#help-10 | Mathematics | Page 214

drifting badger Jul 15, 2023, 10:17 AM

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Weird it says 'defined as' pandaHmm I had to prove that relation in my Analysis exam glassescat

kind hawk Jul 15, 2023, 10:25 AM

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how else do you define an integral along a curve

obtuse pebbleBOT Jul 15, 2023, 10:30 AM

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@shy solar Has your question been resolved?

obtuse pebbleBOT Jul 15, 2023, 10:45 AM

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deep bane Jul 15, 2023, 11:11 AM

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obtuse pebbleBOT Jul 15, 2023, 11:11 AM

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deep bane

deep bane Jul 15, 2023, 11:11 AM

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how to prove OPSM is cyclic

restive sage Jul 15, 2023, 11:11 AM

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Use Taylor's formula to find the linear and quadratic approximation of functions at origin
i. f(x, y) = x * e ^ y
ii. f(x, y) = sinxcosy
iii. f(x, y) = e ^ x * cos y
iv. f(x, y) = ysinx

royal basin Jul 15, 2023, 11:15 AM

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restive sage Use Taylor's formula to find the linear and quadratic approximation of functions...

channel occupied, please open your own. #❓how-to-get-help

wooden cipher Jul 15, 2023, 11:16 AM

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deep bane how to prove OPSM is cyclic

Im not convinced it is

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MOP is acute and MSP is right

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Cyclic quads should have opposute angles equal to 180

obtuse pebbleBOT Jul 15, 2023, 11:26 AM

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@deep bane Has your question been resolved?

deep bane Jul 15, 2023, 11:29 AM

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wooden cipher Cyclic quads should have opposute angles equal to 180

yeah app it is

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deep bane Jul 15, 2023, 11:30 AM

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wooden cipher MOP is acute and MSP is right

MSO is right

obtuse pebbleBOT Jul 15, 2023, 11:41 AM

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sour flume Jul 15, 2023, 11:50 AM

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Hey, I was wondering if I could get some help on mathematics because I’m starting school next month and I wanna get most of my math down, and gets some notes and pointers, I’m going to the 11th grade and I’m scared the score that I’m going to two kids have committed suicide

obtuse pebbleBOT Jul 15, 2023, 11:50 AM

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sour flume Hey, I was wondering if I could get some help on mathematics because I’m startin...

timber island Jul 15, 2023, 11:57 AM

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india?

timber island Jul 15, 2023, 11:58 AM

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sour flume Hey, I was wondering if I could get some help on mathematics because I’m startin...

....

kind hawk Jul 15, 2023, 12:01 PM

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ask an actual math question you need help with

candid yarrow Jul 15, 2023, 12:04 PM

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sour flume Hey, I was wondering if I could get some help on mathematics because I’m startin...

We can help you if you have any homework questions you’re stuck on, feel free to ask

sour flume Jul 15, 2023, 12:05 PM

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Oh sorry

obtuse pebbleBOT Jul 15, 2023, 12:20 PM

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@sour flume Has your question been resolved?

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sacred root Jul 15, 2023, 12:39 PM

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The integer from 1 to 2023 are written on a blackboard. At each step,two randomly chosen numbers are erased and a new number equal to their difference is written on the board,making the total count of numbers on the board lesser by one.This process is repeated until there is only one number remaining.The question is remaining number is even or odd?

obtuse pebbleBOT Jul 15, 2023, 12:39 PM

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sacred root ``` The integer from 1 to 2023 are written on a blackboard. At each step,two ran...

sacred root Jul 15, 2023, 12:39 PM

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Any idea how to do it?

candid yarrow Jul 15, 2023, 12:39 PM

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have you considered parity?

sacred root Jul 15, 2023, 12:40 PM

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What is that?

candid yarrow Jul 15, 2023, 12:40 PM

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the cases when even numbers are erased

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or one odd and one even

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or two odd

sacred root Jul 15, 2023, 12:40 PM

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Oh

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Alr

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So two even/odd numbers are selected then.....

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There difference will be even

wooden cipher Jul 15, 2023, 12:42 PM

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Oh my god this is funny

sacred root Jul 15, 2023, 12:42 PM

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?

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The question?

wooden cipher Jul 15, 2023, 12:42 PM

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I chose this problem of the day in the math olympuad discord a while back

sacred root Jul 15, 2023, 12:43 PM

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Ohhh

sacred root Jul 15, 2023, 12:43 PM

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sacred root So two even/odd numbers are selected then.....

If I choose one odd and one even then the difference will be odd

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That's all I can conclude

kind hawk Jul 15, 2023, 12:45 PM

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try an example

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start with 1 to lets say 7

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how many odds and evens are there after every step

sacred root Jul 15, 2023, 12:46 PM

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Well after each step there is 4 odd and 3 even

kind hawk Jul 15, 2023, 12:47 PM

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well you are getting less numbers so it cant always stay that way

wooden cipher Jul 15, 2023, 12:47 PM

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Nvm i lied

sacred root Jul 15, 2023, 12:47 PM

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1,3,5,7 ( 4 odd) 2,4,6 ( 3 even)

wooden cipher Jul 15, 2023, 12:47 PM

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But i do remember showing it to my friends

kind hawk Jul 15, 2023, 12:47 PM

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yes thats at the start

sacred root Jul 15, 2023, 12:47 PM

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👍

kind hawk Jul 15, 2023, 12:47 PM

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now do a step

sacred root Jul 15, 2023, 12:48 PM

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Wdym by step ?? Like jump to another number?

wooden cipher Jul 15, 2023, 12:48 PM

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What happens if at least one even is involved?

kind hawk Jul 15, 2023, 12:48 PM

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take two random numbers and replace them by their difference

sacred root Jul 15, 2023, 12:48 PM

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Alr

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1 2 3 4 5 6 7
Say (1,2)
1 3 4 5 6 7

wooden cipher Jul 15, 2023, 12:50 PM

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What happens when to the count of odds and evens when its (odd, even) or (even, even)?

kind hawk Jul 15, 2023, 12:51 PM

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wooden cipher What happens when to the count of odds and evens when its (odd, even) or (even,...

let them experiment before going at it from a more abstract perspective

wooden cipher Jul 15, 2023, 12:51 PM

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Ok sorry

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It was my approach tbf, but i understand where youre coming from

sacred root Jul 15, 2023, 12:53 PM

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1 2 3 4 5 6 7
Say (1,2)
1 3 4 5 6 7

So here odd = 4 even = 2

If I take (4,6)

1 2 3 4 5 6 7
1 2 3 2 5 7

odd = 4 even = 2

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So of the last number is odd, then only even number will change

So in the black board the number was upto 2023 so only number of even number will change

kind hawk Jul 15, 2023, 12:56 PM

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what happens if you take (1,5)

sacred root Jul 15, 2023, 12:57 PM

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1 2 3 4 5 6 7

1 3 4 4 7
even = 2 odd = 3

Hmm hmmCat

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So

kind hawk Jul 15, 2023, 12:59 PM

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should be 2 3 4 4 6 7, so even=4 and odd=2

sacred root Jul 15, 2023, 1:02 PM

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hmmCat

candid yarrow Jul 15, 2023, 1:04 PM

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consider the parity of the sum of all the numbers before and after steps

sacred root Jul 15, 2023, 1:04 PM

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If both number are even then number of odd doesn't change but if both numbers are odd then number of odd changes 🤔

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Alr

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1 2 3 4 5 6 7

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Let's say (1,2) is choosen so 1 3 4 5 6 7

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28-26=2

royal basin Jul 15, 2023, 1:06 PM

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hmmCat

royal basin Jul 15, 2023, 1:07 PM

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sacred root If both number are even then number of odd doesn't change but if both numbers ar...

it will help to think about this in more detail. how much does the count of odd numbers on the board change if you use two odd numbers?

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also what about using an even and an odd number?

sacred root Jul 15, 2023, 1:09 PM

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1 2 3 4 5 6 7
Say (1,2) ( even, odd)
1 3 4 5 6 7

So here odd = 4 even = 2

If I take (4,6) (even, even)

1 2 3 4 5 6 7
1 2 3 2 5 7

odd = 4 even = 2

Take (3,5) (odd, odd)

1 2 3 4 5 6 7
1 2 4 2 6 7

Even = 4, odd=2

royal basin Jul 15, 2023, 1:09 PM

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you are not executing it correctly when taking 3 and 5

sacred root Jul 15, 2023, 1:09 PM

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Yes I forgot that

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Sry

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From obv, we can see that if taken (even,even) then even changes by -1, taken (odd,odd) even change by +1 and taken (odd,even) even changes by -1

royal basin Jul 15, 2023, 1:12 PM

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you have managed to skillfully sidestep my question

kind hawk Jul 15, 2023, 1:12 PM

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and how does odd change in each case?

sacred root Jul 15, 2023, 1:13 PM

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Well for EO and for EE it doesn't changes but for OO it changes by -2

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0 => odd, E => even

royal basin Jul 15, 2023, 1:13 PM

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incorrect

sacred root Jul 15, 2023, 1:14 PM

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Now it's correct

royal basin Jul 15, 2023, 1:14 PM

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ok good

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so the count of odd numbers on the board can only ever change by -2.

