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"id": 1035384455990358000,
"author_id": 805217272087838700,
"author_name": "Mathematics Bot",
"timestamp": "10/27/2022 22:48:10",
"content": "Available help channel!",
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},
{
"id": 1035385129637527600,
"author_id": 334583289182552060,
"author_name": "Biblicalwizardx",
"timestamp": "10/27/2022 22:50:51",
"content": "",
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"id": 1035385132556767200,
"author_id": 805217272087838700,
"author_name": "Mathematics Bot",
"timestamp": "10/27/2022 22:50:52",
"content": "Pinned a message.",
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"id": 1035385172054515700,
"author_id": 334583289182552060,
"author_name": "Biblicalwizardx",
"timestamp": "10/27/2022 22:51:01",
"content": "how do I find p?",
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},
{
"id": 1035385694413148300,
"author_id": 334583289182552060,
"author_name": "Biblicalwizardx",
"timestamp": "10/27/2022 22:53:06",
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"author_id": 334583289182552060,
"author_name": "Biblicalwizardx",
"timestamp": "10/27/2022 22:53:30",
"content": "is this correct so far?",
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},
{
"id": 1035389076951552100,
"author_id": 334583289182552060,
"author_name": "Biblicalwizardx",
"timestamp": "10/27/2022 23:06:32",
"content": ".close",
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},
{
"id": 1035389079401005200,
"author_id": 805217272087838700,
"author_name": "Mathematics Bot",
"timestamp": "10/27/2022 23:06:33",
"content": "Channel closed",
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] | help-9 | 766d99af92b9489096ce21d2dfdae9e0 |
200,666 | [
{
"id": 1062295347646431200,
"author_id": 805217272087838700,
"author_name": "Mathematics Bot",
"timestamp": "01/10/2023 04:02:27",
"content": "Available help channel!",
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"reference": null
},
{
"id": 1062296394116911200,
"author_id": 709377021876240500,
"author_name": "fyu",
"timestamp": "01/10/2023 04:06:36",
"content": "i need help substituting this",
"attachments": [],
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},
{
"id": 1062296396729962600,
"author_id": 805217272087838700,
"author_name": "Mathematics Bot",
"timestamp": "01/10/2023 04:06:37",
"content": "Pinned a message.",
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{
"id": 1062296476434321400,
"author_id": 709377021876240500,
"author_name": "fyu",
"timestamp": "01/10/2023 04:06:56",
"content": "y = 2x\n4x + 3y = 20",
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{
"id": 1062296519618871300,
"author_id": 709377021876240500,
"author_name": "fyu",
"timestamp": "01/10/2023 04:07:06",
"content": "sub eq1 to eq2",
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},
{
"id": 1062296676246761500,
"author_id": 182179228840755200,
"author_name": "iCaird",
"timestamp": "01/10/2023 04:07:44",
"content": "Everytime you see y in eq2, replace it with 2x",
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},
{
"id": 1062297206146728000,
"author_id": 183668144404037630,
"author_name": "Ann",
"timestamp": "01/10/2023 04:09:50",
"content": "||inb4 \"4x+32x=20\"||",
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{
"id": 1062297216024326100,
"author_id": 1032444535336358000,
"author_name": "$Vanilla's Social$",
"timestamp": "01/10/2023 04:09:52",
"content": "4x+3(2x)=20",
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{
"id": 1062297349092802600,
"author_id": 709377021876240500,
"author_name": "fyu",
"timestamp": "01/10/2023 04:10:24",
"content": "ahh alr",
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},
{
"id": 1062297388007567400,
"author_id": 182179228840755200,
"author_name": "iCaird",
"timestamp": "01/10/2023 04:10:33",
"content": "Well now we'll never know what they would have done",
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},
{
"id": 1062300536218587100,
"author_id": 709377021876240500,
"author_name": "fyu",
"timestamp": "01/10/2023 04:23:04",
"content": "did i solve this right? \n\n> 4x + 3(2x) = 20\n\n- 4x + 6x = 20\n- 10x = 20 \ndivided both sides by 10\n- __x = 2__",
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{
"id": 1062301136331227100,
"author_id": 182179228840755200,
"author_name": "iCaird",
"timestamp": "01/10/2023 04:25:27",
"content": "Check yourself, plug it back into the top and see if you get 20=20",
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{
"id": 1062302258299150300,
"author_id": 709377021876240500,
"author_name": "fyu",
"timestamp": "01/10/2023 04:29:55",
"content": "- 4 ( 2 ) + 6 ( 2 ) = 20\n- 8 + 12 = 20\n- __20 = 20__",
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},
{
"id": 1062302307196350500,
"author_id": 709377021876240500,
"author_name": "fyu",
"timestamp": "01/10/2023 04:30:06",
"content": "ok tyy",
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{
"id": 1062306506248294400,
"author_id": 805217272087838700,
"author_name": "Mathematics Bot",
"timestamp": "01/10/2023 04:46:47",
"content": "@fyu Has your question been resolved?",
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"author_id": 805217272087838700,
"author_name": "Mathematics Bot",
"timestamp": "01/10/2023 05:01:48",
"content": "Channel closed",
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}
] | help-9 | 09d8c4b448244229b3a28a91ac110fd2 |
200,667 | [
{
"id": 1062314289123303400,
"author_id": 805217272087838700,
"author_name": "Mathematics Bot",
"timestamp": "01/10/2023 05:17:43",
"content": "Available help channel!",
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"reference": null
},
{
"id": 1062317068533387300,
"author_id": 813447252063944800,
"author_name": "adarw",
"timestamp": "01/10/2023 05:28:46",
"content": "How do I make it where only f1 is on the left side",
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"id": 1062317071012220900,
"author_id": 805217272087838700,
"author_name": "Mathematics Bot",
"timestamp": "01/10/2023 05:28:46",
"content": "Pinned a message.",
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"id": 1062317265451757600,
"author_id": 813447252063944800,
"author_name": "adarw",
"timestamp": "01/10/2023 05:29:32",
"content": "nvm",
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{
"id": 1062317271659331700,
"author_id": 813447252063944800,
"author_name": "adarw",
"timestamp": "01/10/2023 05:29:34",
"content": "i got it",
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},
{
"id": 1062317286893031400,
"author_id": 813447252063944800,
"author_name": "adarw",
"timestamp": "01/10/2023 05:29:38",
"content": ".close",
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},
{
"id": 1062317289782919300,
"author_id": 805217272087838700,
"author_name": "Mathematics Bot",
"timestamp": "01/10/2023 05:29:38",
"content": "Channel closed",
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}
] | help-9 | 988ec1ad8b084cdeacf4212cf730ef3b |
200,668 | [
{
"id": 1062319597333778400,
"author_id": 805217272087838700,
"author_name": "Mathematics Bot",
"timestamp": "01/10/2023 05:38:48",
"content": "Available help channel!",
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"reference": null
},
{
"id": 1062323396731486200,
"author_id": 482322393956614200,
"author_name": "tori",
"timestamp": "01/10/2023 05:53:54",
"content": "",
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"id": 1062323399197728900,
"author_id": 805217272087838700,
"author_name": "Mathematics Bot",
"timestamp": "01/10/2023 05:53:55",
"content": "Pinned a message.",
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"id": 1062323425600876700,
"author_id": 482322393956614200,
"author_name": "tori",
"timestamp": "01/10/2023 05:54:01",
"content": "so did i get the right answer for this",
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{
"id": 1062323551933308900,
"author_id": 374795910032523260,
"author_name": "SWR",
"timestamp": "01/10/2023 05:54:31",
"content": "โ",
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},
{
"id": 1062323569012510700,
"author_id": 482322393956614200,
"author_name": "tori",
"timestamp": "01/10/2023 05:54:35",
"content": "i just need to change the sign to positive because my work is wrong",
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},
{
"id": 1062323699262427300,
"author_id": 374795910032523260,
"author_name": "SWR",
"timestamp": "01/10/2023 05:55:06",
"content": "Your x-1 needs to be x+1 as pointed out",
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},
{
"id": 1062323786155839500,
"author_id": 482322393956614200,
"author_name": "tori",
"timestamp": "01/10/2023 05:55:27",
"content": "why did she circle the other signs",
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},
{
"id": 1062323813657890800,
"author_id": 482322393956614200,
"author_name": "tori",
"timestamp": "01/10/2023 05:55:34",
"content": "do they also need to be turned",
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},
{
"id": 1062323864518000800,
"author_id": 374795910032523260,
"author_name": "SWR",
"timestamp": "01/10/2023 05:55:46",
"content": "dunno",
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{
"id": 1062323873271521400,
"author_id": 1003857269802401900,
"author_name": "starlight",
"timestamp": "01/10/2023 05:55:48",
"content": "i think she's pointing out that they are correct",
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{
"id": 1062323887741882400,
"author_id": 482322393956614200,
"author_name": "tori",
"timestamp": "01/10/2023 05:55:51",
"content": "oh",
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{
"id": 1062323890451382300,
"author_id": 374795910032523260,
"author_name": "SWR",
"timestamp": "01/10/2023 05:55:52",
"content": "Maybe to show the difference?",
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{
"id": 1062323909258661900,
"author_id": 482322393956614200,
"author_name": "tori",
"timestamp": "01/10/2023 05:55:56",
"content": "makes sense",
"attachments": [],
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},
{
"id": 1062323928711823500,
"author_id": 482322393956614200,
"author_name": "tori",
"timestamp": "01/10/2023 05:56:01",
"content": "so i have the correct answer",
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{
"id": 1062323937431781400,
"author_id": 482322393956614200,
"author_name": "tori",
"timestamp": "01/10/2023 05:56:03",
"content": "?",
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},
{
"id": 1062323944637595600,
"author_id": 1003857269802401900,
"author_name": "starlight",
"timestamp": "01/10/2023 05:56:05",
"content": "if a is a zero, it means that (x-a) is a factor",
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"id": 1062324034206961700,
"author_id": 374795910032523260,
"author_name": "SWR",
"timestamp": "01/10/2023 05:56:26",
"content": "If you change to x+1, then ye",
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"id": 1062324048022995000,
"author_id": 482322393956614200,
"author_name": "tori",
"timestamp": "01/10/2023 05:56:30",
"content": "okay",
"attachments": [],
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},
{
"id": 1062324120160833700,
"author_id": 482322393956614200,
"author_name": "tori",
"timestamp": "01/10/2023 05:56:47",
"content": "wait",
"attachments": [],
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},
{
"id": 1062324156902948900,
"author_id": 482322393956614200,
"author_name": "tori",
"timestamp": "01/10/2023 05:56:56",
"content": "i need to foil my answer right",
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"id": 1062324177413099500,
"author_id": 482322393956614200,
"author_name": "tori",
"timestamp": "01/10/2023 05:57:00",
"content": "not foul",
"attachments": [],
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},
{
"id": 1062324199856799900,
"author_id": 482322393956614200,
"author_name": "tori",
"timestamp": "01/10/2023 05:57:06",
"content": "but combine",
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},
{
"id": 1062324216508207100,
"author_id": 482322393956614200,
"author_name": "tori",
"timestamp": "01/10/2023 05:57:10",
"content": "foil",
"attachments": [],
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},
{
"id": 1062324327753711600,
"author_id": 482322393956614200,
"author_name": "tori",
"timestamp": "01/10/2023 05:57:36",
"content": "or do i leave it",
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"id": 1062324573313450100,
"author_id": 374795910032523260,
"author_name": "SWR",
"timestamp": "01/10/2023 05:58:35",
"content": "",
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"id": 1062324833603551200,
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"author_name": "tori",
"timestamp": "01/10/2023 05:59:37",
"content": "just like that",
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{
"id": 1062324862179356700,
"author_id": 482322393956614200,
"author_name": "tori",
"timestamp": "01/10/2023 05:59:44",
"content": "there are two tho",
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},
{
"id": 1062325535075745800,
"author_id": 482322393956614200,
"author_name": "tori",
"timestamp": "01/10/2023 06:02:24",
"content": "there are two",
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},
{
"id": 1062325550934392800,
"author_id": 482322393956614200,
"author_name": "tori",
"timestamp": "01/10/2023 06:02:28",
"content": "polynomial functions",
"attachments": [],
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},
{
"id": 1062325652059078700,
"author_id": 482322393956614200,
"author_name": "tori",
"timestamp": "01/10/2023 06:02:52",
"content": "is it even possible to combine",
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"id": 1062326290100781000,
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"timestamp": "01/10/2023 06:05:24",
"content": "",
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"id": 1062326455465422800,
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"author_name": "adarw",
"timestamp": "01/10/2023 06:06:04",
"content": "just curios, what gr are you in?",
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"id": 1062327018303275000,
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"author_name": "adarw",
"timestamp": "01/10/2023 06:08:18",
"content": "@tori",
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{
"id": 1062327117301420200,
"author_id": 482322393956614200,
"author_name": "tori",
"timestamp": "01/10/2023 06:08:41",
"content": "12",
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},
{
"id": 1062327379634167800,
"author_id": 482322393956614200,
"author_name": "tori",
"timestamp": "01/10/2023 06:09:44",
"content": "do i leave it as it is",
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},
{
"id": 1062327500937637900,
"author_id": 813447252063944800,
"author_name": "adarw",
"timestamp": "01/10/2023 06:10:13",
"content": "idk lol",
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{
"id": 1062327515894517800,
"author_id": 482322393956614200,
"author_name": "tori",
"timestamp": "01/10/2023 06:10:16",
"content": "lol",
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},
{
"id": 1062327544680042500,
"author_id": 482322393956614200,
"author_name": "tori",
"timestamp": "01/10/2023 06:10:23",
"content": "she didnโt mark it off",
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},
{
"id": 1062327560014409700,
"author_id": 482322393956614200,
"author_name": "tori",
"timestamp": "01/10/2023 06:10:27",
"content": "so iโll leave it",
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"id": 1062327949451333800,
"author_id": 482322393956614200,
"author_name": "tori",
"timestamp": "01/10/2023 06:12:00",
"content": "aight iโm done",
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},
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"id": 1062327967650418700,
"author_id": 482322393956614200,
"author_name": "tori",
"timestamp": "01/10/2023 06:12:04",
"content": "u can close",
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},
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"id": 1062331743593562200,
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"author_name": "Mathematics Bot",
"timestamp": "01/10/2023 06:27:04",
"content": "@tori Has your question been resolved?",
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"timestamp": "01/10/2023 06:42:05",
"content": "Channel closed",
"attachments": [],
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"reference": null
}
] | help-9 | e76488cc2a5c486290190a734b43df55 |
200,669 | [
{
"id": 1062335772511977500,
"author_id": 805217272087838700,
"author_name": "Mathematics Bot",
"timestamp": "01/10/2023 06:43:05",
"content": "Available help channel!",
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},
{
"id": 1062337117532987500,
"author_id": 448460011815960600,
"author_name": "Jupiter_79",
"timestamp": "01/10/2023 06:48:26",
"content": "Hey how can I simplify this formula?\n\n`75*2+100*2+125*2+150*2+175*2+200*2+225*2+240*2`?\nI want to calculate the power required when I ride a bike with a wattage of 75 watts increasing by 25 watts per 2 minutes when the end wattage is 240 watts\nBut at the increase, it is not required to be exactly 25 but the difference between the current wattage and the final wattage (240 watts)",
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"content": "Pinned a message.",
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"author_name": "Jupiter_79",
"timestamp": "01/10/2023 06:49:14",
"content": "For example with 116 watts it would be\n`75*2+100*2+116*2`",
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"timestamp": "01/10/2023 07:04:14",
"content": "@Jupiter_79 Has your question been resolved?",
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"timestamp": "01/10/2023 07:37:24",
"content": "@Jupiter_79 Has your question been resolved?",
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"id": 1062358897207296000,
"author_id": 811501664367673300,
"author_name": "SilverSoldier",
"timestamp": "01/10/2023 08:14:58",
"content": "2*(sum of multiples of 25 from 75 to 225) + 2\\*240",
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},
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"id": 1062370429907501000,
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"author_name": "Mathematics Bot",
"timestamp": "01/10/2023 09:00:48",
"content": "@Jupiter_79 Has your question been resolved?",
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"author_name": "Mathematics Bot",
"timestamp": "01/10/2023 11:34:33",
"content": "@Jupiter_79 Has your question been resolved?",
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"id": 1062412053287026800,
"author_id": 448460011815960600,
"author_name": "Jupiter_79",
"timestamp": "01/10/2023 11:46:12",
"content": "Hmm can how can I use that as f(x)? So how can I calculate the sum of multiples of 25 from 75 to 225?",
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"id": 1062419783590617200,
"author_id": 132304137583984640,
"author_name": "Denascite",
"timestamp": "01/10/2023 12:16:55",
"content": "75+100+...+225 = 25(3+4+..+9). do you know a formula for the sum of consecutive integers?",
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"author_name": "Mathematics Bot",
"timestamp": "01/10/2023 15:46:12",
"content": "@Jupiter_79 Has your question been resolved?",
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"timestamp": "01/10/2023 19:46:12",
"content": "Channel closed",
"attachments": [],
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}
] | help-9 | f094442beacc4d93ae356c58b2001535 |
200,670 | [
{
"id": 1062533104197185700,
"author_id": 805217272087838700,
"author_name": "Mathematics Bot",
"timestamp": "01/10/2023 19:47:12",
"content": "Available help channel!",
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},
{
"id": 1062533743136473200,
"author_id": 1053456932083605500,
"author_name": "sunnnnnnn",
"timestamp": "01/10/2023 19:49:45",
"content": "heyy",
"attachments": [],
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},
{
"id": 1062533745413988400,
"author_id": 805217272087838700,
"author_name": "Mathematics Bot",
"timestamp": "01/10/2023 19:49:45",
"content": "Pinned a message.",
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"id": 1062533769409609700,
"author_id": 1053456932083605500,
"author_name": "sunnnnnnn",
"timestamp": "01/10/2023 19:49:51",
"content": "",
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"fileSizeBytes": 56095
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{
"id": 1062533779475931100,
"author_id": 1053456932083605500,
"author_name": "sunnnnnnn",
"timestamp": "01/10/2023 19:49:53",
"content": "first part",
"attachments": [],
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},
{
"id": 1062533925785841700,
"author_id": 318024849333288960,
"author_name": "Mortta",
"timestamp": "01/10/2023 19:50:28",
"content": "YK polar form?",
"attachments": [],
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},
{
"id": 1062533987744088200,
"author_id": 1053456932083605500,
"author_name": "sunnnnnnn",
"timestamp": "01/10/2023 19:50:43",
"content": "no",
"attachments": [],
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},
{
"id": 1062534003443380200,
"author_id": 318024849333288960,
"author_name": "Mortta",
"timestamp": "01/10/2023 19:50:47",
"content": "Cos(x) + isin(x)",
"attachments": [],
"mentions": [],
"reference": null
},
{
"id": 1062534092178075600,
"author_id": 1053456932083605500,
"author_name": "sunnnnnnn",
"timestamp": "01/10/2023 19:51:08",
"content": "how does it work",
"attachments": [],
"mentions": [],
"reference": null
},
{
"id": 1062534176861061200,
"author_id": 264901235834880000,
"author_name": "Modus",
"timestamp": "01/10/2023 19:51:28",
"content": "",
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"fileSizeBytes": 28319
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{
"id": 1062534344972968100,
"author_id": 1053456932083605500,
"author_name": "sunnnnnnn",
"timestamp": "01/10/2023 19:52:08",
"content": "uhh",
"attachments": [],
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},
{
"id": 1062534354515001500,
"author_id": 1053456932083605500,
"author_name": "sunnnnnnn",
"timestamp": "01/10/2023 19:52:11",
"content": "how do i start",
"attachments": [],
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},
{
"id": 1062534499482751100,
"author_id": 264901235834880000,
"author_name": "Modus",
"timestamp": "01/10/2023 19:52:45",
"content": "plug n = 1, 2, 3",
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},
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"id": 1062534534043799600,
"author_id": 264901235834880000,
"author_name": "Modus",
"timestamp": "01/10/2023 19:52:53",
"content": "and transfrom into Cartesian",
"attachments": [],
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"reference": null
},
{
"id": 1062534579099021300,
"author_id": 251189299981058050,
"author_name": "tea",
"timestamp": "01/10/2023 19:53:04",
"content": "$z^3 = e^{i(\\frac{ฯ}{2} +2ฮบฯ)} , k\\in\\mathbb{Z}$",
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},
{
"id": 1062534620849115100,
"author_id": 1053456932083605500,
"author_name": "sunnnnnnn",
"timestamp": "01/10/2023 19:53:14",
"content": "oh",
"attachments": [],
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},
{
"id": 1062534672195801200,
"author_id": 251189299981058050,
"author_name": "tea",
"timestamp": "01/10/2023 19:53:26",
"content": "oops I forgot bracket",
"attachments": [],
"mentions": [],
"reference": null
},
{
"id": 1062534721940246500,
"author_id": 510789298321096700,
"author_name": "TeXit",
"timestamp": "01/10/2023 19:53:38",
"content": "**Polipoli โค**",
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"id": 1062534839523360900,
"author_id": 1053456932083605500,
"author_name": "sunnnnnnn",
"timestamp": "01/10/2023 19:54:06",
"content": "do i plug k=0 and plus minus 1?",
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"id": 1062535065147551700,
"author_id": 251189299981058050,
"author_name": "tea",
"timestamp": "01/10/2023 19:55:00",
"content": "seems okay",
"attachments": [],
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},
{
"id": 1062535097099763700,
"author_id": 1053456932083605500,
"author_name": "sunnnnnnn",
"timestamp": "01/10/2023 19:55:08",
"content": "alr",
"attachments": [],
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"reference": null
},
{
"id": 1062535259343814800,
"author_id": 1053456932083605500,
"author_name": "sunnnnnnn",
"timestamp": "01/10/2023 19:55:46",
"content": "what is the answer suppose to be",
"attachments": [],
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},
{
"id": 1062535771556430000,
"author_id": 251189299981058050,
"author_name": "tea",
"timestamp": "01/10/2023 19:57:48",
"content": "I think -i, rt(3)/2 + i/2 and -rt(3)/2 + i/2",
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},
{
"id": 1062535866720981000,
"author_id": 264901235834880000,
"author_name": "Modus",
"timestamp": "01/10/2023 19:58:11",
"content": ",w all 3rd roots of unity",
"attachments": [],
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},
{
"id": 1062535878309851300,
"author_id": 510789298321096700,
"author_name": "TeXit",
"timestamp": "01/10/2023 19:58:14",
"content": "Results provided by WolframAlpha",
"attachments": [],
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},
{
"id": 1062535919279812600,
"author_id": 510789298321096700,
"author_name": "TeXit",
"timestamp": "01/10/2023 19:58:24",
"content": "Result:\n```\n1.7320508075689\n```",
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},
{
"id": 1062535979270942800,
"author_id": 264901235834880000,
"author_name": "Modus",
"timestamp": "01/10/2023 19:58:38",
"content": "/2",
"attachments": [],
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},
{
"id": 1062535986149589100,
"author_id": 264901235834880000,
"author_name": "Modus",
"timestamp": "01/10/2023 19:58:40",
"content": ";d",
"attachments": [],
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},
{
"id": 1062536002721292300,
"author_id": 942843959783333900,
"author_name": "Mehdi_Moulati",
"timestamp": "01/10/2023 19:58:44",
"content": ",w z^3 = i",
"attachments": [],
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"reference": null
},
{
"id": 1062536013555191800,
"author_id": 510789298321096700,
"author_name": "TeXit",
"timestamp": "01/10/2023 19:58:46",
"content": "Results provided by WolframAlpha",
"attachments": [],
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"reference": null
},
{
"id": 1062536045046018000,
"author_id": 1053456932083605500,
"author_name": "sunnnnnnn",
"timestamp": "01/10/2023 19:58:54",
"content": "damn",
"attachments": [],
"mentions": [],
"reference": null
},
{
"id": 1062536084099178500,
"author_id": 251189299981058050,
"author_name": "tea",
"timestamp": "01/10/2023 19:59:03",
"content": "cool!",
"attachments": [],
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{
"id": 1062536130479792300,
"author_id": 1053456932083605500,
"author_name": "sunnnnnnn",
"timestamp": "01/10/2023 19:59:14",
"content": "thanks guys",
"attachments": [],
"mentions": [],
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},
{
"id": 1062536170665414700,
"author_id": 1053456932083605500,
"author_name": "sunnnnnnn",
"timestamp": "01/10/2023 19:59:24",
"content": ".close",
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},
{
"id": 1062536173593034800,
"author_id": 805217272087838700,
"author_name": "Mathematics Bot",
"timestamp": "01/10/2023 19:59:24",
"content": "Channel closed",
"attachments": [],
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"reference": null
}
] | help-9 | b94422a1eae64b898ce59bb45791b2b2 |
200,671 | [
{
"id": 1062542382547095600,
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"author_name": "Mathematics Bot",
"timestamp": "01/10/2023 20:24:05",
"content": "Available help channel!",
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},
{
"id": 1062546898373836900,
"author_id": 187850624421986300,
"author_name": "Circle",
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"timestamp": "01/10/2023 20:42:02",
"content": "Pinned a message.",
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"id": 1062546956968284200,
"author_id": 187850624421986300,
"author_name": "Circle",
"timestamp": "01/10/2023 20:42:15",
"content": "whats this, Kronecker delta",
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},
{
"id": 1062547713541030000,
"author_id": 521464336284254200,
"author_name": "Gamer Dio",
"timestamp": "01/10/2023 20:45:16",
"content": "What specifically are you asking about",
"attachments": [],
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},
{
"id": 1062548071281602700,
"author_id": 788085606483361800,
"author_name": "chartbit",
"timestamp": "01/10/2023 20:46:41",
"content": "That's basically a way of expressing whether the items are the same, so you get 1 if they are and 0 if not, just convenient notation",
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"id": 1062548203234402300,
"author_id": 187850624421986300,
"author_name": "Circle",
"timestamp": "01/10/2023 20:47:12",
"content": "um",
"attachments": [],
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},
{
"id": 1062548252618149900,
"author_id": 187850624421986300,
"author_name": "Circle",
"timestamp": "01/10/2023 20:47:24",
"content": "so like in this case would Kronecker delta be the identity matrix?",
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{
"id": 1062548387628589000,
"author_id": 521464336284254200,
"author_name": "Gamer Dio",
"timestamp": "01/10/2023 20:47:56",
"content": "The Kronecker delta is a function",
"attachments": [],
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},
{
"id": 1062548444222332900,
"author_id": 521464336284254200,
"author_name": "Gamer Dio",
"timestamp": "01/10/2023 20:48:10",
"content": "Takes in two inputs, outputs 1 if they're equal, 0 else",
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},
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"id": 1062548507967377500,
"author_id": 187850624421986300,
"author_name": "Circle",
"timestamp": "01/10/2023 20:48:25",
"content": "hm so",
"attachments": [],
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{
"id": 1062548575164313600,
"author_id": 187850624421986300,
"author_name": "Circle",
"timestamp": "01/10/2023 20:48:41",
"content": "if A = 1 0 \n 0 0",
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},
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"id": 1062548625353347100,
"author_id": 187850624421986300,
"author_name": "Circle",
"timestamp": "01/10/2023 20:48:53",
"content": "then Kronecker delta = 1 0 \n 0 0",
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},
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"id": 1062548644693286900,
"author_id": 521464336284254200,
"author_name": "Gamer Dio",
"timestamp": "01/10/2023 20:48:58",
"content": "$\\delta_{11} = 1$\n\n$\\delta_{12} = 0$",
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},
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"id": 1062548655896285200,
"author_id": 510789298321096700,
"author_name": "TeXit",
"timestamp": "01/10/2023 20:49:00",
"content": "**Gamer Dio**",
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"id": 1062548668772786200,
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"author_name": "Circle",
"timestamp": "01/10/2023 20:49:03",
"content": "if A =\n1 1\n1 1",
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"timestamp": "01/10/2023 20:49:09",
"content": "Kronecker delta = \n1 1\n1 1",
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"timestamp": "01/10/2023 20:49:12",
"content": "yay or",
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"author_name": "Gamer Dio",
"timestamp": "01/10/2023 20:49:17",
"content": "The Kronecker delta isn't a matrix",
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"timestamp": "01/10/2023 20:49:26",
"content": "It takes in two numbers, outputs one",
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"id": 1062548852986622000,
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"timestamp": "01/10/2023 20:49:47",
"content": "ohh",
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"timestamp": "01/10/2023 20:49:49",
"content": "ok but",
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"timestamp": "01/10/2023 20:49:54",
"content": "whats it used for",
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"author_name": "Gamer Dio",
"timestamp": "01/10/2023 20:50:54",
"content": "Like chartbit said, it let's you know if two numbers are equal",
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"id": 1062549246143901800,
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"timestamp": "01/10/2023 20:51:21",
"content": "eh but the",
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"timestamp": "01/10/2023 20:51:22",
"content": "Kronecker delta",
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"author_id": 187850624421986300,
"author_name": "Circle",
"timestamp": "01/10/2023 20:51:33",
"content": "its values more or less allign with the identity matrix right?",
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"id": 1062549314339078100,
"author_id": 187850624421986300,
"author_name": "Circle",
"timestamp": "01/10/2023 20:51:37",
"content": "at least in this case",
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"author_name": "Gamer Dio",
"timestamp": "01/10/2023 20:51:38",
"content": "We can define the identity matrix using it by saying, for instance, the entry $I_{mn} = \\delta_{mn}$",
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"author_name": "TeXit",
"timestamp": "01/10/2023 20:51:41",
"content": "**Gamer Dio**",
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"timestamp": "01/10/2023 20:51:52",
"content": "yea that",
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"timestamp": "01/10/2023 20:51:55",
"content": "hm",
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"author_name": "Circle",
"timestamp": "01/10/2023 20:52:08",
"content": "then i guess there are different ways u can define the Kronecker delta?",
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"author_name": "Gamer Dio",
"timestamp": "01/10/2023 20:52:24",
"content": "The Kronecker delta is pretty much always defined the same way",
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"id": 1062549535156617200,
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"author_name": "Circle",
"timestamp": "01/10/2023 20:52:30",
"content": "oh",
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"id": 1062549550092521500,
"author_id": 521464336284254200,
"author_name": "Gamer Dio",
"timestamp": "01/10/2023 20:52:33",
"content": "1 if the two inputs are the same, 0 otherwise",
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"id": 1062549597748215900,
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"author_name": "Circle",
"timestamp": "01/10/2023 20:52:45",
"content": "so the entries of identity always allign with the Kronecker delta",
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"id": 1062549639536050200,
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"author_name": "Circle",
"timestamp": "01/10/2023 20:52:55",
"content": "ok thats something",
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"author_id": 521464336284254200,
"author_name": "Gamer Dio",
"timestamp": "01/10/2023 20:52:56",
"content": "In this sense, yes",
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"id": 1062549654727831700,
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"author_name": "Circle",
"timestamp": "01/10/2023 20:52:58",
"content": "thanks",
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"id": 1062549691495100400,
"author_id": 187850624421986300,
"author_name": "Circle",
"timestamp": "01/10/2023 20:53:07",
"content": "i thought it was a just this specific case thing",
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"id": 1062549704174485600,
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"author_name": "Circle",
"timestamp": "01/10/2023 20:53:10",
"content": "thanks",
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"id": 1062549711095087200,
"author_id": 187850624421986300,
"author_name": "Circle",
"timestamp": "01/10/2023 20:53:12",
"content": "๐",
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"id": 1062549767110004700,
"author_id": 187850624421986300,
"author_name": "Circle",
"timestamp": "01/10/2023 20:53:25",
"content": ".close",
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"id": 1062549770301874200,
"author_id": 805217272087838700,
"author_name": "Mathematics Bot",
"timestamp": "01/10/2023 20:53:26",
"content": "Channel closed",
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] | help-9 | d1850dd33faf42f6b403c1644cac666a |
200,672 | [
{
"id": 1062550022719287300,
"author_id": 805217272087838700,
"author_name": "Mathematics Bot",
"timestamp": "01/10/2023 20:54:26",
"content": "Available help channel!",
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"id": 1062553732715380700,
"author_id": 900768862927216800,
"author_name": "What da dog",
"timestamp": "01/10/2023 21:09:11",
"content": "Does anyone know what the last label is supposed to be?",
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"id": 1062553735026462700,
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"content": "You have two sides congruent along with the angle in between",
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"content": "What congruence statement involves an angle sandwiched between two sides",
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"id": 1062554362540474500,
"author_id": 900768862927216800,
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"timestamp": "01/10/2023 21:11:41",
"content": "SAS?",
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"content": "Yes",
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"timestamp": "01/10/2023 21:12:11",
"content": "K thanks",
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"content": ".close",
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"content": "Channel closed",
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] | help-9 | 0f40c5c9c62846e1b2f6a980c434b6a4 |
200,673 | [
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"content": "Available help channel!",
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"content": "Could some one please help me with this? (11 Grade Math - Algebra 2 - Quadratic Apllicaions)",
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"id": 1062557568553197700,
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"content": "Pinned a message.",
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"author_id": 532703107768123400,
"author_name": "Skully",
"timestamp": "01/10/2023 21:24:41",
"content": "How big is this angle as a whole? 180?",
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"timestamp": "01/10/2023 21:25:09",
"content": "The b one",
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"content": "A bit too slow! ask this in another one please, you were just slightly beat to it",
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"timestamp": "01/10/2023 21:27:33",
"content": "For b, you're trying to find when h>30, do you know how to do quadratic inequalites?",
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"timestamp": "01/10/2023 21:28:01",
"content": "Nope. They shouldn't be necessary for this.",
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"timestamp": "01/10/2023 21:28:23",
"content": "they are",
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"content": "Well strictly speaking you don't really \"need\" them",
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"content": "We didn't learn them in this unit",
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"timestamp": "01/10/2023 21:28:59",
"content": "But you want to know for how long you're above 30",
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"timestamp": "01/10/2023 21:29:01",
"content": "We're not meant to solve them utilizing inequalities",
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"timestamp": "01/10/2023 21:29:16",
"content": "The quadratic formula and equation are at my disposal though",
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"timestamp": "01/10/2023 21:29:35",
"content": "Maybe you set the equation to 30?",
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"timestamp": "01/10/2023 21:29:36",
"content": "I mean either way they're effectively equivalent",
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"timestamp": "01/10/2023 21:29:50",
"content": "I DONT KNOW THAT SIR",
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"timestamp": "01/10/2023 21:29:54",
"content": "Yeah, find where you're =30",
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"timestamp": "01/10/2023 21:30:06",
"content": "But like, how?",
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"author_name": "chartbit",
"timestamp": "01/10/2023 21:30:09",
"content": "What does that give you?",
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"timestamp": "01/10/2023 21:30:18",
"content": "What do you mean?",
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"timestamp": "01/10/2023 21:30:24",
"content": "Setting it equal to 30?",
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"author_name": "chartbit",
"timestamp": "01/10/2023 21:30:34",
"content": "You just said so here? What do you get as the solutions?",
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"timestamp": "01/10/2023 21:30:46",
"content": "I don't know I be messing it up",
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"timestamp": "01/10/2023 21:30:51",
"content": "You free for vc?",
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"timestamp": "01/10/2023 21:30:59",
"content": "Thanks for your help btw",
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"id": 1062559313148784800,
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"author_name": "chartbit",
"timestamp": "01/10/2023 21:31:21",
"content": "What we said is that you have $-4.9t^2 + 27t + 2.4 = 30$",
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"timestamp": "01/10/2023 21:31:23",
"content": "**chartbit**",
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"timestamp": "01/10/2023 21:31:35",
"content": "Solve that for t, you should get two solutions",
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"timestamp": "01/10/2023 21:31:45",
"content": "I got",
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"author_name": "chartbit",
"timestamp": "01/10/2023 21:32:00",
"content": ",w -4.9t^2 + 27t + 2.4 = 30",
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"timestamp": "01/10/2023 21:32:01",
"content": "But what do I do with both of thems?",
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"timestamp": "01/10/2023 21:32:02",
"content": "Results provided by WolframAlpha",
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"author_name": "chartbit",
"timestamp": "01/10/2023 21:32:11",
"content": "Cool, fair enough",
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"id": 1062559625053999200,
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"author_name": "chartbit",
"timestamp": "01/10/2023 21:32:36",
"content": "You want to find the time where you're above 30, so drawing a picture would really help you",
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"author_name": "ZipIsLive",
"timestamp": "01/10/2023 21:33:04",
"content": "But the graph won't always be super accurate is there a more mathmatical way to determine?",
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"author_name": "ZipIsLive",
"timestamp": "01/10/2023 21:33:18",
"content": "So I can use the principle in the future?",
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"timestamp": "01/10/2023 21:33:19",
"content": "[in this case because the t^2 has a negative coefficient you can kind of tell that you will be above 30 when you're in between those two t values]",
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"timestamp": "01/10/2023 21:33:25",
"content": "It doesn't need to be",
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"author_name": "Mehdi_Moulati",
"timestamp": "01/10/2023 21:33:45",
"content": ",w graph-4.9tยฒ + 27t + 2.4 = 30",
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"timestamp": "01/10/2023 21:33:48",
"content": "Results provided by WolframAlpha",
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"id": 1062559994802884600,
"author_id": 329736383688081400,
"author_name": "ZipIsLive",
"timestamp": "01/10/2023 21:34:04",
"content": "The 4 one?",
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"id": 1062560144019423200,
"author_id": 788085606483361800,
"author_name": "chartbit",
"timestamp": "01/10/2023 21:34:39",
"content": "So you see from the above picture that you're above 30 when you're in between those t values?",
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"id": 1062560524677689500,
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"author_name": "ZipIsLive",
"timestamp": "01/10/2023 21:36:10",
"content": "Do I subtract them?",
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"id": 1062560707217993900,
"author_id": 329736383688081400,
"author_name": "ZipIsLive",
"timestamp": "01/10/2023 21:36:54",
"content": "The two x values?",
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"id": 1062560716634198100,
"author_id": 329736383688081400,
"author_name": "ZipIsLive",
"timestamp": "01/10/2023 21:36:56",
"content": "The roots?",
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"id": 1062561091890200600,
"author_id": 942843959783333900,
"author_name": "Mehdi_Moulati",
"timestamp": "01/10/2023 21:38:25",
"content": "the height is more then 30 when x between 1.35584... and 4.1543...",
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"author_name": "ZipIsLive",
"timestamp": "01/10/2023 21:39:37",
"content": "So answer b: The balloon is in the air 30 m high for 4.1534... secknds?",
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"id": 1062561490785280000,
"author_id": 329736383688081400,
"author_name": "ZipIsLive",
"timestamp": "01/10/2023 21:40:00",
"content": "I be silly wit it",
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{
"id": 1062562089799012400,
"author_id": 942843959783333900,
"author_name": "Mehdi_Moulati",
"timestamp": "01/10/2023 21:42:23",
"content": "the distance between the balloon and the ground is more than 30 m if \nt (time) between 1.35584... and 4.1543...",
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"id": 1062562188885250000,
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"author_name": "ZipIsLive",
"timestamp": "01/10/2023 21:42:47",
"content": "That doesn't feel like a satisfactory answer is there something I'm missing?",
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"id": 1062562233596518500,
"author_id": 329736383688081400,
"author_name": "ZipIsLive",
"timestamp": "01/10/2023 21:42:57",
"content": "I'm certain it's a single answer",
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"id": 1062562449229889500,
"author_id": 329736383688081400,
"author_name": "ZipIsLive",
"timestamp": "01/10/2023 21:43:49",
"content": "It asks \"for how long\", not what time frame",
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"id": 1062562469706473500,
"author_id": 329736383688081400,
"author_name": "ZipIsLive",
"timestamp": "01/10/2023 21:43:54",
"content": "Would I add them?",
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"id": 1062562701336924300,
"author_id": 942843959783333900,
"author_name": "Mehdi_Moulati",
"timestamp": "01/10/2023 21:44:49",
"content": "4.1543 - 1.35584",
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"id": 1062562712254677000,
"author_id": 329736383688081400,
"author_name": "ZipIsLive",
"timestamp": "01/10/2023 21:44:52",
"content": "I appreciate your effort by the way",
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"author_name": "ZipIsLive",
"timestamp": "01/10/2023 21:44:56",
"content": "thank you",
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"author_name": "Mehdi_Moulati",
"timestamp": "01/10/2023 21:45:05",
"content": "nope substract them",
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"timestamp": "01/10/2023 21:45:06",
"content": "makes sense",
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"id": 1062562816101470300,
"author_id": 329736383688081400,
"author_name": "ZipIsLive",
"timestamp": "01/10/2023 21:45:16",
"content": "I appreciate your help",
"attachments": [],
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},
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"id": 1062562888000213000,
"author_id": 942843959783333900,
"author_name": "Mehdi_Moulati",
"timestamp": "01/10/2023 21:45:33",
"content": "anytime",
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"author_name": "ZipIsLive",
"timestamp": "01/10/2023 21:45:45",
"content": "@chartbit Thank you too!",
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"author_name": "ZipIsLive",
"timestamp": "01/10/2023 21:46:07",
"content": "One last question",
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"id": 1062563063909339300,
"author_id": 329736383688081400,
"author_name": "ZipIsLive",
"timestamp": "01/10/2023 21:46:15",
"content": "In terms of the vertex of a parabola",
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"id": 1062563094213181600,
"author_id": 329736383688081400,
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"timestamp": "01/10/2023 21:46:23",
"content": "(x,y)",
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"id": 1062563232109301800,
"author_id": 329736383688081400,
"author_name": "ZipIsLive",
"timestamp": "01/10/2023 21:46:56",
"content": "X = Time and Y= hieght?",
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"id": 1062563582052671600,
"author_id": 942843959783333900,
"author_name": "Mehdi_Moulati",
"timestamp": "01/10/2023 21:48:19",
"content": "yes",
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"author_name": "ZipIsLive",
"timestamp": "01/10/2023 21:49:05",
"content": "Okay! Have a great night! Again thanks for strengthening my understanding of math.",
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"id": 1062563884197756900,
"author_id": 329736383688081400,
"author_name": "ZipIsLive",
"timestamp": "01/10/2023 21:49:31",
"content": "Case Closed if you need to go help others",
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"id": 1062567660950405200,
"author_id": 805217272087838700,
"author_name": "Mathematics Bot",
"timestamp": "01/10/2023 22:04:31",
"content": "@ZipIsLive Has your question been resolved?",
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"timestamp": "01/10/2023 22:04:49",
"content": "Channel closed",
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] | help-9 | f702030fd6274272aa80ab47be778221 |
200,674 | [
{
"id": 1062567985279160300,
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"content": "Available help channel!",
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{
"id": 1062568398271303700,
"author_id": 520824709764612100,
"author_name": "fifty_two",
"timestamp": "01/10/2023 22:07:27",
"content": "\"Prove the set of complex numbers of absolute value 1 i.e., the unit circle in the complex\nplane (under multiplication) is a subgroup of the complex numbers\"",
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"id": 1062568400167129100,
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"timestamp": "01/10/2023 22:07:28",
"content": "Pinned a message.",
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"author_name": "fifty_two",
"timestamp": "01/10/2023 22:08:46",
"content": "The unit circle can be defined as $e^{\\theta i}$ so all I have to do is show that $xy^{-1} \\in \\{e^{\\theta i} \\}$ right?",
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"content": "**fifty\\_two**",
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"timestamp": "01/10/2023 22:23:46",
"content": "@fifty_two Has your question been resolved?",
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] | help-9 | 37d075621f934463927190b76b16c00d |
200,675 | [
{
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"content": "Available help channel!",
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"id": 1062577848507957200,
"author_id": 592148870905987100,
"author_name": "seaturtle",
"timestamp": "01/10/2023 22:45:00",
"content": "someone help i cant figure how to compare the surface areas or find them out in this word problem",
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"content": "Pinned a message.",
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"id": 1062578571777945700,
"author_id": 244390699431100400,
"author_name": "Frosst",
"timestamp": "01/10/2023 22:47:53",
"content": "so you want to compare the surface area before and after the cut and removal of 1 slice",
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"id": 1062578602140500000,
"author_id": 244390699431100400,
"author_name": "Frosst",
"timestamp": "01/10/2023 22:48:00",
"content": "what's the surface area before the cut?",
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"id": 1062578883884495000,
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"author_name": "seaturtle",
"timestamp": "01/10/2023 22:49:07",
"content": "just 2x^2 + 3x",
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"id": 1062578920966336500,
"author_id": 592148870905987100,
"author_name": "seaturtle",
"timestamp": "01/10/2023 22:49:16",
"content": "because it doesnt say any numbers",
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"id": 1062579816982904800,
"author_id": 244390699431100400,
"author_name": "Frosst",
"timestamp": "01/10/2023 22:52:50",
"content": "let's just say it has height 1",
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"id": 1062579826420101100,
"author_id": 244390699431100400,
"author_name": "Frosst",
"timestamp": "01/10/2023 22:52:52",
"content": "and radius 1",
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},
{
"id": 1062579905562423300,
"author_id": 244390699431100400,
"author_name": "Frosst",
"timestamp": "01/10/2023 22:53:11",
"content": "what's the total surface area before you cut the cake",
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"id": 1062580036823167100,
"author_id": 592148870905987100,
"author_name": "seaturtle",
"timestamp": "01/10/2023 22:53:42",
"content": "5",
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},
{
"id": 1062580409944256600,
"author_id": 283323517884432400,
"author_name": "nino",
"timestamp": "01/10/2023 22:55:11",
"content": "i need some help in my channel if anyone is available ive been waiting for a little while and i can't figure the problem out",
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"id": 1062580497135456300,
"author_id": 283323517884432400,
"author_name": "nino",
"timestamp": "01/10/2023 22:55:32",
"content": "#help-6๏ฝlong-wang-้พ็",
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},
{
"id": 1062582045156593700,
"author_id": 592148870905987100,
"author_name": "seaturtle",
"timestamp": "01/10/2023 23:01:41",
"content": "no",
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},
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"id": 1062582062386794600,
"author_id": 592148870905987100,
"author_name": "seaturtle",
"timestamp": "01/10/2023 23:01:45",
"content": ":(",
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},
{
"id": 1062582749770305500,
"author_id": 592148870905987100,
"author_name": "seaturtle",
"timestamp": "01/10/2023 23:04:29",
"content": "i still need help",
"attachments": [],
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},
{
"id": 1062583478799040500,
"author_id": 283323517884432400,
"author_name": "nino",
"timestamp": "01/10/2023 23:07:23",
"content": "i do too",
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"id": 1062585786983260300,
"author_id": 592148870905987100,
"author_name": "seaturtle",
"timestamp": "01/10/2023 23:16:33",
"content": "@Helpers",
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},
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"id": 1062585801780756500,
"author_id": 592148870905987100,
"author_name": "seaturtle",
"timestamp": "01/10/2023 23:16:37",
"content": "help",
"attachments": [],
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},
{
"id": 1062586110041141200,
"author_id": 283323517884432400,
"author_name": "nino",
"timestamp": "01/10/2023 23:17:50",
"content": "so u have 8 slices",
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},
{
"id": 1062586197895036900,
"author_id": 283323517884432400,
"author_name": "nino",
"timestamp": "01/10/2023 23:18:11",
"content": "1 slice is one eighth of the whole thing",
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"id": 1062586298495418400,
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"author_name": "nino",
"timestamp": "01/10/2023 23:18:35",
"content": "so if you remove a slice theres less area",
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"id": 1062586324235853800,
"author_id": 283323517884432400,
"author_name": "nino",
"timestamp": "01/10/2023 23:18:41",
"content": "ur literally removing area",
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"author_id": 283323517884432400,
"author_name": "nino",
"timestamp": "01/10/2023 23:18:52",
"content": "by what percentage?",
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"id": 1062586390837203000,
"author_id": 283323517884432400,
"author_name": "nino",
"timestamp": "01/10/2023 23:18:57",
"content": "the percentage that is equal to 1/8",
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"id": 1062586441139486700,
"author_id": 283323517884432400,
"author_name": "nino",
"timestamp": "01/10/2023 23:19:09",
"content": "so divide 1/8 in a calculator",
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},
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"id": 1062586548262023300,
"author_id": 283323517884432400,
"author_name": "nino",
"timestamp": "01/10/2023 23:19:35",
"content": "the remaining surface area will have decreased",
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},
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"id": 1062586820036137000,
"author_id": 592148870905987100,
"author_name": "seaturtle",
"timestamp": "01/10/2023 23:20:39",
"content": "thats volume",
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},
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"id": 1062586838495281300,
"author_id": 592148870905987100,
"author_name": "seaturtle",
"timestamp": "01/10/2023 23:20:44",
"content": "not surface area",
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},
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"id": 1062588868718760000,
"author_id": 592148870905987100,
"author_name": "seaturtle",
"timestamp": "01/10/2023 23:28:48",
"content": "@Helpers",
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},
{
"id": 1062589194205139000,
"author_id": 283323517884432400,
"author_name": "nino",
"timestamp": "01/10/2023 23:30:05",
"content": "its basically the same",
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"id": 1062589215004688500,
"author_id": 283323517884432400,
"author_name": "nino",
"timestamp": "01/10/2023 23:30:10",
"content": "in that example",
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},
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"id": 1062589509381931100,
"author_id": 592148870905987100,
"author_name": "seaturtle",
"timestamp": "01/10/2023 23:31:20",
"content": "well if so u are wrong cuz of the answer key",
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"id": 1062591305944940500,
"author_id": 592148870905987100,
"author_name": "seaturtle",
"timestamp": "01/10/2023 23:38:29",
"content": "@Helpers",
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"author_id": 805217272087838700,
"author_name": "Mathematics Bot",
"timestamp": "01/10/2023 23:53:29",
"content": "@seaturtle Has your question been resolved?",
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"timestamp": "01/11/2023 00:23:41",
"content": "@seaturtle Has your question been resolved?",
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"content": "Channel closed",
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}
] | help-9 | c9bdbe5b87e14339a25a1aedea066f62 |
200,676 | [
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"content": "Available help channel!",
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"timestamp": "10/27/2022 23:10:52",
"content": "what would you call this equation?",
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"id": 1035390225775595600,
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"author_name": "avidrunner",
"timestamp": "10/27/2022 23:11:06",
"content": "linear equation would be z = 3x + 6 (straight line in 2D)",
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"timestamp": "10/27/2022 23:11:20",
"content": "but this is 3D, due to the third variable, so I'm curious",
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"content": "@avidrunner Has your question been resolved?",
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"timestamp": "10/27/2022 23:41:21",
"content": "Channel closed",
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}
] | help-9 | afd739c4335440de8a0270a3198210a1 |
200,677 | [
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"content": "Available help channel!",
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"id": 1062606828632031200,
"author_id": 385334938427326460,
"author_name": "FlexMan",
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"content": "how to convert this to a single numeric value? (Maple software)",
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"content": "Pinned a message.",
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"content": "@FlexMan Has your question been resolved?",
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"content": "@FlexMan Has your question been resolved?",
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] | help-9 | 7aca43f93c8447379fe6a4ce087cdccd |
200,678 | [
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"content": "yoooo",
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"timestamp": "01/11/2023 01:48:29",
"content": "sup my babies",
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"timestamp": "01/11/2023 01:48:50",
"content": "how do I do this",
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"id": 1062624503999512600,
"author_id": 1015619946451046400,
"author_name": "Springsskateboard",
"timestamp": "01/11/2023 01:50:24",
"content": "I assumed n=6 and n=1 and showed discriminant <0 for their intersection but apparently I canโt assume lol",
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{
"id": 1062624861589082100,
"author_id": 536177306578845700,
"author_name": "Shallow.",
"timestamp": "01/11/2023 01:51:49",
"content": "for 2 circles to not meet sum of their radii < distance between their centers",
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},
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"id": 1062624916794507300,
"author_id": 536177306578845700,
"author_name": "Shallow.",
"timestamp": "01/11/2023 01:52:02",
"content": ":hmmCat:",
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"id": 1062624927989125100,
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"author_name": "Springsskateboard",
"timestamp": "01/11/2023 01:52:05",
"content": "sooo",
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"id": 1062624941708685300,
"author_id": 1015619946451046400,
"author_name": "Springsskateboard",
"timestamp": "01/11/2023 01:52:08",
"content": "how do I apply that here",
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"id": 1062624954782326800,
"author_id": 536177306578845700,
"author_name": "Shallow.",
"timestamp": "01/11/2023 01:52:11",
"content": "but this is for extarnally",
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"id": 1062624978832478300,
"author_id": 536177306578845700,
"author_name": "Shallow.",
"timestamp": "01/11/2023 01:52:17",
"content": "wait",
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{
"id": 1062625005227216900,
"author_id": 1015619946451046400,
"author_name": "Springsskateboard",
"timestamp": "01/11/2023 01:52:23",
"content": "sure",
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"id": 1062625090321268700,
"author_id": 244390699431100400,
"author_name": "Frosst",
"timestamp": "01/11/2023 01:52:44",
"content": "where's the center of the nth circle",
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"id": 1062625152782831700,
"author_id": 244390699431100400,
"author_name": "Frosst",
"timestamp": "01/11/2023 01:52:59",
"content": "how far is it away from the origin (the center of C1)",
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"id": 1062625191437537400,
"author_id": 244390699431100400,
"author_name": "Frosst",
"timestamp": "01/11/2023 01:53:08",
"content": "what's the radius of the nth circle",
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},
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"id": 1062625285217996800,
"author_id": 244390699431100400,
"author_name": "Frosst",
"timestamp": "01/11/2023 01:53:30",
"content": "radius of C1 + radius of Cn > distance between center of Cn and origin",
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"id": 1062625315664429000,
"author_id": 536177306578845700,
"author_name": "Shallow.",
"timestamp": "01/11/2023 01:53:37",
"content": ":hmmCat:",
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"id": 1062625335117615100,
"author_id": 1015619946451046400,
"author_name": "Springsskateboard",
"timestamp": "01/11/2023 01:53:42",
"content": "how do I find the radius of the nth tho?",
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"timestamp": "01/11/2023 01:54:06",
"content": "@Frosst",
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"id": 1062625450196746200,
"author_id": 536177306578845700,
"author_name": "Shallow.",
"timestamp": "01/11/2023 01:54:09",
"content": "oh wait it is external",
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"id": 1062625457423528000,
"author_id": 536177306578845700,
"author_name": "Shallow.",
"timestamp": "01/11/2023 01:54:11",
"content": "icic",
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"id": 1062625490113941500,
"author_id": 536177306578845700,
"author_name": "Shallow.",
"timestamp": "01/11/2023 01:54:19",
"content": "yea so u can apply this",
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"author_name": "Frosst",
"timestamp": "01/11/2023 01:54:25",
"content": "man look at the equation of the Cnth circle",
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"id": 1062625584464810000,
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"timestamp": "01/11/2023 01:54:41",
"content": "ah",
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"id": 1062625590026444800,
"author_id": 1015619946451046400,
"author_name": "Springsskateboard",
"timestamp": "01/11/2023 01:54:43",
"content": "itโs n",
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"id": 1062625609496404000,
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"author_name": "Frosst",
"timestamp": "01/11/2023 01:54:47",
"content": "๐",
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"id": 1062625637833125900,
"author_id": 1015619946451046400,
"author_name": "Springsskateboard",
"timestamp": "01/11/2023 01:54:54",
"content": "so 1+n?",
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"author_name": "Frosst",
"timestamp": "01/11/2023 01:55:04",
"content": "what's 1+n",
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"id": 1062625703163600900,
"author_id": 1015619946451046400,
"author_name": "Springsskateboard",
"timestamp": "01/11/2023 01:55:10",
"content": "if I prove 1+n is > distance between centres of c1 and origin",
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"timestamp": "01/11/2023 01:55:24",
"content": "sum of radius of c1 and cn",
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"id": 1062625768502468600,
"author_id": 244390699431100400,
"author_name": "Frosst",
"timestamp": "01/11/2023 01:55:25",
"content": "not c1 and origin",
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"id": 1062625786517008400,
"author_id": 244390699431100400,
"author_name": "Frosst",
"timestamp": "01/11/2023 01:55:30",
"content": "c1 and origin is the same point",
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"id": 1062625805705945100,
"author_id": 536177306578845700,
"author_name": "Shallow.",
"timestamp": "01/11/2023 01:55:34",
"content": ":pandaHmm:",
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"id": 1062625810705567700,
"author_id": 244390699431100400,
"author_name": "Frosst",
"timestamp": "01/11/2023 01:55:35",
"content": "Cn and origin",
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"id": 1062625820335681500,
"author_id": 1015619946451046400,
"author_name": "Springsskateboard",
"timestamp": "01/11/2023 01:55:38",
"content": "but u said",
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"id": 1062625836727017500,
"author_id": 244390699431100400,
"author_name": "Frosst",
"timestamp": "01/11/2023 01:55:42",
"content": "fuck",
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"id": 1062625861041406000,
"author_id": 244390699431100400,
"author_name": "Frosst",
"timestamp": "01/11/2023 01:55:47",
"content": "well that's not what i meant to say",
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"id": 1062625863738343400,
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"author_name": "Frosst",
"timestamp": "01/11/2023 01:55:48",
"content": "lmao",
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"timestamp": "01/11/2023 01:55:51",
"content": "ah alr",
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"content": "so I must prove 1+n is > distance between origin and centre of Cn",
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"content": "yes but you dont have to prove it",
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"content": "you need to prove that the smallest positive integer n for which this holds is 6",
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"timestamp": "01/11/2023 01:57:48",
"content": "wait how do I find the distance of the origin to the centre of Cn",
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"timestamp": "01/11/2023 01:57:53",
"content": "length formula?",
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"timestamp": "01/11/2023 01:58:55",
"content": "can I just prove intersection between n=1 and n=5 exists but intersection between n=1 and n=6 doesnโt exist",
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"timestamp": "01/11/2023 01:58:58",
"content": "and call it a day",
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"timestamp": "01/11/2023 01:59:17",
"content": "or is that not allowed for prove questions",
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"timestamp": "01/11/2023 02:01:12",
"content": "you can but like",
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"timestamp": "01/11/2023 02:01:27",
"content": "that's harder than doing it the other way with radius",
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"timestamp": "01/11/2023 02:02:22",
"content": "because what if the question said $C_n : (x-n+1)^2 + (y-n+1)^2 = (n)^2+10$",
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"timestamp": "01/11/2023 02:02:23",
"content": "ah ok",
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"timestamp": "01/11/2023 02:02:43",
"content": "ye sheee thatโll be longer",
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"timestamp": "01/11/2023 02:02:57",
"content": "but how do I find the distance between origin and centre of Cn?",
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"timestamp": "01/11/2023 02:03:00",
"content": "**Frosst**",
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"timestamp": "01/11/2023 02:03:00",
"content": "length formula?",
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"timestamp": "01/11/2023 02:03:06",
"content": "i mean you have the point",
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"timestamp": "01/11/2023 02:03:13",
"content": "it's quite literally pythagoras",
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"timestamp": "01/11/2023 02:03:19",
"content": "ye distance formula",
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"timestamp": "01/11/2023 02:03:22",
"content": "yea centre of Cn is (n-1, n-1) right",
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"timestamp": "01/11/2023 02:03:28",
"content": "yes",
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"timestamp": "01/11/2023 02:03:48",
"content": "so I get $\\sqrt{2(n-1)^2}$",
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"timestamp": "01/11/2023 02:03:50",
"content": "**Springsskateboard**",
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"timestamp": "01/11/2023 02:03:58",
"content": "so thats (n-1)โ2",
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"timestamp": "01/11/2023 02:03:59",
"content": "which is $\\sqrt{2}(n-1)$",
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"timestamp": "01/11/2023 02:04:01",
"content": "**Springsskateboard**",
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"timestamp": "01/11/2023 02:04:03",
"content": ":pandaHmm:",
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"timestamp": "01/11/2023 02:04:05",
"content": "the distance from 0,0 to a,a is literally aโ(2)",
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"timestamp": "01/11/2023 02:04:13",
"content": "oh damn",
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"content": ":pandaHmm:",
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"timestamp": "01/11/2023 02:04:23",
"content": "it's just a square",
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"timestamp": "01/11/2023 02:04:32",
"content": "with a as your sidelength",
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"timestamp": "01/11/2023 02:04:40",
"content": "it's just โ2 multiplied by the square side",
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"timestamp": "01/11/2023 02:04:41",
"content": "lol",
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"timestamp": "01/11/2023 02:04:49",
"content": ":pandaHmm:",
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"timestamp": "01/11/2023 02:04:54",
"content": "ah ok",
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"timestamp": "01/11/2023 02:05:05",
"content": "so now I have n+1 > sqrt(2)(n+1)",
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"timestamp": "01/11/2023 02:05:14",
"content": "so I sub n=1 and n=6?",
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"timestamp": "01/11/2023 02:05:17",
"content": "no",
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"timestamp": "01/11/2023 02:05:20",
"content": "hm?",
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"timestamp": "01/11/2023 02:05:27",
"content": "you solve for n where this holds true",
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"timestamp": "01/11/2023 02:05:32",
"content": "oh",
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"timestamp": "01/11/2023 02:05:33",
"content": "OH",
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"timestamp": "01/11/2023 02:05:34",
"content": "then find the smallest positive integer",
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"timestamp": "01/11/2023 02:05:34",
"content": "bruh",
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"author_id": 536177306578845700,
"author_name": "Shallow.",
"timestamp": "01/11/2023 02:05:36",
"content": "where did u get n+1 from",
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"timestamp": "01/11/2023 02:05:39",
"content": ":hmmCat:",
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"timestamp": "01/11/2023 02:05:47",
"content": "sum of radius of C1 and Cn",
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"timestamp": "01/11/2023 02:06:04",
"content": ":hmmCat:",
