |
help-9
|
88cd69bb747b4f6d945ae0c5f50305c5
|
197,025 |
[
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"timestamp": "07/08/2022 06:10:04",
"content": "Available help channel!",
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},
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"id": 994911866864275500,
"author_id": 751516368159113300,
"author_name": "Dato",
"timestamp": "07/08/2022 06:24:33",
"content": "Why singleton set {a} is degenerate case of closed interval [a,b]?",
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"author_id": 751516368159113300,
"author_name": "Dato",
"timestamp": "07/08/2022 06:24:51",
"content": "*Cited from textbook",
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},
{
"id": 994912226488102900,
"author_id": 751516368159113300,
"author_name": "Dato",
"timestamp": "07/08/2022 06:25:59",
"content": "Isnt it a set {a,b}?",
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},
{
"id": 994912392410583000,
"author_id": 141791176540946430,
"author_name": "frownyfrog",
"timestamp": "07/08/2022 06:26:38",
"content": "an interval can't have two points",
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},
{
"id": 994912577270317200,
"author_id": 141791176540946430,
"author_name": "frownyfrog",
"timestamp": "07/08/2022 06:27:23",
"content": "[a,b] can't have finite amount of points in general, except that one",
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},
{
"id": 994912605766426600,
"author_id": 141791176540946430,
"author_name": "frownyfrog",
"timestamp": "07/08/2022 06:27:29",
"content": "where it's one point",
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},
{
"id": 994912812499468300,
"author_id": 751516368159113300,
"author_name": "Dato",
"timestamp": "07/08/2022 06:28:19",
"content": "Why it cant?",
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},
{
"id": 994912889502715900,
"author_id": 141791176540946430,
"author_name": "frownyfrog",
"timestamp": "07/08/2022 06:28:37",
"content": "i don't know why",
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},
{
"id": 994913193879146500,
"author_id": 265853506664136700,
"author_name": "ScapeProf",
"timestamp": "07/08/2022 06:29:50",
"content": "[0,1] means all x in R such that 0<=x<=1",
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"id": 994913254507814900,
"author_id": 265853506664136700,
"author_name": "ScapeProf",
"timestamp": "07/08/2022 06:30:04",
"content": "Why do you say it means {0,1}?",
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},
{
"id": 994913511731896400,
"author_id": 751516368159113300,
"author_name": "Dato",
"timestamp": "07/08/2022 06:31:05",
"content": "Idk. Why it should be just zero?",
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},
{
"id": 994913550197858300,
"author_id": 265853506664136700,
"author_name": "ScapeProf",
"timestamp": "07/08/2022 06:31:14",
"content": "What?",
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},
{
"id": 994913613968060400,
"author_id": 751516368159113300,
"author_name": "Dato",
"timestamp": "07/08/2022 06:31:30",
"content": "{0}",
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},
{
"id": 994913633337360500,
"author_id": 265853506664136700,
"author_name": "ScapeProf",
"timestamp": "07/08/2022 06:31:34",
"content": "What?",
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},
{
"id": 994913704263028900,
"author_id": 265853506664136700,
"author_name": "ScapeProf",
"timestamp": "07/08/2022 06:31:51",
"content": "[0,0] means all x in R such that 0<=x<=0",
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},
{
"id": 994913723032547500,
"author_id": 265853506664136700,
"author_name": "ScapeProf",
"timestamp": "07/08/2022 06:31:56",
"content": "Which is only {0}",
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},
{
"id": 994913742334722000,
"author_id": 265853506664136700,
"author_name": "ScapeProf",
"timestamp": "07/08/2022 06:32:00",
"content": "If that is what you are asking",
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},
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"id": 994913853999681500,
"author_id": 751516368159113300,
"author_name": "Dato",
"timestamp": "07/08/2022 06:32:27",
"content": "No",
"attachments": [],
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},
{
"id": 994913894659272700,
"author_id": 265853506664136700,
"author_name": "ScapeProf",
"timestamp": "07/08/2022 06:32:37",
"content": "Then speak in full sentences",
"attachments": [],
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},
{
"id": 994913972862062600,
"author_id": 751516368159113300,
"author_name": "Dato",
"timestamp": "07/08/2022 06:32:55",
"content": "Why singleton set {a} is degenerate case of closed interval [a,b]?",
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},
{
"id": 994914056911737000,
"author_id": 265853506664136700,
"author_name": "ScapeProf",
"timestamp": "07/08/2022 06:33:15",
"content": "I just told you how",
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},
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"id": 994914083126128800,
"author_id": 265853506664136700,
"author_name": "ScapeProf",
"timestamp": "07/08/2022 06:33:22",
"content": "[a,a]",
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},
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"id": 994914109629927600,
"author_id": 265853506664136700,
"author_name": "ScapeProf",
"timestamp": "07/08/2022 06:33:28",
"content": "Gives {a}",
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},
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"id": 994914133365502100,
"author_id": 265853506664136700,
"author_name": "ScapeProf",
"timestamp": "07/08/2022 06:33:34",
"content": ".",
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},
{
"id": 994914151086436500,
"author_id": 751516368159113300,
"author_name": "Dato",
"timestamp": "07/08/2022 06:33:38",
"content": "Oh",
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},
{
"id": 994914158107697200,
"author_id": 751516368159113300,
"author_name": "Dato",
"timestamp": "07/08/2022 06:33:39",
"content": "Sorry",
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},
{
"id": 994914180991828100,
"author_id": 751516368159113300,
"author_name": "Dato",
"timestamp": "07/08/2022 06:33:45",
"content": "Now i get it",
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},
{
"id": 994914236956430300,
"author_id": 751516368159113300,
"author_name": "Dato",
"timestamp": "07/08/2022 06:33:58",
"content": "Thank you",
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},
{
"id": 994914431031062500,
"author_id": 751516368159113300,
"author_name": "Dato",
"timestamp": "07/08/2022 06:34:44",
"content": "By degenerate case he meant [a]",
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"id": 994914516502597600,
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"timestamp": "07/08/2022 06:35:05",
"content": "[a,a]*",
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},
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"id": 994914595741384700,
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"author_name": "Dato",
"timestamp": "07/08/2022 06:35:24",
"content": ".close",
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},
{
"id": 994914597691719800,
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"timestamp": "07/08/2022 06:35:24",
"content": "Channel closed",
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}
] |
help-9
|
4e367a75b83c4979ab2b4fa3864df251
|
197,026 |
[
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"timestamp": "03/29/2022 23:41:22",
"content": "Available help channel!",
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},
{
"id": 958577626648297600,
"author_id": 418929679165030400,
"author_name": "nebb",
"timestamp": "03/30/2022 00:05:15",
"content": "quick question but where does the -pi/6 come from for multiplying the coordinates?",
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"timestamp": "03/30/2022 00:20:16",
"content": "@nebb Has your question been resolved?",
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help-9
|
c87f8d90514b40d48e0e296e1e578fe6
|
197,027 |
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help-9
|
678a7d5b51c5420392cf4f9118bef24e
|
197,028 |
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{
"id": 994978840059326600,
"author_id": 674994297644384300,
"author_name": "minto7",
"timestamp": "07/08/2022 10:50:41",
"content": "$3+5=2-5x$",
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"timestamp": "07/08/2022 10:50:43",
"content": "**minto7**",
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"timestamp": "07/08/2022 10:50:48",
"content": "can i add up 3+5?",
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"id": 994978923366600700,
"author_id": 264901235834880000,
"author_name": "Modus",
"timestamp": "07/08/2022 10:51:01",
"content": "yes",
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"timestamp": "07/08/2022 10:51:21",
"content": "can i do the same with 5x+3x?",
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"id": 994979023019057300,
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"timestamp": "07/08/2022 10:51:24",
"content": "same side",
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"author_name": "Umbraleviathan",
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"content": "If there is a 5x+3x, then you can combine them",
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"timestamp": "07/08/2022 10:59:14",
"content": "big thanks",
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"timestamp": "07/08/2022 10:59:15",
"content": ".close",
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}
] |
help-9
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c1759afc181944e3a56cf125259754f2
|
197,029 |
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"content": "Available help channel!",
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"id": 994982560423747700,
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"author_name": "Brotally",
"timestamp": "07/08/2022 11:05:28",
"content": "I'm a little confused on this problem",
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"content": "Draw a diagram",
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"author_name": "Brotally",
"timestamp": "07/08/2022 11:08:46",
"content": "uhh i drew a vector going from origin to Q3",
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"content": "It helps if you posted the diagram",
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"timestamp": "07/08/2022 11:11:56",
"content": "something like this",
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"id": 994985090700558500,
"author_id": 610937873981636600,
"author_name": "Brotally",
"timestamp": "07/08/2022 11:15:31",
"content": "so do use the info to make vectors?",
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"content": "@Helpers",
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"content": "@Brotally Has your question been resolved?",
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"timestamp": "07/08/2022 11:58:22",
"content": "@Helpers",
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"id": 994995939817312300,
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"timestamp": "07/08/2022 11:58:38",
"content": "@Helpers",
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"timestamp": "07/08/2022 12:08:39",
"content": "@Brotally Has your question been resolved?",
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"timestamp": "07/08/2022 13:01:53",
"content": "I think the second arrow is wrong",
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"timestamp": "07/08/2022 13:02:01",
"content": "It's supposed to be pointing west of north",
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"author_name": "Eric Tao",
"timestamp": "07/08/2022 13:02:26",
"content": "Once you draw the vectors, find the x and y components of each",
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},
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"author_id": 805217272087838700,
"author_name": "Mathematics Bot",
"timestamp": "07/08/2022 13:22:26",
"content": "@Brotally Has your question been resolved?",
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"author_id": 805217272087838700,
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"timestamp": "07/08/2022 14:22:26",
"content": "Channel closed",
"attachments": [],
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"reference": null
}
] |
help-9
|
cf7f4a492614417cb78d3ff07a9d2a1f
|
197,030 |
[
{
"id": 995032385525661700,
"author_id": 805217272087838700,
"author_name": "Mathematics Bot",
"timestamp": "07/08/2022 14:23:27",
"content": "Available help channel!",
"attachments": [],
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"reference": null
},
{
"id": 995034928125333600,
"author_id": 618992877846134800,
"author_name": "SnowZillin",
"timestamp": "07/08/2022 14:33:33",
"content": "hey im curious on why this is different",
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"timestamp": "07/08/2022 14:33:34",
"content": "Pinned a message.",
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"id": 995035022878851200,
"author_id": 391270706186420200,
"author_name": "illuminator3",
"timestamp": "07/08/2022 14:33:56",
"content": "different to what",
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},
{
"id": 995035038192242700,
"author_id": 618992877846134800,
"author_name": "SnowZillin",
"timestamp": "07/08/2022 14:33:59",
"content": "if -9^2=-9*-9=81 then nothing changed in this equation",
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},
{
"id": 995035058048077800,
"author_id": 618992877846134800,
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"timestamp": "07/08/2022 14:34:04",
"content": "answer",
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},
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"author_id": 618992877846134800,
"author_name": "SnowZillin",
"timestamp": "07/08/2022 14:34:11",
"content": "one solution is 12.29",
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},
{
"id": 995035096937660500,
"author_id": 391270706186420200,
"author_name": "illuminator3",
"timestamp": "07/08/2022 14:34:13",
"content": "oh no",
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},
{
"id": 995035102188945500,
"author_id": 618992877846134800,
"author_name": "SnowZillin",
"timestamp": "07/08/2022 14:34:15",
"content": "other is 14,5",
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},
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"id": 995035103338180700,
"author_id": 391270706186420200,
"author_name": "illuminator3",
"timestamp": "07/08/2022 14:34:15",
"content": "not this again",
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},
{
"id": 995035127468007600,
"author_id": 391270706186420200,
"author_name": "illuminator3",
"timestamp": "07/08/2022 14:34:21",
"content": "$-9^2 \\neq (-9)^2$",
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},
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"author_id": 510789298321096700,
"author_name": "TeXit",
"timestamp": "07/08/2022 14:34:23",
"content": "**illuminator3**",
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"timestamp": "07/08/2022 14:34:31",
"content": "$(-9)^2 = 81$",
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},
{
"id": 995035180626620500,
"author_id": 510789298321096700,
"author_name": "TeXit",
"timestamp": "07/08/2022 14:34:33",
"content": "**illuminator3**",
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"author_id": 391270706186420200,
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"timestamp": "07/08/2022 14:34:36",
"content": "while $$-9^2 = -81$$",
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},
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"id": 995035203653349400,
"author_id": 510789298321096700,
"author_name": "TeXit",
"timestamp": "07/08/2022 14:34:39",
"content": "**illuminator3**",
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"id": 995035243838976100,
"author_id": 618992877846134800,
"author_name": "SnowZillin",
"timestamp": "07/08/2022 14:34:48",
"content": "huh",
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},
{
"id": 995035263757734000,
"author_id": 618992877846134800,
"author_name": "SnowZillin",
"timestamp": "07/08/2022 14:34:53",
"content": "how",
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},
{
"id": 995035302592774300,
"author_id": 748029603087384700,
"author_name": "Yours truly",
"timestamp": "07/08/2022 14:35:03",
"content": "They just showed you how.",
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},
{
"id": 995035322314395800,
"author_id": 391270706186420200,
"author_name": "illuminator3",
"timestamp": "07/08/2022 14:35:07",
"content": "he",
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},
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"id": 995035333441888300,
"author_id": 391270706186420200,
"author_name": "illuminator3",
"timestamp": "07/08/2022 14:35:10",
"content": "$-n = -1 \\cdot n$",
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},
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"id": 995035340781932700,
"author_id": 618992877846134800,
"author_name": "SnowZillin",
"timestamp": "07/08/2022 14:35:12",
"content": "what do u do differently when -9^2 vs (-9)^2",
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},
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"id": 995035344300937300,
"author_id": 510789298321096700,
"author_name": "TeXit",
"timestamp": "07/08/2022 14:35:12",
"content": "**illuminator3**",
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"timestamp": "07/08/2022 14:35:15",
"content": "$-9^2 = -1 \\cdot 9^2 = -81$",
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},
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"id": 995035365171793900,
"author_id": 510789298321096700,
"author_name": "TeXit",
"timestamp": "07/08/2022 14:35:17",
"content": "**illuminator3**",
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"timestamp": "07/08/2022 14:35:28",
"content": "oh",
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"author_id": 391270706186420200,
"author_name": "illuminator3",
"timestamp": "07/08/2022 14:35:28",
"content": "$(-9)^2 = (-1 \\cdot 9)^2 = (-1)^2 \\cdot 9^2 = 1 \\cdot 81 = 81$",
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"id": 995035420259786800,
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"timestamp": "07/08/2022 14:35:31",
"content": "**illuminator3**",
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"timestamp": "07/08/2022 14:35:47",
"content": "ohhh",
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},
{
"id": 995035550065115300,
"author_id": 251063856032382980,
"author_name": "Diesel",
"timestamp": "07/08/2022 14:36:02",
"content": "One is - (9 * 9) and the other is -9 * -9",
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"id": 995035583984435300,
"author_id": 251063856032382980,
"author_name": "Diesel",
"timestamp": "07/08/2022 14:36:10",
"content": "Clear difference",
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},
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"id": 995035585284673700,
"author_id": 618992877846134800,
"author_name": "SnowZillin",
"timestamp": "07/08/2022 14:36:10",
"content": "yeaah",
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},
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"id": 995035609750048900,
"author_id": 618992877846134800,
"author_name": "SnowZillin",
"timestamp": "07/08/2022 14:36:16",
"content": "so",
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},
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"id": 995035639219224700,
"author_id": 618992877846134800,
"author_name": "SnowZillin",
"timestamp": "07/08/2022 14:36:23",
"content": "what would be -9^2 for this one",
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"id": 995035648920658000,
"author_id": 618992877846134800,
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"timestamp": "07/08/2022 14:36:25",
"content": "-81?",
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},
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"id": 995035693095075800,
"author_id": 618992877846134800,
"author_name": "SnowZillin",
"timestamp": "07/08/2022 14:36:36",
"content": "and that would make them equal",
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},
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"id": 995035705346641900,
"author_id": 618992877846134800,
"author_name": "SnowZillin",
"timestamp": "07/08/2022 14:36:39",
"content": "in my ss",
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},
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"id": 995035780810555500,
"author_id": 618992877846134800,
"author_name": "SnowZillin",
"timestamp": "07/08/2022 14:36:57",
"content": "it would",
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"id": 995035790524559500,
"author_id": 618992877846134800,
"author_name": "SnowZillin",
"timestamp": "07/08/2022 14:36:59",
"content": "thats crazy",
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"timestamp": "07/08/2022 14:37:03",
"content": "alr dope ty",
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"id": 995035816554397700,
"author_id": 618992877846134800,
"author_name": "SnowZillin",
"timestamp": "07/08/2022 14:37:05",
"content": ".close",
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},
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"id": 995035818496372900,
"author_id": 805217272087838700,
"author_name": "Mathematics Bot",
"timestamp": "07/08/2022 14:37:06",
"content": "Channel closed",
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}
] |
help-9
|
ae8d2bc6f7d041ea9d0296f1337ef4b4
|
197,031 |
[
{
"id": 995061162813165700,
"author_id": 805217272087838700,
"author_name": "Mathematics Bot",
"timestamp": "07/08/2022 16:17:48",
"content": "Available help channel!",
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},
{
"id": 995065600902705300,
"author_id": 857874096494084100,
"author_name": "Tangerine",
"timestamp": "07/08/2022 16:35:26",
"content": "I have to find the average rate of change between two points. I am lost on what formula to use and how to properly interpret a problem.",
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},
{
"id": 995065603708686300,
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"timestamp": "07/08/2022 16:35:27",
"content": "Pinned a message.",
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"timestamp": "07/08/2022 16:35:51",
"content": "^Question",
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"id": 995065853064261600,
"author_id": 857874096494084100,
"author_name": "Tangerine",
"timestamp": "07/08/2022 16:36:26",
"content": "^ What I think",
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"id": 995067013040971900,
"author_id": 797192290007384000,
"author_name": "Sm3",
"timestamp": "07/08/2022 16:41:03",
"content": "Could you not just use y2-y1 / x2-x1 ?",
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},
{
"id": 995067281572905000,
"author_id": 857874096494084100,
"author_name": "Tangerine",
"timestamp": "07/08/2022 16:42:07",
"content": "I could but thereβs another formula In worried I have to use",
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},
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"id": 995067395892850700,
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"author_name": "Tangerine",
"timestamp": "07/08/2022 16:42:34",
"content": "Idk if itβs this one or the one you mentioned",
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"id": 995068090670919700,
"author_id": 797192290007384000,
"author_name": "Sm3",
"timestamp": "07/08/2022 16:45:20",
"content": "Yes thats the same as the one I mentioned",
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},
{
"id": 995068307277348900,
"author_id": 857874096494084100,
"author_name": "Tangerine",
"timestamp": "07/08/2022 16:46:11",
"content": "So could you walk me through how to use that?",
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},
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"timestamp": "07/08/2022 16:46:44",
"content": "Didnβt you mentioned \n(Y2-Y1)/(X2-X1)",
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"id": 995068729538904000,
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"author_name": "Sm3",
"timestamp": "07/08/2022 16:47:52",
"content": "Yes so since its asking for the rate of change between x = 4 and 6, x2 is 6 and x1 is 4",
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},
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"id": 995068778696159400,
"author_id": 797192290007384000,
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"timestamp": "07/08/2022 16:48:04",
"content": "Then the y value of x=6 is y2",