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this is significant. do you see how?

sacred root Jul 15, 2023, 1:16 PM

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No

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OK wait I'll try myself

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I'll think for a bit

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Thanks

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.close

obtuse pebbleBOT Jul 15, 2023, 1:16 PM

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regal jewel Jul 15, 2023, 1:52 PM

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obtuse pebbleBOT Jul 15, 2023, 1:52 PM

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regal jewel

regal jewel Jul 15, 2023, 1:52 PM

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cant i use natrual log on this question

warm canopy Jul 15, 2023, 1:53 PM

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Why would you, if the question is asking for base 10

regal jewel Jul 15, 2023, 1:53 PM

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i mean if it wasn't base 10?

warm canopy Jul 15, 2023, 2:00 PM

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You can use whatever logs you want whenever you want

candid yarrow Jul 15, 2023, 2:04 PM

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regal jewel cant i use natrual log on this question

yes, try it

obtuse pebbleBOT Jul 15, 2023, 2:09 PM

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@regal jewel Has your question been resolved?

obtuse pebbleBOT Jul 15, 2023, 2:24 PM

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obtuse pebbleBOT Jul 15, 2023, 3:43 PM

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pale raft Jul 15, 2023, 4:07 PM

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1+1=2

obtuse pebbleBOT Jul 15, 2023, 4:07 PM

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pale raft 1+1=2

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Show your work, and if possible, explain where you are stuck.

civic socket Jul 15, 2023, 4:10 PM

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pale raft 1+1=2

<@&268886789983436800>

hot hazel Jul 15, 2023, 4:10 PM

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yeah pls dont abuse help channels

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.close

obtuse pebbleBOT Jul 15, 2023, 4:10 PM

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edgy needle Jul 15, 2023, 4:48 PM

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Hi

obtuse pebbleBOT Jul 15, 2023, 4:48 PM

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edgy needle Hi

edgy needle Jul 15, 2023, 4:48 PM

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I need help with part B

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I wrote

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as axis of symmetry is 2 then it will take 2 more seconds to fall making it 4 seconds,

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But i think they want working

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Because it is 2 marks

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(Btw this is a practice question)

violet vine Jul 15, 2023, 4:52 PM

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Find the x intercepts

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Then choose the positive one

edgy needle Jul 15, 2023, 4:52 PM

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Ok wait

leaden ginkgo Jul 15, 2023, 4:52 PM

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well you could give the diifference of both the roots as your answer, i think?

violet vine Jul 15, 2023, 4:53 PM

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leaden ginkgo well you could give the diifference of both the roots as your answer, i think?

Not sure about that

leaden ginkgo Jul 15, 2023, 4:53 PM

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hmmm

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because like

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https://www.desmos.com/calculator/vff1bhyylp

Desmos

Desmos | Graphing Calculator

violet vine Jul 15, 2023, 4:54 PM

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If u mean in the surd notation, then yes, otherwise I have no idea what u mean

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Yes. Technically you could, but it's not universal so I'd recommend just finding the x intercept, picking the further one and taking the x coordinate of it

edgy needle Jul 15, 2023, 4:55 PM

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i got roots...

violet vine Jul 15, 2023, 4:56 PM

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edgy needle i got roots...

That works (sorry no it doesn't, unless it's an unsimplified then...)

edgy needle Jul 15, 2023, 4:56 PM

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but the x intercepts arent roots

violet vine Jul 15, 2023, 4:56 PM

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I actually have no idea what the answer is lemme check lmao

violet vine Jul 15, 2023, 4:56 PM

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edgy needle but the x intercepts arent roots

Show the working

edgy needle Jul 15, 2023, 4:57 PM

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The scribbles are 256

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Omg nvm

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I see my mistake

violet vine Jul 15, 2023, 4:58 PM

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Well that sorts that out

edgy needle Jul 15, 2023, 4:58 PM

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Wait

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Is the only way i can figure this out

violet vine Jul 15, 2023, 4:58 PM

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U should get 0 for the - and the answer for the +

edgy needle Jul 15, 2023, 4:58 PM

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Is by using quadratic formula

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Or can i factorise

violet vine Jul 15, 2023, 4:59 PM

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edgy needle Or can i factorise

Yes

edgy needle Jul 15, 2023, 4:59 PM

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How can i factorise

violet vine Jul 15, 2023, 4:59 PM

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Wait factorise?

edgy needle Jul 15, 2023, 4:59 PM

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I tried non monic didnt work

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Yes

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And then use the null factor law

violet vine Jul 15, 2023, 4:59 PM

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U can do difference of squares

edgy needle Jul 15, 2023, 5:00 PM

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I only know how to do that when its 2

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Not a trinomial

violet vine Jul 15, 2023, 5:01 PM

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One sec lemme check smth

edgy needle Jul 15, 2023, 5:01 PM

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Omg...

violet vine Jul 15, 2023, 5:01 PM

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(-2t+9)(2t+1) yes u can factorise

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U can use factorization, difference of squares or formula

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But formula is the most braindead so it's my go-to

edgy needle Jul 15, 2023, 5:03 PM

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How do u do difference of squares

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In a trinomial?

violet vine Jul 15, 2023, 5:03 PM

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There's a formula for it

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Wait shit

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Sorry not difference of squares

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I forgot the proper terminology

edgy needle Jul 15, 2023, 5:04 PM

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I can also do this way

violet vine Jul 15, 2023, 5:05 PM

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Complete the squares sorry

violet vine Jul 15, 2023, 5:05 PM

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edgy needle

That's uhm wrong

edgy needle Jul 15, 2023, 5:05 PM

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How

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I got the right answer though

violet vine Jul 15, 2023, 5:05 PM

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-4t * -4t isn't -4t^2

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It's 16t^2

edgy needle Jul 15, 2023, 5:06 PM

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Oh this isa different way

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Wait let me show u

violet vine Jul 15, 2023, 5:06 PM

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Interesting, never learned it

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But yes there are a ton of methods and u only need 1

edgy needle Jul 15, 2023, 5:06 PM

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Yeah lol a lot of people have said dat

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Yeah only my teacher uses it

violet vine Jul 15, 2023, 5:07 PM

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Anyway u got the right answer, congrats

edgy needle Jul 15, 2023, 5:07 PM

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But then we divide both sides by -4t

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Nvm

violet vine Jul 15, 2023, 5:07 PM

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Also the other intersection shouldnt be 0.5 I think

edgy needle Jul 15, 2023, 5:08 PM

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Oh i forgot the negative

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It's -0.5

violet vine Jul 15, 2023, 5:08 PM

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Yep

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Anyway if ur done u can do .close

edgy needle Jul 15, 2023, 5:08 PM

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Ok thanks

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.close

obtuse pebbleBOT Jul 15, 2023, 5:08 PM

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Channel closed

Closed by @edgy needle

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solemn pollen Jul 15, 2023, 5:17 PM

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I’m stuck on this question should I use integration by parts

obtuse pebbleBOT Jul 15, 2023, 5:17 PM

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solemn pollen I’m stuck on this question should I use integration by parts

timid silo Jul 15, 2023, 5:21 PM

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solemn pollen I’m stuck on this question should I use integration by parts

There is no elementary antiderivative to this function first of all

solemn pollen Jul 15, 2023, 5:22 PM

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timid silo There is no elementary antiderivative to this function first of all

So how should I proceed?

sage geode Jul 15, 2023, 5:22 PM

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timid silo There is no elementary antiderivative to this function first of all

Well the indefinite integral here is -0.5 pi ln(2) apparently

timid silo Jul 15, 2023, 5:22 PM

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Unsure. Doesn't sound possible without some advanced techniques

solemn pollen Jul 15, 2023, 5:23 PM

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Oh

solemn pollen Jul 15, 2023, 5:23 PM

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timid silo Unsure. Doesn't sound possible without some advanced techniques

I mean it’s Highschool level math :((

timid silo Jul 15, 2023, 5:23 PM

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Definitely misinterpreting something then?

kind hawk Jul 15, 2023, 5:24 PM

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maybe there is some smart u-sub coupled with trig properties which you gives you the same integral again?

timid silo Jul 15, 2023, 5:24 PM

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Any other context to this question?

solemn pollen Jul 15, 2023, 5:24 PM

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I’ll try doing the problem again from the beginning

solemn pollen Jul 15, 2023, 5:24 PM

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timid silo Any other context to this question?

Nope just that

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Evaluate the integral

timid silo Jul 15, 2023, 5:26 PM

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Oh I think I figured it out? @solemn pollen

sage geode Jul 15, 2023, 5:26 PM

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Oke I solved it

timid silo Jul 15, 2023, 5:26 PM

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You're on the right track with your attempt thonk

sage geode Jul 15, 2023, 5:26 PM

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Oh they definitely are

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I got smth similar

solemn pollen Jul 15, 2023, 5:26 PM

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That’s great what should I do now

sage geode Jul 15, 2023, 5:29 PM

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Oh wait my solution is missing smth

solar trellis Jul 15, 2023, 5:30 PM

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You could try u=pi/2 - x or u=2x

solemn pollen Jul 15, 2023, 5:30 PM

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This is the answer

solar trellis Jul 15, 2023, 5:31 PM

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Yea so the integral you're left with should be I

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After integrating the constant

solemn pollen Jul 15, 2023, 5:32 PM

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Oh yeaaa

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I think I’m getting it

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Yes

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Ur right

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Got it

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Thanks @solar trellis

solar trellis Jul 15, 2023, 5:32 PM

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Wl

solemn pollen Jul 15, 2023, 5:32 PM

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.close

obtuse pebbleBOT Jul 15, 2023, 5:32 PM

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Channel closed

Closed by @solemn pollen

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obtuse pebbleBOT Jul 15, 2023, 6:26 PM

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Available help channel!

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Remember:
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• Be polite and have a nice day!

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

timid silo Jul 15, 2023, 6:41 PM

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obtuse pebbleBOT Jul 15, 2023, 6:41 PM

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timid silo

timid silo Jul 15, 2023, 6:41 PM

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error here?

pseudo swift Jul 15, 2023, 6:41 PM

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what error do you see ?

timid silo Jul 15, 2023, 6:42 PM

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surely -1^2 should become +1 and make the denom 3x+14?

pseudo swift Jul 15, 2023, 6:42 PM

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nope

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(3x+13) - (1^2)

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that's how it should be read

timid silo Jul 15, 2023, 6:43 PM

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sigh ok. not sure when it's that way vs. the way i was thinking?

