#help-10 | Mathematics | Page 479

cosmic kiln Dec 17, 2021, 9:05 AM

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so if i dont do it i wanna know how far my grades gonna do down

royal basin Dec 17, 2021, 9:05 AM

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ok

junior inlet Dec 17, 2021, 9:05 AM

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what's the weight of (the graded part)?

cosmic kiln Dec 17, 2021, 9:05 AM

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and the other two assignments arent in the grade book but their 100s

royal basin Dec 17, 2021, 9:05 AM

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,calc (100 * 25 + 100 * 10)/(25+10+25)

warm shaleBOT Dec 17, 2021, 9:05 AM

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Result:

58.333333333333

cosmic kiln Dec 17, 2021, 9:05 AM

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aint no way boyah

royal basin Dec 17, 2021, 9:06 AM

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,calc (100 * 25 + 100 * 10 + 60 * 35 * 2)/(25+10+25+35+35)

warm shaleBOT Dec 17, 2021, 9:06 AM

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Result:

59.230769230769

cosmic kiln Dec 17, 2021, 9:06 AM

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is my current grade in that result?

royal basin Dec 17, 2021, 9:07 AM

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this is with the 2 sixties you mentioned.

cosmic kiln Dec 17, 2021, 9:08 AM

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would i divide that by 64

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and My final grade would be a 65?

royal basin Dec 17, 2021, 9:10 AM

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??

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where are you getting 64 from?

cosmic kiln Dec 17, 2021, 9:10 AM

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my current grade

royal basin Dec 17, 2021, 9:10 AM

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?????

cosmic kiln Dec 17, 2021, 9:10 AM

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ight look

royal basin Dec 17, 2021, 9:10 AM

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are there some assignments you're not mentioning?

cosmic kiln Dec 17, 2021, 9:10 AM

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#

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The unit 4 exam i got a 64 on but its not in the grade book yet

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and the war of 1812 assignment i got a 100 but its not in yet

royal basin Dec 17, 2021, 9:11 AM

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....

cosmic kiln Dec 17, 2021, 9:12 AM

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same thing with this assignment

royal basin Dec 17, 2021, 9:12 AM

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boy this sure is a fucking lot

cosmic kiln Dec 17, 2021, 9:12 AM

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Ill give you a hug

royal basin Dec 17, 2021, 9:12 AM

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no

short spruce Dec 17, 2021, 9:12 AM

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have you tried just doing the assignment so you don't get a 65

cosmic kiln Dec 17, 2021, 9:12 AM

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I dont have the equipment

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and its 4am

short spruce Dec 17, 2021, 9:12 AM

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sounds like a you problem

cosmic kiln Dec 17, 2021, 9:13 AM

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What does that have to do with the math tho

royal basin Dec 17, 2021, 9:13 AM

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let's see here, hold on

short spruce Dec 17, 2021, 9:13 AM

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well let's do some simple math right

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do assignment? better grade!

cosmic kiln Dec 17, 2021, 9:14 AM

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I dont have the equipment

royal basin Dec 17, 2021, 9:14 AM

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ok no nvm

strong vale Dec 17, 2021, 9:14 AM

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what's going on here

royal basin Dec 17, 2021, 9:14 AM

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turns out i do not have the energy to trudge through this much bureaucracy after all

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or decipher what's meant by what

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bring shit up bring shit down who gives a fuck

short spruce Dec 17, 2021, 9:15 AM

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what does "i don't have the equipment" mean

strong vale Dec 17, 2021, 9:15 AM

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no pen probably

cosmic kiln Dec 17, 2021, 9:16 AM

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I do not have the nesaccary items to complete my task

short spruce Dec 17, 2021, 9:16 AM

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seems like "i don't want to do it :("

cosmic kiln Dec 17, 2021, 9:16 AM

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Seems like your not helpful

glossy yacht Dec 17, 2021, 9:17 AM

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roopopcorn

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Stop playing fortnite and do the bloody work

short spruce Dec 17, 2021, 9:17 AM

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lmfaoo

cosmic kiln Dec 17, 2021, 9:18 AM

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No glue

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or tape

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or scissors

short spruce Dec 17, 2021, 9:18 AM

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and when is it due

cosmic kiln Dec 17, 2021, 9:19 AM

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in 3 hours

glossy yacht Dec 17, 2021, 9:19 AM

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then go out and buy some

cosmic kiln Dec 17, 2021, 9:19 AM

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everythings closed

glossy yacht Dec 17, 2021, 9:20 AM

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definitely a you problem, sounds like you had ages to do it

short spruce Dec 17, 2021, 9:20 AM

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seems you should've thought about this assignment before 4 am lmao

cosmic kiln Dec 17, 2021, 9:20 AM

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Damn yall are useless

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stick to math

glossy yacht Dec 17, 2021, 9:20 AM

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And we should put more effort in than you are because?

junior inlet Dec 17, 2021, 9:20 AM

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cosmic kiln in 3 hours

you know, most channels here take more than 3 hours to resolve

just do the assignment and don't waste your time with this channel

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do .close

glossy yacht Dec 17, 2021, 9:21 AM

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Or on fortnite

short spruce Dec 17, 2021, 9:22 AM

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"i neglected an assignment until it was too late and now i want to know if i'm passing if i don't turn it in, do it for me while i play fortnite or you're useless"

strong vale Dec 17, 2021, 9:24 AM

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cosmic kiln everythings closed

what grade are you in?

short spruce Dec 17, 2021, 9:25 AM

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i think he left lmao

glossy yacht Dec 17, 2021, 9:26 AM

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.close

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sad that not everyone can close

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but makes sense

strong vale Dec 17, 2021, 9:27 AM

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lol

strong vale Dec 17, 2021, 9:27 AM

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cosmic kiln Damn yall are useless

this is not real life, you can't beat me up and make me do your homework haha!

obtuse pebbleBOT Dec 17, 2021, 9:35 AM

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@cosmic kiln Has your question been resolved?

obtuse pebbleBOT Dec 17, 2021, 9:50 AM

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Channel closed

Closed due to timeout

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obtuse pebbleBOT Dec 17, 2021, 1:58 PM

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Available help channel!

Send your question here to claim the channel.

Remember:
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• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
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remote arrow Dec 17, 2021, 2:02 PM

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hi how would i start this question? i’m very confused

obtuse pebbleBOT Dec 17, 2021, 2:02 PM

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remote arrow hi how would i start this question? i’m very confused

remote arrow Dec 17, 2021, 2:02 PM

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high lily Dec 17, 2021, 2:04 PM

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apply properties of parallel lines

remote arrow Dec 17, 2021, 2:06 PM

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shouldn’t i combine like terms first or no?

high lily Dec 17, 2021, 2:07 PM

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you'd first need to apply the appropriate property to set up an equation

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before you can proceed

remote arrow Dec 17, 2021, 2:08 PM

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since it’s parallel wouldn’t it be the same as the left side?

high lily Dec 17, 2021, 2:08 PM

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wouldn't what be the same as the left side

remote arrow Dec 17, 2021, 2:09 PM

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the left side is the same to right side? so 7x would be on the top right and 2x+16 on the bottom right too bc they’re parallel or am i wrong

high lily Dec 17, 2021, 2:10 PM

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you are wrong

remote arrow Dec 17, 2021, 2:11 PM

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let me look at my notes

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i couldn’t find any notes of properties of parallel lines could 9x + 36 = 180 be it bc that’s all i could find in my notes

high lily Dec 17, 2021, 2:18 PM

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9x + 36 = 180
yes

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that's what you get that from applying properties of parallel lines

remote arrow Dec 17, 2021, 2:19 PM

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oh ox let me see what i get

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I got 16 from that is that right?

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x = 16

high lily Dec 17, 2021, 2:20 PM

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yes

remote arrow Dec 17, 2021, 2:20 PM

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ok thanks 😊

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.close

obtuse pebbleBOT Dec 17, 2021, 2:20 PM

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Channel closed

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dusty fjord Dec 17, 2021, 2:28 PM

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obtuse pebbleBOT Dec 17, 2021, 2:28 PM

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dusty fjord

dusty fjord Dec 17, 2021, 2:28 PM

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i need help with e

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Ummm i actually have

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i dont remember it too well tho😓

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is that why im having trouble with e,

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i see thanks

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ill do that

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oh and can you lmk if i got d correct as well too?

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this is what i got

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i found the second derivative (i hope i did it correct) and got acceleration

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oh i see

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so i should be good then

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thank u!

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i just hope i did the derivatives right lmaoo but i think i did

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thank u again for ur help @severe marsh

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gotcha!

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hmm thats odd

rough stratus Dec 17, 2021, 2:44 PM

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dusty fjord this is what i got

You can use some shortcuts to obtain derivatives

dusty fjord Dec 17, 2021, 2:45 PM

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i got -.684 but it doesnt match? Im not sure if i calculated wrong tho..

rough stratus Dec 17, 2021, 2:45 PM

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dusty fjord Dec 17, 2021, 2:45 PM

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rough stratus You can use some shortcuts to obtain derivatives

i see do u know if i did it right? i think the orofessor would prefer if i do it the long way sadly

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oh so i just did an extra step

rough stratus Dec 17, 2021, 2:46 PM

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The product rule in case you didn't know

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P.S I can't understand your handwriting

dusty fjord Dec 17, 2021, 2:46 PM

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i did product rule but with (t+3)(sin(t))

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ah sorry🥲

rough stratus Dec 17, 2021, 2:47 PM

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dusty fjord ah sorry🥲

NP bro if your professor can understand it, there is no problem

dusty fjord Dec 17, 2021, 2:47 PM

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i think i did all the derivatives right tbh but i couldnt get this to match

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i prob could’ve done an easier way tho

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i have a -2+cos(t)/(t+3)^2 in there

warm shaleBOT Dec 17, 2021, 2:49 PM

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dusty fjord Dec 17, 2021, 2:50 PM

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yep

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i distributed the - but yep

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wait

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t+3^2

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i have a (t+3)^2 there too

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oh ok

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and then i found the derivative of that again

warm shaleBOT Dec 17, 2021, 2:51 PM

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#

dusty fjord Dec 17, 2021, 2:52 PM

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yeah i see it

dusty fjord Dec 17, 2021, 2:52 PM

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warm shale

so that means it worked then?