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"timestamp": "01/11/2023 02:06:14",
"content": "so that shud be < sign no?",
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"timestamp": "01/11/2023 02:06:24",
"content": "yeah it should",
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"timestamp": "01/11/2023 02:06:30",
"content": "oh oops",
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"timestamp": "01/11/2023 02:06:38",
"content": "^^",
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"timestamp": "01/11/2023 02:06:52",
"content": "ah right",
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"timestamp": "01/11/2023 02:06:54",
"content": "lemme solve",
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"timestamp": "01/11/2023 02:07:38",
"content": ":hmmCat:",
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"id": 1062628951010328600,
"author_id": 244390699431100400,
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"timestamp": "01/11/2023 02:08:04",
"content": "something feels off",
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"timestamp": "01/11/2023 02:08:16",
"content": "ya",
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"timestamp": "01/11/2023 02:08:49",
"content": "okay ye",
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"timestamp": "01/11/2023 02:08:51",
"content": "smth is off",
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"timestamp": "01/11/2023 02:08:59",
"content": ":pandaHmm:",
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"timestamp": "01/11/2023 02:09:18",
"content": "how about differences of radii > distance between center :hmmCat:",
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"timestamp": "01/11/2023 02:09:45",
"content": "oh difference of radii",
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"timestamp": "01/11/2023 02:09:51",
"content": "so n-1",
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"timestamp": "01/11/2023 02:09:54",
"content": "that doens't sound right",
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"timestamp": "01/11/2023 02:10:05",
"content": "ye shouldnโt it be sum",
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"timestamp": "01/11/2023 02:10:14",
"content": ":hmmCat:",
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"id": 1062629506671718400,
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"timestamp": "01/11/2023 02:10:17",
"content": "hold up",
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"timestamp": "01/11/2023 02:10:23",
"content": "both conditions should satisfy tho",
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"timestamp": "01/11/2023 02:10:28",
"content": ":catFone:",
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"timestamp": "01/11/2023 02:10:28",
"content": "the center of the Cn circle is at (n-1, n-1)",
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"timestamp": "01/11/2023 02:10:35",
"content": "yea",
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"timestamp": "01/11/2023 02:10:37",
"content": "wait what",
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"timestamp": "01/11/2023 02:10:42",
"content": "oh wait yeye",
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"content": "lol",
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"content": "that's the problem",
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"content": "huh",
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"timestamp": "01/11/2023 02:11:04",
"content": "because it should be n+1 on one side",
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"content": "and n-1 on the other",
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"content": "wait why",
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"timestamp": "01/11/2023 02:11:31",
"content": "itโs n-1, n-1 no?",
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"timestamp": "01/11/2023 02:11:35",
"content": "so the sum of the radii is 1 and n = n+1",
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"timestamp": "01/11/2023 02:11:45",
"content": "yeah",
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"author_id": 244390699431100400,
"author_name": "Frosst",
"timestamp": "01/11/2023 02:11:47",
"content": "the center of Cn is at (n-1, n-1)",
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"timestamp": "01/11/2023 02:11:59",
"content": "yes",
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"timestamp": "01/11/2023 02:12:04",
"content": "the distance from the center of Cn to the origin is (n-1)โ2",
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"author_name": "Shallow.",
"timestamp": "01/11/2023 02:12:19",
"content": "ye",
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"id": 1062630031186214900,
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"author_name": "Shallow.",
"timestamp": "01/11/2023 02:12:22",
"content": "checks out",
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"id": 1062630040921190400,
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"author_name": "Shallow.",
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"content": ":pandaHmm:",
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"id": 1062630043903344600,
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"timestamp": "01/11/2023 02:12:25",
"content": "your inequality should say n+1 < (n-1)โ2",
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"id": 1062630077449392300,
"author_id": 536177306578845700,
"author_name": "Shallow.",
"timestamp": "01/11/2023 02:12:33",
"content": ",w n+1<(n-1)โ 2",
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"timestamp": "01/11/2023 02:12:35",
"content": "BRUH when did I change n-1 to n+1",
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"id": 1062630088614613100,
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"author_name": "TeXit",
"timestamp": "01/11/2023 02:12:35",
"content": "Results provided by WolframAlpha",
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"id": 1062630137901887500,
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"timestamp": "01/11/2023 02:12:47",
"content": "idk when I changed that LOL",
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"id": 1062630149759185000,
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"author_name": "Frosst",
"timestamp": "01/11/2023 02:12:50",
"content": "yeah you wrote the wrong hting",
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"id": 1062630152997179400,
"author_id": 244390699431100400,
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"timestamp": "01/11/2023 02:12:51",
"content": "lol",
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"id": 1062630200019521700,
"author_id": 536177306578845700,
"author_name": "Shallow.",
"timestamp": "01/11/2023 02:13:02",
"content": ",w (1 + sqrt2)/(sqrt2-1)",
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},
{
"id": 1062630209632874600,
"author_id": 510789298321096700,
"author_name": "TeXit",
"timestamp": "01/11/2023 02:13:04",
"content": "Results provided by WolframAlpha",
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},
{
"id": 1062630213634236400,
"author_id": 1015619946451046400,
"author_name": "Springsskateboard",
"timestamp": "01/11/2023 02:13:05",
"content": ",w evaluate (1+sqrt(2))/(sqrt(2) -1))",
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"id": 1062630223771877400,
"author_id": 510789298321096700,
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"timestamp": "01/11/2023 02:13:08",
"content": "Results provided by WolframAlpha",
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"id": 1062630232672182300,
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"timestamp": "01/11/2023 02:13:10",
"content": "yep checks out",
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"id": 1062630243145359400,
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"timestamp": "01/11/2023 02:13:12",
"content": "NICE",
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"author_name": "Springsskateboard",
"timestamp": "01/11/2023 02:13:24",
"content": "thanks bros",
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"timestamp": "01/11/2023 02:13:27",
"content": "nws",
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"timestamp": "01/11/2023 02:13:30",
"content": "๐๐๐คโ๏ธ",
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"content": ":pandaHmm:",
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"id": 1062630391183323300,
"author_id": 118663865264242690,
"author_name": "ๅคข้ช",
"timestamp": "01/11/2023 02:13:47",
"content": ":catThink:",
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"id": 1062630408509980700,
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"timestamp": "01/11/2023 02:13:52",
"content": "shallow :catThink:",
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"timestamp": "01/11/2023 02:14:36",
"content": "aye snow",
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"content": "missed u friend",
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"content": ":catFone:",
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"timestamp": "01/11/2023 02:15:10",
"content": "hereโs ur favourite emoji :hmmCat:",
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"content": "Channel closed",
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] | help-9 | b25c2ba25da44668aa26506e7eef07ea |
200,679 | [
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"id": 1062639035971014800,
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"author_name": "markt",
"timestamp": "01/11/2023 02:48:09",
"content": "So I have written this attempt at a proof for what is currently considered to be an unsolved problem, I'm like 80% sure that I've made a mistake somewhere, because a 200 year old problem shoudln't generally be provable in so few pages, but I haven't been able to figure out what's wrong with it. I've typeset it with LaTeX and have it ready as a pdf, and it's less than 4 pages long if you exclude the bibligography. Would someone mind looking it over to see if they can find where it might be wrong?",
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"content": "Pinned a message.",
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] | help-9 | 0dee9a95684144358a26306f79fa9d7b |
200,680 | [
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"author_name": "Snakeuto",
"timestamp": "01/11/2023 03:04:43",
"content": "Hi, can someone help me find the Z score",
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"timestamp": "01/11/2023 03:19:43",
"content": "@Snakeuto Has your question been resolved?",
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"content": "@Helpers",
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"id": 1062649458267000800,
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"timestamp": "01/11/2023 03:29:33",
"content": "It's jsut a z-test",
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"content": "https://en.wikipedia.org/wiki/Z-test",
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"id": 1062649663599169500,
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"timestamp": "01/11/2023 03:30:22",
"content": "https://www.youtube.com/watch?v=zJ8e_wAWUzE&ab_channel=TheOrganicChemistryTutor",
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"timestamp": "01/11/2023 03:30:25",
"content": "here watch this",
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"content": "guy does good vids",
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"timestamp": "01/11/2023 03:37:57",
"content": "how do I plug in the numbers",
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"timestamp": "01/11/2023 03:39:43",
"content": "you could use R",
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"author_name": "llspacebarll",
"timestamp": "01/11/2023 03:39:46",
"content": "or spss",
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"author_name": "llspacebarll",
"timestamp": "01/11/2023 03:39:49",
"content": "or some other stats program",
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"author_name": "llspacebarll",
"timestamp": "01/11/2023 03:39:57",
"content": "or use a z-table and do it the oldshcool way idk",
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"timestamp": "01/11/2023 03:41:01",
"content": "sorry I meant how do I plug in the numbers from my question to the test",
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"timestamp": "01/11/2023 03:42:28",
"content": "you have your observed p so you calculate the Z-statistic and calculate the critical value using a z-table or R",
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"timestamp": "01/11/2023 03:42:43",
"content": "if you watch the video",
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"timestamp": "01/11/2023 03:42:46",
"content": "it may help",
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"author_name": "Snakeuto",
"timestamp": "01/11/2023 03:45:58",
"content": "the video says to use my standard deviation but my question doesnt show one",
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"id": 1062653879851950100,
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"author_name": "llspacebarll",
"timestamp": "01/11/2023 03:47:08",
"content": "https://youtu.be/76VruarGn2Q",
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"id": 1062653934965104600,
"author_id": 133064107380310020,
"author_name": "llspacebarll",
"timestamp": "01/11/2023 03:47:21",
"content": "Here is one for binomial distribution if that is what this is",
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"timestamp": "01/11/2023 03:47:40",
"content": "Standard error is standard deviation divided by sqrt of sample size",
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"timestamp": "01/11/2023 03:47:43",
"content": "So itโs given btw",
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"timestamp": "01/11/2023 03:47:59",
"content": "I donโt know what the data is in this question",
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"author_id": 133064107380310020,
"author_name": "llspacebarll",
"timestamp": "01/11/2023 03:48:14",
"content": "I assume itโs binomial so use the technique in the second video maybe",
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"id": 1062654201429229600,
"author_id": 133064107380310020,
"author_name": "llspacebarll",
"timestamp": "01/11/2023 03:48:24",
"content": "But tbh itโs kinda the same thing anyways",
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"id": 1062654224523071500,
"author_id": 133064107380310020,
"author_name": "llspacebarll",
"timestamp": "01/11/2023 03:48:30",
"content": "So it doesnโt really matter much here",
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"id": 1062657802750935000,
"author_id": 576982329470353500,
"author_name": "Snakeuto",
"timestamp": "01/11/2023 04:02:43",
"content": "im still kinda confused could you show me how to do it step by step",
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"id": 1062658590424449000,
"author_id": 133064107380310020,
"author_name": "llspacebarll",
"timestamp": "01/11/2023 04:05:51",
"content": "Im going to bed so no sorry",
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},
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"id": 1062658626579349500,
"author_id": 133064107380310020,
"author_name": "llspacebarll",
"timestamp": "01/11/2023 04:05:59",
"content": "maybe someone else?",
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"author_id": 576982329470353500,
"author_name": "Snakeuto",
"timestamp": "01/11/2023 04:06:53",
"content": "ok no problem i can figure it out tmrw thankyou",
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"author_id": 576982329470353500,
"author_name": "Snakeuto",
"timestamp": "01/11/2023 04:07:19",
"content": ".close",
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},
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"id": 1062658965462323200,
"author_id": 805217272087838700,
"author_name": "Mathematics Bot",
"timestamp": "01/11/2023 04:07:20",
"content": "Channel closed",
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] | help-9 | 9bd41df070fe446db853efd0a1cdbcf8 |
200,681 | [
{
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"content": "Available help channel!",
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"content": "Pinned a message.",
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"content": "Need help with all, do as many as u want",
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"timestamp": "01/11/2023 04:21:44",
"content": "here, close this please",
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] | help-9 | 00634fab9a42423d8de41ced6d5501dd |
200,682 | [
{
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"content": "Available help channel!",
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"content": "need help asap please",
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"author_id": 860475632139108400,
"author_name": "dimonoc",
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"content": "i donโt understand why everything divided by 2",
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"author_id": 860475632139108400,
"author_name": "dimonoc",
"timestamp": "01/11/2023 04:25:35",
"content": "and then how put in terms of sin only",
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"id": 1062663921032507400,
"author_id": 374795910032523260,
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"timestamp": "01/11/2023 04:27:02",
"content": "It's a tricky step",
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"id": 1062664105992921100,
"author_id": 374795910032523260,
"author_name": "SWR",
"timestamp": "01/11/2023 04:27:46",
"content": "Review your angle sum and difference trig identities",
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"id": 1062664121448935400,
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"timestamp": "01/11/2023 04:27:49",
"content": "That will help you",
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"author_id": 860475632139108400,
"author_name": "dimonoc",
"timestamp": "01/11/2023 04:28:06",
"content": "do you not think iโve already tried?",
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"author_id": 860475632139108400,
"author_name": "dimonoc",
"timestamp": "01/11/2023 04:28:09",
"content": "thatโs why iโm here",
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"id": 1062664481089527800,
"author_id": 374795910032523260,
"author_name": "SWR",
"timestamp": "01/11/2023 04:29:15",
"content": "What have you tried",
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"timestamp": "01/11/2023 04:29:47",
"content": "No I do not. I work with the information you tell me.",
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"author_name": "dimonoc",
"timestamp": "01/11/2023 04:36:21",
"content": "not sure what to say",
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"author_name": "dimonoc",
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"content": "iโve looked at all trig identity",
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"author_name": "dimonoc",
"timestamp": "01/11/2023 04:36:32",
"content": "and cant figure it out",
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"author_name": "SWR",
"timestamp": "01/11/2023 04:38:54",
"content": "Well you have $\\sin(\\theta-\\frac{\\pi}{6})$",
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"author_name": "TeXit",
"timestamp": "01/11/2023 04:38:56",
"content": "**SWR**",
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"author_name": "dimonoc",
"timestamp": "01/11/2023 04:39:07",
"content": "why is that relevant in this question though?",
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"timestamp": "01/11/2023 04:39:19",
"content": "That's angle difference",
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"id": 1062667122284691600,
"author_id": 374795910032523260,
"author_name": "SWR",
"timestamp": "01/11/2023 04:39:45",
"content": "Do you remember your angle difference identity",
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"id": 1062667146196431000,
"author_id": 860475632139108400,
"author_name": "dimonoc",
"timestamp": "01/11/2023 04:39:51",
"content": "yes",
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"id": 1062667221735833600,
"author_id": 860475632139108400,
"author_name": "dimonoc",
"timestamp": "01/11/2023 04:40:09",
"content": "sin(A-B) = sinAcosB - sinBcosA",
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"timestamp": "01/11/2023 04:40:09",
"content": "You should try using it here then",
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"id": 1062667257467121800,
"author_id": 374795910032523260,
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"timestamp": "01/11/2023 04:40:17",
"content": "Yup",
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"id": 1062667278417666000,
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"author_name": "dimonoc",
"timestamp": "01/11/2023 04:40:22",
"content": "but why is it pi and pi/6",
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"author_name": "dimonoc",
"timestamp": "01/11/2023 04:40:32",
"content": "i donโt feel like i could figure that out in the future",
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"id": 1062667401642119300,
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"timestamp": "01/11/2023 04:40:51",
"content": "?",
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"id": 1062667431237128200,
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"timestamp": "01/11/2023 04:40:59",
"content": "Where'd you get pi from",
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"author_name": "dimonoc",
"timestamp": "01/11/2023 04:41:03",
"content": "sorry",
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"author_name": "dimonoc",
"timestamp": "01/11/2023 04:41:06",
"content": "i meant theta",
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"id": 1062667478771183600,
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"timestamp": "01/11/2023 04:41:10",
"content": "Ah",
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"id": 1062667630114259000,
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"timestamp": "01/11/2023 04:41:46",
"content": "Well what is cos(pi/6)",
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"id": 1062667650683121700,
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"timestamp": "01/11/2023 04:41:51",
"content": "And sin",
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"id": 1062667743796662300,
"author_id": 860475632139108400,
"author_name": "dimonoc",
"timestamp": "01/11/2023 04:42:13",
"content": "i donโt know it from the top of my head tbh",
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"id": 1062667766303310000,
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"author_name": "dimonoc",
"timestamp": "01/11/2023 04:42:18",
"content": "i think root3 / 2",
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"id": 1062667780870123500,
"author_id": 860475632139108400,
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"timestamp": "01/11/2023 04:42:22",
"content": "and 1/2",
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"timestamp": "01/11/2023 04:43:15",
"content": "Yup",
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"author_name": "dimonoc",
"timestamp": "01/11/2023 04:43:34",
"content": "so to work this out",
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"id": 1062668083724038300,
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"author_name": "SWR",
"timestamp": "01/11/2023 04:43:34",
"content": "And you can see those are the constants in line 4",
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"id": 1062668104229978100,
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"timestamp": "01/11/2023 04:43:39",
"content": "yes",
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"id": 1062668137209794600,
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"timestamp": "01/11/2023 04:43:47",
"content": "Which is why everything was divided by 2",
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"timestamp": "01/11/2023 04:43:51",
"content": "should i do something like cos theta = constant",
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"author_id": 860475632139108400,
"author_name": "dimonoc",
"timestamp": "01/11/2023 04:43:57",
"content": "and find out the angle?",
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"id": 1062669488136409100,
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"timestamp": "01/11/2023 04:49:09",
"content": "โฆ",
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"id": 1062669645762531300,
"author_id": 374795910032523260,
"author_name": "SWR",
"timestamp": "01/11/2023 04:49:46",
"content": "What you're dealing with is a linear combination of a sine and cosine wave.",
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"content": "Their combination makes a sine wave also",
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"id": 1062669890890240000,
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"timestamp": "01/11/2023 04:50:45",
"content": "This is the approach you should use in such a situation",
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"timestamp": "01/11/2023 05:04:09",
"content": "@dimonoc Has your question been resolved?",
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"content": "Channel closed",
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] | help-9 | 5f0a0280d31140e2835d242d830e346e |
200,683 | [
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"id": 1062678629542277100,
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"content": "how do I get that ch(x+y)=chxchy+shxshy ?",
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"timestamp": "01/11/2023 05:25:30",
"content": "Pinned a message.",
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"content": "I did this in compare to the normal trigonometric functions, but beyond that I'm stuck",
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"author_id": 898875998962061300,
"author_name": "perial",
"timestamp": "01/11/2023 05:39:14",
"content": "@Helpers",
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"id": 1062683844408512500,
"author_id": 446704648485863400,
"author_name": "Castroploiinยน",
"timestamp": "01/11/2023 05:46:12",
"content": "Use the exp definitions of sinh and cosh",
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"id": 1062683992391958500,
"author_id": 446704648485863400,
"author_name": "Castroploiinยน",
"timestamp": "01/11/2023 05:46:47",
"content": "Go from the RHS to the LHS",
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"timestamp": "01/11/2023 05:54:14",
"content": "@perial Has your question been resolved?",
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"timestamp": "01/11/2023 05:59:36",
"content": "Is there a more graphical way? (like using vectors to get cos(x+y) since ch and sh are based on the hyperbola",
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"content": "@perial Has your question been resolved?",
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"content": "Channel closed",
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] | help-9 | da4e23d451d84493bf879cc6738712e9 |
200,684 | [
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"content": "Available help channel!",
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"timestamp": "01/11/2023 06:49:57",
"content": "Can somebody explain me this theorem?",
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"content": ",rccw",
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"content": "@unkeen Has your question been resolved?",
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"content": "@unkeen Has your question been resolved?",
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"content": "Channel closed",
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200,685 | [
{
"id": 1062711832655184000,
"author_id": 187850624421986300,
"author_name": "Circle",
"timestamp": "01/11/2023 07:37:25",
"content": ".reopen",
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},
{
"id": 1062711837239562400,
"author_id": 805217272087838700,
"author_name": "Mathematics Bot",
"timestamp": "01/11/2023 07:37:26",
"content": "โ
",
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},
{
"id": 1062712174977487000,
"author_id": 187850624421986300,
"author_name": "Circle",
"timestamp": "01/11/2023 07:38:46",
"content": "@unkeen 1 seems to say that the terms in the sequence approaches arbitrarily close to M as the n chosen is bigger",
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"id": 1062712249636098300,
"author_id": 187850624421986300,
"author_name": "Circle",
"timestamp": "01/11/2023 07:39:04",
"content": "an example would be",
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"id": 1062712367307300900,
"author_id": 187850624421986300,
"author_name": "Circle",
"timestamp": "01/11/2023 07:39:32",
"content": "{s_n} = {1/n}",
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},
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"id": 1062712447565320200,
"author_id": 187850624421986300,
"author_name": "Circle",
"timestamp": "01/11/2023 07:39:51",
"content": "ok mayb not this actually",
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"id": 1062712471917441000,
"author_id": 187850624421986300,
"author_name": "Circle",
"timestamp": "01/11/2023 07:39:57",
"content": "as theyve sup",
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"id": 1062712594160422900,
"author_id": 187850624421986300,
"author_name": "Circle",
"timestamp": "01/11/2023 07:40:26",
"content": "yea nvm it isnt saying approaches M",
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"id": 1062712632420868100,
"author_id": 187850624421986300,
"author_name": "Circle",
"timestamp": "01/11/2023 07:40:35",
"content": "its saying M works as an upper bound",
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"id": 1062713032410681300,
"author_id": 187850624421986300,
"author_name": "Circle",
"timestamp": "01/11/2023 07:42:11",
"content": "ok yea this ig",
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"id": 1062713074949296100,
"author_id": 187850624421986300,
"author_name": "Circle",
"timestamp": "01/11/2023 07:42:21",
"content": "so say we have",
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"id": 1062713105525772400,
"author_id": 187850624421986300,
"author_name": "Circle",
"timestamp": "01/11/2023 07:42:28",
"content": "sn = 1 - 1/n",
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"id": 1062713209766809600,
"author_id": 187850624421986300,
"author_name": "Circle",
"timestamp": "01/11/2023 07:42:53",
"content": "as n approaches inf sn is upper bounded by 1 aka M = 1",
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"id": 1062713433964957700,
"author_id": 187850624421986300,
"author_name": "Circle",
"timestamp": "01/11/2023 07:43:46",
"content": "then for any epsilon >0 we choose we can find some N such that for all n>N, eps+M > sn",
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"id": 1062713702559789000,
"author_id": 187850624421986300,
"author_name": "Circle",
"timestamp": "01/11/2023 07:44:50",
"content": "ok mayb im not explaining this well",
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"id": 1062713709509759100,
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"timestamp": "01/11/2023 07:44:52",
"content": "hm",
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"id": 1062713714383532000,
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"author_name": "Circle",
"timestamp": "01/11/2023 07:44:53",
"content": "o well",
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"id": 1062713731718590500,
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"author_name": "Circle",
"timestamp": "01/11/2023 07:44:57",
"content": "monologue is fun",
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"timestamp": "01/11/2023 08:07:25",
"content": "@unkeen Has your question been resolved?",
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"author_name": "unkeen",
"timestamp": "01/11/2023 08:08:14",
"content": "Okay thanks",
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"content": "Channel closed",
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] | help-9 | 576c530cd723401898f6a2bd61777d4c |
200,686 | [
{
"id": 1062719885794353200,
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"content": "Available help channel!",
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},
{
"id": 1062721548458405900,
"author_id": 873459676711383000,
"author_name": "Belle_รขme",
"timestamp": "01/11/2023 08:16:01",
"content": "hello anyone knows why n and r have to minus one?",
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"content": "Pinned a message.",
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"timestamp": "01/11/2023 08:31:01",
"content": "@Belle_รขme Has your question been resolved?",
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"content": "@Belle_รขme Has your question been resolved?",
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] | help-9 | 41cd81075a164e79970d3673c2eff44d |
200,687 | [
{
"id": 1035405877517230100,
"author_id": 805217272087838700,
"author_name": "Mathematics Bot",
"timestamp": "10/28/2022 00:13:18",
"content": "Available help channel!",
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},
{
"id": 1035407144859734000,
"author_id": 831763375159509000,
"author_name": "lilyoda210",
"timestamp": "10/28/2022 00:18:20",
"content": "Evaluate y+x(x-y)-5 x=3 and y=-7",
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"id": 1035407146654896100,
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"content": "Pinned a message.",
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"id": 1035407596254937200,
"author_id": 831763375159509000,
"author_name": "lilyoda210",
"timestamp": "10/28/2022 00:20:07",
"content": "I need help",
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},
{
"id": 1035407605285257300,
"author_id": 831763375159509000,
"author_name": "lilyoda210",
"timestamp": "10/28/2022 00:20:10",
"content": "Please",
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"id": 1035408217204867100,
"author_id": 873429663370850300,
"author_name": "waddles",
"timestamp": "10/28/2022 00:22:35",
"content": "plug in x=3 and y=-7",
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{
"id": 1035408268471832600,
"author_id": 239843309206503420,
"author_name": "Pirate",
"timestamp": "10/28/2022 00:22:48",
"content": "So, what does the question ask for specifically. To evaluate this you already have x and y values so you should be able to just plug in 3 for x and 7 for y",
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{
"id": 1035408480355496000,
"author_id": 831763375159509000,
"author_name": "lilyoda210",
"timestamp": "10/28/2022 00:23:38",
"content": "I have no idea what Iโm doing",
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},
{
"id": 1035408630310244500,
"author_id": 831763375159509000,
"author_name": "lilyoda210",
"timestamp": "10/28/2022 00:24:14",
"content": "I was lost during the lesson I didnโt ask for help cause I felt dumb very dumb",
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"id": 1035408822929477600,
"author_id": 239843309206503420,
"author_name": "Pirate",
"timestamp": "10/28/2022 00:25:00",
"content": "For every x replace with 3, for example x+2 = z . x=3 means we can substitute in the value of x into the equation. 3 + 2 = z. z = 5",
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"id": 1035408939212353500,
"author_id": 831763375159509000,
"author_name": "lilyoda210",
"timestamp": "10/28/2022 00:25:28",
"content": "Like I did y+x=-4",
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"id": 1035409023454941300,
"author_id": 831763375159509000,
"author_name": "lilyoda210",
"timestamp": "10/28/2022 00:25:48",
"content": "Then I did -4(x-y)",
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{
"id": 1035409102584696800,
"author_id": 831763375159509000,
"author_name": "lilyoda210",
"timestamp": "10/28/2022 00:26:07",
"content": "So thatโs -4x-10=40",
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},
{
"id": 1035409133110829000,
"author_id": 831763375159509000,
"author_name": "lilyoda210",
"timestamp": "10/28/2022 00:26:14",
"content": "-5 is 35โฆ",
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},
{
"id": 1035409176119230500,
"author_id": 831763375159509000,
"author_name": "lilyoda210",
"timestamp": "10/28/2022 00:26:24",
"content": "but I got it wrong",
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"id": 1035409249993502800,
"author_id": 239843309206503420,
"author_name": "Pirate",
"timestamp": "10/28/2022 00:26:42",
"content": "Correct, you are forgetting PEMDAS",
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"id": 1035409292049797100,
"author_id": 831763375159509000,
"author_name": "lilyoda210",
"timestamp": "10/28/2022 00:26:52",
"content": "Oh thatโs right",
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{
"id": 1035409332029886600,
"author_id": 831763375159509000,
"author_name": "lilyoda210",
"timestamp": "10/28/2022 00:27:01",
"content": "Ok let me try again hold on",
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},
{
"id": 1035409449822715900,
"author_id": 831763375159509000,
"author_name": "lilyoda210",
"timestamp": "10/28/2022 00:27:29",
"content": "-19?",
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},
{
"id": 1035409748868210700,
"author_id": 831763375159509000,
"author_name": "lilyoda210",
"timestamp": "10/28/2022 00:28:41",
"content": "Uh jeez",
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},
{
"id": 1035409907345805300,
"author_id": 831763375159509000,
"author_name": "lilyoda210",
"timestamp": "10/28/2022 00:29:18",
"content": "Would it be -13",
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},
{
"id": 1035409908000096300,
"author_id": 239843309206503420,
"author_name": "Pirate",
"timestamp": "10/28/2022 00:29:19",
"content": "hm lets see, -7 + 3 (3 - -7) - 5 , -7 + 3 (10) -5, -7 +30 - 5, 23 -5, 18",
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"id": 1035410025704865800,
"author_id": 831763375159509000,
"author_name": "lilyoda210",
"timestamp": "10/28/2022 00:29:47",
"content": "I thought it might have been either",
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},
{
"id": 1035410060949602300,
"author_id": 239843309206503420,
"author_name": "Pirate",
"timestamp": "10/28/2022 00:29:55",
"content": "Again, positive - a negative is really a positive + a postive",
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},
{
"id": 1035410205414010900,
"author_id": 239843309206503420,
"author_name": "Pirate",
"timestamp": "10/28/2022 00:30:29",
"content": "So when you evaluate this equation you have to pay close attention to the signs of each number",
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"id": 1035410254147616800,
"author_id": 831763375159509000,
"author_name": "lilyoda210",
"timestamp": "10/28/2022 00:30:41",
"content": "3- -7 = -4",
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},
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"author_name": "lilyoda210",
"timestamp": "10/28/2022 00:30:47",
"content": "Or is is -10",
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"timestamp": "10/28/2022 00:30:59",
"content": "neither",
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"author_name": "lilyoda210",
"timestamp": "10/28/2022 00:31:16",
"content": ". Damn",
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"id": 1035410578371510300,
"author_id": 239843309206503420,
"author_name": "Pirate",
"timestamp": "10/28/2022 00:31:58",
"content": "(3) - (-7). the - - create a positive, so that will end up being 3 + 7",
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"timestamp": "10/28/2022 00:32:14",
"content": "So 10",
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"id": 1035410670256148600,
"author_id": 239843309206503420,
"author_name": "Pirate",
"timestamp": "10/28/2022 00:32:20",
"content": "Yup ๐",
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"id": 1035410728913473500,
"author_id": 831763375159509000,
"author_name": "lilyoda210",
"timestamp": "10/28/2022 00:32:34",
"content": "10+-4",
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"id": 1035410751088771100,
"author_id": 831763375159509000,
"author_name": "lilyoda210",
"timestamp": "10/28/2022 00:32:40",
"content": "-6",
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"id": 1035410782214693000,
"author_id": 831763375159509000,
"author_name": "lilyoda210",
"timestamp": "10/28/2022 00:32:47",
"content": "- 5",
"attachments": [],
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},
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"id": 1035410832831545300,
"author_id": 831763375159509000,
"author_name": "lilyoda210",
"timestamp": "10/28/2022 00:32:59",
"content": "= -11",
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},
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"id": 1035410889739882600,
"author_id": 831763375159509000,
"author_name": "lilyoda210",
"timestamp": "10/28/2022 00:33:13",
"content": "Right?",
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},
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"id": 1035410912003240000,
"author_id": 239843309206503420,
"author_name": "Pirate",
"timestamp": "10/28/2022 00:33:18",
"content": "No...",
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"id": 1035410930982461600,
"author_id": 831763375159509000,
"author_name": "lilyoda210",
"timestamp": "10/28/2022 00:33:22",
"content": "Oof",
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"id": 1035410944454557700,
"author_id": 831763375159509000,
"author_name": "lilyoda210",
"timestamp": "10/28/2022 00:33:26",
"content": "Ok",
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},
{
"id": 1035410967003148300,
"author_id": 831763375159509000,
"author_name": "lilyoda210",
"timestamp": "10/28/2022 00:33:31",
"content": "So letโs start with ten",
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"id": 1035411071634251900,
"author_id": 831763375159509000,
"author_name": "lilyoda210",
"timestamp": "10/28/2022 00:33:56",
"content": "-7+3(10)-5",
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},
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"id": 1035411124411187200,
"author_id": 239843309206503420,
"author_name": "Pirate",
"timestamp": "10/28/2022 00:34:09",
"content": "So what do you do next?",
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"id": 1035411164793942000,
"author_id": 831763375159509000,
"author_name": "lilyoda210",
"timestamp": "10/28/2022 00:34:18",
"content": "addition I beileve",
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"id": 1035411325179928600,
"author_id": 239843309206503420,
"author_name": "Pirate",
"timestamp": "10/28/2022 00:34:56",
"content": "No so remember PEMDAS , Parenthesis, Exponents, Multiplication/Division, Add/ Subtract",
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"id": 1035411379647152100,
"author_id": 239843309206503420,
"author_name": "Pirate",
"timestamp": "10/28/2022 00:35:09",
"content": "We still have multiplication in this problem",
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"id": 1035411416846442500,
"author_id": 239843309206503420,
"author_name": "Pirate",
"timestamp": "10/28/2022 00:35:18",
"content": "3(10) = ?",
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"id": 1035411473066893300,
"author_id": 831763375159509000,
"author_name": "lilyoda210",
"timestamp": "10/28/2022 00:35:32",
"content": "30",
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"id": 1035411599256735700,
"author_id": 831763375159509000,
"author_name": "lilyoda210",
"timestamp": "10/28/2022 00:36:02",
"content": "Ok good because I allways get confused on what I do when thereโs a sec naruto like this:a(b)",
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"id": 1035411713379541100,
"author_id": 239843309206503420,
"author_name": "Pirate",
"timestamp": "10/28/2022 00:36:29",
"content": "Yeah, it can be tricky but just remember that just mean multiplication",
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"id": 1035411784212955100,
"author_id": 239843309206503420,
"author_name": "Pirate",
"timestamp": "10/28/2022 00:36:46",
"content": "so now you have -7 + 30 - 5",
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"id": 1035411799010459600,
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"author_name": "lilyoda210",
"timestamp": "10/28/2022 00:36:49",
"content": "Ok",
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},
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"id": 1035411905206046700,
"author_id": 831763375159509000,
"author_name": "lilyoda210",
"timestamp": "10/28/2022 00:37:15",
"content": "Ok",
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"author_id": 831763375159509000,
"author_name": "lilyoda210",
"timestamp": "10/28/2022 00:37:48",
"content": "Well I would do -7+30 giving me 23 -5 = 18",
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"author_id": 239843309206503420,
"author_name": "Pirate",
"timestamp": "10/28/2022 00:38:32",
"content": "There you go ๐",
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"id": 1035412464168353900,
"author_id": 831763375159509000,
"author_name": "lilyoda210",
"timestamp": "10/28/2022 00:39:28",
"content": "Yes!",
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"author_id": 831763375159509000,
"author_name": "lilyoda210",
"timestamp": "10/28/2022 00:39:38",
"content": "Thank you very much good sir",
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"author_id": 831763375159509000,
"author_name": "lilyoda210",
"timestamp": "10/28/2022 00:40:09",
"content": "I very much hope to get help from you again",
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"id": 1035412660923142300,
"author_id": 831763375159509000,
"author_name": "lilyoda210",
"timestamp": "10/28/2022 00:40:15",
"content": "Thank you.",
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"id": 1035412684897779700,
"author_id": 831763375159509000,
"author_name": "lilyoda210",
"timestamp": "10/28/2022 00:40:21",
"content": "Very blurry much",
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"id": 1035412700710305900,
"author_id": 831763375159509000,
"author_name": "lilyoda210",
"timestamp": "10/28/2022 00:40:24",
"content": "Very*",
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"id": 1035412820516421800,
"author_id": 239843309206503420,
"author_name": "Pirate",
"timestamp": "10/28/2022 00:40:53",
"content": "Your welcome. ๐",
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"author_id": 805217272087838700,
"author_name": "Mathematics Bot",
"timestamp": "10/28/2022 00:55:25",
"content": "@lilyoda210 Has your question been resolved?",
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"timestamp": "10/28/2022 00:55:32",
"content": "Channel closed",
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] | help-9 | f6ff9891048543c9b48519c179da9685 |
200,688 | [
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"content": "Available help channel!",
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"content": "hi",
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{
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"author_name": "๏ผจ๏ฝ
๏ฝ๏ฝ
๏ฝ๏ฝ",
"timestamp": "01/11/2023 09:33:40",
"content": "solve for z in the equation x = 2z+4 and substitute the expression of z in the second",
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"timestamp": "01/11/2023 09:33:49",
"content": "I'm here",
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{
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"author_id": 702136500334100600,
"author_name": "Kakashi_Hatake",
"timestamp": "01/11/2023 09:34:02",
"content": "move 1 over to the other side in eq 2 and we get y -1 = (2z)^2",
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"timestamp": "01/11/2023 09:34:06",
"content": "and x - 4 = 2z",
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"content": "solve",
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"timestamp": "01/11/2023 09:34:12",
"content": "ye I did all that",
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"content": "expand and simplify",
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"timestamp": "01/11/2023 09:34:19",
"content": "bro",
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"timestamp": "01/11/2023 09:34:24",
"content": "check my steps",
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"timestamp": "01/11/2023 09:34:26",
"content": ":catBruh:",
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"id": 1062741364493779100,
"author_id": 598193416173518800,
"author_name": "tofu",
"timestamp": "01/11/2023 09:34:46",
"content": "i just want to know do I do ^2 first or the 4 * first?",
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"timestamp": "01/11/2023 09:34:57",
"content": "what do the order of operations say",
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"timestamp": "01/11/2023 09:35:31",
"content": "do the ^2 for the denominator, the 4s will cancel",
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"timestamp": "01/11/2023 09:35:35",
"content": "and we got no fractions left",
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"timestamp": "01/11/2023 09:36:07",
"content": "recall (b/p)(o/e)(md)as",
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"content": "there are multiple ones and Idk which one to follow",
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"timestamp": "01/11/2023 09:36:19",
"content": "bedmas or badmas or bodmas",
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"content": "idk",
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"content": "they all indicate the same thing",
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"timestamp": "01/11/2023 09:36:29",
"content": "oh ok",
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"timestamp": "01/11/2023 09:36:50",
"content": "just uses slightly different words depending on locale",
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"timestamp": "01/11/2023 09:36:59",
"content": "never head of badmas before though",
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"timestamp": "01/11/2023 09:37:09",
"content": "that just looks `bad` (pun intended) and wrong",
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"content": "can u tell me 1 and i'll always use it so im not confused",
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"timestamp": "01/11/2023 09:42:14",
"content": "if you really want an acronym for the order of operations, the superior one imo is actually \nGEMA",
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"timestamp": "01/11/2023 09:42:56",
"content": "why did they make bedmas and all that other stuff then",
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"timestamp": "01/11/2023 09:43:12",
"content": "different places like to use different words",
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"timestamp": "01/11/2023 09:43:32",
"content": "but effectively the goal of describing what's done first and not what to do is the same",
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"timestamp": "01/11/2023 09:44:56",
"content": "gema is good but i think bedmas is more helpful",
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"timestamp": "01/11/2023 09:45:29",
"content": "viewing stuff in gema is more advantageous",
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"timestamp": "01/11/2023 09:45:47",
"content": "\"division\" and \"subtraction\" is intentionally omitted",
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"id": 1062744216683417600,
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"timestamp": "01/11/2023 09:46:06",
"content": "what about dividing come first than multiplying",
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"timestamp": "01/11/2023 09:46:12",
"content": "it doesn't?",
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"author_id": 220517274845577200,
"author_name": "ramonov",
"timestamp": "01/11/2023 09:46:38",
"content": "well it depends on the order in which things are written",
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"timestamp": "01/11/2023 09:47:03",
"content": "bedmas",
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"id": 1062744506941841500,
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"author_name": "ramonov",
"timestamp": "01/11/2023 09:47:15",
"content": "due to their presence many people misunderstand whether certain multiplication / division is done first",
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"author_id": 220517274845577200,
"author_name": "ramonov",
"timestamp": "01/11/2023 09:48:35",
"content": "its more advantageous to view division as a form of multiplication,\nso you are able to do valid work without having to do stuff in a fixed left to right order",
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"id": 1062745286029623400,
"author_id": 598193416173518800,
"author_name": "tofu",
"timestamp": "01/11/2023 09:50:21",
"content": "so i have 1 + 4 * ( (x^2-8x+16)/4 )",
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"timestamp": "01/11/2023 09:51:52",
"content": "yes",
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"id": 1062746311025238100,
"author_id": 220517274845577200,
"author_name": "ramonov",
"timestamp": "01/11/2023 09:54:25",
"content": "simplify that further",
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"id": 1062747457399816300,
"author_id": 598193416173518800,
"author_name": "tofu",
"timestamp": "01/11/2023 09:58:58",
"content": "ye i got it",
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"id": 1062747490845200500,
"author_id": 598193416173518800,
"author_name": "tofu",
"timestamp": "01/11/2023 09:59:06",
"content": "x^2 - 8x + 17",
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"author_name": "ramonov",
"timestamp": "01/11/2023 10:02:22",
"content": "e.g. viewing\n$$123 \\div 456 \\div 3 \\times 456$$\nas \n$$123\\times \\frac{1}{456} \\times \\frac13 \\times 456$$\nand then applying the commutative property of multiplication, you can pretty much multiply these in any order you want; in an order you feel convenient without worrying about \"dividing\" in an inappropriate order\n$$\\underbrace{123 \\times \\frac13}_{41} \\times \\underbrace{\\frac{1}{456} \\times{456}}_{1}$$",
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"author_name": "TeXit",
"timestamp": "01/11/2023 10:02:27",
"content": "**โamonov**",
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"timestamp": "01/11/2023 10:14:06",
"content": "@tofu Has your question been resolved?",
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"content": "Channel closed",
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] | help-9 | f97f82738af04ace9aad7d1394cca337 |
200,689 | [
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"timestamp": "01/11/2023 10:15:40",
"content": "Available help channel!",
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"author_name": "Sarkes_the_jack",
"timestamp": "01/11/2023 10:20:14",
"content": "Can someone do this for me With Ruffini method?I did the two poly :2 but the rest isn't fine",
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"timestamp": "01/11/2023 10:20:21",
"content": "how do you make Calculus?",
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"timestamp": "01/11/2023 10:20:36",
"content": "We are two lol",
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"timestamp": "01/11/2023 10:21:17",
"content": "@Wandering Trader this is my channel",
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"author_name": "shavet",
"timestamp": "01/11/2023 10:25:22",
"content": "haahahha",
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"author_id": 446704648485863400,
"author_name": "Castroploiinยน",
"timestamp": "01/11/2023 10:25:31",
"content": "People can't give you answers, just directions",
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"timestamp": "01/11/2023 10:25:44",
"content": "Oko",
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{
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"author_id": 989024731132993500,
"author_name": "shavet",
"timestamp": "01/11/2023 10:25:51",
"content": "what is ruffini method",
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{
"id": 1062754234543657000,
"author_id": 989024731132993500,
"author_name": "shavet",
"timestamp": "01/11/2023 10:25:54",
"content": "never heard of it",
"attachments": [],
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},
{
"id": 1062754262918119400,
"author_id": 725642910829379600,
"author_name": "Sarkes_the_jack",
"timestamp": "01/11/2023 10:26:01",
"content": "Oh is this",
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"id": 1062754273013805000,
"author_id": 725642910829379600,
"author_name": "Sarkes_the_jack",
"timestamp": "01/11/2023 10:26:03",
"content": "Wait",
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},
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"id": 1062754355859689500,
"author_id": 446704648485863400,
"author_name": "Castroploiinยน",
"timestamp": "01/11/2023 10:26:23",
"content": "It's a way of computing the division of polynomials by a linear factor",
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"author_id": 989024731132993500,
"author_name": "shavet",
"timestamp": "01/11/2023 10:26:30",
"content": "ohhh",
"attachments": [],
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{
"id": 1062754401690845200,
"author_id": 989024731132993500,
"author_name": "shavet",
"timestamp": "01/11/2023 10:26:34",
"content": "its called ruffini?",
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"id": 1062754416865837200,
"author_id": 725642910829379600,
"author_name": "Sarkes_the_jack",
"timestamp": "01/11/2023 10:26:38",
"content": "Yeah",
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"id": 1062754426793754800,
"author_id": 349354952961032200,
"author_name": "Umbraleviathan",
"timestamp": "01/11/2023 10:26:40",
"content": "Muffin",
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{
"id": 1062754471605698600,
"author_id": 725642910829379600,
"author_name": "Sarkes_the_jack",
"timestamp": "01/11/2023 10:26:51",
"content": "So",
"attachments": [],
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{
"id": 1062754476743729300,
"author_id": 446704648485863400,
"author_name": "Castroploiinยน",
"timestamp": "01/11/2023 10:26:52",
"content": "Do you have to use Ruffini here?",
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{
"id": 1062754543512862700,
"author_id": 725642910829379600,
"author_name": "Sarkes_the_jack",
"timestamp": "01/11/2023 10:27:08",
"content": "Yeah I have to do it if I can do",
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"id": 1062754581207077000,
"author_id": 725642910829379600,
"author_name": "Sarkes_the_jack",
"timestamp": "01/11/2023 10:27:17",
"content": "If it is possible",
"attachments": [],
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"id": 1062754646537543700,
"author_id": 725642910829379600,
"author_name": "Sarkes_the_jack",
"timestamp": "01/11/2023 10:27:32",
"content": "So Have I to send my operations?",
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"id": 1062754668494717000,
"author_id": 446704648485863400,
"author_name": "Castroploiinยน",
"timestamp": "01/11/2023 10:27:37",
"content": "My go-to for division has always been regular-old long division",
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"author_name": "Sarkes_the_jack",
"timestamp": "01/11/2023 10:28:09",
"content": "Oh k",
"attachments": [],
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"author_id": 725642910829379600,
"author_name": "Sarkes_the_jack",
"timestamp": "01/11/2023 10:28:24",
"content": "What I have to do so?",
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"author_name": "Castroploiinยน",
"timestamp": "01/11/2023 10:29:16",
"content": "I don't really know Ruffini's way of doing it, sorry ._.",
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"author_name": "Sarkes_the_jack",
"timestamp": "01/11/2023 10:29:23",
"content": "Oh",
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"id": 1062755189548929200,
"author_id": 725642910829379600,
"author_name": "Sarkes_the_jack",
"timestamp": "01/11/2023 10:29:42",
"content": "Have I to use the @ Helper?",
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"id": 1062755420063666200,
"author_id": 446704648485863400,
"author_name": "Castroploiinยน",
"timestamp": "01/11/2023 10:30:37",
"content": "If after 15 minutes of posting your question, you haven't gotten much help, sure",
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"id": 1062755451671957500,
"author_id": 725642910829379600,
"author_name": "Sarkes_the_jack",
"timestamp": "01/11/2023 10:30:44",
"content": "Okk",
"attachments": [],
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},
{
"id": 1062755506231459800,
"author_id": 725642910829379600,
"author_name": "Sarkes_the_jack",
"timestamp": "01/11/2023 10:30:57",
"content": "I send my operations maybe is better",
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"id": 1062756035871387800,
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"author_name": "Sarkes_the_jack",
"timestamp": "01/11/2023 10:33:04",
"content": "",
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"author_name": "Sarkes_the_jack",
"timestamp": "01/11/2023 10:35:13",
"content": "@Helpers",
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"author_id": 725642910829379600,
"author_name": "Sarkes_the_jack",
"timestamp": "01/11/2023 10:36:32",
"content": "But if no one response what I have to do?",
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"author_name": "Castroploiinยน",
"timestamp": "01/11/2023 10:37:01",
"content": "There's not much to do apart from wait and ping again",
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},
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"id": 1062757098074681500,
"author_id": 725642910829379600,
"author_name": "Sarkes_the_jack",
"timestamp": "01/11/2023 10:37:17",
"content": "Oh",
"attachments": [],
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},
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"id": 1062757175438610600,
"author_id": 725642910829379600,
"author_name": "Sarkes_the_jack",
"timestamp": "01/11/2023 10:37:35",
"content": "But have I maybe to change channel?",
"attachments": [],
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"id": 1062757227871612900,
"author_id": 725642910829379600,
"author_name": "Sarkes_the_jack",
"timestamp": "01/11/2023 10:37:48",
"content": "Or it's useless and I have to just wait",
"attachments": [],
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"author_id": 446704648485863400,
"author_name": "Castroploiinยน",
"timestamp": "01/11/2023 10:37:56",
"content": "You could, but I don't see how that helps",
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"id": 1062757319177412700,
"author_id": 446704648485863400,
"author_name": "Castroploiinยน",
"timestamp": "01/11/2023 10:38:09",
"content": "Your channel is already near the top of the category",
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"id": 1062757330665611400,
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"author_name": "Sarkes_the_jack",
"timestamp": "01/11/2023 10:38:12",
"content": "Uhm fine",
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"id": 1062757392200249500,
"author_id": 725642910829379600,
"author_name": "Sarkes_the_jack",
"timestamp": "01/11/2023 10:38:27",
"content": "Hope that someone knows this method",
"attachments": [],
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"author_name": "Mathematics Bot",
"timestamp": "01/11/2023 10:53:27",
"content": "@Sarkes_the_jack Has your question been resolved?",
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"timestamp": "01/11/2023 10:57:01",
"content": "@Helpers",
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"id": 1062769614846697600,
"author_id": 805217272087838700,
"author_name": "Mathematics Bot",
"timestamp": "01/11/2023 11:27:01",
"content": "@Sarkes_the_jack Has your question been resolved?",
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"author_name": "bl0ss0mtr33",
"timestamp": "01/11/2023 11:59:16",
"content": "@Helpers",
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"timestamp": "01/11/2023 12:27:43",
"content": "@Sarkes_the_jack Has your question been resolved?",
"attachments": [],
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"timestamp": "01/11/2023 14:00:16",
"content": "@Helpers",
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},
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"id": 1062827465170489300,
"author_id": 802295942954221600,
"author_name": "Leele",
"timestamp": "01/11/2023 15:16:54",
"content": "Can you show me how you came to that table? The step before you made it",
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"timestamp": "01/11/2023 15:39:32",
"content": "Wdym",
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"author_name": "Sarkes_the_jack",
"timestamp": "01/11/2023 15:40:03",
"content": "Like o watched i thought and I've done it",
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},
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"id": 1062841206419234800,
"author_id": 802295942954221600,
"author_name": "Leele",
"timestamp": "01/11/2023 16:11:30",
"content": "yep, sorry but english isnt my first langauge and im not very good with it",
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] | help-9 | 6169cf6c4b3e40fa84457d061b6c5ead |
200,690 | [
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"content": "Two office towers are 55m apart. From the top of the shorter tower, the angle of depression to the base of the taller tower is 24. The angel of elevation to the top this tower is 47. Determine the HEIGHT of each tower to nearest metre. Include a labelled diagram.",
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] | help-9 | 6ea086b693574ed8989ce0df77ff261d |
200,691 | [
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"author_name": "hannahh",
"timestamp": "01/11/2023 20:32:53",
"content": "idk what im doing wrong, i thought order doesnt matter but these are supposed to be equal\ndistance formula is sqrt((x_2-x_1)^2+(y_2-y_1)^2)",
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"content": "Why is it minus inside the square root",
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"content": "wdym?",
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"timestamp": "01/11/2023 20:43:11",
"content": "Should be addition",
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"timestamp": "01/11/2023 20:43:34",
"content": "**Mehdi\\_Moulati**",
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"content": "im stupid ty",
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"content": ".close",
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] | help-9 | 47f36fef14184d7bb3e7832d8503337c |
200,692 | [
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"author_name": "okisok",
"timestamp": "01/11/2023 21:11:42",
"content": "Is this formula only applicable when it is maximum frictional force?",
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"id": 1062916994665550000,
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"timestamp": "01/11/2023 21:12:39",
"content": "(Please ping)",
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"author_name": "OssihLikesBlue",
"timestamp": "01/11/2023 21:14:45",
"content": "@okisok sort of and no. You have static friction where F โค mu * N, and then when it starts slipping you have a different coefficient for dynamic friction",
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"timestamp": "01/11/2023 21:18:21",
"content": "Ok thank you!!",
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"id": 1062918450395238500,
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"content": ".close",
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] | help-9 | 383b4b524a024c7f8c38d81dc21512fd |
200,693 | [
{
"id": 1062919188101992400,
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"id": 1062919667716468900,
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"author_name": "Idris",
"timestamp": "01/11/2023 21:23:16",
"content": "how to factor and find roots with this problem\na^2-10a-24=0",
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"id": 1062919860797050900,
"author_id": 1000057838007226500,
"author_name": "VulcanOne",
"timestamp": "01/11/2023 21:24:02",
"content": "So like",
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"id": 1062919896050176000,
"author_id": 1000057838007226500,
"author_name": "VulcanOne",
"timestamp": "01/11/2023 21:24:11",
"content": "You have to find a bunch of pairs",
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"id": 1062919940941824100,
"author_id": 1000057838007226500,
"author_name": "VulcanOne",
"timestamp": "01/11/2023 21:24:22",
"content": "That give you a sum of -10",
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"id": 1062919994377261000,
"author_id": 1000057838007226500,
"author_name": "VulcanOne",
"timestamp": "01/11/2023 21:24:34",
"content": "And at the same time give you a product of -24",
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"id": 1062920009069908100,
"author_id": 314470958402633700,
"author_name": "Idris",
"timestamp": "01/11/2023 21:24:38",
"content": "is it 12a-2a",
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"id": 1062920135930814500,
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"author_name": "VulcanOne",
"timestamp": "01/11/2023 21:25:08",
"content": "(a-12)(a+2) = 0",
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"id": 1062920193426337800,
"author_id": 1000057838007226500,
"author_name": "VulcanOne",
"timestamp": "01/11/2023 21:25:22",
"content": "Like you mean that a = 12 and a=-2?",
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"id": 1062920226712338600,
"author_id": 314470958402633700,
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"timestamp": "01/11/2023 21:25:30",
"content": "no umm",
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"id": 1062920314432000100,
"author_id": 314470958402633700,
"author_name": "Idris",
"timestamp": "01/11/2023 21:25:51",
"content": "like in first step\na^2+12a-2a-24=0",
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"id": 1062920319226085500,
"author_id": 314470958402633700,
"author_name": "Idris",
"timestamp": "01/11/2023 21:25:52",
"content": "right?",
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"id": 1062920470745325600,
"author_id": 1000057838007226500,
"author_name": "VulcanOne",
"timestamp": "01/11/2023 21:26:28",
"content": "No actually",
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"id": 1062920499514048600,
"author_id": 1000057838007226500,
"author_name": "VulcanOne",
"timestamp": "01/11/2023 21:26:35",
"content": "Add up 12-2",
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"id": 1062920516605849600,
"author_id": 1000057838007226500,
"author_name": "VulcanOne",
"timestamp": "01/11/2023 21:26:39",
"content": "You get -10?",
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"id": 1062920543629742100,
"author_id": 314470958402633700,
"author_name": "Idris",
"timestamp": "01/11/2023 21:26:45",
"content": "oh",
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"id": 1062920585837035500,
"author_id": 314470958402633700,
"author_name": "Idris",
"timestamp": "01/11/2023 21:26:55",
"content": "so -12a+2a ?",
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"id": 1062920816787996800,
"author_id": 1000057838007226500,
"author_name": "VulcanOne",
"timestamp": "01/11/2023 21:27:50",
"content": "Yeah",
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"author_id": 314470958402633700,
"author_name": "Idris",
"timestamp": "01/11/2023 21:27:58",
"content": "a^2-12a+2a-24=0",
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},
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"id": 1062921004336287700,
"author_id": 314470958402633700,
"author_name": "Idris",
"timestamp": "01/11/2023 21:28:35",
"content": "then \n(a^2-2a)(12a+24)=0",
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"id": 1062921154530119700,
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"author_name": "VulcanOne",
"timestamp": "01/11/2023 21:29:11",
"content": "Nope",
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"id": 1062921189204431000,
"author_id": 1000057838007226500,
"author_name": "VulcanOne",
"timestamp": "01/11/2023 21:29:19",
"content": "Factor a first",
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{
"id": 1062921245861105700,
"author_id": 314470958402633700,
"author_name": "Idris",
"timestamp": "01/11/2023 21:29:33",
"content": "with -12a or +2a?",
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"id": 1062921458650730600,
"author_id": 314470958402633700,
"author_name": "Idris",
"timestamp": "01/11/2023 21:30:23",
"content": "hm",
"attachments": [],
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},
{
"id": 1062921525386293200,
"author_id": 314470958402633700,
"author_name": "Idris",
"timestamp": "01/11/2023 21:30:39",
"content": "a(a-12+2)-24=0",
"attachments": [],
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},
{
"id": 1062921535595237500,
"author_id": 314470958402633700,
"author_name": "Idris",
"timestamp": "01/11/2023 21:30:42",
"content": "like this?",
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"id": 1062921606713856100,
"author_id": 1000057838007226500,
"author_name": "VulcanOne",
"timestamp": "01/11/2023 21:30:59",
"content": "Well works but not in the way you want",
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{
"id": 1062921650779213800,
"author_id": 1000057838007226500,
"author_name": "VulcanOne",
"timestamp": "01/11/2023 21:31:09",
"content": "You wanna leave one of them",
"attachments": [],
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},
{
"id": 1062921688037208000,
"author_id": 1000057838007226500,
"author_name": "VulcanOne",
"timestamp": "01/11/2023 21:31:18",
"content": "Either 2a or -12a",
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},
{
"id": 1062921764105097300,
"author_id": 314470958402633700,
"author_name": "Idris",
"timestamp": "01/11/2023 21:31:36",
"content": "a(a-2)",
"attachments": [],
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},
{
"id": 1062921820283609300,
"author_id": 314470958402633700,
"author_name": "Idris",
"timestamp": "01/11/2023 21:31:50",
"content": "12(a+2)",
"attachments": [],
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},
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"id": 1062921903163048100,
"author_id": 1000057838007226500,
"author_name": "VulcanOne",
"timestamp": "01/11/2023 21:32:09",
"content": "Why -2?",
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"id": 1062922004572930000,
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"author_name": "Idris",
"timestamp": "01/11/2023 21:32:34",
"content": "right it was supposed to be positive",
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"id": 1062922074420691100,
"author_id": 314470958402633700,
"author_name": "Idris",
"timestamp": "01/11/2023 21:32:50",
"content": "a(a+2)",
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},
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"id": 1062922165462249500,
"author_id": 1000057838007226500,
"author_name": "VulcanOne",
"timestamp": "01/11/2023 21:33:12",
"content": "a(a+2) -12a -24",
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},
{
"id": 1062922210509070300,
"author_id": 1000057838007226500,
"author_name": "VulcanOne",
"timestamp": "01/11/2023 21:33:23",
"content": "That's what we are left with",
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{
"id": 1062922266251370500,
"author_id": 314470958402633700,
"author_name": "Idris",
"timestamp": "01/11/2023 21:33:36",
"content": "-12(a+2) ?",
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"id": 1062922298228736100,