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the other way would be (3x+13)(-1^2)? or (3x+13)(-1)^2?

pseudo swift Jul 15, 2023, 6:44 PM

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timid silo the other way would be (3x+13)(-1^2)? or (3x+13)(-1)^2?

that would be multiplication the way you wrote it

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not addition

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(3x + 13) + (-1)^2 if anything

timid silo Jul 15, 2023, 6:45 PM

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wait it should be subtraction

pseudo swift Jul 15, 2023, 6:45 PM

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timid silo the other way would be (3x+13)(-1^2)? or (3x+13)(-1)^2?

there's no substraction here either

timid silo Jul 15, 2023, 6:47 PM

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right right

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ok i think i see the confusion

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thanks

pseudo swift Jul 15, 2023, 6:47 PM

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timid silo sigh ok. not sure when it's that way vs. the way i was thinking?

it's about the order of operations, you compute powers first, then multiplications/divisions, then additions/substractions

timid silo Jul 15, 2023, 6:49 PM

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!close

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.close

obtuse pebbleBOT Jul 15, 2023, 6:49 PM

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Channel closed

Closed by @frank abyss

Use .reopen if this was a mistake.

obtuse pebbleBOT Jul 15, 2023, 7:06 PM

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vernal cobalt Jul 15, 2023, 7:11 PM

#

I need help with this math question

obtuse pebbleBOT Jul 15, 2023, 7:11 PM

#

vernal cobalt I need help with this math question

vernal cobalt Jul 15, 2023, 7:11 PM

#

Wait

#

I need to find it

#

Ok

#

I got it

#

@royal basin I got it finnaly

royal basin Jul 15, 2023, 7:14 PM

#

why ping me

vernal cobalt Jul 15, 2023, 7:14 PM

#

I

#

Thought you were waiting for me?

royal basin Jul 15, 2023, 7:14 PM

#

i was not

vernal cobalt Jul 15, 2023, 7:14 PM

#

Oh

#

Do you know how to solve this?

royal basin Jul 15, 2023, 7:15 PM

#

i probably do.

vernal cobalt Jul 15, 2023, 7:15 PM

#

Can you help me?

royal basin Jul 15, 2023, 7:15 PM

#

i could if i wanted to.

vernal cobalt Jul 15, 2023, 7:16 PM

#

Please?

royal basin Jul 15, 2023, 7:16 PM

#

i do not have the energy or patience.

vernal cobalt Jul 15, 2023, 7:16 PM

#

Why not?

#

?

buoyant hatch Jul 15, 2023, 7:18 PM

#

alr

#

what is the question

vernal cobalt Jul 15, 2023, 7:18 PM

#

?

buoyant hatch Jul 15, 2023, 7:18 PM

#

lemme try ig

#

oh wtf

#

lemme get pen and paper

royal basin Jul 15, 2023, 7:19 PM

#

!nosols

obtuse pebbleBOT Jul 15, 2023, 7:19 PM

#

As a helper, please do not give out answers that could be copied as a homework solution. Have the student work through the problem themselves and guide them along the way.

royal basin Jul 15, 2023, 7:19 PM

#

saying this preemptively

buoyant hatch Jul 15, 2023, 7:19 PM

#

alr i wont

buoyant hatch Jul 15, 2023, 7:19 PM

#

royal basin saying this preemptively

btw

#

u know how to integral calculus?

vernal cobalt Jul 15, 2023, 7:19 PM

#

royal basin saying this preemptively

Can you help?

royal basin Jul 15, 2023, 7:19 PM

#

i already said no.

vernal cobalt Jul 15, 2023, 7:19 PM

#

Why not?

royal basin Jul 15, 2023, 7:19 PM

#

do you want me to say it seventeen more times so that you get it?

vernal cobalt Jul 15, 2023, 7:19 PM

#

Why not?

buoyant hatch Jul 15, 2023, 7:19 PM

#

royal basin do you want me to say it seventeen more times so that you get it?

u know integral calculus?

#

i need help with a ques

royal basin Jul 15, 2023, 7:20 PM

#

@vernal cobalt i don't have the energy or patience to help you. asking "why not" about that is idiotic.

vernal cobalt Jul 15, 2023, 7:20 PM

#

royal basin <@620512891887419402> i don't have the energy or patience to help you. asking "w...

Can you help me tomorrow then ?

buoyant hatch Jul 15, 2023, 7:20 PM

#

royal basin <@620512891887419402> i don't have the energy or patience to help you. asking "w...

BRUV ERSPOND TO ME PLEASE

royal basin Jul 15, 2023, 7:20 PM

#

you're not entitled to my help.

vernal cobalt Jul 15, 2023, 7:20 PM

#

royal basin you're not entitled to my help.

Why?

royal basin Jul 15, 2023, 7:20 PM

#

buoyant hatch BRUV ERSPOND TO ME PLEASE

and neither are you.

royal basin Jul 15, 2023, 7:21 PM

#

vernal cobalt Why?

!volunteers

obtuse pebbleBOT Jul 15, 2023, 7:21 PM

#

vernal cobalt Why?

Helpers are just people volunteering their time to help you. Be polite.

buoyant hatch Jul 15, 2023, 7:21 PM

#

alr

#

dont mind

vernal cobalt Jul 15, 2023, 7:21 PM

#

royal basin !volunteers

May you please help me?

#

||that is polite||

brisk matrix Jul 15, 2023, 7:23 PM

#

buoyant hatch BRUV ERSPOND TO ME PLEASE

please don't advertise your questions in other channels

buoyant hatch Jul 15, 2023, 7:23 PM

#

alr sorry sir

brisk matrix Jul 15, 2023, 7:23 PM

#

vernal cobalt ||that is polite||

its impolite to repeatedly ask for something after clearly being told no

vernal cobalt Jul 15, 2023, 7:23 PM

#

So when can I get help

brisk matrix Jul 15, 2023, 7:24 PM

#

be patient

#

if someone wants to help they will

#

but berating people for help doesn't make anyone want to help more

vernal cobalt Jul 15, 2023, 7:24 PM

#

.close

obtuse pebbleBOT Jul 15, 2023, 7:24 PM

#

Channel closed

Closed by @vernal cobalt

Use .reopen if this was a mistake.

#

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supple trail Jul 15, 2023, 8:15 PM

#

I have sin²x × cos x and I want to find x by which the expression will be maximum. How to find it?
Remember we haven't studied any derivative!

obtuse pebbleBOT Jul 15, 2023, 8:15 PM

#

supple trail I have sin²x × cos x and I want to find x by which the expression will be maximu...

violet sentinel Jul 15, 2023, 8:18 PM

#

so analytically, what is the maximum of both sin and cos, separately? What is the maximum value for those functions alone?

supple trail Jul 15, 2023, 8:19 PM

#

So if we have sin x , x should be 90

#

And for cos x should be 0

#

And max is 1

violet sentinel Jul 15, 2023, 8:19 PM

#

yep exactly

#

so what that tells us is that when sin(x) = 1, cos(x) = 0 and vice versa

#

since we're multiplying sin^2(x)cos(x), then that means that at their individual maximum values, the function will equal 0

#

so we know the max won't be 1

#

(is the point)

supple trail Jul 15, 2023, 8:21 PM

#

So put 30 = x
It equals to ¼ × ¾

#

It isn't 0

violet sentinel Jul 15, 2023, 8:22 PM

#

yep! Now the question is "is that the maximum"?

#

I doubt it, 3/16 is fairly small 🙂

supple trail Jul 15, 2023, 8:24 PM

#

Actually I calculated by graphing x = 54 but don't know what to do it myself

violet sentinel Jul 15, 2023, 8:24 PM

#

wait where did you get x = 54?

supple trail Jul 15, 2023, 8:25 PM

#

With geogebra I graphed it

violet sentinel Jul 15, 2023, 8:25 PM

#

oh I see

#

yeah that's the correct answer, lol

#

is graphing allowed? Otherwise without deriviatives this will be somewhat difficutl

supple trail Jul 15, 2023, 8:26 PM

#

violet sentinel is graphing allowed? Otherwise without deriviatives this will be somewhat diffic...

Absolutely not

wild swallow Jul 15, 2023, 8:27 PM

#

spoiler: it's not 54 degrees exactly

supple trail Jul 15, 2023, 8:27 PM

#

wild swallow spoiler: it's not 54 degrees exactly

Approximately

violet sentinel Jul 15, 2023, 8:29 PM

#

hmmm

#

I'm thinking but tbh I'm stuck on where to go from here without derivatives

#

one moment

wild swallow Jul 15, 2023, 8:29 PM

#

do you know am-gm?

supple trail Jul 15, 2023, 8:30 PM

#

What? No

wild swallow Jul 15, 2023, 8:30 PM

#

okay do you know about cubic polynomials?

supple trail Jul 15, 2023, 8:30 PM

#

Yeah

wild swallow Jul 15, 2023, 8:31 PM

#

do you know that when they have a double root, then there is a turning point

#

i.e. a local maximum/minimum

supple trail Jul 15, 2023, 8:31 PM

#

Ok

wild swallow Jul 15, 2023, 8:31 PM

#

use that fact, plus the pythagorean identity

supple trail Jul 15, 2023, 8:32 PM

#

Cos x = sqrt3 / 3 right?

wild swallow Jul 15, 2023, 8:33 PM

#

well yes

supple trail Jul 15, 2023, 8:33 PM

#

Tnx 👍

#

.close

obtuse pebbleBOT Jul 15, 2023, 8:33 PM

#

Channel closed

Closed by @supple trail

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placid smelt Jul 15, 2023, 8:49 PM

#

Did they get root(2)/2 and root(3)/2 using special triangles? If so, how?

obtuse pebbleBOT Jul 15, 2023, 8:49 PM

#

placid smelt Did they get root(2)/2 and root(3)/2 using special triangles? If so, how?

civic zealot Jul 15, 2023, 8:51 PM

#

unit circle?

placid smelt Jul 15, 2023, 8:52 PM

#

Is there a way to know without the unit circle?

civic zealot Jul 15, 2023, 8:52 PM

#

the graph of cos(x) and some special points (the ones on the unit circle)
or using triangles i guess is also possible.

placid smelt Jul 15, 2023, 8:53 PM

#

How would it done done using triangles?