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sorry i never checked this before, this is pretty new

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ahh ok gotcha

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I tried checking it but it doesnt match. So im not sure what im doing wrong

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i mean i tried checking if s’(t)= those things

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i get this

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no i dont get it

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it doesnt match

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i replace t=.1 and i do s’(.1)=sin(.1) - (2-cos(.1))/(.1+3)

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and i get -.2243

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.2243

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Okay!

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the middle one is my answer

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oh wait whaa😲

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YESSS

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it worked

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https://tenor.com/view/tanjiro-kamado-kamado-tanjiro-demon-slayer-kimetsu-no-yaiba-gif-21599496

Tenor

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Im a huge one😭

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should i check the other one or am i good

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season 2 you mean? Yeah’n

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!!*

unique solstice Dec 17, 2021, 3:15 PM

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bleak

dusty fjord Dec 17, 2021, 3:16 PM

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HAHAHA

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@severe marsh

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ahh ur prob busy but tysm!!!

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oh how so

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so type this in calculator,

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oh so im nit suppose to use the calculator? i was gonna just match it again

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not

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im kinda confused how to check for acceleration then @severe marsh should i not use thus

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its at the bottom

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@severe marsh so how would i do it then?

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no no

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all the way at the bottom

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i mean this

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yeah my bad that was the substitution

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yeahh

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i think i’ll just leave it like that then, i think its correct (i hope)

dusty fjord Dec 17, 2021, 3:36 PM

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dusty fjord

how could i double check with this?

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LMAO

dusty fjord Dec 17, 2021, 3:36 PM

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dusty fjord

this is it^

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thats t

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I see

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alright thank you!!

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.close

obtuse pebbleBOT Dec 17, 2021, 3:47 PM

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Channel closed

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royal basin Dec 17, 2021, 4:01 PM

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@timid silo go ask a calculator

upbeat plinth Dec 17, 2021, 4:02 PM

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@timid silo pls dont troll

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.close

obtuse pebbleBOT Dec 17, 2021, 4:02 PM

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hasty harbor Dec 17, 2021, 4:08 PM

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By what sort of theorem or statement could I justify $\sum_{n=1}^{\infty}a_n=\sum_{n=1}^{\infty}a_{2n}+\sum_{n=1}^{\infty}a_{2n-1}$. Given that $\sum_{n=1}^{\infty}a_n$ converges.

obtuse pebbleBOT Dec 17, 2021, 4:08 PM

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hasty harbor By what sort of theorem or statement could I justify $\sum_{n=1}^{\infty}a_n=\su...

warm shaleBOT Dec 17, 2021, 4:08 PM

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glomswamp

hasty harbor Dec 17, 2021, 4:08 PM

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Would it just be the algebra of infinite series?

obtuse pebbleBOT Dec 17, 2021, 4:23 PM

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@hasty harbor Has your question been resolved?

royal basin Dec 17, 2021, 4:42 PM

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@hasty harbor you couldnt because this isnt always true

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take the series 1 - 1 + 1/2 - 1/2 + 1/3 - 1/3 + 1/4 - 1/4 + ...

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taking just the even or just the odd terms yields the harmonic series

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i think it might work if you require that the original series (\sum a_n) be absolutely convergent, in which case the two series you're trying to split it into will be absolutely convergent as well

obtuse pebbleBOT Dec 17, 2021, 4:56 PM

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@hasty harbor Has your question been resolved?

obtuse pebbleBOT Dec 17, 2021, 5:26 PM

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Channel closed

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Available help channel!

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Remember:
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woven shoal Dec 17, 2021, 5:51 PM

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could I get help with how they got force 3 and 4

obtuse pebbleBOT Dec 17, 2021, 5:51 PM

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woven shoal could I get help with how they got force 3 and 4

woven shoal Dec 17, 2021, 5:53 PM

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<@&286206848099549185>

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nvm i think i got it

obtuse pebbleBOT Dec 17, 2021, 6:11 PM

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@woven shoal Has your question been resolved?

obtuse pebbleBOT Dec 17, 2021, 6:26 PM

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Channel closed

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Available help channel!

Send your question here to claim the channel.

Remember:
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Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

timid silo Dec 17, 2021, 7:08 PM

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Need urgent help

obtuse pebbleBOT Dec 17, 2021, 7:08 PM

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timid silo Need urgent help

timid silo Dec 17, 2021, 7:08 PM

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My mind is blanking on how to do this

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How would I go about solving

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<@&286206848099549185>

timid silo Dec 17, 2021, 7:18 PM

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timid silo

f(x+h) = (x+h)^2-2(x+h)+9

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then use just do simplifications and so on and you should get a very nice answer

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you should be able to cancel out the denominator after factoring and applying the limit

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Oh okay thank you so much this makes sense

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I'm gonna try it rn

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Im a little stuck rn

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So now that I have this where would I go from here

mild ocean Dec 17, 2021, 7:33 PM

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divide it all by h

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afterwards let h = 0, since there’s no division left

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remember that this is a limit

timid silo Dec 17, 2021, 7:35 PM

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After I do all that I get 2x-2

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Am I supposed to set that equal to zero and solve for x?

mild ocean Dec 17, 2021, 7:36 PM

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no

timid silo Dec 17, 2021, 7:36 PM

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OHH

mild ocean Dec 17, 2021, 7:36 PM

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that’s the answer

timid silo Dec 17, 2021, 7:36 PM

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2x-2 is the answer

mild ocean Dec 17, 2021, 7:36 PM

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yes

timid silo Dec 17, 2021, 7:36 PM

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Damn I've been dancing around that for the past 10 minutes

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Thank you so much

mild ocean Dec 17, 2021, 7:36 PM

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lol it’s fine, derivatives aren’t super easy at first

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whenever you’re done, don’t forget to do .close

timid silo Dec 17, 2021, 7:37 PM

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Thanks quantum glad tidings

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.close

obtuse pebbleBOT Dec 17, 2021, 7:37 PM

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Channel closed

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Remember:
• Ask your math question in a clear, concise manner.
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bleak dragon Dec 17, 2021, 8:21 PM

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My problem was about a thousand characters too long for discord x) So here it is as a text file I guess?
Also: Applied Mathematics warning :)

📎 message.txt

obtuse pebbleBOT Dec 17, 2021, 8:21 PM

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bleak dragon My problem was about a thousand characters too long for discord x) So here it is...

bleak dragon Dec 17, 2021, 8:28 PM

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Considering my approach to this, I want to essentially find the function of a "Spherical Bezier-Curve", which connects two points on a geodesic of a sphere respectivel, where both of the geodesics intersect orthogonally, such that the "ends" of the spherical bezier curves are also orthogonal to the geodesic they lie on. This is defined a little vaguely, but I hope you get the picture.

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I then want to find a function based on this curve, that calculates the "spherical distance" (not linear distance) i.e. arc-length between a given arbitrary point on the surface of the sphere and a point on the bezier-curve based on t (the interpolation value of the bezier curve) which is contrained between 0 and 1. I then also need to find the derivative of this function...

unique solstice Dec 17, 2021, 8:36 PM

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Wots the application of this problem

bleak dragon Dec 17, 2021, 8:36 PM

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Limiting the rotation of a bone transform in an IK Solver.

unique solstice Dec 17, 2021, 8:37 PM

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Is there not an industry standard way to do that?

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IK is common enough that I would think so

bleak dragon Dec 17, 2021, 8:37 PM

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Apperantly not lol. I have searched far and wide

unique solstice Dec 17, 2021, 8:38 PM

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I mean it reminds me of just like

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arccos(a dot b) < angle

bleak dragon Dec 17, 2021, 8:38 PM

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Most IK solvers either just make it a "normal" cone, which is trivial. Or they get around the problem by letting you define a polygonal-shape. However I want to approach this in an analytical way.

bleak dragon Dec 17, 2021, 8:39 PM

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unique solstice arccos(a dot b) < angle

What are a and b there?

unique solstice Dec 17, 2021, 8:40 PM

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a would be the vector down the center of the cone

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And b would be your bone direction vector

bleak dragon Dec 17, 2021, 8:40 PM

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Well yeah that works for a "regular" cone. What makes it hard is that I want my cone to have different angles for all of the cardinal directions

unique solstice Dec 17, 2021, 8:41 PM

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So like an oval cone?

bleak dragon Dec 17, 2021, 8:43 PM

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Sort of. Its hard for me to visualize, but imagine having some forward axis, then you rotate the forward axis in all of the cardinal directions (up, down, left, right) by varying angles. This will give you four points on the surface of the sphere, now you have to connect these 4 points, such that the transition between the curves is smooth, and the curve always lies on the surface of the sphere.

unique solstice Dec 17, 2021, 8:46 PM

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Hmm

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Sounds weird

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Wait and so what's the purpose of this different type

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Over a normal cone

bleak dragon Dec 17, 2021, 8:50 PM

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Think of your wrists. They can rotate up, down, left, and right. But they can rotate more up and down, than left an right. And it can rotate more down than up.
You can rotate your wrist approximately 20° to the right 35° to the left, 85° down and 75° up.