"author_id": 1000057838007226500,
"author_name": "VulcanOne",
"timestamp": "01/11/2023 21:33:44",
"content": "Yeahhh",
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},
{
"id": 1062922314943058000,
"author_id": 314470958402633700,
"author_name": "Idris",
"timestamp": "01/11/2023 21:33:48",
"content": "oooh",
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},
{
"id": 1062922351286693900,
"author_id": 1000057838007226500,
"author_name": "VulcanOne",
"timestamp": "01/11/2023 21:33:56",
"content": "a(a+2)-12(a+2)",
"attachments": [],
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},
{
"id": 1062922414012510200,
"author_id": 314470958402633700,
"author_name": "Idris",
"timestamp": "01/11/2023 21:34:11",
"content": "so then \n(a-12)(a+2)",
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"timestamp": "01/11/2023 21:34:15",
"content": "Yep",
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"author_name": "Idris",
"timestamp": "01/11/2023 21:34:23",
"content": "a-12=0\na=12",
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"author_name": "Idris",
"timestamp": "01/11/2023 21:34:30",
"content": "a+2=0\na=-2",
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"id": 1062922512146640900,
"author_id": 1000057838007226500,
"author_name": "VulcanOne",
"timestamp": "01/11/2023 21:34:35",
"content": ":hyperyay:",
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"id": 1062922514369630300,
"author_id": 314470958402633700,
"author_name": "Idris",
"timestamp": "01/11/2023 21:34:35",
"content": "gotcha",
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"author_name": "Idris",
"timestamp": "01/11/2023 21:34:41",
"content": "thanks for the help mate",
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"id": 1062922559944933400,
"author_id": 1000057838007226500,
"author_name": "VulcanOne",
"timestamp": "01/11/2023 21:34:46",
"content": ":librasmile:",
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"id": 1062922576181088400,
"author_id": 1000057838007226500,
"author_name": "VulcanOne",
"timestamp": "01/11/2023 21:34:50",
"content": "Glad to help",
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"id": 1062922713494212600,
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"author_name": "Idris",
"timestamp": "01/11/2023 21:35:23",
"content": "the problem was i got the roots in opposite, a=-12 and a=2",
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"id": 1062922790623260700,
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"author_name": "Idris",
"timestamp": "01/11/2023 21:35:41",
"content": "now it is right eh",
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"author_id": 1000057838007226500,
"author_name": "VulcanOne",
"timestamp": "01/11/2023 21:36:06",
"content": "Yeah",
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"id": 1062922948798861300,
"author_id": 1000057838007226500,
"author_name": "VulcanOne",
"timestamp": "01/11/2023 21:36:19",
"content": "You gotta check if the sum adds up or not",
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"id": 1062923029249790000,
"author_id": 1000057838007226500,
"author_name": "VulcanOne",
"timestamp": "01/11/2023 21:36:38",
"content": "While keeping the product intact",
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"id": 1062923046173823100,
"author_id": 314470958402633700,
"author_name": "Idris",
"timestamp": "01/11/2023 21:36:42",
"content": "yup that was what I missed",
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"id": 1062923085726105600,
"author_id": 314470958402633700,
"author_name": "Idris",
"timestamp": "01/11/2023 21:36:51",
"content": ".close",
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},
{
"id": 1062923088599195600,
"author_id": 805217272087838700,
"author_name": "Mathematics Bot",
"timestamp": "01/11/2023 21:36:52",
"content": "Channel closed",
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] | help-9 | fdb7e774a6aa412c996a49e073e6a3a5 |
200,694 | [
{
"id": 1062923341654147100,
"author_id": 805217272087838700,
"author_name": "Mathematics Bot",
"timestamp": "01/11/2023 21:37:52",
"content": "Available help channel!",
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},
{
"id": 1062924128929198100,
"author_id": 805217272087838700,
"author_name": "Mathematics Bot",
"timestamp": "01/11/2023 21:41:00",
"content": "Pinned a message.",
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"id": 1062924582094377000,
"author_id": 349354952961032200,
"author_name": "Umbraleviathan",
"timestamp": "01/11/2023 21:42:48",
"content": "Combine each term into one fraction",
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"id": 1062925057237717100,
"author_id": 349354952961032200,
"author_name": "Umbraleviathan",
"timestamp": "01/11/2023 21:44:41",
"content": "No",
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"id": 1062925097058455700,
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"author_name": "Umbraleviathan",
"timestamp": "01/11/2023 21:44:51",
"content": "Legit just like how you combine any other fractions",
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"id": 1062925107875549300,
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"author_name": "Umbraleviathan",
"timestamp": "01/11/2023 21:44:53",
"content": "Common denominator",
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"id": 1062925215102947500,
"author_id": 349354952961032200,
"author_name": "Umbraleviathan",
"timestamp": "01/11/2023 21:45:19",
"content": "You cannot distribute the 3x-4 is; those two terms aren't even factors",
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"timestamp": "01/11/2023 21:46:26",
"content": "Channel closed",
"attachments": [],
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}
] | help-9 | 98737537bcc64759b086683beb9d66f7 |
200,695 | [
{
"id": 1062926653640155300,
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"author_name": "Mathematics Bot",
"timestamp": "01/11/2023 21:51:02",
"content": "Available help channel!",
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{
"id": 1062928413221986400,
"author_id": 314470958402633700,
"author_name": "Idris",
"timestamp": "01/11/2023 21:58:01",
"content": "why can we factor 4x^2-8x+3=0 ; but not x^2-8x+3=0 ?",
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"timestamp": "01/11/2023 21:58:02",
"content": "Pinned a message.",
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"author_id": 468617290083074050,
"author_name": "Baboon",
"timestamp": "01/11/2023 22:00:10",
"content": "x^2 - 8x +3 = 0 can be factored its just that the solutions dont work out to be integers like they normally do when u factor stuff",
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"author_id": 314470958402633700,
"author_name": "Idris",
"timestamp": "01/11/2023 22:00:45",
"content": "yeah, because there are no pairs which sum to -8 and produce +3",
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"id": 1062929427039780900,
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"author_name": "Idris",
"timestamp": "01/11/2023 22:02:03",
"content": "but why can we factor the first question? is it because that x^2 is not 1?",
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"author_id": 485903210272391200,
"author_name": "dldh06",
"timestamp": "01/11/2023 22:02:22",
"content": "Do you know the quadratic formula?",
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"id": 1062929580379340800,
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"author_name": "Idris",
"timestamp": "01/11/2023 22:02:40",
"content": "yes i do",
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"author_name": "dldh06",
"timestamp": "01/11/2023 22:03:09",
"content": "You factor it because b^2 - 4ac is a perfect square",
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"id": 1062929793139609700,
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"timestamp": "01/11/2023 22:03:30",
"content": "If it wasn't a perfect square, you get irrational numbers or complex roots",
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"id": 1062929824362020900,
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"timestamp": "01/11/2023 22:03:38",
"content": "i mean",
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"id": 1062929896097190000,
"author_id": 314470958402633700,
"author_name": "Idris",
"timestamp": "01/11/2023 22:03:55",
"content": "pairs should sum to B and produce to C, right?",
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"id": 1062929981778444300,
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"author_name": "Idris",
"timestamp": "01/11/2023 22:04:15",
"content": "but in both problems, there are no pairs that do this",
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"author_name": "dldh06",
"timestamp": "01/11/2023 22:04:29",
"content": "It's the product of a and c that add up to b",
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"id": 1062930331986042900,
"author_id": 314470958402633700,
"author_name": "Idris",
"timestamp": "01/11/2023 22:05:39",
"content": "when factoring to find roots?",
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"id": 1062930392962834400,
"author_id": 485903210272391200,
"author_name": "dldh06",
"timestamp": "01/11/2023 22:05:53",
"content": "Yes that the process to factor",
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"id": 1062930623246897300,
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"author_name": "Idris",
"timestamp": "01/11/2023 22:06:48",
"content": "but wasn't it that, we should find pairs for bx, that sums to b, and produces c?",
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"id": 1062930716293341300,
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"author_name": "Idris",
"timestamp": "01/11/2023 22:07:11",
"content": "and then factor one of them with ax, and the other one with c?",
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"id": 1062930724904239100,
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"author_name": "dldh06",
"timestamp": "01/11/2023 22:07:13",
"content": "> product of a and c that add up to b",
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"id": 1062930815488643200,
"author_id": 314470958402633700,
"author_name": "Idris",
"timestamp": "01/11/2023 22:07:34",
"content": "ac=b ?",
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"id": 1062930844618084400,
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"author_name": "dldh06",
"timestamp": "01/11/2023 22:07:41",
"content": "No",
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"author_name": "dldh06",
"timestamp": "01/11/2023 22:08:16",
"content": "You take A times C, find the factors that those which add up to B",
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"id": 1062931233715269600,
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"author_name": "Idris",
"timestamp": "01/11/2023 22:09:14",
"content": "but wait",
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"timestamp": "01/11/2023 22:09:55",
"content": "so when it is ax^2+bx+c=0",
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"author_name": "Idris",
"timestamp": "01/11/2023 22:10:26",
"content": "we take a times c",
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"author_name": "dldh06",
"timestamp": "01/11/2023 22:10:36",
"content": "ax^2?",
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"author_name": "Idris",
"timestamp": "01/11/2023 22:10:41",
"content": "yeah sorry",
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"id": 1062931659009294300,
"author_id": 314470958402633700,
"author_name": "Idris",
"timestamp": "01/11/2023 22:10:55",
"content": "we take a times c",
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"id": 1062931872755241000,
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"author_name": "Idris",
"timestamp": "01/11/2023 22:11:46",
"content": "and find the pairs which add up to b?",
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"id": 1062931905915400300,
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"timestamp": "01/11/2023 22:11:54",
"content": "Yes",
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"id": 1062932027789299800,
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"author_name": "Idris",
"timestamp": "01/11/2023 22:12:23",
"content": "and produce ac?",
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"author_name": "dldh06",
"timestamp": "01/11/2023 22:12:27",
"content": "And as mentioned, if it's factorable, then b^2 - 4ac is a perfect square",
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"timestamp": "01/11/2023 22:12:46",
"content": "I don't understand what you mean by produce",
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"id": 1062932175047114800,
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"author_name": "Idris",
"timestamp": "01/11/2023 22:12:58",
"content": "sorry I mean product",
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"id": 1062932185272811600,
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"author_name": "Idris",
"timestamp": "01/11/2023 22:13:01",
"content": "times",
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"timestamp": "01/11/2023 22:13:31",
"content": "This is redundant",
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"author_name": "dldh06",
"timestamp": "01/11/2023 22:13:42",
"content": "You're already doing A times C",
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"author_name": "dldh06",
"timestamp": "01/11/2023 22:13:53",
"content": "To find the factors that add up to B",
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"author_name": "dldh06",
"timestamp": "01/11/2023 22:14:04",
"content": "There's no point to multiply it again",
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"id": 1062932479155130500,
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"author_name": "Idris",
"timestamp": "01/11/2023 22:14:11",
"content": "oh okay",
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"timestamp": "01/11/2023 22:14:25",
"content": "but when it is x^2+bx+c=0",
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"id": 1062932552018559100,
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"author_name": "Idris",
"timestamp": "01/11/2023 22:14:28",
"content": "a is 1",
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"id": 1062932608905916400,
"author_id": 314470958402633700,
"author_name": "Idris",
"timestamp": "01/11/2023 22:14:42",
"content": "so we cannot take a times c",
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"id": 1062932650479845400,
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"timestamp": "01/11/2023 22:14:52",
"content": "Yes you can",
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"timestamp": "01/11/2023 22:14:54",
"content": "a = 1",
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"author_name": "dldh06",
"timestamp": "01/11/2023 22:15:03",
"content": "a times c is possible",
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"id": 1062932710710050800,
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"author_name": "Idris",
"timestamp": "01/11/2023 22:15:06",
"content": "but it becomes the same thing doesn't it",
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"author_name": "dldh06",
"timestamp": "01/11/2023 22:15:41",
"content": "You stated that you can't take a times c",
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"id": 1062932879442714800,
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"timestamp": "01/11/2023 22:15:46",
"content": "I'm saying you can",
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"timestamp": "01/11/2023 22:16:00",
"content": "Sure it equals itself but it's still possible to do a times c",
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"timestamp": "01/11/2023 22:16:09",
"content": "but we cannot find the roots that way",
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"timestamp": "01/11/2023 22:16:29",
"content": "As stated\n> if it's factorable, then b^2 - 4ac is a perfect square",
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"author_id": 485903210272391200,
"author_name": "dldh06",
"timestamp": "01/11/2023 22:16:55",
"content": "x^2-8x+3\nWould that result in a perfect square if you applied b^2 - 4ac?",
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"content": "no",
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"author_name": "dldh06",
"timestamp": "01/11/2023 22:17:37",
"content": "Then you cannot factor x^2-8x+3 to be in the form of (ax + b)(cx + d)",
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"author_name": "Idris",
"timestamp": "01/11/2023 22:17:38",
"content": "or wait",
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"author_name": "Idris",
"timestamp": "01/11/2023 22:18:04",
"content": "it would actually D=16",
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"id": 1062933601060135000,
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"author_name": "dldh06",
"timestamp": "01/11/2023 22:18:38",
"content": "No",
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"id": 1062933624451760100,
"author_id": 485903210272391200,
"author_name": "dldh06",
"timestamp": "01/11/2023 22:18:44",
"content": "How did you even get that?",
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"author_name": "Idris",
"timestamp": "01/11/2023 22:19:07",
"content": "oh sorry i did it with 4x^2",
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"timestamp": "01/11/2023 22:19:25",
"content": "so we cannot factor that one",
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"timestamp": "01/11/2023 22:19:34",
"content": "As you can see for 4x^2-8x+3, that's a perfect square so you can factor it",
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"id": 1062933881197707400,
"author_id": 314470958402633700,
"author_name": "Idris",
"timestamp": "01/11/2023 22:19:45",
"content": "because a = 1 and there are no pairs that sum to b and product c",
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"timestamp": "01/11/2023 22:20:13",
"content": "a can equal to 1 and still factor",
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"id": 1062934046537175200,
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"author_name": "dldh06",
"timestamp": "01/11/2023 22:20:25",
"content": "It doesn't matter if a is or isn't equal to 1",
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"id": 1062934143958274000,
"author_id": 314470958402633700,
"author_name": "Idris",
"timestamp": "01/11/2023 22:20:48",
"content": "but both a=1 and no pairs",
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},
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"id": 1062934154670514200,
"author_id": 314470958402633700,
"author_name": "Idris",
"timestamp": "01/11/2023 22:20:50",
"content": "then cannot factor",
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},
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"id": 1062934170696958100,
"author_id": 314470958402633700,
"author_name": "Idris",
"timestamp": "01/11/2023 22:20:54",
"content": "right?",
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},
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"id": 1062934365887279100,
"author_id": 485903210272391200,
"author_name": "dldh06",
"timestamp": "01/11/2023 22:21:41",
"content": "Because of the factor that b^2 - 4ac is not a perfect square",
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},
{
"id": 1062934391271211000,
"author_id": 485903210272391200,
"author_name": "dldh06",
"timestamp": "01/11/2023 22:21:47",
"content": "That's why you can't factor it",
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},
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"id": 1062934632489828400,
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"author_name": "dldh06",
"timestamp": "01/11/2023 22:22:44",
"content": "x^2 - 4x - 12\na = 1 and it's factorable because b^2 - 4ac is a perfect square",
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{
"id": 1062934808671563800,
"author_id": 314470958402633700,
"author_name": "Idris",
"timestamp": "01/11/2023 22:23:26",
"content": "yeah but i want to factor without doing the quadratic formula",
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},
{
"id": 1062934846801977500,
"author_id": 314470958402633700,
"author_name": "Idris",
"timestamp": "01/11/2023 22:23:35",
"content": "isn't there is a way to know without it?",
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},
{
"id": 1062935009910075500,
"author_id": 485903210272391200,
"author_name": "dldh06",
"timestamp": "01/11/2023 22:24:14",
"content": "If b^2 - 4ac is not a perfect square then you cannot factor it to be in the form of (ax + b)(cx + d)",
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},
{
"id": 1062935212398493700,
"author_id": 314470958402633700,
"author_name": "Idris",
"timestamp": "01/11/2023 22:25:03",
"content": "okay i think i got it",
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},
{
"id": 1062935220552216700,
"author_id": 314470958402633700,
"author_name": "Idris",
"timestamp": "01/11/2023 22:25:04",
"content": "thank you",
"attachments": [],
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},
{
"id": 1062935386374033400,
"author_id": 314470958402633700,
"author_name": "Idris",
"timestamp": "01/11/2023 22:25:44",
"content": ".close",
"attachments": [],
"mentions": [],
"reference": null
},
{
"id": 1062935389612036200,
"author_id": 805217272087838700,
"author_name": "Mathematics Bot",
"timestamp": "01/11/2023 22:25:45",
"content": "Channel closed",
"attachments": [],
"mentions": [],
"reference": null
}
] | help-9 | 2f83c9114ff0428bb6ec46266160250e |
200,696 | [
{
"id": 1062935641844887600,
"author_id": 805217272087838700,
"author_name": "Mathematics Bot",
"timestamp": "01/11/2023 22:26:45",
"content": "Available help channel!",
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"reference": null
},
{
"id": 1062938282062778500,
"author_id": 999947272529920000,
"author_name": "MonkeyMan",
"timestamp": "01/11/2023 22:37:14",
"content": "",
"attachments": [
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"author_name": "Mathematics Bot",
"timestamp": "01/11/2023 22:37:15",
"content": "Pinned a message.",
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"id": 1062938307937444000,
"author_id": 999947272529920000,
"author_name": "MonkeyMan",
"timestamp": "01/11/2023 22:37:21",
"content": "Can someone help me with this",
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},
{
"id": 1062938313109028900,
"author_id": 999947272529920000,
"author_name": "MonkeyMan",
"timestamp": "01/11/2023 22:37:22",
"content": "?",
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},
{
"id": 1062938492067385500,
"author_id": 464042280379088900,
"author_name": "Archi",
"timestamp": "01/11/2023 22:38:04",
"content": "which one",
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},
{
"id": 1062938504327344300,
"author_id": 999947272529920000,
"author_name": "MonkeyMan",
"timestamp": "01/11/2023 22:38:07",
"content": "5",
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},
{
"id": 1062938602574712800,
"author_id": 464042280379088900,
"author_name": "Archi",
"timestamp": "01/11/2023 22:38:31",
"content": "you have the value of y given with respect to x",
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},
{
"id": 1062938617888129200,
"author_id": 464042280379088900,
"author_name": "Archi",
"timestamp": "01/11/2023 22:38:34",
"content": "so in the 2nd eq",
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},
{
"id": 1062938623143583900,
"author_id": 999947272529920000,
"author_name": "MonkeyMan",
"timestamp": "01/11/2023 22:38:36",
"content": "i found x",
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},
{
"id": 1062938650364616700,
"author_id": 999947272529920000,
"author_name": "MonkeyMan",
"timestamp": "01/11/2023 22:38:42",
"content": "but i dont remembre how to find Y",
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},
{
"id": 1062938685068279800,
"author_id": 464042280379088900,
"author_name": "Archi",
"timestamp": "01/11/2023 22:38:50",
"content": "just put the value of x",
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},
{
"id": 1062938705750401200,
"author_id": 464042280379088900,
"author_name": "Archi",
"timestamp": "01/11/2023 22:38:55",
"content": "in the first equation",
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},
{
"id": 1062938731415339000,
"author_id": 464042280379088900,
"author_name": "Archi",
"timestamp": "01/11/2023 22:39:02",
"content": "or the 2nd equation",
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},
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"id": 1062938734489776100,
"author_id": 999947272529920000,
"author_name": "MonkeyMan",
"timestamp": "01/11/2023 22:39:02",
"content": "so",
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},
{
"id": 1062938768329412600,
"author_id": 999947272529920000,
"author_name": "MonkeyMan",
"timestamp": "01/11/2023 22:39:10",
"content": "7 = 2x - 3",
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},
{
"id": 1062938772615987300,
"author_id": 999947272529920000,
"author_name": "MonkeyMan",
"timestamp": "01/11/2023 22:39:11",
"content": "?",
"attachments": [],
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"reference": null
},
{
"id": 1062938865230418000,
"author_id": 464042280379088900,
"author_name": "Archi",
"timestamp": "01/11/2023 22:39:33",
"content": "x = 7 right?",
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},
{
"id": 1062938884046078100,
"author_id": 999947272529920000,
"author_name": "MonkeyMan",
"timestamp": "01/11/2023 22:39:38",
"content": "yes",
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},
{
"id": 1062938903423750100,
"author_id": 464042280379088900,
"author_name": "Archi",
"timestamp": "01/11/2023 22:39:43",
"content": "so y = 2*7 - 3",
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},
{
"id": 1062938941768077300,
"author_id": 999947272529920000,
"author_name": "MonkeyMan",
"timestamp": "01/11/2023 22:39:52",
"content": "whut",
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},
{
"id": 1062938959258337300,
"author_id": 464042280379088900,
"author_name": "Archi",
"timestamp": "01/11/2023 22:39:56",
"content": "as y = 2x-3 you just put the value of x",
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},
{
"id": 1062939010978295800,
"author_id": 999947272529920000,
"author_name": "MonkeyMan",
"timestamp": "01/11/2023 22:40:08",
"content": "ok",
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},
{
"id": 1062939025817735200,
"author_id": 999947272529920000,
"author_name": "MonkeyMan",
"timestamp": "01/11/2023 22:40:12",
"content": "ohhhh",
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},
{
"id": 1062939046961225900,
"author_id": 464042280379088900,
"author_name": "Archi",
"timestamp": "01/11/2023 22:40:17",
"content": "did it click?",
"attachments": [],
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},
{
"id": 1062939078598873100,
"author_id": 999947272529920000,
"author_name": "MonkeyMan",
"timestamp": "01/11/2023 22:40:24",
"content": "yes",
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},
{
"id": 1062939095036338200,
"author_id": 464042280379088900,
"author_name": "Archi",
"timestamp": "01/11/2023 22:40:28",
"content": "nice",
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},
{
"id": 1062939146039083000,
"author_id": 999947272529920000,
"author_name": "MonkeyMan",
"timestamp": "01/11/2023 22:40:40",
"content": "Y = 11",
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},
{
"id": 1062939173457240000,
"author_id": 999947272529920000,
"author_name": "MonkeyMan",
"timestamp": "01/11/2023 22:40:47",
"content": "thnks",
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},
{
"id": 1062939198912483300,
"author_id": 999947272529920000,
"author_name": "MonkeyMan",
"timestamp": "01/11/2023 22:40:53",
"content": ".close",
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},
{
"id": 1062939201575858200,
"author_id": 805217272087838700,
"author_name": "Mathematics Bot",
"timestamp": "01/11/2023 22:40:54",
"content": "Channel closed",
"attachments": [],
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"reference": null
}
] | help-9 | ff49144ce0cd48c8a568d5c66cd8a0ef |
200,697 | [
{
"id": 1062939278289666000,
"author_id": 999947272529920000,
"author_name": "MonkeyMan",
"timestamp": "01/11/2023 22:41:12",
"content": ".reopen",
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},
{
"id": 1062939283910037500,
"author_id": 805217272087838700,
"author_name": "Mathematics Bot",
"timestamp": "01/11/2023 22:41:13",
"content": "โ
",
"attachments": [],
"mentions": [],
"reference": null
},
{
"id": 1062939309042311200,
"author_id": 999947272529920000,
"author_name": "MonkeyMan",
"timestamp": "01/11/2023 22:41:19",
"content": "Yo",
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},
{
"id": 1062939346317086700,
"author_id": 999947272529920000,
"author_name": "MonkeyMan",
"timestamp": "01/11/2023 22:41:28",
"content": "how would I do 6?",
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},
{
"id": 1062939512210202800,
"author_id": 464042280379088900,
"author_name": "Archi",
"timestamp": "01/11/2023 22:42:08",
"content": "same thing",
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},
{
"id": 1062939514663870600,
"author_id": 999947272529920000,
"author_name": "MonkeyMan",
"timestamp": "01/11/2023 22:42:08",
"content": "",
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"id": 1062939542820237300,
"author_id": 999947272529920000,
"author_name": "MonkeyMan",
"timestamp": "01/11/2023 22:42:15",
"content": "well its a fraction",
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"id": 1062939572520095700,
"author_id": 464042280379088900,
"author_name": "Archi",
"timestamp": "01/11/2023 22:42:22",
"content": "yea",
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},
{
"id": 1062939573128286300,
"author_id": 999947272529920000,
"author_name": "MonkeyMan",
"timestamp": "01/11/2023 22:42:22",
"content": "and",
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},
{
"id": 1062939606116470800,
"author_id": 464042280379088900,
"author_name": "Archi",
"timestamp": "01/11/2023 22:42:30",
"content": "put y=1/4x",
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},
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"id": 1062939635401117700,
"author_id": 464042280379088900,
"author_name": "Archi",
"timestamp": "01/11/2023 22:42:37",
"content": "in the 2nd eq",
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},
{
"id": 1062939666564788200,
"author_id": 464042280379088900,
"author_name": "Archi",
"timestamp": "01/11/2023 22:42:44",
"content": "youll get x+x = 8",
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},
{
"id": 1062939692187783200,
"author_id": 464042280379088900,
"author_name": "Archi",
"timestamp": "01/11/2023 22:42:51",
"content": "then just put value of x",
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},
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"id": 1062939701931159600,
"author_id": 464042280379088900,
"author_name": "Archi",
"timestamp": "01/11/2023 22:42:53",
"content": "in first eq",
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},
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"id": 1062940034086477800,
"author_id": 999947272529920000,
"author_name": "MonkeyMan",
"timestamp": "01/11/2023 22:44:12",
"content": "would the equation be X+4y (1/4x) = 8",
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"id": 1062940043544637600,
"author_id": 999947272529920000,
"author_name": "MonkeyMan",
"timestamp": "01/11/2023 22:44:14",
"content": "?",
"attachments": [],
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"reference": null
},
{
"id": 1062940378929573900,
"author_id": 464042280379088900,
"author_name": "Archi",
"timestamp": "01/11/2023 22:45:34",
"content": "x + 4 (1/4x) = 8",
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},
{
"id": 1062940413494833300,
"author_id": 999947272529920000,
"author_name": "MonkeyMan",
"timestamp": "01/11/2023 22:45:43",
"content": "no Y?",
"attachments": [],
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},
{
"id": 1062940572060496000,
"author_id": 999947272529920000,
"author_name": "MonkeyMan",
"timestamp": "01/11/2023 22:46:20",
"content": "wait if you multiple 4 and 1/4 would that be 1",
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},
{
"id": 1062940746891657300,
"author_id": 464042280379088900,
"author_name": "Archi",
"timestamp": "01/11/2023 22:47:02",
"content": "yes",
"attachments": [],
"mentions": [],
"reference": null
},
{
"id": 1062940765153656800,
"author_id": 464042280379088900,
"author_name": "Archi",
"timestamp": "01/11/2023 22:47:06",
"content": "x+1*x",
"attachments": [],
"mentions": [],
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},
{
"id": 1062940780181868700,
"author_id": 464042280379088900,
"author_name": "Archi",
"timestamp": "01/11/2023 22:47:10",
"content": "which is 2x",
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"timestamp": "01/11/2023 22:47:21",
"content": "u put the value of y as 1/4x",
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"timestamp": "01/11/2023 22:47:23",
"content": "so no y",
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"timestamp": "01/11/2023 22:47:37",
"content": "thanks",
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"author_name": "Mathematics Bot",
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] | help-9 | 8a84c5e669174c82a343380eb1241b59 |
200,698 | [
{
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] | help-9 | b177cfbe4aa8410d981e80468c422e1b |
200,699 | [
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"content": "what would 1/2 + 12 be?",
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"timestamp": "01/11/2023 22:53:58",
"content": "In decimals or?",
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"timestamp": "01/11/2023 22:54:01",
"content": "no",
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"content": "fractions",
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"content": "25/2",
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"content": "ok",
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"timestamp": "01/11/2023 22:54:41",
"content": "thx",
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"timestamp": "01/11/2023 22:57:06",
"content": "what would 2 times 1/4",
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"id": 1062943286731481100,
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"timestamp": "01/11/2023 22:57:08",
"content": "be",
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"author_name": "Andersson",
"timestamp": "01/11/2023 22:57:58",
"content": "1/4 +1/4 = 2/4",
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"timestamp": "01/11/2023 22:58:08",
"content": "2/4=1/2",
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"id": 1062943556148396200,
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"timestamp": "01/11/2023 22:58:12",
"content": "ur smart",
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"id": 1062943605653774500,
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"content": "what",
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"timestamp": "01/11/2023 22:58:25",
"content": "wait",
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"content": "what would 1/2+5",
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"content": "be?",
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"content": "11/2",
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"timestamp": "01/11/2023 22:59:05",
"content": "how",
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"id": 1062943947644743700,
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"author_name": "Andersson",
"timestamp": "01/11/2023 22:59:45",
"content": "When you add a whole number and a fraction, make them have the same denominator first",
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"author_name": "Andersson",
"timestamp": "01/11/2023 23:00:02",
"content": "5 in terms of halves would be 10/2",
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"timestamp": "01/11/2023 23:00:13",
"content": "And 10/2 + 1/2 =11/2",
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"timestamp": "01/11/2023 23:00:20",
"content": "ohh",
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"content": "ok",
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"timestamp": "01/11/2023 23:02:01",
"content": "yo can u help me on 9?",
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"author_name": "MonkeyMan",
"timestamp": "01/11/2023 23:02:18",
"content": "wrong onme",
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"author_name": "MonkeyMan",
"timestamp": "01/11/2023 23:05:41",
"content": "",
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"author_name": "Andersson",
"timestamp": "01/11/2023 23:09:04",
"content": "She buys x amount of shirts, and x+7 pants. Those in total are 15. So x+x+7= 15\nStart by removing 7 from each side, and then divide both sides with 2, youll get x which is the amount of shirts she bought, and then you take x+7 to get how many pants she bought",
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"id": 1062946855941587100,
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"author_name": "MonkeyMan",
"timestamp": "01/11/2023 23:11:19",
"content": "remove 7 from each side?",
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"timestamp": "01/11/2023 23:11:39",
"content": "like 15",
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"id": 1062946949780754400,
"author_id": 999947272529920000,
"author_name": "MonkeyMan",
"timestamp": "01/11/2023 23:11:41",
"content": "?",
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"author_name": "Andersson",
"timestamp": "01/11/2023 23:12:27",
"content": "You have x+x+7=15. So do x+x+7-7=15-7",
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"timestamp": "01/11/2023 23:13:02",
"content": "As long as you do the same thing on both sides of the equal sign its still an equal sign",
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"timestamp": "01/11/2023 23:19:57",
"content": "I got it",
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"timestamp": "01/11/2023 23:19:58",
"content": "thx",
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"author_name": "MonkeyMan",
"timestamp": "01/11/2023 23:20:02",
"content": ".close",
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"timestamp": "01/11/2023 23:20:02",
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] | help-9 | b6d9cd1b45c44189bcc066d3228c7c5e |
200,700 | [
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"timestamp": "01/11/2023 23:27:25",
"content": "Do you know what is slope?",
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"content": "a measure of its steepness",
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"timestamp": "01/11/2023 23:28:24",
"content": "And formula?",
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"timestamp": "01/11/2023 23:28:31",
"content": "nope",
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"timestamp": "01/11/2023 23:29:30",
"content": "**Anagh**",
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"timestamp": "01/11/2023 23:29:44",
"content": "ฮ means change",
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"timestamp": "01/11/2023 23:30:20",
"content": "@NotAce_ who gave u the question if u don't know how to find slope",
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"timestamp": "01/11/2023 23:30:34",
"content": "my teacher",
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"author_name": "Anagh",
"timestamp": "01/11/2023 23:31:02",
"content": "He doesn't teach you the method to find slope?",
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"timestamp": "01/11/2023 23:31:08",
"content": "it doesn't make sense how they explain it",
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"timestamp": "01/11/2023 23:32:15",
"content": "Are you familiar with the y=mx+c,@NotAce_",
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"timestamp": "01/11/2023 23:32:59",
"content": "yes",
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"timestamp": "01/11/2023 23:33:21",
"content": "What is m and c here@NotAce_ ?",
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"timestamp": "01/11/2023 23:33:50",
"content": "m is the gradient of the line aint it?",
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"timestamp": "01/11/2023 23:34:04",
"content": "Yes",
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"author_name": "Anagh",
"timestamp": "01/11/2023 23:34:07",
"content": "And c?",
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"timestamp": "01/11/2023 23:34:55",
"content": "and C is the intercept of y",
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"id": 1062952920624140300,
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"author_name": "Anagh",
"timestamp": "01/11/2023 23:35:24",
"content": "So what is the equation of police car?",
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"timestamp": "01/11/2023 23:35:38",
"content": "@NotAce_",
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"author_name": "NotAce_",
"timestamp": "01/11/2023 23:38:10",
"content": "I think it was x=2x+2x=3?",
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"content": "im not to good with slopes or anything",
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"timestamp": "01/11/2023 23:38:56",
"content": "No",
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"timestamp": "01/11/2023 23:39:00",
"content": "Look in the question",
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"id": 1062953914355425400,
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"author_name": "TeXit",
"timestamp": "01/11/2023 23:39:21",
"content": "**Anagh**",
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"timestamp": "01/11/2023 23:39:48",
"content": "**Anagh**",
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"author_id": 722128756851998700,
"author_name": "Anagh",
"timestamp": "01/11/2023 23:40:09",
"content": "What is the value of m in p(x)?",
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"author_id": 803754727107067900,
"author_name": "NotAce_",
"timestamp": "01/11/2023 23:41:03",
"content": "Car(x)=2x+2 Poilice car P(x)=3x?",
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"timestamp": "01/11/2023 23:45:34",
"content": "Yes",
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"content": "@NotAce_",
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"author_id": 803754727107067900,
"author_name": "NotAce_",
"timestamp": "01/11/2023 23:50:13",
"content": "sorry",
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"author_id": 803754727107067900,
"author_name": "NotAce_",
"timestamp": "01/11/2023 23:51:17",
"content": "-2?",
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"id": 1062957311204790300,
"author_id": 722128756851998700,
"author_name": "Anagh",
"timestamp": "01/11/2023 23:52:51",
"content": "Nooo",
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"id": 1062957350358618100,
"author_id": 722128756851998700,
"author_name": "Anagh",
"timestamp": "01/11/2023 23:53:01",
"content": "m is the coefficient of x",
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"id": 1062957436463497200,
"author_id": 722128756851998700,
"author_name": "Anagh",
"timestamp": "01/11/2023 23:53:21",
"content": "What is the coefficient of x in p(x)",
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"id": 1062957533335142400,
"author_id": 722128756851998700,
"author_name": "Anagh",
"timestamp": "01/11/2023 23:53:44",
"content": "@NotAce_",
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"id": 1062957806594052100,
"author_id": 803754727107067900,
"author_name": "NotAce_",
"timestamp": "01/11/2023 23:54:49",
"content": "3",
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"id": 1062957912634425500,
"author_id": 722128756851998700,
"author_name": "Anagh",
"timestamp": "01/11/2023 23:55:15",
"content": "Yes",
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"id": 1062957915683700700,
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"author_name": "Anagh",
"timestamp": "01/11/2023 23:55:15",
"content": "So m=3",
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"id": 1062957991676104800,
"author_id": 722128756851998700,
"author_name": "Anagh",
"timestamp": "01/11/2023 23:55:34",
"content": "So police slope=3",
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"id": 1062958058604601500,
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"author_name": "Anagh",
"timestamp": "01/11/2023 23:55:49",
"content": "Now what is car slope?",
"attachments": [],
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"id": 1062958083959169000,
"author_id": 722128756851998700,
"author_name": "Anagh",
"timestamp": "01/11/2023 23:55:56",
"content": "Can you find it?",
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"id": 1062958097448054900,
"author_id": 803754727107067900,
"author_name": "NotAce_",
"timestamp": "01/11/2023 23:55:59",
"content": "yep",
"attachments": [],
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"id": 1062958184656011300,
"author_id": 803754727107067900,
"author_name": "NotAce_",
"timestamp": "01/11/2023 23:56:20",
"content": "is it coefficeint again?",
"attachments": [],
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"id": 1062958225252696000,
"author_id": 722128756851998700,
"author_name": "Anagh",
"timestamp": "01/11/2023 23:56:29",
"content": "Yes",
"attachments": [],
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"id": 1062958354974113900,
"author_id": 803754727107067900,
"author_name": "NotAce_",
"timestamp": "01/11/2023 23:57:00",
"content": "is it 4?",
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"id": 1062958380219637800,
"author_id": 722128756851998700,
"author_name": "Anagh",
"timestamp": "01/11/2023 23:57:06",
"content": "How",
"attachments": [],
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},
{
"id": 1062958464181207000,
"author_id": 722128756851998700,
"author_name": "Anagh",
"timestamp": "01/11/2023 23:57:26",
"content": "What is coefficient of x in car(x)?",
"attachments": [],
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"id": 1062958521932579000,
"author_id": 510789298321096700,
"author_name": "TeXit",
"timestamp": "01/11/2023 23:57:40",
"content": "**Anagh**",
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"timestamp": "01/12/2023 00:02:29",
"content": "2",
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"id": 1062962771664326700,
"author_id": 722128756851998700,
"author_name": "Anagh",
"timestamp": "01/12/2023 00:14:33",
"content": "Yes",
"attachments": [],
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"id": 1062962837061910500,
"author_id": 722128756851998700,
"author_name": "Anagh",
"timestamp": "01/12/2023 00:14:49",
"content": "How are you so weak in math vro",
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"id": 1062964096753999900,
"author_id": 805217272087838700,
"author_name": "Mathematics Bot",
"timestamp": "01/12/2023 00:19:49",
"content": "@NotAce_ Has your question been resolved?",
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"author_name": "NotAce_",
"timestamp": "01/12/2023 00:20:02",
"content": "I changed schools and the other school I was in was pretty understanding to me but this school that im in confuses me in math",
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"content": "@NotAce_ Has your question been resolved?",
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"content": "@NotAce_ Has your question been resolved?",
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"author_name": "Patrick_Baetman1258",
"timestamp": "01/12/2023 02:03:31",
"content": "Integration Of LogSinX/Cotx",
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"content": "Channel closed",
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] | help-9 | acd8c8ab854c48bfb56a08ae4f0b8ed4 |
200,701 | [
{
"id": 1063002353327947800,
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"content": "Available help channel!",
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"author_id": 914018780420640800,
"author_name": "Fredrick leopard fazbearington",
"timestamp": "01/12/2023 02:54:38",
"content": "Im terrible at algebra and I need help",
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"id": 1063003185997955100,
"author_id": 842836522029678600,
"author_name": "Yeetus",
"timestamp": "01/12/2023 02:55:09",
"content": "Just calculate",
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"id": 1063003225881596000,
"author_id": 842836522029678600,
"author_name": "Yeetus",
"timestamp": "01/12/2023 02:55:18",
"content": "f(1) f(2) f(3) and f(4)",
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"id": 1063003226921762800,
"author_id": 914018780420640800,
"author_name": "Fredrick leopard fazbearington",
"timestamp": "01/12/2023 02:55:18",
"content": "How",
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"id": 1063003334082035700,
"author_id": 842836522029678600,
"author_name": "Yeetus",
"timestamp": "01/12/2023 02:55:44",
"content": "f(1) means you plug in the value 1 for n",
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"id": 1063003359507919000,
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"author_name": "Yeetus",
"timestamp": "01/12/2023 02:55:50",
"content": "So it becomes 1ยณ-8",
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"id": 1063003402382094300,
"author_id": 842836522029678600,
"author_name": "Yeetus",
"timestamp": "01/12/2023 02:56:00",
"content": "Hopefully you can do f(2) next?",
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"id": 1063003454475345900,
"author_id": 914018780420640800,
"author_name": "Fredrick leopard fazbearington",
"timestamp": "01/12/2023 02:56:13",
"content": "I got it now thanks",
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"id": 1063003477393035300,
"author_id": 842836522029678600,
"author_name": "Yeetus",
"timestamp": "01/12/2023 02:56:18",
"content": "No worries!",
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"timestamp": "01/12/2023 03:11:13",
"content": "@Fredrick leopard fazbearington Has your question been resolved?",
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"content": "Channel closed",
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] | help-9 | afd701369228455d931cdf7e80eac0ec |
200,702 | [
{
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"content": "Available help channel!",
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"id": 1063017017755582500,
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"author_name": "nassim",
"timestamp": "01/12/2023 03:50:06",
"content": "Hey, the question for this exercice asks to use the \"Definition of a limit\" to prove the limit shown in the image \nIm a little confused on what they mean by the definition of a limit",
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"content": "Pinned a message.",
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"content": "https://tutorial.math.lamar.edu/classes/calcI/defnoflimit.aspx",
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"timestamp": "01/12/2023 04:04:45",
"content": ".close",
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"content": "Channel closed",
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] | help-9 | 96a1709c9cd84478a8fd278d74d5c0f6 |
200,703 | [
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"content": "Available help channel!",
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{
"id": 1063022292197711900,
"author_id": 807339379344408700,
"author_name": "Major Tom",
"timestamp": "01/12/2023 04:11:04",
"content": "Hellooo I wonder how I could get the rang of this matrice ? I dont know how to do it (I really suck at math and I need to improve my level lol)",
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"content": "@Major Tom Has your question been resolved?",
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] | help-9 | 3998b3dac6f545d99beba37da5a613b8 |
200,704 | [
{
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"author_name": "Doctor beak",
"timestamp": "01/12/2023 04:56:22",
"content": "Hi, I know how to solve eqations of this sort $|x+5|=6$ the problem comes when solving equations with multiple abseloute values, like this \n$||3x+5|-1|=6$ any chance for some help?",
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"author_name": "Mathematics Bot",
"timestamp": "01/12/2023 04:56:22",
"content": "Pinned a message.",
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"author_name": "TeXit",
"timestamp": "01/12/2023 04:56:25",
"content": "**Doctor beak**",
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"author_name": "SWR",
"timestamp": "01/12/2023 04:57:00",
"content": "You need to consider each absolute value separately",
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"author_name": "Doctor beak",
"timestamp": "01/12/2023 04:58:05",
"content": "So what does this mean in practice?",
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"author_name": "SWR",
"timestamp": "01/12/2023 04:58:34",
"content": "Mean you need to consider a positive and negative case and subcases for each extra absolute value",
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"id": 1063034299005276300,
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"timestamp": "01/12/2023 04:58:47",
"content": "So ||3x+5|-1|=6",
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"timestamp": "01/12/2023 04:59:14",
"content": "You consider +(|3x+5|-1)=6 and -(|3x+5|-1)=6",
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"id": 1063034480853536800,
"author_id": 374795910032523260,
"author_name": "SWR",
"timestamp": "01/12/2023 04:59:30",
"content": "Then in those two cases, you must also break into two subcases",
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"timestamp": "01/12/2023 05:00:05",
"content": "+(+(3x+5)-1)=5, +(-(3x+5)-1)=6, -(+(3x+5)-1)=5, and -(-(3x+5)-1)=6",
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"id": 1063034682968637400,
"author_id": 910777539444744200,
"author_name": "Mr. Gamer",
"timestamp": "01/12/2023 05:00:18",
"content": "Let y = |3x+5|, then can you solve:\n|y-1| = 6?",
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"id": 1063034760194170900,
"author_id": 374795910032523260,
"author_name": "SWR",
"timestamp": "01/12/2023 05:00:37",
"content": "yes",
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"author_id": 899691752531828900,
"author_name": "Doctor beak",
"timestamp": "01/12/2023 05:01:02",
"content": "Oh I tried that already, It worked only for 1 soulution",
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"timestamp": "01/12/2023 05:01:18",
"content": "You should get 4",
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"author_id": 910777539444744200,
"author_name": "Mr. Gamer",
"timestamp": "01/12/2023 05:01:22",
"content": "You should get 4 equations",
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"id": 1063034973638119400,
"author_id": 910777539444744200,
"author_name": "Mr. Gamer",
"timestamp": "01/12/2023 05:01:27",
"content": "With some possible extraneous solns",
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"id": 1063035055280234500,
"author_id": 899691752531828900,
"author_name": "Doctor beak",
"timestamp": "01/12/2023 05:01:47",
"content": "-4 and 2/3",
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"id": 1063035180979322900,
"author_id": 374795910032523260,
"author_name": "SWR",
"timestamp": "01/12/2023 05:02:17",
"content": "show your work",
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"author_id": 910777539444744200,
"author_name": "Mr. Gamer",
"timestamp": "01/12/2023 05:02:17",
"content": "You should get 4 equations",
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},
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"id": 1063035225220845600,
"author_id": 374795910032523260,
"author_name": "SWR",
"timestamp": "01/12/2023 05:02:27",
"content": "Before we say anything else, explain your process",
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"id": 1063035258561368000,
"author_id": 899691752531828900,
"author_name": "Doctor beak",
"timestamp": "01/12/2023 05:02:35",
"content": "Ok",
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"id": 1063036058318667900,
"author_id": 899691752531828900,
"author_name": "Doctor beak",
"timestamp": "01/12/2023 05:05:46",
"content": "$y=|3x+5|\n|y-1|=6\n\ny=7, y=-5\n\n3x+5=7\n3x=2\nX=\\frac {2} {3}$",
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"id": 1063036221141565400,
"author_id": 374795910032523260,
"author_name": "SWR",
"timestamp": "01/12/2023 05:06:25",
"content": "Don't worry too hard about LateX here, I can read what you're saying",
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"id": 1063036221967831200,
"author_id": 510789298321096700,
"author_name": "TeXit",
"timestamp": "01/12/2023 05:06:25",
"content": "**Doctor beak**\n```latex\n$y=|3x+5|\n|y-1|=6\n\ny=7, y=-5\n\n3x+5=7\n3x=2\nX=\\frac {2} {3}$\n```Compilation error:```! Missing $ inserted.\n<inserted text> \n $\nl.59 \n \nI've inserted a begin-math/end-math symbol since I think\nyou left one out. Proceed, with fingers crossed.```",
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"author_name": "Mr. Gamer",
"timestamp": "01/12/2023 05:06:56",
"content": "Remember",
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"author_id": 910777539444744200,
"author_name": "Mr. Gamer",
"timestamp": "01/12/2023 05:07:03",
"content": "y = |3x+5|",
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"author_id": 910777539444744200,
"author_name": "Mr. Gamer",
"timestamp": "01/12/2023 05:07:13",
"content": "y is NOT 3x+5",
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},
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"id": 1063036506807214100,
"author_id": 899691752531828900,
"author_name": "Doctor beak",
"timestamp": "01/12/2023 05:07:33",
"content": "Yeah Ik that's just one case",
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},
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"id": 1063036577816772700,
"author_id": 374795910032523260,
"author_name": "SWR",
"timestamp": "01/12/2023 05:07:50",
"content": "I'm just curious which case(s) you missed",
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"id": 1063036666404687900,
"author_id": 899691752531828900,
"author_name": "Doctor beak",
"timestamp": "01/12/2023 05:08:11",
"content": "But it didn't work out in the 2nd case",
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"id": 1063036724709707800,
"author_id": 374795910032523260,
"author_name": "SWR",
"timestamp": "01/12/2023 05:08:25",
"content": "how so",
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"id": 1063037759759056900,
"author_id": 899691752531828900,
"author_name": "Doctor beak",
"timestamp": "01/12/2023 05:12:32",
"content": "Nvm",
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"id": 1063037784245420200,
"author_id": 899691752531828900,
"author_name": "Doctor beak",
"timestamp": "01/12/2023 05:12:38",
"content": "I figured it out",
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},
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"id": 1063037798862573600,
"author_id": 899691752531828900,
"author_name": "Doctor beak",
"timestamp": "01/12/2023 05:12:41",
"content": "Thx",
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},
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"id": 1063037861710012400,
"author_id": 899691752531828900,
"author_name": "Doctor beak",
"timestamp": "01/12/2023 05:12:56",
"content": "It worked out in the end",
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},
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"id": 1063037922313506800,
"author_id": 899691752531828900,
"author_name": "Doctor beak",
"timestamp": "01/12/2023 05:13:10",
"content": ".close",
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},
{
"id": 1063037925035622500,
"author_id": 805217272087838700,
"author_name": "Mathematics Bot",
"timestamp": "01/12/2023 05:13:11",
"content": "Channel closed",
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}
] | help-9 | 6a69257d9eed4eb8a2200963da41c6fc |
200,705 | [
{
"id": 1063038178472230900,
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"author_name": "Mathematics Bot",
"timestamp": "01/12/2023 05:14:12",
"content": "Available help channel!",
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},
{
"id": 1063039485249597400,
"author_id": 695333753005801600,
"author_name": "knownymous",
"timestamp": "01/12/2023 05:19:23",
"content": "is x.|sinx| differentiable at 0 ?",
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},
{
"id": 1063039488521146400,
"author_id": 805217272087838700,
"author_name": "Mathematics Bot",
"timestamp": "01/12/2023 05:19:24",
"content": "Pinned a message.",
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"author_id": 695333753005801600,
"author_name": "knownymous",
"timestamp": "01/12/2023 05:19:29",
"content": "i guess it isnt right ?",
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},
{
"id": 1063039863852650600,
"author_id": 391896531747340300,
"author_name": "Ankit",
"timestamp": "01/12/2023 05:20:53",
"content": "It is",
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"id": 1063040185169891300,
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"author_name": "knownymous",
"timestamp": "01/12/2023 05:22:10",
"content": "how ?",
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{
"id": 1063040296662864000,
"author_id": 183668144404037630,
"author_name": "Ann",
"timestamp": "01/12/2023 05:22:37",
"content": "apply the definition of the derivative",
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{
"id": 1063040339453169700,
"author_id": 183668144404037630,
"author_name": "Ann",
"timestamp": "01/12/2023 05:22:47",
"content": "to find f'(0) for f(x) = x |sin(x)|",
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},
{
"id": 1063040373280231600,
"author_id": 183668144404037630,
"author_name": "Ann",
"timestamp": "01/12/2023 05:22:55",
"content": "you will find that f'(0) exists and is equal to 0",
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{
"id": 1063040492473962600,
"author_id": 695333753005801600,
"author_name": "knownymous",
"timestamp": "01/12/2023 05:23:23",
"content": "f(x) - f(Xo) / x - X0 ?",
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"id": 1063040571565932700,
"author_id": 695333753005801600,
"author_name": "knownymous",
"timestamp": "01/12/2023 05:23:42",
"content": "end up with |sin(x)|",
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"id": 1063041682876149800,
"author_id": 788085606483361800,
"author_name": "chartbit",
"timestamp": "01/12/2023 05:28:07",
"content": "Consider what happens as you approach from the left and the right",
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"id": 1063041889776967800,
"author_id": 788085606483361800,
"author_name": "chartbit",
"timestamp": "01/12/2023 05:28:56",
"content": "in any case, should be clear what happens when x approaches zero",
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"author_name": "Mathematics Bot",
"timestamp": "01/12/2023 05:38:42",
"content": "@knownymous Has your question been resolved?",
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"timestamp": "01/12/2023 05:41:14",
"content": "Channel closed",
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}
] | help-9 | 8fbec137e95b4b43841b52b573e167ba |
200,706 | [
{
"id": 1063050057626173400,
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"author_name": "Mathematics Bot",
"timestamp": "01/12/2023 06:01:24",
"content": "Available help channel!",
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},
{
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"timestamp": "01/12/2023 06:03:55",
"content": "Pinned a message.",
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"id": 1063051151836184600,
"author_id": 437166198166257660,
"author_name": "Master Oogway",
"timestamp": "01/12/2023 06:05:45",
"content": "Rationalize",
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},
{
"id": 1063051189018705900,
"author_id": 842836522029678600,
"author_name": "Yeetus",
"timestamp": "01/12/2023 06:05:53",
"content": "Multiple both the nominator and denominator by 1+3sqrt(3)",
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"id": 1063052100545810600,
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"timestamp": "01/12/2023 06:09:31",
"content": "Channel closed",
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}
] | help-9 | f24517f110704c4393d0f7575ac239c9 |
200,707 | [
{
"id": 1063058949915562100,
"author_id": 805217272087838700,
"author_name": "Mathematics Bot",
"timestamp": "01/12/2023 06:36:44",
"content": "Available help channel!",
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},
{
"id": 1063063728280584200,
"author_id": 798393295311077400,
"author_name": "Wattzyn",
"timestamp": "01/12/2023 06:55:43",
"content": "how to get percentage ?",
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"id": 1063063730797158400,
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"author_name": "Mathematics Bot",
"timestamp": "01/12/2023 06:55:44",
"content": "Pinned a message.",
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}
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{
"id": 1063064281668665500,
"author_id": 798393295311077400,
"author_name": "Wattzyn",
"timestamp": "01/12/2023 06:57:55",
"content": "@Helpers",
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},
{
"id": 1063064478578655200,
"author_id": 1062977936216563800,
"author_name": "ref",
"timestamp": "01/12/2023 06:58:42",
"content": "Red = 10",
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},
{
"id": 1063064591204106400,
"author_id": 1062977936216563800,
"author_name": "ref",
"timestamp": "01/12/2023 06:59:09",
"content": "p% = 38/88 = idk\nb % = 40/88 = idk\nr% = 10/88 = idk",
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},
{
"id": 1063064630584414200,
"author_id": 1062977936216563800,
"author_name": "ref",
"timestamp": "01/12/2023 06:59:18",
"content": "@Wattzyn",
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{
"id": 1063064686255411300,
"author_id": 798393295311077400,
"author_name": "Wattzyn",
"timestamp": "01/12/2023 06:59:31",
"content": "how did you it ?",
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},
{
"id": 1063064756153495600,
"author_id": 798393295311077400,
"author_name": "Wattzyn",
"timestamp": "01/12/2023 06:59:48",
"content": "like whats the formula",
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},
{
"id": 1063064889830146000,
"author_id": 761095788960284700,
"author_name": "fantastic mr. fox",
"timestamp": "01/12/2023 07:00:20",
"content": "!15m",
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},
{
"id": 1063064891021344800,
"author_id": 805217272087838700,
"author_name": "Mathematics Bot",
"timestamp": "01/12/2023 07:00:20",
"content": "Please only use the @Helpers ping **once** if your question has not been answered **for 15 minutes**. Please do not ping or DM individual users about your question.",
"attachments": [],
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},
{
"id": 1063064937708130300,
"author_id": 798393295311077400,
"author_name": "Wattzyn",
"timestamp": "01/12/2023 07:00:31",
"content": "38 divide by 88 ?",
"attachments": [],
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},
{
"id": 1063064956062400500,
"author_id": 272519528561246200,
"author_name": "Andersson",
"timestamp": "01/12/2023 07:00:36",
"content": "The part divided on the whole, so for purple it would be 38/88",
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},
{
"id": 1063065063176536200,
"author_id": 798393295311077400,
"author_name": "Wattzyn",
"timestamp": "01/12/2023 07:01:01",
"content": "is / divison ?",
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},
{
"id": 1063065082248048600,
"author_id": 272519528561246200,
"author_name": "Andersson",
"timestamp": "01/12/2023 07:01:06",
"content": "Yep",
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"author_name": "Wattzyn",
"timestamp": "01/12/2023 07:01:12",
"content": "okay thanks",
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"author_name": "Andersson",
"timestamp": "01/12/2023 07:02:50",
"content": "So in this case it would be 38/88 = 0.4318, which would be equal to 43.18%. You can then round it tp 43% if necessary",
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"timestamp": "01/12/2023 07:07:06",
"content": "thanks",
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"content": "@Wattzyn Has your question been resolved?",
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"content": "Channel closed",
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] | help-9 | 8ae5e84421bc474d8fd7ee245054944f |
200,708 | [
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"content": "Available help channel!",
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"content": "@Moderators",
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] | help-9 | c4d560db3ee5490e864bdb6d948c191e |
200,709 | [
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"content": "how would this be written in index form?",
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] | help-9 | 9583c56936734cde893cf7c19f595a97 |
200,710 | [
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"author_name": "RokettoJanpu",
"timestamp": "01/12/2023 07:43:59",
"content": "ty",
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"id": 1063079717558816800,
"author_id": 886005523042959400,
"author_name": "glpsi",
"timestamp": "01/12/2023 07:59:15",
"content": "I have the following inequality \n\n$$\n\\left\\|A x+b\\right\\|_2 \\leq c^T x+d\n$$\n\nwhere $\\left\\| \\right\\|_2 $ is the Euclidean norm,\n\n$$A = \\begin{bmatrix}\nz*T(x) & 0\\\\ \n 0 &1 \n\\end{bmatrix}, b = \\begin{bmatrix}\n 0\\\\ \n 0 \n\\end{bmatrix}, c = \\begin{bmatrix}\n K\\\\ \n 0 \n\\end{bmatrix}, d = R+z*E.$$\n\nWhat is the most elegant way of putting condition on $z$ to satisfy the first inequality?\n\nI thought about squaring both side and obtaining $$\n\\left[\\begin{array}{ll}\n1 & x^T\n\\end{array}\\right] P\\left[\\begin{array}{l}\n1 \\\\\nx\n\\end{array}\\right] \\leq 0\n$$ \nand analysing positive definiteness of matrix $P$, but not sure if that is correct/the best way to solve it.",
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"timestamp": "01/12/2023 07:59:16",
"content": "Pinned a message.",
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"id": 1063079736399626200,
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"author_name": "TeXit",
"timestamp": "01/12/2023 07:59:20",
"content": "**glpsi**",
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"timestamp": "01/12/2023 08:00:13",
"content": "What I mean with squaring is saying (Ax+b)(Ax+b)<= (cx+d)(cx+d)",
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"content": "@glpsi Has your question been resolved?",
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"content": "@glpsi Has your question been resolved?",
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"content": "@glpsi Has your question been resolved?",
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"content": "Channel closed",
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] | help-9 | a88bca0ab98e403c8826efa452a7386a |
200,711 | [
{
"id": 1063124536553377900,
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"author_name": "Mathematics Bot",
"timestamp": "01/12/2023 10:57:21",
"content": "Available help channel!",
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{
"id": 1063125693157883900,
"author_id": 171648065281851400,
"author_name": "Wass",
"timestamp": "01/12/2023 11:01:57",
"content": "Hi",
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"id": 1063125695745761400,
"author_id": 805217272087838700,
"author_name": "Mathematics Bot",
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"content": "Pinned a message.",
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"author_id": 171648065281851400,
"author_name": "Wass",
"timestamp": "01/12/2023 11:02:12",
"content": "I was reading about gradient descent on Wikipedia",
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"id": 1063125769699725300,
"author_id": 171648065281851400,
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"timestamp": "01/12/2023 11:02:15",
"content": "https://en.wikipedia.org/wiki/Gradient_descent",
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"id": 1063125861290750000,
"author_id": 171648065281851400,
"author_name": "Wass",
"timestamp": "01/12/2023 11:02:37",
"content": "And found out about this gamma choice that guarantees convergence",
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"content": "",
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"author_name": "Wass",
"timestamp": "01/12/2023 11:03:07",
"content": "But, is this any formal theorem or is this proved somewhere? Where can I find it? It's not referenced on the article and can't find it",
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"id": 1063126517397323800,
"author_id": 349354952961032200,
"author_name": "Umbraleviathan",
"timestamp": "01/12/2023 11:05:13",
"content": "I mean",
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"author_id": 349354952961032200,
"author_name": "Umbraleviathan",
"timestamp": "01/12/2023 11:05:16",
"content": "Trajectories on a gradient field",
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"id": 1063126613933436900,
"author_id": 349354952961032200,
"author_name": "Umbraleviathan",
"timestamp": "01/12/2023 11:05:36",
"content": "I can explain what's going on verbally but not with a formal proof",
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"id": 1063126764429267000,
"author_id": 171648065281851400,
"author_name": "Wass",
"timestamp": "01/12/2023 11:06:12",
"content": "I can more or less see what's going on",
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"id": 1063126814232424400,
"author_id": 171648065281851400,
"author_name": "Wass",
"timestamp": "01/12/2023 11:06:24",
"content": "But I'd like to see a formal proof",
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"id": 1063126856234180700,
"author_id": 171648065281851400,
"author_name": "Wass",
"timestamp": "01/12/2023 11:06:34",
"content": "No idea how I can find it right?",
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"id": 1063128128878284800,
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"author_name": "Umbraleviathan",
"timestamp": "01/12/2023 11:11:37",
"content": "https://people.seas.harvard.edu/~yaron/AM221-S16/lecture_notes/AM221_lecture9.pdf maybe this",
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"timestamp": "01/12/2023 11:21:34",
"content": "@Wass Has your question been resolved?",
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"timestamp": "01/12/2023 11:36:35",
"content": "Channel closed",
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] | help-9 | d8d12075189647c8a333a59c56806588 |
200,712 | [
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"timestamp": "01/12/2023 11:46:54",
"content": "Available help channel!",
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{
"id": 1063140447318454300,
"author_id": 540915846076432450,
"author_name": "General.Admiral MWstudios",
"timestamp": "01/12/2023 12:00:34",
"content": "Decompose in factorsa) 3x^3 +12x^2 +12x . b) 2x^3-12x^2+18x",
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"content": "Pinned a message.",
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"author_id": 540915846076432450,
"author_name": "General.Admiral MWstudios",
"timestamp": "01/12/2023 12:00:59",
"content": "i tried making them but i keep getting the wrong answer every time",
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"id": 1063140831063724200,
"author_id": 540915846076432450,
"author_name": "General.Admiral MWstudios",