#

Because no special triangle has 2

#

like root(2)/2 can't be seen from a special traingle as far as I know

civic zealot Jul 15, 2023, 8:54 PM

#

#

pi/6 is 30 degrees
pi/4 is 45 degrees

placid smelt Jul 15, 2023, 8:55 PM

#

ok but how do we know that a is 2 in this case

civic zealot Jul 15, 2023, 8:55 PM

#

cos(x) = adj/hyp

placid smelt Jul 15, 2023, 8:55 PM

#

ik that lol

#

but how do we know a is 2

civic zealot Jul 15, 2023, 8:55 PM

#

a isn't 2

placid smelt Jul 15, 2023, 8:55 PM

#

hmm

#

if we look for cos(pi/6)

#

we have Aroot(3)/2A

#

which is root(3)/2

#

which is right

#

but

#

for cos(pi/4)

#

we have a/aroot(2)

#

which isn't root(2)/2

#

...?

civic zealot Jul 15, 2023, 8:57 PM

#

now cancel the a and rationalize the denominator

placid smelt Jul 15, 2023, 8:58 PM

#

well we have 1/sqrt(2)

#

To rationalize I multiply by sqrt(2)/sqrt(2)?

civic zealot Jul 15, 2023, 8:58 PM

#

yep

placid smelt Jul 15, 2023, 8:58 PM

#

ahhh

#

tysm!

#

.close

obtuse pebbleBOT Jul 15, 2023, 8:59 PM

#

Channel closed

Closed by @placid smelt

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queen parcel Jul 15, 2023, 9:09 PM

#

How do i simplify the first part of the intergral without a calculator?

obtuse pebbleBOT Jul 15, 2023, 9:09 PM

#

queen parcel How do i simplify the first part of the intergral without a calculator?

kind hawk Jul 15, 2023, 9:10 PM

#

u-sub

queen parcel Jul 15, 2023, 9:10 PM

#

sorry i meant when i finish everything i get 68^(3/2)/18 - (4/9)

#

is that the most i can simplify w/o a calculator

kind hawk Jul 15, 2023, 9:12 PM

#

you could combine the fractions but not much more

queen parcel Jul 15, 2023, 9:12 PM

#

also would that be right?

#

im checking all my work again

#

but im not so sure

kind hawk Jul 15, 2023, 9:14 PM

#

you could just check with wolframalpha

queen parcel Jul 15, 2023, 9:14 PM

#

for 68^3/2 its giving me 17sqrt(17)

#

im kinda conflicted with the no calculator rule

polar fossil Jul 15, 2023, 9:15 PM

#

\begin{align*}
\int_0^4 x^2\sqrt{4+x^3}\dd{x} &= \int \frac{\sqrt u}{3}\dd{u} \
&= \frac13\cdot \frac23 u^{\frac32} \
&= \left.\frac29(4+x^3)^{\frac32}\right|_0^4 \
&= \frac29(4+64) - \frac89 \
\end{align*}

warm shaleBOT Jul 15, 2023, 9:16 PM

#

Hayley

kind hawk Jul 15, 2023, 9:16 PM

#

!nosols etc

obtuse pebbleBOT Jul 15, 2023, 9:16 PM

#

As a helper, please do not give out answers that could be copied as a homework solution. Have the student work through the problem themselves and guide them along the way.

polar fossil Jul 15, 2023, 9:16 PM

#

i was mostly just checking because it looks like you might have moved the 2 somewhere it shouldn't be

#

you'll still end up with a sqrt17 in there somewhere though which is fine

queen parcel Jul 15, 2023, 9:17 PM

#

how would i get to sqrt17 from

kind hawk Jul 15, 2023, 9:17 PM

#

sqrt(68) = sqrt(4*17) = 2 sqrt(17)

queen parcel Jul 15, 2023, 9:18 PM

#

thank you sm

obtuse pebbleBOT Jul 15, 2023, 9:33 PM

#

@queen parcel Has your question been resolved?

#

Channel closed

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mental gulch Jul 15, 2023, 9:45 PM

#

Hi i need help, ive to maximize a function subject to another function. Can someone help me? if they know economy might be better. But all help is well received

obtuse pebbleBOT Jul 15, 2023, 9:45 PM

#

mental gulch Hi i need help, ive to maximize a function subject to another function. Can some...

mental gulch Jul 15, 2023, 9:46 PM

#

the axis x has q_1 and the axis y has q_2

#

this is how i reached to that anwser:

#

but thats not the way i should reach it

#

CPO means FOC

#

<@&286206848099549185>

obtuse pebbleBOT Jul 15, 2023, 10:15 PM

#

@mental gulch Has your question been resolved?

mental gulch Jul 15, 2023, 10:18 PM

#

<@&286206848099549185>

obtuse pebbleBOT Jul 15, 2023, 10:48 PM

#

@mental gulch Has your question been resolved?

mental gulch Jul 15, 2023, 10:48 PM

#

NO

#

😭

#

<@&286206848099549185> ?

obtuse pebbleBOT Jul 15, 2023, 11:57 PM

#

@mental gulch Has your question been resolved?

mental gulch Jul 15, 2023, 11:58 PM

#

/close

#

.close

obtuse pebbleBOT Jul 15, 2023, 11:58 PM

#

Channel closed

Closed by @mental gulch

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vagrant arch Jul 16, 2023, 12:10 AM

#

can this be differenciated with product rule?

obtuse pebbleBOT Jul 16, 2023, 12:10 AM

#

vagrant arch can this be differenciated with product rule?

vagrant arch Jul 16, 2023, 12:10 AM

#

if no, why?

#

OH SHIT MB

#

.close

obtuse pebbleBOT Jul 16, 2023, 12:10 AM

#

Channel closed

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silver flint Jul 16, 2023, 12:25 AM

#

how do you find the related rate

obtuse pebbleBOT Jul 16, 2023, 12:25 AM

#

silver flint how do you find the related rate

silver flint Jul 16, 2023, 12:25 AM

#

i know that da/dt = 6

#

and we need to find dr/dt when A = 9

teal turret Jul 16, 2023, 12:27 AM

#

Yep

#

What’s formula do we use for area of circle

silver flint Jul 16, 2023, 12:28 AM

#

so sorry could you give me like 5 mins

#

i think im onto something

#

thx

obtuse pebbleBOT Jul 16, 2023, 12:43 AM

#

@silver flint Has your question been resolved?

silver flint Jul 16, 2023, 12:46 AM

#

hey i figured it out stephen thanks btw

obtuse pebbleBOT Jul 16, 2023, 12:47 AM

#

Channel closed

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ripe fiber Jul 16, 2023, 1:01 AM

#

need help

obtuse pebbleBOT Jul 16, 2023, 1:01 AM

#

ripe fiber need help

ripe fiber Jul 16, 2023, 1:01 AM

#

grizzled shore Jul 16, 2023, 1:01 AM

#

What do you need help with?

ripe fiber Jul 16, 2023, 1:01 AM

#

#

3,2 is A

grizzled shore Jul 16, 2023, 1:01 AM

#

What is the distance formula?

ripe fiber Jul 16, 2023, 1:02 AM

#

i dont know

#

thats why im asking

grizzled shore Jul 16, 2023, 1:02 AM

#

Have you heard of the Pythagoras theorem

ripe fiber Jul 16, 2023, 1:02 AM

#

yes

grizzled shore Jul 16, 2023, 1:03 AM

#

Could you apply it here?

ripe fiber Jul 16, 2023, 1:03 AM

#

yes

#

so its asking for hypotenus?

grizzled shore Jul 16, 2023, 1:03 AM

#

Pretty much

#

That’s what distance is

#

Well, at this level at least

ripe fiber Jul 16, 2023, 1:04 AM

#

this is grade 10 math

grizzled shore Jul 16, 2023, 1:04 AM

#

Yeah

ripe fiber Jul 16, 2023, 1:04 AM

#

ok thank you

#

.close

obtuse pebbleBOT Jul 16, 2023, 1:04 AM

#

Channel closed

Closed by @ripe fiber

Use .reopen if this was a mistake.

grizzled shore Jul 16, 2023, 1:04 AM

#

We call it Euclidean distance

obsidian wren Jul 16, 2023, 1:05 AM

#

can you help me frost

obtuse pebbleBOT Jul 16, 2023, 1:11 AM

#

Available help channel!

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vagrant arch Jul 16, 2023, 1:34 AM

#

can someone help identify what's the answer when 3(1-5x^3)^2(-15x^2) is differentiated

obtuse pebbleBOT Jul 16, 2023, 1:34 AM

#

vagrant arch can someone help identify what's the answer when 3(1-5x^3)^2(-15x^2) is differen...

vagrant arch Jul 16, 2023, 1:35 AM

#

the answer I'm getting is -450x^7-45x^4+90x I don't think it's right

brisk grove Jul 16, 2023, 1:37 AM

#

what have you tried

#

show your work

high lily Jul 16, 2023, 1:38 AM

#

ideally you'd leave the result in factored form

vagrant arch Jul 16, 2023, 1:38 AM

#

this is the answer in the answer sheet

#

I just want to know if the answer sheet is right or not

urban patrol Jul 16, 2023, 1:38 AM

#

,w differentiate 3(1-5x^3)^2(-15x^2)

warm shaleBOT Jul 16, 2023, 1:38 AM

#

Results provided by WolframAlpha

Click here to refine your query online
Upgrade to WolframAlpha Pro!

vagrant arch Jul 16, 2023, 1:38 AM

#

yes it is

urban patrol Jul 16, 2023, 1:38 AM

#

,w calculate 90*25

warm shaleBOT Jul 16, 2023, 1:38 AM

#

Results provided by WolframAlpha

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urban patrol Jul 16, 2023, 1:39 AM

#

yup

vagrant arch Jul 16, 2023, 1:39 AM

#

hold on imma send a pic

#

#

holy shit I finally got it

#

.close

obtuse pebbleBOT Jul 16, 2023, 1:46 AM

#

Channel closed

Closed by @vagrant arch

Use .reopen if this was a mistake.

high lily Jul 16, 2023, 1:47 AM

#

notation crimes

obtuse pebbleBOT Jul 16, 2023, 1:47 AM

#

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vagrant arch Jul 16, 2023, 1:47 AM