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So I'd like to incorporate that into my IK Solver...However, that requires solving this problem...

unique solstice Dec 17, 2021, 8:53 PM

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I kinda see what you mean by bezier

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You could make a custom form of the dot product trick that has the radius of the cone as a function of the angle from some upper bone vector

bleak dragon Dec 17, 2021, 8:54 PM

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You can use the Casteljau-Algorithm to construct a Bezier-Curve using Linear Interpolations. However that only works for affine spaces.
You can however use the same idea in SO-3 using Slerp

unique solstice Dec 17, 2021, 8:58 PM

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I'm not sure it sounds very complex

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But it could just be my lack of understanding

bleak dragon Dec 17, 2021, 8:58 PM

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I guess Im gonna ping the Helpers?

unique solstice Dec 17, 2021, 8:59 PM

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You might wanna go to a specialized channel for help with linear algebra stuff

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But I feel like there's a simpler solution

obtuse pebbleBOT Dec 17, 2021, 9:13 PM

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@bleak dragon Has your question been resolved?

bleak dragon Dec 17, 2021, 9:15 PM

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<@&286206848099549185> This is a much more complex problem than I originally anticipated. Would appreciate if I could get some help or at least an idea of how to better approach this :)

obtuse pebbleBOT Dec 17, 2021, 9:45 PM

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@bleak dragon Has your question been resolved?

unique solstice Dec 17, 2021, 9:50 PM

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https://gyazo.com/555c74f8ad32e9f0c4f291028475b7cb.mp4

▶ Play video

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I mean it wouldnt be that hard to define a cone with a changing radius

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Based on a polar function like that or something

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Thered be two angles

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α, the thing you wanna limit, and the dot product angle of the bone

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β, the angle of rotation of the bone around the joint head on based on the upwards direction

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For every β there would be a maximum allowable α based on some polar function

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Which could change to fit to any shape you want

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If that doesnt make sense with the weird isosceles view

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Heres a side and head on view of α and β

bleak dragon Dec 17, 2021, 10:31 PM

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Hmm I think I understand...However how do you find the spherically closest point on the boundary then?

unique solstice Dec 17, 2021, 10:36 PM

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I would probably just like

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mag(bone-origin)

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Then uhhh

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Well you could construct a vector using α and β I suppose

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And use that magnitude

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Prob a better way though

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Yeah def

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So by the definition of being spherically closest itd be perpendicular to the closest edge of the thing

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Which has already been calculated using the big alpha angle

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Calculated by your polar function

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So you could say

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$\sin(A - \alpha)=\frac{opp}{||bone node - origin||}$

warm shaleBOT Dec 17, 2021, 10:45 PM

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PapaBread

unique solstice Dec 17, 2021, 10:46 PM

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Then you could do bone-origin cross product with front vector then itself or something

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Then multiply that by opp and add it onto bone

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And you should get the endpoint closest point

obtuse pebbleBOT Dec 17, 2021, 11:31 PM

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@bleak dragon Has your question been resolved?

bleak dragon Dec 17, 2021, 11:40 PM

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I will think about this again tomorrow...

obtuse pebbleBOT Dec 17, 2021, 11:40 PM

#

Channel closed

Closed by @bleak dragon

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tired shell Dec 17, 2021, 11:53 PM

#

A circle with radius r has area 505. Compute the area of a circle with diameter 2r.

obtuse pebbleBOT Dec 17, 2021, 11:53 PM

#

tired shell A circle with radius r has area 505. Compute the area of a circle with diameter...

tired shell Dec 17, 2021, 11:54 PM

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Is it just times two?

forest sinew Dec 17, 2021, 11:56 PM

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plumorant

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thonk

high lily Dec 17, 2021, 11:56 PM

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wdym by it

forest sinew Dec 17, 2021, 11:56 PM

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why are you asking this

nocturne minnow Dec 17, 2021, 11:58 PM

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tired shell A circle with radius r has area 505. Compute the area of a circle with diameter...

Area of a circle formula is $A = \pi \cdot r^2$, right?

soft sail Dec 17, 2021, 11:58 PM

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"with diameter 2r" catGiggle

warm shaleBOT Dec 17, 2021, 11:58 PM

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dldh06

high lily Dec 17, 2021, 11:58 PM

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formula for area isn't even needed

nocturne minnow Dec 17, 2021, 11:58 PM

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So it's not just double, it's more like the area is squared

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Or something like that

tired shell Dec 17, 2021, 11:59 PM

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505*4=2020

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oh that makes sense since this is a 2020 question, thanks!

high lily Dec 17, 2021, 11:59 PM

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"with diameter 2r"

tired shell Dec 17, 2021, 11:59 PM

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.close

obtuse pebbleBOT Dec 17, 2021, 11:59 PM

#

Channel closed

Closed by @tired shell

Use .reopen if this was a mistake.

mild ocean Dec 17, 2021, 11:59 PM

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flonshed

high lily Dec 17, 2021, 11:59 PM

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no

soft sail Dec 17, 2021, 11:59 PM

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that's wrong

forest sinew Dec 18, 2021, 12:00 AM

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lol

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you dont need any formulas

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well maybe the formula for diameter

thorny dome Dec 18, 2021, 12:00 AM

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The question is strange

high lily Dec 18, 2021, 12:01 AM

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year specific questions usually have the year in the question rather than the answer

thorny dome Dec 18, 2021, 12:03 AM

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tired shell A circle with radius r has area 505. Compute the area of a circle with diameter...

Radius length r = diameter length 2r

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Seems like it's the same circle to me

obtuse pebbleBOT Dec 18, 2021, 12:03 AM

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fickle swan Dec 18, 2021, 12:42 AM

#

tired shell A circle with radius r has area 505. Compute the area of a circle with diameter...

Its so ez

obtuse pebbleBOT Dec 18, 2021, 12:42 AM

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fickle swan Its so ez

fickle swan Dec 18, 2021, 12:42 AM

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Since diameter is always double right?

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So

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The circle will always be the same

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As long as the diameter is double the radius

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Oh wait

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Sorry helpers

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Sorry for wasting ur time

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Ill close this now

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.close

obtuse pebbleBOT Dec 18, 2021, 12:46 AM

#

Channel closed

Closed by @fickle swan

Use .reopen if this was a mistake.

obtuse pebbleBOT Dec 18, 2021, 7:53 AM

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novel flint Dec 18, 2021, 7:54 AM

#

obtuse pebbleBOT Dec 18, 2021, 7:54 AM

#

novel flint

novel flint Dec 18, 2021, 7:54 AM

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it is showing up as wrong

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waitnvm

#

.close

obtuse pebbleBOT Dec 18, 2021, 7:56 AM

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Channel closed

Closed by @novel flint

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static patio Dec 18, 2021, 8:08 AM

#

obtuse pebbleBOT Dec 18, 2021, 8:08 AM

#

static patio

static patio Dec 18, 2021, 8:08 AM

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Is this proof of partial order correct ?

warm shaleBOT Dec 18, 2021, 8:20 AM

#

#

#

obtuse pebbleBOT Dec 18, 2021, 8:31 AM

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@static patio Has your question been resolved?

static patio Dec 18, 2021, 8:32 AM

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i picked number 1

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is a k from Z

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ups, k is from N

warm shaleBOT Dec 18, 2021, 8:44 AM

#

static patio Dec 18, 2021, 8:45 AM

#

#

,rotate

warm shaleBOT Dec 18, 2021, 8:45 AM

#

static patio Dec 18, 2021, 8:45 AM

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Why ?

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What is missing ?

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That's how we do it in school

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Computer science

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yes, its not course for pure mathematicians

warm shaleBOT Dec 18, 2021, 8:57 AM

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static patio Dec 18, 2021, 9:00 AM

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that similiar to what i did

warm shaleBOT Dec 18, 2021, 9:01 AM

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static patio Dec 18, 2021, 9:02 AM

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i have found it there

#

https://math.stackexchange.com/questions/988363/equivalence-relations-on-set-of-ordered-pairs

Mathematics Stack Exchange

Equivalence Relations on Set of Ordered Pairs

Let $\mathbb{R}$ be the relation on $\mathbb{Z} \times \mathbb{Z}$, that is elements of this relation are pairs of pairs of integers, such that $((a,b),(c,d)) \in \mathbb{R}$ if and only if $a-d = ...

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everywhere its different so i am confused

warm shaleBOT Dec 18, 2021, 9:03 AM

#

#

static patio Dec 18, 2021, 9:05 AM

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but its reflexivity and we want only one element

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like aRa

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(a,b)R(a,b)

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i know

warm shaleBOT Dec 18, 2021, 9:06 AM

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static patio Dec 18, 2021, 9:06 AM

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((a,b),(a,b)) would be N^2 x N^2

warm shaleBOT Dec 18, 2021, 9:06 AM

#

static patio Dec 18, 2021, 9:07 AM

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if i had worked with only with relation on NxN

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I would write for all (a,a)

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?