"timestamp": "01/12/2023 12:02:06",
"content": "sorry if my english isn't the best , it's my second language , thy the lack of vocabulary .",
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{
"id": 1063141034617487400,
"author_id": 540915846076432450,
"author_name": "General.Admiral MWstudios",
"timestamp": "01/12/2023 12:02:54",
"content": "i have way more exercises than this one , it's just that i want to learn how to make them , then do my homework alone and chceck if it's good or not",
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"id": 1063141107300577300,
"author_id": 540915846076432450,
"author_name": "General.Admiral MWstudios",
"timestamp": "01/12/2023 12:03:12",
"content": "> ***`ping me when someone is able to help me , till then i'll give it a shot`***",
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"id": 1063142098045513900,
"author_id": 1014976320918257800,
"author_name": "ripassa",
"timestamp": "01/12/2023 12:07:08",
"content": "@Helpers",
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"id": 1063142145957040100,
"author_id": 540915846076432450,
"author_name": "General.Admiral MWstudios",
"timestamp": "01/12/2023 12:07:19",
"content": "ah , thx",
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"author_name": "ripassa",
"timestamp": "01/12/2023 12:07:32",
"content": "I need help too๐ฅต",
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"id": 1063142293533634600,
"author_id": 540915846076432450,
"author_name": "General.Admiral MWstudios",
"timestamp": "01/12/2023 12:07:55",
"content": "i'd gladly help you but i probably wouldn't even know what it's about",
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"timestamp": "01/12/2023 12:08:03",
"content": "a page with exercises",
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"author_name": "ripassa",
"timestamp": "01/12/2023 12:08:21",
"content": "formulas of triangle square and trapezium",
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"id": 1063142557581856800,
"author_id": 1014976320918257800,
"author_name": "ripassa",
"timestamp": "01/12/2023 12:08:57",
"content": "Like the Area",
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"id": 1063142648937992200,
"author_id": 540915846076432450,
"author_name": "General.Admiral MWstudios",
"timestamp": "01/12/2023 12:09:19",
"content": "oh , isn't that mostly just remembering the formula ?",
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"author_name": "General.Admiral MWstudios",
"timestamp": "01/12/2023 12:09:36",
"content": "do you know the formulas for them ?",
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"timestamp": "01/12/2023 12:09:49",
"content": "No",
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"timestamp": "01/12/2023 12:10:01",
"content": "haven't you noted it anywhere?",
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"id": 1063142857688481800,
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"timestamp": "01/12/2023 12:10:09",
"content": "i dont really get what you mean by triangle square",
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"author_name": "ripassa",
"timestamp": "01/12/2023 12:13:48",
"content": "wait",
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"author_id": 805217272087838700,
"author_name": "Mathematics Bot",
"timestamp": "01/12/2023 12:25:09",
"content": "@General.Admiral MWstudios Has your question been resolved?",
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"content": "I meant that by square",
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"content": ".. a square?",
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"content": "so.",
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"content": "the area ?",
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"content": "yea",
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"content": "l^2 ig ?",
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"content": "The perimeter is 4l",
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"content": "the Area is l^2",
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"content": "for the square",
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"timestamp": "01/12/2023 12:28:03",
"content": "what triangle ?",
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"content": "K wait",
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"timestamp": "01/12/2023 12:28:53",
"content": "so isosceles ?",
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"content": "Is ^times ?",
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"content": "it's power",
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"content": "power is how it's named",
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"timestamp": "01/12/2023 12:29:18",
"content": "lemme tell u want my teacher said",
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"timestamp": "01/12/2023 12:29:18",
"content": "but uhm",
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"content": "Square",
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"content": "2^2 = 4 . 3^2 = 9 . 4^2 = 16",
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"content": "a x b = โฆ. For square",
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"timestamp": "01/12/2023 12:30:21",
"content": "g x h : 2",
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"timestamp": "01/12/2023 12:30:59",
"content": "got any numbers ?",
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"timestamp": "01/12/2023 12:31:05",
"content": "Yea",
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"author_name": "General.Admiral MWstudios",
"timestamp": "01/12/2023 12:31:06",
"content": "or , could u send me a photo?",
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"timestamp": "01/12/2023 12:31:12",
"content": "K",
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"timestamp": "01/12/2023 12:31:29",
"content": "But it german so u wouldnโt understand",
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"timestamp": "01/12/2023 12:31:33",
"content": "doesnt matter",
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"content": "4 x 4 = 16 [cm2]",
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"timestamp": "01/12/2023 12:33:16",
"content": ", rotate",
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"timestamp": "01/12/2023 12:34:24",
"content": "yeah.. dont remember doing something like this",
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"timestamp": "01/12/2023 12:34:28",
"content": "we did similar , but not like this",
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"timestamp": "01/12/2023 12:34:31",
"content": "cant help you . sorry mate",
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"timestamp": "01/12/2023 12:34:47",
"content": "Np homie Iโm gonna make it",
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"timestamp": "01/12/2023 12:34:52",
"content": "alr , gl",
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"timestamp": "01/12/2023 12:35:01",
"content": "thx gl too",
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"timestamp": "01/12/2023 12:35:23",
"content": "ty",
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"timestamp": "01/12/2023 13:05:23",
"content": "@General.Admiral MWstudios Has your question been resolved?",
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"content": "@General.Admiral MWstudios Has your question been resolved?",
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"content": "yeah.. I'll go and sleep",
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"timestamp": "01/12/2023 15:36:16",
"content": "y'all can close this channel. no one helped me but it's alright",
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"id": 1063221805336252400,
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"content": ".close",
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"content": "Channel closed",
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] | help-9 | f56e8535074644fca26ddaf74d777731 |
200,713 | [
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"content": "Available help channel!",
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"timestamp": "01/12/2023 17:27:33",
"content": "can anyone explain this to me?",
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"id": 1063222763814391900,
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"content": "i have no idea where these numbers are coming from",
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"id": 1063222817618939900,
"author_id": 485164773647056900,
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"timestamp": "01/12/2023 17:27:53",
"content": "What numbers",
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"id": 1063222831846019100,
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"content": "1/3",
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"id": 1063222913232293900,
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"content": "What's integral of 3x+4",
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"id": 1063222914876452900,
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"content": "you substitute dx for du/3",
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"id": 1063222926188482600,
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"content": "hence 1/3",
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"content": "Derivative *",
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"content": "where is the 1 coming from",
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"content": "U subsitute 3x+4",
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"timestamp": "01/12/2023 17:28:55",
"content": "U set it equal to u",
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"content": "3x+4=u",
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"content": "$\\dd x = \\frac{\\dd u}{3} = \\frac{1}{3} \\cdot \\dd u$",
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"timestamp": "01/12/2023 17:29:48",
"content": "**Gijs**",
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"timestamp": "01/12/2023 17:30:18",
"content": "that makes no sense to me at all",
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"author_name": "heavy",
"timestamp": "01/12/2023 17:30:37",
"content": "which part exactly?",
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"timestamp": "01/12/2023 17:30:41",
"content": "any of it",
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"id": 1063223537906757600,
"author_id": 270678085983141900,
"author_name": "Nattly",
"timestamp": "01/12/2023 17:30:45",
"content": "where is the 3 coming from",
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"author_id": 485164773647056900,
"author_name": "Gooaaa",
"timestamp": "01/12/2023 17:30:54",
"content": "Just watch usub integral videos",
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"author_id": 646026076950233100,
"author_name": "mreow",
"timestamp": "01/12/2023 17:31:03",
"content": "~~dx is derivative of u du~~",
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"id": 1063223973019668500,
"author_id": 646026076950233100,
"author_name": "mreow",
"timestamp": "01/12/2023 17:32:28",
"content": "HUH",
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"author_name": "mreow",
"timestamp": "01/12/2023 17:32:44",
"content": "bro crossing out died",
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"author_id": 356908116429897700,
"author_name": "Kaynex",
"timestamp": "01/12/2023 17:32:52",
"content": "* screws with it",
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"author_name": "mreow",
"timestamp": "01/12/2023 17:33:13",
"content": "nope",
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"id": 1063224244911227000,
"author_id": 646026076950233100,
"author_name": "mreow",
"timestamp": "01/12/2023 17:33:33",
"content": "~a~",
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"author_id": 646026076950233100,
"author_name": "mreow",
"timestamp": "01/12/2023 17:33:38",
"content": "nothin",
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"author_name": "Gooaaa",
"timestamp": "01/12/2023 17:33:41",
"content": "~~a~~",
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"author_id": 485164773647056900,
"author_name": "Gooaaa",
"timestamp": "01/12/2023 17:33:45",
"content": "Two times",
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"id": 1063224366244048900,
"author_id": 646026076950233100,
"author_name": "mreow",
"timestamp": "01/12/2023 17:34:02",
"content": "ooh",
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"id": 1063224372124467300,
"author_id": 646026076950233100,
"author_name": "mreow",
"timestamp": "01/12/2023 17:34:04",
"content": "ty",
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"author_name": "Kaynex",
"timestamp": "01/12/2023 17:34:07",
"content": "x = 3u + 4\n\nTaking \"the derivative\" of both sides:\ndx = 3 du\n\nNow I get it, u-sub notation is kinda sus. But that's just the way it is. It ends up being really helpful this way.",
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"author_name": "Nattly",
"timestamp": "01/12/2023 17:34:40",
"content": "๐ค",
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"author_id": 394938706760302600,
"author_name": "heavy",
"timestamp": "01/12/2023 17:34:47",
"content": "u sub is awesome",
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"author_name": "heavy",
"timestamp": "01/12/2023 17:34:52",
"content": "its like the reverse chain rule",
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"author_id": 270678085983141900,
"author_name": "Nattly",
"timestamp": "01/12/2023 17:36:01",
"content": "but in the example its 3x+4=u?",
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"timestamp": "01/12/2023 17:36:09",
"content": "Yes",
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"author_name": "Nattly",
"timestamp": "01/12/2023 17:36:09",
"content": "are x and u interchangeable?",
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"id": 1063225344557068300,
"author_id": 356908116429897700,
"author_name": "Kaynex",
"timestamp": "01/12/2023 17:37:55",
"content": "*whoops*",
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"author_name": "Kaynex",
"timestamp": "01/12/2023 17:38:07",
"content": "Ignore me I misread the example. Glad you caught that",
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"author_id": 356908116429897700,
"author_name": "Kaynex",
"timestamp": "01/12/2023 17:38:16",
"content": "Do exactly what I did, but correctly",
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"id": 1063225503823188000,
"author_id": 270678085983141900,
"author_name": "Nattly",
"timestamp": "01/12/2023 17:38:33",
"content": "so u=3x+4?",
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"author_name": "Kaynex",
"timestamp": "01/12/2023 17:39:12",
"content": "Ye. Then \"the derivative\" of both sides:\ndu = 3 dx\n\nRearrange:\ndx = du/3",
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"id": 1063225791716004000,
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"author_name": "Nattly",
"timestamp": "01/12/2023 17:39:42",
"content": "and the derivitive of any letter is just one?",
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"author_name": "Nattly",
"timestamp": "01/12/2023 17:39:49",
"content": "so that makes 1= 1/3",
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"id": 1063225824494506000,
"author_id": 270678085983141900,
"author_name": "Nattly",
"timestamp": "01/12/2023 17:39:50",
"content": "?",
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"id": 1063225840537714700,
"author_id": 510789298321096700,
"author_name": "TeXit",
"timestamp": "01/12/2023 17:39:54",
"content": "**Mehdi\\_Moulati**",
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"author_name": "Kaynex",
"timestamp": "01/12/2023 17:40:04",
"content": "Derivative of x is dx.",
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"author_name": "Kaynex",
"timestamp": "01/12/2023 17:40:18",
"content": "There's a dx in there, and it sticks around",
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"author_name": "Nattly",
"timestamp": "01/12/2023 17:42:08",
"content": "i dont think i understand what du/dx actualy means",
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"author_name": "Kaynex",
"timestamp": "01/12/2023 17:42:26",
"content": "Oh, du/dx is \"the derivative of u, with respect to x\"",
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"id": 1063226559613378700,
"author_id": 270678085983141900,
"author_name": "Nattly",
"timestamp": "01/12/2023 17:42:45",
"content": "what does \"respect to x\" mean?",
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"author_id": 270678085983141900,
"author_name": "Nattly",
"timestamp": "01/12/2023 17:42:55",
"content": "sorry if im really not getting this",
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"author_name": "Kaynex",
"timestamp": "01/12/2023 17:43:16",
"content": "So for example, if:\nw = tยฒ\n\nThen dw/dt = 2t",
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"author_name": "Kaynex",
"timestamp": "01/12/2023 17:43:40",
"content": "This notation is helpful when multiple variables start relating to eachother",
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"author_name": "Nattly",
"timestamp": "01/12/2023 17:44:31",
"content": "i always found f=(t)^2 f='(2t) to make much more sense",
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"id": 1063227172225024100,
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"author_name": "Nattly",
"timestamp": "01/12/2023 17:45:11",
"content": "does d in your example mean \"the determinent of\"",
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"author_name": "Nattly",
"timestamp": "01/12/2023 17:45:12",
"content": "?",
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"id": 1063227288277241900,
"author_id": 646026076950233100,
"author_name": "mreow",
"timestamp": "01/12/2023 17:45:39",
"content": "d is hust a notation used in derivatives to denote really small bits of variables",
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"id": 1063227317440229500,
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"author_name": "Nattly",
"timestamp": "01/12/2023 17:45:46",
"content": "for example \"the determinant of w\" divided by \"the determinant of t\" = 2t",
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"author_name": "mreow",
"timestamp": "01/12/2023 17:45:54",
"content": "d or delta in partial derivatives",
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"id": 1063227419751891000,
"author_id": 270678085983141900,
"author_name": "Nattly",
"timestamp": "01/12/2023 17:46:10",
"content": "what",
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"id": 1063227465058767000,
"author_id": 646026076950233100,
"author_name": "mreow",
"timestamp": "01/12/2023 17:46:21",
"content": "do you know derivatives?",
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"id": 1063227524060033200,
"author_id": 270678085983141900,
"author_name": "Nattly",
"timestamp": "01/12/2023 17:46:35",
"content": "i think?",
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"id": 1063227597959471200,
"author_id": 270678085983141900,
"author_name": "Nattly",
"timestamp": "01/12/2023 17:46:53",
"content": "lower the power by one and times it by the number infront",
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"id": 1063227688166379600,
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"author_name": "Nattly",
"timestamp": "01/12/2023 17:47:14",
"content": "3x^3 = 9x^2",
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"id": 1063227726904959100,
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"author_name": "mreow",
"timestamp": "01/12/2023 17:47:23",
"content": "thats the power rule but it is part of derivatives as a whole",
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"id": 1063227828180627600,
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"author_name": "Nattly",
"timestamp": "01/12/2023 17:47:48",
"content": "then what do you mean and how does it help figure out integration",
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"id": 1063227860258668700,
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"author_name": "mreow",
"timestamp": "01/12/2023 17:47:55",
"content": "you know how a derivative is denoted d/dx(f(x)) sometimes",
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"author_name": "Nattly",
"timestamp": "01/12/2023 17:48:04",
"content": "sure?",
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"id": 1063227964512276500,
"author_id": 270678085983141900,
"author_name": "Nattly",
"timestamp": "01/12/2023 17:48:20",
"content": "i think",
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"author_name": "mreow",
"timestamp": "01/12/2023 17:48:44",
"content": "well using a theorem i forgot the name of, dy/dx = dy/du * du/dx, for all du",
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"id": 1063228153516007400,
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"author_name": "Nattly",
"timestamp": "01/12/2023 17:49:05",
"content": "for all?",
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"author_name": "mreow",
"timestamp": "01/12/2023 17:49:37",
"content": "well, for all where du isnt 0 but yes",
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"author_name": "mreow",
"timestamp": "01/12/2023 17:49:55",
"content": "in cases like those you usually dont need u sub in the first place",
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"author_name": "mreow",
"timestamp": "01/12/2023 17:50:22",
"content": "and wdym by determinant here?",
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"id": 1063228627728212000,
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"author_name": "mreow",
"timestamp": "01/12/2023 17:50:58",
"content": "if youre talking about the proprierty of square matricies that is not right",
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"id": 1063229537858638000,
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"author_name": "Nattly",
"timestamp": "01/12/2023 17:54:35",
"content": "what",
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"id": 1063229566002413600,
"author_id": 270678085983141900,
"author_name": "Nattly",
"timestamp": "01/12/2023 17:54:42",
"content": "the hell are sqyare matricies",
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"author_name": "mreow",
"timestamp": "01/12/2023 17:56:52",
"content": "so wth did you use determinant for",
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"author_name": "Nattly",
"timestamp": "01/12/2023 17:57:09",
"content": "i have no idea",
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"id": 1063230256221266000,
"author_id": 270678085983141900,
"author_name": "Nattly",
"timestamp": "01/12/2023 17:57:26",
"content": "im just suppose to know how to find it",
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"id": 1063230367944954000,
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"author_name": "mreow",
"timestamp": "01/12/2023 17:57:53",
"content": "d is not a value",
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"id": 1063230394515849200,
"author_id": 646026076950233100,
"author_name": "mreow",
"timestamp": "01/12/2023 17:57:59",
"content": "its not a standalone number",
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"id": 1063230483284119700,
"author_id": 646026076950233100,
"author_name": "mreow",
"timestamp": "01/12/2023 17:58:21",
"content": "dx or du or whatever variable youre taking the derivative with respect to is",
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"id": 1063230730647384200,
"author_id": 270678085983141900,
"author_name": "Nattly",
"timestamp": "01/12/2023 17:59:20",
"content": "does d just denote \"the derivative\" of the number or letter its beside?",
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"author_name": "mreow",
"timestamp": "01/12/2023 18:00:23",
"content": "basically, $\\frac{d}{dx}f(x)=\\lim_{h\\to 0} \\frac{f(x+h) - f(h)}{h}$",
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"id": 1063231006540308500,
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"author_name": "TeXit",
"timestamp": "01/12/2023 18:00:25",
"content": "**Kel.plush**",
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"timestamp": "01/12/2023 18:00:35",
"content": "this is the limit definition",
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"author_name": "Nattly",
"timestamp": "01/12/2023 18:02:21",
"content": "ok, why is that relevant?",
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"id": 1063231575279546400,
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"author_name": "mreow",
"timestamp": "01/12/2023 18:02:41",
"content": "it is so you can see what it really is, conceptually",
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"author_name": "mreow",
"timestamp": "01/12/2023 18:03:30",
"content": "its taking the slope of an infinitely small section of f(x), for the entire f(x)",
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"content": "ok but why is that relevent",
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"content": "i dont see the point in doing so",
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"content": "what the derivative in general?",
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"content": "ye",
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"timestamp": "01/12/2023 18:09:48",
"content": "it finds the rate of change of any function at any point",
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"timestamp": "01/12/2023 18:10:39",
"content": "well those that are differentiable but were mostly talking about those rn",
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"timestamp": "01/12/2023 18:20:15",
"content": "ok uh",
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"timestamp": "01/12/2023 18:20:17",
"content": "again",
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"timestamp": "01/12/2023 18:20:29",
"content": "why is it relevent when trying to work out integration",
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"id": 1063239744428986400,
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"timestamp": "01/12/2023 18:35:09",
"content": "you know what?",
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"timestamp": "01/12/2023 18:35:13",
"content": "this is getting off topic",
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"author_name": "Nattly",
"timestamp": "01/12/2023 18:35:31",
"content": "why does du/dx=3?",
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"id": 1063239875312222200,
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"author_name": "Nattly",
"timestamp": "01/12/2023 18:35:40",
"content": "from the equasion where does 3 come from?",
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"timestamp": "01/12/2023 18:35:46",
"content": "is it the 3x?",
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"timestamp": "01/12/2023 18:37:27",
"content": "Do you need help @Nattly",
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"content": "yea",
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"content": "With what exactly",
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"content": "@Nattly",
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"id": 1063241123625181300,
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"timestamp": "01/12/2023 18:40:37",
"content": "what i just mentioned",
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"author_name": "el pepega",
"timestamp": "01/12/2023 18:42:18",
"content": "Do you know how to differentiate?",
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"timestamp": "01/12/2023 18:50:54",
"content": "depends on what you mean",
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"timestamp": "01/12/2023 18:51:11",
"content": "i know the different rules such as power, chain and quotient rules",
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"timestamp": "01/12/2023 18:51:29",
"content": "This requires no rules",
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"timestamp": "01/12/2023 18:51:36",
"content": "Itโs simple differentiation",
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"timestamp": "01/12/2023 18:52:40",
"content": "uh",
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"author_name": "Nattly",
"timestamp": "01/12/2023 18:52:55",
"content": "so (3x+4) = 3?",
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"timestamp": "01/12/2023 18:53:03",
"content": "The derivative yes",
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"timestamp": "01/12/2023 18:53:07",
"content": "isnt that the power rule?",
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"timestamp": "01/12/2023 18:53:12",
"content": "No",
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"timestamp": "01/12/2023 18:53:18",
"content": "@-@",
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"author_id": 527109388209619000,
"author_name": "el pepega",
"timestamp": "01/12/2023 18:53:41",
"content": "3x^1",
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"author_id": 527109388209619000,
"author_name": "el pepega",
"timestamp": "01/12/2023 18:53:58",
"content": "Times power with constant and decrease power by one",
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"id": 1063244590062260400,
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"author_name": "el pepega",
"timestamp": "01/12/2023 18:54:24",
"content": "(3*1)x(x^0)",
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"id": 1063244673453396000,
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"author_name": "Nattly",
"timestamp": "01/12/2023 18:54:44",
"content": "yea?",
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"id": 1063244742122541200,
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"author_name": "el pepega",
"timestamp": "01/12/2023 18:55:00",
"content": "Yes",
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"author_name": "el pepega",
"timestamp": "01/12/2023 18:55:21",
"content": "Then why would you be confused as to why itโs =3",
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"timestamp": "01/12/2023 18:56:38",
"content": "so continuing this",
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"content": "du = 1?",
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"timestamp": "01/12/2023 18:57:08",
"content": "and dx = 3?",
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"timestamp": "01/12/2023 19:00:04",
"content": "If du/dx=3",
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"timestamp": "01/12/2023 19:00:10",
"content": "Rearrange for terms of dx",
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"timestamp": "01/12/2023 19:00:20",
"content": "Dx=1/3du",
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"timestamp": "01/12/2023 19:00:31",
"content": "This would then be subbed into the integral",
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"author_name": "Nattly",
"timestamp": "01/12/2023 19:02:14",
"content": "then why does it then say 1/3โซu^5du",
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"content": "The dx is 1/3du",
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"timestamp": "01/12/2023 19:03:50",
"content": "They subbed that it",
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"timestamp": "01/12/2023 19:04:03",
"content": "And because 1/3 is a constant it can be moved outside the integral",
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"author_name": "el pepega",
"timestamp": "01/12/2023 19:04:28",
"content": "If you need more help with this stuff lmk because Iโm also learning it rj",
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"timestamp": "01/12/2023 19:04:30",
"content": "Rn*",
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"timestamp": "01/12/2023 19:05:32",
"content": "yes definitly",
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"timestamp": "01/12/2023 19:05:41",
"content": "this makes very little sense rn",
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"timestamp": "01/12/2023 19:06:03",
"content": "it feels like the example skipped so many steps",
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"author_name": "el pepega",
"timestamp": "01/12/2023 19:09:22",
"content": "Well I have to go rn but I recommend not thinking too hard about it",
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"id": 1063248393213849600,
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"timestamp": "01/12/2023 19:09:31",
"content": "Itโs pretty straightforward once you learn the method",
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"id": 1063248436331294700,
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"timestamp": "01/12/2023 19:09:41",
"content": "Just do it in steps and youโll be fine",
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"id": 1063249520202367000,
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"timestamp": "01/12/2023 19:13:59",
"content": ",n,",
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"timestamp": "01/12/2023 19:29:00",
"content": "@Nattly Has your question been resolved?",
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"timestamp": "01/12/2023 19:49:54",
"content": "close.",
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},
{
"id": 1063258565747429500,
"author_id": 270678085983141900,
"author_name": "Nattly",
"timestamp": "01/12/2023 19:49:56",
"content": ".close",
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"author_id": 805217272087838700,
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"timestamp": "01/12/2023 19:49:57",
"content": "Channel closed",
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] | help-9 | 8a9947939c0e4727b0a68f2d03c672e2 |
200,714 | [
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"timestamp": "01/12/2023 19:50:57",
"content": "Available help channel!",
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"id": 1063262662852612200,
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"content": "Pinned a message.",
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"timestamp": "01/12/2023 20:07:04",
"content": "I know its vertical",
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"id": 1063263094626852900,
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"content": "normally, a table should be symmetric",
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"id": 1063263134401437800,
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"content": "that should help you for part 1",
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"id": 1063263474022625400,
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"timestamp": "01/12/2023 20:09:26",
"content": "How do i find the value of n?",
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"content": "n will be obvious once you solved part 1)",
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"content": "what",
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{
"id": 1063264105286357000,
"author_id": 244806629839732740,
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"timestamp": "01/12/2023 20:11:57",
"content": "why is VZX=VZX+WZY",
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"id": 1063264128543756400,
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"content": "the third line makes no sense",
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"id": 1063264194876682200,
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"timestamp": "01/12/2023 20:12:18",
"content": "the idea is that a table should be symmetric, otherwise the top would not be even",
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"timestamp": "01/12/2023 20:12:26",
"content": "therefore the two angles should be equal to each other",
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"timestamp": "01/12/2023 20:12:33",
"content": "therefore we do VZX=WZY",
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"timestamp": "01/12/2023 20:12:35",
"content": "then solve for n",
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"author_name": "sheldon",
"timestamp": "01/12/2023 20:12:36",
"content": "Just ignore the vzx its muscle memory",
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"timestamp": "01/12/2023 20:12:52",
"content": "The third line",
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"timestamp": "01/12/2023 20:13:01",
"content": "I was too lazy to write value of n",
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"timestamp": "01/12/2023 20:13:18",
"content": "the third line is just no true though",
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"timestamp": "01/12/2023 20:13:24",
"content": "Yep",
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"timestamp": "01/12/2023 20:17:30",
"content": "Problem is I dont know how to do that",
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"timestamp": "01/12/2023 20:17:40",
"content": "wdym",
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"timestamp": "01/12/2023 20:17:46",
"content": "VZX=WZY",
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"timestamp": "01/12/2023 20:17:50",
"content": "then solve for n",
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"author_name": "sheldon",
"timestamp": "01/12/2023 20:21:34",
"content": "I'm guessing its (n + 35) and (2n - 25)",
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"timestamp": "01/12/2023 20:22:49",
"content": "yeah, those are given",
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"author_name": "sheldon",
"timestamp": "01/12/2023 20:23:53",
"content": "Was it correct?",
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"content": "?",
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"timestamp": "01/12/2023 20:27:32",
"content": "you have not yet solved it i think",
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"timestamp": "01/12/2023 20:27:41",
"content": "you located the angles that were given",
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"timestamp": "01/12/2023 20:27:49",
"content": "now you should be able to solve it",
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"timestamp": "01/12/2023 20:30:42",
"content": "So do i do it like this again",
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"timestamp": "01/12/2023 20:33:02",
"content": "How?",
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"content": "Do i add VZX = WZY together i dont really know how to solve it",
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"timestamp": "01/12/2023 20:34:57",
"content": "Or like this",
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"content": "@sheldon Has your question been resolved?",
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"content": "@sheldon Has your question been resolved?",
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"content": "@sheldon Has your question been resolved?",
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"content": "@sheldon Has your question been resolved?",
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] | help-9 | a5d929831eab4b34b04e9760818749fa |
200,715 | [
{
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"content": "Available help channel!",
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"author_id": 214286694478774270,
"author_name": "normalAtmosphericPa=101,325",
"timestamp": "01/13/2023 02:39:27",
"content": "Can someone please explain why the difference in the contribution to the dot product is 2|x-y| ?",
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"timestamp": "01/13/2023 02:43:13",
"content": "That's a GTIN-13 (a type of error detecting code vector)",
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"author_name": "actinium226",
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"content": "Looks like you'll either have (x+3y) - (y+3x) or (3x + y) - (3y+x). The first way gives -2x+2y, the second way gives 2x-2y, either way in magnitude they're both 2|x-y|",
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"author_name": "normalAtmosphericPa=101,325",
"timestamp": "01/13/2023 02:46:54",
"content": "Wait why do we want the difference between these 2 cases?",
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"author_name": "normalAtmosphericPa=101,325",
"timestamp": "01/13/2023 02:47:03",
"content": "I thought we should look at the difference between the contributions of the 2 entries?",
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"timestamp": "01/13/2023 02:47:24",
"content": "i.e. case 1: x+3y, then should we look at |x-3y|",
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"timestamp": "01/13/2023 02:47:36",
"content": "and then case 2: 3x+y, then look at |3x-y|",
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"timestamp": "01/13/2023 02:48:10",
"content": "i.e. one entry is contributing \"x or 3x\", and next adjacent term contributes \"3y or y\" towards the dot product",
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"timestamp": "01/13/2023 02:48:21",
"content": "Right? a",
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"timestamp": "01/13/2023 02:49:05",
"content": "and then, shouldn't try do something along the lines of showing that with either case 1 or case 2, their difference contributes zero to the total dot product, and hence wouldn't be detected.",
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"content": "I'm not sure I follow you exactly, but let's look at case 1. For the sake of argument let's say x is supposed to be the first element in the array, and y is supposed to be the second. Then the check is x + 3y + .... + check_digit. If they're swapped you'd get y + 3x + ... + check_digit. The difference between the two of them is -2x+2y -> 2(y-x). So if y-x=5, then the first code = the second code + 10, but since we're in z10, those two are the same",
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"timestamp": "01/13/2023 02:56:30",
"content": "I see",
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"timestamp": "01/13/2023 02:56:35",
"content": "Thank you",
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"timestamp": "01/13/2023 03:08:12",
"content": "wait, what does \"mistakenly transposed\" mean?",
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"timestamp": "01/13/2023 03:08:27",
"content": "does it refer to how x and y may not be in the correct positions?",
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"timestamp": "01/13/2023 03:09:54",
"content": "and thus, if we show that 2|x-y| = 0, it implies that shifting the position of x,y by 1 unit to either the left or right in the array/sum does nothing to alter the dot product (and hence this \"mistake\" won't be detected)",
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"timestamp": "01/13/2023 03:11:58",
"content": "I'm assuming that this explanation follows my assumption above, right?",
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"content": "@normalAtmosphericPa=101,325 Has your question been resolved?",
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] | help-9 | 1cf5fb560a6e4441ac83ccbb96bcfe79 |
200,716 | [
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"id": 1063380569276284900,
"author_id": 1022141568737607800,
"author_name": "โกA(lex)โก",
"timestamp": "01/13/2023 03:54:44",
"content": "What is the least number of colors needed to color a map of the United States? Do not consider adjacent states that meet only at a corner. Suppose that Michigan is one region. Consider the vertices representing Alaska and Hawaii as isolated vertices",
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"timestamp": "01/13/2023 03:54:51",
"content": "sooooooo",
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"timestamp": "01/13/2023 03:55:45",
"content": "well, four-color theorem...",
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"author_id": 1022141568737607800,
"author_name": "โกA(lex)โก",
"timestamp": "01/13/2023 03:55:45",
"content": "i tried out the four-colour theorem and i am pretty sure it must be 4 right?",
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"content": "can you find a quartet of mutually adjacent states?",
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"timestamp": "01/13/2023 03:56:16",
"content": "also do you have a blank map on hand",
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"author_name": "โกA(lex)โก",
"timestamp": "01/13/2023 03:56:39",
"content": "let me try and find",
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"timestamp": "01/13/2023 03:57:51",
"content": "i found a transparent one too",
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"timestamp": "01/13/2023 03:58:29",
"content": "hm i guess like some states around kentucky?",
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"timestamp": "01/13/2023 03:59:21",
"content": "kentucky is connected to llinois, Indiana, Ohio, West Virginia, Virginia, Tennessee and Missouri",
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"timestamp": "01/13/2023 03:59:36",
"content": "so if we assign some colour to kentucky like blue",
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"content": "lemme trace this map",
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"content": "the east coast is a bit :bleak:",
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"timestamp": "01/13/2023 04:01:45",
"content": "yes a lot of states pffft",
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"content": "can i have the transparent map",
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"content": "its gonna be easier this way i think",
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"content": "3 doesnt work",
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"content": "oh sure here",
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"content": "quality kind of eh",
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"content": "ah yeah you're right, 3 colors will not work",
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"author_name": "Camilleone",
"timestamp": "01/13/2023 04:03:47",
"content": "start from washington, assign numbers to oregon and idaho, and proceed south",
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"timestamp": "01/13/2023 04:03:52",
"content": "i think",
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"timestamp": "01/13/2023 04:03:54",
"content": "to me Colorado, Kansas, New Mexico, Texas, Oklahoma",
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"content": "cant be 3",
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"content": "you'll get a contradiction",
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"content": "Nevada borders an odd number of states",
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"content": "haha i love how all of you gave up on the east coast",
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"timestamp": "01/13/2023 04:04:34",
"content": "if the US were 3-colorable, the states surrounding Nevada (OR, ID, UT, AZ, CA) would have to alternate between the two colors other than NV's",
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"content": "but there are 5 of them so we can't do that",
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"content": "yeah that makes sense",
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"content": "so i guess it has to be four?",
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"content": "yes",
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"timestamp": "01/13/2023 04:05:13",
"content": "makes sense, thank you",
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"content": "4-color thm says a 4-coloring always exists and we just ruled out a 3-coloring",
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"timestamp": "01/13/2023 04:05:23",
"content": "yep",
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"timestamp": "01/13/2023 04:05:33",
"content": "Isn't this suppose to take a thousand years for a computer?",
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"timestamp": "01/13/2023 04:05:41",
"content": "alright thanks everyone!",
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"timestamp": "01/13/2023 04:05:42",
"content": ".close",
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] | help-9 | 340c6ea7d0984c1f8c74e6c4edf4b042 |
200,717 | [
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"timestamp": "01/13/2023 04:05:59",
"content": "@okeconomics it's the PROOF of the 4-color thm that took a long time for a computer. that's different than finding a 4-coloring for a particular graph!",
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"content": "pretty bleak question but",
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"content": "i assume if you let the vertices of the graph be the animals",
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"timestamp": "01/13/2023 04:19:11",
"content": "and some undirected edge be between the two animals?",
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"timestamp": "01/13/2023 04:21:28",
"content": "so like if we say $V$ = set of all animals or something and $E$ = (a,b) : animal a eats animal b",
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"timestamp": "01/13/2023 04:21:30",
"content": "**โกA(lex)โก**",
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"content": ":thonk:",
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"timestamp": "01/13/2023 04:22:11",
"content": "yea that's the right graph",
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"timestamp": "01/13/2023 04:22:39",
"content": "oh right so if we colour so that the adjacent vertices have different colours then",
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"author_name": "๐๐๐ถ๐๐๐ถ๐",
"timestamp": "01/13/2023 04:22:46",
"content": "now think about how the chromatic number of the graph relates to the problem",
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"timestamp": "01/13/2023 04:22:55",
"content": "the minimal numbers of colours also represents the least amount of habitats possible?",
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"content": "i guess?",
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"content": "yeah i mean i assume the number of different habitats IS also the minimum amount of different colours you can have, no?",
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"content": "needed to colour the vertices that is",
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"timestamp": "01/13/2023 04:24:51",
"content": "hmm shouldn't be anything to assume there",
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"timestamp": "01/13/2023 04:25:04",
"content": "that sounds like assuming the answer",
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"timestamp": "01/13/2023 04:25:14",
"content": "um",
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"timestamp": "01/13/2023 04:26:11",
"content": "if two vertices (animals) are adjacent then one of the animals will eat the other, so the two animals cannot be in the same habitat (aka you need to assign different colours to the vertices)",
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"timestamp": "01/13/2023 04:26:13",
"content": "thats my reasoning",
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"timestamp": "01/13/2023 04:27:28",
"content": "let C be the chromatic number of the graph, you want that\n1) you can make a safe zoo with C habitats, and\n2) if you have less than C habitats, you can't make a safe zoo",
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"content": ":sad_think: alright",
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"timestamp": "01/13/2023 04:29:50",
"content": "drawing a picture example should help if you need",
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"timestamp": "01/13/2023 04:32:41",
"content": "i mean i think i got it, but what am i exactly missing still?",
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"timestamp": "01/13/2023 04:33:04",
"content": "what's your explanation for 1 and 2?",
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"timestamp": "01/13/2023 04:33:31",
"content": "that's pretty much the whole problem",
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"timestamp": "01/13/2023 04:34:48",
"content": "this i suppose? :thonk: if the zoo did not have C amount of habitats then that would mean you have some adjacent same colours, aka the animals are now with each other",
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"timestamp": "01/13/2023 04:34:55",
"content": "Vertices\n=Set of all animals\n\nEdges\n={(u,v)โฃAnimal u eats animal v}\nโ",
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"timestamp": "01/13/2023 04:36:16",
"content": "ok good enough ig for 2",
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"timestamp": "01/13/2023 04:36:44",
"content": "uhh for 1",
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"timestamp": "01/13/2023 04:37:18",
"content": "@โกA(lex)โก well a zoo exists then c amount of habitat exists.",
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"timestamp": "01/13/2023 04:37:27",
"content": "there needs to be C different habitats for there to be minimal different of colours between the vertices",
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"timestamp": "01/13/2023 04:37:35",
"content": "idk what better explanation i can come up with",
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"timestamp": "01/13/2023 04:37:37",
"content": "lemme think",
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"timestamp": "01/13/2023 04:37:55",
"content": "don't overthink 1",
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"id": 1063391843548680200,
"author_id": 907880343313457200,
"author_name": "okeconomics",
"timestamp": "01/13/2023 04:39:32",
"content": "@โกA(lex)โก the problem cannot be solved for a non- numerical amount of habitats you need to know the number of habitats to solve it.",
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"timestamp": "01/13/2023 04:39:57",
"content": "wot",
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"author_name": "โกA(lex)โก",
"timestamp": "01/13/2023 04:40:08",
"content": "did u run that in chatgpt and copy paste it dude lol",
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"id": 1063392048889200600,
"author_id": 907880343313457200,
"author_name": "okeconomics",
"timestamp": "01/13/2023 04:40:21",
"content": "No",
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"id": 1063392113024323600,
"author_id": 984319941417251000,
"author_name": "๐๐๐ถ๐๐๐ถ๐",
"timestamp": "01/13/2023 04:40:36",
"content": "that doesn't make enough sense to be chatgpt",
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"id": 1063392189385806000,
"author_id": 1022141568737607800,
"author_name": "โกA(lex)โก",
"timestamp": "01/13/2023 04:40:54",
"content": "are u implying that chatgpt makes sense? haha",
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"id": 1063392250228396000,
"author_id": 984319941417251000,
"author_name": "๐๐๐ถ๐๐๐ถ๐",
"timestamp": "01/13/2023 04:41:09",
"content": "no i was implying that message made no sense lol",
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"id": 1063392625270472700,
"author_id": 1022141568737607800,
"author_name": "โกA(lex)โก",
"timestamp": "01/13/2023 04:42:38",
"content": "yeah sorry i cant really find another explanation for 1 haha",
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"id": 1063392737824616400,
"author_id": 1022141568737607800,
"author_name": "โกA(lex)โก",
"timestamp": "01/13/2023 04:43:05",
"content": "i feel like i will just be repeating what i already said",
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"author_id": 984319941417251000,
"author_name": "๐๐๐ถ๐๐๐ถ๐",
"timestamp": "01/13/2023 04:43:47",
"content": "you can make a safe zoo by putting all color 1 animals in a pen, all color 2 animals in another pen, and so on",
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"id": 1063393105748955100,
"author_id": 1022141568737607800,
"author_name": "โกA(lex)โก",
"timestamp": "01/13/2023 04:44:33",
"content": "oh you just wanted me to say that?",
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"id": 1063393123050455000,
"author_id": 1022141568737607800,
"author_name": "โกA(lex)โก",
"timestamp": "01/13/2023 04:44:37",
"content": "oof i really was overthinking it",
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"author_name": "๐๐๐ถ๐๐๐ถ๐",
"timestamp": "01/13/2023 04:44:56",
"content": "yes? lol",
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"author_id": 1022141568737607800,
"author_name": "โกA(lex)โก",
"timestamp": "01/13/2023 04:45:02",
"content": "makes sense ig",
"attachments": [],
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"id": 1063393232572141600,
"author_id": 1022141568737607800,
"author_name": "โกA(lex)โก",
"timestamp": "01/13/2023 04:45:03",
"content": "ty",
"attachments": [],
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},
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"id": 1063393238083448800,
"author_id": 1022141568737607800,
"author_name": "โกA(lex)โก",
"timestamp": "01/13/2023 04:45:04",
"content": ".close",
"attachments": [],
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},
{
"id": 1063393241099145200,
"author_id": 805217272087838700,
"author_name": "Mathematics Bot",
"timestamp": "01/13/2023 04:45:05",
"content": "Channel closed",
"attachments": [],
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"reference": null
}
] | help-9 | c4b2008ca51f4879b95c2f1dd7b70437 |
200,718 | [
{
"id": 1063393251626852500,
"author_id": 984319941417251000,
"author_name": "๐๐๐ถ๐๐๐ถ๐",
"timestamp": "01/13/2023 04:45:08",
"content": "np ^^",
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"timestamp": "01/13/2023 04:46:05",
"content": "Available help channel!",
"attachments": [],
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},
{
"id": 1063397133316804600,
"author_id": 1053456932083605500,
"author_name": "sunnnnnnn",
"timestamp": "01/13/2023 05:00:33",
"content": "hey",
"attachments": [],
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},
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"id": 1063397135791427700,
"author_id": 805217272087838700,
"author_name": "Mathematics Bot",
"timestamp": "01/13/2023 05:00:34",
"content": "Pinned a message.",
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"content": "",
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"author_id": 1053456932083605500,
"author_name": "sunnnnnnn",
"timestamp": "01/13/2023 05:00:41",
"content": "how?",
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"id": 1063397310895243400,
"author_id": 411882877933060100,
"author_name": "๏ผจ๏ฝ
๏ฝ๏ฝ
๏ฝ๏ฝ",
"timestamp": "01/13/2023 05:01:15",
"content": "wdym how",
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},
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"id": 1063397327362085000,
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"author_name": "๏ผจ๏ฝ
๏ฝ๏ฝ
๏ฝ๏ฝ",
"timestamp": "01/13/2023 05:01:19",
"content": "what have you tried",
"attachments": [],
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},
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"id": 1063397359008096300,
"author_id": 1053456932083605500,
"author_name": "sunnnnnnn",
"timestamp": "01/13/2023 05:01:27",
"content": "i donโt know where to start",
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},
{
"id": 1063397401815154700,
"author_id": 411882877933060100,
"author_name": "๏ผจ๏ฝ
๏ฝ๏ฝ
๏ฝ๏ฝ",
"timestamp": "01/13/2023 05:01:37",
"content": "do you know the formula of work",
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},
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"id": 1063397523319955500,
"author_id": 1053456932083605500,
"author_name": "sunnnnnnn",
"timestamp": "01/13/2023 05:02:06",
"content": "W = fd?",
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},
{
"id": 1063397548032806900,
"author_id": 411882877933060100,
"author_name": "๏ผจ๏ฝ
๏ฝ๏ฝ
๏ฝ๏ฝ",
"timestamp": "01/13/2023 05:02:12",
"content": "yes",
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{
"id": 1063397597382983700,
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"author_name": "๏ผจ๏ฝ
๏ฝ๏ฝ
๏ฝ๏ฝ",
"timestamp": "01/13/2023 05:02:24",
"content": "now the graph gives you everything",
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"id": 1063397789322715100,
"author_id": 1053456932083605500,
"author_name": "sunnnnnnn",
"timestamp": "01/13/2023 05:03:09",
"content": "2x40?",
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"id": 1063397862270054500,
"author_id": 1053456932083605500,
"author_name": "sunnnnnnn",
"timestamp": "01/13/2023 05:03:27",
"content": "wait no",
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"author_name": "๏ผจ๏ฝ
๏ฝ๏ฝ
๏ฝ๏ฝ",
"timestamp": "01/13/2023 05:03:41",
"content": "dont forget to convert",
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"author_id": 1053456932083605500,
"author_name": "sunnnnnnn",
"timestamp": "01/13/2023 05:03:54",
"content": "W= f(2)",
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},
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"id": 1063398007615262700,
"author_id": 1053456932083605500,
"author_name": "sunnnnnnn",
"timestamp": "01/13/2023 05:04:01",
"content": "itโs 80 right",
"attachments": [],
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"author_id": 411882877933060100,
"author_name": "๏ผจ๏ฝ
๏ฝ๏ฝ
๏ฝ๏ฝ",
"timestamp": "01/13/2023 05:04:03",
"content": "what",
"attachments": [],
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"id": 1063398083339243500,
"author_id": 411882877933060100,
"author_name": "๏ผจ๏ฝ
๏ฝ๏ฝ
๏ฝ๏ฝ",
"timestamp": "01/13/2023 05:04:20",
"content": "what is f(2)",
"attachments": [],
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"id": 1063398123550036000,
"author_id": 1053456932083605500,
"author_name": "sunnnnnnn",
"timestamp": "01/13/2023 05:04:29",
"content": "force x 2",
"attachments": [],
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},
{
"id": 1063398170740138000,
"author_id": 411882877933060100,
"author_name": "๏ผจ๏ฝ
๏ฝ๏ฝ
๏ฝ๏ฝ",
"timestamp": "01/13/2023 05:04:40",
"content": "I said, dont forget to convert",
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"author_name": "sunnnnnnn",
"timestamp": "01/13/2023 05:04:41",
"content": "force is 40N",
"attachments": [],
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},
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"id": 1063398278894457000,
"author_id": 1053456932083605500,
"author_name": "sunnnnnnn",
"timestamp": "01/13/2023 05:05:06",
"content": "convert how?",
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{
"id": 1063398326197821400,
"author_id": 411882877933060100,
"author_name": "๏ผจ๏ฝ
๏ฝ๏ฝ
๏ฝ๏ฝ",
"timestamp": "01/13/2023 05:05:17",
"content": "and also the wire is already extended by a force of 60N",
"attachments": [],
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},
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"author_id": 1053456932083605500,
"author_name": "sunnnnnnn",
"timestamp": "01/13/2023 05:05:50",
"content": "so I -60?",
"attachments": [],
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{
"id": 1063398572894204000,
"author_id": 1053456932083605500,
"author_name": "sunnnnnnn",
"timestamp": "01/13/2023 05:06:16",
"content": "minus 60N?",
"attachments": [],
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},
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"id": 1063398627084615800,
"author_id": 411882877933060100,
"author_name": "๏ผจ๏ฝ
๏ฝ๏ฝ
๏ฝ๏ฝ",
"timestamp": "01/13/2023 05:06:29",
"content": "why minus ?",
"attachments": [],
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},
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"id": 1063398763307208700,
"author_id": 1053456932083605500,
"author_name": "sunnnnnnn",
"timestamp": "01/13/2023 05:07:02",
"content": "since work already done",
"attachments": [],
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},
{
"id": 1063398850225774700,
"author_id": 411882877933060100,
"author_name": "๏ผจ๏ฝ
๏ฝ๏ฝ
๏ฝ๏ฝ",
"timestamp": "01/13/2023 05:07:22",
"content": "thats not how it works",
"attachments": [],
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},
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"id": 1063399039443415200,
"author_id": 1053456932083605500,
"author_name": "sunnnnnnn",
"timestamp": "01/13/2023 05:08:08",
"content": "oh how does it work?",
"attachments": [],
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๏ฝ๏ฝ
๏ฝ๏ฝ",
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๏ฝ๏ฝ
๏ฝ๏ฝ",
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"author_name": "๏ผจ๏ฝ
๏ฝ๏ฝ
๏ฝ๏ฝ",
"timestamp": "01/13/2023 05:08:27",
"content": ",w calc 60 * 2.10^-3",
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},
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"id": 1063399198998933500,
"author_id": 411882877933060100,
"author_name": "๏ผจ๏ฝ
๏ฝ๏ฝ
๏ฝ๏ฝ",
"timestamp": "01/13/2023 05:08:46",
"content": ",w calc 40 \\times 2 \\times 10^{-3}",
"attachments": [],
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},
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"id": 1063399407267086300,
"author_id": 510789298321096700,
"author_name": "TeXit",
"timestamp": "01/13/2023 05:09:35",
"content": "Results provided by WolframAlpha",
"attachments": [],
"mentions": [],
"reference": null
},
{
"id": 1063399483217543200,
"author_id": 411882877933060100,
"author_name": "๏ผจ๏ฝ
๏ฝ๏ฝ
๏ฝ๏ฝ",
"timestamp": "01/13/2023 05:09:53",
"content": "hmm",
"attachments": [],
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},
{
"id": 1063399614876745700,
"author_id": 411882877933060100,
"author_name": "๏ผจ๏ฝ
๏ฝ๏ฝ
๏ฝ๏ฝ",
"timestamp": "01/13/2023 05:10:25",
"content": "you calculate the work, we dont care about the sign right now",
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"id": 1063399832343027700,
"author_id": 1053456932083605500,
"author_name": "sunnnnnnn",
"timestamp": "01/13/2023 05:11:17",
"content": "so",
"attachments": [],
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},
{
"id": 1063399870972563500,
"author_id": 1053456932083605500,
"author_name": "sunnnnnnn",
"timestamp": "01/13/2023 05:11:26",
"content": "40 x 2?",
"attachments": [],
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๏ฝ๏ฝ
๏ฝ๏ฝ",
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๏ฝ๏ฝ
๏ฝ๏ฝ",
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"id": 1063400141786189800,
"author_id": 411882877933060100,
"author_name": "๏ผจ๏ฝ
๏ฝ๏ฝ
๏ฝ๏ฝ",
"timestamp": "01/13/2023 05:12:30",
"content": "wait a sec",
"attachments": [],
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},
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"id": 1063400233813430300,
"author_id": 1053456932083605500,
"author_name": "sunnnnnnn",
"timestamp": "01/13/2023 05:12:52",
"content": ",w (5 \\times 10^(-3))(100)/2 - (60)(3 \\times 10^(-3))/2",
"attachments": [],
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},
{
"id": 1063400273885806600,
"author_id": 1053456932083605500,
"author_name": "sunnnnnnn",
"timestamp": "01/13/2023 05:13:02",
"content": "nope",
"attachments": [],
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},
{
"id": 1063400732960763900,
"author_id": 411882877933060100,
"author_name": "๏ผจ๏ฝ
๏ฝ๏ฝ
๏ฝ๏ฝ",
"timestamp": "01/13/2023 05:14:51",
"content": "They said the wire is already extended by a force of 60N, and we want to know how much work is done to increase the extension of the wire by 2mm. So maybe that means we go from 3 mm to 5mm\n\nW = 100(5.10^-3) - 60(3.10^-3)",
"attachments": [],
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},
{
"id": 1063400823075389400,
"author_id": 411882877933060100,
"author_name": "๏ผจ๏ฝ
๏ฝ๏ฝ
๏ฝ๏ฝ",
"timestamp": "01/13/2023 05:15:13",
"content": ",w calc 100(5 \\times 10^{-3}) - 60(3 \\times 10^{-3})",
"attachments": [],
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"reference": null
},
{
"id": 1063400840850849900,
"author_id": 510789298321096700,
"author_name": "TeXit",
"timestamp": "01/13/2023 05:15:17",
"content": "Results provided by WolframAlpha",
"attachments": [],
"mentions": [],
"reference": null
},
{
"id": 1063400881325879300,
"author_id": 411882877933060100,
"author_name": "๏ผจ๏ฝ
๏ฝ๏ฝ
๏ฝ๏ฝ",
"timestamp": "01/13/2023 05:15:27",
"content": "hmm maybe no",
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},
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"id": 1063401122963918800,
"author_id": 1053456932083605500,
"author_name": "sunnnnnnn",
"timestamp": "01/13/2023 05:16:24",
"content": "hmmm",
"attachments": [],
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"reference": null
},
{
"id": 1063401291243606100,
"author_id": 510789298321096700,
"author_name": "TeXit",
"timestamp": "01/13/2023 05:17:04",
"content": "Results provided by WolframAlpha",
"attachments": [],
"mentions": [],
"reference": null
},
{
"id": 1063401323552321700,
"author_id": 1053456932083605500,
"author_name": "sunnnnnnn",
"timestamp": "01/13/2023 05:17:12",
"content": "WAIT",
"attachments": [],
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"reference": null
},
{
"id": 1063401355982667800,
"author_id": 1053456932083605500,
"author_name": "sunnnnnnn",
"timestamp": "01/13/2023 05:17:20",
"content": "is it c?",
"attachments": [],
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},
{
"id": 1063401463268778100,
"author_id": 411882877933060100,
"author_name": "๏ผจ๏ฝ
๏ฝ๏ฝ
๏ฝ๏ฝ",
"timestamp": "01/13/2023 05:17:45",
"content": "why did you divide 100 by 2",
"attachments": [],
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},
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"id": 1063401552519368700,
"author_id": 1053456932083605500,
"author_name": "sunnnnnnn",
"timestamp": "01/13/2023 05:18:07",
"content": "oh cuz area of triangle I think?",
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},
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"author_id": 411882877933060100,
"author_name": "๏ผจ๏ฝ
๏ฝ๏ฝ
๏ฝ๏ฝ",
"timestamp": "01/13/2023 05:19:03",
"content": "oh well, I just remembered that work is the area under the graph",
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},
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"id": 1063402016489091200,
"author_id": 411882877933060100,
"author_name": "๏ผจ๏ฝ
๏ฝ๏ฝ
๏ฝ๏ฝ",
"timestamp": "01/13/2023 05:19:57",
"content": "I guess you are correct",
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},
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"id": 1063403531010322400,
"author_id": 1053456932083605500,
"author_name": "sunnnnnnn",
"timestamp": "01/13/2023 05:25:58",
"content": "thanks!",
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},
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"id": 1063403546768318600,
"author_id": 1053456932083605500,
"author_name": "sunnnnnnn",
"timestamp": "01/13/2023 05:26:02",
"content": ".close",
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},
{
"id": 1063403549821767700,
"author_id": 805217272087838700,
"author_name": "Mathematics Bot",
"timestamp": "01/13/2023 05:26:03",
"content": "Channel closed",
"attachments": [],
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"reference": null
}
] | help-9 | 41300162fb3940aba770a9be0106463d |
200,719 | [
{
"id": 1063403801761042400,
"author_id": 805217272087838700,
"author_name": "Mathematics Bot",
"timestamp": "01/13/2023 05:27:03",
"content": "Available help channel!",
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"reference": null
},
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"id": 1063404182431862800,
"author_id": 954062091269075000,
"author_name": "pipinstallbrain",
"timestamp": "01/13/2023 05:28:34",
"content": "Can anyone tell me whatโs wrong here, or is this correct? I donโt have a solution manual and the calculator answer looks different, any help would be appreciated. Thanks in advance",
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"timestamp": "01/13/2023 05:28:34",
"content": "Pinned a message.",
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"id": 1063404297842344000,
"author_id": 718461587236716500,
"author_name": "NEONPerseus",
"timestamp": "01/13/2023 05:29:01",
"content": "It's correct",
"attachments": [],
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},
{
"id": 1063404362346532900,
"author_id": 954062091269075000,
"author_name": "pipinstallbrain",
"timestamp": "01/13/2023 05:29:17",
"content": "Ahh thankyou",
"attachments": [],
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},
{
"id": 1063404434983501800,
"author_id": 718461587236716500,
"author_name": "NEONPerseus",
"timestamp": "01/13/2023 05:29:34",
"content": "np",
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},
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"id": 1063404441383993500,
"author_id": 954062091269075000,
"author_name": "pipinstallbrain",
"timestamp": "01/13/2023 05:29:35",
"content": "Wolfram alpha answer was a bit strange",
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},
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"id": 1063404470744141800,
"author_id": 954062091269075000,
"author_name": "pipinstallbrain",
"timestamp": "01/13/2023 05:29:42",
"content": ".com",
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},
{
"id": 1063404486300807200,
"author_id": 954062091269075000,
"author_name": "pipinstallbrain",
"timestamp": "01/13/2023 05:29:46",
"content": "Aaaargh",
"attachments": [],
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},
{
"id": 1063404498665615400,
"author_id": 954062091269075000,
"author_name": "pipinstallbrain",
"timestamp": "01/13/2023 05:29:49",
"content": ".close",
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},
{
"id": 1063404502012665900,
"author_id": 805217272087838700,
"author_name": "Mathematics Bot",
"timestamp": "01/13/2023 05:29:50",
"content": "Channel closed",
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}
] | help-9 | 6de71adb2ee44fb28f9a8fa622dec023 |
200,720 | [
{
"id": 1035424449148768300,
"author_id": 365766068616036350,
"author_name": "Mz",
"timestamp": "10/28/2022 01:27:05",
"content": "still dont know lmao",
"attachments": [],
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"reference": null
},
{
"id": 1035425679233261600,
"author_id": 805217272087838700,
"author_name": "Mathematics Bot",
"timestamp": "10/28/2022 01:31:59",
"content": "Available help channel!",
"attachments": [],
"mentions": [],
"reference": null
},
{
"id": 1035426043525341300,
"author_id": 208188247291985920,
"author_name": "halalchad",
"timestamp": "10/28/2022 01:33:26",
"content": "",
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"author_name": "Mathematics Bot",
"timestamp": "10/28/2022 01:33:26",
"content": "Pinned a message.",
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{
"id": 1035426257116074000,
"author_id": 208188247291985920,
"author_name": "halalchad",
"timestamp": "10/28/2022 01:34:16",
"content": "is the solution for the first part โ(2r-1)ยฒ-โ(2r)ยฒ?",
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},
{
"id": 1035426426016518100,
"author_id": 208188247291985920,
"author_name": "halalchad",
"timestamp": "10/28/2022 01:34:57",
"content": "with both upper limits as 2n?",
"attachments": [],
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},
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"id": 1035426809182961700,
"author_id": 208188247291985920,
"author_name": "halalchad",
"timestamp": "10/28/2022 01:36:28",
"content": "i seem to be missing something because I can't prove S2n",
"attachments": [],
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},
{
"id": 1035430584954142700,
"author_id": 805217272087838700,
"author_name": "Mathematics Bot",
"timestamp": "10/28/2022 01:51:28",
"content": "@halalchad Has your question been resolved?",
"attachments": [],
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"author_name": "Mathematics Bot",
"timestamp": "10/28/2022 02:06:29",
"content": "Channel closed",
"attachments": [],
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}
] | help-9 | 37feef1e503a4fadac37b6f52c7a09a1 |