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},
{
"id": 995068827203293200,
"author_id": 797192290007384000,
"author_name": "Sm3",
"timestamp": "07/08/2022 16:48:15",
"content": "With the y value of x=4 as y1",
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},
{
"id": 995069122167701600,
"author_id": 857874096494084100,
"author_name": "Tangerine",
"timestamp": "07/08/2022 16:49:26",
"content": "The graph is dynamic",
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"id": 995069176764960900,
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"author_name": "Tangerine",
"timestamp": "07/08/2022 16:49:39",
"content": "For I = 4 I got (4, 144)",
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},
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"id": 995069243752206300,
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"timestamp": "07/08/2022 16:49:55",
"content": "",
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"id": 995069848377892900,
"author_id": 857874096494084100,
"author_name": "Tangerine",
"timestamp": "07/08/2022 16:52:19",
"content": "Got it correct ππ½. Think I just need to practice and build my confident",
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},
{
"id": 995069883912044500,
"author_id": 857874096494084100,
"author_name": "Tangerine",
"timestamp": "07/08/2022 16:52:27",
"content": "thank you!",
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},
{
"id": 995069913809047800,
"author_id": 797192290007384000,
"author_name": "Sm3",
"timestamp": "07/08/2022 16:52:34",
"content": "Nice job",
"attachments": [],
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},
{
"id": 995069952853811200,
"author_id": 857874096494084100,
"author_name": "Tangerine",
"timestamp": "07/08/2022 16:52:44",
"content": "Just the whole βfunctionβ confuses me",
"attachments": [],
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},
{
"id": 995069987528126600,
"author_id": 797192290007384000,
"author_name": "Sm3",
"timestamp": "07/08/2022 16:52:52",
"content": "Yeah",
"attachments": [],
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},
{
"id": 995070032377815200,
"author_id": 797192290007384000,
"author_name": "Sm3",
"timestamp": "07/08/2022 16:53:03",
"content": "F(x) is mostly just a replacement for y",
"attachments": [],
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},
{
"id": 995070049914200200,
"author_id": 857874096494084100,
"author_name": "Tangerine",
"timestamp": "07/08/2022 16:53:07",
"content": "Stuff like this",
"attachments": [],
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},
{
"id": 995070180759703600,
"author_id": 857874096494084100,
"author_name": "Tangerine",
"timestamp": "07/08/2022 16:53:38",
"content": "Mostly?",
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},
{
"id": 995070363627159700,
"author_id": 857874096494084100,
"author_name": "Tangerine",
"timestamp": "07/08/2022 16:54:22",
"content": "Thatβs a really good way to think of it. I think you made it click for me, I asked my teacher. She kinda danced around that answer i feel like lol",
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"timestamp": "07/08/2022 16:54:39",
"content": "Glad I could help",
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"author_id": 857874096494084100,
"author_name": "Tangerine",
"timestamp": "07/08/2022 16:55:46",
"content": ".close",
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},
{
"id": 995070719052484600,
"author_id": 805217272087838700,
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"timestamp": "07/08/2022 16:55:46",
"content": "Channel closed",
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}
] |
help-9
|
90788bb032044825b36e9bbdf4ef8038
|
197,032 |
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"id": 995077421105680400,
"author_id": 805217272087838700,
"author_name": "Mathematics Bot",
"timestamp": "07/08/2022 17:22:24",
"content": "Available help channel!",
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},
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"author_name": "kangaroo rat",
"timestamp": "07/08/2022 18:21:14",
"content": "Can you tell me how product rule helps with multiplying in derivatives?",
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},
{
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"timestamp": "07/08/2022 18:21:15",
"content": "Pinned a message.",
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"author_id": 600510288067952600,
"author_name": "GarlicBredFries",
"timestamp": "07/08/2022 18:22:32",
"content": "Can you maybe expand a little more on what youre asking",
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},
{
"id": 995093444588486800,
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"author_name": "kangaroo rat",
"timestamp": "07/08/2022 18:26:05",
"content": "Someone said product rule help with multiplying derivatives like d/dx $3x^2*4x^3$",
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"timestamp": "07/08/2022 18:26:07",
"content": "**kangaroo rat**",
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"timestamp": "07/08/2022 18:26:30",
"content": "@GarlicBredFries does that help?",
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"author_name": "Denascite",
"timestamp": "07/08/2022 18:27:04",
"content": "well if you are just multiplying powers of x then you don't need the product rule",
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"id": 995093714349346800,
"author_id": 132304137583984640,
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"timestamp": "07/08/2022 18:27:09",
"content": "do you know what the product rule is?",
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"author_name": "GarlicBredFries",
"timestamp": "07/08/2022 18:27:34",
"content": "Multiplying derivatives?",
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},
{
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"author_id": 600510288067952600,
"author_name": "GarlicBredFries",
"timestamp": "07/08/2022 18:28:17",
"content": "Yeah i dont think product rule is necessary here",
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},
{
"id": 995094071246848100,
"author_id": 953140475693514800,
"author_name": "kangaroo rat",
"timestamp": "07/08/2022 18:28:34",
"content": "Yeah like if you were asked to find the derivative of $3x^2*4x^3$",
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"author_name": "TeXit",
"timestamp": "07/08/2022 18:28:37",
"content": "**kangaroo rat**",
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"timestamp": "07/08/2022 18:28:42",
"content": "Oh",
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"id": 995094225777598500,
"author_id": 132304137583984640,
"author_name": "Denascite",
"timestamp": "07/08/2022 18:29:11",
"content": "$3x^2\\cdot 4x^3=12x^5$",
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},
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"id": 995094235340611700,
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"author_name": "TeXit",
"timestamp": "07/08/2022 18:29:13",
"content": "**Denascite**",
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"timestamp": "07/08/2022 18:29:16",
"content": "and then you can use the normal power rule",
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"timestamp": "07/08/2022 18:29:29",
"content": "Oh",
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"author_name": "Denascite",
"timestamp": "07/08/2022 18:30:08",
"content": "the product rule is for example used to differentiate $f(x)=x\\cdot \\cos(x)$ where you can't just \"combine\" the factors",
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"timestamp": "07/08/2022 18:30:11",
"content": "**Denascite**",
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"timestamp": "07/08/2022 18:30:52",
"content": "Is that the same with +- and division",
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"author_name": "Denascite",
"timestamp": "07/08/2022 18:31:10",
"content": "what do you mean +- and division",
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{
"id": 995094866566586400,
"author_id": 953140475693514800,
"author_name": "kangaroo rat",
"timestamp": "07/08/2022 18:31:44",
"content": "like if instead of * it was +",
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"author_name": "Denascite",
"timestamp": "07/08/2022 18:31:45",
"content": "if you want to differentiate $ax^n + bx^m$ then you can apply the power rule to each term individually to get $nax^{n-1}+mbx^{m-1}$",
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"id": 995094937681023100,
"author_id": 261933205387477000,
"author_name": "riemann",
"timestamp": "07/08/2022 18:32:01",
"content": "you need to know all these\nhttps://www.math.ucdavis.edu/~kouba/Math17BHWDIRECTORY/Derivatives.pdf",
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"timestamp": "07/08/2022 18:32:15",
"content": "**Denascite**",
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"author_name": "riemann",
"timestamp": "07/08/2022 18:32:23",
"content": "if you haven't seen these derived, you should find videos on them",
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"timestamp": "07/08/2022 18:32:52",
"content": "but for $\\frac{ax^n}{bx^m}=\\frac{a}{b}x^{n-m}$ you use the normal power rule again",
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"id": 995095162525069300,
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"author_name": "TeXit",
"timestamp": "07/08/2022 18:32:54",
"content": "**Denascite**",
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"author_name": "kangaroo rat",
"timestamp": "07/08/2022 18:33:20",
"content": "Do you get this?",
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"id": 995095310105854000,
"author_id": 132304137583984640,
"author_name": "Denascite",
"timestamp": "07/08/2022 18:33:29",
"content": "I answered that",
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"author_name": "kangaroo rat",
"timestamp": "07/08/2022 18:33:39",
"content": "Iβll do that I know the first couple",
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"author_name": "kangaroo rat",
"timestamp": "07/08/2022 18:34:19",
"content": "And you added a + in",
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"author_name": "Denascite",
"timestamp": "07/08/2022 18:34:56",
"content": "I put a + instead of a *. just like you wanted",
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"id": 995095876160729100,
"author_id": 132304137583984640,
"author_name": "Denascite",
"timestamp": "07/08/2022 18:35:44",
"content": "the derivative of $3x^2+4x^3$ is $6x+12x^2$. here with some explicit numbers",
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"id": 995095886856204300,
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"author_name": "TeXit",
"timestamp": "07/08/2022 18:35:47",
"content": "**Denascite**",
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"timestamp": "07/08/2022 18:35:53",
"content": "apply power rule to each term individually",
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},
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"author_id": 953140475693514800,
"author_name": "kangaroo rat",
"timestamp": "07/08/2022 18:37:01",
"content": "Does power rule also work for multiplying, dividing and subtracting?",
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"author_name": "Denascite",
"timestamp": "07/08/2022 18:37:17",
"content": "subtraction yes. multiplyign and division no",
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"id": 995096277157150800,
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"author_name": "Denascite",
"timestamp": "07/08/2022 18:37:20",
"content": "like I said earlier",
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"author_name": "kangaroo rat",
"timestamp": "07/08/2022 18:37:34",
"content": "What do I use 4 them",
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"timestamp": "07/08/2022 18:37:45",
"content": "This",
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"author_name": "kangaroo rat",
"timestamp": "07/08/2022 18:37:52",
"content": "And what else",
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"author_id": 132304137583984640,
"author_name": "Denascite",
"timestamp": "07/08/2022 18:38:50",
"content": "if you have two powers of x that you multiply or divide. then you first have to combine them and second use the power rule",
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"author_name": "Denascite",
"timestamp": "07/08/2022 18:39:02",
"content": "but it is important that you combine them",
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"author_name": "kangaroo rat",
"timestamp": "07/08/2022 18:39:53",
"content": "Oh so you multiply or divide the terms then find the derivative of what u got?",
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"id": 995096963898937300,
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"timestamp": "07/08/2022 18:40:04",
"content": "yes",
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"author_name": "kangaroo rat",
"timestamp": "07/08/2022 18:40:15",
"content": "Oh",
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},
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"id": 995097085634416800,
"author_id": 953140475693514800,
"author_name": "kangaroo rat",
"timestamp": "07/08/2022 18:40:33",
"content": "Thanks",
"attachments": [],
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"author_name": "kangaroo rat",
"timestamp": "07/08/2022 18:40:43",
"content": "Really appreciate it",
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},
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"author_id": 953140475693514800,
"author_name": "kangaroo rat",
"timestamp": "07/08/2022 18:40:50",
"content": ".close",
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},
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"id": 995097161471631500,
"author_id": 805217272087838700,
"author_name": "Mathematics Bot",
"timestamp": "07/08/2022 18:40:51",
"content": "Channel closed",
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}
] |
help-9
|
aecbeb35ab414041ac87a0fab77e883d
|
197,033 |
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"id": 995097415084429400,
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"author_name": "Mathematics Bot",
"timestamp": "07/08/2022 18:41:51",
"content": "Available help channel!",
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},
{
"id": 995099054910484500,
"author_id": 229388277281456130,
"author_name": "πππΌπΏΞ",
"timestamp": "07/08/2022 18:48:22",
"content": "Hey, so I'm doing a laplace course, when it comes to Heaviside questions like this, am i not supposed to use \nL[H(t-to)] = (e^-sto)/s.",
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"content": "Pinned a message.",
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"timestamp": "07/08/2022 19:03:23",
"content": "@πππΌπΏΞ Has your question been resolved?",
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] |
help-9
|
6c4a03f9bf7b438b87cac0a374f21543
|
197,034 |
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"author_name": "Mathematics Bot",
"timestamp": "07/08/2022 19:19:24",
"content": "Available help channel!",
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},
{
"id": 995108418232778900,
"author_id": 424749714358140900,
"author_name": "Jaistyy",
"timestamp": "07/08/2022 19:25:35",
"content": "",
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"content": "Pinned a message.",
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"author_id": 424749714358140900,
"author_name": "Jaistyy",
"timestamp": "07/08/2022 19:26:13",
"content": "I have to use one of these formulas and I am not sure which one",
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"id": 995108593349173200,
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"id": 995110864585769100,
"author_id": 209300311091838980,
"author_name": "Peacemaker II",
"timestamp": "07/08/2022 19:35:18",
"content": "I would just think about it intuitively",
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"author_id": 209300311091838980,
"author_name": "Peacemaker II",
"timestamp": "07/08/2022 19:35:35",
"content": "how many of the 26 cards are not face cards?",
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},
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"id": 995110976368160800,
"author_id": 209300311091838980,
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"timestamp": "07/08/2022 19:35:45",
"content": "and how many of those are aces?",
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},
{
"id": 995111445115191400,
"author_id": 424749714358140900,
"author_name": "Jaistyy",
"timestamp": "07/08/2022 19:37:36",
"content": "6 are not face cards that are red",
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"author_id": 424749714358140900,
"author_name": "Jaistyy",
"timestamp": "07/08/2022 19:37:48",
"content": "that leaves us with 20 cards",
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},
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"id": 995111532620959900,
"author_id": 424749714358140900,
"author_name": "Jaistyy",
"timestamp": "07/08/2022 19:37:57",
"content": "1 ace of hearts and 1 ace of diamonds",
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"id": 995111553948991500,
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"author_name": "Jaistyy",
"timestamp": "07/08/2022 19:38:02",
"content": "so 2/20",
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"author_name": "Jaistyy",
"timestamp": "07/08/2022 19:38:19",
"content": "but I think im supossed to solve using one of those formulas",
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"author_name": "Jaistyy",
"timestamp": "07/08/2022 19:38:35",
"content": "would it be an independent event?",
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"timestamp": "07/08/2022 19:39:38",
"content": "I mean that would be how I'd do it",
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"timestamp": "07/08/2022 19:49:48",
"content": "@Helpers",
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"author_name": "Mathematics Bot",
"timestamp": "07/08/2022 20:04:48",
"content": "@Jaistyy Has your question been resolved?",
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"timestamp": "07/08/2022 20:19:49",
"content": "Channel closed",
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] |
help-9
|
da18620e13bd4c689ba40b8e2bc5d5b8
|
197,035 |
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"timestamp": "07/08/2022 20:20:49",
"content": "Available help channel!",
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"id": 995132994257965200,
"author_id": 596938745379291100,
"author_name": "liluzibird",
"timestamp": "07/08/2022 21:03:14",
"content": "can someone check this for me pls",
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"content": "Pinned a message.",
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"timestamp": "07/08/2022 21:18:14",
"content": "@liluzibird Has your question been resolved?",
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"author_id": 596938745379291100,
"author_name": "liluzibird",
"timestamp": "07/08/2022 21:32:18",
"content": "Greetings @Helpers , sorry for ping. Just need some help on a few questions",
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},
{
"id": 995144904059662500,
"author_id": 261933205387477000,
"author_name": "riemann",
"timestamp": "07/08/2022 21:50:34",
"content": "You should be using chain rule somewhere",
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},
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"id": 995145052835811300,
"author_id": 261933205387477000,
"author_name": "riemann",
"timestamp": "07/08/2022 21:51:09",
"content": "$d/dt (s^2) = 2s ds/dt$",
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},
{
"id": 995145062147170400,
"author_id": 510789298321096700,
"author_name": "TeXit",
"timestamp": "07/08/2022 21:51:11",
"content": "**riemann**",
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"timestamp": "07/08/2022 22:02:18",
"content": "@liluzibird Has your question been resolved?",
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"author_name": "liluzibird",
"timestamp": "07/08/2022 22:11:22",
"content": "I don't think that's the issue",
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"author_name": "liluzibird",
"timestamp": "07/08/2022 22:11:38",
"content": "I think the issue is I plugged in the wrong values for x and y",
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"author_name": "liluzibird",
"timestamp": "07/08/2022 22:11:47",
"content": "Just looked it over and found that mistake",
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"id": 995150311398318100,
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"author_name": "liluzibird",
"timestamp": "07/08/2022 22:12:03",
"content": "x=84 and y=45",
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},
{
"id": 995150330176221300,
"author_id": 596938745379291100,
"author_name": "liluzibird",
"timestamp": "07/08/2022 22:12:07",
"content": "would that be correct?",
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"id": 995151608331649000,
"author_id": 456226577798135800,
"author_name": "Deleted User",
"timestamp": "07/08/2022 22:17:12",
"content": "@liluzibird I donβt really see anything glaringly wrong about what youβre doing, but I tried it a different way. Do you have a way to still check the answer?",
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"author_name": "liluzibird",
"timestamp": "07/08/2022 22:17:35",
"content": "uh nope",
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"id": 995151777445970000,
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"timestamp": "07/08/2022 22:17:52",
"content": "Rip :[",
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"id": 995151797494763600,
"author_id": 596938745379291100,
"author_name": "liluzibird",
"timestamp": "07/08/2022 22:17:57",
"content": "but I'm pretty sure my answer is wrong since I got x and y wrong",
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"id": 995151842310881400,
"author_id": 596938745379291100,
"author_name": "liluzibird",
"timestamp": "07/08/2022 22:18:08",
"content": "I'm doing it again with the correct values",
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},
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"id": 995151888888627300,
"author_id": 596938745379291100,
"author_name": "liluzibird",
"timestamp": "07/08/2022 22:18:19",
"content": "do you have x=84 and y=45?",
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"id": 995152318624440400,
"author_id": 456226577798135800,
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"timestamp": "07/08/2022 22:20:01",
"content": "Yup",
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"author_id": 596938745379291100,
"author_name": "liluzibird",
"timestamp": "07/08/2022 22:34:23",
"content": "@Deleted User ~22.94996065 knots",
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"id": 995157481502286000,
"author_id": 596938745379291100,
"author_name": "liluzibird",
"timestamp": "07/08/2022 22:40:32",
"content": "spicyboi?",
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},
{
"id": 995157499797831700,
"author_id": 596938745379291100,
"author_name": "liluzibird",
"timestamp": "07/08/2022 22:40:37",
"content": "tell me when you get back",
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"timestamp": "07/08/2022 22:46:15",
"content": "@liluzibird Yup",
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"author_name": "liluzibird",
"timestamp": "07/08/2022 22:46:27",
"content": "wooo baby",
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"id": 995158981897105500,
"author_id": 596938745379291100,
"author_name": "liluzibird",
"timestamp": "07/08/2022 22:46:30",
"content": "one more",
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},
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"author_name": "liluzibird",
"timestamp": "07/08/2022 22:46:39",
"content": "",
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"author_name": "liluzibird",
"timestamp": "07/08/2022 22:47:10",
"content": "I don't really understand this",
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},
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"id": 995160849213816800,
"author_id": 456226577798135800,
"author_name": "Deleted User",
"timestamp": "07/08/2022 22:53:55",
"content": "You know",
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"timestamp": "07/08/2022 22:54:00",
"content": "I donβt really either",
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},
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"id": 995160921787859100,
"author_id": 596938745379291100,
"author_name": "liluzibird",
"timestamp": "07/08/2022 22:54:12",
"content": "π¦",