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i dont know

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let it be

warm shaleBOT Dec 18, 2021, 9:09 AM

#

static patio Dec 18, 2021, 9:09 AM

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we dont do it in this way in school

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also some lecture books do not have this kind of notation

warm shaleBOT Dec 18, 2021, 9:10 AM

#

#

static patio Dec 18, 2021, 9:12 AM

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be we want only one same element

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we dont do it like this in school

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let it be

plain owl Dec 18, 2021, 9:13 AM

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Aren't the individual elements just (a,b)

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And all elements of the form (ka,kb) where k is a positive integer are in the same equivalence class

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Writing for all ((a,b),(a,b)) or for all (a,b) shouldn't matter

static patio Dec 18, 2021, 9:18 AM

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i dont really now

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everywhere is different notation, Im confused

warm shaleBOT Dec 18, 2021, 9:21 AM

#

static patio Dec 18, 2021, 9:21 AM

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i will do it somehow

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...

plain owl Dec 18, 2021, 9:22 AM

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$\forall (a,b)\in \mathbb{N}^2$

warm shaleBOT Dec 18, 2021, 9:22 AM

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Euclid31415

#

#

static patio Dec 18, 2021, 9:24 AM

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ok

#

.close

obtuse pebbleBOT Dec 18, 2021, 9:27 AM

#

Channel closed

Closed by @static patio

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timid silo Dec 18, 2021, 9:45 AM

#

could someone please explain to me where the -3 comes from in this?

obtuse pebbleBOT Dec 18, 2021, 9:45 AM

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timid silo could someone please explain to me where the -3 comes from in this?

elder oasis Dec 18, 2021, 9:48 AM

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(a+b)²= a²+2ab+b².
In your case -½x is your a
And 3 is your b

timid silo Dec 18, 2021, 9:51 AM

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sorry i do not understand

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within the distribution of the ^2 how do we get -3?

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i understand the rest just not the -3?

high lily Dec 18, 2021, 9:55 AM

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can you expand (a+b)^2?

timid silo Dec 18, 2021, 10:02 AM

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a^2+b^2?

high lily Dec 18, 2021, 10:02 AM

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no

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that is not the correct expansion

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$(1+1)^2 \neq 1+1$

warm shaleBOT Dec 18, 2021, 10:03 AM

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ℝamonov

timid silo Dec 18, 2021, 10:04 AM

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high lily can you expand (a+b)^2?

would this be ab^2

high lily Dec 18, 2021, 10:04 AM

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no

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do you know what it means to square something

timid silo Dec 18, 2021, 10:05 AM

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yeah

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by itself

high lily Dec 18, 2021, 10:05 AM

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yes

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apply that to (a+b)^2

timid silo Dec 18, 2021, 10:05 AM

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a^2b^2

high lily Dec 18, 2021, 10:05 AM

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no

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what do you immediately get when applying the definition of squaring to (a+b)^2

timid silo Dec 18, 2021, 10:07 AM

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a^2+2ab+b^2

high lily Dec 18, 2021, 10:07 AM

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not quite what I was asking
you jumped ahead and that is the correct expansion

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and apply that to what you had in your original question

timid silo Dec 18, 2021, 10:10 AM

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hold on writing it now

elder oasis Dec 18, 2021, 10:11 AM

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timid silo Dec 18, 2021, 10:18 AM

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yeah this is long as fuck i am trying to think of a better way to do this than the foil method

high lily Dec 18, 2021, 10:19 AM

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remember (a+b)^2 = a^2 +2ab + b^2 and/or binomial theorem

timid silo Dec 18, 2021, 10:19 AM

#

high lily Dec 18, 2021, 10:21 AM

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whut

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are you doing

timid silo Dec 18, 2021, 10:22 AM

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multiplying everything

high lily Dec 18, 2021, 10:22 AM

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you have (-1/2 x +3)^2 in the question
NOT (-1/2 + x + 3)^2

timid silo Dec 18, 2021, 10:33 AM

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high lily you have (-1/2 x +3)^2 in the question NOT (-1/2 + x + 3)^2

so what have i done wrong

high lily Dec 18, 2021, 10:33 AM

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you have (-1/2 x +3)^2 in the question
NOT (-1/2 + x + 3)^2
you didn't set up your multiplication table properly

timid silo Dec 18, 2021, 10:34 AM

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high lily > you have (-1/2 x +3)^2 in the question > NOT (-1/2 + x + 3)^2 you didn't set ...

high lily Dec 18, 2021, 10:34 AM

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why did you split the -1/2 x like that

timid silo Dec 18, 2021, 10:34 AM

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because it is ^2

high lily Dec 18, 2021, 10:34 AM

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no

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that does not explain why you split the -1/2 x

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in
-1/2 x + 3
-1/2 x is your first term
and 3 is your second term

timid silo Dec 18, 2021, 10:35 AM

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ohhh

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hold on i will change

#

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i forgot the x in -3x

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but that should be correct

timid silo Dec 18, 2021, 10:45 AM

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high lily that does not explain why you split the -1/2 x

thank you for your help this has just blew my mind

obtuse pebbleBOT Dec 18, 2021, 11:00 AM

#

@timid silo Has your question been resolved?

#

Channel closed

Closed by @oblique talon

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obtuse pebbleBOT Dec 18, 2021, 1:33 PM

#

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wintry iris Dec 18, 2021, 2:31 PM

#

if (2^a)(3^b)=(2^c)(3^d) does this mean that a=c and b=d?

obtuse pebbleBOT Dec 18, 2021, 2:31 PM

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wintry iris if (2^a)(3^b)=(2^c)(3^d) does this mean that a=c and b=d?

wintry iris Dec 18, 2021, 2:37 PM

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both of em should be natural numbers

brave bramble Dec 18, 2021, 2:38 PM

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Yes! Because prime factorization is unique.

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As long as a,b,c,d are natural

wintry iris Dec 18, 2021, 2:40 PM

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Thank you!

#

.close

obtuse pebbleBOT Dec 18, 2021, 2:40 PM

#

Channel closed

Closed by @wintry iris

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clear sinew Dec 18, 2021, 3:13 PM

#

Let $$Q \in \mathbb{R}^{n \times n} $$ be an orthogonal matrix. Then $$ \det{Q} = \pm 1 $$. Now, when Q is a householder matrix $$Q_v$$, then $$ \det{Q_v} = -1 $$. I can't wrap my head around why the determinant of the householder matrix equals -1?

obtuse pebbleBOT Dec 18, 2021, 3:13 PM

#

clear sinew Let $$Q \in \mathbb{R}^{n \times n} $$ be an orthogonal matrix. Then $$ \det{Q} ...

warm shaleBOT Dec 18, 2021, 3:14 PM

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mrbrown

obtuse pebbleBOT Dec 18, 2021, 3:28 PM

#

@clear sinew Has your question been resolved?

dawn parrot Dec 18, 2021, 3:43 PM

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clear sinew Let $$Q \in \mathbb{R}^{n \times n} $$ be an orthogonal matrix. Then $$ \det{Q} ...

recall: determinant=product of eigenvalues

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and there is very nice properties of thr householder matrix in that regards

clear sinew Dec 18, 2021, 3:43 PM

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that makes me question: What are the eigenvalues of an orthogonal matrix?

dawn parrot Dec 18, 2021, 3:44 PM

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if its orthogonal then +-1

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i assume you know that

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cause of the definition you sent

clear sinew Dec 18, 2021, 3:46 PM

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I know that for householder we have following properties:
(i) Q is symmetric
(ii) Q^2 = I
(iii) Qy = v <=> (y^T)v = 0
(iv) Qv = -v

clear sinew Dec 18, 2021, 3:46 PM

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dawn parrot cause of the definition you sent

makes sense. That would mean that all the n Eigenvalues are either 1 or -1

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$$ \lambda_1 = \pm 1, \lambda_2 = \pm 1, ..., \lambda_n =\pm 1 $$

warm shaleBOT Dec 18, 2021, 3:47 PM

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mrbrown

dawn parrot Dec 18, 2021, 3:48 PM

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right so now you have an issue of who is + and who is -

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good thing for you

clear sinew Dec 18, 2021, 3:48 PM

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yeah! 😄

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I'd need to figure out if I have an odd or even amount of -1

dawn parrot Dec 18, 2021, 3:50 PM

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another hint
Qu=u if u is orthogonal to v

clear sinew Dec 18, 2021, 3:52 PM

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v is the normal vector to the "mirror-plane" right?

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and u is the "Point" i want to mirror

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If u is orthogonal to v then the scalar product of v and u is 0.

dawn parrot Dec 18, 2021, 3:57 PM

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yes v is the normal vector
and u is a vector orthogonal to v

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to which is there is n-1 independent vects of them

clear sinew Dec 18, 2021, 4:00 PM

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Oh wait

#

Now I understand 💡

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A property of Eigenvalues is $$Ax = \lambda x$$ (correct if I say something wrong please.

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Now if $$Qu = u \implies \lambda = 1$$

warm shaleBOT Dec 18, 2021, 4:03 PM

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mrbrown

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mrbrown

clear sinew Dec 18, 2021, 4:04 PM

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Ok, I just don't know how multiple Eigenvalues apply to the statement $$Ax = \lambda x$$

warm shaleBOT Dec 18, 2021, 4:04 PM

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mrbrown

clear sinew Dec 18, 2021, 4:04 PM

#

But if I understood it correctly I have two cases with householder matrices.

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If $$Qu = u \implies \lambda = 1$$ and if $$ Qu = -u \implies \lambda = -1 $$

warm shaleBOT Dec 18, 2021, 4:06 PM

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mrbrown

clear sinew Dec 18, 2021, 4:06 PM

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Ok, now I need to figure out the amounts of +1 and -1. You said "to which is there is n-1 independent vects of them"

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I can't figure it out 🙈. How do we arrive at the conclusion $$ Qu = u \implies (n-1) independent vecs$$

warm shaleBOT Dec 18, 2021, 4:08 PM

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mrbrown

dawn parrot Dec 18, 2021, 4:10 PM

#

yet another recall
dimW+dimW^T=n
so alll you have to prove is...

clear sinew Dec 18, 2021, 4:23 PM

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🤯 😅

obtuse pebbleBOT Dec 18, 2021, 4:53 PM

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@clear sinew Has your question been resolved?

clear sinew Dec 18, 2021, 5:29 PM

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dawn parrot yet another recall dimW+dimW^T=n so alll you have to prove is...