#

what's a notation crime

obtuse pebbleBOT Jul 16, 2023, 1:47 AM

#

vagrant arch what's a notation crime

high lily Jul 16, 2023, 1:48 AM

#

extremely bad notation

vagrant arch Jul 16, 2023, 1:48 AM

#

wym

high lily Jul 16, 2023, 1:48 AM

#

your use of =

vagrant arch Jul 16, 2023, 1:49 AM

#

wait is that it

plucky rivet Jul 16, 2023, 1:49 AM

#

tell us what tan^(-2) (x) mean

vagrant arch Jul 16, 2023, 1:49 AM

#

anything else

high lily Jul 16, 2023, 1:49 AM

#

it's supposed to mean that it's equal to whatever is above
yet it isn't entirely clear when your taking derivatives etc

vagrant arch Jul 16, 2023, 1:49 AM

#

oh yeah I'm aware of that

#

but I didn't plan to show it to anyone so that's why I did it that way

high lily Jul 16, 2023, 1:50 AM

#

not recommended

vagrant arch Jul 16, 2023, 1:50 AM

#

yeah I'll write the full thing if it's an exam

high lily Jul 16, 2023, 1:50 AM

#

the work you do should reflect what you'd write in the test

vagrant arch Jul 16, 2023, 1:50 AM

#

ok

high lily Jul 16, 2023, 1:50 AM

#

don't get into bad habits

vagrant arch Jul 16, 2023, 1:50 AM

#

yessir

#

dab me up

#

.close

obtuse pebbleBOT Jul 16, 2023, 1:51 AM

#

Channel closed

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timid silo Jul 16, 2023, 2:20 AM

#

looking to quickly hop into a vc for a problem if that's cool

obtuse pebbleBOT Jul 16, 2023, 2:20 AM

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timid silo looking to quickly hop into a vc for a problem if that's cool

timid silo Jul 16, 2023, 2:21 AM

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it's complex analysis

candid yarrow Jul 16, 2023, 2:35 AM

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how about just here

obtuse pebbleBOT Jul 16, 2023, 2:40 AM

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@timid silo Has your question been resolved?

timid silo Jul 16, 2023, 2:46 AM

#

.close

obtuse pebbleBOT Jul 16, 2023, 2:46 AM

#

Channel closed

Closed by @lavish storm

Use .reopen if this was a mistake.

obtuse pebbleBOT Jul 16, 2023, 3:21 AM

#

Available help channel!

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orchid pine Jul 16, 2023, 3:47 AM

#

obtuse pebbleBOT Jul 16, 2023, 3:47 AM

#

orchid pine

orchid pine Jul 16, 2023, 3:47 AM

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Apologize for the glare

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Can someone tell me what I’m missing on this?

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The right limit is -5, how is this whole limit exist as 3

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Better picture if needed

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Better pic if needed

violet sentinel Jul 16, 2023, 3:50 AM

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not quite. Remember it's only -5 at a single point: where x = 1. Remember the limit represents what is approaching.

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aka, the limit from the right side is not -5

orchid pine Jul 16, 2023, 3:50 AM

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But if x on the right side is equal to 1

runic void Jul 16, 2023, 3:51 AM

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that’s just a removable discontinuity you have

orchid pine Jul 16, 2023, 3:51 AM

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I haven’t gotten up to that yet 😦

violet sentinel Jul 16, 2023, 3:51 AM

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orchid pine But if x on the right side is equal to 1

no it only equals -5 at one single point

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this is what your function looks like

#

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if you notice, if you approach from the left or right side, the continuous function "approaches" the value of 3

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even though at x = 1, it's equal to -5

orchid pine Jul 16, 2023, 3:53 AM

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Should I know this without plugging this into anywhere? Possibly stupid question

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Like looking at what it looks like

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Before answering

runic void Jul 16, 2023, 3:54 AM

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Limits are not what happens at the point x=a, it’s more of where the neighbourhood of x=a approaches

orchid pine Jul 16, 2023, 3:54 AM

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Yeah, I get that part

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Maybe I’m just being too robotic by trying to just solve them and move through the test

runic void Jul 16, 2023, 3:55 AM

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Only way to get a sense of the limit value is to plug values closer to 1

orchid pine Jul 16, 2023, 3:55 AM

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Through a table right

runic void Jul 16, 2023, 3:55 AM

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0.99999 ish

orchid pine Jul 16, 2023, 3:55 AM

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Yeah yeah

runic void Jul 16, 2023, 3:55 AM

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or 1.000001

orchid pine Jul 16, 2023, 3:55 AM

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Ngl I was trying to avoid that

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But I guess that really is the surefire way to see for real huh

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I’m still a little confused on it though, as for what I should think when I see something like this next time

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To me it looks like the whole right side is -5 and it doesn’t exist because the left is 3

runic void Jul 16, 2023, 3:58 AM

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any point in the right and left side of x=1 is determined by -x^2-2x+6

orchid pine Jul 16, 2023, 3:58 AM

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Why does this apply to the right

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It doesn’t list it as applying to the right in f(x)

runic void Jul 16, 2023, 3:59 AM

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x not equal imply both directions

orchid pine Jul 16, 2023, 3:59 AM

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What

runic void Jul 16, 2023, 3:59 AM

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Think about it as a number line

runic void Jul 16, 2023, 3:59 AM

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violet sentinel

^

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notice the green dot below

orchid pine Jul 16, 2023, 4:00 AM

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Yeah

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I just don’t fully understand why just because the left side isn’t when x=1 it’s implied it’s to both

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That’s what’s in the answer description too I just don’t can’t find the reasoning for it

violet sentinel Jul 16, 2023, 4:04 AM

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https://tenor.com/view/cute-fingers-gif-20081440

Tenor

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This is how I imagine it

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follow the function on both sides. Do they end up at the same destination (even if it doesn't exist)? Then the limit exists at that point

orchid pine Jul 16, 2023, 4:06 AM

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I feel so dumb

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They would either cross?

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I’m doing this without using any form of calculator

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Is that bad

violet sentinel Jul 16, 2023, 4:12 AM

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so none of them cross

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it's just where they meet. If they meet in the same spot (aka at f(1) = 3 in your example), then the general limit exists

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here let me see if I can make some general explanations

orchid pine Jul 16, 2023, 4:14 AM

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violet sentinel so none of them cross

I worded that poorly 😖

orchid pine Jul 16, 2023, 4:16 AM

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violet sentinel it's just where they meet. If they meet in the same spot (aka at f(1) = 3 in you...

Okay yeah that part I get

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I just don’t understand why the right side doesn’t equal -5

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If that’s the only thing in the right limit

violet sentinel Jul 16, 2023, 4:17 AM

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consider this example:
The left hand limit at x = 4 is y = 5.
The right hand limit at x = 4 is y = -14.

So the left hand limit exists and the right hand limit exists. But the limit at x = 4 does not exist because the LH limit does not equal the RH limit

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In this example:
The left hand limit at x = 4 is -14
The right hand limit at x = 4 is -14.

Since LH limit = RH limit, then the general limit exists because they both approach the same point

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now here's the tricky question

orchid pine Jul 16, 2023, 4:19 AM

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Hit me

violet sentinel Jul 16, 2023, 4:21 AM

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This is similar to your problem. this is function where there's a discontinuity at x = 4. So the function is continuous except at x = 4

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But since the LH limit approaches the open point and the RH limit approaches the open point (aka where x doesn't exist in the function), then the limit at x = 4 exists and is 11

orchid pine Jul 16, 2023, 4:24 AM

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So all it is is that one point?

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OHHH

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I think I understand

violet sentinel Jul 16, 2023, 4:25 AM

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great! 😄

orchid pine Jul 16, 2023, 4:25 AM

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So because only one side can logically exist there “it takes over” ?

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Is that it? Or a bad way to think about it

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Otherwise no limit would exist in where x would approach?

violet sentinel Jul 16, 2023, 4:26 AM

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not sure what you mean by that lol

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okay let me try this

orchid pine Jul 16, 2023, 4:26 AM

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Which part

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So basically

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If there’s an area where the limit doesn’t exist on one side, but does on the other, the side where it does not exist is covered by the side that does?

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Like where doc said it’s implied?

orchid pine Jul 16, 2023, 4:28 AM

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runic void x not equal imply both directions

^ ?

violet sentinel Jul 16, 2023, 4:31 AM

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I don't think that's quite correct.

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hmmmm

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okay let's consider this analogy

orchid pine Jul 16, 2023, 4:32 AM

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I appreciate you helping me with this

violet sentinel Jul 16, 2023, 4:32 AM

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imagine that there was a crazy rollercoaster where a cart from both sides can go on the same track at the same time.

orchid pine Jul 16, 2023, 4:32 AM

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Okay

violet sentinel Jul 16, 2023, 4:33 AM

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meaning that the rollercoaster as two ends, both ends contain a cart, the both launch at the same time, and they meet in the middle

orchid pine Jul 16, 2023, 4:33 AM

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Yup

violet sentinel Jul 16, 2023, 4:33 AM

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now imagine there's a gap/hole right where they would meet

orchid pine Jul 16, 2023, 4:33 AM

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Yep yep

violet sentinel Jul 16, 2023, 4:33 AM

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at the same time, they approach the hole.

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ehhh nvm that's a bad analogy lol

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I"m losing it

orchid pine Jul 16, 2023, 4:34 AM

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Nah I got it

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Does the -5 fall in the hole while the 3 keeps going the same direction into the way where -5 was going

violet sentinel Jul 16, 2023, 4:34 AM

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I think I gotta head to bed, I'm tired lol

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this video I think can help fill in any final gaps

orchid pine Jul 16, 2023, 4:35 AM

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Does it though???

violet sentinel Jul 16, 2023, 4:35 AM

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https://www.youtube.com/watch?v=WT7oxiiFYt8&ab_channel=TheOrganicChemistryTutor

YouTube

The Organic Chemistry Tutor

3 Step Continuity Test, Discontinuity, Piecewise Functions & Limits...

This calculus video tutorial explains how to identify points of discontinuity or to prove a function is continuous / discontinuous at a point by using the 3 step continuity test. This involves evaluating piecewise functions using one sided limits. The first step is to determine if the function is defined at the given point. The second step is...