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"author_id": 456226577798135800,
"author_name": "Deleted User",
"timestamp": "07/08/2022 22:54:26",
"content": "I guess itβs a MVT question, but itβs worded a little weirdly",
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"timestamp": "07/08/2022 22:54:41",
"content": ":thonk:",
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{
"id": 995161146715811800,
"author_id": 596938745379291100,
"author_name": "liluzibird",
"timestamp": "07/08/2022 22:55:06",
"content": "what are the letters you just said",
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"timestamp": "07/08/2022 22:55:58",
"content": "Mean value theorem",
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"author_name": "liluzibird",
"timestamp": "07/08/2022 22:56:34",
"content": "oh ok",
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"timestamp": "07/08/2022 22:57:05",
"content": "Iβm gonna gun it and say false too",
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"timestamp": "07/08/2022 23:06:39",
"content": "hmm you sure?",
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"timestamp": "07/08/2022 23:06:44",
"content": "you really really sure?",
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"timestamp": "07/08/2022 23:08:40",
"content": "yo",
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"timestamp": "07/08/2022 23:08:42",
"content": "what's up",
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"content": "yooo eric",
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"content": "lol if you don't know the answer then don't try to help someone with it",
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"timestamp": "07/08/2022 23:09:06",
"content": "can you explain this mate",
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"content": "lemme see",
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"timestamp": "07/08/2022 23:09:15",
"content": "hmm",
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"timestamp": "07/08/2022 23:09:26",
"content": "yes the answer is false",
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"timestamp": "07/08/2022 23:09:27",
"content": "why tho",
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"timestamp": "07/08/2022 23:09:31",
"content": "can you give a counterexample for f",
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"timestamp": "07/08/2022 23:10:07",
"content": "counterexample? you want one that's true?",
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"timestamp": "07/08/2022 23:10:22",
"content": "I previously got this one wrong",
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"timestamp": "07/08/2022 23:10:38",
"content": "and this is true",
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"timestamp": "07/08/2022 23:10:54",
"content": "I notice that the y is - and + on the false one",
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"timestamp": "07/08/2022 23:11:11",
"content": "and on the true it is same polarity",
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"content": "I don't know if I should use that word in math",
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"timestamp": "07/08/2022 23:11:39",
"content": "polarity is a term used in math right",
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"timestamp": "07/08/2022 23:12:18",
"content": "nono, I meant that can you find a function f such that there is no horizontal tangent line",
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"timestamp": "07/08/2022 23:13:25",
"content": "a function f(x) that doesn't have horizontal line",
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"timestamp": "07/08/2022 23:13:43",
"content": "right",
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"timestamp": "07/08/2022 23:13:47",
"content": "and that goes through the points",
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"timestamp": "07/08/2022 23:13:51",
"content": "(-1, -7) and (4, -3)",
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"timestamp": "07/08/2022 23:14:40",
"content": "a regular linear line function would do",
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"timestamp": "07/08/2022 23:15:04",
"content": "yep!",
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"author_name": "Eric Tao",
"timestamp": "07/08/2022 23:15:12",
"content": "and therefore the statement that it has to have a horizontal tangent line is false",
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"timestamp": "07/08/2022 23:15:39",
"content": "?",
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"author_name": "liluzibird",
"timestamp": "07/08/2022 23:16:01",
"content": "oh",
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"author_name": "liluzibird",
"timestamp": "07/08/2022 23:16:03",
"content": "ohhhhhhhhhhhhh",
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"author_name": "liluzibird",
"timestamp": "07/08/2022 23:16:10",
"content": "π§ =small",
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"author_name": "Eric Tao",
"timestamp": "07/08/2022 23:25:02",
"content": "nooo you're good",
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"timestamp": "07/08/2022 23:25:19",
"content": "this question is true because of rolle's theorem (or the mean value theorem, if you haven't learned rolle's theorem)",
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"timestamp": "07/08/2022 23:25:47",
"content": "the average rate of change from x=-3 to x=1 is 0 so therefore there must be some point whose derivative is 0",
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"author_name": "liluzibird",
"timestamp": "07/08/2022 23:27:21",
"content": "ok so derivative only exists when slope is 0?",
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"author_name": "liluzibird",
"timestamp": "07/08/2022 23:27:53",
"content": "I remember that it was tangent line slope 0 makes it have derivative",
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"timestamp": "07/08/2022 23:29:21",
"content": "No",
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"id": 995169794196254800,
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"author_name": "Eric Tao",
"timestamp": "07/08/2022 23:29:28",
"content": "the derivative is the slope of the tangent line",
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"author_name": "Eric Tao",
"timestamp": "07/08/2022 23:29:35",
"content": "if the slope of the tangent line is zero, that means it's horizontal",
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"timestamp": "07/08/2022 23:30:18",
"content": "oh yeah mbad yeah we use derivative to find the slope of tan line yes",
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"timestamp": "07/08/2022 23:31:28",
"content": "I feel like this is wrong",
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"timestamp": "07/08/2022 23:31:29",
"content": "yep",
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"author_name": "Eric Tao",
"timestamp": "07/08/2022 23:31:36",
"content": "uhh lemme see",
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"timestamp": "07/08/2022 23:31:36",
"content": "noooooooo",
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"timestamp": "07/08/2022 23:31:39",
"content": "oh ok",
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"timestamp": "07/08/2022 23:31:44",
"content": "I was saying yep to this",
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"timestamp": "07/08/2022 23:31:45",
"content": "lol",
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"author_name": "Eric Tao",
"timestamp": "07/08/2022 23:33:23",
"content": "so how'd you get your answer",
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"author_name": "liluzibird",
"timestamp": "07/08/2022 23:33:43",
"content": "let me draw",
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"author_name": "liluzibird",
"timestamp": "07/08/2022 23:41:18",
"content": "something like this",
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"author_name": "Eric Tao",
"timestamp": "07/08/2022 23:42:05",
"content": "da/dt should be 3 cm^2/min",
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"timestamp": "07/08/2022 23:42:07",
"content": "not 84",
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"author_name": "Eric Tao",
"timestamp": "07/08/2022 23:42:12",
"content": "that's where it went wrong",
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"author_name": "liluzibird",
"timestamp": "07/08/2022 23:44:09",
"content": "ohhhh",
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"author_name": "liluzibird",
"timestamp": "07/08/2022 23:47:34",
"content": "-15/8?",
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"timestamp": "07/08/2022 23:48:15",
"content": "seems legit",
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"id": 995174544589475800,
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"author_name": "Eric Tao",
"timestamp": "07/08/2022 23:48:20",
"content": "go for it",
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{
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"author_id": 596938745379291100,
"author_name": "liluzibird",
"timestamp": "07/08/2022 23:49:39",
"content": "how advanced do you have to be to get the role advanced",
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"id": 995175350218793000,
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"author_name": "Eric Tao",
"timestamp": "07/08/2022 23:51:32",
"content": "you don't get it, you can just add it to yourself if you want",
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{
"id": 995175427071021000,
"author_id": 531535537362829300,
"author_name": "Eric Tao",
"timestamp": "07/08/2022 23:51:51",
"content": "but it's like undergraduate and beyond topics in this server",
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"timestamp": "07/08/2022 23:52:38",
"content": "hmm",
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{
"id": 995175639114076200,
"author_id": 596938745379291100,
"author_name": "liluzibird",
"timestamp": "07/08/2022 23:52:41",
"content": "alright",
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"id": 995175905615937500,
"author_id": 531535537362829300,
"author_name": "Eric Tao",
"timestamp": "07/08/2022 23:53:45",
"content": "if you scroll down to #get-advanced-access you'll see the button",
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"author_name": "Eric Tao",
"timestamp": "07/08/2022 23:53:55",
"content": "wouldn't recommend unless you actually want to talk about those topics though",
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"author_name": "Eric Tao",
"timestamp": "07/08/2022 23:53:56",
"content": "lol",
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"author_id": 596938745379291100,
"author_name": "liluzibird",
"timestamp": "07/08/2022 23:54:33",
"content": "yeah I'm not ready for that",
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{
"id": 995176211519115300,
"author_id": 531535537362829300,
"author_name": "Eric Tao",
"timestamp": "07/08/2022 23:54:58",
"content": "no biggie",
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{
"id": 995176240761815000,
"author_id": 531535537362829300,
"author_name": "Eric Tao",
"timestamp": "07/08/2022 23:55:05",
"content": "if you want to be, then someday you will be :)",
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{
"id": 995176390901116900,
"author_id": 596938745379291100,
"author_name": "liluzibird",
"timestamp": "07/08/2022 23:55:41",
"content": "I'm trying not to go insane",
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{
"id": 995176457405989000,
"author_id": 531535537362829300,
"author_name": "Eric Tao",
"timestamp": "07/08/2022 23:55:56",
"content": "that's a good goal! I hope you succeed",
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{
"id": 995176839540658200,
"author_id": 596938745379291100,
"author_name": "liluzibird",
"timestamp": "07/08/2022 23:57:28",
"content": "and what are Very Cool PPL",
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"author_id": 596938745379291100,
"author_name": "liluzibird",
"timestamp": "07/08/2022 23:57:37",
"content": "you know there should be a channel that explains roles",
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{
"id": 995176956649816200,
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"author_name": "liluzibird",
"timestamp": "07/08/2022 23:57:55",
"content": "ohh info",
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{
"id": 995176968859427000,
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"author_name": "liluzibird",
"timestamp": "07/08/2022 23:57:58",
"content": "got it",
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"id": 995177093073739900,
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"author_name": "Eric Tao",
"timestamp": "07/08/2022 23:58:28",
"content": "LOL I have no idea what very cool ppl is",
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"timestamp": "07/08/2022 23:58:52",
"content": "#info",
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"author_name": "Eric Tao",
"timestamp": "07/08/2022 23:58:56",
"content": "ah",
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"timestamp": "07/08/2022 23:58:58",
"content": "ty",
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"timestamp": "07/08/2022 23:59:22",
"content": "Riemann should be honorable",
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"author_id": 596938745379291100,
"author_name": "liluzibird",
"timestamp": "07/08/2022 23:59:27",
"content": "he has helped me a lot",
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"author_name": "Eric Tao",
"timestamp": "07/08/2022 23:59:55",
"content": "@riemann ^",
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"timestamp": "07/09/2022 00:00:15",
"content": "No idea how ppl get honorable",
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"author_name": "liluzibird",
"timestamp": "07/09/2022 00:00:35",
"content": "\"these are people who have consistently demonstrated courtesy, reasonability, and helpfulness around the server; and whom we consider to be exemplary members of our community.\"",
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"timestamp": "07/09/2022 00:00:54",
"content": "I think you definitely fit the description",
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"timestamp": "07/09/2022 00:01:12",
"content": "I've never had an honorable person help me",
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"author_name": "Eric Tao",
"timestamp": "07/09/2022 00:01:16",
"content": "LOL",
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"timestamp": "07/09/2022 00:01:19",
"content": "maybe they help more advanced people",
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"author_name": "riemann",
"timestamp": "07/09/2022 00:05:09",
"content": "Thanks, that's kind of you",
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"author_id": 596938745379291100,
"author_name": "liluzibird",
"timestamp": "07/09/2022 00:20:39",
"content": "I think I did something wrong",
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"id": 995182763508498600,
"author_id": 531535537362829300,
"author_name": "Eric Tao",
"timestamp": "07/09/2022 00:21:00",
"content": "what do you think you did wrong",
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"author_id": 596938745379291100,
"author_name": "liluzibird",
"timestamp": "07/09/2022 00:21:18",
"content": "number doesn't look nice",
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"author_name": "Eric Tao",
"timestamp": "07/09/2022 00:22:19",
"content": "that's okay",
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"author_name": "Eric Tao",
"timestamp": "07/09/2022 00:22:21",
"content": "looks right to me",
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"id": 995183111031750700,
"author_id": 531535537362829300,
"author_name": "Eric Tao",
"timestamp": "07/09/2022 00:22:23",
"content": "have confidence",
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"author_id": 596938745379291100,
"author_name": "liluzibird",
"timestamp": "07/09/2022 00:23:01",
"content": ":catshrug:",
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"id": 995183356536946800,
"author_id": 596938745379291100,
"author_name": "liluzibird",
"timestamp": "07/09/2022 00:23:21",
"content": "I build my confidence and then it is wrong",
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"id": 995183402837872600,
"author_id": 531535537362829300,
"author_name": "Eric Tao",
"timestamp": "07/09/2022 00:23:32",
"content": "you are good at this",
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"id": 995183408995119100,
"author_id": 531535537362829300,
"author_name": "Eric Tao",
"timestamp": "07/09/2022 00:23:34",
"content": "have no fear",
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"author_id": 805217272087838700,
"author_name": "Mathematics Bot",
"timestamp": "07/09/2022 01:23:22",
"content": "@liluzibird Has your question been resolved?",
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"author_name": "Mathematics Bot",
"timestamp": "07/09/2022 01:23:39",
"content": "Channel closed",
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}
] |
help-9
|
9b1fbd5701484ed1a94112c860a0812e
|
197,036 |
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"author_name": "Mathematics Bot",
"timestamp": "07/09/2022 08:43:26",
"content": "Available help channel!",
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"content": "Pinned a message.",
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"author_id": 764959481070616600,
"author_name": "Toby",
"timestamp": "07/09/2022 09:33:02",
"content": "what have you tried?",
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"timestamp": "07/09/2022 09:33:15",
"content": "Trial and error π",
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"author_name": "Toby",
"timestamp": "07/09/2022 09:33:46",
"content": "try modding out by q",
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"author_id": 781228420997840900,
"author_name": "FireBlazer",
"timestamp": "07/09/2022 09:34:18",
"content": "Should I first multiply both sides by the denominator of the fraction?",
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"timestamp": "07/09/2022 09:34:50",
"content": "yeah",
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"id": 995322216088613000,
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"author_name": "Toby",
"timestamp": "07/09/2022 09:35:08",
"content": "assume that $q\\nmid 345$",
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"timestamp": "07/09/2022 09:35:22",
"content": "**Toby**",
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"timestamp": "07/09/2022 09:36:29",
"content": "So the right side will be congruent to 0 (mod q) but how should I know what the residue of the left side is modulo q?",
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"timestamp": "07/09/2022 09:36:50",
"content": "if the right side is 0 mod q, then so is the left",
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"id": 995322748203184300,
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"author_name": "Toby",
"timestamp": "07/09/2022 09:37:15",
"content": ",w (p^3-2017)/(q^3-345)=q^3, solve in Z",
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"id": 995322767325003800,
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"timestamp": "07/09/2022 09:37:19",
"content": "Results provided by WolframAlpha",
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"id": 995322855728357400,
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"timestamp": "07/09/2022 09:37:41",
"content": ",w factor 2017",
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"id": 995322862456012800,
"author_id": 510789298321096700,
"author_name": "TeXit",
"timestamp": "07/09/2022 09:37:42",
"content": "Results provided by WolframAlpha",
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},
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"id": 995322866713235600,
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"timestamp": "07/09/2022 09:37:43",
"content": ",w factor 345",
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"id": 995322873264754800,
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"author_name": "TeXit",
"timestamp": "07/09/2022 09:37:45",
"content": "Results provided by WolframAlpha",
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"id": 995322889911935000,
"author_id": 781228420997840900,
"author_name": "FireBlazer",
"timestamp": "07/09/2022 09:37:49",
"content": "Yeah I'm kind of required to show my work...",
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"author_name": "Toby",
"timestamp": "07/09/2022 09:38:05",
"content": "yeah, I'm going to think for a moment. didn't expect so little solutions",
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"timestamp": "07/09/2022 09:46:56",
"content": "Thats probably the only solution because the numbers dont look so convenient as to give us multiple solutions",
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"timestamp": "07/09/2022 09:47:03",
"content": "But how do I find that value?",
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"timestamp": "07/09/2022 09:47:13",
"content": ",w (p^3-2017)/(q^3-345)=q^3, solve in Z",
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"timestamp": "07/09/2022 09:47:18",
"content": "Results provided by WolframAlpha",
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},
{
"id": 995325770975158300,
"author_id": 781228420997840900,
"author_name": "FireBlazer",
"timestamp": "07/09/2022 09:49:16",
"content": "Are you still there?",
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"id": 995326343430537300,
"author_id": 764959481070616600,
"author_name": "Toby",
"timestamp": "07/09/2022 09:51:32",
"content": "yeah i am",
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"id": 995327204621811700,
"author_id": 781228420997840900,
"author_name": "FireBlazer",
"timestamp": "07/09/2022 09:54:57",
"content": "Is there any particular casework that can be done?",
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"id": 995327285894844500,
"author_id": 764959481070616600,
"author_name": "Toby",
"timestamp": "07/09/2022 09:55:17",
"content": "try doing mod 3 first, then you get a condition on p and q",
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{
"id": 995327312008577000,
"author_id": 764959481070616600,
"author_name": "Toby",
"timestamp": "07/09/2022 09:55:23",
"content": "that's all i have rn lol",
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"id": 995328133110702100,
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"author_name": "Toby",
"timestamp": "07/09/2022 09:58:39",
"content": "then mod 5 as well",
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"id": 995328219186204700,
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"author_name": "Toby",
"timestamp": "07/09/2022 09:58:59",
"content": "and you can easily find 11,7 from those two sets of conditions",
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"author_name": "Toby",
"timestamp": "07/09/2022 09:59:17",
"content": "not sure how to prove no other solutions exist yet",
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},
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"id": 995330655451873400,
"author_id": 781228420997840900,
"author_name": "FireBlazer",
"timestamp": "07/09/2022 10:08:40",
"content": ":/",
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},
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"author_id": 805217272087838700,
"author_name": "Mathematics Bot",
"timestamp": "07/09/2022 10:23:40",
"content": "@FireBlazer Has your question been resolved?",
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"author_name": "FireBlazer",
"timestamp": "07/09/2022 10:23:57",
"content": "I still need help π¦",
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"id": 995334531651489800,
"author_id": 781228420997840900,
"author_name": "FireBlazer",
"timestamp": "07/09/2022 10:24:04",
"content": "Can anyone lend me a hand on this problem?",
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},
{
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"timestamp": "07/09/2022 10:27:21",
"content": "I have a solution I think",
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"id": 995335475101446400,
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"author_name": "Toby",
"timestamp": "07/09/2022 10:27:49",
"content": "taking mod 7, we get $p^3-1\\equiv q^6-2q^3\\pmod 7$",
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"author_name": "TeXit",
"timestamp": "07/09/2022 10:27:52",
"content": "**Toby**",
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"author_name": "Toby",
"timestamp": "07/09/2022 10:29:11",