After my research, it seems like the span{v} plays a role in this.

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I won't be able to solve this with my rusty knowledge about eigenvalues and span.

dawn parrot Dec 18, 2021, 5:43 PM

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well the goal is to improve that rusty knowledge
you'll get the hang of it
more hints and it'll just be giving the answer lol

clear sinew Dec 18, 2021, 5:52 PM

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😄

clear sinew Dec 18, 2021, 6:16 PM

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I stumbled across another problem

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The householder transformation is given by $$Q = I - 2 \frac{vv^T}{v^Tv} $$

warm shaleBOT Dec 18, 2021, 6:17 PM

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mrbrown

clear sinew Dec 18, 2021, 6:17 PM

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I tried to calculate the determinant for a 2x2 matrix xD

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first of all $$ I - 2 \frac{vv^T}{v^Tv} = \begin{pmatrix} 1 & 0 \ 0 & 1 \end{pmatrix} - \frac{2}{v_{1}^{2} + v_{2}^{2}} \begin{pmatrix} v_{1}^{2} & v_1 v_2 \ v_2 v_1 & v_{2}^{2} \end{pmatrix} $$

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😵

warm shaleBOT Dec 18, 2021, 6:24 PM

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mrbrown

clear sinew Dec 18, 2021, 6:24 PM

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nice

#

$$ = \begin{pmatrix} 1 - \frac{2}{v_{1}^{2} + v_{2}^{2}}v_{1}^{2} & -\frac{2}{v_{1}^{2} + v_{2}^{2}} v_1 v_2 \ -\frac{2}{v_{1}^{2} + v_{2}^{2}} v_1 v_2 & 1 - \frac{2}{v_{1}^{2} + v_{2}^{2}}v_{2}^{2}\end{pmatrix} $$

warm shaleBOT Dec 18, 2021, 6:28 PM

#

mrbrown

clear sinew Dec 18, 2021, 6:29 PM

#

$$ \det{Q} = \begin{vmatrix} 1 - \frac{2}{v_{1}^{2} + v_{2}^{2}}v_{1}^{2} & -\frac{2}{v_{1}^{2} + v_{2}^{2}} v_1 v_2 \ -\frac{2}{v_{1}^{2} + v_{2}^{2}} v_1 v_2 & 1 - \frac{2}{v_{1}^{2} + v_{2}^{2}}v_{2}^{2}\end{vmatrix} $$

warm shaleBOT Dec 18, 2021, 6:30 PM

#

mrbrown

clear sinew Dec 18, 2021, 6:35 PM

#

$$ = \left( 1 - \frac{2}{v_{1}^{2} + v_{2}^{2}}v_{1}^{2} \right) \left( 1 - \frac{2}{v_{1}^{2} + v_{2}^{2}}v_{2}^{2} \right) - \left( \frac{2}{v_{1}^{2} + v_{2}^{2}} v_1 v_2 \right)^{2} $$

warm shaleBOT Dec 18, 2021, 6:35 PM

#

mrbrown

clear sinew Dec 18, 2021, 6:37 PM

#

$$ = 1 - \frac{2}{v_{1}^{2} + v_{2}^{2}}v_{2}^{2} - \frac{2}{v_{1}^{2} + v_{2}^{2}}v_{1}^{2} + \left( \frac{2}{v_{1}^{2} + v_{2}^{2}} v_1 v_2 \right)^{2} - \left( \frac{2}{v_{1}^{2} + v_{2}^{2}} v_1 v_2 \right)^{2} $$

warm shaleBOT Dec 18, 2021, 6:37 PM

#

mrbrown

clear sinew Dec 18, 2021, 6:38 PM

#

$$ = 1 - \frac{2}{v_{1}^{2} + v_{2}^{2}}v_{2}^{2} - \frac{2}{v_{1}^{2} + v_{2}^{2}}v_{1}^{2} \neq -1 ? $$

warm shaleBOT Dec 18, 2021, 6:38 PM

#

mrbrown

clear sinew Dec 18, 2021, 6:38 PM

#

oh

#

I didn't see something

#

$$ =1 - 2 \left( \frac{v_2^2 + v_1^2}{v_1^2 + v_2^2 } \right) = -1 $$

warm shaleBOT Dec 18, 2021, 6:39 PM

#

mrbrown

clear sinew Dec 18, 2021, 6:41 PM

#

ok

clear sinew Dec 18, 2021, 7:16 PM

#

$$ Q = Q^T $$ this means the eigenvectors of Q are orthogonal to each other

warm shaleBOT Dec 18, 2021, 7:17 PM

#

mrbrown

clear sinew Dec 18, 2021, 8:09 PM

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I give up lol

#

maybe another time, for now I will just memorize it.

#

wow 5 hours spent on this

#

thanks for the help, i learnt a little bit but my rusty knowledge wasn't enough 😅

#

.close

obtuse pebbleBOT Dec 18, 2021, 8:10 PM

#

Channel closed

Closed by @clear sinew

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ebon cave Dec 18, 2021, 8:13 PM

#

.reopen

#

obtuse pebbleBOT Dec 18, 2021, 8:14 PM

#

ebon cave

ebon cave Dec 18, 2021, 8:14 PM

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so the problem is to walk across from AC or ABC

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all the lengths are there and u are given to rate of change for the first and second path

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the first AC is 2km/h and the second is 4km/h

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u wanna see which one is the fastest

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and i feel like im missing something

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i have layed out each trajectory and stuff and im trying to figure out relationships to make me unstuck the angle

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but i can seem to get anywhere

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so any clue would be appreciated thanks

#

#

the first trajectory is easy but its the ABC one im stuck on

#

its a calc question (differential only ) and theres no area involved so im quite confused

obtuse pebbleBOT Dec 18, 2021, 8:41 PM

#

@ebon cave Has your question been resolved?

obtuse pebbleBOT Dec 18, 2021, 9:11 PM

#

@ebon cave Has your question been resolved?

obtuse pebbleBOT Dec 18, 2021, 10:22 PM

#

@ebon cave Has your question been resolved?

wary vigil Dec 18, 2021, 10:46 PM

#

if i'm getting it correct then you need to check which is faster

#

going from A to C with 2km/h

#

or from A to B to C with 4km/h

#

?

#

is that right?

#

there's the theorems you can use @ebon cave

#

1st is thales

#

and 2nd is angle to point on circle is 1/2 angle to center of circle

#

angle at the centre theorem

obtuse pebbleBOT Dec 18, 2021, 11:22 PM

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thick torrent Dec 18, 2021, 11:35 PM

#

Could someone help me check my answer for the area bounded by these 3 lines in the first quadrant, marked by orange? I was wrong 2 previous times. My answer is: 46/21

obtuse pebbleBOT Dec 18, 2021, 11:35 PM

#

thick torrent Could someone help me check my answer for the area bounded by these 3 lines in t...

mild ocean Dec 18, 2021, 11:44 PM

#

flonshed

#

i will try

#

but i can’t guarantee my attempts will be successful

lost cloak Dec 18, 2021, 11:46 PM

#

thick torrent Could someone help me check my answer for the area bounded by these 3 lines in t...

Yep I also got 46/21

obtuse pebbleBOT Dec 18, 2021, 11:51 PM

#

@thick torrent Has your question been resolved?

thick torrent Dec 18, 2021, 11:56 PM

#

Thanks! It was correct. catthumbsup

obtuse pebbleBOT Dec 18, 2021, 11:56 PM

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glossy yacht Dec 19, 2021, 12:07 AM

#

for two sets $A$ and $B$, is it sufficient to say that they cannot be put have a one to one correspondence if $|A| \neq |B|$?

obtuse pebbleBOT Dec 19, 2021, 12:07 AM

#

glossy yacht for two sets $A$ and $B$, is it sufficient to say that they cannot be put have a...

warm shaleBOT Dec 19, 2021, 12:09 AM

#

Xetrov

obtuse pebbleBOT Dec 19, 2021, 12:22 AM

#

@glossy yacht Has your question been resolved?

obtuse pebbleBOT Dec 19, 2021, 12:52 AM

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@glossy yacht Has your question been resolved?

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Channel closed

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obtuse pebbleBOT Dec 19, 2021, 4:35 AM

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wanton leaf Dec 19, 2021, 5:33 AM

#

Hello! i need help, I have 2 functions, and questions asking (f+g)(x). what does this answer mean in relation to the two functions? (f-g)(x). why does it matter which order we subtract the functions?(fg)(x)Does it matter which order we multiply in?

obtuse pebbleBOT Dec 19, 2021, 5:33 AM

#

wanton leaf Hello! i need help, I have 2 functions, and questions asking (f+g)(x). what does...

quaint glen Dec 19, 2021, 5:39 AM

#

(f+g)(x)=f(x)+g(x), (f-g)(x)=f(x)-g(x) and (fg)(x)=f(x)g(x)

timid silo Dec 19, 2021, 5:39 AM

#

^^^^^

quaint glen Dec 19, 2021, 5:39 AM

#

why does it matter which order we subtract the functions
because subtraction isn't commutative in general.

wanton leaf Dec 19, 2021, 5:39 AM

#

what about multiplication?

quaint glen Dec 19, 2021, 5:40 AM

#

multiplication is commutative, so fg=gf

wanton leaf Dec 19, 2021, 5:40 AM

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so it does not matter

quaint glen Dec 19, 2021, 5:40 AM

#

Nope.

wanton leaf Dec 19, 2021, 5:40 AM

#

sweet thank u sm u have no idea how much this helps!