▶ Play video

orchid pine Jul 16, 2023, 4:35 AM

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If the hole is the limit does the 3 keep going into the -5 lane that came from there or

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Metaphorically speaking

violet sentinel Jul 16, 2023, 4:37 AM

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violet sentinel https://tenor.com/view/cute-fingers-gif-20081440

what I mean is this. Basically a way to look at it is look at your limit point in question: take your left pointer finger, put it on the left side of the graph. Do the same with your right pointer finger on the right side of the graph. Start moving them to the point in question. Do they meet at the same place (even though this point may not actually exits in the function)? If so, then the limit exists. This is where the RH limit = LH limit

orchid pine Jul 16, 2023, 4:37 AM

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Awesome okay gotcha

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Thank you so much mellow drama llama

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Have a fantastic night and thank you again 🙏🏻

violet sentinel Jul 16, 2023, 4:38 AM

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yeah no worries. Hopefully this was helpful! Take care

orchid pine Jul 16, 2023, 4:39 AM

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.close

obtuse pebbleBOT Jul 16, 2023, 4:39 AM

#

Channel closed

Closed by @orchid pine

Use .reopen if this was a mistake.

obtuse pebbleBOT Jul 16, 2023, 5:33 AM

#

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silver nova Jul 16, 2023, 5:38 AM

#

hi,
the blue line is f(x) = sqrt(x) +2,
the green line is g(x) = - sqrt (x) +2
the red line is y=x^2-4x+4
and the area within these graphs is 9

obtuse pebbleBOT Jul 16, 2023, 5:38 AM

#

silver nova hi, the blue line is f(x) = sqrt(x) +2, the green line is g(x) = - sqrt (x) +2 ...

silver nova Jul 16, 2023, 5:38 AM

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i was having trouble with this quetion, this was the answer

#

but i dont understand what they did

#

this was the question

obtuse pebbleBOT Jul 16, 2023, 5:54 AM

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@silver nova Has your question been resolved?

obtuse pebbleBOT Jul 16, 2023, 6:24 AM

#

@silver nova Has your question been resolved?

viral blade Jul 16, 2023, 6:58 AM

#

silver nova

They calculated the area above the line in terms of d and set it equal to half the total area

obtuse pebbleBOT Jul 16, 2023, 7:24 AM

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@silver nova Has your question been resolved?

silver nova Jul 16, 2023, 8:25 AM

#

viral blade They calculated the area above the line in terms of d and set it equal to half t...

thank you, but why is it the second expression being taken away and what does it represent, in terms of area in the graph?

viral blade Jul 16, 2023, 8:37 AM

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silver nova thank you, but why is it the second expression being taken away and what does it...

the left expression is the area under the red curve and the right expression is the area under the blue curve

#

both of them start at the point the horizontal line intersects the graph and end at 4

silver nova Jul 16, 2023, 8:46 AM

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ohh i see thank you very much

#

.close

obtuse pebbleBOT Jul 16, 2023, 8:46 AM

#

Channel closed

Closed by @silver nova

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#

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forest tide Jul 16, 2023, 8:52 AM

#

Can anyone help me with 22 pls

obtuse pebbleBOT Jul 16, 2023, 8:52 AM

#

forest tide Can anyone help me with 22 pls

#

@forest tide Has your question been resolved?

runic void Jul 16, 2023, 9:08 AM

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what are i,j,k in 3 space?

#

@forest tide

obtuse pebbleBOT Jul 16, 2023, 9:22 AM

#

Channel closed

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deft sun Jul 16, 2023, 9:34 AM

#

G is a planar graph with 5 nodes G = (V,E)
H is a non planar graph with 6 nodes that is made by adding 1 node to G with a degree of 2
prove that H is Eulerian

obtuse pebbleBOT Jul 16, 2023, 9:34 AM

#

deft sun G is a planar graph with 5 nodes G = (V,E) H is a non planar graph with 6 nodes ...

deft sun Jul 16, 2023, 9:34 AM

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I know that H contains K5

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and G has no more than 9 edges

royal basin Jul 16, 2023, 9:36 AM

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hold on

forest tide Jul 16, 2023, 9:36 AM

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runic void what are i,j,k in 3 space?

Hii

royal basin Jul 16, 2023, 9:36 AM

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how do you know H contains K5 and not K3,3

royal basin Jul 16, 2023, 9:37 AM

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forest tide Hii

you were gone for too long and your channel timed out. you will have to open a new one, sorry.

forest tide Jul 16, 2023, 9:37 AM

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obtuse pebble

.reopen

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Ohkk

royal basin Jul 16, 2023, 9:37 AM

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no, you cannot reopen a channel opened by somebody else.

forest tide Jul 16, 2023, 9:38 AM

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Ok sry

royal basin Jul 16, 2023, 9:38 AM

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deft sun G is a planar graph with 5 nodes G = (V,E) H is a non planar graph with 6 nodes ...

does "adding 1 node with degree 2 to G" mean we place a new node and connect it with 2 edges to two of the existing nodes?

deft sun Jul 16, 2023, 9:39 AM

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I think so

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sorry for the bad translation

deft sun Jul 16, 2023, 9:40 AM

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royal basin how do you know H contains K5 and not K3,3

its becuase it has only 6 nodes and one of them has a degree of 2

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which rules k3,3 out

royal basin Jul 16, 2023, 9:40 AM

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ah wait ok youre right

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alright

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so then hm

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doesnt this mean H can only look like this

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oh wait no not necessarily

deft sun Jul 16, 2023, 9:41 AM

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but this is impossible

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becuase k5 is not planar

royal basin Jul 16, 2023, 9:42 AM

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yeah but H is also nonplanar?

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ok wait hold up

#

#

we could have this

deft sun Jul 16, 2023, 9:42 AM

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But G is

royal basin Jul 16, 2023, 9:42 AM

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with 6 being the new vertex

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if we excise vertex 6 from that is the rest planar

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ok yeah it is

deft sun Jul 16, 2023, 9:43 AM

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oh I see

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we still need to prove that H is Eulerian

deft sun Jul 16, 2023, 9:45 AM

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deft sun and G has no more than 9 edges

this should help

royal basin Jul 16, 2023, 9:45 AM

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i have a feeling that theres only one thing G can be

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like how else are you gonna have a 6-vertex H with a K5 minor

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i dont think there any options for that other than the two i showed

deft sun Jul 16, 2023, 9:46 AM

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yeah right

royal basin Jul 16, 2023, 9:46 AM

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is that a "ok yeah i got you" or "no way that's true"

deft sun Jul 16, 2023, 9:47 AM

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haha

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I get it but I would still like to prove it becuase its good practice for me WanWan

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but I could do that later

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of its a problem

royal basin Jul 16, 2023, 9:47 AM

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i mean "G is determined uniquely up to iso" is proof enough imo

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or H

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H has to contain a K5 minor, and since H has 6 nodes total, this means either it has a genunie K5 subgraph or it's this

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we could "insert" vertex 6 into any of those edges but it doesnt matter bc iso

deft sun Jul 16, 2023, 9:50 AM

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it is a good proof
I think lets try to continue and I might try to find a different (equaly correct) proof later

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wait we can just count

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and see that all nodes have an even degree

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which proves it

royal basin Jul 16, 2023, 9:51 AM

#

#

or you could do this

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which proves it in an even more undisputable way

deft sun Jul 16, 2023, 9:52 AM

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oh nice

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you see like this proof is perfect but I feel like my teacher wanted us to solve it in a different way akabeko

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but either way thanks for helping me catbread

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if we have 10 or more and 11 or less edges that means we have 20 or 22 sum of degrees

we have 5x4 and that means the last one is 2 which means they are all even

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is this any good?

royal basin Jul 16, 2023, 10:01 AM

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nyeh?

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not sure

deft sun Jul 16, 2023, 10:02 AM

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eh and I also need to prove its Hamiltonian

deft sun Jul 16, 2023, 10:03 AM

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deft sun if we have 10 or more and 11 or less edges that means we have 20 or 22 sum of de...

ye this kinda suck

royal basin Jul 16, 2023, 10:03 AM

#

deft sun Jul 16, 2023, 10:04 AM

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ye

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sadcat

royal basin Jul 16, 2023, 10:07 AM

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honestly i love picture proofs like this

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which cannot be argued against

deft sun Jul 16, 2023, 10:08 AM

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true but they take a bit of creativity and are not always possible

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and I could easly use it incorrectly

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thats why the long boring proofs are better for me

#

I tried to redo my proof I hope it came out ok

royal basin Jul 16, 2023, 10:09 AM

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how could you possibly fuck up proving that a graph is hami by DRAWING a hami path on it

deft sun Jul 16, 2023, 10:10 AM

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hahahazha

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I dunno drawing is kinda difficult

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becuase H contains k5 or a (i dunno how its called in english)
it must have 5 nodes with a degree of 4 and we know the node we added isnt one of these becuase it has the degree of 2
so the degrees are 4,4,4,4,2 which proves it

#

I feel like this is better

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I will try to do hami now whatcanisay

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Ore's theorem works here right?

royal basin Jul 16, 2023, 10:18 AM

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dunno

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i don't have much patience for fancy theorems when constructive proof go brrr

deft sun Jul 16, 2023, 10:19 AM

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ok ok I have one last thing I need to find

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the number of Faces

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yay

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thanks for you help Ann
sorry for being annoying fishthonk

#

.close

obtuse pebbleBOT Jul 16, 2023, 10:28 AM

#

Channel closed

Closed by @deft sun

Use .reopen if this was a mistake.

#

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hallow olive Jul 16, 2023, 10:48 AM

#

obtuse pebbleBOT Jul 16, 2023, 10:48 AM

#

hallow olive

hallow olive Jul 16, 2023, 10:48 AM

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How do I solve this?