"content": "then case by case, we see that (over $\\mathbb{F}_7$) either $p\\equiv 0$ and $q\\equiv 1,2,4$ or $p\\equiv 1,2,4$ and $q\\equiv 0$. Thus in either case, since p,q are prime, one of them must be 7",
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"timestamp": "07/09/2022 10:29:33",
"content": "**Toby**",
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"author_id": 764959481070616600,
"author_name": "Toby",
"timestamp": "07/09/2022 10:29:41",
"content": "then it's easy to see which one is 7 by trying them out",
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"id": 995336203052253200,
"author_id": 781228420997840900,
"author_name": "FireBlazer",
"timestamp": "07/09/2022 10:30:43",
"content": "What does the F with the 7 next to it mean?",
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"timestamp": "07/09/2022 10:31:19",
"content": "oh, it means I'm too lazy to write mod 7 after each equivalence",
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"id": 995336382492967000,
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"timestamp": "07/09/2022 10:31:26",
"content": "dw about it",
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"author_name": "FireBlazer",
"timestamp": "07/09/2022 10:31:33",
"content": "oh ok thx",
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"timestamp": "07/09/2022 10:33:09",
"content": "there's also a small extra case you need to do when the denominator is 0 mod 7",
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"timestamp": "07/09/2022 10:34:52",
"content": "How do I address that?",
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"content": "2 isn't a cubic residue mod 7",
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"content": "How did you come up with these cases?",
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"content": "plug in each possible value on each side then compare",
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"timestamp": "07/09/2022 10:51:03",
"content": ".close",
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"timestamp": "07/09/2022 10:51:03",
"content": "Channel closed",
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}
] |
help-9
|
68108bd2bd214bb9b34b7a84b4a02dbc
|
197,037 |
[
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"timestamp": "03/30/2022 00:29:58",
"content": "Available help channel!",
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"id": 958585707486671000,
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"author_name": "zenzeix",
"timestamp": "03/30/2022 00:37:22",
"content": "How to do question d?",
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"content": "Pinned a message.",
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"author_id": 217686845394386940,
"author_name": "jswatj",
"timestamp": "03/30/2022 00:44:06",
"content": "What is the question asking you to do",
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"author_id": 367951296357072900,
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"timestamp": "03/30/2022 00:44:30",
"content": "Prove that left hand side equals to right hand side",
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"author_id": 217686845394386940,
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"timestamp": "03/30/2022 00:44:51",
"content": "What facts do you know about sin/cos?",
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"id": 958587615903350900,
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"content": "theorems/definitions",
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"id": 958587699919454200,
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"author_name": "zenzeix",
"timestamp": "03/30/2022 00:45:17",
"content": "I do know but not entirely familiar",
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"timestamp": "03/30/2022 00:45:24",
"content": "Like for example",
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"author_name": "jswatj",
"timestamp": "03/30/2022 00:45:33",
"content": "1=sin^2(x)+cos^2(x)?",
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"author_name": "zenzeix",
"timestamp": "03/30/2022 00:45:46",
"content": "Yes I have been taught that",
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"timestamp": "03/30/2022 00:47:13",
"content": "So",
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"author_name": "jswatj",
"timestamp": "03/30/2022 00:47:18",
"content": "can you use it anywhere?",
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"author_id": 367951296357072900,
"author_name": "zenzeix",
"timestamp": "03/30/2022 00:47:41",
"content": "I donβt really see it",
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"author_id": 217686845394386940,
"author_name": "jswatj",
"timestamp": "03/30/2022 00:48:06",
"content": "for d) right?",
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"timestamp": "03/30/2022 00:48:11",
"content": "Yes",
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"timestamp": "03/30/2022 00:49:05",
"content": "Look at the terms in the equation",
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"author_name": "jswatj",
"timestamp": "03/30/2022 00:49:09",
"content": "can anything be changed?",
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"author_id": 367951296357072900,
"author_name": "zenzeix",
"timestamp": "03/30/2022 00:49:56",
"content": "Sorry I am still unsure",
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"timestamp": "03/30/2022 00:51:17",
"content": "try replacing 1",
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"author_name": "jswatj",
"timestamp": "03/30/2022 00:51:24",
"content": "with the equation i gave you",
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"timestamp": "03/30/2022 00:51:43",
"content": "cos^2(x)-sin^2(x)=(?) -2sin^2(x)",
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"timestamp": "03/30/2022 00:52:00",
"content": "Oooo",
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"author_name": "zenzeix",
"timestamp": "03/30/2022 00:52:12",
"content": "Ok I get what you are saying",
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"timestamp": "03/30/2022 00:52:23",
"content": "Thanks for the help",
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"timestamp": "03/30/2022 00:52:42",
"content": ".close",
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"content": "Channel closed",
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] |
help-9
|
0bb535c7ad3e4f358f70613148dd6de1
|
197,038 |
[
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"content": "Available help channel!",
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"timestamp": "07/09/2022 11:02:57",
"content": "All I know is that I need to use CRT (Chinese Remainder Theorem) but I'm not sure in which way...",
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"timestamp": "07/09/2022 11:10:26",
"content": "Can anyone help me?",
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"timestamp": "07/09/2022 11:15:44",
"content": "Anyone?",
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"author_name": "Toby",
"timestamp": "07/09/2022 11:17:10",
"content": "I have a way that doesn't involve the CRT",
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"timestamp": "07/09/2022 11:17:19",
"content": "Can you tell me?",
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"author_name": "Toby",
"timestamp": "07/09/2022 11:24:43",
"content": "if n=3, {m!+2,m!+3,....,m!+m} are all composite as they are divisible by at least {2,3,...} respectively. If n=4, we can set m'=m!+m and the set {m'!+m!+2,...,m'!+m!+m} are all divisible by at least {m!+2,...} respectively, ie has at least 4 divisors. Now keep going inductively till you hit your desired n",
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"timestamp": "07/09/2022 11:25:37",
"content": "the size of the numbers do grow uncontrollably, so someone else might have a more efficient answer",
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"timestamp": "07/09/2022 11:26:50",
"content": "I think the most efficient answer would involve CRT...",
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"timestamp": "07/09/2022 11:26:54",
"content": "probably",
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"timestamp": "07/09/2022 11:26:56",
"content": "Do you know a way to use it?",
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"id": 995350366680002600,
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"timestamp": "07/09/2022 11:27:00",
"content": "no",
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"timestamp": "07/09/2022 11:28:20",
"content": "you only need a proof of concept though, right? you don't need to explicitly calculate a list?",
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"timestamp": "07/09/2022 11:29:47",
"content": "no, I just need to prove the given hypothesis",
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"timestamp": "07/09/2022 11:30:00",
"content": "nested factorials should work then...",
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"id": 995351934192074900,
"author_id": 145216269971488770,
"author_name": "Maldor",
"timestamp": "07/09/2022 11:33:13",
"content": "Pick $m$ integers $n_1,...,n_m$ which are coprime and each have at least $n$ factors. Now consider $\\begin{cases}x=0 \\ mod(n_1) \\\\ x=-1 \\ mod (n_2) \\\\ ... \\\\ x=-m+1 \\ mod(n_m)\\end{cases}$",
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"timestamp": "07/09/2022 11:34:38",
"content": "ooooh CRT?!",
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"timestamp": "07/09/2022 11:34:54",
"content": "By CRT such a solution exists, and by construction $x$ is divisible by $n_1$, $x+1$ is divisible by $n_2$ and so on",
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"id": 995352451848880100,
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"author_name": "TeXit",
"timestamp": "07/09/2022 11:35:17",
"content": "**Maldor**",
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"timestamp": "07/09/2022 11:36:09",
"content": "**Maldor**",
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"timestamp": "07/09/2022 11:36:30",
"content": "Forgot the negatives",
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"author_name": "FireBlazer",
"timestamp": "07/09/2022 11:36:46",
"content": "Okay, is that it for the proof?",
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"timestamp": "07/09/2022 11:37:23",
"content": "Think so, just make sure it satisfies all the requirements stated in CRT",
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"timestamp": "07/09/2022 11:38:15",
"content": "It does; $n_1, ... , n_m$ are coprime, so by CRT, there exists an $x$ that satisfies the system of congruences.",
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"timestamp": "07/09/2022 11:38:18",
"content": "**FireBlazer**",
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"timestamp": "07/09/2022 11:39:28",
"content": "Right, maybe you also need to say that you would pick $n_k > k+1$ or something but it might not be necessary",
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"timestamp": "07/09/2022 11:39:31",
"content": "**Maldor**",
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"timestamp": "07/09/2022 11:40:40",
"content": "Okay, thanks.",
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"timestamp": "07/09/2022 11:41:39",
"content": "Np",
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"author_id": 859166603114315800,
"author_name": "giannis_money",
"timestamp": "07/09/2022 11:41:43",
"content": "it would be sufficient to say that n_k has at least n-2 divisors right?",
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"timestamp": "07/09/2022 11:43:03",
"content": "wait nvm n_k could be x+k",
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"timestamp": "07/09/2022 11:50:17",
"content": ".close",
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"timestamp": "07/09/2022 11:50:18",
"content": "Channel closed",
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}
] |
help-9
|
9ffe5047b5b94e4289b82d31c20b5a98
|
197,039 |
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"timestamp": "07/09/2022 13:30:19",
"content": "Available help channel!",
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"id": 995384023411068900,
"author_id": 816885647125905400,
"author_name": "Loloitsjo",
"timestamp": "07/09/2022 13:40:44",
"content": "What is a surjective function?",
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"author_id": 391270706186420200,
"author_name": "illuminator3",
"timestamp": "07/09/2022 13:42:22",
"content": "Let $f: X \\to Y$ then $f$ is a surjective function iff $\\forall y \\in Y, \\exists x \\in X : f(x) = y$",
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"id": 995384444074590200,
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"content": "**illuminator3**",
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"content": "@Loloitsjo Has your question been resolved?",
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] |
help-9
|
08b00f8c81284ffc9169e4f84b01d042
|
197,040 |
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"author_id": 403257113360728060,
"author_name": "Shuban",
"timestamp": "07/09/2022 16:13:29",
"content": "For this question, I would be evaluating the integral from 1 to 6 right?",
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"author_id": 403257113360728060,
"author_name": "Shuban",
"timestamp": "07/09/2022 16:13:42",
"content": "Because those are the x values at which the two graphs intersect?",
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"id": 995423232553386000,
"author_id": 349354952961032200,
"author_name": "Umbraleviathan",
"timestamp": "07/09/2022 16:16:32",
"content": "Yes",
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"author_name": "Shuban",
"timestamp": "07/09/2022 16:19:00",
"content": "I don't get then why my teachers answer key says 3 to 1.",
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"timestamp": "07/09/2022 16:23:00",
"content": "3 to 1",
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"id": 995424865697927200,
"author_id": 349354952961032200,
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"timestamp": "07/09/2022 16:23:02",
"content": "?",
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"id": 995424894114349200,
"author_id": 349354952961032200,
"author_name": "Umbraleviathan",
"timestamp": "07/09/2022 16:23:08",
"content": "3 lower bound, 1 upper bound?",
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"id": 995424912758014000,
"author_id": 403257113360728060,
"author_name": "Shuban",
"timestamp": "07/09/2022 16:23:13",
"content": "Yea",
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"id": 995424934916538500,
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"author_name": "Shuban",
"timestamp": "07/09/2022 16:23:18",
"content": "I don't understand why it says that",
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"timestamp": "07/09/2022 16:23:18",
"content": "Bruh that shit gonna be negative",
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"id": 995424968127021000,
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"content": "It's 1 to 6",
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"author_name": "Shuban",
"timestamp": "07/09/2022 16:23:51",
"content": "Alright, I'll just do the calculation going 1 to 6.",
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"timestamp": "07/09/2022 16:24:06",
"content": ".close",
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"timestamp": "07/09/2022 16:24:06",
"content": "Channel closed",
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] |
help-9
|
92af1cfb18ee4bbfbc1bb8dc9c89bfef
|
197,041 |
[
{
"id": 995425388396302500,
"author_id": 805217272087838700,
"author_name": "Mathematics Bot",
"timestamp": "07/09/2022 16:25:06",
"content": "Available help channel!",
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},
{
"id": 995426400154681500,
"author_id": 773175139553902600,
"author_name": "adveniatregnumtuum",
"timestamp": "07/09/2022 16:29:07",
"content": "Hello,",
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"id": 995426402151174300,
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"author_name": "adveniatregnumtuum",
"timestamp": "07/09/2022 16:29:32",
"content": "I asked this once but the person had to leave afk, ill ask here",
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"author_id": 773175139553902600,
"author_name": "adveniatregnumtuum",
"timestamp": "07/09/2022 16:30:21",
"content": "Using that formula to simplify, I am confused as to why I couldn't simplify the following into xΒ²",
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"timestamp": "07/09/2022 16:30:42",
"content": "(Red arrows and question mark is my question)",
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{
"id": 995426925428359300,
"author_id": 773175139553902600,
"author_name": "adveniatregnumtuum",
"timestamp": "07/09/2022 16:31:13",
"content": "For 2xyΒ², does the Β² power only belong to the y variable?",
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"id": 995427112733380700,
"author_id": 773175139553902600,
"author_name": "adveniatregnumtuum",
"timestamp": "07/09/2022 16:31:57",
"content": "If it had a parenthesis, such as (2xy)Β² , only then would the x become xΒ², is this correct?",
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"id": 995427250268811300,
"author_id": 773175139553902600,
"author_name": "adveniatregnumtuum",
"timestamp": "07/09/2022 16:32:30",
"content": "But the way it is written, 2xyΒ² , the Β² exponent only belongs to y variable, ? Am I understaning it right?",
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"id": 995427295542137000,
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"author_name": "Andrea276",
"timestamp": "07/09/2022 16:32:41",
"content": "Yes",
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"content": "Yes",
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"timestamp": "07/09/2022 16:33:52",
"content": "Ohhh okay, yeah makes sense, I won't forget now, thank you Andrea276",
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"timestamp": "07/09/2022 16:33:56",
"content": ".close",
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] |
help-9
|
165f5d552c33489586c7cf73c7cb062a
|
197,042 |
[
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"content": "Available help channel!",
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{
"id": 995430741674573800,
"author_id": 527680034522136600,
"author_name": "John-waterpriest",
"timestamp": "07/09/2022 16:46:23",
"content": "Hi",
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"id": 995430743780118500,
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"author_name": "John-waterpriest",
"timestamp": "07/09/2022 16:46:39",
"content": "Erm Iβve wanted to factor this polynomial",
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"id": 995430919093625000,
"author_id": 527680034522136600,
"author_name": "John-waterpriest",
"timestamp": "07/09/2022 16:47:05",
"content": "Iβve been told by my teacher when I was in class to use quadratics",
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"id": 995430969597235200,
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"timestamp": "07/09/2022 16:47:17",
"content": "The quadratic formula specifically",
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"id": 995431036467032000,
"author_id": 527680034522136600,
"author_name": "John-waterpriest",
"timestamp": "07/09/2022 16:47:33",
"content": "But this polynomial has a fourth exponent",
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"id": 995431119157727200,
"author_id": 527680034522136600,
"author_name": "John-waterpriest",
"timestamp": "07/09/2022 16:47:53",
"content": "I looked up the answers but couldnβt find how they did it",
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"id": 995431206877409400,
"author_id": 192406306924134400,
"author_name": "TheZachMan",
"timestamp": "07/09/2022 16:48:13",
"content": "yeah, you can't solve this with the quadratic formula",
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"id": 995431248648491000,
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"timestamp": "07/09/2022 16:48:23",
"content": "Oh ok",
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},
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"id": 995432039526441000,
"author_id": 859166603114315800,
"author_name": "giannis_money",
"timestamp": "07/09/2022 16:51:32",
"content": "Trial and error",
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},
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"id": 995432626280206300,
"author_id": 145216269971488770,
"author_name": "Maldor",
"timestamp": "07/09/2022 16:53:52",
"content": "You can use the rational root theorem",
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},
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"id": 995433059883155500,
"author_id": 306476267916492800,
"author_name": "1080p",
"timestamp": "07/09/2022 16:55:35",
"content": "(x + a)(x + b)(x + c)(x + d)\na * b * c * d = -10\nso they can be 10, 5, 2, 1 with odd number of negative",
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"id": 995433153533595600,
"author_id": 306476267916492800,
"author_name": "1080p",
"timestamp": "07/09/2022 16:55:58",
"content": "5 2 1 1 or 10 1 1 1 1",
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"author_name": "Mathematics Bot",
"timestamp": "07/09/2022 17:03:24",
"content": "@John-waterpriest Has your question been resolved?",
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"timestamp": "07/09/2022 17:06:18",
"content": "Oh",
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"timestamp": "07/09/2022 17:06:21",
"content": "Yes",
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"author_name": "John-waterpriest",
"timestamp": "07/09/2022 17:06:24",
"content": "Thanks gui s",
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"timestamp": "07/09/2022 17:06:26",
"content": "Channel closed",
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}
] |
help-9
|
3ba82a2054fa440489e51b4ea19c0011
|
197,043 |
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"author_name": "Mathematics Bot",
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"content": "Pinned a message.",
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"timestamp": "07/09/2022 17:26:04",
"content": "Channel closed",
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}
] |
help-9
|
4fc4c790dc804fae886ec39677b094f0
|
197,044 |
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{
"id": 995442984936022000,
"author_id": 805217272087838700,
"author_name": "Mathematics Bot",
"timestamp": "07/09/2022 17:35:02",
"content": "Available help channel!",
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},
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"id": 995450465431060500,
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"content": "Pinned a message.",
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"timestamp": "07/09/2022 18:05:13",
"content": "what have you tried so far",
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"timestamp": "07/09/2022 18:07:12",
"content": "this is my parametric equation",
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"timestamp": "07/09/2022 18:07:22",
"content": "but I don't know if it's right",
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"id": 995451140357497000,
"author_id": 531535537362829300,
"author_name": "Eric Tao",
"timestamp": "07/09/2022 18:07:26",
"content": "how did you get it?",
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"id": 995451337816948700,
"author_id": 896625754383724500,
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"timestamp": "07/09/2022 18:08:13",
"content": "the equations for x and z are incorrect",
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"timestamp": "07/09/2022 18:08:20",
"content": "yeah",
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"timestamp": "07/09/2022 18:08:27",
"content": "but hagsir how did you get it",
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"id": 995451522479558700,
"author_id": 264545343268585470,
"author_name": "hagsir",
"timestamp": "07/09/2022 18:08:57",
"content": "one moment",
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"author_name": "hagsir",
"timestamp": "07/09/2022 18:09:48",
"content": "I can't translate all this but I followed this exercise",
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"timestamp": "07/09/2022 18:10:01",
"content": "can you understand?",
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"id": 995451889418240100,
"author_id": 531535537362829300,
"author_name": "Eric Tao",
"timestamp": "07/09/2022 18:10:25",