#

.close

obtuse pebbleBOT Dec 19, 2021, 5:41 AM

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Channel closed

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cloud patio Dec 19, 2021, 6:47 AM

#

Can someone tell me how to solve question 1 and 2? (I just need hints)

obtuse pebbleBOT Dec 19, 2021, 6:47 AM

#

cloud patio Can someone tell me how to solve question 1 and 2? (I just need hints)

obtuse pebbleBOT Dec 19, 2021, 7:02 AM

#

@cloud patio Has your question been resolved?

obtuse pebbleBOT Dec 19, 2021, 7:32 AM

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@cloud patio Has your question been resolved?

obtuse pebbleBOT Dec 19, 2021, 8:02 AM

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cloud patio Dec 19, 2021, 8:05 AM

#

No

obtuse pebbleBOT Dec 19, 2021, 8:05 AM

#

cloud patio No

cloud patio Dec 19, 2021, 8:06 AM

#

.close

obtuse pebbleBOT Dec 19, 2021, 8:06 AM

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Channel closed

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obtuse pebbleBOT Dec 19, 2021, 1:18 PM

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timid silo Dec 19, 2021, 1:48 PM

#

The height of a projectile can be described by the Vertical Motion Model: h = -16t2 + vt + s, where t is
the time (in seconds) the object has been in the air, v is the initial vertical velocity (in feet per second)
and s is the initial height (in feet). To catch a Frisbee, a dog leaps into the air with an initial velocity of 23
feet per second.

obtuse pebbleBOT Dec 19, 2021, 1:48 PM

#

timid silo The height of a projectile can be described by the Vertical Motion Model: h = -1...

timid silo Dec 19, 2021, 1:48 PM

#

Write a model for the height of the dog above the ground.

#

what is a model?

#

do they mean -16^t2+23t

#

I'm assuming s is 0?

#

.close

obtuse pebbleBOT Dec 19, 2021, 1:52 PM

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Channel closed

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lost bay Dec 19, 2021, 2:09 PM

#

How would I approach solving this

obtuse pebbleBOT Dec 19, 2021, 2:09 PM

#

lost bay How would I approach solving this

#

@lost bay Has your question been resolved?

obtuse pebbleBOT Dec 19, 2021, 2:54 PM

#

@lost bay Has your question been resolved?

obtuse pebbleBOT Dec 19, 2021, 3:54 PM

#

@lost bay Has your question been resolved?

lost bay Dec 19, 2021, 3:54 PM

#

No motherfucker it has not been solved

#

Why ask if you can clearly see there’s no response - stupid bot

novel knoll Dec 19, 2021, 3:56 PM

#

Language my friend

#

And a) is just computing derivative

lost bay Dec 19, 2021, 4:12 PM

#

novel knoll And a) is just computing derivative

How do you know - what indicates it’s a derivative

turbid wolf Dec 19, 2021, 4:36 PM

#

lost bay Why ask if you can clearly see there’s no response - stupid bot

I had the same question but I figured it may be assuming that you solved it on your own, or found help somewhere else, even on in this server in another channel

lost bay Dec 19, 2021, 4:37 PM

#

turbid wolf I had the same question but I figured it may be assuming that you solved it on y...

ahhh I see

obtuse pebbleBOT Dec 19, 2021, 6:37 PM

#

@lost bay Has your question been resolved?

novel knoll Dec 19, 2021, 7:54 PM

#

lost bay How do you know - what indicates it’s a derivative

a) is verify the formula given for the partial derivatives - wdym how did I know its a derivative?

lost bay Dec 19, 2021, 7:55 PM

#

novel knoll a) is verify the formula given for the partial derivatives - wdym how did I know...

Haven't learnt partial derivatives - I meant how did you recognise they were derivatives

#

Quite new to calculus

novel knoll Dec 19, 2021, 7:55 PM

#

$\partial…$ means the partial derivative

lost bay Dec 19, 2021, 7:55 PM

#

Is it just partial derivatives you're seeing here? Is there anything else you think I should know - I'm almost looking at a blank slate

#

My lawd - My brain doesn't work at all

#

But still - haven't worked with them before - I've clearly got some work to do

warm shaleBOT Dec 19, 2021, 7:56 PM

#

ScapeProf

spiral maple Dec 19, 2021, 10:26 PM

#

quite new to calculus

Doin multivar calc sully

mild ocean Dec 19, 2021, 10:30 PM

#

flonshed

#

also i just realized this person has two channels open

#

angerywoog

hot hazel Dec 19, 2021, 10:33 PM

#

.close

obtuse pebbleBOT Dec 19, 2021, 10:33 PM

#

Channel closed

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untold pike Dec 19, 2021, 10:47 PM

#

obtuse pebbleBOT Dec 19, 2021, 10:47 PM

#

untold pike

untold pike Dec 19, 2021, 10:47 PM

#

I tried to solve it and I got 36.869 or something like that

#

Is this right?

daring parcel Dec 19, 2021, 10:48 PM

#

What is your question exactly?

untold pike Dec 19, 2021, 10:49 PM

#

daring parcel What is your question exactly?

Oh sorry

#

What's the value of x?

daring parcel Dec 19, 2021, 10:51 PM

#

x is the angle here? You have a right triangle, the length of the hypothenus and the length of the opposite side to your angle, can you think of any ways to use this data to your advantage?

untold pike Dec 19, 2021, 10:51 PM

#

3/4
Shift>tan>3/4=36.869

untold pike Dec 19, 2021, 10:51 PM

#

daring parcel x is the angle here? You have a right triangle, the length of the hypothenus and...

Yakitori_huh

#

Noice

daring parcel Dec 19, 2021, 10:52 PM

#

Close

#

It's not tan though

untold pike Dec 19, 2021, 10:53 PM

#

What?

#

Oppo/adj

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How it's now tan?

#

Not*

daring parcel Dec 19, 2021, 10:53 PM

#

That's not adjacent though

#

It's opposite/hypothenus

untold pike Dec 19, 2021, 10:53 PM

#

Ohhhhhhhhhhhhhhhh

#

Sin

daring parcel Dec 19, 2021, 10:53 PM

#

Yes!

#

So we have sin(x) = 3/4

#

We now must solve for x

untold pike Dec 19, 2021, 10:54 PM

#

I don't believe I fall to this mistake 😭😭

untold pike Dec 19, 2021, 10:54 PM

#

daring parcel So we have sin(x) = 3/4

=48.59

daring parcel Dec 19, 2021, 10:54 PM

#

It happens 🙂

untold pike Dec 19, 2021, 10:54 PM

#

daring parcel It happens 🙂

Yeah 🫂💔

untold pike Dec 19, 2021, 10:54 PM

#

untold pike =48.59

Right? Yakitori_huh Yakitori_wait_what

daring parcel Dec 19, 2021, 10:55 PM

#

Yes 🙂

untold pike Dec 19, 2021, 10:55 PM

#

Noice

#

Thanks for help Yakitori_give_me_hug Yakitori_heartlove

daring parcel Dec 19, 2021, 10:55 PM

#

Nw!

untold pike Dec 19, 2021, 10:55 PM

#

btw, this question is not about math, but did I make any mistake in grammar/spelling?

#

I'm trying to improve my English skills, If I made any mistake pls let me know about it oCMz75

daring parcel Dec 19, 2021, 10:56 PM

#

No everything seemed good

untold pike Dec 19, 2021, 10:56 PM

#

Noice, thanks again for help Yakitori_give_me_hug Yakitori_heartlove

daring parcel Dec 19, 2021, 10:56 PM

#

❤️

untold pike Dec 19, 2021, 10:56 PM

#

.close

obtuse pebbleBOT Dec 19, 2021, 10:56 PM

#

Channel closed

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vale bobcat Dec 19, 2021, 11:32 PM

#

I'm stuck on what to do

obtuse pebbleBOT Dec 19, 2021, 11:32 PM

#

vale bobcat I'm stuck on what to do

vale bobcat Dec 19, 2021, 11:37 PM

#

.close

obtuse pebbleBOT Dec 19, 2021, 11:37 PM

#

Channel closed

Closed by @vale bobcat

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whole delta Dec 19, 2021, 11:42 PM

#

vale bobcat I'm stuck on what to do

not sure if you solved this problem bc you closed the channel but you can do 10 choose 3 on a calculator

#

lemme get the formula real quick

obtuse pebbleBOT Dec 20, 2021, 3:52 AM

#

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Channel closed

Closed due to the original message being deleted

carmine pewter Dec 20, 2021, 3:54 AM

#

stare

obtuse pebbleBOT Dec 20, 2021, 9:51 AM

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cloud patio Dec 20, 2021, 9:58 AM

#

how is
$d ((dy / dx) × (dy /dx))/dx$
equal to
$(d(dy / dx) / dθ) x (dθ / dx)$

obtuse pebbleBOT Dec 20, 2021, 9:58 AM

#

cloud patio how is $d ((dy / dx) × (dy /dx))/dx$ equal to $(d(dy / dx) / dθ) x (dθ / dx)$

cloud patio Dec 20, 2021, 9:58 AM

#

basically how did we arrive step 2 from step 1

#

i get that they differentiated but it doesn't check out

slow wedge Dec 20, 2021, 10:00 AM

#

Well df/dx= d theta/dx * df/dtheta by the chain rule

#

Apply this to f= dy/dx

cloud patio Dec 20, 2021, 10:02 AM

#

where is f

#

Im confused

slow wedge Dec 20, 2021, 10:03 AM

#

slow wedge Well df/dx= d theta/dx * df/dtheta by the chain rule

This is just what the chain rule generally is for any function f

#

Your problem applies this to f=dy/dx

cloud patio Dec 20, 2021, 10:05 AM

#

thats not the problem i had i think you're explaining the wrong statement

#

i am talking about the second statement

slow wedge Dec 20, 2021, 10:05 AM

#

You are trying to see how you go from step 1 to step 2 right

cloud patio Dec 20, 2021, 10:05 AM

#

marked with '2'