#

When solving I got

(x-3/(x+2)

#

And the questuon asked which is NOT a vertical asymptote

high lily Jul 16, 2023, 10:50 AM

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,rotate

warm shaleBOT Jul 16, 2023, 10:50 AM

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high lily Jul 16, 2023, 10:50 AM

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can you show your work

hallow olive Jul 16, 2023, 10:52 AM

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That's how I solved it

#

rn_image_picker_lib_temp_0823faac-a439-4621-9fdb-8788fee4fe0e.jpg

high lily Jul 16, 2023, 10:53 AM

#

you didn't factorise x^2 +2x - 3 correctly

hallow olive Jul 16, 2023, 10:54 AM

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My bad

#

Thanks

#

.close

obtuse pebbleBOT Jul 16, 2023, 10:55 AM

#

Channel closed

Closed by @hallow olive

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Remember:
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umbral nest Jul 16, 2023, 11:05 AM

#

how is root 2 / 2 equals to 1/ root 2

obtuse pebbleBOT Jul 16, 2023, 11:05 AM

#

umbral nest how is root 2 / 2 equals to 1/ root 2

gaunt tiger Jul 16, 2023, 11:06 AM

#

sqrt(2)/2 = sqrt(2)/(sqrt(2)*sqrt(2)) = 1/sqrt(2)

prisma hatch Jul 16, 2023, 11:07 AM

#

$\frac{\sqrt {2}}{2}=\frac{\sqrt {2}}{\sqrt {2}\sqrt {2}}$

royal basin Jul 16, 2023, 11:07 AM

#

$\frac{\sqrt{2}}{2} = \frac{\sqrt{2}}{\sqrt{2} \cdot \sqrt{2}} = \frac{1}{\sqrt{2}}$

warm shaleBOT Jul 16, 2023, 11:07 AM

#

Ann

umbral nest Jul 16, 2023, 11:07 AM

#

ohh makes sense!

warm shaleBOT Jul 16, 2023, 11:07 AM

#

pro_hecker_pj

umbral nest Jul 16, 2023, 11:07 AM

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thank youu

#

amazing ppl

#

.close

obtuse pebbleBOT Jul 16, 2023, 11:07 AM

#

Channel closed

Closed by @umbral nest

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#

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steady parcel Jul 16, 2023, 12:43 PM

#

can some1 help me factorise this?

obtuse pebbleBOT Jul 16, 2023, 12:43 PM

#

steady parcel can some1 help me factorise this?

steady parcel Jul 16, 2023, 12:43 PM

#

15x + y - xy - 15

balmy mortar Jul 16, 2023, 12:45 PM

#

!status

obtuse pebbleBOT Jul 16, 2023, 12:45 PM

#

What step are you on?
1. I don't know where to begin
2. I have begun but got stuck midway
3. I got an answer but I'm told it's wrong
4. I got an answer and would like my work checked
5. I have a question about someone else's worked solution
6. None of the above

high lily Jul 16, 2023, 12:54 PM

#

consider factorisation by grouping

steady parcel Jul 16, 2023, 12:57 PM

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yh when i group there r no common factors

royal basin Jul 16, 2023, 12:59 PM

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what are you grouping with what?

steady parcel Jul 16, 2023, 1:00 PM

#

15x + y - xy - 15

balmy mortar Jul 16, 2023, 1:00 PM

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obtuse pebble ``` What step are you on? 1. I don't know where to begin 2. I have begun but got...

show what exactly uve tried so we can help better

steady parcel Jul 16, 2023, 1:00 PM

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factorization

#

ooo

high lily Jul 16, 2023, 1:00 PM

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you've just reposted the question

steady parcel Jul 16, 2023, 1:01 PM

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i tried doing this (15x + y) - (xy - 15) and bringing out the common factors

steady parcel Jul 16, 2023, 1:01 PM

#

high lily you've just reposted the question

im not supposedto?

high lily Jul 16, 2023, 1:02 PM

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not by itself when being asked to show work

steady parcel Jul 16, 2023, 1:02 PM

#

o

high lily Jul 16, 2023, 1:02 PM

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as that's no indication of having done anything

balmy mortar Jul 16, 2023, 1:03 PM

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steady parcel i tried doing this (15x + y) - (xy - 15) and bringing out the common factors

right so as you say, that doesn't help. Try another grouping.

steady parcel Jul 16, 2023, 1:03 PM

#

ok

high lily Jul 16, 2023, 1:03 PM

#

also you didn't actually factor out the - properly

steady parcel Jul 16, 2023, 1:04 PM

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balmy mortar right so as you say, that doesn't help. Try another grouping.

Not working

steady parcel Jul 16, 2023, 1:04 PM

#

high lily also you didn't actually factor out the - properly

how do i do that?

balmy mortar Jul 16, 2023, 1:04 PM

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steady parcel Not working

well if u dont show us what isnt working

high lily Jul 16, 2023, 1:04 PM

#

$-p-q \redneq -(p-q)$

balmy mortar Jul 16, 2023, 1:04 PM

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no one can help

warm shaleBOT Jul 16, 2023, 1:04 PM

#

ℝamonov

balmy mortar Jul 16, 2023, 1:05 PM

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yeah lets first resolve this issue

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you need to be able to factor properly

steady parcel Jul 16, 2023, 1:05 PM

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i tried (15x - xy) - (15 + y)

high lily Jul 16, 2023, 1:06 PM

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grouping like that, the (15x+xy) can be factorised

steady parcel Jul 16, 2023, 1:06 PM

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yh but wat abt the second 1

high lily Jul 16, 2023, 1:06 PM

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well you can leave that as is for now

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what do you have after factoring the (15x+xy)

steady parcel Jul 16, 2023, 1:07 PM

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u get x(15 + y)

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ooooo

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bruh its (15x - xy)

#

.close

obtuse pebbleBOT Jul 16, 2023, 1:21 PM

#

Channel closed

Closed by @steady parcel

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autumn kiln Jul 16, 2023, 1:30 PM

#

obtuse pebbleBOT Jul 16, 2023, 1:30 PM

#

autumn kiln

pine sail Jul 16, 2023, 1:31 PM

#

!status

obtuse pebbleBOT Jul 16, 2023, 1:31 PM

#

What step are you on?
1. I don't know where to begin
2. I have begun but got stuck midway
3. I got an answer but I'm told it's wrong
4. I got an answer and would like my work checked
5. I have a question about someone else's worked solution
6. None of the above

autumn kiln Jul 16, 2023, 1:33 PM

#

pine sail !status

1

pine sail Jul 16, 2023, 1:33 PM

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Try having only a base of 3.

warm shaleBOT Jul 16, 2023, 1:35 PM

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! What the hell am I doing here?

autumn kiln Jul 16, 2023, 1:38 PM

#

pine sail Try having only a base of 3.

I got this

pine sail Jul 16, 2023, 1:39 PM

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It's wrong.

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Somewhat.

autumn kiln Jul 16, 2023, 1:39 PM

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oh I forgot the 1/

pine sail Jul 16, 2023, 1:39 PM

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Yes.

autumn kiln Jul 16, 2023, 1:39 PM

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The fraction part for the second bit

pine sail Jul 16, 2023, 1:39 PM

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Yes, now for the 1/that term

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You can multiply both sides by that term.

autumn kiln Jul 16, 2023, 1:43 PM

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novel grotto Jul 16, 2023, 1:45 PM

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ah but

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one of these solutions needs to be rejected

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whcih one and why

autumn kiln Jul 16, 2023, 1:46 PM

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novel grotto whcih one and why

Oh the -3 because then in the original equation it’ll be log base -2 which isn’t possible

autumn kiln Jul 16, 2023, 1:47 PM

#

autumn kiln

Actually it doesn’t work in this equation either bc the rhs will be log(-2)

#

thanks guys👍

#

.close

obtuse pebbleBOT Jul 16, 2023, 1:48 PM

#

Channel closed

Closed by @autumn kiln

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obtuse pebbleBOT Jul 16, 2023, 2:20 PM

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zealous hornet Jul 16, 2023, 2:42 PM

#

obtuse pebbleBOT Jul 16, 2023, 2:42 PM

#

zealous hornet

zealous hornet Jul 16, 2023, 2:42 PM

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where do i begin with this question

jagged falcon Jul 16, 2023, 2:43 PM

#

What's the surface area of a cylinder?

zealous hornet Jul 16, 2023, 2:44 PM

#

2pirh +2pir^2

timid silo Jul 16, 2023, 2:45 PM

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h = 2r

jagged falcon Jul 16, 2023, 2:45 PM

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And do you know the relation between h at r here?

royal basin Jul 16, 2023, 2:45 PM

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@timid silo was better to let op discover that himself

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now youve robbed him of that opportunity

timid silo Jul 16, 2023, 2:45 PM

#

alr

zealous hornet Jul 16, 2023, 2:46 PM

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i already knew h =2r but idk where i go from there after subtituting values

timid silo Jul 16, 2023, 2:46 PM

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zealous hornet i already knew h =2r but idk where i go from there after subtituting values

how about u show the last step where u got stuck at.

fiery cairn Jul 16, 2023, 2:46 PM

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.reopen

jagged falcon Jul 16, 2023, 2:47 PM

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Yeah, so you get 6pir^2=314whatever. Can you solve for r?

#

What? They said they don't know where to go AFTER substituting values, so they already have this equation

obtuse pebbleBOT Jul 16, 2023, 3:01 PM

#

@zealous hornet Has your question been resolved?

obtuse pebbleBOT Jul 16, 2023, 3:16 PM

#

Channel closed

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obtuse pebbleBOT Jul 16, 2023, 3:43 PM

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shell moth Jul 16, 2023, 4:05 PM

#

obtuse pebbleBOT Jul 16, 2023, 4:05 PM

#

shell moth

shell moth Jul 16, 2023, 4:06 PM

#

rn_image_picker_lib_temp_0337017a-adc0-4b79-8cf8-49a4d06f1e9b.jpg

#

Can't I use this to solve the above problem

#

Because I tried doing it and got the wrong answer

knotty crow Jul 16, 2023, 4:07 PM

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show your work if possible

shell moth Jul 16, 2023, 4:10 PM

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Wait

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As i was rewriting it to take a picture

#

I found a mistake

#

That's prolly what I messed up

#

#

@knotty crow

#

It's right thus far no?