"content": "which one did you follow?",
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"author_id": 531535537362829300,
"author_name": "Eric Tao",
"timestamp": "07/09/2022 18:10:30",
"content": "a b c or d",
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},
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"id": 995451937396883600,
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"timestamp": "07/09/2022 18:10:36",
"content": "b",
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},
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"id": 995452002328916000,
"author_id": 531535537362829300,
"author_name": "Eric Tao",
"timestamp": "07/09/2022 18:10:51",
"content": "okay can you explain how they did it",
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},
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"author_name": "hagsir",
"timestamp": "07/09/2022 18:11:12",
"content": "can you see the x/3 = (y+7)/-1 = (z-3)/6",
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"timestamp": "07/09/2022 18:11:17",
"content": "yup",
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"author_name": "hagsir",
"timestamp": "07/09/2022 18:11:44",
"content": "I replaced it with (1 - 2x)/3 = y/4 = (2z + 1)/4",
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"timestamp": "07/09/2022 18:11:49",
"content": "right",
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"author_name": "Eric Tao",
"timestamp": "07/09/2022 18:11:54",
"content": "and then what did you do",
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"author_name": "hagsir",
"timestamp": "07/09/2022 18:12:28",
"content": "I found this after replacing",
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"timestamp": "07/09/2022 18:13:02",
"content": "okay I see",
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"author_name": "Eric Tao",
"timestamp": "07/09/2022 18:13:14",
"content": "but that problem is different from yours because there's 2x instead of x",
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"id": 995452622263812100,
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"author_name": "Eric Tao",
"timestamp": "07/09/2022 18:13:19",
"content": "and 2z instead of z",
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"author_name": "Eric Tao",
"timestamp": "07/09/2022 18:13:23",
"content": "so how would you change it?",
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},
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"author_name": "hagsir",
"timestamp": "07/09/2022 18:13:31",
"content": "wait let me see",
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"timestamp": "07/09/2022 18:17:33",
"content": "does that resolve the issue?",
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},
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"id": 995453781863047300,
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"timestamp": "07/09/2022 18:17:56",
"content": "not quite",
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"author_name": "Eric Tao",
"timestamp": "07/09/2022 18:18:03",
"content": "let's think about it this way",
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"author_name": "Eric Tao",
"timestamp": "07/09/2022 18:18:15",
"content": "we have $$\\frac{1-2x}3 = \\frac{y}4 = \\frac{2z+1}4$$",
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},
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"author_name": "TeXit",
"timestamp": "07/09/2022 18:18:18",
"content": "**Eric Tao (he/him)**",
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"timestamp": "07/09/2022 18:18:21",
"content": "we can set this all equal to t as follows:",
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"timestamp": "07/09/2022 18:18:26",
"content": "$$\\frac{1-2x}3 = \\frac{y}4 = \\frac{2z+1}4 = t$$",
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"timestamp": "07/09/2022 18:18:28",
"content": "**Eric Tao (he/him)**",
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"timestamp": "07/09/2022 18:18:35",
"content": "now we can solve for x, y, z in terms of t",
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"timestamp": "07/09/2022 18:18:39",
"content": "does that make sense",
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"timestamp": "07/09/2022 18:18:43",
"content": "yes",
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"timestamp": "07/09/2022 18:18:54",
"content": "alright so we have $$\\frac{1-2x}3 = t$$",
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"timestamp": "07/09/2022 18:18:57",
"content": "**Eric Tao (he/him)**",
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"timestamp": "07/09/2022 18:19:14",
"content": "$$1-2x = 3t$$\n$$-2x = 3t-1$$\n$$x = -\\frac32t + \\frac12$$",
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"timestamp": "07/09/2022 18:19:18",
"content": "**Eric Tao (he/him)**",
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"timestamp": "07/09/2022 18:19:23",
"content": "Make sense?",
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"timestamp": "07/09/2022 18:19:27",
"content": "yesyes",
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"timestamp": "07/09/2022 18:19:28",
"content": "wait",
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"timestamp": "07/09/2022 18:19:32",
"content": "I will send the answer that a friend made",
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"timestamp": "07/09/2022 18:20:16",
"content": "nevermind",
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},
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"timestamp": "07/09/2022 18:20:46",
"content": "but i understand what you did, thanks, I think i can do the rest",
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"timestamp": "07/09/2022 18:20:50",
"content": "cool",
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"timestamp": "07/09/2022 18:20:52",
"content": "good luck!",
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"timestamp": "07/09/2022 18:21:26",
"content": "I'll type .close after posting the answer here and could you check if it's right?",
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"timestamp": "07/09/2022 18:23:52",
"content": "$$y = 4t$$",
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"author_name": "TeXit",
"timestamp": "07/09/2022 18:23:54",
"content": "**hagsir**",
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"timestamp": "07/09/2022 18:26:01",
"content": "$$z = -\\frac12 +\\frac42t$$",
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"timestamp": "07/09/2022 18:26:04",
"content": "**hagsir**",
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"timestamp": "07/09/2022 18:26:27",
"content": "@Eric Tao is this right?",
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"timestamp": "07/09/2022 18:27:21",
"content": "yup that's right, 4/2 is 2 though",
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"timestamp": "07/09/2022 18:27:27",
"content": "so next you need to find the line parallel to that",
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"timestamp": "07/09/2022 18:27:39",
"content": "yep",
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"author_id": 264545343268585470,
"author_name": "hagsir",
"timestamp": "07/09/2022 18:34:26",
"content": "thanks for helping me",
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},
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"id": 995457975760212000,
"author_id": 264545343268585470,
"author_name": "hagsir",
"timestamp": "07/09/2022 18:34:36",
"content": ".close",
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},
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"author_id": 805217272087838700,
"author_name": "Mathematics Bot",
"timestamp": "07/09/2022 18:34:36",
"content": "Channel closed",
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}
] |
help-9
|
1324c4846e6e49dc9c52cfde9ce3831e
|
197,045 |
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"content": "Available help channel!",
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"id": 995459955484266500,
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"author_name": "Mathematics Bot",
"timestamp": "07/09/2022 18:42:28",
"content": "Pinned a message.",
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"author_id": 281221474604548100,
"author_name": "PoisonedFood",
"timestamp": "07/09/2022 18:42:33",
"content": "Complex Variables",
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"id": 995460018352705700,
"author_id": 531535537362829300,
"author_name": "Eric Tao",
"timestamp": "07/09/2022 18:42:43",
"content": "LOL the wording of the question",
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"id": 995460042990026900,
"author_id": 281221474604548100,
"author_name": "PoisonedFood",
"timestamp": "07/09/2022 18:42:49",
"content": "Iβm not sure how to start or do this",
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"id": 995460091442630700,
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"timestamp": "07/09/2022 18:43:00",
"content": "I think using that it is analytic then then the integral is 0",
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"timestamp": "07/09/2022 18:43:11",
"content": "But not much more what to do with that.",
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"id": 995460191854268400,
"author_id": 281221474604548100,
"author_name": "PoisonedFood",
"timestamp": "07/09/2022 18:43:24",
"content": "I told you these last two were like riddles",
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"author_name": "PoisonedFood",
"timestamp": "07/09/2022 18:43:31",
"content": "",
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"id": 995460617349648400,
"author_id": 531535537362829300,
"author_name": "Eric Tao",
"timestamp": "07/09/2022 18:45:05",
"content": "this is definitely the cauchy integral formula",
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"id": 995460632218456200,
"author_id": 531535537362829300,
"author_name": "Eric Tao",
"timestamp": "07/09/2022 18:45:09",
"content": "use the general form",
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"author_name": "Eric Tao",
"timestamp": "07/09/2022 18:45:27",
"content": "",
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"id": 995461148113645600,
"author_id": 281221474604548100,
"author_name": "PoisonedFood",
"timestamp": "07/09/2022 18:47:12",
"content": "Ehh, Iβm not sure how to see the connection",
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},
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"id": 995461214090051700,
"author_id": 531535537362829300,
"author_name": "Eric Tao",
"timestamp": "07/09/2022 18:47:28",
"content": "what part are you struggling with",
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},
{
"id": 995461235950755800,
"author_id": 531535537362829300,
"author_name": "Eric Tao",
"timestamp": "07/09/2022 18:47:33",
"content": "what is a here?",
"attachments": [],
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},
{
"id": 995461248986656900,
"author_id": 281221474604548100,
"author_name": "PoisonedFood",
"timestamp": "07/09/2022 18:47:36",
"content": "Is a zero in this case?",
"attachments": [],
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},
{
"id": 995461255995347100,
"author_id": 531535537362829300,
"author_name": "Eric Tao",
"timestamp": "07/09/2022 18:47:38",
"content": "yes",
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},
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"id": 995461459192582100,
"author_id": 281221474604548100,
"author_name": "PoisonedFood",
"timestamp": "07/09/2022 18:48:26",
"content": "So, n = 0 then g(0) = 1/4",
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},
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"id": 995461602902024200,
"author_id": 531535537362829300,
"author_name": "Eric Tao",
"timestamp": "07/09/2022 18:49:00",
"content": "well wait it has to work for all n",
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},
{
"id": 995461622946611200,
"author_id": 281221474604548100,
"author_name": "PoisonedFood",
"timestamp": "07/09/2022 18:49:05",
"content": "n = 1 then gβ(0) = 1/4 also",
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},
{
"id": 995461655330816000,
"author_id": 531535537362829300,
"author_name": "Eric Tao",
"timestamp": "07/09/2022 18:49:13",
"content": "I have an idea",
"attachments": [],
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},
{
"id": 995461725648330900,
"author_id": 531535537362829300,
"author_name": "Eric Tao",
"timestamp": "07/09/2022 18:49:30",
"content": "wait actually",
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},
{
"id": 995461743985832000,
"author_id": 531535537362829300,
"author_name": "Eric Tao",
"timestamp": "07/09/2022 18:49:34",
"content": "nvm the way you're doing it is perfect",
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"id": 995461788558704600,
"author_id": 531535537362829300,
"author_name": "Eric Tao",
"timestamp": "07/09/2022 18:49:45",
"content": "yeah so g(0) = 1/4, g'(0) = 1/4",
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},
{
"id": 995461866547585200,
"author_id": 531535537362829300,
"author_name": "Eric Tao",
"timestamp": "07/09/2022 18:50:03",
"content": "what can we say about $g^{(n)}(0)$ for any $n$?",
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},
{
"id": 995461876278370300,
"author_id": 510789298321096700,
"author_name": "TeXit",
"timestamp": "07/09/2022 18:50:06",
"content": "**Eric Tao (he/him)**",
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"id": 995462749549244500,
"author_id": 281221474604548100,
"author_name": "PoisonedFood",
"timestamp": "07/09/2022 18:53:34",
"content": "gββ(0) = 1/32",
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},
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"id": 995462944802492500,
"author_id": 531535537362829300,
"author_name": "Eric Tao",
"timestamp": "07/09/2022 18:54:20",
"content": "how did you get that",
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},
{
"id": 995462949906952300,
"author_id": 281221474604548100,
"author_name": "PoisonedFood",
"timestamp": "07/09/2022 18:54:22",
"content": "gβββ(0) = 1/384",
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},
{
"id": 995463007842873300,
"author_id": 281221474604548100,
"author_name": "PoisonedFood",
"timestamp": "07/09/2022 18:54:35",
"content": "n = 2 so use the formula in the problem",
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},
{
"id": 995463072540016800,
"author_id": 281221474604548100,
"author_name": "PoisonedFood",
"timestamp": "07/09/2022 18:54:51",
"content": "4^n * n!",
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},
{
"id": 995463092785914000,
"author_id": 531535537362829300,
"author_name": "Eric Tao",
"timestamp": "07/09/2022 18:54:56",
"content": "oh I see the problem",
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},
{
"id": 995463101434572900,
"author_id": 281221474604548100,
"author_name": "PoisonedFood",
"timestamp": "07/09/2022 18:54:58",
"content": "1/16*2",
"attachments": [],
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"reference": null
},
{
"id": 995463116345311200,
"author_id": 531535537362829300,
"author_name": "Eric Tao",
"timestamp": "07/09/2022 18:55:01",
"content": "you need to multiply both sides by n!",
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},
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"id": 995463141121077200,
"author_id": 531535537362829300,
"author_name": "Eric Tao",
"timestamp": "07/09/2022 18:55:07",
"content": "if you want to use this formula",
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},
{
"id": 995463356259500000,
"author_id": 281221474604548100,
"author_name": "PoisonedFood",
"timestamp": "07/09/2022 18:55:58",
"content": "Still gββ(0)= 1/16",
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},
{
"id": 995463370276868100,
"author_id": 281221474604548100,
"author_name": "PoisonedFood",
"timestamp": "07/09/2022 18:56:02",
"content": "Not 4",
"attachments": [],
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},
{
"id": 995463486941450200,
"author_id": 281221474604548100,
"author_name": "PoisonedFood",
"timestamp": "07/09/2022 18:56:30",
"content": "Is this the geometric series associated with 1/1-(1/4)?",
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},
{
"id": 995463645721006200,
"author_id": 531535537362829300,
"author_name": "Eric Tao",
"timestamp": "07/09/2022 18:57:07",
"content": "first though what's the power series for g",
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},
{
"id": 995463692365860900,
"author_id": 531535537362829300,
"author_name": "Eric Tao",
"timestamp": "07/09/2022 18:57:19",
"content": "if you know the values of all the derivatives",
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},
{
"id": 995463969550635000,
"author_id": 281221474604548100,
"author_name": "PoisonedFood",
"timestamp": "07/09/2022 18:58:25",
"content": "g^n(0)/n!",
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},
{
"id": 995463981210816600,
"author_id": 281221474604548100,
"author_name": "PoisonedFood",
"timestamp": "07/09/2022 18:58:27",
"content": "Right?",
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},
{
"id": 995464166645190800,
"author_id": 531535537362829300,
"author_name": "Eric Tao",
"timestamp": "07/09/2022 18:59:12",
"content": "yep!",
"attachments": [],
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},
{
"id": 995464312275619800,
"author_id": 531535537362829300,
"author_name": "Eric Tao",
"timestamp": "07/09/2022 18:59:46",
"content": "wait sorry I gotta go eat",
"attachments": [],
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},
{
"id": 995464405267534000,
"author_id": 281221474604548100,
"author_name": "PoisonedFood",
"timestamp": "07/09/2022 19:00:09",
"content": "No problem. Iβm free all night. Just hacking away whenever I can.",
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},
{
"id": 995464446304591900,
"author_id": 281221474604548100,
"author_name": "PoisonedFood",
"timestamp": "07/09/2022 19:00:18",
"content": "Iβll be here unless someone else gets to it.",
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},
{
"id": 995464467846541300,
"author_id": 281221474604548100,
"author_name": "PoisonedFood",
"timestamp": "07/09/2022 19:00:23",
"content": "If not no big deal.",
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},
{
"id": 995465262847504500,
"author_id": 281221474604548100,
"author_name": "PoisonedFood",
"timestamp": "07/09/2022 19:03:33",
"content": "@Helpers",
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},
{
"id": 995467547350679600,
"author_id": 281221474604548100,
"author_name": "PoisonedFood",
"timestamp": "07/09/2022 19:12:38",
"content": "From what I can see is that g(a) = 1 + 1/4 + 1/16 + 1/64 + . . . = g(a) = 1/[1-(1/4)]",
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},
{
"id": 995468333086417200,
"author_id": 531535537362829300,
"author_name": "Eric Tao",
"timestamp": "07/09/2022 19:15:45",
"content": "okay here's a way of solving this problem which I think is pretty neat",
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},
{
"id": 995468375507607700,
"author_id": 531535537362829300,
"author_name": "Eric Tao",
"timestamp": "07/09/2022 19:15:55",
"content": "first of all, do you know how to write the first few terms of the power series of g?",
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},
{
"id": 995468767742148700,
"author_id": 281221474604548100,
"author_name": "PoisonedFood",
"timestamp": "07/09/2022 19:17:29",
"content": "I did this wrong",
"attachments": [],
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},
{
"id": 995469019094208500,
"author_id": 281221474604548100,
"author_name": "PoisonedFood",
"timestamp": "07/09/2022 19:18:29",
"content": "Okay so g^n(a) = g(a) + gβ(a) + gββ(a)/2 + gβββ(a)/6 + β¦",
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},
{
"id": 995469309608480900,
"author_id": 531535537362829300,
"author_name": "Eric Tao",
"timestamp": "07/09/2022 19:19:38",
"content": "not quite",
"attachments": [],
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"reference": null
},
{
"id": 995469393788145800,
"author_id": 531535537362829300,
"author_name": "Eric Tao",
"timestamp": "07/09/2022 19:19:58",
"content": "so the formula for the taylor series is like, g(z) = g(0) + g'(0)z + g''(0)/2 z^2 + ... right?",
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},
{
"id": 995470299787169800,
"author_id": 281221474604548100,
"author_name": "PoisonedFood",
"timestamp": "07/09/2022 19:23:34",
"content": "Why am I incorporating z now?",
"attachments": [],
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},
{
"id": 995470826348482700,
"author_id": 531535537362829300,
"author_name": "Eric Tao",
"timestamp": "07/09/2022 19:25:39",
"content": "aren't you trying to find g(z)",
"attachments": [],
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"reference": null
},
{
"id": 995470951661715500,
"author_id": 281221474604548100,
"author_name": "PoisonedFood",
"timestamp": "07/09/2022 19:26:09",
"content": "Oh yeah π
",
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},
{
"id": 995471014320423000,
"author_id": 281221474604548100,
"author_name": "PoisonedFood",
"timestamp": "07/09/2022 19:26:24",
"content": "Okay I see what I did wrong",
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},
{
"id": 995471046046126100,
"author_id": 281221474604548100,
"author_name": "PoisonedFood",
"timestamp": "07/09/2022 19:26:32",
"content": "Forgot the z^n terms",
"attachments": [],
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},
{
"id": 995472269944041500,
"author_id": 281221474604548100,
"author_name": "PoisonedFood",
"timestamp": "07/09/2022 19:31:24",
"content": "So it is 1+ z/4 + z^2/16",
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},
{
"id": 995472285743984600,
"author_id": 281221474604548100,
"author_name": "PoisonedFood",
"timestamp": "07/09/2022 19:31:27",
"content": ". . .",
"attachments": [],
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"reference": null
},
{
"id": 995472303372636200,
"author_id": 531535537362829300,
"author_name": "Eric Tao",
"timestamp": "07/09/2022 19:31:32",
"content": "yeah",
"attachments": [],
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},
{
"id": 995472315586449400,
"author_id": 531535537362829300,
"author_name": "Eric Tao",
"timestamp": "07/09/2022 19:31:35",
"content": "well",
"attachments": [],
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},
{
"id": 995472348432060400,
"author_id": 531535537362829300,
"author_name": "Eric Tao",
"timestamp": "07/09/2022 19:31:42",
"content": "you need to divide by n! too",
"attachments": [],
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},
{
"id": 995473163364339700,
"author_id": 281221474604548100,
"author_name": "PoisonedFood",
"timestamp": "07/09/2022 19:34:57",
"content": "I thought we multiplied by n! On both sides to get the Cauchy formula on the left and cancel the one on the right?",
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},
{
"id": 995473259220971600,
"author_id": 531535537362829300,
"author_name": "Eric Tao",
"timestamp": "07/09/2022 19:35:19",
"content": "but the taylor series has /n!",
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},
{
"id": 995473294633488400,
"author_id": 531535537362829300,
"author_name": "Eric Tao",
"timestamp": "07/09/2022 19:35:28",
"content": "g(n)(0)/n! z^n",
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},
{
"id": 995475279361351800,
"author_id": 281221474604548100,
"author_name": "PoisonedFood",
"timestamp": "07/09/2022 19:43:21",
"content": "Okay, so:\n\ng(z) = 1 + z/4 + z^2/32 + . . .",
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},
{
"id": 995475772368244900,
"author_id": 531535537362829300,
"author_name": "Eric Tao",
"timestamp": "07/09/2022 19:45:19",
"content": "yup",
"attachments": [],
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},
{
"id": 995475825799471200,
"author_id": 531535537362829300,
"author_name": "Eric Tao",
"timestamp": "07/09/2022 19:45:31",
"content": "and what function is that the taylor series for?",
"attachments": [],
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},
{
"id": 995476253924667500,
"author_id": 281221474604548100,
"author_name": "PoisonedFood",
"timestamp": "07/09/2022 19:47:13",
"content": "1/1-(z/4)",
"attachments": [],
"mentions": [],
"reference": null
},
{
"id": 995476269485531300,
"author_id": 281221474604548100,
"author_name": "PoisonedFood",
"timestamp": "07/09/2022 19:47:17",
"content": "Yay?",
"attachments": [],
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},
{
"id": 995476287298736100,
"author_id": 281221474604548100,
"author_name": "PoisonedFood",
"timestamp": "07/09/2022 19:47:21",
"content": "Nay?",
"attachments": [],