#

yeah

slow wedge Dec 20, 2021, 10:06 AM

#

Well i am telling you how,

#

So d^2y/dx^2 is the same as d/dx(dy/dx) right

#

And then use the chain rule, which says you differentiate theta with x first and then this with theta

cloud patio Dec 20, 2021, 10:06 AM

#

dy / dx = dy / dθ × dθ / dx right?

slow wedge Dec 20, 2021, 10:07 AM

#

Yeah

cloud patio Dec 20, 2021, 10:07 AM

#

then you differentiate that

slow wedge Dec 20, 2021, 10:07 AM

#

So we arent using product rule or whatever

#

In what you wrote

cloud patio Dec 20, 2021, 10:07 AM

#

and you somehow get this

slow wedge Dec 20, 2021, 10:07 AM

#

Replace y with dy/dx

cloud patio Dec 20, 2021, 10:07 AM

#

replace y with what

#

i dont get it how can you replace a variable with its derivative

slow wedge Dec 20, 2021, 10:08 AM

#

cloud patio dy / dx = dy / dθ × dθ / dx right?

So this

#

Is not only true for y

#

But for any function right

cloud patio Dec 20, 2021, 10:08 AM

#

yeah

#

because dθ cancel out

slow wedge Dec 20, 2021, 10:08 AM

#

So instead of y if it were the function dy/dx it would still be true yeah

cloud patio Dec 20, 2021, 10:08 AM

#

rught

slow wedge Dec 20, 2021, 10:09 AM

#

Right so what does that tell you

#

When you have dy/dx in this guy

cloud patio Dec 20, 2021, 10:09 AM

#

oooo

#

i kinda get it now

#

so those dθ's in the second step are just remains from thr first step

#

okay I get it

slow wedge Dec 20, 2021, 10:10 AM

#

Nice

cloud patio Dec 20, 2021, 10:10 AM

#

thank you

#

.close

obtuse pebbleBOT Dec 20, 2021, 10:10 AM

#

Channel closed

Closed by @cloud patio

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obtuse pebbleBOT Dec 20, 2021, 11:22 AM

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worthy dune Dec 20, 2021, 12:52 PM

#

does 0.9 recurring really equal 1 tho

obtuse pebbleBOT Dec 20, 2021, 12:52 PM

#

worthy dune does 0.9 recurring really equal 1 tho

worthy dune Dec 20, 2021, 12:52 PM

#

i mean sure 0.3 recurring is equal to 1/3

#

and 1/3 x 3 is 3/3

#

which is 0.3 recurring x3

#

which is 0.9 recurring

#

but is 0.9 recurring actually 1

willow onyx Dec 20, 2021, 12:57 PM

#

its infinetly close to one but its just not enough to be one

mighty geyser Dec 20, 2021, 12:58 PM

#

worthy dune but is 0.9 recurring actually 1

yes

#

for any two real numbers, if they are distinct, you can find a real number between them

worthy dune Dec 20, 2021, 12:59 PM

#

hmph

#

screw math

#

math confuse

mighty geyser Dec 20, 2021, 12:59 PM

#

think about how you would define 0.9 recurring

worthy dune Dec 20, 2021, 12:59 PM

#

0.9999999999999999

#

e

mighty geyser Dec 20, 2021, 12:59 PM

#

it's the limit of a sequence

#

0.9, 0.99, 0.999, 0.9999...
yeah?

worthy dune Dec 20, 2021, 1:00 PM

#

right but like 0.9 recurring could never actually equal 1 tho right

mighty geyser Dec 20, 2021, 1:00 PM

#

the question is how you would define 0.9 recurring

worthy dune Dec 20, 2021, 1:00 PM

#

also have 1 more question

#

1+1=

willow onyx Dec 20, 2021, 1:00 PM

#

oh frik

willow onyx Dec 20, 2021, 1:01 PM

#

worthy dune 1+1=

3 duh

worthy dune Dec 20, 2021, 1:01 PM

#

such hard

worthy dune Dec 20, 2021, 1:01 PM

#

willow onyx 3 duh

ggs lets goo

mighty geyser Dec 20, 2021, 1:01 PM

#

please don't troll lol

worthy dune Dec 20, 2021, 1:01 PM

#

ok anyway

worthy dune Dec 20, 2021, 1:01 PM

#

mighty geyser the question is how you would define 0.9 recurring

wdym define tho

willow onyx Dec 20, 2021, 1:01 PM

#

if its not 1 its not 1

worthy dune Dec 20, 2021, 1:01 PM

#

doesnt still never equal 1 tho

#

yeah

willow onyx Dec 20, 2021, 1:01 PM

#

if its 0. something

#

its not one

mighty geyser Dec 20, 2021, 1:01 PM

#

alright, what does 3.1415926... mean?

willow onyx Dec 20, 2021, 1:01 PM

#

its lower than one

worthy dune Dec 20, 2021, 1:01 PM

#

pi

#

but

willow onyx Dec 20, 2021, 1:01 PM

#

mighty geyser alright, what does 3.1415926... mean?

pi

worthy dune Dec 20, 2021, 1:01 PM

#

its like infinite

#

so

mighty geyser Dec 20, 2021, 1:02 PM

#

but it's not pi yet

worthy dune Dec 20, 2021, 1:02 PM

#

yeah

#

but

mighty geyser Dec 20, 2021, 1:02 PM

#

at every step when we keep adding digits, it's not pi yet

worthy dune Dec 20, 2021, 1:02 PM

#

0.9 recurring will still never be 1 even if continue long time

#

yes

#

like 0.9 will never be 1

mighty geyser Dec 20, 2021, 1:02 PM

#

but how can you be so sure 3.1415926... is pi

willow onyx Dec 20, 2021, 1:02 PM

#

ask vsauce

mighty geyser Dec 20, 2021, 1:02 PM

#

you continue a long time and you still have finitely many digits
it's still not pi

willow onyx Dec 20, 2021, 1:03 PM

#

true

mighty geyser Dec 20, 2021, 1:03 PM

#

so, pi is simply the limit of the sequence
3, 3.1, 3.14, 3.141, 3.1415, 3.14159, ...

#

none of the individual terms are pi

#

likewise for
0.9, 0.99, 0.999, 0.9999, .... none of the individual terms are 1

#

but the limit is

willow onyx Dec 20, 2021, 1:04 PM

#

ohhhhh

#

@worthy dune come back

worthy dune Dec 20, 2021, 1:07 PM

#

im back

#

hm

#

but

#

this is confuse

mighty geyser Dec 20, 2021, 1:08 PM

#

the question is "what is an infinite decimal"

worthy dune Dec 20, 2021, 1:08 PM

#

if it doenst doesnt start with 1 its not 1?

#

ok

#

never ending stuf

#

yes

mighty geyser Dec 20, 2021, 1:08 PM

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and if you look at pi, it has an neverending decimal representation

worthy dune Dec 20, 2021, 1:08 PM

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also how many other people has asked this question here

mighty geyser Dec 20, 2021, 1:08 PM

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none of the truncations equal to pi

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many many others, I can be sure

worthy dune Dec 20, 2021, 1:08 PM

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lmao

mighty geyser Dec 20, 2021, 1:09 PM

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it is confusing when people first encounter the concept of numbers with more than one decimal representation

worthy dune Dec 20, 2021, 1:09 PM

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lol

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still kinda confuse

mighty geyser Dec 20, 2021, 1:10 PM

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alright, you got the 3.14159... is pi bit, right?

worthy dune Dec 20, 2021, 1:10 PM

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yes

mighty geyser Dec 20, 2021, 1:10 PM

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and you understand no matter how many digits we present, it's not pi

worthy dune Dec 20, 2021, 1:10 PM

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yes

mighty geyser Dec 20, 2021, 1:10 PM

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likewise for 0.99999...

worthy dune Dec 20, 2021, 1:10 PM

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yes'

mighty geyser Dec 20, 2021, 1:10 PM

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no matter how many digits we present, it's still not 1

worthy dune Dec 20, 2021, 1:10 PM

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yes

mighty geyser Dec 20, 2021, 1:11 PM

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but when you go to infinitely many digits, we define it as the limit of the sequence

worthy dune Dec 20, 2021, 1:11 PM

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ok

mighty geyser Dec 20, 2021, 1:12 PM

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so how we define 0.99999... is just the limit of
0.9, 0.99, 0.999, ...
do you know how limits are defined, epsilon-N?

worthy dune Dec 20, 2021, 1:12 PM

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i am only grade 8 chill bruh

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lmao

mighty geyser Dec 20, 2021, 1:13 PM

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there's a pretty formal definition of limits that would help deal with this problem

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essentially it's like a game

worthy dune Dec 20, 2021, 1:13 PM

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ok

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ill do this when im like actually ok at math

mighty geyser Dec 20, 2021, 1:13 PM

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Alice will say a particular epsilon, say "0.00001"

worthy dune Dec 20, 2021, 1:13 PM

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ok

mighty geyser Dec 20, 2021, 1:13 PM

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then Bob will try to find some N such that after the Nth term, all the values do not differ from 1 by more than epsilon