200,721 | [
{
"id": 1063406711274217500,
"author_id": 805217272087838700,
"author_name": "Mathematics Bot",
"timestamp": "01/13/2023 05:38:37",
"content": "Available help channel!",
"attachments": [],
"mentions": [],
"reference": null
},
{
"id": 1063407430249234400,
"author_id": 954062091269075000,
"author_name": "pipinstallbrain",
"timestamp": "01/13/2023 05:41:28",
"content": "Can anyone help me with this, the answer is wrong as I see the right answer is -2/x^3",
"attachments": [
{
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"timestamp": "01/13/2023 05:41:29",
"content": "Pinned a message.",
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"id": 1063407664819880000,
"author_id": 954062091269075000,
"author_name": "pipinstallbrain",
"timestamp": "01/13/2023 05:42:24",
"content": "Where am i making the mistake? :c",
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},
{
"id": 1063408158053240800,
"author_id": 277133612812468220,
"author_name": "HeadShotCem",
"timestamp": "01/13/2023 05:44:22",
"content": "Notice that for f(x) = 1/x^2, youโre trying to find this:\nlim (f(x+h)-f(x))/(h) as h โ> 0\nwhich is essentially equal to f'(x)",
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"id": 1063408340031504400,
"author_id": 788085606483361800,
"author_name": "chartbit",
"timestamp": "01/13/2023 05:45:05",
"content": "How comes you didnโt expand the numerator?",
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"id": 1063408398118432800,
"author_id": 788085606483361800,
"author_name": "chartbit",
"timestamp": "01/13/2023 05:45:19",
"content": "Does that not give you something nice?",
"attachments": [],
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},
{
"id": 1063408428434870300,
"author_id": 954062091269075000,
"author_name": "pipinstallbrain",
"timestamp": "01/13/2023 05:45:26",
"content": "I canโt use derivatives or Lยดopitals, just by factorizing",
"attachments": [],
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},
{
"id": 1063408474400231600,
"author_id": 954062091269075000,
"author_name": "pipinstallbrain",
"timestamp": "01/13/2023 05:45:37",
"content": "Aaaaaah right, that was easier",
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"id": 1063408599117861000,
"author_id": 954062091269075000,
"author_name": "pipinstallbrain",
"timestamp": "01/13/2023 05:46:07",
"content": "How was I not able to see it at that moment in time :c wer brainnnnn!",
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},
{
"id": 1063408684165763100,
"author_id": 788085606483361800,
"author_name": "chartbit",
"timestamp": "01/13/2023 05:46:27",
"content": "Hahah trust me Iโm pretty much the same like most of the time :kekw:",
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"id": 1063408957995094000,
"author_id": 954062091269075000,
"author_name": "pipinstallbrain",
"timestamp": "01/13/2023 05:47:32",
"content": "Thankyou frens, Iโll be back if I still get stuck.",
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},
{
"id": 1063408977855139800,
"author_id": 954062091269075000,
"author_name": "pipinstallbrain",
"timestamp": "01/13/2023 05:47:37",
"content": "โค๏ธ",
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},
{
"id": 1063409000273694800,
"author_id": 954062091269075000,
"author_name": "pipinstallbrain",
"timestamp": "01/13/2023 05:47:42",
"content": ".close",
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},
{
"id": 1063409003067097100,
"author_id": 805217272087838700,
"author_name": "Mathematics Bot",
"timestamp": "01/13/2023 05:47:43",
"content": "Channel closed",
"attachments": [],
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"reference": null
}
] | help-9 | fbb1be8ee54a4e03bbda34f3eca64c4a |
200,722 | [
{
"id": 1063409966578405500,
"author_id": 805217272087838700,
"author_name": "Mathematics Bot",
"timestamp": "01/13/2023 05:51:33",
"content": "Available help channel!",
"attachments": [],
"mentions": [],
"reference": null
},
{
"id": 1063410970929672200,
"author_id": 904360321903366100,
"author_name": "JockeMรถll",
"timestamp": "01/13/2023 05:55:32",
"content": "Find the primitive function for x*arctan(x) using Partial integration",
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},
{
"id": 1063410973085536300,
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"content": "Pinned a message.",
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"author_id": 904360321903366100,
"author_name": "JockeMรถll",
"timestamp": "01/13/2023 05:55:41",
"content": "I have a question about this exercise",
"attachments": [],
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},
{
"id": 1063411087791374300,
"author_id": 904360321903366100,
"author_name": "JockeMรถll",
"timestamp": "01/13/2023 05:56:00",
"content": "",
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"id": 1063411250375180300,
"author_id": 904360321903366100,
"author_name": "JockeMรถll",
"timestamp": "01/13/2023 05:56:39",
"content": "The polynomial division part of the question..",
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},
{
"id": 1063411463097696300,
"author_id": 904360321903366100,
"author_name": "JockeMรถll",
"timestamp": "01/13/2023 05:57:30",
"content": "I got 1 + ((-1)/(x^2+1)) using polynomial division",
"attachments": [],
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},
{
"id": 1063411582643740700,
"author_id": 904360321903366100,
"author_name": "JockeMรถll",
"timestamp": "01/13/2023 05:57:58",
"content": "how do I turn this into x^2-(x^2+1) + 1 in the numerator?",
"attachments": [],
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},
{
"id": 1063411670833180700,
"author_id": 182179228840755200,
"author_name": "iCaird",
"timestamp": "01/13/2023 05:58:19",
"content": "Add and subtract xยฒ",
"attachments": [],
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"reference": null
},
{
"id": 1063411767172153300,
"author_id": 182179228840755200,
"author_name": "iCaird",
"timestamp": "01/13/2023 05:58:42",
"content": "But you don't really need to do that, leave it as -1",
"attachments": [],
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"reference": null
},
{
"id": 1063411794565152800,
"author_id": 182179228840755200,
"author_name": "iCaird",
"timestamp": "01/13/2023 05:58:49",
"content": "What they did was weird",
"attachments": [],
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"reference": null
},
{
"id": 1063412052670025900,
"author_id": 788085606483361800,
"author_name": "chartbit",
"timestamp": "01/13/2023 05:59:50",
"content": "For me, I personally prefer the โadding zeroโ when it comes to these, in that noticing that you can write x^2 = x^2 + 1 - 1",
"attachments": [],
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},
{
"id": 1063412169678532700,
"author_id": 182179228840755200,
"author_name": "iCaird",
"timestamp": "01/13/2023 06:00:18",
"content": "They decided to add and subtract xยฒ+1 from the original numerator which is silly when you can just do what chartbit said",
"attachments": [],
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},
{
"id": 1063412405775900800,
"author_id": 904360321903366100,
"author_name": "JockeMรถll",
"timestamp": "01/13/2023 06:01:14",
"content": "ah okey, my professor said that if the numerator and denominator looks quite the same, I should use polynomial division",
"attachments": [],
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"reference": null
},
{
"id": 1063412509928857600,
"author_id": 182179228840755200,
"author_name": "iCaird",
"timestamp": "01/13/2023 06:01:39",
"content": "\"Adding zero\" can often save you the trouble so check for that first",
"attachments": [],
"mentions": [],
"reference": null
},
{
"id": 1063412735855046800,
"author_id": 904360321903366100,
"author_name": "JockeMรถll",
"timestamp": "01/13/2023 06:02:33",
"content": "And I'm supposed to apply that only when the nominator and denominator looks like this in my example?",
"attachments": [],
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},
{
"id": 1063412840716841000,
"author_id": 904360321903366100,
"author_name": "JockeMรถll",
"timestamp": "01/13/2023 06:02:58",
"content": "numerator and denominator*",
"attachments": [],
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},
{
"id": 1063412971642036200,
"author_id": 904360321903366100,
"author_name": "JockeMรถll",
"timestamp": "01/13/2023 06:03:29",
"content": "Nvm, I'll look more into the adding zero technique online, thanks alot everybody!",
"attachments": [],
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},
{
"id": 1063413116626546800,
"author_id": 182179228840755200,
"author_name": "iCaird",
"timestamp": "01/13/2023 06:04:04",
"content": "Just learn to generally look for it, think \"does adding and subtracting something help me simplify?\"",
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},
{
"id": 1063413479035375600,
"author_id": 904360321903366100,
"author_name": "JockeMรถll",
"timestamp": "01/13/2023 06:05:30",
"content": "Alright, I'll make sure to remember this, thanks bro!",
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},
{
"id": 1063413541043974100,
"author_id": 904360321903366100,
"author_name": "JockeMรถll",
"timestamp": "01/13/2023 06:05:45",
"content": ".close",
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},
{
"id": 1063413543984177200,
"author_id": 805217272087838700,
"author_name": "Mathematics Bot",
"timestamp": "01/13/2023 06:05:46",
"content": "Channel closed",
"attachments": [],
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}
] | help-9 | 837d176474014e05a84fa9816eda6916 |
200,723 | [
{
"id": 1063413796351246300,
"author_id": 805217272087838700,
"author_name": "Mathematics Bot",
"timestamp": "01/13/2023 06:06:46",
"content": "Available help channel!",
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},
{
"id": 1063415209609404500,
"author_id": 830816571818770400,
"author_name": "azurelmao",
"timestamp": "01/13/2023 06:12:23",
"content": "I'm so confused rn. How can I make this square appear like it's rotating around its center?\nhttps://www.desmos.com/calculator/ehbkvuw5wc",
"attachments": [],
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},
{
"id": 1063415211714936800,
"author_id": 805217272087838700,
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"timestamp": "01/13/2023 06:12:23",
"content": "Pinned a message.",
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"id": 1063416825012047900,
"author_id": 847570371870851100,
"author_name": "AntonyDP",
"timestamp": "01/13/2023 06:18:48",
"content": "You have to first translate all the points by the - vector that corresponds to the center of location, essentially moving it to the origin, then you have to rotate as you're doing and finally translate it back + center vector",
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"timestamp": "01/13/2023 06:27:23",
"content": "@azurelmao Has your question been resolved?",
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] | help-9 | 53fb83e50400415481e99366b4ec0ba1 |
200,724 | [
{
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"author_name": "Mathematics Bot",
"timestamp": "01/13/2023 06:29:43",
"content": "Available help channel!",
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"author_name": "radio",
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"author_name": "radio",
"timestamp": "01/13/2023 06:33:57",
"content": "I tried using combinatorics but I honestly am stuck with this question. If someone could even point me on where to go it would be greatly appreciated.",
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"timestamp": "01/13/2023 06:48:57",
"content": "@radio Has your question been resolved?",
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"author_id": 446704648485863400,
"author_name": "Castroploiinยน",
"timestamp": "01/13/2023 07:00:05",
"content": "'tis like Traveling Salesman except you remove an imaginary edge between Alex and Bryn",
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"author_id": 847570371870851100,
"author_name": "AntonyDP",
"timestamp": "01/13/2023 07:01:47",
"content": "Yeah, if you're satisfied with a computer generated solution one could write an integer linear programming model to brute force it",
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"timestamp": "01/13/2023 07:02:35",
"content": "NP-hard",
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"timestamp": "01/13/2023 07:20:53",
"content": "@radio Has your question been resolved?",
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"author_name": "AntonyDP",
"timestamp": "01/13/2023 07:22:50",
"content": "I'm not exactly sure but such a model should look something like this",
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"timestamp": "01/13/2023 07:25:53",
"content": "Settings those constraints and a dummy maximization function (such as maximize 1 such that...) A solver should give you the number of solutions",
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"author_name": "AntonyDP",
"timestamp": "01/13/2023 07:26:26",
"content": "@Castroploiinยน \nDoes it look right to you?",
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"timestamp": "01/13/2023 07:27:17",
"content": "Sorry, I just know the fancy terminology. I don't know Integer linear programming",
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"timestamp": "01/13/2023 07:29:50",
"content": "It's alright. \nAnyway I'm pretty interested if someone knows an exact theoretical answer",
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"timestamp": "01/13/2023 07:50:53",
"content": "Channel closed",
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}
] | help-9 | c6c028ac090146ac8255b659ea10f3a8 |
200,725 | [
{
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"author_name": "Mathematics Bot",
"timestamp": "01/13/2023 07:51:54",
"content": "Available help channel!",
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},
{
"id": 1063443988151013400,
"author_id": 332561465405866000,
"author_name": "Kepe",
"timestamp": "01/13/2023 08:06:44",
"content": "When drawing the graph of a function, why is it useful to find out the monotony intervals?\nAfter having the zero points, turning points, inflection points, there shouldn't be a need for finding out on which intervals the function is decreasing or increasing, right?",
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"author_name": "Kepe",
"timestamp": "01/13/2023 08:07:33",
"content": "When finding the turning points of the function, you will find the monotony intervals, but you don't need to further use them, right?",
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"author_name": "Denascite",
"timestamp": "01/13/2023 08:13:47",
"content": "well ok you don't explicitly need to write them down I guess but it's certainly helpful to keep in mind",
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"author_name": "Denascite",
"timestamp": "01/13/2023 08:14:07",
"content": "like you said, you essentially know them from the turning points anyway",
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"author_name": "Kepe",
"timestamp": "01/13/2023 08:14:55",
"content": "And for inflection points, you try to make the graph linear near them, right?",
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"author_name": "Denascite",
"timestamp": "01/13/2023 08:16:02",
"content": "I suppose if you wanna view it like that, yes",
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"author_name": "Denascite",
"timestamp": "01/13/2023 08:16:16",
"content": "if you zoom in enough any (differentiable) graph should essentially look linear near a point",
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"author_name": "Kepe",
"timestamp": "01/13/2023 08:16:28",
"content": "Why are monotony intervals helpful?",
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"author_id": 132304137583984640,
"author_name": "Denascite",
"timestamp": "01/13/2023 08:16:40",
"content": "well to know if you are supposed to draw up or down?",
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"author_name": "Kepe",
"timestamp": "01/13/2023 08:17:09",
"content": "Well you will know the turning points, which occur at the edges of the monotony intervals",
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"author_name": "Denascite",
"timestamp": "01/13/2023 08:18:06",
"content": "something something saddle points",
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"author_name": "Denascite",
"timestamp": "01/13/2023 08:18:13",
"content": "but you are kinda overthinking this",
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"timestamp": "01/13/2023 08:18:54",
"content": "We know that between the two turning points, it will be strictly monotonic decreasing",
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"author_name": "Kepe",
"timestamp": "01/13/2023 08:20:18",
"content": "Oh",
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"author_name": "Denascite",
"timestamp": "01/13/2023 08:20:21",
"content": "great so you calculated the interval",
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"author_name": "Denascite",
"timestamp": "01/13/2023 08:20:26",
"content": "and how does that not help",
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"author_name": "Denascite",
"timestamp": "01/13/2023 08:20:36",
"content": "how did you want to graph without thinking about which one is bigger or lower",
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"author_name": "Kepe",
"timestamp": "01/13/2023 08:21:21",
"content": "What do you mean with I calculated the interval? I set f'(x) = 0 and tested with f'' which gave nonzero values",
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"author_name": "Kepe",
"timestamp": "01/13/2023 08:22:03",
"content": "I do have the monotony intervals, those are between the turning points, yes, but I don't need to look at if f is strictly monotonic increasing or decreasing in them",
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"timestamp": "01/13/2023 08:22:22",
"content": "I get that by connecting the turning points",
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"author_name": "Denascite",
"timestamp": "01/13/2023 08:22:40",
"content": "so by calculating the turning points you calculated the monotony intervals already",
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"author_name": "Kepe",
"timestamp": "01/13/2023 08:22:49",
"content": "yeah",
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"author_name": "Denascite",
"timestamp": "01/13/2023 08:23:13",
"content": "yes but you need to do that step of calculating the y-coordinate of the turning points",
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"id": 1063448256027299800,
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"author_name": "Denascite",
"timestamp": "01/13/2023 08:23:42",
"content": "you need more than just the x-coordinates which is what you get from just setting f'(x)=0",
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"author_name": "Denascite",
"timestamp": "01/13/2023 08:24:19",
"content": "you need that extra step. and whether you wanna call it \"determining monotony intervals\" or \"determining y-coordinates of turning points\" really doesn't matter much",
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"author_name": "Denascite",
"timestamp": "01/13/2023 08:24:24",
"content": "the point is that the step is necessary",
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"author_name": "Kepe",
"timestamp": "01/13/2023 08:27:01",
"content": "Alright, thanks\nCalculating the zero points of f, the turning points, inflection points and behaviour at x to plus/minus infinity is pretty much all you can do to draw a decent graph, right?",
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"author_name": "Denascite",
"timestamp": "01/13/2023 08:28:04",
"content": "well you could always calculate some random points to include them",
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"timestamp": "01/13/2023 08:28:12",
"content": "yeah",
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"author_name": "Kepe",
"timestamp": "01/13/2023 08:28:24",
"content": "thanks",
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"author_name": "Kepe",
"timestamp": "01/13/2023 08:28:30",
"content": ".close",
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"author_name": "Mathematics Bot",
"timestamp": "01/13/2023 08:28:31",
"content": "Channel closed",
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] | help-9 | f1b54ab681a1467fbbc7a3296a6463aa |
200,726 | [
{
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"author_name": "Mathematics Bot",
"timestamp": "01/13/2023 08:29:31",
"content": "Available help channel!",
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{
"id": 1063451651186380900,
"author_id": 668946291824263200,
"author_name": "Afr4zTh3Alc4traZ",
"timestamp": "01/13/2023 08:37:11",
"content": "This is all I know rn",
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"timestamp": "01/13/2023 08:37:12",
"content": "Pinned a message.",
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"id": 1063451808586027100,
"author_id": 349354952961032200,
"author_name": "Umbraleviathan",
"timestamp": "01/13/2023 08:37:49",
"content": "Use Isosceles triangle properties",
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"id": 1063451830455111800,
"author_id": 349354952961032200,
"author_name": "Umbraleviathan",
"timestamp": "01/13/2023 08:37:54",
"content": "You can easily find m2",
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"id": 1063451872213610600,
"author_id": 668946291824263200,
"author_name": "Afr4zTh3Alc4traZ",
"timestamp": "01/13/2023 08:38:04",
"content": "I did",
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"id": 1063452018263478300,
"author_id": 349354952961032200,
"author_name": "Umbraleviathan",
"timestamp": "01/13/2023 08:38:39",
"content": "You can then find the angle supplementary to m3",
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"id": 1063452045945868400,
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"author_name": "Umbraleviathan",
"timestamp": "01/13/2023 08:38:45",
"content": "Or rather",
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"id": 1063452059380224000,
"author_id": 349354952961032200,
"author_name": "Umbraleviathan",
"timestamp": "01/13/2023 08:38:48",
"content": "Use external angle theorem",
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"id": 1063452080502743000,
"author_id": 349354952961032200,
"author_name": "Umbraleviathan",
"timestamp": "01/13/2023 08:38:53",
"content": "To directly get angle 3",
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"id": 1063452121963430000,
"author_id": 668946291824263200,
"author_name": "Afr4zTh3Alc4traZ",
"timestamp": "01/13/2023 08:39:03",
"content": "Yo I actually didnโt see that",
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"id": 1063452130435936300,
"author_id": 668946291824263200,
"author_name": "Afr4zTh3Alc4traZ",
"timestamp": "01/13/2023 08:39:05",
"content": "Thank you",
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{
"id": 1063452151084482700,
"author_id": 349354952961032200,
"author_name": "Umbraleviathan",
"timestamp": "01/13/2023 08:39:10",
"content": "Np",
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"id": 1063452273172303900,
"author_id": 668946291824263200,
"author_name": "Afr4zTh3Alc4traZ",
"timestamp": "01/13/2023 08:39:39",
"content": "And then I can use the isos triangle thrm for the triangle with angles 3 and 4 and say that m<3 = m<4?",
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"timestamp": "01/13/2023 08:40:13",
"content": "Sure",
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"author_name": "Afr4zTh3Alc4traZ",
"timestamp": "01/13/2023 08:40:33",
"content": "Alright thanks",
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"author_id": 668946291824263200,
"author_name": "Afr4zTh3Alc4traZ",
"timestamp": "01/13/2023 08:40:37",
"content": ".close",
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"author_id": 805217272087838700,
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"timestamp": "01/13/2023 08:40:38",
"content": "Channel closed",
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] | help-9 | d6723647d76843ccab9f7d6e0914eada |
200,727 | [
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"id": 1063454181387665400,
"author_id": 805217272087838700,
"author_name": "Mathematics Bot",
"timestamp": "01/13/2023 08:47:14",
"content": "Available help channel!",
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"id": 1063455810321129600,
"author_id": 313298495417221100,
"author_name": "avidrunner",
"timestamp": "01/13/2023 08:53:43",
"content": "why does the third polynomial touch the x-axis so much?",
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"content": "Pinned a message.",
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"author_id": 1000057838007226500,
"author_name": "VulcanOne",
"timestamp": "01/13/2023 08:54:20",
"content": "Because of the amount of roots it has",
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"author_name": "๐๐๐ถ๐๐๐ถ๐",
"timestamp": "01/13/2023 08:54:21",
"content": "well it has a lot of roots lol",
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"author_name": "avidrunner",
"timestamp": "01/13/2023 08:54:25",
"content": "and does the third polynomial still count as a 4th degree polynomial? just with a double root?",
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"timestamp": "01/13/2023 08:54:40",
"content": "it does not",
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"author_name": "VulcanOne",
"timestamp": "01/13/2023 08:54:40",
"content": "Nope",
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"timestamp": "01/13/2023 08:54:45",
"content": "it has 4 roots to be precise, right?",
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"timestamp": "01/13/2023 08:54:46",
"content": "no i think its a 8th degree",
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"timestamp": "01/13/2023 08:54:52",
"content": ":hmmCat:",
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"timestamp": "01/13/2023 08:54:56",
"content": "Oh, but the highest degree is 4",
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"author_name": "้ปๆณข็ใชๅฝผๅฅณ",
"timestamp": "01/13/2023 08:55:02",
"content": "they multiply",
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"timestamp": "01/13/2023 08:55:08",
"content": "3 distinct roots",
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"author_name": "AntonyDP",
"timestamp": "01/13/2023 08:55:15",
"content": "Expand the polinomial",
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"author_name": "VulcanOne",
"timestamp": "01/13/2023 08:55:35",
"content": "But one has multiplicity 4, one has multiplicity 3, and one has multiplicity 1",
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"timestamp": "01/13/2023 08:55:39",
"content": "but if that's the case, the first two polynomials would be degree 6 and degree 10",
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"timestamp": "01/13/2023 08:55:43",
"content": "x^4 * x^3 * x = x^8",
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"author_name": "้ปๆณข็ใชๅฝผๅฅณ",
"timestamp": "01/13/2023 08:55:51",
"content": "first two would be degree 7",
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"timestamp": "01/13/2023 08:56:12",
"content": "First one is 3rd degree",
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"content": "why 7 each?",
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"timestamp": "01/13/2023 08:56:13",
"content": "whattt",
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"author_name": "้ปๆณข็ใชๅฝผๅฅณ",
"timestamp": "01/13/2023 08:56:14",
"content": "^",
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"author_name": "้ปๆณข็ใชๅฝผๅฅณ",
"timestamp": "01/13/2023 08:56:27",
"content": "exponential rules",
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"timestamp": "01/13/2023 08:56:28",
"content": "Second one is 4th degree",
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"author_name": "jay.",
"timestamp": "01/13/2023 08:56:37",
"content": "what..? the first would be 3 and the second would be 4",
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"timestamp": "01/13/2023 08:56:47",
"content": "what the heck is happening rn",
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"timestamp": "01/13/2023 08:56:49",
"content": "yeah.. I see it this way too",
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"timestamp": "01/13/2023 08:56:58",
"content": "Yep",
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"author_name": "AntonyDP",
"timestamp": "01/13/2023 08:57:06",
"content": "In the first two polinomial you have additions and subtractions,\nThe third one have multiplication",
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"timestamp": "01/13/2023 08:57:07",
"content": "what do you mean exponential rules?",
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"timestamp": "01/13/2023 08:57:07",
"content": "so the thing ur having trouble with is the third one?",
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"author_name": "้ปๆณข็ใชๅฝผๅฅณ",
"timestamp": "01/13/2023 08:57:35",
"content": "if u expand (x-2)^4, the highest term is x^4",
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"author_name": "โกA(lex)โก",
"timestamp": "01/13/2023 08:57:43",
"content": "look up fundamental theorem of algebra btw @avidrunner",
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"author_name": "โกA(lex)โก",
"timestamp": "01/13/2023 08:57:46",
"content": "would help i think",
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"id": 1063456835732000800,
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"author_name": "jay.",
"timestamp": "01/13/2023 08:57:47",
"content": "can somebody use the wolframalpha comman thing to expand the third polynominal?",
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"id": 1063456860885237900,
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"timestamp": "01/13/2023 08:57:53",
"content": "idk how to do that",
"attachments": [],
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},
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"author_id": 783697943176675300,
"author_name": "้ปๆณข็ใชๅฝผๅฅณ",
"timestamp": "01/13/2023 08:58:00",
"content": "same for the other ones, u just multiply each expansion's highest degrees together to get the highest final degrees",
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"id": 1063456970566283300,
"author_id": 1000057838007226500,
"author_name": "VulcanOne",
"timestamp": "01/13/2023 08:58:19",
"content": ",w expand (x-2)^4",
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},
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"id": 1063456982792671400,
"author_id": 510789298321096700,
"author_name": "TeXit",
"timestamp": "01/13/2023 08:58:22",
"content": "Results provided by WolframAlpha",
"attachments": [],
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"reference": null
},
{
"id": 1063457034831409200,
"author_id": 1000057838007226500,
"author_name": "VulcanOne",
"timestamp": "01/13/2023 08:58:35",
"content": ",w expand (x+1)^3",
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},
{
"id": 1063457047238148200,
"author_id": 510789298321096700,
"author_name": "TeXit",
"timestamp": "01/13/2023 08:58:38",
"content": "Results provided by WolframAlpha",
"attachments": [],
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},
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"id": 1063457063293947900,
"author_id": 1000057838007226500,
"author_name": "VulcanOne",
"timestamp": "01/13/2023 08:58:41",
"content": "Here",
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},
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"id": 1063457127647150100,
"author_id": 1022141568737607800,
"author_name": "โกA(lex)โก",
"timestamp": "01/13/2023 08:58:57",
"content": "ah pascal's triangle",
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"id": 1063457137143070800,
"author_id": 1022141568737607800,
"author_name": "โกA(lex)โก",
"timestamp": "01/13/2023 08:58:59",
"content": "my beloved",
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},
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"author_id": 984319941417251000,
"author_name": "๐๐๐ถ๐๐๐ถ๐",
"timestamp": "01/13/2023 08:59:04",
"content": "i think it would help to have fewer than 20 people trying to explain different things at the same time",
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"timestamp": "01/13/2023 08:59:19",
"content": "https://tenor.com/view/pascal-nier-automata-heart-locket-pascal-my-beloved-love-wins-gif-21665525",
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"id": 1063457240205496300,
"author_id": 806790920770814000,
"author_name": "jay.",
"timestamp": "01/13/2023 08:59:24",
"content": ",w expand (x-2)^4*(x+1)^2*(x-1)",
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},
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"author_id": 510789298321096700,
"author_name": "TeXit",
"timestamp": "01/13/2023 08:59:27",
"content": "Results provided by WolframAlpha",
"attachments": [],
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},
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"id": 1063457279086702600,
"author_id": 313298495417221100,
"author_name": "avidrunner",
"timestamp": "01/13/2023 08:59:33",
"content": "this is not true, is it?",
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"id": 1063457293364101100,
"author_id": 1000057838007226500,
"author_name": "VulcanOne",
"timestamp": "01/13/2023 08:59:36",
"content": "Wronge",
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"id": 1063457322107682800,
"author_id": 806790920770814000,
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"timestamp": "01/13/2023 08:59:43",
"content": "oh shoot typo",
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{
"id": 1063457396116168800,
"author_id": 806790920770814000,
"author_name": "jay.",
"timestamp": "01/13/2023 09:00:01",
"content": ",w expand (x-2)^4(x+1)^3(x-1)",
"attachments": [],
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},
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"id": 1063457410427138200,
"author_id": 510789298321096700,
"author_name": "TeXit",
"timestamp": "01/13/2023 09:00:04",
"content": "Results provided by WolframAlpha",
"attachments": [],
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"reference": null
},
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"id": 1063457424641638400,
"author_id": 783697943176675300,
"author_name": "้ปๆณข็ใชๅฝผๅฅณ",
"timestamp": "01/13/2023 09:00:08",
"content": "why",
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"author_name": "jay.",
"timestamp": "01/13/2023 09:00:27",
"content": "@avidrunner what's the degree of the polynominal here?",
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"timestamp": "01/13/2023 09:00:32",
"content": "first is degree 3, second is degree 4",
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"timestamp": "01/13/2023 09:00:33",
"content": "Because they have 3rd and 4th powers respectively",
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"timestamp": "01/13/2023 09:00:38",
"content": "Yeah exactly",
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"timestamp": "01/13/2023 09:01:18",
"content": "so first two multiply is a a 7th degree polynomial?",
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"content": "No don't multiply them",
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"content": "?",
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"timestamp": "01/13/2023 09:01:47",
"content": "why would you multiply that oh my god",
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"content": "Individually they are 3rd degree and 4th degree respectively",
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"content": "you only go by the highest power of the polynomial",
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"timestamp": "01/13/2023 09:01:57",
"content": "yeah",
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"timestamp": "01/13/2023 09:02:00",
"content": ":catThimc: ok",
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"timestamp": "01/13/2023 09:02:05",
"content": "that makes sense now for the third polynomial",
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"content": "I would need to expand",
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"timestamp": "01/13/2023 09:02:15",
"content": "degree 4 is misleading",
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"content": "yeah",
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"timestamp": "01/13/2023 09:02:21",
"content": "Actually you don't",
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"timestamp": "01/13/2023 09:02:24",
"content": "oh?",
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"timestamp": "01/13/2023 09:02:30",
"content": "You add up the multiplicities together",
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"timestamp": "01/13/2023 09:02:34",
"content": "4+3+1",
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"timestamp": "01/13/2023 09:02:37",
"content": "8",
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"timestamp": "01/13/2023 09:02:40",
"content": "because they are in brackets?",
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"timestamp": "01/13/2023 09:02:45",
"content": "Yeah",
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"timestamp": "01/13/2023 09:02:47",
"content": "well technically you don't need to expand",
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"timestamp": "01/13/2023 09:02:54",
"content": "we call them factors?",
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"timestamp": "01/13/2023 09:02:54",
"content": "Doesn't need a nighttime of expansion",
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"timestamp": "01/13/2023 09:03:01",
"content": "Roots",
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"content": "the brackets",
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"content": "we call them factors?",
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"timestamp": "01/13/2023 09:03:08",
"content": "you just need to know the highest degree",
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"timestamp": "01/13/2023 09:03:24",
"content": "yeah i think so",
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"timestamp": "01/13/2023 09:03:26",
"content": "multiplying factors",
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"timestamp": "01/13/2023 09:03:51",
"content": "the amount of x-intercepts (roots) generally means the degree of the polynomial. but sometimes there can be double root. or imaginary roots",
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"timestamp": "01/13/2023 09:03:54",
"content": "The brackets are factors yes",
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"timestamp": "01/13/2023 09:04:00",
"content": "Yep",
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"timestamp": "01/13/2023 09:04:05",
"content": "so maybe the roots are a bad way to guess the degree",
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"timestamp": "01/13/2023 09:04:13",
"content": "No that aren't",
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"content": "it's always the algebra that says",
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"timestamp": "01/13/2023 09:04:24",
"content": "but I just stated here",
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"timestamp": "01/13/2023 09:04:26",
"content": "the amount of x-intercepts (roots) generally means the degree of the polynomial. but sometimes there can be double root. or imaginary roots",
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"content": "if you look at the graph, it may be hard to tell",
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"timestamp": "01/13/2023 09:04:42",
"content": "without seeing the algebra",
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"timestamp": "01/13/2023 09:04:42",
"content": "That's why there are multiplicities",
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"timestamp": "01/13/2023 09:04:55",
"content": "Oh on the graph",
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"timestamp": "01/13/2023 09:04:58",
"content": "you can tell just by looking at the graph?",
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"timestamp": "01/13/2023 09:05:10",
"content": "With enough practice, you can yeah",
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"timestamp": "01/13/2023 09:05:58",
"content": "Some rules of thumb you follow will help you pick up the roots multiplicities",
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"timestamp": "01/13/2023 09:06:32",
"content": "With this graph you can tell what the algebra would be?",
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"timestamp": "01/13/2023 09:06:36",
"content": "Yeah",
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"timestamp": "01/13/2023 09:06:43",
"content": "lol whaaaa",
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"timestamp": "01/13/2023 09:06:49",
"content": "that seems like sorcery to me",
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"timestamp": "01/13/2023 09:06:49",
"content": "Okay so",
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"timestamp": "01/13/2023 09:07:22",
"content": "You have 2 possible outcomes of the polynomial in terms of being odd or even powered",
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"timestamp": "01/13/2023 09:07:41",
"content": "it would have to be even, no? quadrant 1 and quadrant 2",
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"timestamp": "01/13/2023 09:07:47",
"content": "Either both ends point up or down, or one end goes up and one goes down",
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"timestamp": "01/13/2023 09:07:56",
"content": "yeah",
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"timestamp": "01/13/2023 09:07:59",
"content": "Both ends are together",
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"timestamp": "01/13/2023 09:08:03",
"content": "So it's even powered",
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"timestamp": "01/13/2023 09:08:07",
"content": "right",
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"timestamp": "01/13/2023 09:08:07",
"content": "And positive",
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"timestamp": "01/13/2023 09:08:15",
"content": "Because points up",
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"timestamp": "01/13/2023 09:08:21",
"content": "That's one rule",
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"timestamp": "01/13/2023 09:08:22",
"content": "if end behaviour was quadrant 1 and quadrant 3 it would be odd",
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"timestamp": "01/13/2023 09:08:30",
"content": "Yeah",
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"timestamp": "01/13/2023 09:08:32",
"content": "or quadrant 2 and quadrant 4 would also be odd end behavior",
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"timestamp": "01/13/2023 09:08:39",
"content": "Yeah",
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"timestamp": "01/13/2023 09:08:54",
"content": "That's for odd and even powers",
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"timestamp": "01/13/2023 09:09:04",
"content": "that part I do see, but I don't see how I can get to the exact algebra bang on just by looking at the graph",
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"timestamp": "01/13/2023 09:09:17",
"content": "You will also expect the multiplicity to match the powers",
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"timestamp": "01/13/2023 09:09:43",
"content": "Wait we'll get to the root rules",
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"timestamp": "01/13/2023 09:10:00",
"content": ",w graph x^2",
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"timestamp": "01/13/2023 09:10:02",
"content": "Results provided by WolframAlpha",
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"content": "yeah so judging by the graph it looks like it's at least power 4, at the very least",
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"content": "What do you notice about this shape?",
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"content": "Leave this for now",
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"timestamp": "01/13/2023 09:10:58",
"content": "It touches the x axis on one point right?",
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"content": "double root",
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"content": "Yeah",
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"timestamp": "01/13/2023 09:11:18",
"content": ",w graph x^3",
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"content": "Results provided by WolframAlpha",
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"timestamp": "01/13/2023 09:11:27",
"content": "Wb this?",
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"timestamp": "01/13/2023 09:11:30",
"content": "quadratic function",
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"timestamp": "01/13/2023 09:11:35",
"content": "cubic function",
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"timestamp": "01/13/2023 09:11:53",
"content": "Okay but I want you to recognize that",
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"content": "parabola",
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"timestamp": "01/13/2023 09:12:19",
"content": "When the graph has this shape, where it looks like it is barely touching the x axis, this means it is a double root",
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"content": "yeah",
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"content": "just touches x axis at one spot",
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"timestamp": "01/13/2023 09:12:39",
"content": "but both x values do",
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"timestamp": "01/13/2023 09:13:02",
"content": "When it has this shape, where it has an s-shape, you expect a triple root",
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"content": "double root: it touches the x axis twice at exactly the same spot",
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"timestamp": "01/13/2023 09:13:22",
"content": "OK",
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"timestamp": "01/13/2023 09:13:32",
"content": ",w graph x^4",
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"content": "odd end behavior",
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"content": "Results provided by WolframAlpha",
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"content": "This one looks like it is punching the x-axis",
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"timestamp": "01/13/2023 09:14:00",
"content": "Or resting on it",
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"timestamp": "01/13/2023 09:14:06",
"content": "yes, this degree 4 is more \"steep\" than degree 2",
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"timestamp": "01/13/2023 09:14:13",
"content": "Yep",
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"timestamp": "01/13/2023 09:14:13",
"content": "not sure if steep is the correct math term",
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"timestamp": "01/13/2023 09:14:21",
"content": "More \"shallow\"",
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"content": "Shallow on the x-axis",
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"content": "i've heard Professor Leonard use another word, I'm not sure if it's even a math term or one he made up",
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"timestamp": "01/13/2023 09:14:50",
"content": "What's it?",
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"timestamp": "01/13/2023 09:14:54",
"content": "higher velocity or something along those terms, lemme check",
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"content": "can't find the exact video but he may have just said rises more \"sharply\"",
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"timestamp": "01/13/2023 09:17:05",
"content": "or \"dynamic\"",
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"content": "Those all seem valid",
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"content": "anyways, the exact math term for this is prob a small detail that I won't be tested on (hopefully)",
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"timestamp": "01/13/2023 09:17:45",
"content": "Hopefully",
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"timestamp": "01/13/2023 09:17:48",
"content": "Anyways",
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"timestamp": "01/13/2023 09:17:58",
"content": "Let's apply the knowledge we gained on the polynomial",
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"timestamp": "01/13/2023 09:18:08",
"content": "OK sorry to interrupt, so we are getting at how to find the exact algebra just by looking at a graph",
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"timestamp": "01/13/2023 09:18:14",
"content": "Yeah",
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"content": "Looking at the graph, we look to the end behavior",
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"timestamp": "01/13/2023 09:18:42",
"content": "yes",
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"content": "It shows that both ends are together upwards",
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"timestamp": "01/13/2023 09:18:51",
"content": "yes",
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"timestamp": "01/13/2023 09:19:05",
"content": "even end behavior, positive multiplicity",
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"timestamp": "01/13/2023 09:19:09",
"content": "Yep",
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"timestamp": "01/13/2023 09:19:31",
"content": "Now we have roots -1, 1, and 2",
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"content": "I mean.. maybe? 2 is a bit dicey",
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"content": "could it be 2, or 1.99",
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"timestamp": "01/13/2023 09:20:18",
"content": "Well the mark is on 2",
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"content": "it is?",
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"content": "So we expect it to be 2",
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"content": "it's on a lot of the x-axis",
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"content": "oh you mean they labeled 2 on the graph?",
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"timestamp": "01/13/2023 09:20:38",
"content": "Yep",
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"content": "alright, I suppose that's a keypoint to go by",
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"content": "if it's labeled",
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"timestamp": "01/13/2023 09:20:51",
"content": "Yep",
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"timestamp": "01/13/2023 09:21:08",
"content": "i'll have to remember that",
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"timestamp": "01/13/2023 09:21:48",
"content": "We now expect our $y = a(x+1)^{m_1} (x-1)^{m_2} (x-2)^{m_3}$",
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"timestamp": "01/13/2023 09:21:50",
"content": "**VulcanOne**",
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"timestamp": "01/13/2023 09:22:10",
"content": "wait",
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"timestamp": "01/13/2023 09:22:13",
"content": "why a only once?",
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"timestamp": "01/13/2023 09:22:17",
"content": "a is a factor we will find using the y-intercept",
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"content": "how do we know that?",
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"timestamp": "01/13/2023 09:22:53",
"content": "The polynomial sometimes can be scaled by some factor when having the same roots",
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"timestamp": "01/13/2023 09:23:05",
"content": "So we find it by using the y-intercept",
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"timestamp": "01/13/2023 09:23:32",
"content": "alright, I don't quite understand but it's OK, I will continue listening, and ask questions at the end",
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"timestamp": "01/13/2023 09:23:43",
"content": "Alrighty",
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"timestamp": "01/13/2023 09:23:52",
"content": "Now let's look at each root",
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"content": "Starting with -1",
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"timestamp": "01/13/2023 09:24:11",
"content": "-1 shows an s-shape",
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"timestamp": "01/13/2023 09:24:37",
"content": "S-shape rings a bell in our mind that it is a triple root",
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"timestamp": "01/13/2023 09:25:09",
"content": "So that root is 3rd power",
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"timestamp": "01/13/2023 09:26:35",
"content": "ohh dang, it is! the algebra for this is just in the middle of the polynomial. but that's fine, due to the power of the commutative property.",
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"timestamp": "01/13/2023 09:26:54",
"content": "we also wanna order it higher power to lowest power",
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"timestamp": "01/13/2023 09:27:01",
"content": "Sure",
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"timestamp": "01/13/2023 09:27:09",
"content": "I think the first power throws me off, it doesn't meant it's the first shape on the graph",
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"timestamp": "01/13/2023 09:27:17",
"content": "but now I remember",
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"timestamp": "01/13/2023 09:27:29",
"content": "Okay",
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"timestamp": "01/13/2023 09:27:47",
"content": "(x+1)^3 is now figured",
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"timestamp": "01/13/2023 09:27:56",
"content": "interesting..",
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"timestamp": "01/13/2023 09:27:58",
"content": "Now let's move on to (x-1)",
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"timestamp": "01/13/2023 09:28:06",
"content": "https://cdn.discordapp.com/attachments/486844875632017408/1063461956788437002/Screenshot_2023-01-13_at_9.17.57_AM.png",
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"timestamp": "01/13/2023 09:28:12",
"content": "I would have said x^3 but that would be (0,0) for the x-intercept",
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"timestamp": "01/13/2023 09:28:18",
"content": "we want (-1,0) for the x-intercept",
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"timestamp": "01/13/2023 09:28:22",
"content": "so it's (x+1)^3",
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"timestamp": "01/13/2023 09:28:25",
"content": "Yep",
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"timestamp": "01/13/2023 09:28:38",
"content": "great!",
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"timestamp": "01/13/2023 09:28:41",
"content": "Now the root (x-1)",
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"timestamp": "01/13/2023 09:28:51",
"content": "It looks like it slices through it",
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"timestamp": "01/13/2023 09:29:08",
"content": "It feels like a straight line",
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"author_name": "avidrunner",
"timestamp": "01/13/2023 09:29:35",
"content": "you mean from (-1,0) to (0,-16)?",
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"timestamp": "01/13/2023 09:29:35",
"content": "What does this tell us?",
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"timestamp": "01/13/2023 09:29:50",
"content": "The root at (1,0)",
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"timestamp": "01/13/2023 09:30:05",
"content": "straight line at the root?",
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"timestamp": "01/13/2023 09:30:09",
"content": "Yeah",
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"timestamp": "01/13/2023 09:30:14",
"content": "",
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"timestamp": "01/13/2023 09:30:23",
"content": "No x=1",
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"timestamp": "01/13/2023 09:30:27",
"content": "oh",
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"timestamp": "01/13/2023 09:30:37",
"content": "We figured x=-1 already",
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"timestamp": "01/13/2023 09:30:46",
"content": "Yep",
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"timestamp": "01/13/2023 09:31:00",
"content": "this means it's a single x-intercept",
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"timestamp": "01/13/2023 09:31:03",
"content": "Yep",
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"timestamp": "01/13/2023 09:31:04",
"content": "not a double",
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"timestamp": "01/13/2023 09:31:14",
"content": "Not a double or a triple",
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"timestamp": "01/13/2023 09:31:29",
"content": "So it's (x-1)^1",
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"timestamp": "01/13/2023 09:31:34",
"content": "I haven't seen a triple x intercept before",
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"author_name": "avidrunner",
"timestamp": "01/13/2023 09:31:39",
"content": "it can happen?",
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"timestamp": "01/13/2023 09:31:43",
"content": "Yeah",
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"timestamp": "01/13/2023 09:31:51",
"content": "Look at x=-1",
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"timestamp": "01/13/2023 09:31:54",
"content": "S shape",
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"timestamp": "01/13/2023 09:32:31",
"content": "https://tenor.com/view/hhh-dx-dgeneration-x-wwf-wwe-gif-11489884",
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"id": 1063465625235755000,
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"author_name": "avidrunner",
"timestamp": "01/13/2023 09:32:43",
"content": "it can go higher than Triple X?",
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"timestamp": "01/13/2023 09:32:48",
"content": "Yeah",
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"timestamp": "01/13/2023 09:32:54",
"content": "wth lol",
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"timestamp": "01/13/2023 09:32:56",
"content": "Quadruple x",
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"timestamp": "01/13/2023 09:33:01",
"content": "never seen this before haha",
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"timestamp": "01/13/2023 09:33:15",
"content": "This one is an example",
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"timestamp": "01/13/2023 09:33:31",
"content": "oh lol.. of course",
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"timestamp": "01/13/2023 09:33:40",
"content": "quad root?",
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"timestamp": "01/13/2023 09:33:42",
"content": "Yep",
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"timestamp": "01/13/2023 09:33:55",
"content": "interesting... I thought it was still double but steeper curve",
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"timestamp": "01/13/2023 09:34:04",
"content": "good to know it's actually quad root",
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"timestamp": "01/13/2023 09:34:23",
"content": ":catthumbsup:",
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"timestamp": "01/13/2023 09:34:26",
"content": "Now",
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"timestamp": "01/13/2023 09:34:34",
"content": "We figured two roots",
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"timestamp": "01/13/2023 09:34:41",
"content": "Last root is now x=2",
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"timestamp": "01/13/2023 09:34:54",
"content": "OK",
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"timestamp": "01/13/2023 09:35:01",
"content": "https://cdn.discordapp.com/attachments/486844875632017408/1063461956788437002/Screenshot_2023-01-13_at_9.17.57_AM.png",
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"timestamp": "01/13/2023 09:35:12",
"content": "Looking at x=2",
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"timestamp": "01/13/2023 09:35:44",
"content": "It looks super shallow",
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"timestamp": "01/13/2023 09:36:01",
"content": "And has its part above the x-axis",
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"timestamp": "01/13/2023 09:36:10",
"content": "This feels like the quad root",
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"timestamp": "01/13/2023 09:36:10",
"content": "this appears to be quad root, or maybe a double root, or maybe even a 6x root, how can you tell for sure?",
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"timestamp": "01/13/2023 09:36:29",
"content": "it definitely is even but how do you know the exact amount of roots?",
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"timestamp": "01/13/2023 09:36:53",
"content": "\"feels\" may be troublesome in math haha",
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"timestamp": "01/13/2023 09:36:57",
"content": "6x is gonna behave more like a straight line going near x-axis",
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"timestamp": "01/13/2023 09:37:25",
"content": "unless there is transformation also happening?",
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"timestamp": "01/13/2023 09:37:26",
"content": "Lol in other places after school you won't be required to analyze functions this way",
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"timestamp": "01/13/2023 09:37:44",
"content": "transformation can make all of this stuff look squished or stretched",
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"timestamp": "01/13/2023 09:37:50",
"content": "to give misleading readings anyways",
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"timestamp": "01/13/2023 09:38:01",
"content": "Scaling you mean",
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"content": "anything, yeah",
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"timestamp": "01/13/2023 09:38:23",
"content": "vertical compression, vertical stretch, horizontal compression, horizontal stretch",
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"timestamp": "01/13/2023 09:38:47",
"content": "Yeah but if need be, you can always zoom on your root and analyze its behavior",
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"timestamp": "01/13/2023 09:38:56",
"content": "But for school purposes",
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"content": "You can say that max analysis will be on quad root",
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"timestamp": "01/13/2023 09:40:01",
"content": "No. We are talking about looking at a graph and being able to write the algebra perfectly every single time. I don't know if it can be done. For some simple ones yes.... And we can guess, but to know for sure... I'm just not sure",
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"timestamp": "01/13/2023 09:40:33",
"content": "Lemme demonstrate what higher powers than 4 look like",
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"timestamp": "01/13/2023 09:40:39",
"content": ",w graph x^5",
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"timestamp": "01/13/2023 09:40:41",
"content": "Results provided by WolframAlpha",
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"timestamp": "01/13/2023 09:40:57",
"content": "Looks like a triple root",
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"timestamp": "01/13/2023 09:41:03",
"content": "now take that and add vertical stretch",
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"timestamp": "01/13/2023 09:41:08",
"content": "But a bit shallower",
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"timestamp": "01/13/2023 09:41:18",
"content": ",w graph x^6",
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"timestamp": "01/13/2023 09:41:21",
"content": "Results provided by WolframAlpha",
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"timestamp": "01/13/2023 09:41:30",
"content": "Looks like a quad root",
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"timestamp": "01/13/2023 09:41:35",
"content": "Just a bit shallower",
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"timestamp": "01/13/2023 09:41:41",
"content": "again, with vertical compression it may look even more shallow",
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"timestamp": "01/13/2023 09:41:54",
"content": "The higher the powers, the straighter the end behavior will be",
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"timestamp": "01/13/2023 09:42:05",
"content": "hmmmm",
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"timestamp": "01/13/2023 09:42:12",
"content": "So for our purposes",
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"timestamp": "01/13/2023 09:42:21",
"content": "Our max is quad root",
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"timestamp": "01/13/2023 09:42:40",
"content": "We will assume single, double, triple or quad only",
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"timestamp": "01/13/2023 09:42:43",
"content": "No more than those",
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"timestamp": "01/13/2023 09:43:06",
"content": "Because visually things will get bad afterwards",
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"timestamp": "01/13/2023 09:43:23",
"content": "can you spot imaginary roots just by observing the graph?",
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"timestamp": "01/13/2023 09:43:56",
"content": "Imaginary are like real roots just shifted up or down",
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"timestamp": "01/13/2023 09:44:19",
"content": "they do not cross the x-axis",
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"timestamp": "01/13/2023 09:44:23",
"content": "True",
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"timestamp": "01/13/2023 09:44:42",
"content": "But if you shifted the x-axis upwards or downwards then it will cross it",
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"timestamp": "01/13/2023 09:45:08",
"content": "And imaginary roots can only be found in a quadratic parenthesis",
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"timestamp": "01/13/2023 09:45:32",
"content": "how so?",
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"timestamp": "01/13/2023 09:45:43",
"content": "Like x^2 + 100",
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"timestamp": "01/13/2023 09:46:04",
"content": "Or x^2 +x+1",
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"timestamp": "01/13/2023 09:46:21",
"content": "You will not find them like roots with imaginary numbers",
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"timestamp": "01/13/2023 09:46:42",
"content": "Or else you will have to use complex plane",
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"timestamp": "01/13/2023 09:46:58",
"content": "OK",
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"timestamp": "01/13/2023 09:47:19",
"content": "Again, for our purposes, your school won't give you an imaginary root and tell you to know where it goes",
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"timestamp": "01/13/2023 09:47:34",
"content": "lol hopefully not",
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"timestamp": "01/13/2023 09:47:46",
"content": "Anyways",
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"timestamp": "01/13/2023 09:47:46",
"content": "the professor said Calculus at university is higher level than Calculus at college",
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"timestamp": "01/13/2023 09:48:00",
"content": "Yep",
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"timestamp": "01/13/2023 09:48:33",
"content": "you can flip a quadratic and the flipped quadratic will have roots as shown in the pic, note sure if this goes for any degree polynomial tho",
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"timestamp": "01/13/2023 09:49:01",
"content": "Hmm",
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"timestamp": "01/13/2023 09:49:19",
"content": "so -b/2a finds the axis of symmetry",
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"timestamp": "01/13/2023 09:49:23",
"content": "Ye",
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"timestamp": "01/13/2023 09:49:31",
"content": "and the only thing different is the letter i added in front of the radical",
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"timestamp": "01/13/2023 09:49:37",
"content": "Yep",
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"timestamp": "01/13/2023 09:49:41",
"content": "this will work to find imaginary roots??",
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"timestamp": "01/13/2023 09:49:49",
"content": "Yeah",
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"timestamp": "01/13/2023 09:49:55",
"content": "so for example $x^2+1$ flipped is $-x^2+1$ so it will have imaginary roots $$x=\\pm\\frac{i\\sqrt{0+4}}{2}=i$$",
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"timestamp": "01/13/2023 09:49:57",
"content": "**Duh Hello**",
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"timestamp": "01/13/2023 09:50:24",
"content": "x^2 + x +1?",
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"timestamp": "01/13/2023 09:50:29",
"content": "an interesting visualization of it",
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"timestamp": "01/13/2023 09:50:43",
"content": "you change the sign of everything that contains x",
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"timestamp": "01/13/2023 09:50:50",
"content": "Okay",
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"timestamp": "01/13/2023 09:50:55",
"content": "so $x^2+x+1$ becomes $-x^2-x+1$",
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"timestamp": "01/13/2023 09:50:57",
"content": "**Duh Hello**",
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"timestamp": "01/13/2023 09:51:09",
"content": ":noted:",
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"timestamp": "01/13/2023 09:51:13",
"content": "lol.. who in the hell figured this out",
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"timestamp": "01/13/2023 09:51:28",
"content": "i just found some random article about it since i was curious lol https://digitalcommons.unl.edu/cgi/viewcontent.cgi?article=1034&context=mathmidexppap",
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"timestamp": "01/13/2023 09:51:34",
"content": "very easy read",
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"timestamp": "01/13/2023 09:51:49",
"content": "Thank you for this",
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"timestamp": "01/13/2023 09:51:50",
"content": "they only mention quadratics tho, was hoping they would generalize it",
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"timestamp": "01/13/2023 09:53:48",
"content": "Hopefully in the future we will find a generalized way to find roots",
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"timestamp": "01/13/2023 09:53:57",
"content": "For imaginary and real roots",
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"timestamp": "01/13/2023 09:53:59",
"content": "Anyways",
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"timestamp": "01/13/2023 09:54:02",
"content": "@avidrunner",
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"timestamp": "01/13/2023 09:54:09",
"content": "https://tenor.com/view/math-school-gif-23547212",
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"timestamp": "01/13/2023 09:54:25",
"content": "We found the multiplicity for all the 3 roots",
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"timestamp": "01/13/2023 09:54:28",
"content": "Right?",
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"timestamp": "01/13/2023 09:54:34",
"content": "haha always and forever, but as long as I am learning...",
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"content": "๐",
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"timestamp": "01/13/2023 09:55:14",
"content": "$y=a(x-2)^4 (x+1)^3 (x-1)$",
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"timestamp": "01/13/2023 09:55:17",
"content": "**VulcanOne**",
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"content": "We found all of the multiplicities",
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"content": "Now the last thing is the scale factor a",
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"timestamp": "01/13/2023 09:55:47",
"content": "that checks out, but in this case there is no \"a\" at all",
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"timestamp": "01/13/2023 09:55:48",
"content": "Ye",
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"content": "We have a y-intercept y=-16",
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"content": "This gives us an equation",
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"content": "At x=0, y=-16",
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"timestamp": "01/13/2023 09:56:29",
"content": "Plug",
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"timestamp": "01/13/2023 09:56:48",
"content": "$-16=a(0-2)^4 (0+1)^3 (0-1)$",
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"content": "2^4 = 16 and 1 to any power is 1",
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"timestamp": "01/13/2023 09:58:05",
"content": "amazing!",
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"content": "**VulcanOne**",
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"content": "-16 = -16a",
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"content": "a=1",
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"timestamp": "01/13/2023 09:59:06",
"content": "lol",
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"content": "it's so simple",
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"timestamp": "01/13/2023 09:59:20",
"content": "it's just remembering the rules to follow",
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"timestamp": "01/13/2023 09:59:27",
"content": "Yep",
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"timestamp": "01/13/2023 09:59:35",
"content": "Some practice will help",
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"timestamp": "01/13/2023 09:59:37",
"content": "the algebra kinda does the work for you",
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"content": ":librasmile:",
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"timestamp": "01/13/2023 09:59:43",
"content": "Exactly",
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"timestamp": "01/13/2023 09:59:45",
"content": "Also",
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"author_name": "VulcanOne",
"timestamp": "01/13/2023 09:59:56",
"content": "My professor taught us in an intuitive manner",
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"author_name": "VulcanOne",
"timestamp": "01/13/2023 10:00:27",
"content": "And told us that we won't be doing more than single, double, triple or quad roots by just looking",
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"timestamp": "01/13/2023 10:00:44",
"content": "Ah OK",
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"author_name": "VulcanOne",
"timestamp": "01/13/2023 10:00:44",
"content": "So yeee",