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First time I'm ever using that formula so just making sure ig

knotty crow Jul 16, 2023, 4:14 PM

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seems good

#

now just solve for the limit of the exponent

shell moth Jul 16, 2023, 4:15 PM

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Yeh multiplied it by the conjugate and it gave me the right thing

#

Noice

#

Thanks

#

.close

obtuse pebbleBOT Jul 16, 2023, 4:15 PM

#

Channel closed

Closed by @shell moth

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timid silo Jul 16, 2023, 4:23 PM

#

Hi! I've been trying to do this question for a quiz on trigometric derivatives, and I'm not exactly sure where to start. It wants me to find an "equivalent expression" though I'm not sure how. I don't know if there is some way to factor this or if there is some rule I missed- I tried deriving it but the denominator remains as pi-pi=0. Thanks! https://i.imgur.com/xBFgp4i.png

Imgur

obtuse pebbleBOT Jul 16, 2023, 4:23 PM

#

timid silo Hi! I've been trying to do this question for a quiz on trigometric derivatives, ...

pseudo swift Jul 16, 2023, 4:24 PM

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trigometric derivatives

#

you said it yourself

knotty crow Jul 16, 2023, 4:24 PM

#

Do you mean you have used l'Hospital?

pseudo swift Jul 16, 2023, 4:24 PM

#

looks oddly like a derivative

timid silo Jul 16, 2023, 4:24 PM

#

knotty crow Do you mean you have used l'Hospital?

Haven't got there yet

polar fossil Jul 16, 2023, 4:25 PM

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,tex .sum diff trig

knotty crow Jul 16, 2023, 4:25 PM

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Definition

timid silo Jul 16, 2023, 4:25 PM

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pseudo swift *trigometric derivatives*

Like I said when I try to derive it the denominator stays as pi-pi and I don't really see a way to remove that discontinuity

warm shaleBOT Jul 16, 2023, 4:25 PM

#

Hayley

polar fossil Jul 16, 2023, 4:25 PM

#

do you know these?

fierce lagoon Jul 16, 2023, 4:25 PM

#

timid silo Hi! I've been trying to do this question for a quiz on trigometric derivatives, ...

A quiz?

timid silo Jul 16, 2023, 4:25 PM

#

polar fossil do you know these?

Nope

polar fossil Jul 16, 2023, 4:25 PM

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oh those won't help you nvm

timid silo Jul 16, 2023, 4:25 PM

#

fierce lagoon A quiz?

Yep

fierce lagoon Jul 16, 2023, 4:25 PM

#

We don't provide help with quizzes or tests

timid silo Jul 16, 2023, 4:25 PM

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:(

wise talon Jul 16, 2023, 4:26 PM

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first definition is only true if f is defined on an interval sotrue (or all of R)

polar fossil Jul 16, 2023, 4:27 PM

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all of R is an interval

jagged falcon Jul 16, 2023, 4:27 PM

#

timid silo Hi! I've been trying to do this question for a quiz on trigometric derivatives, ...

Can you see what happens if I replace x by pi+h, and h tends to 0?

timid silo Jul 16, 2023, 4:27 PM

#

jagged falcon Can you see what happens if I replace x by pi+h, and h tends to 0?

Ah I think I see where this is going now- I'll try that rq, thanks :D

#

OH okay I had to use a bit of my big boy brain- I was tryna think forward when I had to think in reverse that the equation literally just represents the derivative of sin(pi) which is just cos(pi)- I knew it was simple and I was just overthinking it lmao. Thanks everyone for your help!

#

.close

obtuse pebbleBOT Jul 16, 2023, 4:34 PM

#

Channel closed

Closed by @rare sleet

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obtuse pebbleBOT Jul 16, 2023, 5:18 PM

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final lily Jul 16, 2023, 5:21 PM

#

This is the PMF of Poisson Binomial distribution. anyone here know a way to calculate CDF of Poisson Binomial distribution without needing to calculate all the probability one by one? because this is compute expensive

obtuse pebbleBOT Jul 16, 2023, 5:21 PM

#

final lily This is the PMF of Poisson Binomial distribution. anyone here know a way to calc...

final lily Jul 16, 2023, 5:21 PM

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This is the CDF

#

I can find the mean, the STDEV, and the Variance

#

uh... are my question clear?

#

I just want a more efficient way to calculate the CDF, maybe anyone know another way to calculate the CDF?

#

there is also another formula in that Poisson Binomial Wiki, it use Fourier Transform so it's should be more efficient, but I don't even know if this is CDF or PMF, there is also many symbol that I don't understand there

polar fossil Jul 16, 2023, 5:38 PM

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final lily there is also another formula in that Poisson Binomial Wiki, it use Fourier Tran...

since it's P(K = k) that's PMF

final lily Jul 16, 2023, 5:38 PM

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ah... I see....

final lily Jul 16, 2023, 5:43 PM

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polar fossil since it's P(K = k) that's PMF

Hayley do you understand this? Like do you know which part of this is the CDF?

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anyone? OhNo_cat

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<@&286206848099549185> help please pandaWow

bold carbon Jul 16, 2023, 5:55 PM

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bro what is that lmao

final lily Jul 16, 2023, 5:55 PM

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it's Poisson Binomial distribution

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should I post the wiki link here?

bold carbon Jul 16, 2023, 5:55 PM

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i see

#

im not sure i can help u lmao

#

that looks really tough

polar fossil Jul 16, 2023, 5:56 PM

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final lily Hayley do you understand this? Like do you know which part of this is the CDF?

not in any meaningful way sadCat

final lily Jul 16, 2023, 5:56 PM

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bold carbon that looks really tough

yeah I'm going crazi, been searching a way to understand this for month sadcat

bold carbon Jul 16, 2023, 5:56 PM

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i see

#

gl

final lily Jul 16, 2023, 5:56 PM

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polar fossil not in any meaningful way <:sadCat:707696328213397566>

I see... thanks at least you tried

bold carbon Jul 16, 2023, 5:58 PM

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what class is this

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i see its more or less a stats topic

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since its a type of probability distribution

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lmao i feel so dumb

final lily Jul 16, 2023, 6:01 PM

#

bold carbon i see its more or less a stats topic

it's not on any class I do this myself

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I need this, not because of studying...

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which is why I'm still searching away even after month sadcat

bold carbon Jul 16, 2023, 6:02 PM

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i see

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is this ck12.org

final lily Jul 16, 2023, 6:04 PM

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I don't know I found this on random place on internet, I don't even remember where

bold carbon Jul 16, 2023, 6:05 PM

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i see

#

alr bye

final lily Jul 16, 2023, 6:05 PM

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okay sad

obtuse pebbleBOT Jul 16, 2023, 6:20 PM

#

@final lily Has your question been resolved?

obtuse pebbleBOT Jul 16, 2023, 6:53 PM

#

@final lily Has your question been resolved?

obtuse pebbleBOT Jul 16, 2023, 7:23 PM

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timid silo Jul 16, 2023, 7:53 PM

#

is the norm of this partition -1.1 or +1.1?

obtuse pebbleBOT Jul 16, 2023, 7:53 PM

#

timid silo is the norm of this partition -1.1 or +1.1?

kind hawk Jul 16, 2023, 7:55 PM

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not sure what the norm of a partition is, but usually norms are non-negative (just from the word alone)

#

I guess largest length of subinterval?

timid silo Jul 16, 2023, 7:55 PM

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yes

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I wasn't sure how it is noted

kind hawk Jul 16, 2023, 7:57 PM

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then +1.1

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lengths are also non-negative

obtuse pebbleBOT Jul 16, 2023, 8:10 PM

#

@timid silo Has your question been resolved?

obtuse pebbleBOT Jul 16, 2023, 8:25 PM

#

Channel closed

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obtuse pebbleBOT Jul 16, 2023, 10:05 PM

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long hedge Jul 16, 2023, 10:06 PM

#

how did ln 2 get on top

obtuse pebbleBOT Jul 16, 2023, 10:06 PM

#

long hedge how did ln 2 get on top

errant lark Jul 16, 2023, 10:08 PM

#

long hedge how did ln 2 get on top

You mean... in the last line ?

long hedge Jul 16, 2023, 10:08 PM

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yes

errant lark Jul 16, 2023, 10:09 PM

#

They have just divided both the sides with 12*ln(1+0.5/12).

long hedge Jul 16, 2023, 10:09 PM

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errant lark They have just divided both the sides with 12*ln(1+0.5/12).

hmmCat

errant lark Jul 16, 2023, 10:09 PM

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so that they could separate variable t to the one side.

errant lark Jul 16, 2023, 10:10 PM

#

long hedge <:hmmCat:831508801646755850>

It's a fairly simple thing. You separate out the variable you need the value for on one side.

obtuse pebbleBOT Jul 16, 2023, 10:24 PM

#

@long hedge Has your question been resolved?

obtuse pebbleBOT Jul 16, 2023, 10:39 PM

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Channel closed

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woeful folio Jul 16, 2023, 10:43 PM

#

obtuse pebbleBOT Jul 16, 2023, 10:43 PM

#

woeful folio

silent thorn Jul 16, 2023, 10:44 PM

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woeful folio

use points

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thats the easiest way

#

or you can get the maxima and minima of the function and graph it like that

woeful folio Jul 16, 2023, 10:45 PM

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So like when x =3 then I put three into the equation to get y

silent thorn Jul 16, 2023, 10:45 PM

#

yes

woeful folio Jul 16, 2023, 10:45 PM

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But it isn’t labelled

silent thorn Jul 16, 2023, 10:45 PM

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thats fine, it doesnt have to be perfect

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just draw a rough picture

woeful folio Jul 16, 2023, 10:46 PM

#

Complete the square to get points of rotation?

silent thorn Jul 16, 2023, 10:47 PM

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woeful folio Complete the square to get points of rotation?

no, thats only in second degree functions

#

you can use the cubic formula, but its super long and messy

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as i said, just use points

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it saves you the hassle

woeful folio Jul 16, 2023, 10:48 PM

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Wait bro I got a solution

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Let me find y

#

So let x=0

silent thorn Jul 16, 2023, 10:48 PM

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y=1

woeful folio Jul 16, 2023, 10:49 PM

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So it will intersect y axis at 1

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Can’t I complete the square and get rotation points?

silent thorn Jul 16, 2023, 10:50 PM

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woeful folio Can’t I complete the square and get rotation points?

what dpo you mean by points of rotation?

#

you mean like critical points?

woeful folio Jul 16, 2023, 10:50 PM

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Where it rotates bro

silent thorn Jul 16, 2023, 10:50 PM

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those are called critical points, you gotta differentiate the function