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"reference": null
},
{
"id": 995476591083798700,
"author_id": 531535537362829300,
"author_name": "Eric Tao",
"timestamp": "07/09/2022 19:48:34",
"content": "not quite",
"attachments": [],
"mentions": [],
"reference": null
},
{
"id": 995476617235280000,
"author_id": 531535537362829300,
"author_name": "Eric Tao",
"timestamp": "07/09/2022 19:48:40",
"content": "it's not quite a geometric series is it",
"attachments": [],
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"reference": null
},
{
"id": 995476724336840700,
"author_id": 281221474604548100,
"author_name": "PoisonedFood",
"timestamp": "07/09/2022 19:49:06",
"content": "Hmmm",
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},
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"id": 995476742674321400,
"author_id": 281221474604548100,
"author_name": "PoisonedFood",
"timestamp": "07/09/2022 19:49:10",
"content": "Let me think for a second",
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},
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"id": 995476804770992100,
"author_id": 281221474604548100,
"author_name": "PoisonedFood",
"timestamp": "07/09/2022 19:49:25",
"content": "Is that e^(z/4)",
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},
{
"id": 995476862048424100,
"author_id": 281221474604548100,
"author_name": "PoisonedFood",
"timestamp": "07/09/2022 19:49:38",
"content": "?",
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{
"id": 995476924900061200,
"author_id": 531535537362829300,
"author_name": "Eric Tao",
"timestamp": "07/09/2022 19:49:53",
"content": "yep!",
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},
{
"id": 995477551688458200,
"author_id": 281221474604548100,
"author_name": "PoisonedFood",
"timestamp": "07/09/2022 19:52:23",
"content": "Hmm okay.",
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},
{
"id": 995477608835850200,
"author_id": 281221474604548100,
"author_name": "PoisonedFood",
"timestamp": "07/09/2022 19:52:37",
"content": "Iβm gonna post my next question in just a second, thank you!!",
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},
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"id": 995477624103121000,
"author_id": 281221474604548100,
"author_name": "PoisonedFood",
"timestamp": "07/09/2022 19:52:40",
"content": ".close",
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},
{
"id": 995477625755672700,
"author_id": 805217272087838700,
"author_name": "Mathematics Bot",
"timestamp": "07/09/2022 19:52:41",
"content": "Channel closed",
"attachments": [],
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}
] |
help-9
|
b29e83821a324c49aab4d514d634fca5
|
197,046 |
[
{
"id": 995483441388855300,
"author_id": 805217272087838700,
"author_name": "Mathematics Bot",
"timestamp": "07/09/2022 20:15:47",
"content": "Available help channel!",
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},
{
"id": 995484140331872300,
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"content": "Pinned a message.",
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"id": 995484159638245400,
"author_id": 281221474604548100,
"author_name": "PoisonedFood",
"timestamp": "07/09/2022 20:18:38",
"content": "Complex Variables",
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},
{
"id": 995484222036918300,
"author_id": 281221474604548100,
"author_name": "PoisonedFood",
"timestamp": "07/09/2022 20:18:53",
"content": "I believe I did this right. Iβm not sure.",
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"id": 995484885722603600,
"author_id": 610882153819144200,
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"timestamp": "07/09/2022 20:21:31",
"content": "yup it's not harmonic",
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{
"id": 995485045001306200,
"author_id": 610882153819144200,
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"timestamp": "07/09/2022 20:22:09",
"content": "u(x, y) MUST be harmonic",
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},
{
"id": 995485090585002000,
"author_id": 281221474604548100,
"author_name": "PoisonedFood",
"timestamp": "07/09/2022 20:22:20",
"content": "So, boom problem solved?",
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{
"id": 995485126886686700,
"author_id": 281221474604548100,
"author_name": "PoisonedFood",
"timestamp": "07/09/2022 20:22:29",
"content": "I just felt like it was too simple of an answer.",
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"id": 995485161103831200,
"author_id": 610882153819144200,
"author_name": "zuko",
"timestamp": "07/09/2022 20:22:37",
"content": "ikr!",
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"id": 995485195459366900,
"author_id": 610882153819144200,
"author_name": "zuko",
"timestamp": "07/09/2022 20:22:45",
"content": "i took my exam in this like 10 days ago",
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},
{
"id": 995485259275706400,
"author_id": 610882153819144200,
"author_name": "zuko",
"timestamp": "07/09/2022 20:23:01",
"content": "they usually give U and ask you to get the function f",
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},
{
"id": 995485284282155100,
"author_id": 281221474604548100,
"author_name": "PoisonedFood",
"timestamp": "07/09/2022 20:23:06",
"content": "You happen to be going to Illinois online?",
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},
{
"id": 995485312035860600,
"author_id": 610882153819144200,
"author_name": "zuko",
"timestamp": "07/09/2022 20:23:13",
"content": "no",
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},
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"id": 995485326824964100,
"author_id": 281221474604548100,
"author_name": "PoisonedFood",
"timestamp": "07/09/2022 20:23:17",
"content": "Dang",
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},
{
"id": 995485361071456300,
"author_id": 281221474604548100,
"author_name": "PoisonedFood",
"timestamp": "07/09/2022 20:23:25",
"content": "Was hoping I found a study buddy",
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},
{
"id": 995485394579763200,
"author_id": 281221474604548100,
"author_name": "PoisonedFood",
"timestamp": "07/09/2022 20:23:33",
"content": "Thanks though!",
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},
{
"id": 995485401877844100,
"author_id": 610882153819144200,
"author_name": "zuko",
"timestamp": "07/09/2022 20:23:35",
"content": "sorry :)",
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},
{
"id": 995485425139458000,
"author_id": 610882153819144200,
"author_name": "zuko",
"timestamp": "07/09/2022 20:23:40",
"content": "ur wlc",
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},
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"id": 995485447939694600,
"author_id": 281221474604548100,
"author_name": "PoisonedFood",
"timestamp": "07/09/2022 20:23:46",
"content": ".close",
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},
{
"id": 995485449416085600,
"author_id": 805217272087838700,
"author_name": "Mathematics Bot",
"timestamp": "07/09/2022 20:23:46",
"content": "Channel closed",
"attachments": [],
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}
] |
help-9
|
bb8a8aae725449b59a09e5363b00684a
|
197,047 |
[
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"timestamp": "07/10/2022 02:08:50",
"content": "Available help channel!",
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"timestamp": "07/10/2022 03:21:15",
"content": "Channel closed",
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}
] |
help-9
|
7d82d5ffe9134eb58a4deb873657b56e
|
197,048 |
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{
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"timestamp": "03/30/2022 00:53:43",
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},
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"timestamp": "03/30/2022 01:08:30",
"content": "I found the derivative",
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"author_id": 292351992242896900,
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"content": "Iβm not sure what to do from there",
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"timestamp": "03/30/2022 01:08:57",
"content": "(Question 16 from the sheet sent above)",
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"id": 958596150863233000,
"author_id": 510789298321096700,
"author_name": "TeXit",
"timestamp": "03/30/2022 01:18:52",
"content": "**sadkid**",
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"author_id": 217686845394386940,
"author_name": "jswatj",
"timestamp": "03/30/2022 01:19:07",
"content": "if each tangent must be positive then shouldn't ad-bc>0?",
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"timestamp": "03/30/2022 01:19:46",
"content": "how did i mess up my derivative?",
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"timestamp": "03/30/2022 01:20:13",
"content": "but showing algebraically",
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"content": "-(ax+b)(c)=-ax-bc",
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"timestamp": "03/30/2022 01:20:41",
"content": "u have -ax+bc",
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"id": 958596639382188000,
"author_id": 485164773647056900,
"author_name": "Gooaaa",
"timestamp": "03/30/2022 01:20:48",
"content": "^",
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"content": "wdym",
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"author_name": "SihathPlaysBass",
"timestamp": "03/30/2022 01:21:13",
"content": "dont i have to show it using the derivative",
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"id": 958596777693544400,
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"author_name": "SihathPlaysBass",
"timestamp": "03/30/2022 01:21:21",
"content": "cus thats what this whole homework is about",
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"id": 958596805677973500,
"author_id": 217686845394386940,
"author_name": "jswatj",
"timestamp": "03/30/2022 01:21:28",
"content": "didn't you just find the derivative?",
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"id": 958596807380836400,
"author_id": 292351992242896900,
"author_name": "SihathPlaysBass",
"timestamp": "03/30/2022 01:21:28",
"content": "which is why im confused",
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"timestamp": "03/30/2022 01:21:31",
"content": "yeah",
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"id": 958596836787114000,
"author_id": 292351992242896900,
"author_name": "SihathPlaysBass",
"timestamp": "03/30/2022 01:21:35",
"content": "but what do i do from there",
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"id": 958596972326052000,
"author_id": 217686845394386940,
"author_name": "jswatj",
"timestamp": "03/30/2022 01:22:08",
"content": "what does it mean for tangents to be positive?",
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"id": 958597003510681600,
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"timestamp": "03/30/2022 01:22:15",
"content": "slope",
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"id": 958597014818537600,
"author_id": 292351992242896900,
"author_name": "SihathPlaysBass",
"timestamp": "03/30/2022 01:22:18",
"content": "of tangents",
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"id": 958597019616829400,
"author_id": 292351992242896900,
"author_name": "SihathPlaysBass",
"timestamp": "03/30/2022 01:22:19",
"content": "i think",
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"id": 958597033076342800,
"author_id": 217686845394386940,
"author_name": "jswatj",
"timestamp": "03/30/2022 01:22:22",
"content": "okay",
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"id": 958597050394628100,
"author_id": 292351992242896900,
"author_name": "SihathPlaysBass",
"timestamp": "03/30/2022 01:22:26",
"content": "like derivative is positive it means",
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"id": 958597061446623200,
"author_id": 217686845394386940,
"author_name": "jswatj",
"timestamp": "03/30/2022 01:22:29",
"content": "and what is a tangent to f(x)",
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"id": 958597065259225100,
"author_id": 217686845394386940,
"author_name": "jswatj",
"timestamp": "03/30/2022 01:22:30",
"content": "yes",
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"author_name": "SihathPlaysBass",
"timestamp": "03/30/2022 01:22:48",
"content": "well f'(x)",
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"id": 958597159928873000,
"author_id": 292351992242896900,
"author_name": "SihathPlaysBass",
"timestamp": "03/30/2022 01:22:52",
"content": "which is what i found",
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"id": 958597248852320300,
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"author_name": "jswatj",
"timestamp": "03/30/2022 01:23:14",
"content": "Yes",
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},
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"id": 958597295677522000,
"author_id": 217686845394386940,
"author_name": "jswatj",
"timestamp": "03/30/2022 01:23:25",
"content": "so what condition on a,b,c,d makes f'(x)>0?",
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"id": 958597428301410300,
"author_id": 292351992242896900,
"author_name": "SihathPlaysBass",
"timestamp": "03/30/2022 01:23:56",
"content": "ad + bc > 0 ??",
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"id": 958597449998549000,
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"author_name": "jswatj",
"timestamp": "03/30/2022 01:24:01",
"content": "yup",
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"id": 958597480063316000,
"author_id": 292351992242896900,
"author_name": "SihathPlaysBass",
"timestamp": "03/30/2022 01:24:09",
"content": "so thats my answer??",
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"id": 958597504629366800,
"author_id": 217686845394386940,
"author_name": "jswatj",
"timestamp": "03/30/2022 01:24:14",
"content": "but it should be ad-bc",
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},
{
"id": 958597532777328600,
"author_id": 217686845394386940,
"author_name": "jswatj",
"timestamp": "03/30/2022 01:24:21",
"content": "from what we fixed before",
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"id": 958597542826881200,
"author_id": 292351992242896900,
"author_name": "SihathPlaysBass",
"timestamp": "03/30/2022 01:24:24",
"content": "why?",
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},
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"id": 958597584748953600,
"author_id": 292351992242896900,
"author_name": "SihathPlaysBass",
"timestamp": "03/30/2022 01:24:34",
"content": "how",
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},
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"timestamp": "03/30/2022 01:24:38",
"content": "^",
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"timestamp": "03/30/2022 01:25:04",
"content": "oh",
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"timestamp": "03/30/2022 01:25:08",
"content": "you are correct",
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"timestamp": "03/30/2022 01:25:09",
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"timestamp": "03/30/2022 01:25:13",
"content": "thank you so much!",
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"author_name": "SihathPlaysBass",
"timestamp": "03/30/2022 01:26:11",
"content": ".close",
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"timestamp": "03/30/2022 01:26:11",
"content": "Channel closed",
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}
] |
help-9
|
c6c290f01a8d4151a3f8d7a2a17ac660
|
197,049 |
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"timestamp": "07/10/2022 03:29:28",
"content": "Available help channel!",
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"content": "@Fin Has your question been resolved?",
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"content": "are confusing me",
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"content": "can you show what you've done so far",
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"author_name": "Fin",
"timestamp": "07/10/2022 03:55:25",
"content": "10^-3 x^3(-3) y^2(-3)/5^-3 x^(-3)(-3) y^(4)(-3)",
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"content": "can you write that out on paper",
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"timestamp": "07/10/2022 04:01:26",
"content": "but i dont got a phone",
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"content": "so i cant send it to u",
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"content": "$\\frac{10^{-3}x^{3(-3)}y^{2(-3)}}{5^{-3}x^{(-3)(-3)}y^{4(-3)}}$",
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"content": "**βamonov**",
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"timestamp": "07/10/2022 04:14:24",
"content": "note that there are things that you could've done first like simplify the 10/5 to 2 to make work easier,\nbut did you do anything after this?",
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"content": "ill try that",
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"content": "Im confused on",
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"timestamp": "07/10/2022 04:15:48",
"content": "what 5^-3",
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"content": "would be",
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"timestamp": "07/10/2022 04:16:29",
"content": "$a^{-n} = \\frac{1}{a^n}$",
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"timestamp": "07/10/2022 04:16:32",
"content": "**βamonov**",
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"content": "1/125",
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"content": "im stuck at",
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"timestamp": "07/10/2022 04:20:20",
"content": "1/25 x^-9 y^-6/1/8 x^9 y^-12",
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"timestamp": "07/10/2022 04:23:31",
"content": "$\\frac{\\frac{1}{25}x^{-9}y^{-6}}{\\frac18 x^9 y^{-12}}$",
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"timestamp": "07/10/2022 04:23:51",
"content": "**βamonov**",
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"content": "ye",
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"content": "thats it",
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"timestamp": "07/10/2022 04:24:10",
"content": "except its",
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"content": "1/125",
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"timestamp": "07/10/2022 04:24:50",
"content": "for which thing",
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"content": "the",
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"timestamp": "07/10/2022 04:25:33",
"content": "numerator",
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"timestamp": "07/10/2022 04:25:39",
"content": "5^(-3)",
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"timestamp": "07/10/2022 04:25:42",
"content": "is 1/125",
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"timestamp": "07/10/2022 04:29:42",
"content": "can you retype what you hav",
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"timestamp": "07/10/2022 04:30:20",
"content": "1/125x^-9y^-6/1/8x x^9 y^-12",
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"timestamp": "07/10/2022 04:36:24",
"content": "how are you getting from $\\frac{10^{-3}}{5^{-3}}$ to \n$$\\frac{\\br{\\frac{1}{125}}}{\\br{\\frac18}}$$",
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"timestamp": "07/10/2022 04:36:41",
"content": "**βamonov**",
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"content": "because",
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"timestamp": "07/10/2022 04:37:07",
"content": "u said",
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"timestamp": "07/10/2022 04:37:20",
"content": "to",
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"timestamp": "07/10/2022 04:37:26",
"content": "simplify it",
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"timestamp": "07/10/2022 04:37:29",
"content": "10/5=5/1",
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"author_id": 183668144404037630,
"author_name": "Ann",
"timestamp": "07/10/2022 04:37:46",
"content": "10/5 is not equal to 5/2",
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"timestamp": "07/10/2022 04:37:58",
"content": "> 10/5=5/2\ni said to simplify it \ni never said to make 10/5 equal to 5/2",
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"timestamp": "07/10/2022 04:38:59",
"content": "oh okie",
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"content": "mb",
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"timestamp": "07/10/2022 04:39:37",
"content": "1/125 x^-9 y^-6/1^-3 x^9 y^-12",
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"timestamp": "07/10/2022 04:40:38",
"content": "the 1^-3 is unnecessary",
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"timestamp": "07/10/2022 04:41:03",
"content": "and also you really should've been using parentheses to clearly indicate numerators and denominators of your fraction",
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"content": "yea",
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"content": "it's fine on paper",
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"timestamp": "07/10/2022 04:41:22",
"content": "but",
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"timestamp": "07/10/2022 04:41:27",
"content": "on pc it's quite messy",
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"content": "fine on paper yes if written properly\non computer, they're necessary to clearly communicate in plain text",
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"timestamp": "07/10/2022 04:42:06",
"content": "anyway\n$$\\frac{\\frac{1}{125} x^{-9}y^{-6}}{x^9 y^{-12}}$$",
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"author_name": "Fin",
"timestamp": "07/10/2022 04:42:18",
"content": "ok",
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"author_name": "TeXit",
"timestamp": "07/10/2022 04:42:30",
"content": "**βamonov**",
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"timestamp": "07/10/2022 04:42:43",
"content": "is that what you currently have",
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"timestamp": "07/10/2022 04:42:48",
"content": "yep",
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"content": "can you try simplifying this",
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"content": "ok",
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"timestamp": "07/10/2022 04:44:01",
"content": "I got",
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"author_name": "Fin",
"timestamp": "07/10/2022 04:44:23",
"content": "1/125 x^(9) y^(12)/x^(9) y^(6)",
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"timestamp": "07/10/2022 04:44:43",
"content": "wait also, didn't catch this earlier but how did you get the 1/125",
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"content": "uhh",
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"timestamp": "07/10/2022 04:45:09",
"content": "well 5^-3",
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"author_name": "Fin",
"timestamp": "07/10/2022 04:45:09",
"content": "is",
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"author_name": "Fin",
"timestamp": "07/10/2022 04:45:10",
"content": "0.008",
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"author_name": "Fin",
"timestamp": "07/10/2022 04:45:23",
"content": "and so is 1/125",
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"author_name": "ramonov",
"timestamp": "07/10/2022 04:45:27",
"content": "if you were going the simplication route,",
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"author_name": "ramonov",
"timestamp": "07/10/2022 04:45:32",
"content": "where's the 5 coming from",
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"author_name": "Fin",
"timestamp": "07/10/2022 04:45:41",
"content": "oh shoot",
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"content": "mb",
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"timestamp": "07/10/2022 04:45:43",
"content": "10/5 = ?",
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"id": 995611774592225400,
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"author_name": "Fin",
"timestamp": "07/10/2022 04:45:44",
"content": "im tired",
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"id": 995611781319884800,
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"author_name": "Fin",
"timestamp": "07/10/2022 04:45:46",
"content": "LOL",
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"author_name": "Fin",
"timestamp": "07/10/2022 04:45:47",
"content": "sorry",
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"id": 995611849213092000,
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"author_name": "Fin",