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"author_name": "avidrunner",
"timestamp": "01/13/2023 10:01:22",
"content": "So some key takeaways: I need to remember that the algebra for the polynomial does not need to be in the same order as the shapes and curves on the graph",
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"timestamp": "01/13/2023 10:01:37",
"content": "Yep",
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"id": 1063473171472322700,
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"author_name": "avidrunner",
"timestamp": "01/13/2023 10:02:42",
"content": "when I see (x-2)^3 in a polynomial, that tells me the x intercept is at x=2 and it will have odd end behavior",
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"timestamp": "01/13/2023 10:03:07",
"content": "but combined with everything else there may be transformations or flipping at play",
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"timestamp": "01/13/2023 10:04:00",
"content": "so I need to take everything into account, not just say blindly that (x-2)^3 will always show up on any graph with end behavior in quadrant 1 and quadrant 3 without looking at the rest of the polynomial too. in particular, is there an \"a\"",
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"timestamp": "01/13/2023 10:04:39",
"content": "Yep",
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"timestamp": "01/13/2023 10:05:03",
"content": "I made 3 versions which helps me to understand vertical transformations with \"a\"",
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"content": "https://www.desmos.com/calculator/vg3hequrrs",
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"timestamp": "01/13/2023 10:05:49",
"content": "Woah that's cool",
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"content": "https://tenor.com/view/pretty-cool-awesome-amazing-great-well-done-gif-20618877",
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"content": ":woah:",
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"timestamp": "01/13/2023 10:07:01",
"content": "thanks for the help @VulcanOne !",
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"timestamp": "01/13/2023 10:07:11",
"content": "Glad to help :)",
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] | help-9 | bc430551d3724992b808d56b1f975950 |
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"content": "you cant \"replace\" asymptotic equivalents like this",
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"content": "essentially you have $\\frac{x^2+1}{x+1} = x + e(x)$ with $lim(e(x)/x) = 0$ or $e(x) = o(x)$",
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"content": "**Benjamin**",
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"content": "but since when you take a=1",
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"content": "the x term will cancel out",
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"content": "you'll be left with",
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"content": "e(x) - b",
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"content": "but e(x) is not necessarely going to 0",
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"content": "so you have to make b cancel out with e(x)",
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"content": "Channel closed",
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}
] | help-9 | ebce9a0bdbf24de7a35819c1c685933d |
200,729 | [
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"author_id": 769235990328901800,
"author_name": "Bakajal",
"timestamp": "01/13/2023 10:43:48",
"content": "What are asymptotic equivalents?",
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"id": 1063487969543061600,
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"author_name": "avidrunner",
"timestamp": "01/13/2023 11:01:30",
"content": "How do you get from top line to bottom line?",
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"content": "Pinned a message.",
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"author_name": "avidrunner",
"timestamp": "01/13/2023 11:03:30",
"content": "this is according to Wolfram Alpha, how to simplify",
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"content": "and I don't understand the last line, how it can get there",
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"timestamp": "01/13/2023 11:04:30",
"content": "it feels like we are changing the denominators for each term we are subtracting",
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"timestamp": "01/13/2023 11:04:53",
"content": "and somehow we get to this",
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"timestamp": "01/13/2023 11:05:06",
"content": "the asymptote",
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"timestamp": "01/13/2023 11:06:03",
"content": "where did the 115, 8, 49 come from?",
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"timestamp": "01/13/2023 11:21:03",
"content": "@avidrunner Has your question been resolved?",
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"content": "Channel closed",
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] | help-9 | b9f70eba096546589c54215053a71ec4 |
200,730 | [
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"content": "Available help channel!",
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"timestamp": "01/13/2023 11:39:27",
"content": "can someone please explain this question",
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"content": ":hmmCat:",
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"timestamp": "01/13/2023 11:50:29",
"content": "nvm i got it ๐",
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"author_name": "โฐ. fir3",
"timestamp": "01/13/2023 11:50:31",
"content": ".close",
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"content": "Channel closed",
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] | help-9 | 19dd067e30cb45ee82b093130fa88a58 |
200,731 | [
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"author_name": "-Zednar",
"timestamp": "10/21/2022 17:32:23",
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"content": "@-Zednar Has your question been resolved?",
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] | help-9 | b953010441cf487ab7e5f49f2f4366d4 |
200,732 | [
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"id": 1035464199654096900,
"author_id": 409449546637377540,
"author_name": "Chep",
"timestamp": "10/28/2022 04:05:03",
"content": "i need some help with python and a graph plot, if anyone has used matplotlib before and can help, let me know",
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] | help-9 | ecfc5de428084608ae413fb08ffaea51 |
200,733 | [
{
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"id": 1063508419748827100,
"author_id": 290178138640613400,
"author_name": "elasmoterium",
"timestamp": "01/13/2023 12:22:46",
"content": "hello i need to prove that composition of function is a function, i did it, just want somebody to check",
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"timestamp": "01/13/2023 12:23:04",
"content": "send it here",
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"author_name": "SilverSoldier",
"timestamp": "01/13/2023 12:25:37",
"content": "what u want to show is that for every c there is an a",
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"author_id": 811501664367673300,
"author_name": "SilverSoldier",
"timestamp": "01/13/2023 12:25:45",
"content": "not that for every a there is a c",
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"author_name": "SilverSoldier",
"timestamp": "01/13/2023 12:26:08",
"content": "r u trying to show this function is bijective?",
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"id": 1063509459210620900,
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"author_name": "SilverSoldier",
"timestamp": "01/13/2023 12:26:54",
"content": "like u r trying to show that the compsition of two bijective functions is also bijevtive",
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"content": "no no i just want to prove that the composition is a function",
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"timestamp": "01/13/2023 12:29:40",
"content": "uh wait what i did",
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"author_name": "elasmoterium",
"timestamp": "01/13/2023 12:30:42",
"content": "nvm i think its correct but idk",
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"author_name": "SilverSoldier",
"timestamp": "01/13/2023 12:30:49",
"content": "if f is a function then it need not be the case that f(a1) = f(a2) implies a1 = a2",
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"id": 1063510610249257000,
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"author_name": "SilverSoldier",
"timestamp": "01/13/2023 12:31:28",
"content": "or that for all b in B there exists a in A such that f(a) = b",
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"timestamp": "01/13/2023 12:31:36",
"content": "this is also not necessary if f is just a function",
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"timestamp": "01/13/2023 12:31:59",
"content": "there are functions where only one of these things holds, and also functions where neither one of these two things hold",
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"author_name": "elasmoterium",
"timestamp": "01/13/2023 12:33:05",
"content": "in my notes i have two conditions for function and one is that every x have only one y",
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"timestamp": "01/13/2023 12:33:33",
"content": "yes",
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"timestamp": "01/13/2023 12:33:42",
"content": "and i think its that think isn't it?",
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"timestamp": "01/13/2023 12:34:02",
"content": "no, every x has only one y doesnt mean that different x's cant have the same y",
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"timestamp": "01/13/2023 12:34:17",
"content": "maybe x = 1 has y = 5, and x = 2 also has y = 5",
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"timestamp": "01/13/2023 12:34:32",
"content": "so x=1 has y=5, and thats only one value of y for x = 1",
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"timestamp": "01/13/2023 12:35:04",
"content": "its not like when x = 1, y can be either 5 or 10 or something else",
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"timestamp": "01/13/2023 12:35:07",
"content": "for example y = x^2",
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"author_name": "elasmoterium",
"timestamp": "01/13/2023 12:36:57",
"content": "yee i see it, it would be condition for injection then but",
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"timestamp": "01/13/2023 12:37:26",
"content": "did i use it?",
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"timestamp": "01/13/2023 12:37:46",
"content": "i cant find it",
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"author_name": "elasmoterium",
"timestamp": "01/13/2023 12:38:16",
"content": "i was using a1=a2=>f(a1)=f(a2)",
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"timestamp": "01/13/2023 12:38:22",
"content": "i think its not the same",
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"timestamp": "01/13/2023 12:49:18",
"content": "ah yes sorry i didnt notice that",
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"timestamp": "01/13/2023 12:49:25",
"content": "it is not the same",
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"id": 1063516359922819100,
"author_id": 290178138640613400,
"author_name": "elasmoterium",
"timestamp": "01/13/2023 12:54:19",
"content": "but now im wondering if i use right condition",
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"content": "is it the same thing",
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"timestamp": "01/13/2023 12:56:14",
"content": "also that i didnt use it here",
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"content": "yeah sorry i just saw that and i assumed u did the injectivity surjectivity thing",
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"timestamp": "01/13/2023 13:11:26",
"content": "@elasmoterium Has your question been resolved?",
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"content": "@elasmoterium Has your question been resolved?",
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"timestamp": "01/13/2023 13:45:39",
"content": "What is question?",
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"timestamp": "01/13/2023 13:46:09",
"content": "@elasmoterium",
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"timestamp": "01/13/2023 13:46:43",
"content": "prove that composition of functions is a function",
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"author_name": "!๐๐ช๐ฝ๐ฑ๐ถ๐ฎ๐ฝ๐ฒ๐ฌ๐ผ-๐ฎ๐น๐ฒ๐ฌ!",
"timestamp": "01/13/2023 13:46:51",
"content": "https://giphy.com/gifs/nehumanesociety-funny-dog-3o7527pa7qs9kCG78A",
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"author_name": "elasmoterium",
"timestamp": "01/13/2023 13:47:42",
"content": "u know that thing f function and g function and u need show that g(f(x)) is also a function",
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"timestamp": "01/13/2023 14:29:28",
"content": "@Helpers ๐ ๐",
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"author_name": "Heleyrine",
"timestamp": "01/13/2023 15:15:33",
"content": "Assume x_1 = x_2. Since f is a function, then f(x_1) = f(x_2). \nThink of f(x_1) as y_1 and think of f(x_2) as y_2. \nThen since g is a function, assuming f's Range is a subset of g's Domain, then g(y_1) = g(y_2). Then g(f(x_1) = g(f(x_2)) and the theorem is proven.",
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"timestamp": "01/13/2023 15:19:50",
"content": "yea thank u but is my way to do it wrong?",
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"timestamp": "01/13/2023 15:20:06",
"content": "its here",
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"author_name": "Heleyrine",
"timestamp": "01/13/2023 15:22:42",
"content": "Oh, usually we define gof as the basis definition of composition and then prove that it is indeed equal to g(f(x)), as working with gof is a tad more complicated. It seems you've approached it from the other way around.",
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"timestamp": "01/13/2023 15:24:15",
"content": "If you already know that gof is a function and your assumption is that g(f(x)) is equal to it, then g(f(x)) by equality would also be a function",
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"author_name": "elasmoterium",
"timestamp": "01/13/2023 15:24:43",
"content": "no no i dont know if gof is a function",
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"author_name": "elasmoterium",
"timestamp": "01/13/2023 15:24:48",
"content": "i want to prove that",
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"author_name": "elasmoterium",
"timestamp": "01/13/2023 15:25:05",
"content": "i know only that g is function and f is function",
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"timestamp": "01/13/2023 15:25:24",
"content": "and gof=g(f(x))",
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"timestamp": "01/13/2023 15:26:03",
"content": "teacher said that is no need to prove that so i just use it as synonims",
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"timestamp": "01/13/2023 15:29:02",
"content": "Oh, I understand now. I'm sorry.\nWell, your aim was to show through the fact that gof is a function, and g(f(x)) is equal to it, then g(f(x)) is a function. Am I correct?",
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"timestamp": "01/13/2023 15:30:17",
"content": "no no",
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"timestamp": "01/13/2023 15:30:27",
"content": "we want to show that gof is function",
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"author_name": "elasmoterium",
"timestamp": "01/13/2023 15:30:40",
"content": "we know that f is function and g is function",
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"author_name": "elasmoterium",
"timestamp": "01/13/2023 15:30:54",
"content": "and we also know gof=g(f(x))",
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"timestamp": "01/13/2023 15:31:47",
"content": "Aha, but you wrote you want to show that g(f(x)) is a function here?",
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"timestamp": "01/13/2023 15:32:19",
"content": "yea because i thought its the same as gof",
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"timestamp": "01/13/2023 15:32:57",
"content": "i was told the definition of composition of function is gof=g(f(x))",
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"timestamp": "01/13/2023 15:33:18",
"content": "and now i want to prove that that composition is also a function",
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"timestamp": "01/13/2023 15:44:23",
"content": "Well, not exactly. I may be missing on a detail, but usually gof is defined as a general relation not a function, which then is proven to be a function when both f and g are functions.",
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"content": "yea and this is literally what i need to prove",
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"content": "I'm not sure how your teacher approached the subject; but sure, if they are assumed to be equal, you already proved that g(f(x)) is a function in your first paragraph. \nThe second one seems to be rather a repetition of the first? Am I missing something?",
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"timestamp": "01/13/2023 15:47:05",
"content": "hm i was told that there are two conditions for relation to be a function",
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"timestamp": "01/13/2023 15:47:18",
"content": "wait i will show u them",
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"timestamp": "01/13/2023 15:48:06",
"content": "and first i wanted to prove first one and then the second one",
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"timestamp": "01/13/2023 15:48:55",
"content": "first one that for every x there is y that f(x)=y and then that every x have no more than one y that f(x)=y",
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"timestamp": "01/13/2023 15:50:27",
"content": "Right. You showed that A is equal to the Domain and then proved the thing I wrote above.\nI understand. I think the rigor of your writing is pretty good! You did very well. I'm sorry for not being too helpful, It is a tad bit late here.",
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"timestamp": "01/13/2023 15:52:23",
"content": "thank u very much",
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"timestamp": "01/13/2023 15:52:31",
"content": ".close",
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"author_name": "Mathematics Bot",
"timestamp": "01/13/2023 15:52:32",
"content": "Channel closed",
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] | help-9 | 1331817b65ab402c8ecd89a91a8ec9dc |
200,734 | [
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"content": "Available help channel!",
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"content": "Pinned a message.",
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"timestamp": "01/13/2023 16:22:29",
"content": "why does 1 lose its square root",
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"id": 1063568754295980200,
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"timestamp": "01/13/2023 16:22:31",
"content": "but 2 does not",
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"id": 1063568905060229100,
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"timestamp": "01/13/2023 16:23:07",
"content": ",calc sqrt(1)",
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"id": 1063568906867974300,
"author_id": 510789298321096700,
"author_name": "TeXit",
"timestamp": "01/13/2023 16:23:07",
"content": "Result:\n```\n1\n```",
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"timestamp": "01/13/2023 16:23:20",
"content": ",calc sqrt(2)",
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"timestamp": "01/13/2023 16:23:20",
"content": "Result:\n```\n1.4142135623731\n```",
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"timestamp": "01/13/2023 16:24:08",
"content": "so because 2 doesnt have a whole square root",
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"id": 1063569169389473800,
"author_id": 236252356553998340,
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"timestamp": "01/13/2023 16:24:10",
"content": "it doesnt break down?",
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"id": 1063569294354550900,
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"author_name": "etics",
"timestamp": "01/13/2023 16:24:39",
"content": "1 x 1 = 1",
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"id": 1063569324532572200,
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"content": "1^2 = 1",
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"id": 1063569426420605000,
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"author_name": "etics",
"timestamp": "01/13/2023 16:25:11",
"content": "thus โ1",
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"id": 1063569450214895700,
"author_id": 565459730458345500,
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"timestamp": "01/13/2023 16:25:17",
"content": "= 1",
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"id": 1063569968236593300,
"author_id": 236252356553998340,
"author_name": "Goldi",
"timestamp": "01/13/2023 16:27:20",
"content": "ok so just to double check",
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"timestamp": "01/13/2023 16:27:30",
"content": "square roots dont break down if it doesnt have a whole number to break down into",
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"timestamp": "01/13/2023 16:27:43",
"content": "so say for eample",
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"timestamp": "01/13/2023 16:27:45",
"content": "it was",
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"author_name": "Goldi",
"timestamp": "01/13/2023 16:27:50",
"content": "2 sqrt over 1 sqrt",
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"id": 1063570114135470100,
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"timestamp": "01/13/2023 16:27:55",
"content": "would 1 being the denominator still break down",
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"id": 1063570125250371600,
"author_id": 236252356553998340,
"author_name": "Goldi",
"timestamp": "01/13/2023 16:27:58",
"content": "while 2 remains?",
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"id": 1063570151376695400,
"author_id": 236252356553998340,
"author_name": "Goldi",
"timestamp": "01/13/2023 16:28:04",
"content": "to become \n2 sqrt over 1?",
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"id": 1063570207274176500,
"author_id": 788085606483361800,
"author_name": "chartbit",
"timestamp": "01/13/2023 16:28:17",
"content": "As in $\\frac{\\sqrt{2}}{\\sqrt{1}}$?",
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"id": 1063570218628153300,
"author_id": 510789298321096700,
"author_name": "TeXit",
"timestamp": "01/13/2023 16:28:20",
"content": "**chartbit**",
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"id": 1063570228476387300,
"author_id": 236252356553998340,
"author_name": "Goldi",
"timestamp": "01/13/2023 16:28:22",
"content": "yes",
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},
{
"id": 1063570314858070100,
"author_id": 788085606483361800,
"author_name": "chartbit",
"timestamp": "01/13/2023 16:28:43",
"content": "Yep you know $\\sqrt{1} = 1$ so you convert it",
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},
{
"id": 1063570324299456600,
"author_id": 510789298321096700,
"author_name": "TeXit",
"timestamp": "01/13/2023 16:28:45",
"content": "**chartbit**",
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"id": 1063570460777922600,
"author_id": 236252356553998340,
"author_name": "Goldi",
"timestamp": "01/13/2023 16:29:18",
"content": "hmmmm gosh darn trig",
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},
{
"id": 1063570467950178400,
"author_id": 788085606483361800,
"author_name": "chartbit",
"timestamp": "01/13/2023 16:29:19",
"content": "Similar with e.g. $\\sqrt{4} = 2$",
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},
{
"id": 1063570476586246300,
"author_id": 510789298321096700,
"author_name": "TeXit",
"timestamp": "01/13/2023 16:29:21",
"content": "**chartbit**",
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"id": 1063570512246223000,
"author_id": 236252356553998340,
"author_name": "Goldi",
"timestamp": "01/13/2023 16:29:30",
"content": "gonna blow my brain up",
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},
{
"id": 1063570586724479100,
"author_id": 236252356553998340,
"author_name": "Goldi",
"timestamp": "01/13/2023 16:29:48",
"content": "have to learn precalc in less than a month",
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},
{
"id": 1063570607700181100,
"author_id": 236252356553998340,
"author_name": "Goldi",
"timestamp": "01/13/2023 16:29:53",
"content": "AHHHHHHHH",
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},
{
"id": 1063570628084502700,
"author_id": 236252356553998340,
"author_name": "Goldi",
"timestamp": "01/13/2023 16:29:57",
"content": "thank u for your time",
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},
{
"id": 1063570707386224800,
"author_id": 236252356553998340,
"author_name": "Goldi",
"timestamp": "01/13/2023 16:30:16",
"content": ".close",
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},
{
"id": 1063570709915381900,
"author_id": 805217272087838700,
"author_name": "Mathematics Bot",
"timestamp": "01/13/2023 16:30:17",
"content": "Channel closed",
"attachments": [],
"mentions": [],
"reference": null
}
] | help-9 | 8fb5bc025c9b45179cee9a3ca82170fe |
200,735 | [
{
"id": 1063571249797812200,
"author_id": 805217272087838700,
"author_name": "Mathematics Bot",
"timestamp": "01/13/2023 16:32:26",
"content": "Available help channel!",
"attachments": [],
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"reference": null
},
{
"id": 1063572007435903000,
"author_id": 805217272087838700,
"author_name": "Mathematics Bot",
"timestamp": "01/13/2023 16:35:26",
"content": "Pinned a message.",
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"reference": {
"messageId": 1063572001358352500,
"channelId": 486844875632017400,
"guildId": null
}
},
{
"id": 1063572206279458800,
"author_id": 600510288067952600,
"author_name": "GarlicBredFries",
"timestamp": "01/13/2023 16:36:14",
"content": "if it is coninuous, then the limit from both sides are equal",
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},
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"id": 1063572722824782000,
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"author_name": "GarlicBredFries",
"timestamp": "01/13/2023 16:38:25",
"content": "i forgot the equal but you get the point",
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{
"id": 1063572790294351900,
"author_id": 600510288067952600,
"author_name": "GarlicBredFries",
"timestamp": "01/13/2023 16:38:33",
"content": "put the condition in curly braces",
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"reference": null
},
{
"id": 1063572978694115500,
"author_id": 805217272087838700,
"author_name": "Mathematics Bot",
"timestamp": "01/13/2023 16:39:18",
"content": "Channel closed",
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}
] | help-9 | 7a5bdd1aacf14b4a975c0ec2591d524d |
200,736 | [
{
"id": 1063574532323033200,
"author_id": 805217272087838700,
"author_name": "Mathematics Bot",
"timestamp": "01/13/2023 16:45:28",
"content": "Available help channel!",
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"reference": null
},
{
"id": 1063574900218007700,
"author_id": 298282589247111200,
"author_name": "PopFarts",
"timestamp": "01/13/2023 16:46:56",
"content": "Is there a problem with my book or is my brain just broke?",
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"timestamp": "01/13/2023 16:46:57",
"content": "Pinned a message.",
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"author_id": 600510288067952600,
"author_name": "GarlicBredFries",
"timestamp": "01/13/2023 16:47:22",
"content": "thats correct",
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},
{
"id": 1063575044292350000,
"author_id": 600510288067952600,
"author_name": "GarlicBredFries",
"timestamp": "01/13/2023 16:47:30",
"content": "OH WAIT",
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},
{
"id": 1063575115385798700,
"author_id": 600510288067952600,
"author_name": "GarlicBredFries",
"timestamp": "01/13/2023 16:47:47",
"content": "yeah the + and - are switched",
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},
{
"id": 1063575154099245200,
"author_id": 600510288067952600,
"author_name": "GarlicBredFries",
"timestamp": "01/13/2023 16:47:57",
"content": "oh wait no",
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},
{
"id": 1063575174156406800,
"author_id": 298282589247111200,
"author_name": "PopFarts",
"timestamp": "01/13/2023 16:48:01",
"content": "See that's what I thought I'm sitting there solving this problem and it keeps telling me I'm wrong",
"attachments": [],
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"reference": null
},
{
"id": 1063575227172393000,
"author_id": 298282589247111200,
"author_name": "PopFarts",
"timestamp": "01/13/2023 16:48:14",
"content": "Okay now I'm confused again very confused now",
"attachments": [],
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"reference": null
},
{
"id": 1063575294545514500,
"author_id": 600510288067952600,
"author_name": "GarlicBredFries",
"timestamp": "01/13/2023 16:48:30",
"content": "using FOIL, the factoring checks out",
"attachments": [],
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},
{
"id": 1063575456852480100,
"author_id": 298282589247111200,
"author_name": "PopFarts",
"timestamp": "01/13/2023 16:49:09",
"content": "It seems like -3x + 2x would be a negative x",
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},
{
"id": 1063575595474223100,
"author_id": 424654701909377000,
"author_name": "Spreeter",
"timestamp": "01/13/2023 16:49:42",
"content": "whats the problem here",
"attachments": [],
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},
{
"id": 1063575690215182300,
"author_id": 600510288067952600,
"author_name": "GarlicBredFries",
"timestamp": "01/13/2023 16:50:04",
"content": "no, there is a +2(2x)",
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},
{
"id": 1063575719319437400,
"author_id": 600510288067952600,
"author_name": "GarlicBredFries",
"timestamp": "01/13/2023 16:50:11",
"content": "so that makes +4x",
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},
{
"id": 1063575826597155000,
"author_id": 298282589247111200,
"author_name": "PopFarts",
"timestamp": "01/13/2023 16:50:37",
"content": "I got you thank you my brain was broken",
"attachments": [],
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},
{
"id": 1063575980008030300,
"author_id": 298282589247111200,
"author_name": "PopFarts",
"timestamp": "01/13/2023 16:51:13",
"content": "Do I need to do anything to free up the channel?",
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},
{
"id": 1063576166256095200,
"author_id": 600510288067952600,
"author_name": "GarlicBredFries",
"timestamp": "01/13/2023 16:51:58",
"content": "use .close",
"attachments": [],
"mentions": [],
"reference": null
},
{
"id": 1063576196530585600,
"author_id": 298282589247111200,
"author_name": "PopFarts",
"timestamp": "01/13/2023 16:52:05",
"content": "Thanks again",
"attachments": [],
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"reference": null
},
{
"id": 1063576209662955500,
"author_id": 298282589247111200,
"author_name": "PopFarts",
"timestamp": "01/13/2023 16:52:08",
"content": ". Close",
"attachments": [],
"mentions": [],
"reference": null
},
{
"id": 1063576226389827600,
"author_id": 600510288067952600,
"author_name": "GarlicBredFries",
"timestamp": "01/13/2023 16:52:12",
"content": "no space",
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},
{
"id": 1063576240591732900,
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"author_name": "PopFarts",
"timestamp": "01/13/2023 16:52:16",
"content": ".close",
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"reference": null
},
{
"id": 1063576244265959600,
"author_id": 805217272087838700,
"author_name": "Mathematics Bot",
"timestamp": "01/13/2023 16:52:16",
"content": "Channel closed",
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}
] | help-9 | 81991c402f1644dbac56936e2ffa7534 |
200,737 | [
{
"id": 1063577428796129300,
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"author_name": "Mathematics Bot",
"timestamp": "01/13/2023 16:56:59",
"content": "Available help channel!",
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},
{
"id": 1063577924336365600,
"author_id": 846868140272123900,
"author_name": "PM",
"timestamp": "01/13/2023 16:58:57",
"content": "Not so sure hot to answer this question.",
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"timestamp": "01/13/2023 16:58:58",
"content": "Pinned a message.",
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"id": 1063578403044864000,
"author_id": 1000057838007226500,
"author_name": "VulcanOne",
"timestamp": "01/13/2023 17:00:51",
"content": "It asks you to calculate the mean, median, mode without removing outliers",
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},
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"id": 1063578460632657900,
"author_id": 1000057838007226500,
"author_name": "VulcanOne",
"timestamp": "01/13/2023 17:01:05",
"content": "Then it asks you to remove the outliers and calculate mean and median",
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"id": 1063578566870179800,
"author_id": 1000057838007226500,
"author_name": "VulcanOne",
"timestamp": "01/13/2023 17:01:30",
"content": "And see which one of those 5 calculations gives the highest number",
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"id": 1063579595653255200,
"author_id": 846868140272123900,
"author_name": "PM",
"timestamp": "01/13/2023 17:05:35",
"content": "Thank you!",
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},
{
"id": 1063579599583326300,
"author_id": 846868140272123900,
"author_name": "PM",
"timestamp": "01/13/2023 17:05:36",
"content": ".close",
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{
"id": 1063579602464800800,
"author_id": 805217272087838700,
"author_name": "Mathematics Bot",
"timestamp": "01/13/2023 17:05:37",
"content": "Channel closed",
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}
] | help-9 | 523e5c87aa8b41a98a24cbe4ec4f8d61 |
200,738 | [
{
"id": 1063580453342298100,
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"author_name": "Mathematics Bot",
"timestamp": "01/13/2023 17:09:00",
"content": "Available help channel!",
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},
{
"id": 1063580674486964200,
"author_id": 405495558170738700,
"author_name": "Ragi",
"timestamp": "01/13/2023 17:09:53",
"content": "hi i was wondering how i can find combinations of ten people sitting in a row of ten seats is",
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{
"id": 1063580679838892200,
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"timestamp": "01/13/2023 17:09:54",
"content": "Pinned a message.",
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"id": 1063580994743046300,
"author_id": 598041720583618600,
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"timestamp": "01/13/2023 17:11:09",
"content": "that isn't a combination",
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"id": 1063581038892294100,
"author_id": 1000057838007226500,
"author_name": "VulcanOne",
"timestamp": "01/13/2023 17:11:20",
"content": "Permutation",
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},
{
"id": 1063581063584153600,
"author_id": 1000057838007226500,
"author_name": "VulcanOne",
"timestamp": "01/13/2023 17:11:25",
"content": "Also",
"attachments": [],
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},
{
"id": 1063581095959994400,
"author_id": 1000057838007226500,
"author_name": "VulcanOne",
"timestamp": "01/13/2023 17:11:33",
"content": "10 seats for 10 people",
"attachments": [],
"mentions": [],
"reference": null
},
{
"id": 1063581116730200000,
"author_id": 598041720583618600,
"author_name": "Disorganized",
"timestamp": "01/13/2023 17:11:38",
"content": "How many ways to seat the first person?",
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},
{
"id": 1063581148556562600,
"author_id": 598041720583618600,
"author_name": "Disorganized",
"timestamp": "01/13/2023 17:11:46",
"content": "@Ragi",
"attachments": [],
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},
{
"id": 1063581217947136000,
"author_id": 598041720583618600,
"author_name": "Disorganized",
"timestamp": "01/13/2023 17:12:02",
"content": "in an empty row of 10 seats",
"attachments": [],
"mentions": [],
"reference": null
},
{
"id": 1063581289799745700,
"author_id": 405495558170738700,
"author_name": "Ragi",
"timestamp": "01/13/2023 17:12:19",
"content": "The ten Asian American/Pacific Islander women (from all parties) want a group photo of themselves in the U.S. Capital building. If there are ten chairs lined up in a row in the Capital for the photo, how many different ways can the women be seated?",
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{
"id": 1063581372284936200,
"author_id": 405495558170738700,
"author_name": "Ragi",
"timestamp": "01/13/2023 17:12:39",
"content": "this was the question i wasn't told about permutation in class, i think it might be on the lecture next week",
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"id": 1063581518766813200,
"author_id": 598041720583618600,
"author_name": "Disorganized",
"timestamp": "01/13/2023 17:13:14",
"content": "@Ragi I don't think this more precise question has changed the problem",
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"id": 1063581565013209100,
"author_id": 598041720583618600,
"author_name": "Disorganized",
"timestamp": "01/13/2023 17:13:25",
"content": "you have 10 distinguishable people",
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},
{
"id": 1063581584470577300,
"author_id": 405495558170738700,
"author_name": "Ragi",
"timestamp": "01/13/2023 17:13:30",
"content": "yes",
"attachments": [],
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},
{
"id": 1063581593643532400,
"author_id": 598041720583618600,
"author_name": "Disorganized",
"timestamp": "01/13/2023 17:13:32",
"content": "who must be seated among 10 spots",
"attachments": [],
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},
{
"id": 1063581639508250600,
"author_id": 598041720583618600,
"author_name": "Disorganized",
"timestamp": "01/13/2023 17:13:43",
"content": "count the number of ways the FIRST person can be seated.",
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"id": 1063581659552825300,
"author_id": 405495558170738700,
"author_name": "Ragi",
"timestamp": "01/13/2023 17:13:48",
"content": "10",
"attachments": [],
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},
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"id": 1063581699373547500,
"author_id": 598041720583618600,
"author_name": "Disorganized",
"timestamp": "01/13/2023 17:13:57",
"content": "ok. Now there are 9 seats left.",
"attachments": [],
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},
{
"id": 1063581734601490400,
"author_id": 598041720583618600,
"author_name": "Disorganized",
"timestamp": "01/13/2023 17:14:05",
"content": "count the number of ways to seat the next person",
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},
{
"id": 1063581790641602600,
"author_id": 405495558170738700,
"author_name": "Ragi",
"timestamp": "01/13/2023 17:14:19",
"content": "ten",
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},
{
"id": 1063581825378820100,
"author_id": 598041720583618600,
"author_name": "Disorganized",
"timestamp": "01/13/2023 17:14:27",
"content": "in 9 spots?",
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},
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"id": 1063581844148326500,
"author_id": 405495558170738700,
"author_name": "Ragi",
"timestamp": "01/13/2023 17:14:32",
"content": "oh 9",
"attachments": [],
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},
{
"id": 1063581858442530800,
"author_id": 598041720583618600,
"author_name": "Disorganized",
"timestamp": "01/13/2023 17:14:35",
"content": "ok.",
"attachments": [],
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},
{
"id": 1063581869842645000,
"author_id": 405495558170738700,
"author_name": "Ragi",
"timestamp": "01/13/2023 17:14:38",
"content": "and then for the next 8",
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},
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"id": 1063581871713296400,
"author_id": 598041720583618600,
"author_name": "Disorganized",
"timestamp": "01/13/2023 17:14:38",
"content": "and so on.",
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},
{
"id": 1063581921784901800,
"author_id": 405495558170738700,
"author_name": "Ragi",
"timestamp": "01/13/2023 17:14:50",
"content": "ohhh so i just add the total as i go on",
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"id": 1063582090702114800,
"author_id": 598041720583618600,
"author_name": "Disorganized",
"timestamp": "01/13/2023 17:15:30",
"content": "no",
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},
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"id": 1063582102391619700,
"author_id": 598041720583618600,
"author_name": "Disorganized",
"timestamp": "01/13/2023 17:15:33",
"content": "multiply",
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},
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"id": 1063582129214201900,
"author_id": 598041720583618600,
"author_name": "Disorganized",
"timestamp": "01/13/2023 17:15:40",
"content": "this principle has a name",
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},
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"id": 1063582143583899800,
"author_id": 598041720583618600,
"author_name": "Disorganized",
"timestamp": "01/13/2023 17:15:43",
"content": "...that I forgot",
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},
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"id": 1063582188681040000,
"author_id": 598041720583618600,
"author_name": "Disorganized",
"timestamp": "01/13/2023 17:15:54",
"content": "@VulcanOne",
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"id": 1063582201746297000,
"author_id": 598041720583618600,
"author_name": "Disorganized",
"timestamp": "01/13/2023 17:15:57",
"content": "?",
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"id": 1063582230489878500,
"author_id": 405495558170738700,
"author_name": "Ragi",
"timestamp": "01/13/2023 17:16:04",
"content": "oh wait so multiply by 10*9*8*7 and so on",
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"id": 1063582235732738000,
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"author_name": "Ragi",
"timestamp": "01/13/2023 17:16:05",
"content": "gothca",
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"id": 1063582258600104200,
"author_id": 598041720583618600,
"author_name": "Disorganized",
"timestamp": "01/13/2023 17:16:10",
"content": "anyway, this is a factorial",
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"id": 1063582315411943600,
"author_id": 1000057838007226500,
"author_name": "VulcanOne",
"timestamp": "01/13/2023 17:16:24",
"content": "Product",
"attachments": [],
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},
{
"id": 1063582376002846800,
"author_id": 1000057838007226500,
"author_name": "VulcanOne",
"timestamp": "01/13/2023 17:16:38",
"content": "Lemme show the formula",
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"id": 1063582391077179500,
"author_id": 405495558170738700,
"author_name": "Ragi",
"timestamp": "01/13/2023 17:16:42",
"content": "the number i got is insanely high",
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},
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"id": 1063582462543921200,
"author_id": 1000057838007226500,
"author_name": "VulcanOne",
"timestamp": "01/13/2023 17:16:59",
"content": "$n! = \\prod_{r=1}^n r$",
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},
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"id": 1063582532727214100,
"author_id": 598041720583618600,
"author_name": "Disorganized",
"timestamp": "01/13/2023 17:17:16",
"content": "yeah, \"rule of product\"",
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"id": 1063582594760986800,
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"author_name": "TeXit",
"timestamp": "01/13/2023 17:17:31",
"content": "**VulcanOne**",
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"timestamp": "01/13/2023 17:17:41",
"content": "yup",
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"timestamp": "01/13/2023 17:18:05",
"content": "factorials are the fastest-growing algorithms that exist",
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"timestamp": "01/13/2023 17:18:14",
"content": "...",
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"id": 1063582780962918400,
"author_id": 1000057838007226500,
"author_name": "VulcanOne",
"timestamp": "01/13/2023 17:18:15",
"content": "Other than x^x",
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},
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"id": 1063582811812003800,
"author_id": 598041720583618600,
"author_name": "Disorganized",
"timestamp": "01/13/2023 17:18:22",
"content": "I was just thinking of that",
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},
{
"id": 1063582826164920300,
"author_id": 598041720583618600,
"author_name": "Disorganized",
"timestamp": "01/13/2023 17:18:26",
"content": "but couldn't name it",
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},
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"id": 1063582841675460600,
"author_id": 132304137583984640,
"author_name": "Denascite",
"timestamp": "01/13/2023 17:18:29",
"content": "lol what",
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"id": 1063582856980463600,
"author_id": 1000057838007226500,
"author_name": "VulcanOne",
"timestamp": "01/13/2023 17:18:33",
"content": "Tetration",
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},
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"id": 1063582874856603600,
"author_id": 598041720583618600,
"author_name": "Disorganized",
"timestamp": "01/13/2023 17:18:37",
"content": "^ YES.",
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"id": 1063582883773694100,
"author_id": 405495558170738700,
"author_name": "Ragi",
"timestamp": "01/13/2023 17:18:39",
"content": "thanks so much yall this was very helpful. I appreciate the help big time",
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"id": 1063582906146107500,
"author_id": 598041720583618600,
"author_name": "Disorganized",
"timestamp": "01/13/2023 17:18:45",
"content": "https://tenor.com/view/yes-rick-morty-snap-gif-5747281",
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"id": 1063583130902077400,
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"author_name": "VulcanOne",
"timestamp": "01/13/2023 17:19:38",
"content": "Powersets tho",
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},
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"id": 1063583164410376200,
"author_id": 1000057838007226500,
"author_name": "VulcanOne",
"timestamp": "01/13/2023 17:19:46",
"content": "They are the fastest",
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},
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"id": 1063583325052223500,
"author_id": 405495558170738700,
"author_name": "Ragi",
"timestamp": "01/13/2023 17:20:25",
"content": "going to look them up anyway thanks",
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},
{
"id": 1063583330068611100,
"author_id": 405495558170738700,
"author_name": "Ragi",
"timestamp": "01/13/2023 17:20:26",
"content": ".close",
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},
{
"id": 1063583333021405200,
"author_id": 805217272087838700,
"author_name": "Mathematics Bot",
"timestamp": "01/13/2023 17:20:27",
"content": "Channel closed",
"attachments": [],
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}
] | help-9 | acfc19bb4e3f4e929074b3a81e582d01 |
200,739 | [
{
"id": 1063592486926307300,
"author_id": 805217272087838700,
"author_name": "Mathematics Bot",
"timestamp": "01/13/2023 17:56:49",
"content": "Available help channel!",
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},
{
"id": 1063593958971814000,
"author_id": 805217272087838700,
"author_name": "Mathematics Bot",
"timestamp": "01/13/2023 18:02:40",
"content": "Pinned a message.",
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"id": 1063593981126127700,
"author_id": 904770140443390000,
"author_name": "MG!",
"timestamp": "01/13/2023 18:02:45",
"content": "hi guys",
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},
{
"id": 1063594051150041200,
"author_id": 904770140443390000,
"author_name": "MG!",
"timestamp": "01/13/2023 18:03:02",
"content": "can somebody help me with part a",
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},
{
"id": 1063594437244104700,
"author_id": 598041720583618600,
"author_name": "Disorganized",
"timestamp": "01/13/2023 18:04:34",
"content": "ok",
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},
{
"id": 1063594971875258400,
"author_id": 598041720583618600,
"author_name": "Disorganized",
"timestamp": "01/13/2023 18:06:41",
"content": "$$\n\\begin{bmatrix}\n-\\frac{1}{\\sqrt{2}} & \\frac{1}{\\sqrt{2}}\\\\\n-\\frac{1}{\\sqrt{2}} & -\\frac{1}{\\sqrt{2}}\\\\\n\\end{bmatrix}\n\\begin{bmatrix}\nx\\\\\ny\\\\\n\\end{bmatrix}\n$$",
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},
{
"id": 1063595041119014900,
"author_id": 814011116836880400,
"author_name": "aboulkokk",
"timestamp": "01/13/2023 18:06:58",
"content": "Hello",
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},
{
"id": 1063595073306103900,
"author_id": 904770140443390000,
"author_name": "MG!",
"timestamp": "01/13/2023 18:07:06",
"content": "hi",
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},
{
"id": 1063595099822506000,
"author_id": 814011116836880400,
"author_name": "aboulkokk",
"timestamp": "01/13/2023 18:07:12",
"content": "I hope iโm not interrupting",
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},
{
"id": 1063595231670440000,
"author_id": 814011116836880400,
"author_name": "aboulkokk",
"timestamp": "01/13/2023 18:07:43",
"content": "Can you guys help me with the spectral theorem",
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},
{
"id": 1063595260875395100,
"author_id": 510789298321096700,
"author_name": "TeXit",
"timestamp": "01/13/2023 18:07:50",
"content": "**Disorganized**",
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"author_id": 814011116836880400,
"author_name": "aboulkokk",
"timestamp": "01/13/2023 18:07:57",
"content": "iโm a bit confused",
"attachments": [],
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"reference": null
},
{
"id": 1063595359449915400,
"author_id": 598041720583618600,
"author_name": "Disorganized",
"timestamp": "01/13/2023 18:08:14",
"content": "this channel is taken man",
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"id": 1063595419420074000,
"author_id": 904770140443390000,
"author_name": "MG!",
"timestamp": "01/13/2023 18:08:28",
"content": "hi so you can choose your own help channel above",
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"id": 1063595461807718400,
"author_id": 904770140443390000,
"author_name": "MG!",
"timestamp": "01/13/2023 18:08:38",
"content": "so 12 21 and 24 are good for the moment",
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"id": 1063595473065230500,
"author_id": 814011116836880400,
"author_name": "aboulkokk",
"timestamp": "01/13/2023 18:08:41",
"content": "Oh iโm sorry iโm new to this",
"attachments": [],
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"reference": null
},
{
"id": 1063595493541826700,
"author_id": 904770140443390000,
"author_name": "MG!",
"timestamp": "01/13/2023 18:08:46",
"content": "don't worry",
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},
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"id": 1063595503083855900,
"author_id": 598041720583618600,
"author_name": "Disorganized",
"timestamp": "01/13/2023 18:08:48",
"content": "ok, @MG! , what are the dimensions of the resultant matrix here",
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"id": 1063595535438708900,
"author_id": 598041720583618600,
"author_name": "Disorganized",
"timestamp": "01/13/2023 18:08:56",
"content": "or of this operation here",
"attachments": [],
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},
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"id": 1063595577704714200,
"author_id": 904770140443390000,
"author_name": "MG!",
"timestamp": "01/13/2023 18:09:06",
"content": "as in the standard anticlockwise transformation?",
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},
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"id": 1063595638069153900,
"author_id": 598041720583618600,
"author_name": "Disorganized",
"timestamp": "01/13/2023 18:09:20",
"content": "I don't think about it that way",
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},
{
"id": 1063595661355913300,
"author_id": 904770140443390000,
"author_name": "MG!",
"timestamp": "01/13/2023 18:09:26",
"content": "costheta -sintheta",
"attachments": [],
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"reference": null
},
{
"id": 1063595679127183400,
"author_id": 598041720583618600,
"author_name": "Disorganized",
"timestamp": "01/13/2023 18:09:30",
"content": "I'm just asking what the dimensions of the result will be",
"attachments": [],
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"reference": null
},
{
"id": 1063595688908304400,
"author_id": 904770140443390000,
"author_name": "MG!",
"timestamp": "01/13/2023 18:09:32",
"content": "sintheta costheta",
"attachments": [],
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"reference": null
},
{
"id": 1063595720822767600,
"author_id": 904770140443390000,
"author_name": "MG!",
"timestamp": "01/13/2023 18:09:40",
"content": "oh",
"attachments": [],
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},
{
"id": 1063595776980291700,
"author_id": 598041720583618600,
"author_name": "Disorganized",
"timestamp": "01/13/2023 18:09:53",
"content": "and how you know",
"attachments": [],
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},
{
"id": 1063595851898949600,
"author_id": 904770140443390000,
"author_name": "MG!",
"timestamp": "01/13/2023 18:10:11",
"content": "sorry what do you mean by dimensions",
"attachments": [],
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},
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"id": 1063595920270307300,
"author_id": 598041720583618600,
"author_name": "Disorganized",
"timestamp": "01/13/2023 18:10:28",
"content": "what are the dimensions of M?",
"attachments": [],
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},
{
"id": 1063595949873709000,
"author_id": 598041720583618600,
"author_name": "Disorganized",
"timestamp": "01/13/2023 18:10:35",
"content": "how many rows, how many columns?",
"attachments": [],
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},
{
"id": 1063595961580011600,
"author_id": 598041720583618600,
"author_name": "Disorganized",
"timestamp": "01/13/2023 18:10:37",
"content": "(mxn)",
"attachments": [],
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},
{
"id": 1063595969247203500,
"author_id": 904770140443390000,
"author_name": "MG!",
"timestamp": "01/13/2023 18:10:39",
"content": "oh",
"attachments": [],
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},
{
"id": 1063596022456135700,
"author_id": 904770140443390000,
"author_name": "MG!",
"timestamp": "01/13/2023 18:10:52",
"content": "m is a 2x2 matrix",
"attachments": [],
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},
{
"id": 1063596048624398500,
"author_id": 598041720583618600,
"author_name": "Disorganized",
"timestamp": "01/13/2023 18:10:58",
"content": "ok, how about the vector?",
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},
{
"id": 1063596125325623400,
"author_id": 598041720583618600,
"author_name": "Disorganized",
"timestamp": "01/13/2023 18:11:16",
"content": "how many rows, how many columns?",
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},
{
"id": 1063596250567545000,
"author_id": 598041720583618600,
"author_name": "Disorganized",
"timestamp": "01/13/2023 18:11:46",
"content": "just count them man",
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},
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"author_id": 904770140443390000,
"author_name": "MG!",
"timestamp": "01/13/2023 18:11:51",
"content": "what vector are we talking about",
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"timestamp": "01/13/2023 18:11:59",
"content": "[x,y]",
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"timestamp": "01/13/2023 18:12:09",
"content": "oh 1x2",
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"timestamp": "01/13/2023 18:12:12",
"content": "no",
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"timestamp": "01/13/2023 18:12:23",
"content": "oh 2x1 sorry",
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"timestamp": "01/13/2023 18:12:27",
"content": "right",
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"timestamp": "01/13/2023 18:12:31",
"content": "how did we know",
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"author_name": "MG!",
"timestamp": "01/13/2023 18:12:40",
"content": "2 rows 1 column",
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"timestamp": "01/13/2023 18:12:41",
"content": "it had to be a column vector and not a row vector",
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"timestamp": "01/13/2023 18:12:45",
"content": "?",
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"timestamp": "01/13/2023 18:13:36",
"content": "im saying that the condition for 2 matrixes to multiply is to have the first one's column and the second's row to be the same",
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"timestamp": "01/13/2023 18:13:43",
"content": "yes",
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"timestamp": "01/13/2023 18:13:49",
"content": "yeah",
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"timestamp": "01/13/2023 18:13:49",
"content": "the interior dimensions must match",
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"timestamp": "01/13/2023 18:14:03",
"content": "ok, so what are the *resultant dimensions*?",
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"timestamp": "01/13/2023 18:14:19",
"content": "so by the end of this multiplication you have a 2x2",
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"timestamp": "01/13/2023 18:14:19",
"content": "the dimensions of this calculation",
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"timestamp": "01/13/2023 18:14:22",
"content": "right",
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"timestamp": "01/13/2023 18:14:27",
"content": "the external dimensions",
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"author_name": "MG!",
"timestamp": "01/13/2023 18:14:33",
"content": "alright",
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"timestamp": "01/13/2023 18:14:39",
"content": "see here's the thing",
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"timestamp": "01/13/2023 18:14:44",
"content": "and that sounds right since we are supposed to plug in a point and spit out a point.",
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"timestamp": "01/13/2023 18:15:20",
"content": "i tried to simply use inverse trigs to work out the value of theta",
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"timestamp": "01/13/2023 18:15:28",
"content": "no forget all that",
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"id": 1063597203098181600,
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"timestamp": "01/13/2023 18:15:33",
"content": "cool",
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"author_name": "MG!",
"timestamp": "01/13/2023 18:15:54",
"content": "so the next step is just use the inverse of the matrix provided?",
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"timestamp": "01/13/2023 18:16:03",
"content": "ok so the resultant is",
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"timestamp": "01/13/2023 18:16:06",
"content": "use that and multiply it by both sides?",
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"timestamp": "01/13/2023 18:16:13",
"content": "\\begin{bmatrix}\nu\\\\\nv\\\\\n\\end{bmatrix}\n$$",
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"timestamp": "01/13/2023 18:16:14",
"content": "is that your solution",
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"author_name": "TeXit",
"timestamp": "01/13/2023 18:16:28",
"content": "**Disorganized**\nCompile Error! Click the :errors: reaction for more information.\n(You may edit your message to recompile.)",
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"timestamp": "01/13/2023 18:16:54",
"content": "the coordinates of `u` are (1,1).\nthe coordinates of `v` are (2,1)",
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"timestamp": "01/13/2023 18:17:02",
"content": "ok",
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"timestamp": "01/13/2023 18:17:03",
"content": "here's how you do it now",
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"id": 1063597787532497000,
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"timestamp": "01/13/2023 18:17:53",
"content": "you read the coordinates in row col order",
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"timestamp": "01/13/2023 18:18:23",
"content": "rotation by 225 anticlockwise",
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"id": 1063597927924252800,
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"author_name": "MG!",
"timestamp": "01/13/2023 18:18:26",
"content": "lol",
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"timestamp": "01/13/2023 18:18:33",
"content": "that's the answer",
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"id": 1063597963974299600,
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"timestamp": "01/13/2023 18:18:35",
"content": "You match the elements in M and in [x,y] directly",
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"timestamp": "01/13/2023 18:18:53",
"content": "so u is going to be first row matched with first column (adding those elementwise products)",
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"timestamp": "01/13/2023 18:19:26",
"content": "fine",
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"id": 1063598181386047500,
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"timestamp": "01/13/2023 18:19:27",
"content": "v is going to be the second row matched with the first column",
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"id": 1063598199182463000,
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"timestamp": "01/13/2023 18:19:31",
"content": "ok",
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"timestamp": "01/13/2023 18:19:40",
"content": "there is after all only 1 column in [x,y]",
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"timestamp": "01/13/2023 18:19:50",
"content": "so here's how you can write it",
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"timestamp": "01/13/2023 18:21:51",
"content": "$$\n\\begin{bmatrix}\n-\\frac{1}{\\sqrt{2}} x + \\frac{1}{\\sqrt{2}} y\\\\\n-\\frac{1}{\\sqrt{2}} x - \\frac{1}{\\sqrt{2}} y\\\\\n\\end{bmatrix}\n$$",
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"id": 1063598880417128600,
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"timestamp": "01/13/2023 18:22:13",
"content": "oh",
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"timestamp": "01/13/2023 18:22:28",
"content": "**Disorganized**",
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"timestamp": "01/13/2023 18:22:46",
"content": "that's quite convoluted",
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"timestamp": "01/13/2023 18:23:07",
"content": "is it? It's literally the definition of matrix multiplication",
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"id": 1063599150039584900,
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"author_name": "MG!",
"timestamp": "01/13/2023 18:23:18",
"content": "oh no",
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"id": 1063599159711641600,
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"timestamp": "01/13/2023 18:23:20",
"content": "not this one",
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"id": 1063599181652045800,
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"timestamp": "01/13/2023 18:23:25",
"content": "the one i saw before it changes",
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"timestamp": "01/13/2023 18:23:27",
"content": "that is a 2x1 matrix (i.e. a vector)",
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"id": 1063599216481542100,
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"timestamp": "01/13/2023 18:23:33",
"content": "i guess you altered it",
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"timestamp": "01/13/2023 18:23:43",
"content": "yeah I janked up the LaTeX",
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"timestamp": "01/13/2023 18:23:43",
"content": "nvm",
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"timestamp": "01/13/2023 18:23:53",
"content": "ok lol",
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"id": 1063599315844608000,
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"timestamp": "01/13/2023 18:23:57",
"content": "so what's next",
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"timestamp": "01/13/2023 18:24:50",
"content": "so far we managed to insert x and y into the transformation matrix",
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"timestamp": "01/13/2023 18:24:53",
"content": "well this is arguably the answer to part a but it is also possible to interpret that as a sequence of transformations",
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"id": 1063599578223497300,
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"timestamp": "01/13/2023 18:25:00",
"content": "right",
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"timestamp": "01/13/2023 18:25:03",
"content": "here's the thing",
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"timestamp": "01/13/2023 18:25:07",
"content": "you can get part b now by plugging in p and q",
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"timestamp": "01/13/2023 18:25:18",
"content": "ok hang on a sec",
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"timestamp": "01/13/2023 18:26:00",
"content": "oh not quite",
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"timestamp": "01/13/2023 18:26:04",
"content": "more complicated",
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"timestamp": "01/13/2023 18:26:05",
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"timestamp": "01/13/2023 18:26:06",
"content": "here",
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"timestamp": "01/13/2023 18:26:08",
"content": "need the inverse matrix",
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"timestamp": "01/13/2023 18:26:19",
"content": "blech",
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"timestamp": "01/13/2023 18:26:21",
"content": "you see that's what confuses me",
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"timestamp": "01/13/2023 18:26:33",
"content": "i subbed in the values",
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"timestamp": "01/13/2023 18:26:41",
"content": "yet cos and sin are replying differently",
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"timestamp": "01/13/2023 18:27:00",
"content": "hence it is quite hard to distinguish which one i should use",
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"id": 1063600160409653200,
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"timestamp": "01/13/2023 18:27:18",
"content": "in the case of sin we have",
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"timestamp": "01/13/2023 18:27:20",
"content": "-45",
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"timestamp": "01/13/2023 18:27:29",
"content": "ok so you got like cos(theta) = -1/sqrt(2) and such?",
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"author_id": 598041720583618600,
"author_name": "Disorganized",
"timestamp": "01/13/2023 18:27:40",
"content": "these are all multiples of 45 degrees",
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"id": 1063600256492769300,
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"author_name": "Disorganized",
"timestamp": "01/13/2023 18:27:41",
"content": "yeah",
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},
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"id": 1063600267133714600,
"author_id": 904770140443390000,
"author_name": "MG!",
"timestamp": "01/13/2023 18:27:44",
"content": "yeah pretty much",
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"id": 1063600305046028300,
"author_id": 904770140443390000,
"author_name": "MG!",
"timestamp": "01/13/2023 18:27:53",
"content": "that's not what the answer suggests though",
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},
{
"id": 1063600317679284400,
"author_id": 598041720583618600,
"author_name": "Disorganized",
"timestamp": "01/13/2023 18:27:56",
"content": "I mean it has to be one angle",
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},
{
"id": 1063600334162907100,
"author_id": 904770140443390000,
"author_name": "MG!",
"timestamp": "01/13/2023 18:28:00",
"content": "true",
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},
{
"id": 1063600382875545600,
"author_id": 904770140443390000,
"author_name": "MG!",
"timestamp": "01/13/2023 18:28:12",
"content": "thetas are unified",
"attachments": [],
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},
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"id": 1063600412193730800,
"author_id": 598041720583618600,
"author_name": "Disorganized",
"timestamp": "01/13/2023 18:28:19",
"content": "where is cosine equal to -sine",
"attachments": [],
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},
{
"id": 1063600491348635800,
"author_id": 598041720583618600,
"author_name": "Disorganized",
"timestamp": "01/13/2023 18:28:37",
"content": "I think that's quad II and IV",
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},
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"id": 1063600513045758000,
"author_id": 904770140443390000,
"author_name": "MG!",
"timestamp": "01/13/2023 18:28:43",
"content": "",
"attachments": [
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"id": 1063600562014265500,
"author_id": 904770140443390000,
"author_name": "MG!",
"timestamp": "01/13/2023 18:28:54",
"content": "the answer sheet is quite lazy",
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},
{
"id": 1063600621846007800,
"author_id": 904770140443390000,
"author_name": "MG!",
"timestamp": "01/13/2023 18:29:08",
"content": "was not bothered to elaborate lol",
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},
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"id": 1063600659942875300,
"author_id": 598041720583618600,
"author_name": "Disorganized",
"timestamp": "01/13/2023 18:29:18",
"content": "ooh that's quad III",
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},
{
"id": 1063600678834016300,
"author_id": 598041720583618600,
"author_name": "Disorganized",
"timestamp": "01/13/2023 18:29:22",
"content": "I\"m losing it",
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},
{
"id": 1063600767455473800,
"author_id": 904770140443390000,
"author_name": "MG!",
"timestamp": "01/13/2023 18:29:43",
"content": "what",
"attachments": [],
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},
{
"id": 1063601039875506300,
"author_id": 598041720583618600,
"author_name": "Disorganized",
"timestamp": "01/13/2023 18:30:48",
"content": "my touch with the unit circle",
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},
{
"id": 1063601052752031900,
"author_id": 598041720583618600,
"author_name": "Disorganized",
"timestamp": "01/13/2023 18:30:51",
"content": "anyway",
"attachments": [],
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"reference": null
},
{
"id": 1063601066668724200,
"author_id": 598041720583618600,
"author_name": "Disorganized",
"timestamp": "01/13/2023 18:30:55",
"content": "this value makes sense",
"attachments": [],
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},
{
"id": 1063601154061246500,
"author_id": 904770140443390000,
"author_name": "MG!",
"timestamp": "01/13/2023 18:31:15",
"content": "fair enough",
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},
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"id": 1063601195454828700,
"author_id": 598041720583618600,
"author_name": "Disorganized",
"timestamp": "01/13/2023 18:31:25",
"content": "sine and cosine are always equal when you have theta = 45 + k\\*90",
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},
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"id": 1063601283770101900,
"author_id": 598041720583618600,
"author_name": "Disorganized",
"timestamp": "01/13/2023 18:31:46",
"content": "you need the negative value of sine (an odd function) to equal cosine",
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},
{
"id": 1063601297053466800,
"author_id": 904770140443390000,
"author_name": "MG!",
"timestamp": "01/13/2023 18:31:49",
"content": "so in this case k is 2?",
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},
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"id": 1063601326057070600,
"author_id": 598041720583618600,
"author_name": "Disorganized",
"timestamp": "01/13/2023 18:31:56",
"content": "yeah",
"attachments": [],
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"reference": null
},
{
"id": 1063601343517958100,
"author_id": 598041720583618600,
"author_name": "Disorganized",
"timestamp": "01/13/2023 18:32:01",
"content": "225 degrees",
"attachments": [],
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"reference": null
},
{
"id": 1063601350396616800,
"author_id": 904770140443390000,
"author_name": "MG!",
"timestamp": "01/13/2023 18:32:02",
"content": "is it mandatory though?",
"attachments": [],
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"reference": null
},
{
"id": 1063601357606617100,
"author_id": 904770140443390000,
"author_name": "MG!",
"timestamp": "01/13/2023 18:32:04",
"content": "like",
"attachments": [],
"mentions": [],
"reference": null
},
{
"id": 1063601396894671000,
"author_id": 598041720583618600,
"author_name": "Disorganized",
"timestamp": "01/13/2023 18:32:13",
"content": "you can figure it out by plugging in values, memorizing, testing",
"attachments": [],
"mentions": [],
"reference": null
},
{
"id": 1063601401441300500,
"author_id": 904770140443390000,
"author_name": "MG!",
"timestamp": "01/13/2023 18:32:14",
"content": "if i place 45 degrees as my answer",
"attachments": [],
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"reference": null
},
{
"id": 1063601420017860600,
"author_id": 598041720583618600,
"author_name": "Disorganized",
"timestamp": "01/13/2023 18:32:19",
"content": "no",
"attachments": [],
"mentions": [],
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},
{
"id": 1063601434374963200,
"author_id": 598041720583618600,
"author_name": "Disorganized",
"timestamp": "01/13/2023 18:32:22",
"content": "225",
"attachments": [],
"mentions": [],
"reference": null
},
{
"id": 1063601452473385100,
"author_id": 904770140443390000,
"author_name": "MG!",
"timestamp": "01/13/2023 18:32:27",
"content": "ok",
"attachments": [],
"mentions": [],
"reference": null