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if Bob can win no matter what positive epsilon says, then the limit is 1

worthy dune Dec 20, 2021, 1:14 PM

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i dont understand rip

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this is very confusing

mighty geyser Dec 20, 2021, 1:14 PM

#

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alright so imagine we plot the terms of this sequence on this graph

worthy dune Dec 20, 2021, 1:15 PM

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yes

mighty geyser Dec 20, 2021, 1:15 PM

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Alice will select a small horizontal band around the limit, 1

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and Bob will have to say how far right you have to go such that the points plotted will never leave the band from that point onwards

worthy dune Dec 20, 2021, 1:16 PM

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im very confused still

mighty geyser Dec 20, 2021, 1:16 PM

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IF
no matter what small horizontal band Alice chooses
Bob can go far enough to stay within that band
THEN
the sequence has a limit

worthy dune Dec 20, 2021, 1:16 PM

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when do you learn this epsilon thing

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what grade

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or university

mighty geyser Dec 20, 2021, 1:17 PM

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hmm Khanacademy probably has a video on it

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lemme find

worthy dune Dec 20, 2021, 1:17 PM

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wait

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but what grade

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or when did you learn it

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or smthn

mighty geyser Dec 20, 2021, 1:17 PM

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I think 9?

worthy dune Dec 20, 2021, 1:17 PM

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grade 9

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middle schol?

mighty geyser Dec 20, 2021, 1:18 PM

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but for different countries it might not map on that cleanly

worthy dune Dec 20, 2021, 1:18 PM

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ok

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i should sleep now

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bye and thanks

clear sinew Dec 20, 2021, 1:18 PM

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I learnt it in university lol

worthy dune Dec 20, 2021, 1:19 PM

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what year

mighty geyser Dec 20, 2021, 1:19 PM

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probably first year

worthy dune Dec 20, 2021, 1:19 PM

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wait

clear sinew Dec 20, 2021, 1:19 PM

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first year

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yea

worthy dune Dec 20, 2021, 1:19 PM

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so element you learnt in grade 9 middle school

clear sinew Dec 20, 2021, 1:19 PM

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it was so confusing

worthy dune Dec 20, 2021, 1:19 PM

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or

worthy dune Dec 20, 2021, 1:19 PM

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clear sinew it was so confusing

is it still confusing

mighty geyser Dec 20, 2021, 1:19 PM

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yeah I only could find limit of a function on KA

worthy dune Dec 20, 2021, 1:20 PM

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bruh

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have no idea still

clear sinew Dec 20, 2021, 1:20 PM

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not anymore thankfully. I accepted that mathematics is, let's say somewhat flexible. I used to believe that maths is... stiff.

mighty geyser Dec 20, 2021, 1:20 PM

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https://www.khanacademy.org/math/ap-calculus-bc/bc-series-new/bc-series-optional/v/definition-of-limit-of-a-sequence-and-sequence-convergence

Khan Academy

Formal definition for limit of a sequence (video) | Khan Academy

A sequence is "converging" if its terms approach a specific value at infinity. This video is a more formal definition of what it means for a sequence to converge.

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found it

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Math is just the rigourous language we use to explain ideas

clear sinew Dec 20, 2021, 1:20 PM

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I think Element118 explained it very nicely. That's the explanation that clicked with me.

worthy dune Dec 20, 2021, 1:21 PM

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clear sinew not anymore thankfully. I accepted that mathematics is, let's say somewhat flexi...

somewhat flexible

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hm

clear sinew Dec 20, 2021, 1:21 PM

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mighty geyser Math is just the rigourous language we use to explain ideas

indeed 😄

worthy dune Dec 20, 2021, 1:21 PM

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clear sinew I think Element118 explained it very nicely. That's the explanation that clicked...

im still have no idea what he was talking about

mighty geyser Dec 20, 2021, 1:21 PM

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KA has about the same visualisation

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might want to watch that linked video

worthy dune Dec 20, 2021, 1:22 PM

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ok

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thank you

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i am going to close now

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i might learn this a bit later

clear sinew Dec 20, 2021, 1:22 PM

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wait borio

worthy dune Dec 20, 2021, 1:22 PM

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when im actually smart

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yeah

clear sinew Dec 20, 2021, 1:22 PM

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let's look at the function f(x) = e^(-x) for example

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looks like this when plotted with geogebra

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now what would your guess be if we go further to the right?

worthy dune Dec 20, 2021, 1:23 PM

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im just confused now

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what

clear sinew Dec 20, 2021, 1:23 PM

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sorry

worthy dune Dec 20, 2021, 1:23 PM

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i obviously havent learnt any of this

mighty geyser Dec 20, 2021, 1:24 PM

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what does the graph seem to approach as it goes to the right

worthy dune Dec 20, 2021, 1:24 PM

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our school has a really bad math system

worthy dune Dec 20, 2021, 1:24 PM

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mighty geyser > what does the graph seem to approach as it goes to the right

smaller

mighty geyser Dec 20, 2021, 1:24 PM

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towards 0, yeah?

worthy dune Dec 20, 2021, 1:24 PM

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yes

clear sinew Dec 20, 2021, 1:24 PM

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👍 🙂

worthy dune Dec 20, 2021, 1:24 PM

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but never reaching 0 right

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or

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lol

clear sinew Dec 20, 2021, 1:25 PM

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I think yes lol

worthy dune Dec 20, 2021, 1:25 PM

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oke

clear sinew Dec 20, 2021, 1:25 PM

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but the point is now, let's say you have me as someone who wants to oppose you

worthy dune Dec 20, 2021, 1:25 PM

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yes

clear sinew Dec 20, 2021, 1:26 PM

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so, I am claiming "no, Borio, the graph will jump and rise again if we go far another to the right"

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enough*

worthy dune Dec 20, 2021, 1:26 PM

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ok

clear sinew Dec 20, 2021, 1:26 PM

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we arrive at Element118 explanation:

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wait

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i'll rephrase my words

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"the graph will never go below 0.1"

worthy dune Dec 20, 2021, 1:27 PM

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ok

clear sinew Dec 20, 2021, 1:27 PM

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but you want to show me that the graph does go below 0.1

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what do you do?

worthy dune Dec 20, 2021, 1:28 PM

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idk

clear sinew Dec 20, 2021, 1:28 PM

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$$ f(x) = e^{-x} $$

warm shaleBOT Dec 20, 2021, 1:28 PM

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mrbrown

clear sinew Dec 20, 2021, 1:28 PM

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let's make it easier

worthy dune Dec 20, 2021, 1:28 PM

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i still dont know what f(x)

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what is f(x)

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i havent learnt this

clear sinew Dec 20, 2021, 1:29 PM

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ohhhhhh ok

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it's called a function

worthy dune Dec 20, 2021, 1:29 PM

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i know that much

clear sinew Dec 20, 2021, 1:29 PM

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you can plug in values x and it gives you a value f(x)

worthy dune Dec 20, 2021, 1:29 PM

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yes

clear sinew Dec 20, 2021, 1:30 PM

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is e^(-x) the confusing part?

worthy dune Dec 20, 2021, 1:30 PM

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not really

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ok

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um

clear sinew Dec 20, 2021, 1:30 PM

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hmm

worthy dune Dec 20, 2021, 1:30 PM

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lol

clear sinew Dec 20, 2021, 1:30 PM

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😅

worthy dune Dec 20, 2021, 1:30 PM

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mind blank

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its almost 12 here

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i really should sleep

clear sinew Dec 20, 2021, 1:30 PM

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okokokok

worthy dune Dec 20, 2021, 1:30 PM

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anyway thank you

clear sinew Dec 20, 2021, 1:30 PM

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😄

worthy dune Dec 20, 2021, 1:30 PM

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very much

clear sinew Dec 20, 2021, 1:30 PM

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thank you too

worthy dune Dec 20, 2021, 1:31 PM

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i have learnt like a bit

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it has broadened my view of math i guess

clear sinew Dec 20, 2021, 1:31 PM

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i think it will work out 🙂

worthy dune Dec 20, 2021, 1:31 PM

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and that im behind in math rip

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or am i

clear sinew Dec 20, 2021, 1:31 PM

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haha

worthy dune Dec 20, 2021, 1:31 PM

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do you at all remember what you learnt in grade 8 middle school

clear sinew Dec 20, 2021, 1:31 PM

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it is a good thing to realize something like that, I used to believe i was the pinnacle lol and unviersity killed me 😂

worthy dune Dec 20, 2021, 1:32 PM

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bruh

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is university that hard

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damn

clear sinew Dec 20, 2021, 1:32 PM

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i don't remember exactly. I knew about functions and somoe geometry

worthy dune Dec 20, 2021, 1:32 PM

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oke

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my school has a really bad math system

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sadge

mighty geyser Dec 20, 2021, 1:33 PM

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hmm maybe you can look at khanacademy

worthy dune Dec 20, 2021, 1:33 PM

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i could

clear sinew Dec 20, 2021, 1:33 PM

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no, it is actually doable imo, but need to discplined and definitely visit the counselling hours and ask quesitons, no matter how the lecturers react. Just ask ask ask. That was the best advice a friend of mine gave me. I improved siginificantly by asking about stuff i didn't understand.

worthy dune Dec 20, 2021, 1:33 PM

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but i should sleep lmao

mighty geyser Dec 20, 2021, 1:33 PM

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they are a pretty good starter sits and you can learn stuff from it

worthy dune Dec 20, 2021, 1:33 PM

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yeah