"timestamp": "07/10/2022 04:46:02",
"content": "2*",
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"author_name": "ramonov",
"timestamp": "07/10/2022 04:46:27",
"content": "what do you have now?",
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"author_name": "Fin",
"timestamp": "07/10/2022 04:46:28",
"content": "so it would be",
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"timestamp": "07/10/2022 04:46:29",
"content": "1/8",
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"id": 995611970227159200,
"author_id": 991855742086815900,
"author_name": "Fin",
"timestamp": "07/10/2022 04:46:31",
"content": "on top?",
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"id": 995612005035675600,
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"author_name": "Fin",
"timestamp": "07/10/2022 04:46:39",
"content": "or 0.125",
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"timestamp": "07/10/2022 04:46:47",
"content": "fractions are better",
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"id": 995612108580454500,
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"author_name": "Fin",
"timestamp": "07/10/2022 04:47:04",
"content": "alr",
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"timestamp": "07/10/2022 04:47:12",
"content": "damn I couldnt do 10/5 π",
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"timestamp": "07/10/2022 04:47:35",
"content": "here is my options",
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"content": "not what i asked for",
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"content": "i think i messed up",
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"id": 995613406440730800,
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"timestamp": "07/10/2022 04:52:13",
"content": "oh wait i got it",
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"id": 995613409804566500,
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"content": "lol",
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"content": ".close",
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}
] |
help-9
|
d57d0a61e856473e8dff21960e3b3f11
|
197,050 |
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"timestamp": "07/10/2022 05:11:56",
"content": "Hey, I am trying to develop a proof for $\\sum_{k=0}^n (-1)^{n-k} \\binom{n}{k} k^n = n!$. \n\nContext:\n\n$\\Delta^n_h f(x) = \\sum_{k=0}^n (-1)^{n-k} \\binom{n}{k} f(x+kh)$, which for $f(x) = x^n$ should be $\\Delta^n_h=n!h^n$\n\nMy idea is to do it by induction but I am somehow getting stuck - any help more than welcome π",
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"content": "**wassp**",
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"content": "@Helpers ping ping π",
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"content": "@wassp Has your question been resolved?",
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"content": "@wassp Has your question been resolved?",
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"content": "Channel closed",
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] |
help-9
|
62fd97a4b2d64240b9ecd6c49b93254b
|
197,051 |
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"content": "Available help channel!",
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"content": "if i wanted to right this in the exponential form with a base of 2",
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"timestamp": "07/10/2022 07:19:20",
"content": "perhaps you would need to remember that 4 = 2^2 and that sqrt(x) = x^(1/2)",
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"timestamp": "07/10/2022 07:22:49",
"content": "yeah",
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"content": "but how do i remove the square root",
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"timestamp": "07/10/2022 07:23:12",
"content": "iβm confused",
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"timestamp": "07/10/2022 07:25:48",
"content": "> and that sqrt(x) = x^(1/2)",
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"timestamp": "07/10/2022 07:29:27",
"content": "is this correct so far?",
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"timestamp": "07/10/2022 07:31:26",
"content": "so far so good",
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"timestamp": "07/10/2022 07:31:47",
"content": "iβm not sure what i would do next tho",
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"timestamp": "07/10/2022 07:32:30",
"content": "you have 2a * (1/2)",
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"timestamp": "07/10/2022 07:33:55",
"content": "yeah",
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"content": "so what do you get",
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"content": "no idea",
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"id": 995654397541498900,
"author_id": 852256521986768900,
"author_name": ".,..",
"timestamp": "07/10/2022 07:35:06",
"content": "aaa",
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"id": 995654401584795600,
"author_id": 852256521986768900,
"author_name": ".,..",
"timestamp": "07/10/2022 07:35:07",
"content": "a",
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"id": 995654484657184800,
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"author_name": "HeadShotCem",
"timestamp": "07/10/2022 07:35:27",
"content": "2^a / 2",
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"author_name": "HeadShotCem",
"timestamp": "07/10/2022 07:35:38",
"content": "= 2^(a-1)",
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"id": 995654940443816000,
"author_id": 733275240515371000,
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"timestamp": "07/10/2022 07:37:16",
"content": "oh yh iβve got it now",
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"content": "ty",
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"author_name": "Mathematics Bot",
"timestamp": "07/10/2022 07:52:17",
"content": "@Dabush27 Has your question been resolved?",
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"timestamp": "07/10/2022 07:52:28",
"content": "Channel closed",
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] |
help-9
|
943ebb7a0043401cada2ff56a1eaa145
|
197,052 |
[
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"timestamp": "07/10/2022 07:53:28",
"content": "Available help channel!",
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"content": "Pinned a message.",
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] |
help-9
|
dc22ede2874740299ec3bd32ef0e29c2
|
197,053 |
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"timestamp": "07/10/2022 08:22:41",
"content": "Available help channel!",
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"id": 995669661540696200,
"author_id": 456226577798135800,
"author_name": "Deleted User",
"timestamp": "07/10/2022 08:35:45",
"content": "",
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"content": "Pinned a message.",
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"id": 995669773138542700,
"author_id": 456226577798135800,
"author_name": "Deleted User",
"timestamp": "07/10/2022 08:36:12",
"content": "I can't understand why it goes to -infinite",
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"id": 995669820194443300,
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"author_name": "Deleted User",
"timestamp": "07/10/2022 08:36:23",
"content": "Like.. I can't understand the explanation",
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"id": 995669968060424300,
"author_id": 456226577798135800,
"author_name": "Deleted User",
"timestamp": "07/10/2022 08:36:59",
"content": "Which steps are done in the middle?",
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"timestamp": "07/10/2022 08:40:25",
"content": "consider where\nx^2 -4x + 3 is negative and where its positive",
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"id": 995671012119163000,
"author_id": 183668144404037630,
"author_name": "Ann",
"timestamp": "07/10/2022 08:41:07",
"content": "factoring it as (x-1)(x-3) might also help",
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"id": 995671323013554300,
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"timestamp": "07/10/2022 08:42:22",
"content": "other argument: the denominator has derivative -2 at x=1 so it decreases, since it's 0 at 1, that means it's negative to the right of 1",
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"timestamp": "07/10/2022 08:46:49",
"content": "Thank you!",
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"timestamp": "07/10/2022 08:46:53",
"content": ".close",
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] |
help-9
|
34893b65d6c64662a528e111d4e12a70
|
197,054 |
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"content": "Available help channel!",
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"content": "help please",
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"content": "what have you tried",
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"author_name": "Umbraleviathan",
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"content": "Power theorem case 2",
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"timestamp": "07/10/2022 09:13:28",
"content": "i have no idea what that is",
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"timestamp": "07/10/2022 09:14:18",
"content": "Google it then",
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"timestamp": "07/10/2022 09:14:43",
"content": "the specific cases go by other names",
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"timestamp": "07/10/2022 09:14:50",
"content": "here you have two secants",
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"content": "https://naperville203geometry.weebly.com/power-theorems.html",
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"timestamp": "07/10/2022 09:15:02",
"content": "There's this I guess",
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"author_name": "ramonov",
"timestamp": "07/10/2022 09:15:03",
"content": "and you can apply what some may refer to as the secant-secant theorem",
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"timestamp": "07/10/2022 09:15:20",
"content": "First thing on Google if you search up \"power theorem formulas\"",
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"timestamp": "07/10/2022 09:15:31",
"content": "the name of the theorem pretty much describes what its used for",
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"author_name": "milkman",
"timestamp": "07/10/2022 09:16:12",
"content": "this\\",
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"id": 995679846346805200,
"author_id": 866794957784481800,
"author_name": "milkman",
"timestamp": "07/10/2022 09:16:14",
"content": "is confusing",
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"author_name": "ramonov",
"timestamp": "07/10/2022 09:16:16",
"content": "power of a point is more general and also covers sec-tan, tan-tan",
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"id": 995679878538072000,
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"timestamp": "07/10/2022 09:16:21",
"content": "wait",
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"id": 995679888952545400,
"author_id": 600510288067952600,
"author_name": "GarlicBredFries",
"timestamp": "07/10/2022 09:16:24",
"content": "Ah power of a point",
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"id": 995679902101680100,
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"timestamp": "07/10/2022 09:16:27",
"content": "Ram couldnt i do cross multiply",
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"timestamp": "07/10/2022 09:16:33",
"content": "like for similar triangles",
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"timestamp": "07/10/2022 09:16:39",
"content": "could that work?",
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"timestamp": "07/10/2022 09:16:42",
"content": "be more specific",
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"author_name": "Umbraleviathan",
"timestamp": "07/10/2022 09:16:45",
"content": "Just use secant-secant power theorem",
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"timestamp": "07/10/2022 09:16:45",
"content": "what are you multiplying",
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"author_name": "milkman",
"timestamp": "07/10/2022 09:17:01",
"content": "so we wanna find C so 11/20 * 13/c ???",
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"timestamp": "07/10/2022 09:17:02",
"content": "i really have a disdain for how cross-multiplication is just thrown around",
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"timestamp": "07/10/2022 09:17:36",
"content": "did i get it right",
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"timestamp": "07/10/2022 09:17:41",
"content": "no",
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"timestamp": "07/10/2022 09:17:50",
"content": "wait but could cross multiply work tho",
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"timestamp": "07/10/2022 09:17:51",
"content": "there is no equation",
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"author_name": "ramonov",
"timestamp": "07/10/2022 09:18:07",
"content": "that will not result in an equation telling you what c is",
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"author_name": "Umbraleviathan",
"timestamp": "07/10/2022 09:18:12",
"content": "11(11+20) = 13(13+c)",
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"author_name": "Umbraleviathan",
"timestamp": "07/10/2022 09:18:25",
"content": "That's the sec-sec power theorem (or, case 2)",
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"author_name": "ramonov",
"timestamp": "07/10/2022 09:18:45",
"content": "look up the sec-sec theorem and set up your equation properly",
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"id": 995680554647302100,
"author_id": 220517274845577200,
"author_name": "ramonov",
"timestamp": "07/10/2022 09:19:03",
"content": "instead of disregarding everything we've been saying and trying to half-ass it on your own",
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"timestamp": "07/10/2022 09:19:15",
"content": "can u give me the formula",
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"timestamp": "07/10/2022 09:19:25",
"content": "im sorry :((",
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"timestamp": "07/10/2022 09:19:25",
"content": "look up secant secant theorem",
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"timestamp": "07/10/2022 09:19:29",
"content": "ok",
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"id": 995680687850004600,
"author_id": 220517274845577200,
"author_name": "ramonov",
"timestamp": "07/10/2022 09:19:34",
"content": "as we've been saying over three times now",
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"timestamp": "07/10/2022 09:19:47",
"content": "ok",
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"author_id": 349354952961032200,
"author_name": "Umbraleviathan",
"timestamp": "07/10/2022 09:19:59",
"content": "**it's literally right here**",
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"author_name": "Umbraleviathan",
"timestamp": "07/10/2022 09:20:03",
"content": "Maybe *read*",
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"id": 995680847434887300,
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"timestamp": "07/10/2022 09:20:12",
"content": "ok",
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"timestamp": "07/10/2022 09:21:22",
"content": "i got this",
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"timestamp": "07/10/2022 09:22:01",
"content": "looks ok",
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"timestamp": "07/10/2022 09:22:12",
"content": "Yeah",
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"author_name": "ramonov",
"timestamp": "07/10/2022 09:22:12",
"content": "unless told otherwise, just leave c as 172/13",
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"timestamp": "07/10/2022 09:23:01",
"content": "ok",
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"timestamp": "07/10/2022 09:23:12",
"content": "wait ineed to take notes",
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"timestamp": "07/10/2022 09:24:46",
"content": "@Umbraleviathan this circle diagram is different from the question",
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"timestamp": "07/10/2022 09:25:07",
"content": "Because that's the chord-chord",
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"timestamp": "07/10/2022 09:25:13",
"content": "Again, read the whole page",
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"timestamp": "07/10/2022 09:25:16",
"content": "There are 3 cases",
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"author_name": "Umbraleviathan",
"timestamp": "07/10/2022 09:25:28",
"content": "What you want is secant-secant",
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"id": 995682331522257000,
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"author_name": "milkman",
"timestamp": "07/10/2022 09:26:06",
"content": "oh",
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"id": 995682469154128000,
"author_id": 866794957784481800,
"author_name": "milkman",
"timestamp": "07/10/2022 09:26:39",
"content": "need to take more notes",
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},
{
"id": 995682524326015000,
"author_id": 349354952961032200,
"author_name": "Umbraleviathan",
"timestamp": "07/10/2022 09:26:52",
"content": "I mean at this point it's just you needing to read the full page",
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"timestamp": "07/10/2022 09:30:44",
"content": "ya",
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"timestamp": "07/10/2022 09:32:57",
"content": "i got it thanks",
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"id": 995684175170502700,
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"author_name": "milkman",
"timestamp": "07/10/2022 09:33:26",
"content": "if its backwards like this does it still work?",
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"author_name": "Umbraleviathan",
"timestamp": "07/10/2022 09:34:07",
"content": "As long as it's two secants that meet externally, it applies",
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"timestamp": "07/10/2022 09:34:33",
"content": "okok",
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"timestamp": "07/10/2022 09:34:39",
"content": "i got its its 7/2",
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"author_name": "milkman",
"timestamp": "07/10/2022 09:34:48",
"content": "thanks :)))",
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"author_name": "milkman",
"timestamp": "07/10/2022 09:36:32",
"content": "@Umbraleviathan dio u have a formula for this?",
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"author_name": "Umbraleviathan",
"timestamp": "07/10/2022 09:39:37",
"content": "A minute mark is 6Β°, halfway between each hour mark is 15Β°",
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"author_name": "milkman",
"timestamp": "07/10/2022 09:40:30",
"content": "wait wha",
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"id": 995686034828427300,
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"timestamp": "07/10/2022 09:40:49",
"content": "ik a minutes= 6 degree",
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"author_name": "milkman",
"timestamp": "07/10/2022 09:40:54",
"content": "cuz 360/60",
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"id": 995686141435052200,
"author_id": 349354952961032200,
"author_name": "Umbraleviathan",
"timestamp": "07/10/2022 09:41:15",
"content": "You know how analog clocks work?",
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"author_name": "Umbraleviathan",
"timestamp": "07/10/2022 09:41:40",
"content": "At 1:30, the minute hand will be on the 6 Hour Mark, the hour will be between the 1 and 2 marks",
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"timestamp": "07/10/2022 09:44:02",
"content": "this is confusing",
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"timestamp": "07/10/2022 09:44:19",
"content": "ok yea i get it nw",
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"timestamp": "07/10/2022 09:45:00",
"content": "so =90*6",
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"id": 995687125645271000,
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"author_name": "milkman",
"timestamp": "07/10/2022 09:45:09",
"content": "1 hour =60 and + 30 min",
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"id": 995687824747659300,
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"timestamp": "07/10/2022 09:47:56",
"content": "ok this is confusing",
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"id": 995688174611333200,
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"author_name": "milkman",
"timestamp": "07/10/2022 09:49:19",
"content": "ok im gonna come back to that",
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"id": 995688196459466900,
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"author_name": "milkman",
"timestamp": "07/10/2022 09:49:25",
"content": "can u help with this",
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"content": "@milkman Has your question been resolved?",
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"content": "@milkman Has your question been resolved?",
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"content": "Channel closed",
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] |
help-9
|
bf4aa9457829441d86cfafb978e51a5e
|
197,055 |
[
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"timestamp": "07/10/2022 11:05:30",
"content": "Available help channel!",
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"author_id": 838773920349946000,
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"timestamp": "07/10/2022 11:09:13",
"content": "so i have a physics question: the question translated is 2 weights with m1 being 10kg and m2 being 5kg are placed like in the picture where there both connected by a string and you need to find out what a (acceleration) of the weights is",
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"content": "this is how i solved it but its marked as wrong",
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"content": "friction is negligible",
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"timestamp": "07/10/2022 11:25:16",
"content": "@Helpers",
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"content": "@ghostkiller8804 Has your question been resolved?",
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"content": "pls this is not that hard of a question",
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] |
help-9
|
5b26436eb7014df582207b8729d1dc4a
|
197,056 |
[
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}
] |
help-9
|
6107701795274df0894c042556ba61c3
|
197,057 |
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"timestamp": "07/10/2022 12:21:47",
"content": "I can't understand the steps for that underlined part to tend to 1",
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"timestamp": "07/10/2022 12:44:44",
"content": "You break the root onto the numerator and denominator",
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"timestamp": "07/10/2022 13:05:16",
"content": "Sorry I'm not understanding",
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"timestamp": "07/10/2022 13:07:10",
"content": "The 1/(n^1/n) tends to 1 for the rest to make sense but is that something \"to know\"? That the (n^1/n) tends to 1 for n->infinite",
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"content": "No okay I got it",
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"author_id": 456226577798135800,
"author_name": "Deleted User",
"timestamp": "07/10/2022 13:08:47",
"content": "Solved, thank you",
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"author_id": 456226577798135800,
"author_name": "Deleted User",
"timestamp": "07/10/2022 13:08:50",
"content": ".close",
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"id": 995738385203331200,
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"author_name": "Mathematics Bot",
"timestamp": "07/10/2022 13:08:50",
"content": "Channel closed",
"attachments": [],
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}
] |
help-9
|
9c60f9ff5cc548b48995e6c63844c90a
|
197,058 |
[
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"timestamp": "07/10/2022 13:44:53",
"content": "Available help channel!",
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},
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"id": 995748043553001500,
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"content": "Pinned a message.",