},
{
"id": 1063601495460814800,
"author_id": 904770140443390000,
"author_name": "MG!",
"timestamp": "01/13/2023 18:32:37",
"content": "that's great",
"attachments": [],
"mentions": [],
"reference": null
},
{
"id": 1063601516696572000,
"author_id": 904770140443390000,
"author_name": "MG!",
"timestamp": "01/13/2023 18:32:42",
"content": "thank you for the help",
"attachments": [],
"mentions": [],
"reference": null
},
{
"id": 1063601596270903300,
"author_id": 598041720583618600,
"author_name": "Disorganized",
"timestamp": "01/13/2023 18:33:01",
"content": "part b requires inverse matrix",
"attachments": [],
"mentions": [],
"reference": null
},
{
"id": 1063601645889519700,
"author_id": 904770140443390000,
"author_name": "MG!",
"timestamp": "01/13/2023 18:33:13",
"content": "yeah im fine with that part",
"attachments": [],
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},
{
"id": 1063601661672693900,
"author_id": 598041720583618600,
"author_name": "Disorganized",
"timestamp": "01/13/2023 18:33:16",
"content": "ok good",
"attachments": [],
"mentions": [],
"reference": null
},
{
"id": 1063601678496059400,
"author_id": 904770140443390000,
"author_name": "MG!",
"timestamp": "01/13/2023 18:33:20",
"content": "cool",
"attachments": [],
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"reference": null
},
{
"id": 1063601847685873800,
"author_id": 805217272087838700,
"author_name": "Mathematics Bot",
"timestamp": "01/13/2023 18:34:01",
"content": "Channel closed",
"attachments": [],
"mentions": [],
"reference": null
}
] | help-9 | e0f764b92d524513aa5c652a30315588 |
200,740 | [
{
"id": 1063602098345885700,
"author_id": 805217272087838700,
"author_name": "Mathematics Bot",
"timestamp": "01/13/2023 18:35:01",
"content": "Available help channel!",
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"reference": null
},
{
"id": 1063602438927568900,
"author_id": 819818586965016600,
"author_name": "Junโพ",
"timestamp": "01/13/2023 18:36:22",
"content": "How?",
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}
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{
"id": 1063602440483639400,
"author_id": 805217272087838700,
"author_name": "Mathematics Bot",
"timestamp": "01/13/2023 18:36:22",
"content": "Pinned a message.",
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}
},
{
"id": 1063602502890705000,
"author_id": 261933205387477000,
"author_name": "riemann",
"timestamp": "01/13/2023 18:36:37",
"content": "use pythagorean theorem",
"attachments": [],
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"reference": null
},
{
"id": 1063602543642550300,
"author_id": 485164773647056900,
"author_name": "Gooaaa",
"timestamp": "01/13/2023 18:36:47",
"content": "?",
"attachments": [],
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},
{
"id": 1063602612601106400,
"author_id": 349354952961032200,
"author_name": "Umbraleviathan",
"timestamp": "01/13/2023 18:37:03",
"content": "Pythagorean identity*",
"attachments": [],
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"reference": null
},
{
"id": 1063602655072632800,
"author_id": 349354952961032200,
"author_name": "Umbraleviathan",
"timestamp": "01/13/2023 18:37:13",
"content": "Lol @riemann big Brian moment :jonathan:",
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{
"id": 1063602791014223900,
"author_id": 819818586965016600,
"author_name": "Junโพ",
"timestamp": "01/13/2023 18:37:46",
"content": "Wait can i split it into sin x^2 and sin x?",
"attachments": [],
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},
{
"id": 1063603078084956300,
"author_id": 819818586965016600,
"author_name": "Junโพ",
"timestamp": "01/13/2023 18:38:54",
"content": "like rewriting it into a product",
"attachments": [],
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},
{
"id": 1063603114919350400,
"author_id": 485164773647056900,
"author_name": "Gooaaa",
"timestamp": "01/13/2023 18:39:03",
"content": "Yes",
"attachments": [],
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},
{
"id": 1063603146028490800,
"author_id": 485164773647056900,
"author_name": "Gooaaa",
"timestamp": "01/13/2023 18:39:10",
"content": "Then write sin^2x in other form",
"attachments": [],
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"reference": null
},
{
"id": 1063603184322482200,
"author_id": 819818586965016600,
"author_name": "Junโพ",
"timestamp": "01/13/2023 18:39:19",
"content": "Ok",
"attachments": [],
"mentions": [],
"reference": null
},
{
"id": 1063603333857804400,
"author_id": 819818586965016600,
"author_name": "Junโพ",
"timestamp": "01/13/2023 18:39:55",
"content": "Iโll do that then, thanks all",
"attachments": [],
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},
{
"id": 1063603347573178400,
"author_id": 819818586965016600,
"author_name": "Junโพ",
"timestamp": "01/13/2023 18:39:58",
"content": ".close",
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},
{
"id": 1063603351989796900,
"author_id": 805217272087838700,
"author_name": "Mathematics Bot",
"timestamp": "01/13/2023 18:39:59",
"content": "Channel closed",
"attachments": [],
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"reference": null
}
] | help-9 | ccf25bb335b844ff93c0744f793469e7 |
200,741 | [
{
"id": 1063604693697315000,
"author_id": 261933205387477000,
"author_name": "riemann",
"timestamp": "01/13/2023 18:45:19",
"content": "ty umbra",
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},
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"id": 1063604970915635200,
"author_id": 805217272087838700,
"author_name": "Mathematics Bot",
"timestamp": "01/13/2023 18:46:25",
"content": "Available help channel!",
"attachments": [],
"mentions": [],
"reference": null
},
{
"id": 1063605558898344000,
"author_id": 809856158911299600,
"author_name": "j4w4",
"timestamp": "01/13/2023 18:48:46",
"content": "Are a tail of zeros defined as non-repeating for rational numbers?",
"attachments": [],
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"reference": null
},
{
"id": 1063605561163264000,
"author_id": 805217272087838700,
"author_name": "Mathematics Bot",
"timestamp": "01/13/2023 18:48:46",
"content": "Pinned a message.",
"attachments": [],
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{
"id": 1063605806102225000,
"author_id": 809856158911299600,
"author_name": "j4w4",
"timestamp": "01/13/2023 18:49:45",
"content": ".5 would be considered rational because, at first glance, it is not repeating, unless an infinite supply of zeros are added to it.",
"attachments": [],
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},
{
"id": 1063605981981970600,
"author_id": 809856158911299600,
"author_name": "j4w4",
"timestamp": "01/13/2023 18:50:26",
"content": "So, in the world of mathematics, my question is whether that issue has been formally addressed.",
"attachments": [],
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},
{
"id": 1063606086898299000,
"author_id": 1003857269802401900,
"author_name": "starlight",
"timestamp": "01/13/2023 18:50:51",
"content": "you don't define \"a tail of zeros\" as repeating",
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},
{
"id": 1063606116224880800,
"author_id": 1003857269802401900,
"author_name": "starlight",
"timestamp": "01/13/2023 18:50:58",
"content": "bc the zeros are meaningless",
"attachments": [],
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},
{
"id": 1063606180536135800,
"author_id": 1003857269802401900,
"author_name": "starlight",
"timestamp": "01/13/2023 18:51:14",
"content": "as the value of 0.50000.. and 0.5 are equal",
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},
{
"id": 1063606213713084500,
"author_id": 809856158911299600,
"author_name": "j4w4",
"timestamp": "01/13/2023 18:51:22",
"content": "Okay, thank you.",
"attachments": [],
"mentions": [],
"reference": null
},
{
"id": 1063606227076137000,
"author_id": 809856158911299600,
"author_name": "j4w4",
"timestamp": "01/13/2023 18:51:25",
"content": ".close",
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},
{
"id": 1063606229852762100,
"author_id": 805217272087838700,
"author_name": "Mathematics Bot",
"timestamp": "01/13/2023 18:51:26",
"content": "Channel closed",
"attachments": [],
"mentions": [],
"reference": null
}
] | help-9 | 346cb6c1ebd44adab5ce1ef93e8ee72c |
200,742 | [
{
"id": 1063607147012833400,
"author_id": 809856158911299600,
"author_name": "j4w4",
"timestamp": "01/13/2023 18:55:04",
"content": "Are there many numbers that repeat with more than 1 decimal place?",
"attachments": [],
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},
{
"id": 1063607271977918500,
"author_id": 261933205387477000,
"author_name": "riemann",
"timestamp": "01/13/2023 18:55:34",
"content": ",calc 12/99",
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"reference": null
},
{
"id": 1063607273584349200,
"author_id": 510789298321096700,
"author_name": "TeXit",
"timestamp": "01/13/2023 18:55:34",
"content": "Result:\n```\n0.12121212121212\n```",
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},
{
"id": 1063607327682461700,
"author_id": 809856158911299600,
"author_name": "j4w4",
"timestamp": "01/13/2023 18:55:47",
"content": "What fraction is that, 1/8?",
"attachments": [],
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},
{
"id": 1063607493206491100,
"author_id": 809856158911299600,
"author_name": "j4w4",
"timestamp": "01/13/2023 18:56:27",
"content": "So what's the equivalent rational number in fraction form?",
"attachments": [],
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"reference": null
},
{
"id": 1063607650228654200,
"author_id": 809856158911299600,
"author_name": "j4w4",
"timestamp": "01/13/2023 18:57:04",
"content": "Thank You!",
"attachments": [],
"mentions": [],
"reference": null
},
{
"id": 1063607805531140200,
"author_id": 809856158911299600,
"author_name": "j4w4",
"timestamp": "01/13/2023 18:57:41",
"content": "But that's only an example but didn't really answer the question. Are there lots, like, has somebody created a graph or chart of them?",
"attachments": [],
"mentions": [],
"reference": null
},
{
"id": 1063608086343979000,
"author_id": 805217272087838700,
"author_name": "Mathematics Bot",
"timestamp": "01/13/2023 18:58:48",
"content": "Available help channel!",
"attachments": [],
"mentions": [],
"reference": null
},
{
"id": 1063608211971772400,
"author_id": 809856158911299600,
"author_name": "j4w4",
"timestamp": "01/13/2023 18:59:18",
"content": "But that's only an example but didn't really answer the question. Are there lots, like, has somebody created a graph or chart of them?",
"attachments": [],
"mentions": [],
"reference": null
},
{
"id": 1063608215549518000,
"author_id": 805217272087838700,
"author_name": "Mathematics Bot",
"timestamp": "01/13/2023 18:59:19",
"content": "Pinned a message.",
"attachments": [],
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"messageId": 1063608211971772400,
"channelId": 486844875632017400,
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{
"id": 1063608800755581000,
"author_id": 182179228840755200,
"author_name": "iCaird",
"timestamp": "01/13/2023 19:01:38",
"content": "any possible finite repeating pattern exists",
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},
{
"id": 1063608801741258800,
"author_id": 261933205387477000,
"author_name": "riemann",
"timestamp": "01/13/2023 19:01:39",
"content": "it's not really interesting enough to publish",
"attachments": [],
"mentions": [],
"reference": null
},
{
"id": 1063608805511938000,
"author_id": 984319941417251000,
"author_name": "๐๐๐ถ๐๐๐ถ๐",
"timestamp": "01/13/2023 19:01:40",
"content": "you can throw anything into a calculator lol",
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"author_id": 984319941417251000,
"author_name": "๐๐๐ถ๐๐๐ถ๐",
"timestamp": "01/13/2023 19:02:01",
"content": "and if you make up a repeating pattern, the fraction form can be found",
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"author_name": "j4w4",
"timestamp": "01/13/2023 19:02:12",
"content": "Actually, that's not true. I've decided to Google the matter and there is a ton of hits for the subject matter.",
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"content": "It's not about the numbers themselves but gaining a clearer understanding of the definitions and distinctions between rational/irrational numbers.",
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"content": "Riemann was using publish in a specific context",
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"timestamp": "01/13/2023 19:04:40",
"content": "People publish web pages with data. So, I was too. People talk about it. His opinion is that he isn't very interested which is fine. Other people are, that will always be the case with any subject matter in life.",
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"timestamp": "01/13/2023 19:05:14",
"content": "publish and writing blogs are different things",
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"author_name": "j4w4",
"timestamp": "01/13/2023 19:05:45",
"content": "Well, I didn't realize my question was in the context of a published book. I apologize for that. ๐",
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"id": 1063609842650063000,
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"timestamp": "01/13/2023 19:05:47",
"content": "if you just wanted a blog, you could have just google'd like you did and skipped this",
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"id": 1063609845737066600,
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"author_name": "๐๐๐ถ๐๐๐ถ๐",
"timestamp": "01/13/2023 19:05:48",
"content": "but 'publish' and somebody creating a graph or chart of them are different anyway",
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"content": "Publishing is exponentially easier these days because of the Internet. It's not confined to the world of printing presses.",
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"timestamp": "01/13/2023 19:07:05",
"content": "what even are you talking about anymore. if you're done, close the channel",
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"timestamp": "01/13/2023 19:07:16",
"content": "by publish he means \"publish a paper in a reputable mathematical journal\"",
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"id": 1063610318569357300,
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"timestamp": "01/13/2023 19:07:40",
"content": "or the arxiv :roopopcorn:",
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"timestamp": "01/13/2023 19:15:41",
"content": "Okay, I guess that's what he thought I meant. So, it was a misunderstanding. Good enough.",
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"id": 1063612350969680000,
"author_id": 809856158911299600,
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"timestamp": "01/13/2023 19:15:45",
"content": ".close",
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},
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"id": 1063612353721155600,
"author_id": 805217272087838700,
"author_name": "Mathematics Bot",
"timestamp": "01/13/2023 19:15:46",
"content": "Channel closed",
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}
] | help-9 | 56dd916380eb4adbb75b9fef5dada38e |
200,743 | [
{
"id": 1035479121721049100,
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"author_id": 897843705522835500,
"author_name": "'OneBullet.",
"timestamp": "10/28/2022 05:13:39",
"content": "y = -4x + 5\ny = 6x",
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},
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},
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"id": 1035481561413455900,
"author_id": 856447591834976300,
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"content": "6x = -4x + 5",
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},
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"id": 1035481591486632000,
"author_id": 798556451139223600,
"author_name": "meckron",
"timestamp": "10/28/2022 05:14:09",
"content": "with what?",
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},
{
"id": 1035481626173505500,
"author_id": 856447591834976300,
"author_name": "Ryuzaki",
"timestamp": "10/28/2022 05:14:17",
"content": "6x + 4x = (-4x + 4x) + 5",
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},
{
"id": 1035481645928677400,
"author_id": 856447591834976300,
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"content": "10x = 0 + 5",
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{
"id": 1035481656003412000,
"author_id": 856447591834976300,
"author_name": "Ryuzaki",
"timestamp": "10/28/2022 05:14:25",
"content": "what is x?",
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},
{
"id": 1035481686483415200,
"author_id": 897843705522835500,
"author_name": "'OneBullet.",
"timestamp": "10/28/2022 05:14:32",
"content": "3",
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},
{
"id": 1035481698944688100,
"author_id": 856447591834976300,
"author_name": "Ryuzaki",
"timestamp": "10/28/2022 05:14:35",
"content": "no",
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},
{
"id": 1035481732486529000,
"author_id": 897843705522835500,
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"timestamp": "10/28/2022 05:14:43",
"content": "hmmmm",
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{
"id": 1035481780523905000,
"author_id": 856447591834976300,
"author_name": "Ryuzaki",
"timestamp": "10/28/2022 05:14:54",
"content": "for which value of x does 10x equal 5",
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},
{
"id": 1035481869128581100,
"author_id": 897843705522835500,
"author_name": "'OneBullet.",
"timestamp": "10/28/2022 05:15:15",
"content": "dvide",
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},
{
"id": 1035481890280452200,
"author_id": 897843705522835500,
"author_name": "'OneBullet.",
"timestamp": "10/28/2022 05:15:20",
"content": "2",
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"id": 1035481930549973000,
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"author_name": "Ryuzaki",
"timestamp": "10/28/2022 05:15:30",
"content": "divide by 2, yes",
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"id": 1035481946849026000,
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"timestamp": "10/28/2022 05:15:34",
"content": "aka 1/2",
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{
"id": 1035482963216977900,
"author_id": 897843705522835500,
"author_name": "'OneBullet.",
"timestamp": "10/28/2022 05:19:36",
"content": "ุ",
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"url": "https://cdn.discordapp.com/attachments/486844875632017408/1035482962784960563/d0c636f16f1551f0b212e34d39d3d7ae.png",
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"id": 1035483157018988500,
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"author_name": "'OneBullet.",
"timestamp": "10/28/2022 05:20:22",
"content": "@Ryuzaki",
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"id": 1035483233963491300,
"author_id": 856447591834976300,
"author_name": "Ryuzaki",
"timestamp": "10/28/2022 05:20:41",
"content": "cool",
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},
{
"id": 1035483376272035800,
"author_id": 897843705522835500,
"author_name": "'OneBullet.",
"timestamp": "10/28/2022 05:21:15",
"content": ":confused_monkey:",
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"id": 1035483555993768000,
"author_id": 897843705522835500,
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"timestamp": "10/28/2022 05:21:58",
"content": "answer ?",
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"author_id": 877944036395212800,
"author_name": "miky",
"timestamp": "10/28/2022 05:22:04",
"content": "bro pulled out collatz conjecture ๐ญ",
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"author_id": 877944036395212800,
"author_name": "miky",
"timestamp": "10/28/2022 05:22:37",
"content": "ุญุจูุจู",
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},
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"id": 1035483831467266200,
"author_id": 897843705522835500,
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"timestamp": "10/28/2022 05:23:03",
"content": "ุงูููู",
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},
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"id": 1035483833014947800,
"author_id": 856447591834976300,
"author_name": "Ryuzaki",
"timestamp": "10/28/2022 05:23:04",
"content": "stop sending ambiguous images and asking for answers to questions you haven't asked",
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"author_id": 897843705522835500,
"author_name": "'OneBullet.",
"timestamp": "10/28/2022 05:24:07",
"content": ".close",
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},
{
"id": 1035484100011770000,
"author_id": 805217272087838700,
"author_name": "Mathematics Bot",
"timestamp": "10/28/2022 05:24:07",
"content": "Channel closed",
"attachments": [],
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"reference": null
}
] | help-9 | fa1a9e99161841c3bfab8110c231f70d |
200,744 | [
{
"id": 1063612606495064200,
"author_id": 805217272087838700,
"author_name": "Mathematics Bot",
"timestamp": "01/13/2023 19:16:46",
"content": "Available help channel!",
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},
{
"id": 1063612956128063600,
"author_id": 236252356553998340,
"author_name": "Goldi",
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"timestamp": "01/13/2023 19:18:10",
"content": "Pinned a message.",
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{
"id": 1063613005788618900,
"author_id": 236252356553998340,
"author_name": "Goldi",
"timestamp": "01/13/2023 19:18:21",
"content": "4 pi - 2 pi - pi over 4",
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},
{
"id": 1063613033156448300,
"author_id": 236252356553998340,
"author_name": "Goldi",
"timestamp": "01/13/2023 19:18:28",
"content": "how does that equal pi over 4",
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},
{
"id": 1063613090605842400,
"author_id": 236252356553998340,
"author_name": "Goldi",
"timestamp": "01/13/2023 19:18:41",
"content": "forget the bottom for a sec.\n\n4 pi - 2 pi - pi",
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},
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"id": 1063613108888797200,
"author_id": 318024849333288960,
"author_name": "Mortta",
"timestamp": "01/13/2023 19:18:46",
"content": "Yea",
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},
{
"id": 1063613124973961200,
"author_id": 236252356553998340,
"author_name": "Goldi",
"timestamp": "01/13/2023 19:18:49",
"content": "is 2 pi - pi",
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},
{
"id": 1063613148344631300,
"author_id": 236252356553998340,
"author_name": "Goldi",
"timestamp": "01/13/2023 19:18:55",
"content": "oh i see",
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},
{
"id": 1063613160319373400,
"author_id": 236252356553998340,
"author_name": "Goldi",
"timestamp": "01/13/2023 19:18:58",
"content": "2 pi - pi = pi",
"attachments": [],
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},
{
"id": 1063613174047322100,
"author_id": 318024849333288960,
"author_name": "Mortta",
"timestamp": "01/13/2023 19:19:01",
"content": "Yes",
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},
{
"id": 1063613231454769200,
"author_id": 236252356553998340,
"author_name": "Goldi",
"timestamp": "01/13/2023 19:19:15",
"content": "ahh yes, hello stupidity",
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},
{
"id": 1063613235292537000,
"author_id": 236252356553998340,
"author_name": "Goldi",
"timestamp": "01/13/2023 19:19:16",
"content": "thank u",
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},
{
"id": 1063613247959339100,
"author_id": 318024849333288960,
"author_name": "Mortta",
"timestamp": "01/13/2023 19:19:19",
"content": "???",
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},
{
"id": 1063613251444814000,
"author_id": 236252356553998340,
"author_name": "Goldi",
"timestamp": "01/13/2023 19:19:20",
"content": ".close",
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},
{
"id": 1063613254183686100,
"author_id": 805217272087838700,
"author_name": "Mathematics Bot",
"timestamp": "01/13/2023 19:19:20",
"content": "Channel closed",
"attachments": [],
"mentions": [],
"reference": null
}
] | help-9 | a86f3b924890490ab3d650cf48f5e064 |
200,745 | [
{
"id": 1063613265491546100,
"author_id": 318024849333288960,
"author_name": "Mortta",
"timestamp": "01/13/2023 19:19:23",
"content": "Didnโt even say nothin",
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"id": 1063613272672194700,
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"timestamp": "01/13/2023 19:19:25",
"content": ".reopen",
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"id": 1063613276598059100,
"author_id": 805217272087838700,
"author_name": "Mathematics Bot",
"timestamp": "01/13/2023 19:19:26",
"content": "โ
",
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},
{
"id": 1063613280461017200,
"author_id": 236252356553998340,
"author_name": "Goldi",
"timestamp": "01/13/2023 19:19:27",
"content": "my stupidity",
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},
{
"id": 1063613291034857500,
"author_id": 236252356553998340,
"author_name": "Goldi",
"timestamp": "01/13/2023 19:19:29",
"content": ".close",
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},
{
"id": 1063613294167990300,
"author_id": 805217272087838700,
"author_name": "Mathematics Bot",
"timestamp": "01/13/2023 19:19:30",
"content": "Channel closed",
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}
] | help-9 | c275e6c643ca412ba7010b7275b6330c |
200,746 | [
{
"id": 1063615492528537600,
"author_id": 236252356553998340,
"author_name": "Goldi",
"timestamp": "01/13/2023 19:28:14",
"content": "",
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"id": 1063615545527763000,
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"author_name": "Goldi",
"timestamp": "01/13/2023 19:28:27",
"content": "a^2 + b^2 = c^2 yea",
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},
{
"id": 1063615559146688500,
"author_id": 236252356553998340,
"author_name": "Goldi",
"timestamp": "01/13/2023 19:28:30",
"content": "but why cant i do",
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"id": 1063615599638479000,
"author_id": 236252356553998340,
"author_name": "Goldi",
"timestamp": "01/13/2023 19:28:39",
"content": "9^2 + 18^2 = c^2",
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"id": 1063615612548563000,
"author_id": 236252356553998340,
"author_name": "Goldi",
"timestamp": "01/13/2023 19:28:43",
"content": "what am i misreading",
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"id": 1063615641099194400,
"author_id": 236252356553998340,
"author_name": "Goldi",
"timestamp": "01/13/2023 19:28:49",
"content": "i know its wrong but i cant explain why",
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},
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"id": 1063623528076804100,
"author_id": 805217272087838700,
"author_name": "Mathematics Bot",
"timestamp": "01/13/2023 20:00:10",
"content": "Available help channel!",
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"reference": null
},
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"id": 1063626589172138000,
"author_id": 521837027919003650,
"author_name": "hi123",
"timestamp": "01/13/2023 20:12:20",
"content": "",
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"id": 1063626592955412600,
"author_id": 805217272087838700,
"author_name": "Mathematics Bot",
"timestamp": "01/13/2023 20:12:20",
"content": "Pinned a message.",
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"id": 1063626638031589400,
"author_id": 521837027919003650,
"author_name": "hi123",
"timestamp": "01/13/2023 20:12:31",
"content": "The answer is there but Idk how to get there pls help",
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},
{
"id": 1063628002371567600,
"author_id": 264901235834880000,
"author_name": "Modus",
"timestamp": "01/13/2023 20:17:57",
"content": "how you can denote three consecutive odd integers",
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},
{
"id": 1063628042532032600,
"author_id": 264901235834880000,
"author_name": "Modus",
"timestamp": "01/13/2023 20:18:06",
"content": "using some variable",
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},
{
"id": 1063628136207622300,
"author_id": 521837027919003650,
"author_name": "hi123",
"timestamp": "01/13/2023 20:18:28",
"content": "x",
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},
{
"id": 1063628157745373200,
"author_id": 521837027919003650,
"author_name": "hi123",
"timestamp": "01/13/2023 20:18:34",
"content": "x+2",
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},
{
"id": 1063628162031943700,
"author_id": 521837027919003650,
"author_name": "hi123",
"timestamp": "01/13/2023 20:18:35",
"content": "x+4",
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},
{
"id": 1063628227425337300,
"author_id": 264901235834880000,
"author_name": "Modus",
"timestamp": "01/13/2023 20:18:50",
"content": "**odd**",
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},
{
"id": 1063628271138381800,
"author_id": 521837027919003650,
"author_name": "hi123",
"timestamp": "01/13/2023 20:19:01",
"content": "x",
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},
{
"id": 1063628377313005700,
"author_id": 264901235834880000,
"author_name": "Modus",
"timestamp": "01/13/2023 20:19:26",
"content": "I mean, they can be odd, but only and only if x is odd",
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"id": 1063628533500489700,
"author_id": 521837027919003650,
"author_name": "hi123",
"timestamp": "01/13/2023 20:20:03",
"content": "x+1, x+3, x+5",
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},
{
"id": 1063628700152774700,
"author_id": 264901235834880000,
"author_name": "Modus",
"timestamp": "01/13/2023 20:20:43",
"content": "let's stay with x, x + 2 and x + 4 for odd x",
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},
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"id": 1063628769501380600,
"author_id": 264901235834880000,
"author_name": "Modus",
"timestamp": "01/13/2023 20:20:59",
"content": "now what's sum of squares of the first and the third",
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},
{
"id": 1063628802418286600,
"author_id": 521837027919003650,
"author_name": "hi123",
"timestamp": "01/13/2023 20:21:07",
"content": "170",
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},
{
"id": 1063628858483544000,
"author_id": 264901235834880000,
"author_name": "Modus",
"timestamp": "01/13/2023 20:21:21",
"content": "but in terms of x",
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},
{
"id": 1063629280405373000,
"author_id": 521837027919003650,
"author_name": "hi123",
"timestamp": "01/13/2023 20:23:01",
"content": "(x)^2+ (x+4)^2= x^2+ x^2+8x+16= **2x^2+8x+16**",
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},
{
"id": 1063629749928337500,
"author_id": 264901235834880000,
"author_name": "Modus",
"timestamp": "01/13/2023 20:24:53",
"content": "= 170",
"attachments": [],
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},
{
"id": 1063629760145658000,
"author_id": 264901235834880000,
"author_name": "Modus",
"timestamp": "01/13/2023 20:24:56",
"content": "solve for x",
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"reference": null
},
{
"id": 1063630313361776600,
"author_id": 521837027919003650,
"author_name": "hi123",
"timestamp": "01/13/2023 20:27:08",
"content": "x=7 or x=-11",
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},
{
"id": 1063630390335639600,
"author_id": 264901235834880000,
"author_name": "Modus",
"timestamp": "01/13/2023 20:27:26",
"content": "now find possible sets of numbers",
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},
{
"id": 1063630444345696300,
"author_id": 264901235834880000,
"author_name": "Modus",
"timestamp": "01/13/2023 20:27:39",
"content": "plugging x = 7 and x = -11 respectively",
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},
{
"id": 1063631147298472000,
"author_id": 521837027919003650,
"author_name": "hi123",
"timestamp": "01/13/2023 20:30:26",
"content": "7, 9, 11",
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},
{
"id": 1063631170530717700,
"author_id": 521837027919003650,
"author_name": "hi123",
"timestamp": "01/13/2023 20:30:32",
"content": "and",
"attachments": [],
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"reference": null
},
{
"id": 1063631247152259200,
"author_id": 521837027919003650,
"author_name": "hi123",
"timestamp": "01/13/2023 20:30:50",
"content": "-11, -9, -7",
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},
{
"id": 1063631270208360400,
"author_id": 521837027919003650,
"author_name": "hi123",
"timestamp": "01/13/2023 20:30:56",
"content": "Thanks I get it now",
"attachments": [],
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"reference": null
},
{
"id": 1063631535993000000,
"author_id": 521837027919003650,
"author_name": "hi123",
"timestamp": "01/13/2023 20:31:59",
"content": ".close",
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},
{
"id": 1063631538887065700,
"author_id": 805217272087838700,
"author_name": "Mathematics Bot",
"timestamp": "01/13/2023 20:32:00",
"content": "Channel closed",
"attachments": [],
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"reference": null
}
] | help-9 | 3350788c27b74197864c7890768a684f |
200,747 | [
{
"id": 1063631790834720800,
"author_id": 805217272087838700,
"author_name": "Mathematics Bot",
"timestamp": "01/13/2023 20:33:00",
"content": "Available help channel!",
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},
{
"id": 1063633846534426800,
"author_id": 805217272087838700,
"author_name": "Mathematics Bot",
"timestamp": "01/13/2023 20:41:10",
"content": "Pinned a message.",
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"channelId": 486844875632017400,
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{
"id": 1063634285552222200,
"author_id": 1000057838007226500,
"author_name": "VulcanOne",
"timestamp": "01/13/2023 20:42:55",
"content": "Sorry but I can't pick up on the answer",
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"reference": null
},
{
"id": 1063634335284084700,
"author_id": 1000057838007226500,
"author_name": "VulcanOne",
"timestamp": "01/13/2023 20:43:06",
"content": "Could you write the answer on a new page?",
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},
{
"id": 1063634447657881700,
"author_id": 1000057838007226500,
"author_name": "VulcanOne",
"timestamp": "01/13/2023 20:43:33",
"content": "No I meant your answer",
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},
{
"id": 1063634536002490400,
"author_id": 1000057838007226500,
"author_name": "VulcanOne",
"timestamp": "01/13/2023 20:43:54",
"content": "There is a solid single answer that will solve this question\\",
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"reference": null
},
{
"id": 1063634560966991900,
"author_id": 1000057838007226500,
"author_name": "VulcanOne",
"timestamp": "01/13/2023 20:44:00",
"content": "Nothing is impossible",
"attachments": [],
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"reference": null
},
{
"id": 1063634670035685400,
"author_id": 1000057838007226500,
"author_name": "VulcanOne",
"timestamp": "01/13/2023 20:44:26",
"content": "If you have an answer, please post it clearly and label it as the answer",
"attachments": [],
"mentions": [],
"reference": null
},
{
"id": 1063634793973153800,
"author_id": 1000057838007226500,
"author_name": "VulcanOne",
"timestamp": "01/13/2023 20:44:56",
"content": "Hmm",
"attachments": [],
"mentions": [],
"reference": null
},
{
"id": 1063634855436501000,
"author_id": 1000057838007226500,
"author_name": "VulcanOne",
"timestamp": "01/13/2023 20:45:10",
"content": "The question wants the volume",
"attachments": [],
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"reference": null
},
{
"id": 1063634911384326300,
"author_id": 1000057838007226500,
"author_name": "VulcanOne",
"timestamp": "01/13/2023 20:45:24",
"content": "What is volume?",
"attachments": [],
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},
{
"id": 1063634932691374200,
"author_id": 1000057838007226500,
"author_name": "VulcanOne",
"timestamp": "01/13/2023 20:45:29",
"content": "Formula of volume?",
"attachments": [],
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},
{
"id": 1063635120235483300,
"author_id": 1000057838007226500,
"author_name": "VulcanOne",
"timestamp": "01/13/2023 20:46:14",
"content": "Can we also say it is Area x length?",
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},
{
"id": 1063635219174916100,
"author_id": 1000057838007226500,
"author_name": "VulcanOne",
"timestamp": "01/13/2023 20:46:37",
"content": "Volume is LxWxH",
"attachments": [],
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},
{
"id": 1063635229790707700,
"author_id": 1000057838007226500,
"author_name": "VulcanOne",
"timestamp": "01/13/2023 20:46:40",
"content": "Right?",
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},
{
"id": 1063635273872842900,
"author_id": 1000057838007226500,
"author_name": "VulcanOne",
"timestamp": "01/13/2023 20:46:50",
"content": "What if we make WxH = Area",
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},
{
"id": 1063635397143441400,
"author_id": 1000057838007226500,
"author_name": "VulcanOne",
"timestamp": "01/13/2023 20:47:20",
"content": "Volume will be Area x Length right?",
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},
{
"id": 1063635466869538800,
"author_id": 1000057838007226500,
"author_name": "VulcanOne",
"timestamp": "01/13/2023 20:47:36",
"content": "Hmm",
"attachments": [],
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},
{
"id": 1063635532111954000,
"author_id": 1000057838007226500,
"author_name": "VulcanOne",
"timestamp": "01/13/2023 20:47:52",
"content": "Volume is in cubic units of length right?",
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},
{
"id": 1063635605105410000,
"author_id": 1000057838007226500,
"author_name": "VulcanOne",
"timestamp": "01/13/2023 20:48:09",
"content": "Why?",
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},
{
"id": 1063635692644737000,
"author_id": 1000057838007226500,
"author_name": "VulcanOne",
"timestamp": "01/13/2023 20:48:30",
"content": "If we go through it slowly, we will get it nicely",
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"mentions": [],
"reference": null
},
{
"id": 1063635735158214800,
"author_id": 1000057838007226500,
"author_name": "VulcanOne",
"timestamp": "01/13/2023 20:48:40",
"content": "Volume = Area x Length\\",
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},
{
"id": 1063635774119104500,
"author_id": 1000057838007226500,
"author_name": "VulcanOne",
"timestamp": "01/13/2023 20:48:49",
"content": "This means",
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},
{
"id": 1063635849432019100,
"author_id": 1000057838007226500,
"author_name": "VulcanOne",
"timestamp": "01/13/2023 20:49:07",
"content": "That we can get the area of the trapezoid",
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},
{
"id": 1063635887742791700,
"author_id": 1000057838007226500,
"author_name": "VulcanOne",
"timestamp": "01/13/2023 20:49:17",
"content": "And multiply it by the length",
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},
{
"id": 1063635934593159300,
"author_id": 1000057838007226500,
"author_name": "VulcanOne",
"timestamp": "01/13/2023 20:49:28",
"content": "True",
"attachments": [],
"mentions": [],
"reference": null
},
{
"id": 1063635954889412600,
"author_id": 1000057838007226500,
"author_name": "VulcanOne",
"timestamp": "01/13/2023 20:49:33",
"content": "However",
"attachments": [],
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},
{
"id": 1063636046635614200,
"author_id": 1000057838007226500,
"author_name": "VulcanOne",
"timestamp": "01/13/2023 20:49:54",
"content": "The volume should not have addition in it",
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"reference": null
},
{
"id": 1063636151811977200,
"author_id": 1000057838007226500,
"author_name": "VulcanOne",
"timestamp": "01/13/2023 20:50:19",
"content": "Hmm",
"attachments": [],
"mentions": [],
"reference": null
},
{
"id": 1063636186385633400,
"author_id": 1000057838007226500,
"author_name": "VulcanOne",
"timestamp": "01/13/2023 20:50:28",
"content": "Okay add volumes ye",
"attachments": [],
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},
{
"id": 1063636221630365800,
"author_id": 1000057838007226500,
"author_name": "VulcanOne",
"timestamp": "01/13/2023 20:50:36",
"content": "But not in the sense that I mean",
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},
{
"id": 1063636332234158100,
"author_id": 1000057838007226500,
"author_name": "VulcanOne",
"timestamp": "01/13/2023 20:51:03",
"content": "I can't pick up on your work",
"attachments": [],
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"reference": null
},
{
"id": 1063636374399496300,
"author_id": 1000057838007226500,
"author_name": "VulcanOne",
"timestamp": "01/13/2023 20:51:13",
"content": "I don't know where to look",
"attachments": [],
"mentions": [],
"reference": null
},
{
"id": 1063636550690287600,
"author_id": 1000057838007226500,
"author_name": "VulcanOne",
"timestamp": "01/13/2023 20:51:55",
"content": "In your solution yes",
"attachments": [],
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},
{
"id": 1063636616134009000,
"author_id": 1000057838007226500,
"author_name": "VulcanOne",
"timestamp": "01/13/2023 20:52:10",
"content": "But the question can be easy if you go through it slowly",
"attachments": [],
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"reference": null
},
{
"id": 1063638033179607200,
"author_id": 950492608428376000,
"author_name": "Aftershock",
"timestamp": "01/13/2023 20:57:48",
"content": "im like on 5th level, so idk what this is",
"attachments": [],
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},
{
"id": 1063638919641571500,
"author_id": 805217272087838700,
"author_name": "Mathematics Bot",
"timestamp": "01/13/2023 21:01:19",
"content": "Channel closed",
"attachments": [],
"mentions": [],
"reference": null
}
] | help-9 | ced11704930448d69eba099784447d93 |
200,748 | [
{
"id": 1063639170586771500,
"author_id": 805217272087838700,
"author_name": "Mathematics Bot",
"timestamp": "01/13/2023 21:02:19",
"content": "Available help channel!",
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},
{
"id": 1063643603848671200,
"author_id": 236252356553998340,
"author_name": "Goldi",
"timestamp": "01/13/2023 21:19:56",
"content": "",
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"timestamp": "01/13/2023 21:19:57",
"content": "Pinned a message.",
"attachments": [],
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{
"id": 1063643617920561300,
"author_id": 236252356553998340,
"author_name": "Goldi",
"timestamp": "01/13/2023 21:20:00",
"content": "during the simplification",
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},
{
"id": 1063643647691739300,
"author_id": 236252356553998340,
"author_name": "Goldi",
"timestamp": "01/13/2023 21:20:07",
"content": "why is b^2 not broken down until later",
"attachments": [],
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"reference": null
},
{
"id": 1063643727471587500,
"author_id": 236252356553998340,
"author_name": "Goldi",
"timestamp": "01/13/2023 21:20:26",
"content": "i thought what u do to one side u have to do to the other",
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},
{
"id": 1063643780311425200,
"author_id": 236252356553998340,
"author_name": "Goldi",
"timestamp": "01/13/2023 21:20:38",
"content": "or is that more a 1 for 1 thing",
"attachments": [],
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},
{
"id": 1063643812565618700,
"author_id": 236252356553998340,
"author_name": "Goldi",
"timestamp": "01/13/2023 21:20:46",
"content": "square one thing on one side, square one thing on the other",
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},
{
"id": 1063643828810162300,
"author_id": 391896531747340300,
"author_name": "Ankit",
"timestamp": "01/13/2023 21:20:50",
"content": "They did show the โ sign on left side",
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},
{
"id": 1063643872753881100,
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"timestamp": "01/13/2023 21:21:00",
"content": "Just for that",
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"author_id": 236252356553998340,
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"timestamp": "01/13/2023 21:21:09",
"content": "so thats the case?",
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"timestamp": "01/13/2023 21:21:11",
"content": "eye for an eye?",
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"content": "not entire equilibrium",
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"content": "they subbed in known values for a^2 and c^2",
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"author_name": "Ankit",
"timestamp": "01/13/2023 21:21:28",
"content": "Yeah the second last step shows that they're taking root on both sides",
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"timestamp": "01/13/2023 21:21:38",
"content": "yea but when both sides are rooted previously",
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"content": "b isnt until later",
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"content": "which step are u talking about",
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"timestamp": "01/13/2023 21:22:18",
"content": "when 1/2^2 turns into 1/4",
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"timestamp": "01/13/2023 21:22:23",
"content": "and 1^2 turns into 1",
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"content": "yeah",
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"author_name": "hibyehibye",
"timestamp": "01/13/2023 21:22:29",
"content": "but you dont know the value of b^2",
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"content": "b remains unchanged until later",
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"timestamp": "01/13/2023 21:22:31",
"content": "well b^2 turns into b^2",
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"content": "so you cant simplify it",
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"content": "ohhh shoot i see what i did wrong",
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"content": "b x b",
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"timestamp": "01/13/2023 21:23:22",
"content": "is just b^2",
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"content": "ok i got mixed upt hanks",
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"content": ".close",
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"content": "Channel closed",
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] | help-9 | 442a24b878c44ef5b171b3256d7e378a |
200,749 | [
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"content": ",w NSolve[-2x^3 - 2x^2 + 8x == -3, x]",
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"content": "What the actual shit",
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"content": "can u tell me? i got the past 3 correct with the calculator, but its down bc my computer is whack",
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"timestamp": "01/13/2023 21:39:01",
"content": "Well I mean the graphing calculator should tell you explicitly",
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"content": "ik",
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"content": "the calculator is not working",
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"timestamp": "01/13/2023 21:39:15",
"content": "Desmos always tells",
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"content": "thats the problem",
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"content": "omg, thank you so much!",
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"content": "i might come back tho",
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"timestamp": "01/13/2023 21:40:56",
"content": ".close",
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] | help-9 | eb865ef9c7244aabad1fec4596ab0359 |
200,750 | [
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"content": "@alexisreen Has your question been resolved?",
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"content": "What is your question exactly",
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"content": "center of mass",
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"content": "C = integral z dm / m",
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"content": "I answered that here",
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"timestamp": "01/13/2023 22:16:28",
"content": "m = ?",
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"timestamp": "01/13/2023 22:16:32",
"content": "That formula looks wrong",
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"id": 1063657870278803600,
"author_id": 261933205387477000,
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"timestamp": "01/13/2023 22:16:38",
"content": "https://youtu.be/SWu_i-19Rn0",
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"id": 1063657894005968900,
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"timestamp": "01/13/2023 22:16:43",
"content": "Start around 21:00",
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"timestamp": "01/13/2023 22:17:18",
"content": "Use uniform density to calculate denominator",
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"content": "@alexisreen Has your question been resolved?",
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] | help-9 | 19f4ac0fa68247f293ca46038ae44f59 |
200,751 | [
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"id": 1063678894059835400,
"author_id": 687497805958217700,
"author_name": "Willow",
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"content": "$x^2+(2\\cdot\\Delta x\\cdot x) + \\Delta x^2 - 4x - 4 \\Delta x$",
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"timestamp": "01/13/2023 23:40:12",
"content": "**Willow**",
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"timestamp": "01/13/2023 23:40:22",
"content": "so far, I have:",
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"content": "$x^2+(2\\Delta x^2) + \\Delta x^2 - 4x - 4 \\Delta x$\n\n$x^2 + 3\\Delta x^2 - 4x - 4 \\Delta x$",
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"timestamp": "01/13/2023 23:40:26",
"content": "**Willow**",
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"timestamp": "01/13/2023 23:40:31",
"content": "correct?",
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"id": 1063679734208286700,
"author_id": 702550180154835000,
"author_name": "GameSwitch",
"timestamp": "01/13/2023 23:43:30",
"content": "you're simplifying it?",
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"timestamp": "01/13/2023 23:43:37",
"content": "or factorising it?",
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"timestamp": "01/13/2023 23:44:49",
"content": "get an availale help channel",
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"author_name": "Willow",
"timestamp": "01/13/2023 23:45:19",
"content": "The original problem is Find the limit of \n\n$\\frac{x^2+(2\\cdot\\Delta x\\cdot x) + \\Delta x^2 - 4x - 4 \\Delta x}{\\Delta x}$",
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"timestamp": "01/13/2023 23:45:41",
"content": "**Willow**",
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"timestamp": "01/13/2023 23:45:52",
"content": "As?",
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"timestamp": "01/13/2023 23:46:06",
"content": "Therefore, I think this is simplifying",
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"timestamp": "01/13/2023 23:46:36",
"content": "oh, \n\n$f(x) = x^2 - 4x$",
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"timestamp": "01/13/2023 23:46:39",
"content": "**Willow**",
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"author_name": "Willow",
"timestamp": "01/13/2023 23:46:51",
"content": "but please don't tell me the answer",
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"timestamp": "01/13/2023 23:46:58",
"content": "I'm just doing the steps slowly",
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"author_name": "Umbraleviathan",
"timestamp": "01/13/2023 23:47:22",
"content": "Are you computing it's derivative?",
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"timestamp": "01/13/2023 23:47:47",
"content": "#85 here",
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"timestamp": "01/13/2023 23:47:52",
"content": "Yeah that's the derivative definition",
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"timestamp": "01/13/2023 23:48:10",
"content": "my teacher called it the difference quotient",
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"timestamp": "01/13/2023 23:48:42",
"content": "indeed it is",
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"author_name": "Willow",
"timestamp": "01/13/2023 23:49:06",
"content": "two names for the same idea?",
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"author_name": "ramonov",
"timestamp": "01/13/2023 23:49:08",
"content": "the expression without the limit is a difference quotient",
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"timestamp": "01/13/2023 23:49:27",
"content": "ah, ok",
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"author_name": "ramonov",
"timestamp": "01/13/2023 23:49:46",
"content": "taking the lim as Delta(x) โ 0 gives the derivative",
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"timestamp": "01/13/2023 23:49:53",
"content": "(by definition)",
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"author_id": 307914411648090100,
"author_name": "Stephen",
"timestamp": "01/13/2023 23:49:55",
"content": "Limit of the difference quotient^",
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"timestamp": "01/13/2023 23:49:58",
"content": "you forgot another part here",
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"author_name": "Umbraleviathan",
"timestamp": "01/13/2023 23:50:06",
"content": "What you might realize is that derivatives are linear. So you can apply it to each term",
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"author_name": "Willow",
"timestamp": "01/13/2023 23:50:16",
"content": "yes, I just noticed an error",
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"timestamp": "01/13/2023 23:50:24",
"content": "I'm re-writing by hand now",
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"timestamp": "01/13/2023 23:50:59",
"content": "$\\frac{x^2+(2\\cdot\\Delta x\\cdot x) + \\Delta x^2 - 4x - 4 \\Delta x - x^2 + 4x}{\\Delta x}$",
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"timestamp": "01/13/2023 23:51:02",
"content": "**GameSwitch**",
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"timestamp": "01/13/2023 23:51:07",
"content": "this is the correct equation",
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"timestamp": "01/13/2023 23:51:34",
"content": "๐ฆ",
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"author_name": "Willow",
"timestamp": "01/13/2023 23:51:39",
"content": "why did you give me the answer?",
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"author_id": 349354952961032200,
"author_name": "Umbraleviathan",
"timestamp": "01/13/2023 23:51:46",
"content": "$\\limit{\\frac{(x+h)^2 - x^2}{h}}{h}{0} + \\limit{\\frac{-4(x+h) + 4x}{h}}{h}{0}$",
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"author_name": "riemann",
"timestamp": "01/13/2023 23:51:48",
"content": "don't do that",
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"timestamp": "01/13/2023 23:51:49",
"content": "**Umbraleviathan**",
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"timestamp": "01/13/2023 23:51:57",
"content": "Like that kinda",
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"author_name": "Umbraleviathan",
"timestamp": "01/13/2023 23:52:01",
"content": "If need be",
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"timestamp": "01/13/2023 23:52:20",
"content": "wdym",
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"timestamp": "01/13/2023 23:52:56",
"content": "give away answers",
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"timestamp": "01/13/2023 23:53:08",
"content": "oh.",
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"timestamp": "01/13/2023 23:53:34",
"content": "umm",
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"timestamp": "01/13/2023 23:54:06",
"content": "๐คฆโโ๏ธ mb",
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"timestamp": "01/13/2023 23:54:10",
"content": "sorry",
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"author_id": 261933205387477000,
"author_name": "riemann",
"timestamp": "01/13/2023 23:54:24",
"content": "a lot of people make the mistake. just try not to do it again",
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"id": 1063682501849141400,
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"timestamp": "01/13/2023 23:54:30",
"content": "k sure",
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"author_name": "Willow",
"timestamp": "01/13/2023 23:54:38",
"content": "I got a 45 (an F) on a quiz today, so I really need to do the work myself",
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"timestamp": "01/13/2023 23:57:10",
"content": "Ok, now, I have:",
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"author_name": "Willow",
"timestamp": "01/13/2023 23:57:11",
"content": "$x^2+(2\\cdot\\Delta x\\cdot x) + \\Delta x^2 - 4x - 4 \\Delta x - x^2 + 4x$",
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"timestamp": "01/13/2023 23:57:13",
"content": "**Willow**",
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"timestamp": "01/13/2023 23:57:23",
"content": "I will simplify it now",
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"id": 1063684012452880500,
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"timestamp": "01/14/2023 00:00:30",
"content": "this:",
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"id": 1063684014986236000,
"author_id": 687497805958217700,
"author_name": "Willow",
"timestamp": "01/14/2023 00:00:31",
"content": "$\\frac{3\\Delta x^2 - 4 \\Delta x}{\\Delta x}$",
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"timestamp": "01/14/2023 00:00:34",
"content": "**Willow**",
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"timestamp": "01/14/2023 00:01:37",
"content": "you didn't multiply properly",
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"author_id": 220517274845577200,
"author_name": "ramonov",
"timestamp": "01/14/2023 00:01:59",
"content": "$\\Delta{x} \\cdot x$ isn't $\\Delta{x}^2$",
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"timestamp": "01/14/2023 00:02:01",
"content": "**โamonov**",
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"timestamp": "01/14/2023 00:02:09",
"content": "exactly thats what i was thinking",
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"timestamp": "01/14/2023 00:02:34",
"content": "the entire $\\Delta{x}$ is it's own expression",
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"timestamp": "01/14/2023 00:02:36",
"content": "**โamonov**",
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"timestamp": "01/14/2023 00:02:46",
"content": "ah, ok",
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"timestamp": "01/14/2023 00:02:51",
"content": "let me try again, then",
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"author_name": "ramonov",
"timestamp": "01/14/2023 00:02:55",
"content": "$\\Delta$ isn't a mysterious magic value being multiplied to x",
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"id": 1063684632010293200,
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"timestamp": "01/14/2023 00:02:58",
"content": "**โamonov**",
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"timestamp": "01/14/2023 00:03:26",
"content": "$\\Delta{x}\\cdot x$ can be more nicely written as $x\\Delta{x}$",
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"timestamp": "01/14/2023 00:03:28",
"content": "**โamonov**",
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"timestamp": "01/14/2023 00:05:21",
"content": "How are you getting your Tex to look so nice with the white background?",
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"timestamp": "01/14/2023 00:05:48",
"content": "`,texconfig colour white`",
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"author_id": 687497805958217700,
"author_name": "Willow",
"timestamp": "01/14/2023 00:06:03",
"content": "I just run that command once here?",
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"content": "yeh",
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"timestamp": "01/14/2023 00:06:15",
"content": ",texconfig colour white",
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"author_name": "TeXit",
"timestamp": "01/14/2023 00:06:15",
"content": "You have switched to the `white` colourscheme.",
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"author_name": "Nilocnus",
"timestamp": "01/14/2023 00:06:28",
"content": "I think it's for this very reason that using delta symbols in actual algebraic expression solving can be easily misunderstood. Separate question, but is that why Delta x is typically referred to as the \"h\" variable in the difference quotient?",
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"timestamp": "01/14/2023 00:06:47",
"content": "change in x",
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"timestamp": "01/14/2023 00:07:51",
"content": "You're referring to this?\nhttps://discord.com/channels/268882317391429632/486844875632017408/1063681823709855864",
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"timestamp": "01/14/2023 00:09:10",
"content": "yes",
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"timestamp": "01/14/2023 00:13:34",
"content": "rewritten:",
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"timestamp": "01/14/2023 00:13:35",
"content": "$x^2+(2\\cdot\\Delta x\\cdot x) + \\Delta x^2 - 4x - 4 \\Delta x - x^2 + 4x$ \\\\\n\n$x^2+(2x\\Delta x) + \\Delta x^2 - 4x - 4 \\Delta x - x^2 + 4x$ \\\\\n\n$2x\\Delta x + \\Delta x^2 - 4\\Delta x$ \\\\\n\n$\\frac{2x\\Delta x + \\Delta x^2 - 4\\Delta x}{\\Delta x}$",
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"author_name": "Willow",
"timestamp": "01/14/2023 00:14:20",
"content": "I need some spaces between the equations for clarity.",
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"timestamp": "01/14/2023 00:14:26",
"content": "let me search for how to do that",
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"author_name": "ramonov",
"timestamp": "01/14/2023 00:16:30",
"content": "`\\\\` for new line, `\\\\ \\\\` for more space",
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"timestamp": "01/14/2023 00:17:23",
"content": "**Willow**",
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"timestamp": "01/14/2023 00:17:45",
"content": "ideally that Delta(x) denominator would be present at the very start",
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"timestamp": "01/14/2023 00:17:54",
"content": "ok, that's better. But there is no way to have the Tex appear directly under the post where Tex input is?",
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"timestamp": "01/14/2023 00:18:24",
"content": "you mean like this $\\Delta x 2x$ ?",
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"timestamp": "01/14/2023 00:18:26",
"content": "**Willow**",
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"timestamp": "01/14/2023 00:18:27",
"content": "the bot needs to generate a new post when you edit",
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"timestamp": "01/14/2023 00:18:49",
"content": "`you mean like this $\\Delta x 2x$ ?`\nno, i mean that denominator would be present at the very start",
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"timestamp": "01/14/2023 00:19:04",
"content": "it's quite messy, but I guess I have no other option",
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"timestamp": "01/14/2023 00:19:49",
"content": "oh, I just removed it to focus on the simplification since I have trouble with that",
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"timestamp": "01/14/2023 00:20:00",
"content": "best to type everything in full context",
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"timestamp": "01/14/2023 00:20:04",
"content": "but otherwise, is it all correct so far?",
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"timestamp": "01/14/2023 00:20:18",
"content": "ok, I will from now on. you have a good point",
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"timestamp": "01/14/2023 00:20:27",
"content": "yes",
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"timestamp": "01/14/2023 00:20:31",
"content": "but in that case, I should include the limit notation also",
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"content": "yes",
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"timestamp": "01/14/2023 00:20:56",
"content": "ok, best to get into the habit even if it's tedious",
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"timestamp": "01/14/2023 00:25:04",
"content": "final answer should be:",
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"timestamp": "01/14/2023 00:25:05",
"content": "$\\lim_{\\Delta x \\to 0}\\frac{2x\\Delta x + \\Delta x^2 - 4\\Delta x}{\\Delta x} = 2x + \\Delta x - 4$",
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"timestamp": "01/14/2023 00:25:07",
"content": "**Willow**",
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"timestamp": "01/14/2023 00:25:16",
"content": "correct?",
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"timestamp": "01/14/2023 00:25:42",
"content": "not quite",
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"timestamp": "01/14/2023 00:25:53",
"content": "what's that Delta(x) still doing there",
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"timestamp": "01/14/2023 00:26:09",
"content": "take the limit for all Delta(x) present",
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"timestamp": "01/14/2023 00:26:21",
"content": "oh, wait",
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"timestamp": "01/14/2023 00:26:28",
"content": "at the end, I plug in the `0`",
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"timestamp": "01/14/2023 00:26:52",
"content": "$2x + (\\Delta \\cdot 0) - 4$",
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"timestamp": "01/14/2023 00:26:54",
"content": "**Willow**",
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"timestamp": "01/14/2023 00:26:58",
"content": "no",
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"timestamp": "01/14/2023 00:27:00",
"content": "No",
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"timestamp": "01/14/2023 00:27:09",
"content": "Delta x itself tends to 0",
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"timestamp": "01/14/2023 00:27:16",
"content": "Youโre resolving the limit at that step",
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"content": "huh?",
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"timestamp": "01/14/2023 00:27:31",
"content": "I don't understand",
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"timestamp": "01/14/2023 00:27:39",
"content": "> the entire Delta(x) is it's own expression",
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"author_name": "Ann",
"timestamp": "01/14/2023 00:27:47",
"content": "as confusing as it seems, ฮx is its own **variable**.",
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"timestamp": "01/14/2023 00:27:55",
"content": "it is not Delta times x",
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"timestamp": "01/14/2023 00:27:57",
"content": "The limit doesnโt disappear until you make delta x = 0",
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"timestamp": "01/14/2023 00:28:17",
"content": "oh, yes, that's right",
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"content": "$\\Delta x$ appears underneath the limit function",
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"timestamp": "01/14/2023 00:28:31",
"content": "**Willow**",
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"content": "$\\lim_{\\Delta x \\to 0}\\frac{2x\\Delta x + \\Delta x^2 - 4\\Delta x}{\\Delta x} = \\lim_{\\Delta x \\to 0} 2x + \\Delta x - 4$",
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"timestamp": "01/14/2023 00:28:36",
"content": "delta x is different variable basically",
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"content": "**Frosst**",
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"timestamp": "01/14/2023 00:28:37",
"content": "$\\Delta x = (x + \\Delta x) - x$",
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"timestamp": "01/14/2023 00:28:41",
"content": "and its value is 0",
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"timestamp": "01/14/2023 00:28:50",
"content": "here",
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"timestamp": "01/14/2023 00:28:52",
"content": "**GameSwitch**",
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"content": "You havenโt resolved the limit yet on that last part",
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"content": "$\\lim_{\\text{this}\\to 0} (2x + \\text{this} - 4)$",
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"timestamp": "01/14/2023 00:29:13",
"content": "**โamonov**",
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"author_id": 183668144404037630,
"author_name": "Ann",
"timestamp": "01/14/2023 00:29:17",
"content": "... now i realize there might be too many cooks in the kitchen",
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"timestamp": "01/14/2023 00:29:27",
"content": "it should be this, then:",
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"timestamp": "01/14/2023 00:29:28",
"content": "$2x + (0) - 4$",
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"author_id": 510789298321096700,
"author_name": "TeXit",
"timestamp": "01/14/2023 00:29:30",
"content": "**Willow**",
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"author_name": "ramonov",
"timestamp": "01/14/2023 00:29:52",
"content": "yeh",
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"timestamp": "01/14/2023 00:29:54",
"content": "yes, this. ty",
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"author_name": "ramonov",
"timestamp": "01/14/2023 00:30:07",
"content": "and that can be simplified written more nicely",
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"id": 1063691481778495600,
"author_id": 244390699431100400,
"author_name": "Frosst",
"timestamp": "01/14/2023 00:30:11",
"content": "Once you do this step the limit disappears",
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"author_name": "Willow",
"timestamp": "01/14/2023 00:30:58",
"content": "final answer re-written:",
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"author_name": "Willow",
"timestamp": "01/14/2023 00:30:59",
"content": "$\\lim_{\\Delta x \\to 0}\\frac{2x\\Delta x + \\Delta x^2 - 4\\Delta x}{\\Delta x} = 2x + (0) - 4 = 2x - 4$",
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"id": 1063691728386801700,
"author_id": 220517274845577200,
"author_name": "ramonov",
"timestamp": "01/14/2023 00:31:10",
"content": "no",
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"author_id": 220517274845577200,
"author_name": "ramonov",
"timestamp": "01/14/2023 00:31:21",
"content": "how are you getting +4 at the end",
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"timestamp": "01/14/2023 00:31:25",
"content": "**Willow**",
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"timestamp": "01/14/2023 00:31:28",
"content": "yes",
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"author_id": 687497805958217700,
"author_name": "Willow",
"timestamp": "01/14/2023 00:31:36",
"content": "it was a typo, sorry",
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"id": 1063693173920116900,
"author_id": 687497805958217700,
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"timestamp": "01/14/2023 00:36:55",
"content": "ty all",
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"timestamp": "01/14/2023 00:36:56",
"content": ".close",
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"id": 1063693183655088100,
"author_id": 805217272087838700,
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"content": "Channel closed",
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] | help-9 | 0df64f5a2e7a479d89045cf5f663e060 |
200,752 | [
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"author_name": "Mathematics Bot",
"timestamp": "01/14/2023 00:41:49",
"content": "Available help channel!",
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},
{
"id": 1063698096946683900,
"author_id": 598412021800894500,
"author_name": "TheLonelyPotato",
"timestamp": "01/14/2023 00:56:28",
"content": "for this question, would it not suffice to",
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"author_id": 598412021800894500,
"author_name": "TheLonelyPotato",
"timestamp": "01/14/2023 00:56:46",
"content": "find two vectors parallel to the plane, find their vector product and",
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},
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"author_id": 598412021800894500,
"author_name": "TheLonelyPotato",
"timestamp": "01/14/2023 00:57:16",
"content": "then find the dot product of that normal vector, then use that vector and either one of the points to express the plane in the form r . n = c",
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"author_name": "TheLonelyPotato",
"timestamp": "01/14/2023 00:57:53",
"content": "for example, the two vectors parallel to the plane would be (1, -3, -5) and (2-1, 2-2, 1-0) = (1, 0, 1)",
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"author_name": "TheLonelyPotato",
"timestamp": "01/14/2023 00:58:58",
"content": "their cross product (1, -3, -5) x (1, 0, 1) = (-3, 4, 3)",
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"timestamp": "01/14/2023 00:59:12",
"content": "(-3, 4, 3) . (1, 2, 0) = 5",
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"timestamp": "01/14/2023 00:59:35",
"content": "so then the plane in that form is ```r . (-3, 4, 3) = 5```",
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"id": 1063700252433060000,
"author_id": 598412021800894500,
"author_name": "TheLonelyPotato",
"timestamp": "01/14/2023 01:05:02",
"content": "Hello darkness, my old frieeeend ๐ข",
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"id": 1063700396947800000,
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"author_name": "Saccharine",
"timestamp": "01/14/2023 01:05:37",
"content": "yes",
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"author_name": "TheLonelyPotato",
"timestamp": "01/14/2023 01:05:55",
"content": "this is wrong though",
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"author_id": 598412021800894500,
"author_name": "TheLonelyPotato",
"timestamp": "01/14/2023 01:06:07",
"content": "the answer is",
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"timestamp": "01/14/2023 01:06:39",
"content": "@Saccharine",
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"author_name": "TheLonelyPotato",
"timestamp": "01/14/2023 01:07:15",
"content": "fwiw, this is their working",
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"author_name": "TheLonelyPotato",
"timestamp": "01/14/2023 01:07:36",
"content": "I just feel my \"method\" (to be confirmed if it even works lmao) to be easier",
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"author_id": 598412021800894500,
"author_name": "TheLonelyPotato",
"timestamp": "01/14/2023 01:08:14",
"content": "* I understand what they've done ofc",
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"id": 1063701253378560000,
"author_id": 704179090395103200,
"author_name": "Saccharine",
"timestamp": "01/14/2023 01:09:01",
"content": "you've done the cross product wrong",
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"id": 1063701287088177300,