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"timestamp": "07/10/2022 13:47:57",
"content": "Channel closed",
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}
] |
help-9
|
af18a32b00904724a0c081beac2c151e
|
197,059 |
[
{
"id": 958642842845188100,
"author_id": 805217272087838700,
"author_name": "Mathematics Bot",
"timestamp": "03/30/2022 04:24:24",
"content": "Available help channel!",
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},
{
"id": 958645079063556100,
"author_id": 533068175370223600,
"author_name": "likooooooo",
"timestamp": "03/30/2022 04:33:17",
"content": "Hello guys, does anyone know how to explain this to me?",
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"id": 958645081110347800,
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"content": "Pinned a message.",
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"author_name": "likooooooo",
"timestamp": "03/30/2022 04:33:55",
"content": "not the answer just like the graph in general?",
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"id": 958645640118829000,
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"author_name": "likooooooo",
"timestamp": "03/30/2022 04:35:31",
"content": "is the line in the rectangular box the median?",
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"id": 958646249999990800,
"author_id": 485903210272391200,
"author_name": "dldh06",
"timestamp": "03/30/2022 04:37:56",
"content": "I think that concept is a box and whisker plot",
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"id": 958646310939017200,
"author_id": 485903210272391200,
"author_name": "dldh06",
"timestamp": "03/30/2022 04:38:11",
"content": "So the box with lines is box and whisker",
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"id": 958646364730978300,
"author_id": 485903210272391200,
"author_name": "dldh06",
"timestamp": "03/30/2022 04:38:24",
"content": "The graph on the bottom is a histogram type of plot",
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"timestamp": "03/30/2022 04:50:31",
"content": "@likooooooo Has your question been resolved?",
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"content": "Channel closed",
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help-9
|
75fbcf0fd3ab4cac83f3e70765d9c78c
|
197,060 |
[
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"author_name": "Mathematics Bot",
"timestamp": "07/10/2022 14:17:01",
"content": "Available help channel!",
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"content": "Pinned a message.",
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"content": "given that this is a multiple choice question the least thinking-intensive option is to check each answer option against the given recurrence relation",
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"timestamp": "07/10/2022 14:36:34",
"content": "yeah, you can just check it gives the right answer for a1, a2, and a3",
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"author_name": "Eric Tao",
"timestamp": "07/10/2022 14:36:54",
"content": "alternatively, you know it has to be a quadratic since you're adding a linear term each time, so you can use lagrange interpolation",
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"timestamp": "07/10/2022 14:43:44",
"content": "@sushi Has your question been resolved?",
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"author_name": "Ann",
"timestamp": "07/10/2022 14:55:19",
"content": "get to what exactly",
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"id": 995765225548685300,
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"author_name": "Asagao ζι‘",
"timestamp": "07/10/2022 14:55:30",
"content": "you could use discrete calculus",
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"id": 995765226223968300,
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"author_name": "Ann",
"timestamp": "07/10/2022 14:55:30",
"content": "i do not understand your question",
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"author_name": "Asagao ζι‘",
"timestamp": "07/10/2022 14:56:39",
"content": "don't :sully: me",
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"content": "I mean yeah discrete calculus is the best way to do this",
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"timestamp": "07/10/2022 14:57:04",
"content": "^ @sushi",
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"author_name": "Ann",
"timestamp": "07/10/2022 14:57:27",
"content": "do you mean how to arrive at the answer without going through the options",
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"timestamp": "07/10/2022 14:57:42",
"content": "in this case you can express a_n as a sum",
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"author_name": "Ann",
"timestamp": "07/10/2022 14:58:07",
"content": "no, not every **sum** equals n(n-1)/2...",
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"author_name": "Ann",
"timestamp": "07/10/2022 14:58:20",
"content": "specifically $a_n = a_1 + \\sum_{k=2}^n 10k$ if i did not fuck up",
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"timestamp": "07/10/2022 14:58:22",
"content": "**Ann**",
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"timestamp": "07/10/2022 14:58:33",
"content": "i may have made an off by 1 error somewhere but i do not believe i have",
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"timestamp": "07/10/2022 14:58:41",
"content": "looks good to me",
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"timestamp": "07/10/2022 14:58:45",
"content": "Channel closed",
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help-9
|
1b9699682b4640699b30ca5873a8d7cd
|
197,061 |
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"id": 995766062731755600,
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"timestamp": "07/10/2022 14:58:49",
"content": ".reopen",
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"id": 995766068033368000,
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"timestamp": "07/10/2022 14:58:51",
"content": "β
",
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"author_name": "Eric Tao",
"timestamp": "07/10/2022 14:58:56",
"content": "I mean it does end up being k(k-1)/2 almost",
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"timestamp": "07/10/2022 14:59:09",
"content": "but not quite",
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"author_name": "Ann",
"timestamp": "07/10/2022 14:59:10",
"content": "@sushi stop pressing yes on the \"has your q been resolved\" when it hasnt",
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"author_name": "Asagao ζι‘",
"timestamp": "07/10/2022 14:59:18",
"content": "one question",
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"id": 995766197968707600,
"author_id": 907667015756574800,
"author_name": "Asagao ζι‘",
"timestamp": "07/10/2022 14:59:22",
"content": "why does k go from 2",
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"timestamp": "07/10/2022 14:59:23",
"content": "and not 1",
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"timestamp": "07/10/2022 14:59:36",
"content": "(? I thought that the bot generated the yes button)",
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"author_name": "Ann",
"timestamp": "07/10/2022 14:59:37",
"content": "the first application of the recurrence would be at n=2",
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"author_name": "Asagao ζι‘",
"timestamp": "07/10/2022 15:00:15",
"content": "oh ig that makes sense",
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"timestamp": "07/10/2022 15:00:49",
"content": "it timed out lol",
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"id": 995766821401657300,
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"author_name": "Asagao ζι‘",
"timestamp": "07/10/2022 15:01:50",
"content": "well n(n+1)/2",
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"id": 995767939749912700,
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"author_name": "Asagao ζι‘",
"timestamp": "07/10/2022 15:06:17",
"content": "what",
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"id": 995768018359558300,
"author_id": 907667015756574800,
"author_name": "Asagao ζι‘",
"timestamp": "07/10/2022 15:06:36",
"content": "do you know how summation works",
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"author_name": "Asagao ζι‘",
"timestamp": "07/10/2022 15:07:44",
"content": "${\\displaystyle \\sum _{i=0}^{n}i=\\sum _{i=1}^{n}i={\\frac {n(n+1)}{2}}\\qquad }$",
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"id": 995768317421834400,
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"author_name": "TeXit",
"timestamp": "07/10/2022 15:07:47",
"content": "**Asagao ζι‘**",
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"timestamp": "07/10/2022 15:08:13",
"content": "from where",
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"id": 995768474137788400,
"author_id": 907667015756574800,
"author_name": "Asagao ζι‘",
"timestamp": "07/10/2022 15:08:24",
"content": "from the beginning or from the point where you have the sum",
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"author_name": "Eric Tao",
"timestamp": "07/10/2022 15:10:54",
"content": "if you can find the sum of k then you can find the sum of 10k",
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"id": 995769230479863900,
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"timestamp": "07/10/2022 15:11:25",
"content": "multiply it by 10",
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"author_name": "Asagao ζι‘",
"timestamp": "07/10/2022 15:11:29",
"content": "${\\displaystyle \\sum _{n=s}^{t}C\\cdot f(n)=C\\cdot \\sum _{n=s}^{t}f(n)\\quad }$",
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"id": 995769260985028700,
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"timestamp": "07/10/2022 15:11:32",
"content": "**Asagao ζι‘**",
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"author_name": "Asagao ζι‘",
"timestamp": "07/10/2022 15:11:40",
"content": "distributivity is a thing",
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"timestamp": "07/10/2022 15:11:41",
"content": "no",
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"author_name": "Asagao ζι‘",
"timestamp": "07/10/2022 15:12:06",
"content": "you can just take out constant multiples from the sum",
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"timestamp": "07/10/2022 15:13:29",
"content": "not quite",
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"id": 995769803983818800,
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"author_name": "Asagao ζι‘",
"timestamp": "07/10/2022 15:13:41",
"content": "because the sum is from 2 to n",
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"id": 995769866298589200,
"author_id": 907667015756574800,
"author_name": "Asagao ζι‘",
"timestamp": "07/10/2022 15:13:56",
"content": "except the identity only works for 1 to n",
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"id": 995770044518760600,
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"author_name": "Asagao ζι‘",
"timestamp": "07/10/2022 15:14:39",
"content": "yes",
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"id": 995770084314329200,
"author_id": 907667015756574800,
"author_name": "Asagao ζι‘",
"timestamp": "07/10/2022 15:14:48",
"content": "yeah",
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"id": 995770584367648800,
"author_id": 265853506664136700,
"author_name": "ScapeProf",
"timestamp": "07/10/2022 15:16:47",
"content": "Its just reading",
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"author_id": 265853506664136700,
"author_name": "ScapeProf",
"timestamp": "07/10/2022 15:16:53",
"content": "Not decimal or integer value",
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},
{
"id": 995770617418752100,
"author_id": 907667015756574800,
"author_name": "Asagao ζι‘",
"timestamp": "07/10/2022 15:16:55",
"content": "^",
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},
{
"id": 995770635907256300,
"author_id": 265853506664136700,
"author_name": "ScapeProf",
"timestamp": "07/10/2022 15:17:00",
"content": "Try giving answer as that then?",
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},
{
"id": 995771026166251600,
"author_id": 531535537362829300,
"author_name": "Eric Tao",
"timestamp": "07/10/2022 15:18:33",
"content": "yes convert it to a decimal",
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},
{
"id": 995775522753757300,
"author_id": 805217272087838700,
"author_name": "Mathematics Bot",
"timestamp": "07/10/2022 15:36:25",
"content": "@sushi Has your question been resolved?",
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"timestamp": "07/10/2022 16:07:42",
"content": "Channel closed",
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}
] |
help-9
|
308585e830844557a232c9303906c7e8
|
197,062 |
[
{
"id": 995783648408252400,
"author_id": 805217272087838700,
"author_name": "Mathematics Bot",
"timestamp": "07/10/2022 16:08:42",
"content": "Available help channel!",
"attachments": [],
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"reference": null
},
{
"id": 995789377810735100,
"author_id": 144557771675664400,
"author_name": "nirnael",
"timestamp": "07/10/2022 16:31:28",
"content": "if a complex function can be represented as vectors from the poles and zeros, the angle of the function at some point should be angle of zeros - angle of poles. In this case, the zero angle is atan(-sqrt(10)) which becomes 180-atan(sqrt(10)). However, that seems to be incorrect and it's actually -72 degrees. I tried it 10 times and I just can't find where the error is",
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"id": 995789380847419400,
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"author_name": "Mathematics Bot",
"timestamp": "07/10/2022 16:31:29",
"content": "Pinned a message.",
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}
},
{
"id": 995789726999130100,
"author_id": 144557771675664400,
"author_name": "nirnael",
"timestamp": "07/10/2022 16:32:51",
"content": "if you represent the function in algebraic form a+i*b, it correctly gives -72, but why is the vector representation failing here?",
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},
{
"id": 995793502854197200,
"author_id": 805217272087838700,
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"timestamp": "07/10/2022 16:47:52",
"content": "@nirnael Has your question been resolved?",
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"id": 995797445176996000,
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"author_name": "nirnael",
"timestamp": "07/10/2022 17:03:31",
"content": "@Helpers",
"attachments": [],
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"reference": null
},
{
"id": 995799266310238300,
"author_id": 531535537362829300,
"author_name": "Eric Tao",
"timestamp": "07/10/2022 17:10:46",
"content": "wait what do you mean by representing it as vectors from the poles and zeros? never seen this before",
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},
{
"id": 995799288988831900,
"author_id": 531535537362829300,
"author_name": "Eric Tao",
"timestamp": "07/10/2022 17:10:51",
"content": "can you link a resource",
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},
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"id": 995800417508266000,
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"author_name": "nirnael",
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"content": "",
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"author_name": "Eric Tao",
"timestamp": "07/10/2022 17:16:38",
"content": "ohh that's what you mean okay got it",
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},
{
"id": 995800766398873600,
"author_id": 531535537362829300,
"author_name": "Eric Tao",
"timestamp": "07/10/2022 17:16:43",
"content": "lemme look at your work",
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},
{
"id": 995800896988528800,
"author_id": 531535537362829300,
"author_name": "Eric Tao",
"timestamp": "07/10/2022 17:17:14",
"content": "what number are you evaluating your function at?",
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},
{
"id": 995800977863102600,
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"author_name": "nirnael",
"timestamp": "07/10/2022 17:17:34",
"content": "infinitesimally close to the upper pole",
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},
{
"id": 995801015771209900,
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"author_name": "nirnael",
"timestamp": "07/10/2022 17:17:43",
"content": "from below",
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},
{
"id": 995801133551468700,
"author_id": 531535537362829300,
"author_name": "Eric Tao",
"timestamp": "07/10/2022 17:18:11",
"content": "hmm so j(sqrt(10) - epsilon) where epsilon is just some number",
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},
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"id": 995801410857861200,
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"author_name": "nirnael",
"timestamp": "07/10/2022 17:19:17",
"content": "yeah. In this case the upper pole contributes -90, the lower +90 and the zero the atan",
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},
{
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"author_name": "nirnael",
"timestamp": "07/10/2022 17:19:42",
"content": "this feels like a basic trig mistake, but I just don't see it",
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},
{
"id": 995801570216255600,
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"author_name": "Eric Tao",
"timestamp": "07/10/2022 17:19:55",
"content": "yeah this should be simple to work out gimme a sec",
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{
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"author_name": "Eric Tao",
"timestamp": "07/10/2022 17:24:17",
"content": "okay I'm getting the angle in either case as arctan(-sqrt(10) + epsilon)",
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"author_name": "Eric Tao",
"timestamp": "07/10/2022 17:25:07",
"content": "or -72.45 degrees",
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},
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"id": 995803153280815200,
"author_id": 531535537362829300,
"author_name": "Eric Tao",
"timestamp": "07/10/2022 17:26:12",
"content": "how did you get 180 - atan(sqrt(10)) here",
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"author_name": "Eric Tao",
"timestamp": "07/10/2022 17:26:40",
"content": "ohhh wait I think I see where you're getting confused",
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},
{
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"author_name": "Eric Tao",
"timestamp": "07/10/2022 17:27:08",
"content": "this assumes that the coefficient for s is 1",
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"id": 995803476045091000,
"author_id": 531535537362829300,
"author_name": "Eric Tao",
"timestamp": "07/10/2022 17:27:29",
"content": "you can easily put your formula in that form if you write it as -(s-1)/(s^2+10)",
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},
{
"id": 995803515307950200,
"author_id": 531535537362829300,
"author_name": "Eric Tao",
"timestamp": "07/10/2022 17:27:39",
"content": "but of course the - adds a 180 degree difference in phase",
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},
{
"id": 995803535167991900,
"author_id": 531535537362829300,
"author_name": "Eric Tao",
"timestamp": "07/10/2022 17:27:43",
"content": "hope this helps?",
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},
{
"id": 995803705683222500,
"author_id": 144557771675664400,
"author_name": "nirnael",
"timestamp": "07/10/2022 17:28:24",
"content": "ohhhh",
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},
{
"id": 995803780589289500,
"author_id": 144557771675664400,
"author_name": "nirnael",
"timestamp": "07/10/2022 17:28:42",
"content": "right, it wasnt in standard form",
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},
{
"id": 995803912487571500,
"author_id": 531535537362829300,
"author_name": "Eric Tao",
"timestamp": "07/10/2022 17:29:13",
"content": "π",
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},
{
"id": 995803951385542800,
"author_id": 144557771675664400,
"author_name": "nirnael",
"timestamp": "07/10/2022 17:29:23",
"content": "yeah, I see it now. Thanks",
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},
{
"id": 995804032042020900,
"author_id": 144557771675664400,
"author_name": "nirnael",
"timestamp": "07/10/2022 17:29:42",
"content": ".close",
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},
{
"id": 995804033744904300,
"author_id": 805217272087838700,
"author_name": "Mathematics Bot",
"timestamp": "07/10/2022 17:29:42",
"content": "Channel closed",
"attachments": [],
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}
] |
help-9
|
4cf83acc9eff40c48b263e16f5c0123f
|
197,063 |
[
{
"id": 995831976017793000,
"author_id": 805217272087838700,
"author_name": "Mathematics Bot",
"timestamp": "07/10/2022 19:20:44",
"content": "Available help channel!",
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"reference": null
},
{
"id": 995837856205520900,
"author_id": 904112740401037300,
"author_name": "wowa",
"timestamp": "07/10/2022 19:44:06",
"content": "",
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"url": "https://cdn.discordapp.com/attachments/486844875632017408/995837855265988669/Screenshot_2022-07-10_164333.png",
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"timestamp": "07/10/2022 19:44:07",
"content": "Pinned a message.",
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{
"id": 995837880100458500,
"author_id": 904112740401037300,
"author_name": "wowa",
"timestamp": "07/10/2022 19:44:12",
"content": "my book says this isn't a transitive relation",
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},
{
"id": 995837975655092200,
"author_id": 904112740401037300,
"author_name": "wowa",
"timestamp": "07/10/2022 19:44:35",
"content": "but this is right? since there are no relation (a,b) (b,c) (a,c), it doesn't fail the transitive relation definition",
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},
{
"id": 995838242731601900,
"author_id": 531535537362829300,
"author_name": "Eric Tao",
"timestamp": "07/10/2022 19:45:38",
"content": "it is not transitive",
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},
{
"id": 995838273081589800,
"author_id": 531535537362829300,
"author_name": "Eric Tao",
"timestamp": "07/10/2022 19:45:46",
"content": "for example, 2,4 and 4,2 are both in it but not 2,2",
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},
{
"id": 995838304756961300,
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"author_name": "Eric Tao",
"timestamp": "07/10/2022 19:45:53",
"content": "also, 4,2 and 2,4 are both in it but not 4,4",
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},
{
"id": 995838440627257300,
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"author_name": "wowa",
"timestamp": "07/10/2022 19:46:26",
"content": "ahhh i goofed",
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},
{
"id": 995838468469051400,
"author_id": 904112740401037300,
"author_name": "wowa",
"timestamp": "07/10/2022 19:46:32",
"content": "ty for pointing that out",
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"id": 995838504087068800,
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"author_name": "wowa",
"timestamp": "07/10/2022 19:46:41",
"content": ".close",
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},
{
"id": 995838508126191600,
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"timestamp": "07/10/2022 19:46:42",
"content": "Channel closed",
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}
] |
help-9
|
b447fc873c6a4eb59298d610df182d31
|
197,064 |
[
{
"id": 995847477842411600,
"author_id": 805217272087838700,
"author_name": "Mathematics Bot",
"timestamp": "07/10/2022 20:22:20",
"content": "Available help channel!",
"attachments": [],
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"reference": null
},
{
"id": 995849367720316900,
"author_id": 805217272087838700,
"author_name": "Mathematics Bot",
"timestamp": "07/10/2022 20:29:51",
"content": "Pinned a message.",
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"id": 995849376004046800,
"author_id": 510789298321096700,
"author_name": "TeXit",
"timestamp": "07/10/2022 20:29:53",
"content": "**Carpetoid**\nCompile Error! Click the :errors: reaction for more information.\n(You may edit your message to recompile.)",
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"timestamp": "07/10/2022 20:30:05",
"content": "Channel closed",
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}
] |
help-9
|
be637ff2951647248622420d85883642
|
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