"author_id": 704179090395103200,
"author_name": "Saccharine",
"timestamp": "01/14/2023 01:09:09",
"content": ",w cross product of (1, -3, -5) and (1, 0, 1)",
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"id": 1063701297716527100,
"author_id": 510789298321096700,
"author_name": "TeXit",
"timestamp": "01/14/2023 01:09:11",
"content": "Results provided by WolframAlpha",
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"id": 1063701333611401200,
"author_id": 704179090395103200,
"author_name": "Saccharine",
"timestamp": "01/14/2023 01:09:20",
"content": "this result makes more sense yeah?",
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"author_name": "Saccharine",
"timestamp": "01/14/2023 01:10:14",
"content": "you're basically doing the same thing as what they're doing, in the sense that the cross product is just a formula for the solution of the system of linear equations",
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"author_id": 598412021800894500,
"author_name": "TheLonelyPotato",
"timestamp": "01/14/2023 01:11:38",
"content": "then the equation for the plane is this, right?",
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"author_name": "TheLonelyPotato",
"timestamp": "01/14/2023 01:11:45",
"content": "is this synonymous to what they've written",
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"id": 1063702070059876400,
"author_id": 704179090395103200,
"author_name": "Saccharine",
"timestamp": "01/14/2023 01:12:16",
"content": "well",
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"id": 1063702107263344600,
"author_id": 704179090395103200,
"author_name": "Saccharine",
"timestamp": "01/14/2023 01:12:25",
"content": "note that the vector that you have is -3 times their vector",
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"id": 1063702138024378400,
"author_id": 704179090395103200,
"author_name": "Saccharine",
"timestamp": "01/14/2023 01:12:32",
"content": "so r dot -3v = -3(5)",
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"id": 1063702187500388500,
"author_id": 598412021800894500,
"author_name": "TheLonelyPotato",
"timestamp": "01/14/2023 01:12:44",
"content": "huh",
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"id": 1063702194576183300,
"author_id": 704179090395103200,
"author_name": "Saccharine",
"timestamp": "01/14/2023 01:12:45",
"content": "and indeed, if you divide out both sides by -3",
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"id": 1063702205305212900,
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"author_name": "Saccharine",
"timestamp": "01/14/2023 01:12:48",
"content": "you get what they have",
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"id": 1063702208098598900,
"author_id": 598412021800894500,
"author_name": "TheLonelyPotato",
"timestamp": "01/14/2023 01:12:49",
"content": "ty so much!",
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"id": 1063702244228346000,
"author_id": 598412021800894500,
"author_name": "TheLonelyPotato",
"timestamp": "01/14/2023 01:12:57",
"content": "just to confirm",
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"id": 1063702298989166700,
"author_id": 598412021800894500,
"author_name": "TheLonelyPotato",
"timestamp": "01/14/2023 01:13:10",
"content": "is this the correct formula?",
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"author_id": 598412021800894500,
"author_name": "TheLonelyPotato",
"timestamp": "01/14/2023 01:13:30",
"content": "I just messed up in my calculation?",
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"id": 1063702384766881900,
"author_id": 704179090395103200,
"author_name": "Saccharine",
"timestamp": "01/14/2023 01:13:31",
"content": "honestly wouldn't know looks like it though",
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"id": 1063702425174822900,
"author_id": 704179090395103200,
"author_name": "Saccharine",
"timestamp": "01/14/2023 01:13:40",
"content": "I don't remember the formulae for this stuff",
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"timestamp": "01/14/2023 01:13:49",
"content": "all g, thanks!",
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"author_id": 598412021800894500,
"author_name": "TheLonelyPotato",
"timestamp": "01/14/2023 01:13:51",
"content": ".close",
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"id": 1063702471433789600,
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"timestamp": "01/14/2023 01:13:51",
"content": "Channel closed",
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}
] | help-9 | cb9356a2c3204966885d74ca689bf810 |
200,753 | [
{
"id": 1063739621718114300,
"author_id": 805217272087838700,
"author_name": "Mathematics Bot",
"timestamp": "01/14/2023 03:41:29",
"content": "Available help channel!",
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},
{
"id": 1063741608597659800,
"author_id": 709377021876240500,
"author_name": "fyu",
"timestamp": "01/14/2023 03:49:22",
"content": "hi can someone teach me how to solve, im rlly strugglin with this\n\n```\nx - y = - 3\n3x + y = 19\n```",
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"id": 1063741610854195200,
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"timestamp": "01/14/2023 03:49:23",
"content": "Pinned a message.",
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{
"id": 1063741735924146200,
"author_id": 331558346333224960,
"author_name": "jan Niku",
"timestamp": "01/14/2023 03:49:53",
"content": "What class?",
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},
{
"id": 1063741780639621200,
"author_id": 331558346333224960,
"author_name": "jan Niku",
"timestamp": "01/14/2023 03:50:03",
"content": "there are a lot of common methods for approaching these.",
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},
{
"id": 1063741874747224000,
"author_id": 709377021876240500,
"author_name": "fyu",
"timestamp": "01/14/2023 03:50:26",
"content": "sub",
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},
{
"id": 1063741890836574200,
"author_id": 331558346333224960,
"author_name": "jan Niku",
"timestamp": "01/14/2023 03:50:30",
"content": "sub?",
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},
{
"id": 1063741906699432000,
"author_id": 709377021876240500,
"author_name": "fyu",
"timestamp": "01/14/2023 03:50:33",
"content": "ye",
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},
{
"id": 1063741926207131600,
"author_id": 331558346333224960,
"author_name": "jan Niku",
"timestamp": "01/14/2023 03:50:38",
"content": "well I was gonna say",
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"author_id": 704179090395103200,
"author_name": "Saccharine",
"timestamp": "01/14/2023 03:50:39",
"content": "LU decomposition with partial pivoting obviously",
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},
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"id": 1063742027143065600,
"author_id": 331558346333224960,
"author_name": "jan Niku",
"timestamp": "01/14/2023 03:51:02",
"content": "The very first thing i'd notice",
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"timestamp": "01/14/2023 03:51:08",
"content": "is that you have -y and +y",
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"content": "in one equation and the other",
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"content": "you should try adding these equations to each other",
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"timestamp": "01/14/2023 03:51:27",
"content": "you should get some cancellation.",
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"content": "@fyu can you try that?",
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"timestamp": "01/14/2023 03:53:03",
"content": "or we can walk through just naive substitution, too",
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"author_name": "โกA(lex)โก",
"timestamp": "01/14/2023 03:53:10",
"content": "You are a monster for even suggesting LU factorisation",
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"timestamp": "01/14/2023 03:53:17",
"content": "this",
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"timestamp": "01/14/2023 04:04:45",
"content": "yow ๐ญ",
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"timestamp": "01/14/2023 04:08:10",
"content": "hi",
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"timestamp": "01/14/2023 04:09:07",
"content": ".",
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"author_name": "Saccharine",
"timestamp": "01/14/2023 04:10:51",
"content": "I'm guessing you don't want to learn how the singular value decomposition could help you here",
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"timestamp": "01/14/2023 04:11:14",
"content": "You want to know how to use the substitution method or something?",
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"timestamp": "01/14/2023 04:11:27",
"content": "yes",
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"author_name": "Saccharine",
"timestamp": "01/14/2023 04:12:11",
"content": "so substitution involves solving for either x or y and then plugging it into the other equation",
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"timestamp": "01/14/2023 04:12:28",
"content": "In this example, we might rearrange the first equation to x = y - 3",
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"timestamp": "01/14/2023 04:12:31",
"content": "do you see how that happened?",
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"content": "yes",
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"timestamp": "01/14/2023 04:13:22",
"content": "i arranged mine to y = 3 - x",
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"timestamp": "01/14/2023 04:13:52",
"content": "i want to solve for x first",
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"timestamp": "01/14/2023 04:14:54",
"content": "well you said y = 3 - x, so you've solved for y",
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"timestamp": "01/14/2023 04:17:17",
"content": "soo 3(y-3) + y = 19",
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"content": "yeah basically",
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"timestamp": "01/14/2023 04:17:52",
"content": "and then solve for y",
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"timestamp": "01/14/2023 04:17:57",
"content": "and then substitute back into find x",
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"content": "ok ill solve",
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"content": "how do u solve this",
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"timestamp": "01/14/2023 04:28:45",
"content": "remember back to the days when they went over this",
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"timestamp": "01/14/2023 04:28:54",
"content": "group all the terms of y on one side",
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"timestamp": "01/14/2023 04:28:58",
"content": "group all the numbers on the other side",
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"timestamp": "01/14/2023 04:29:05",
"content": "3(y-3) + y = 19",
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"content": "let's distribute the 3 over the (y-3)",
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"timestamp": "01/14/2023 04:29:16",
"content": "that gives us 3y - 9 + y = 19",
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"content": "now we group the y terms",
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"content": "4y - 9 = 19",
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"content": "then we group the numbers",
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"content": "4y = 28",
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"content": "divide both sides by y",
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"timestamp": "01/14/2023 04:29:36",
"content": "y = 7",
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"timestamp": "01/14/2023 04:33:00",
"content": "where did 9 come from? did we multiply",
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"content": "3(y-3) = 3y-9",
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"content": "https://www.khanacademy.org/math/algebra-home/alg-basic-eq-ineq probably should review if you can't do it",
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"content": "@fyu Has your question been resolved?",
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"content": ".close",
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] | help-9 | 0542138cae9a4aee93e9fc53d56f72b5 |
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] | help-9 | e2103034ab244907834b780de49a6bec |
200,755 | [
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"content": "Can someone help me with this particular question, content is based on double integrals and having trouble figuring out bounds etc",
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"content": "Basically, we want to find the region D as a union of regions",
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"content": "Oh hm. Are you meant to do it using Rectangular coordinates?",
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"content": "It is not specified, I assume so",
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"content": "Although I am still confused about the rectangular, polar, cylindrical and the other ones",
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"content": "I won't lie I think polar would be really nice here but hmm",
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"content": "It feels weird to explain the concept. But try and make zones where the bounding curves in either the x-direction of y-direction are simple. For example:",
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"timestamp": "01/14/2023 05:17:03",
"content": "Yeah I have done that",
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"content": "You can always split it as a sum of double integrals too, probably the harder way",
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"content": "I have split it up into three distinct regions I am just having trouble get the bounds",
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"content": "For example the one that you have shaded",
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"content": "Show the ones you have chosen, please.",
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"content": "We can start with the blue region first?",
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"timestamp": "01/14/2023 05:19:04",
"content": "Ok. That's a good way to split it up.",
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"content": "Sure",
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"timestamp": "01/14/2023 05:19:15",
"content": "We need to find the y values of intersection.",
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"content": "So if we look at the region it is enclosed by e and a",
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"content": "And the red line",
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"content": "So I am assuming I need to find where e and d cross?",
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"content": "Then find that y coordinate",
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"content": "Yeah I really think polar would be so much better here lmao but that's just me",
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"content": "For the blue region, we are concerned with where x = -y^2 intersects y = x + 2.",
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"content": "Actually eh",
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"content": "You will have a lot more integrals with polar",
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"content": "It would be crazy to use polar here.",
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"content": "Yeah u probably will have like 7 double integrals",
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"content": "Kind of funny",
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"content": "The bounds would be horrendous.",
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"timestamp": "01/14/2023 05:21:13",
"content": "Yeah I guess",
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"content": "I used Desmos to save time:",
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"content": "Sure",
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"content": "Oh wait",
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"content": "You actually just found all the y values first and then do the x",
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"content": "For the blue region, in the x-direction, the lower bounding curve is x = 2 - y and the upper bounding curve is x = sqrt(2 - y).",
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"timestamp": "01/14/2023 05:24:17",
"content": "That is way smarter",
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"timestamp": "01/14/2023 05:24:27",
"content": "Yeah can you give me 5 minutes",
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"content": "going to do this first and check with the concept",
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"content": "really been struggling with getting the bounds and applying fubinis theorem",
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"content": "I wanted to give you this frame work to get the other bounds.",
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"content": "Think of it in terms of lower and upper bounding curves in the positive x-direction (in this case, the analogous version exists for the y-direction. A similar thing works for triple integrals and bounding surfaces.).",
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"timestamp": "01/14/2023 05:27:22",
"content": "Oh so I am messed up",
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"content": "I think I don't really get this bounds thing",
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"content": "For example the blue region, I look at it and I see",
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"content": "Ok. Between the lines y = 1 and y = 2 we have the blue region. And in the x-direction, the lower bounding curve is e and the upper bounding curve is a. We need to solve a and e for x as functions of y.",
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"timestamp": "01/14/2023 05:28:38",
"content": "I see",
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"timestamp": "01/14/2023 05:28:50",
"content": "Between the lines y = 0 and y = 1 we have the purple region. And ....",
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"content": "Could we just work with one region first",
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"content": "How do you know which type of region it is, eg type 1 and type 2",
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"content": "I have nothing more to add anyway now.",
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"content": "Sure",
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"content": "For the blue region I have got the y bounds as you have",
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"content": "Generally it could be either.",
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"timestamp": "01/14/2023 05:29:58",
"content": "But we need the bounding curves to be a single function.",
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"content": "The blue region would have to be split further if we consider the bounding curves to be in the y direction.",
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"timestamp": "01/14/2023 05:30:40",
"content": "fuck wait I did this all wrong",
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"content": "give a minute to read what you have said",
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"content": "Since I am doin this by hand for pracice",
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"content": "If we want to get the region of blue we would have to equate e and d, e and a",
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"content": "We will get the upper and lower bounds of y this way?",
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"content": "But I have some interesting values",
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"content": "For example if I equation e and d I get a quadratic of the form y^2+y-2=0",
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"content": "Which the y values would be y= -2 and y=1",
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"content": "In this case do I just say",
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"timestamp": "01/14/2023 05:35:39",
"content": "\"Looking at the graph the value can not physically be y=-2\"",
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"content": "So we just disregard the y=-2 value?",
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"content": "We can see visually e and a will intersect at x = 0. We can get y = 2 quickly. We used the diagram instead of verifying it, technically the diagram could not be to scale or something that e and b intersect at y = 1.",
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"content": "I see",
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"content": "And if I equate e and a I get x^2-x=0 which the x values would be x = 0 and x = 1",
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"content": "Get the x values and plug it back in and I get y=2 and y=3",
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"timestamp": "01/14/2023 05:37:34",
"content": "So the then y=2 and y=3",
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"timestamp": "01/14/2023 05:37:45",
"content": "How am I supposed to know which y value to choose",
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"content": "It's because x = - y^2 has two \"branches\" which can both intersect the line which is represented in a small part by equation e.",
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"content": "I see",
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"timestamp": "01/14/2023 05:39:13",
"content": "So y=-2 would be that little point where d intersects c?",
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"content": "The line intersects the parabola twice, it's just off the view of the diagram.",
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"content": "Oh man my basics",
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"content": "This bound stuff is hard!!!",
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"content": "Yeah I understand now",
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"timestamp": "01/14/2023 05:40:45",
"content": "But when e and a are equated",
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"content": "We want that y upper bound",
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"content": "This is why the algebra gives the the other. You just have to use logic of the region to determine it's y = 1.",
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"content": "I get y = 2 and y = 3, how would I know which one which",
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"timestamp": "01/14/2023 05:41:18",
"content": "wait im actually",
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"content": "i got the y values wrong",
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"timestamp": "01/14/2023 05:41:25",
"content": "what is wrong with me today sorry",
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"content": "It's because you're rushing.",
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"content": "The only thing which matters for now is the concept and when you're not rushing the calculations it should all work.",
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"content": "Okay so I got y = 2 and y = 1",
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"content": "Using logic I guess, if we already know e and d intersection when y = 1",
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"content": "We must pick y = 2 to be where e and a meet",
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"content": "You could imagine one could make a few different regions if you chose the ranges of the lines differently.",
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"content": "I'd imagine",
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"content": "So now I have declared that the blue region is enclosed by y = 1 and y = 2",
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"content": "This is the main part that confuses me actually",
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"content": "Usually when we have a region of type 1 or type 2, we will get one variable with \"constants\" while the other has some variables",
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"content": "Well a lower bounding curve can be a constant curve.",
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"content": "In the view of lower and upper bounding curves it becomes trivial, in my opinion.",
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"content": "Like how do you conclude this",
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"timestamp": "01/14/2023 05:45:40",
"content": "Could you elaborate a little please",
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"timestamp": "01/14/2023 05:47:17",
"content": "x^2 = 2 - y gives us x = +-sqrt(2 - y) but since the diagram shows we are only have x>=0 we use the positive one.",
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"timestamp": "01/14/2023 05:47:19",
"content": "This might be a very very dumb question",
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"timestamp": "01/14/2023 05:47:25",
"content": "but why dont we just found these points",
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"timestamp": "01/14/2023 05:47:37",
"content": "What points?",
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"timestamp": "01/14/2023 05:48:00",
"content": "I think I am missing something fundamental here",
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"timestamp": "01/14/2023 05:48:19",
"content": "The x values of where they intersect will not go into our double integral so it would be a waste of time.",
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"timestamp": "01/14/2023 05:48:22",
"content": "If we can find those pink points and then the y values we would have some bound values for integration?",
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"timestamp": "01/14/2023 05:48:52",
"content": "$\\int_{y = 1}^{2} \\dd{y} \\int_{y - 2}^{\\sqrt{2 - y}} f(x, y) \\dd{x}$",
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"timestamp": "01/14/2023 05:49:03",
"content": "**stabulo**",
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"timestamp": "01/14/2023 05:49:23",
"content": "There's nowhere for the x values to go in the integral.",
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"timestamp": "01/14/2023 05:49:47",
"content": "What is this notation? Are these two seperate integrals to be multipled together once evaluated?",
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"content": "We only require the fact that the region lies between y = 1 and y = 2 bound it.",
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"timestamp": "01/14/2023 05:50:09",
"content": "Maybe we should dive a bit deeper for your understanding.",
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"timestamp": "01/14/2023 05:50:14",
"content": "Please do",
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"timestamp": "01/14/2023 05:50:15",
"content": "I apologise",
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"timestamp": "01/14/2023 05:50:57",
"content": "I sort of understand what you are saying, if we evaluate that last integral, we woul get like xf(x,y) I think",
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"timestamp": "01/14/2023 05:51:19",
"content": "Since it is a function both x and y we would still have both values of x and y after evaluating the integral with the bounds?",
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"timestamp": "01/14/2023 05:51:21",
"content": "Can you give this a quick read, please.",
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"timestamp": "01/14/2023 05:51:33",
"content": "The main bit is the definition of the double integral.",
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"content": "The fact we can compute it as a so called iterated integral is due to a theorem:",
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"timestamp": "01/14/2023 05:53:00",
"content": ":angerysad: :angerysad: :angerysad:",
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"timestamp": "01/14/2023 05:53:08",
"content": "To try and simplify it.",
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"timestamp": "01/14/2023 05:53:24",
"content": "The double integral is a sum but there's tools we use to calculate it rather than going to it's definition.",
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"timestamp": "01/14/2023 05:53:52",
"content": "One tool is considering the iterated integral which works like a single integral feeding into another single integral which we know how to do.",
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"timestamp": "01/14/2023 05:54:31",
"content": "Why do I feel like reading this makes sense but not sure what it has to do with my specific problem",
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"timestamp": "01/14/2023 05:54:37",
"content": "Which just means i dont understand it properly",
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"timestamp": "01/14/2023 05:54:38",
"content": "Notice in the hypothesis of Theorem 2, we require \"R_x\" this means we are between x = a and x = b and then there's a single upper and lower bounding curve.",
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"timestamp": "01/14/2023 05:54:56",
"content": "Sure",
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"timestamp": "01/14/2023 05:55:10",
"content": "In your case, we are between y = 1 and y = 2. We have a lower and bounding curve.",
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"timestamp": "01/14/2023 05:55:18",
"content": "We need no additional information.",
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"timestamp": "01/14/2023 05:55:18",
"content": "I think the main get away is that if I have some two constants in variables x then the y's would have some curve encasing it",
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"timestamp": "01/14/2023 05:55:31",
"content": "Wait",
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"timestamp": "01/14/2023 05:55:53",
"content": "Um this is a dumb question but like",
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"timestamp": "01/14/2023 05:56:37",
"content": "I still dont get the double integration stuff since we are using a coordinate system in R2 to solve a double integral and I thought",
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"timestamp": "01/14/2023 05:56:45",
"content": "Wait i am slowly",
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"timestamp": "01/14/2023 05:56:56",
"content": "When we get the bounds",
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"timestamp": "01/14/2023 05:57:13",
"content": "This is dumb but the thing is in 3d right?",
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"timestamp": "01/14/2023 05:57:55",
"content": "The definition of a double integral is given in Definition 3.",
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"timestamp": "01/14/2023 05:59:08",
"content": "We want to find the limit sum but it's very hard directly so we use theorems...",
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"timestamp": "01/14/2023 05:59:23",
"content": "Damn",
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"timestamp": "01/14/2023 05:59:26",
"content": "This shit hard af",
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"timestamp": "01/14/2023 05:59:30",
"content": "To use these theorems we need to find the appropriate bounding curves.",
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"timestamp": "01/14/2023 05:59:57",
"content": "If you're struggling still you might have to go to Paul's online notes.",
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"timestamp": "01/14/2023 06:00:03",
"content": "Indeed",
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"author_name": "JAck",
"timestamp": "01/14/2023 06:00:33",
"content": "Feels like this is a good topic to understand properly rather than figuring out why things work",
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"id": 1063774672291905500,
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"timestamp": "01/14/2023 06:00:45",
"content": "Correct me if I am wrong but",
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"timestamp": "01/14/2023 06:01:09",
"content": "\"Single\" integration is to find the area under a curve",
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"timestamp": "01/14/2023 06:01:16",
"content": "Yes.",
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"timestamp": "01/14/2023 06:01:25",
"content": "\"Double\" integration is then",
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"timestamp": "01/14/2023 06:01:39",
"content": "It can be used to find volume, yes.",
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"timestamp": "01/14/2023 06:02:30",
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"timestamp": "01/14/2023 06:02:44",
"content": "Okay so I guess for now, until I understand this intuitively I have to just go by the fact that",
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"timestamp": "01/14/2023 06:02:55",
"content": "if I have some region D and x is between two constants then the values of y must be between two curves",
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"timestamp": "01/14/2023 06:02:57",
"content": "vice versa",
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"timestamp": "01/14/2023 06:03:06",
"content": "That is a correct assumption?",
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"timestamp": "01/14/2023 06:04:28",
"content": "It's as though the first integral is a curve and it reduces us a dimension and then we can only be between the two end points of it's projection of the axis below it.",
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"timestamp": "01/14/2023 06:04:52",
"content": "Oh man that just got a whole lot more confusing",
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"timestamp": "01/14/2023 06:05:10",
"content": "And my lecturer doesnt even explain what this whole rectular region means",
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"timestamp": "01/14/2023 06:05:13",
"content": "Anyways, thank you a lot",
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"author_name": "stabulo",
"timestamp": "01/14/2023 06:06:18",
"content": "I'm not too sure on the confusion, sadly.",
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"timestamp": "01/14/2023 06:07:13",
"content": "I guess I have to hit the books and find something to supplement my learn",
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"timestamp": "01/14/2023 06:07:25",
"content": "Think of this as we're between x = a and x = b and between y = g_1(x) and y = g_2(x).",
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"timestamp": "01/14/2023 06:07:46",
"content": "Oh wait",
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"content": "If I treat this as one integral conceptually",
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"timestamp": "01/14/2023 06:08:13",
"content": "We have like two constants",
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"timestamp": "01/14/2023 06:08:17",
"content": "x = a and x = b",
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"author_name": "stabulo",
"timestamp": "01/14/2023 06:08:20",
"content": "g_1(x) is the lower bounding curve in the y direction and g_2(x) is the upper.",
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"timestamp": "01/14/2023 06:08:28",
"content": "And the lower and upper bound is the curves g1(x) and g2(x)",
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"id": 1063776649902051500,
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"timestamp": "01/14/2023 06:08:37",
"content": "If I want the \"area\" of this",
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"id": 1063776776448385000,
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"timestamp": "01/14/2023 06:09:07",
"content": "Just set f(x, y) = 1.",
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"id": 1063776816826962000,
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"timestamp": "01/14/2023 06:09:17",
"content": "Sure",
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"id": 1063776851316711600,
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"timestamp": "01/14/2023 06:09:25",
"content": "We get a double integral of the form like",
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"timestamp": "01/14/2023 06:10:25",
"content": "int g2x, g1x (int b, a) dydx",
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"id": 1063777146025300000,
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"timestamp": "01/14/2023 06:10:35",
"content": "I think the dydx order is wrong actually",
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"author_name": "JAck",
"timestamp": "01/14/2023 06:10:57",
"content": "If I integrate 1 id get b - a and integrate that wrt to x id get bx - ba",
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"author_name": "stabulo",
"timestamp": "01/14/2023 06:11:01",
"content": "Yeah. The outer integral has to have the constants or you'll get a variable output.",
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"id": 1063777297884266500,
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"timestamp": "01/14/2023 06:11:11",
"content": "Yeah indeed",
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"id": 1063777313663221800,
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"timestamp": "01/14/2023 06:11:15",
"content": "Makes more sense now",
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"author_name": "JAck",
"timestamp": "01/14/2023 06:11:25",
"content": "I think I need to hit the books and have a reread on this whole topic",
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"id": 1063777387826925700,
"author_id": 744079361463943200,
"author_name": "JAck",
"timestamp": "01/14/2023 06:11:33",
"content": "Thank you so much for staying with me",
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},
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"id": 1063777402964156500,
"author_id": 744079361463943200,
"author_name": "JAck",
"timestamp": "01/14/2023 06:11:36",
"content": "Have a good day",
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},
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"id": 1063777411675738200,
"author_id": 744079361463943200,
"author_name": "JAck",
"timestamp": "01/14/2023 06:11:38",
"content": ".close",
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"id": 1063777416343982100,
"author_id": 805217272087838700,
"author_name": "Mathematics Bot",
"timestamp": "01/14/2023 06:11:40",
"content": "Channel closed",
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] | help-9 | bf4da65c76f44939b6e7aba14aa682de |
200,756 | [
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"id": 1063777505716224000,
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"timestamp": "01/14/2023 06:12:01",
"content": "๐",
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"content": "Available help channel!",
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"id": 1063778898917195800,
"author_id": 489473096730935300,
"author_name": "Rainyzack81",
"timestamp": "01/14/2023 06:17:33",
"content": "Can someone tell me what I did wrong",
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"id": 1063778900838195200,
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"content": "Pinned a message.",
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"author_id": 788085606483361800,
"author_name": "chartbit",
"timestamp": "01/14/2023 06:24:18",
"content": "Looks an awfully lot like B to me rather than B^{-1} - was it its own inverse?",
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"timestamp": "01/14/2023 06:25:07",
"content": "Arenโt u supposed to inverse it after u times A and B",
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"timestamp": "01/14/2023 06:25:12",
"content": "That why it in brackets",
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"id": 1063780826468335600,
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"author_name": "chartbit",
"timestamp": "01/14/2023 06:25:13",
"content": "Also you could use $(AB^{-1})^{-1} = B A^{-1}$ to save some time?",
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"timestamp": "01/14/2023 06:25:15",
"content": "**chartbit**",
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"author_name": "Rainyzack81",
"timestamp": "01/14/2023 06:25:39",
"content": "Ty for the tip",
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"timestamp": "01/14/2023 06:25:42",
"content": "I try that way",
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"author_name": "chartbit",
"timestamp": "01/14/2023 06:26:24",
"content": "You have that youโre doing the product of A and the *inverse of* B, then you invert that",
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"author_name": "Rainyzack81",
"timestamp": "01/14/2023 06:28:20",
"content": "I need glasses bad",
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"id": 1063781624468226200,
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"author_name": "Rainyzack81",
"timestamp": "01/14/2023 06:28:23",
"content": "Thanks",
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"author_name": "Rainyzack81",
"timestamp": "01/14/2023 06:29:16",
"content": "Also Iโm assuming the reason why this works is cus inverse time a inverse turns it back to normals",
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"author_name": "Rainyzack81",
"timestamp": "01/14/2023 06:29:20",
"content": "But why wouldnโt it be",
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"id": 1063781895122468900,
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"timestamp": "01/14/2023 06:29:27",
"content": "(A^-1)B?",
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"id": 1063782572192174100,
"author_id": 704179090395103200,
"author_name": "Saccharine",
"timestamp": "01/14/2023 06:32:09",
"content": "it gets flipped because of how inverses work",
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"id": 1063782596661751800,
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"author_name": "Saccharine",
"timestamp": "01/14/2023 06:32:15",
"content": "yknow (AB)^-1 = B^-1 A^-1",
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"author_name": "Saccharine",
"timestamp": "01/14/2023 06:32:26",
"content": "because if you look at the defn of inverses you need them to multiply out to I",
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"timestamp": "01/14/2023 06:32:32",
"content": "so (AB)^-1 AB has to be I",
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"timestamp": "01/14/2023 06:32:35",
"content": "Saved me the pain of mobile typesetting :catlove:",
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"author_name": "Saccharine",
"timestamp": "01/14/2023 06:32:38",
"content": "and that only works if it's B^-1 A^-1 A B",
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"timestamp": "01/14/2023 06:39:29",
"content": "Oh ok",
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"author_name": "Rainyzack81",
"timestamp": "01/14/2023 06:39:30",
"content": "Ty",
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"author_name": "Mathematics Bot",
"timestamp": "01/14/2023 06:54:31",
"content": "@Rainyzack81 Has your question been resolved?",
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"timestamp": "01/14/2023 07:09:31",
"content": "Channel closed",
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] | help-9 | c9162214f0c3427bb32c78f866f97e4f |
200,757 | [
{
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"author_id": 805217272087838700,
"author_name": "Mathematics Bot",
"timestamp": "01/14/2023 07:10:31",
"content": "Available help channel!",
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},
{
"id": 1063794367963336800,
"author_id": 1022141568737607800,
"author_name": "โกA(lex)โก",
"timestamp": "01/14/2023 07:19:01",
"content": "a) Draw the complete binary tree with 15 vertices that represents a tree-connected network of 15 processors.\n\nb) Show how 16 numbers can be added using the 15 processors in part (a) using four steps",
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"timestamp": "01/14/2023 07:19:02",
"content": "Pinned a message.",
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"author_name": "โกA(lex)โก",
"timestamp": "01/14/2023 07:19:05",
"content": "so for part a",
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},
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"id": 1063794390444814300,
"author_id": 1022141568737607800,
"author_name": "โกA(lex)โก",
"timestamp": "01/14/2023 07:19:07",
"content": "i drew this",
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},
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"id": 1063794394844627100,
"author_id": 1022141568737607800,
"author_name": "โกA(lex)โก",
"timestamp": "01/14/2023 07:19:08",
"content": "[10\\textwidth]\\begin{tikzcd}\n&&&&&&&P_{1}\n\\ar[lllld, no head] \\ar[rrrrd, no head] \\\\\n&&&P_{2} \\ar[lld, no head] \\ar[rrd, no head]\n&&&&&&&&P_{3} \\ar[lld, no head] \\ar[rrd, no head] \\\\\n&P_{4} \\ar[ld, no head] \\ar[rd, no head] \n&&&&P_{5} \\ar[ld, no head] \\ar[rd, no head]\n &&&&P_{6} \\ar[ld, no head] \\ar[rd, no head] \n&&&&P_{7} \\ar[ld, no head] \\ar[rd, no head] \\\\\nP_8 &&P_9 &&P_{10} &&P_{11} &&P_{12} &&P_{13} &&P_{14} &&P_{15}\n\\end{tikzcd}",
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"id": 1063794467636781000,
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"author_name": "TeXit",
"timestamp": "01/14/2023 07:19:25",
"content": "**โกA(lex)โก**",
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"author_name": "โกA(lex)โก",
"timestamp": "01/14/2023 07:19:45",
"content": "which i think is right? but i dont understand how to do part b? what does it mean by four steps?",
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"id": 1063796010607968300,
"author_id": 183668144404037630,
"author_name": "Ann",
"timestamp": "01/14/2023 07:25:33",
"content": "yeah its unclear what constitutes a \"step\"",
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"id": 1063796531637002400,
"author_id": 183668144404037630,
"author_name": "Ann",
"timestamp": "01/14/2023 07:27:37",
"content": "but maybe processors 8 through 15 could each receive two of the sixteen addends, and then have each processor execute the following instructions:\n```\nUnless you are a leaf, listen for numbers reported by your two child nodes.\nIf you are a leaf, add the two numbers you received.\nIf you are not a leaf, add the numbers reported by your two child notes.\nIf you are not the root, report the sum to your parent node.\nIf you are the root, output the sum.\n```",
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"timestamp": "01/14/2023 07:28:38",
"content": "Oh hm :thonk:",
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"timestamp": "01/14/2023 07:31:36",
"content": "i mean to make it more clear, lets say the values for the 16 numbers be $a_1$ to $a_{16}$ or something",
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"timestamp": "01/14/2023 07:31:39",
"content": "**โกA(lex)โก**",
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"timestamp": "01/14/2023 07:32:18",
"content": "so we have \n\\[\nP_8 = a_1 + a_2, P_9 = a_3 + a_4 \\hdots P_{15} = a_{15} + a_{16}\n\\] i imagine?",
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"content": "**โกA(lex)โก**",
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"timestamp": "01/14/2023 07:32:29",
"content": "yeah ig",
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"timestamp": "01/14/2023 07:32:39",
"content": "those are the sums computed by the leaf processors",
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"timestamp": "01/14/2023 07:32:42",
"content": "yeah",
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"timestamp": "01/14/2023 07:32:53",
"content": "so ig thats our supposed \"first step\"",
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"timestamp": "01/14/2023 07:33:03",
"content": "uhh",
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"timestamp": "01/14/2023 07:35:01",
"content": "what now hm",
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"timestamp": "01/14/2023 07:50:01",
"content": "@โกA(lex)โก Has your question been resolved?",
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"content": "@โกA(lex)โก Has your question been resolved?",
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"timestamp": "01/14/2023 09:20:57",
"content": "@โกA(lex)โก Has your question been resolved?",
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"timestamp": "01/14/2023 10:01:23",
"content": "@Helpers hii",
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"author_name": "โกA(lex)โก",
"timestamp": "01/14/2023 10:01:29",
"content": "any thoughts?",
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"author_name": "DerpZ",
"timestamp": "01/14/2023 11:34:33",
"content": "what is a step",
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"author_name": "DerpZ",
"timestamp": "01/14/2023 11:34:46",
"content": "also these things seem more suited to a cs server or #discrete-math",
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"timestamp": "01/14/2023 11:35:03",
"content": "according to my hi decoding chart",
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"timestamp": "01/14/2023 11:35:45",
"content": "its just graph theory",
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"timestamp": "01/14/2023 11:35:51",
"content": "doubt any cs guys would be invested in that",
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"timestamp": "01/14/2023 11:36:01",
"content": "graph theory is discrete math",
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"timestamp": "01/14/2023 11:36:06",
"content": "yeah",
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"content": "",
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"timestamp": "01/14/2023 11:36:14",
"content": "ok so this chart says that",
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"timestamp": "01/14/2023 11:36:16",
"content": "ur lgbt",
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"timestamp": "01/14/2023 11:36:24",
"content": ":thinkspin:",
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"author_name": "DerpZ",
"timestamp": "01/14/2023 11:36:37",
"content": "since we take the charts truthiness to be an axiom",
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"timestamp": "01/14/2023 11:36:44",
"content": "ok fr what is a step",
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"timestamp": "01/14/2023 11:36:52",
"content": "i have no clue that was my question earlier",
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"timestamp": "01/14/2023 11:36:59",
"content": "i am assuming they mean like",
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"author_name": "โกA(lex)โก",
"timestamp": "01/14/2023 11:37:04",
"content": "do it in 4 lines?",
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"timestamp": "01/14/2023 11:37:11",
"content": "or in 4 operations",
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"timestamp": "01/14/2023 11:37:13",
"content": "maybe a step is like",
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"timestamp": "01/14/2023 11:37:15",
"content": "1 instruction",
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"timestamp": "01/14/2023 11:37:17",
"content": "or smth",
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"id": 1063859385941643300,
"author_id": 1022141568737607800,
"author_name": "โกA(lex)โก",
"timestamp": "01/14/2023 11:37:23",
"content": "but regardless i still need to know the answer",
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"timestamp": "01/14/2023 11:38:01",
"content": "16 numbers with 15 processors and 4 steps",
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"timestamp": "01/14/2023 11:38:04",
"content": "right",
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"timestamp": "01/14/2023 11:38:37",
"content": "your tree has a height of 4",
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"timestamp": "01/14/2023 11:38:46",
"content": "you can probably use that",
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"author_name": "โกA(lex)โก",
"timestamp": "01/14/2023 11:38:56",
"content": "yes i already know of that",
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"timestamp": "01/14/2023 11:40:28",
"content": "ngl im lost s",
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"id": 1063860171278921900,
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"author_name": "DerpZ",
"timestamp": "01/14/2023 11:40:30",
"content": "sorry",
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"timestamp": "01/14/2023 11:45:48",
"content": "its okay no worries haha",
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"timestamp": "01/14/2023 12:56:36",
"content": "@โกA(lex)โก calculate P5,P6,P7,P8",
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"timestamp": "01/14/2023 12:57:21",
"content": "\"calculate\"?",
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"timestamp": "01/14/2023 12:57:40",
"content": "You know P(9-16) right",
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"timestamp": "01/14/2023 12:58:05",
"content": "err no, i just know what they sum to here",
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"timestamp": "01/14/2023 12:58:22",
"content": "?",
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"timestamp": "01/14/2023 12:58:32",
"content": "That would be calculating them though",
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"timestamp": "01/14/2023 12:59:04",
"content": "how though",
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"timestamp": "01/14/2023 12:59:48",
"content": "You're given a1,a2,...,a16 right",
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"timestamp": "01/14/2023 12:59:56",
"content": "yes",
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"timestamp": "01/14/2023 13:00:06",
"content": "and P9=a1+a2",
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"timestamp": "01/14/2023 13:00:18",
"content": "P10=a3+a4",
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"timestamp": "01/14/2023 13:00:20",
"content": "...",
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"author_name": "โกA(lex)โก",
"timestamp": "01/14/2023 13:00:50",
"content": "i believe it is P8 = a1 + a2, P9 = a3 + a4 ...",
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"author_name": "!๐๐ช๐ฝ๐ฑ๐ถ๐ฎ๐ฝ๐ฒ๐ฌ๐ผ-๐ฎ๐น๐ฒ๐ฌ!",
"timestamp": "01/14/2023 13:00:56",
"content": "LMAO",
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"timestamp": "01/14/2023 13:01:10",
"content": "ok P(8-15) then",
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"timestamp": "01/14/2023 13:01:13",
"content": "What?",
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"timestamp": "01/14/2023 13:01:20",
"content": "yeah until 15",
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"timestamp": "01/14/2023 13:01:21",
"content": "sure",
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"author_name": "โกA(lex)โก",
"timestamp": "01/14/2023 13:01:25",
"content": "im with u so far",
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"timestamp": "01/14/2023 13:01:41",
"content": "So now u need P4-P7",
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"timestamp": "01/14/2023 13:01:48",
"content": "Mean this https://www.google.com/search?q=lmao+meaning&oq=LMAO+&aqs=chrome.1.0i271j0i67j69i57j0i512l5j46i512j0i512.3180j0j7&sourceid=chrome&ie=UTF-8",
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"timestamp": "01/14/2023 13:02:10",
"content": "oh wait is it quite literally just",
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"timestamp": "01/14/2023 13:02:35",
"content": "$P_4 = P_8 + P_9,...,P_7 = P_{14} + P_{15}$",
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"timestamp": "01/14/2023 13:02:37",
"content": "**โกA(lex)โก**",
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"timestamp": "01/14/2023 13:02:58",
"content": "Yeah",
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"author_name": "โกA(lex)โก",
"timestamp": "01/14/2023 13:03:14",
"content": "Yeah I know what it means, just don't understand what necessitated you saying that there",
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"timestamp": "01/14/2023 13:03:33",
"content": "so thats step 2",
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"timestamp": "01/14/2023 13:03:35",
"content": "in step 3",
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"author_name": "โกA(lex)โก",
"timestamp": "01/14/2023 13:03:39",
"content": "we will climb the tree",
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"timestamp": "01/14/2023 13:03:42",
"content": "and in step 4",
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"timestamp": "01/14/2023 13:03:43",
"content": "hm",
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"author_name": "โกA(lex)โก",
"timestamp": "01/14/2023 13:04:05",
"content": "Just $P_1 = P_2 + P_3$",
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"timestamp": "01/14/2023 13:04:07",
"content": "**โกA(lex)โก**",
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"author_name": "VulcanOne",
"timestamp": "01/14/2023 13:04:08",
"content": "@!๐๐ช๐ฝ๐ฑ๐ถ๐ฎ๐ฝ๐ฒ๐ฌ๐ผ-๐ฎ๐น๐ฒ๐ฌ! dude",
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"timestamp": "01/14/2023 13:04:15",
"content": "lol",
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"author_name": "monikanicity",
"timestamp": "01/14/2023 13:04:43",
"content": "P1 = P3+P4",
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"author_name": "monikanicity",
"timestamp": "01/14/2023 13:04:52",
"content": "P0 = P1+P2",
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"id": 1063881418503114800,
"author_id": 1022141568737607800,
"author_name": "โกA(lex)โก",
"timestamp": "01/14/2023 13:04:56",
"content": "wait really?",
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"id": 1063881424761004000,
"author_id": 1022141568737607800,
"author_name": "โกA(lex)โก",
"timestamp": "01/14/2023 13:04:57",
"content": "but why",
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"id": 1063881490364104800,
"author_id": 260118674306760700,
"author_name": "monikanicity",
"timestamp": "01/14/2023 13:05:13",
"content": "Oh nvm",
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"id": 1063881530881097900,
"author_id": 260118674306760700,
"author_name": "monikanicity",
"timestamp": "01/14/2023 13:05:22",
"content": "I'm being dumb",
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"timestamp": "01/14/2023 13:05:25",
"content": "Ur right",
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"author_id": 1022141568737607800,
"author_name": "โกA(lex)โก",
"timestamp": "01/14/2023 13:05:39",
"content": "ignore. they like trolling from what i have noticed in the other help channels",
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"author_id": 1022141568737607800,
"author_name": "โกA(lex)โก",
"timestamp": "01/14/2023 13:05:43",
"content": "YAY",
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"author_name": "โกA(lex)โก",
"timestamp": "01/14/2023 13:05:48",
"content": "finally done with this stupid question",
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"author_name": "โกA(lex)โก",
"timestamp": "01/14/2023 13:06:02",
"content": "making this was the fun part and it says something",
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"author_name": "VulcanOne",
"timestamp": "01/14/2023 13:06:06",
"content": "@moder momenr",
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"id": 1063881762771574900,
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"author_name": "VulcanOne",
"timestamp": "01/14/2023 13:06:18",
"content": "Oops",
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"id": 1063881767091712100,
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"author_name": "monikanicity",
"timestamp": "01/14/2023 13:06:19",
"content": "nice",
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"id": 1063881771340533800,
"author_id": 1022141568737607800,
"author_name": "โกA(lex)โก",
"timestamp": "01/14/2023 13:06:20",
"content": "lmfao",
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"id": 1063881865020325900,
"author_id": 1022141568737607800,
"author_name": "โกA(lex)โก",
"timestamp": "01/14/2023 13:06:42",
"content": "anyways ty moni appreciate it, now i just have to worry about that weird limit question",
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"id": 1063881867977298000,
"author_id": 1022141568737607800,
"author_name": "โกA(lex)โก",
"timestamp": "01/14/2023 13:06:43",
"content": ".close",
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"author_name": "Mathematics Bot",
"timestamp": "01/14/2023 13:06:44",
"content": "Channel closed",
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] | help-9 | 0242fd53f36446349143eea5e11db640 |
200,758 | [
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"id": 1063881929277059100,
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"id": 1063883390014726100,
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"author_name": "Arten",
"timestamp": "01/14/2023 13:12:46",
"content": "incredibly simple and stupid high school grade question but is there a way to accurately determine the period of a sinusoidal graph without just eyeing it out? Im in highschool rn and my teacher isnt answering me. mb for the really simple question lol",
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"timestamp": "01/14/2023 13:13:18",
"content": "Depends",
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"id": 1063883543345901600,
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"timestamp": "01/14/2023 13:13:22",
"content": "Are you given a function",
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"id": 1063883557312934000,
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"timestamp": "01/14/2023 13:13:26",
"content": "yes",
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"author_id": 349354952961032200,
"author_name": "Umbraleviathan",
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"content": "$$y = \\sin(a(x+b))$$\n\nThe period will be $\\frac{2\\pi}{a}$",
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"id": 1063883746761265300,
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"timestamp": "01/14/2023 13:14:11",
"content": "**Umbraleviathan**",
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"timestamp": "01/14/2023 13:14:33",
"content": "i see i see",
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"id": 1063883862280777900,
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"timestamp": "01/14/2023 13:14:38",
"content": "thank you!",
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"timestamp": "01/14/2023 13:29:38",
"content": "@Arten Has your question been resolved?",
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"timestamp": "01/14/2023 13:29:54",
"content": "Channel closed",
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] | help-9 | 6673c051cd814e738321b296baa05068 |
200,759 | [
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"content": "Available help channel!",
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"id": 1063889751939223600,
"author_id": 864507729598873600,
"author_name": "mags",
"timestamp": "01/14/2023 13:38:02",
"content": "hello does anyone here familiar in general tree under data structure and algorithms? i just want to ask a question",
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"author_name": "hibyehibye",
"timestamp": "01/14/2023 13:38:31",
"content": "just write ur question",
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"id": 1063889909628276700,
"author_id": 1048823396781273100,
"author_name": "hibyehibye",
"timestamp": "01/14/2023 13:38:40",
"content": "if someone knows they'll answer it",
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"timestamp": "01/14/2023 13:42:19",
"content": ".close",
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"id": 1063890831968309200,
"author_id": 805217272087838700,
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"timestamp": "01/14/2023 13:42:20",
"content": "Channel closed",
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] | help-9 | d325eb37375042bbb146cb4ec8fa619e |
200,760 | [
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"author_name": "Xerv",
"timestamp": "01/14/2023 13:44:52",
"content": "anyone wanna help me with math?",
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"id": 1063891629360029800,
"author_id": 788085606483361800,
"author_name": "chartbit",
"timestamp": "01/14/2023 13:45:30",
"content": "(open a new channel and post a question in it)",
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"id": 1063891691863556100,
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"timestamp": "01/14/2023 13:45:45",
"content": "might be sarcasm",
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"timestamp": "01/14/2023 13:46:32",
"content": "Wouldn't be surprised if it was and it flew over my head :kekw:",
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"timestamp": "01/14/2023 13:48:06",
"content": "Available help channel!",
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},
{
"id": 1063892651822293100,
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"author_name": "SnatchingL's",
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"content": "Pinned a message.",
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"author_id": 473966179510386700,
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"timestamp": "01/14/2023 13:49:51",
"content": "Iโm not sure where to start on this problem",
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"content": "Itโs calc 2",
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"content": "Do I split into two different derivatives?",
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"content": "Are u just integrating or are u finding yโ",
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"content": "@SnatchingL's",
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"content": "not an elementary integral",
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"content": "Finding yโ",
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"content": "you can compute it using a Taylor series",
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"content": "makes more sense",
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"content": "Ok so break into 2 integrals",
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"content": "Its just FTC from there",
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"timestamp": "01/14/2023 13:53:58",
"content": "Yeah",
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"timestamp": "01/14/2023 13:54:02",
"content": "That makes sense",
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"timestamp": "01/14/2023 13:54:06",
"content": "Thank you guys",
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] | help-9 | cbfe08a0668c49fdbcc5ec24a001931f |
200,761 | [
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"timestamp": "01/14/2023 14:35:16",
"content": "or is there something more to it",
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"content": "x is easy but i don't get y because it doesn't say anything about isoceles",
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"timestamp": "01/14/2023 14:35:37",
"content": "OBC is",
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"timestamp": "01/14/2023 14:36:15",
"content": "ig yeah because both radi are the same lenght",
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"timestamp": "01/14/2023 14:36:25",
"content": "nvm lol",
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"timestamp": "01/14/2023 14:36:30",
"content": "i was just overthinking",
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"content": "Do you know how to get x?",
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"timestamp": "01/14/2023 14:51:30",
"content": "@rak* Has your question been resolved?",
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] | help-9 | 83788ee2b1164a8c9ab5c12977a3c649 |
200,762 | [
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"content": "need help on b",
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"timestamp": "01/14/2023 15:19:23",
"content": "nvm",
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"content": ".close",
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] | help-9 | 9b868bbe42374b9c8451a9476a06ec25 |
200,763 | [
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] | help-9 | 9a1fe1713c6b4b3bbbef4187a7c0160e |
200,764 | [
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"id": 1063921840935931900,
"author_id": 290178138640613400,
"author_name": "elasmoterium",
"timestamp": "01/14/2023 15:45:33",
"content": "f ( f: X--> Y) is surjective and gof is injective, show that g (g: Y--->Z) is injective",
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"timestamp": "01/14/2023 15:45:50",
"content": "is it correct proof",
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"id": 1063923419378364400,
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"author_name": "chartbit",
"timestamp": "01/14/2023 15:51:49",
"content": "Iโd say that you should start off by saying โlet $y_1, y_2 \\in Y$ be such that $g(y_1)=g(y_2)$โ to make it clear what youโre doing",
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"timestamp": "01/14/2023 15:51:52",
"content": "**chartbit**",
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"author_name": "elasmoterium",
"timestamp": "01/14/2023 15:53:36",
"content": "oh okay and then the rest is okay?",
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"content": "I would say it could be made a little bit clearer imo",
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"timestamp": "01/14/2023 15:55:11",
"content": "hmm i will try again",
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"timestamp": "01/14/2023 15:56:12",
"content": "Like I would suggest justifying this",
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"timestamp": "01/14/2023 15:58:29",
"content": "That bit (circled about gf) is right though",
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"content": "Then use injectivity of gf to force x1=x2",
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"content": "hm u meant something like (gof(x1)=gof(x2)=>x1=x2 )=>( g(f(x1))=g(f(x2))=> x1=x2)?",
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"content": "What I mean is that to justify why theyโre the same, you have gf(x1)=g(y1) and gf(x2)=g(y2), but as g(y1)=g(y2) you know that gf(x1)=gf(x2)",
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"timestamp": "01/14/2023 16:04:31",
"content": "Then you know that gf is injective, therefore x1=x2",
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"timestamp": "01/14/2023 16:04:49",
"content": "At which point you know f(x1)=f(x2)",
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"id": 1063926798691336400,
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"timestamp": "01/14/2023 16:05:15",
"content": "(Apologies for lack of typesetting btw, itโs a pain on mobile :catscream:)",
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"timestamp": "01/14/2023 16:06:16",
"content": "aa yea i see it",
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"timestamp": "01/14/2023 16:06:22",
"content": "But the above steps should be enough and clear, do you think so? :happyCat:",
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"timestamp": "01/14/2023 16:09:16",
"content": "something like that?",
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"author_name": "elasmoterium",
"timestamp": "01/14/2023 16:10:22",
"content": "hmmm something is still needed to show f(x1)=f(x2) right?",
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"timestamp": "01/14/2023 16:12:06",
"content": "Hmmm I would say to put in my justification as to why theyโre equal before the blue circled bit, but itโs looking better!",
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"content": "As long as you show that x1=x2 then youโre fine, functions are well defined (meaning that if you give the same inputs, you get the same output)",
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{
"id": 1063928947638804600,
"author_id": 788085606483361800,
"author_name": "chartbit",
"timestamp": "01/14/2023 16:13:47",
"content": "For my blue circled you just need something like this here!",
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{
"id": 1063930253103333500,
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"content": "",
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"author_name": "elasmoterium",
"timestamp": "01/14/2023 16:20:14",
"content": "so i have to assume that y1=y2?",
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{
"id": 1063931036737732600,
"author_id": 788085606483361800,
"author_name": "chartbit",
"timestamp": "01/14/2023 16:22:06",
"content": "Replace this with f(x1)=f(x2)",
"attachments": [
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"id": 1063931602733908000,
"author_id": 788085606483361800,
"author_name": "chartbit",
"timestamp": "01/14/2023 16:24:20",
"content": "Oh I mistyped in my earlier post ๐คฆโโ๏ธ",
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},
{
"id": 1063931699102240800,
"author_id": 788085606483361800,
"author_name": "chartbit",
"timestamp": "01/14/2023 16:24:43",
"content": "Thatโs what we were aiming to show, given that g(y1)=g(y2)",
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"author_name": "elasmoterium",
"timestamp": "01/14/2023 16:25:32",
"content": "ok my brain is processing it",
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},
{
"id": 1063931904556023900,
"author_id": 788085606483361800,
"author_name": "chartbit",
"timestamp": "01/14/2023 16:25:32",
"content": "In this post I wrongly stated that y1=y2 but itโs that we had g(y1)=g(y2) (Iโve gone and corrected it now, sorry about that!)",
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{
"id": 1063932770382004200,
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"author_name": "elasmoterium",
"timestamp": "01/14/2023 16:28:59",
"content": "",
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"author_id": 290178138640613400,
"author_name": "elasmoterium",
"timestamp": "01/14/2023 16:29:25",
"content": "ok now i get it i think",
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},
{
"id": 1063932935583060000,
"author_id": 290178138640613400,
"author_name": "elasmoterium",
"timestamp": "01/14/2023 16:29:38",
"content": "thank uu very muuch",
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},
{
"id": 1063933050355994800,
"author_id": 290178138640613400,
"author_name": "elasmoterium",
"timestamp": "01/14/2023 16:30:06",
"content": ".close",
"attachments": [],
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"reference": null
},
{
"id": 1063933053564637200,
"author_id": 805217272087838700,
"author_name": "Mathematics Bot",
"timestamp": "01/14/2023 16:30:06",
"content": "Channel closed",
"attachments": [],
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"reference": null
}
] | help-9 | 936b51d5eae44922b3ec8fdb03bf47ae |
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