#help-42 | Mathematics | Page 114

granite spade Dec 3, 2024, 3:09 AM

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@rustic osprey wait sorry one last question

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this is the interval

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pi/8 and 7pi/8

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so n wouldnt work here in this scenario

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correct?

rustic osprey Dec 3, 2024, 3:09 AM

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yeah I know

granite spade Dec 3, 2024, 3:10 AM

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just wanted to clarify

rustic osprey Dec 3, 2024, 3:10 AM

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I was trying to get you to arrive at the general solution and then find all n s.t. it's in the interval

granite spade Dec 3, 2024, 3:10 AM

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okay

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so that would mean

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besides pi/2

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umm

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wait is that it

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is it just pi/2

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no other values?

rustic osprey Dec 3, 2024, 3:11 AM

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yeah

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only $n=1$ makes $\frac{n \pi}{2}$ lie in $\left[\frac{\pi}{8}, \frac{7\pi}{8} \right]$

potent lotusBOT Dec 3, 2024, 3:11 AM

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Civil Service Pigeon

granite spade Dec 3, 2024, 3:11 AM

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thank you so much

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i will definitely ping you in the future youre the best tutor i had

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LOL

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have a good night!

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.close

calm coralBOT Dec 3, 2024, 3:12 AM

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Channel closed

Closed by @granite spade

Use .reopen if this was a mistake.

rustic osprey Dec 3, 2024, 3:12 AM

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granite spade i will definitely ping you in the future youre the best tutor i had

oh uh

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about that

granite spade Dec 3, 2024, 3:12 AM

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oh

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LMFAOAOAOIH

rustic osprey Dec 3, 2024, 3:12 AM

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most helpers don't like to be pinged individually, myself included

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!noping

calm coralBOT Dec 3, 2024, 3:12 AM

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Please do not ping individual helpers unprompted.

granite spade Dec 3, 2024, 3:12 AM

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oh oops

rustic osprey Dec 3, 2024, 3:12 AM

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we had to make this lol

granite spade Dec 3, 2024, 3:12 AM

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gotcha

rustic osprey Dec 3, 2024, 3:12 AM

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rustic osprey most helpers don't like to be pinged individually, myself included

on this note, don't send ppl message requests out of the blue either

granite spade Dec 3, 2024, 3:13 AM

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i wont dont worry

rustic osprey Dec 3, 2024, 3:13 AM

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a lot of us just auto reject them

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myself included lol

rustic osprey Dec 3, 2024, 3:13 AM

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granite spade i wont dont worry

catthumbsup

calm coralBOT Dec 3, 2024, 3:27 AM

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tall moon Dec 3, 2024, 3:56 AM

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let $xy=z^2$ prove that there is always $p,q,r$ where $\gcd(q,r)=1$ and
$$x=pq^2$$
$$y=pr^2$$
$$z=pqr$$

calm coralBOT Dec 3, 2024, 3:56 AM

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tall moon let $xy=z^2$ prove that there is always $p,q,r$ where $\gcd(q,r)=1$ and $$x=pq^...

potent lotusBOT Dec 3, 2024, 3:56 AM

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Skissue ping4response

tall moon Dec 3, 2024, 3:56 AM

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this question is wierd im not sure what path i go for

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note p,q,r,x,y,z are natural numbers

calm coralBOT Dec 3, 2024, 4:15 AM

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@tall moon Has your question been resolved?

wanton wave Dec 3, 2024, 4:40 AM

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Okay maybe I'm being dumb but I don't think this is true. Isn't this a counterexample?

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(x,y,z) = (8,18,12)

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8*18 = 12^2

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If x = pq^2 = 8, and gcd(p,q)=1, then the only possibility is p=8, q=1.

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But if p=8 and y = pr^2 = 18, then r is not a natural number.

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@tall moon

tall moon Dec 3, 2024, 4:42 AM

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p=2 q=2 r=3?

wanton wave Dec 3, 2024, 4:42 AM

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but gcd(p,q)=1

tall moon Dec 3, 2024, 4:42 AM

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wait

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wait

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wait

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oh its gcd(q,r)=1

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whoops

wanton wave Dec 3, 2024, 4:43 AM

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oh, that seems more plausible lol

tall moon Dec 3, 2024, 4:43 AM

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let $xy=z^2$ prove that there is always $p,q,r$ where $\gcd(q,r)=1$ and
$$x=pq^2$$
$$y=pr^2$$
$$z=pqr$$

potent lotusBOT Dec 3, 2024, 4:43 AM

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Skissue ping4response

tall moon Dec 3, 2024, 4:43 AM

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streak of me fucking up the question

calm coralBOT Dec 3, 2024, 5:13 AM

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@tall moon Has your question been resolved?

calm coralBOT Dec 3, 2024, 6:13 AM

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@tall moon Has your question been resolved?

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mossy wigeon Dec 3, 2024, 7:43 AM

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v_c has higher speed right?

calm coralBOT Dec 3, 2024, 7:43 AM

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mossy wigeon v_c has higher speed right?

graceful dust Dec 3, 2024, 7:43 AM

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hi

mossy wigeon Dec 3, 2024, 7:43 AM

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hiii

dark fox Dec 3, 2024, 7:51 AM

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hiiiii

limpid pilot Dec 3, 2024, 7:52 AM

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mossy wigeon v_c has higher speed right?

yes

mossy wigeon Dec 3, 2024, 7:52 AM

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limpid pilot yes

thing is

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idk

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cuz

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im getting a 50% response ofr both

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someone said

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since its elastic they share KE

dark fox Dec 3, 2024, 7:53 AM

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It is a yes

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Conservation of momentum

swift laurel Dec 3, 2024, 7:56 AM

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we're not given whether it's elastic, but all we need for the problem is conservation of momentum anyway

mossy wigeon Dec 3, 2024, 7:57 AM

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swift laurel we're not given whether it's elastic, but all we need for the problem is conserv...

so v_c isa faster?

swift laurel Dec 3, 2024, 7:58 AM

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it must be

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you can write v_A and v_C in terms of the initial speed of the ball B, the masses, and the final speed of the ball B to demonstrate that

mossy wigeon Dec 3, 2024, 8:02 AM

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swift laurel you can write v_A and v_C in terms of the initial speed of the ball B, the masse...

okay my logic was that if i do a system of like conservation pf=pi

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since the b ball goes back

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the velocity of the ball becomes negative for final therefore the box must have higher velocity

swift laurel Dec 3, 2024, 8:03 AM

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yes. you can express that mathematically by expressing the initial and final momentum of the system in terms of the variables mentioned above

mossy wigeon Dec 3, 2024, 8:04 AM

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ah okay

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tyty

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.close

calm coralBOT Dec 3, 2024, 8:04 AM

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calm coralBOT Dec 3, 2024, 8:19 AM

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fleet raptor Dec 3, 2024, 8:28 AM

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why does it give 1 even though i specified the bounds

calm coralBOT Dec 3, 2024, 8:28 AM

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fleet raptor why does it give 1 even though i specified the bounds

fleet raptor Dec 3, 2024, 8:28 AM

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4-4 = 0 so that lies outside of 1-3 or -1--3

limpid pilot Dec 3, 2024, 8:29 AM

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this is math server

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ask here: https://discord.gg/python

fleet raptor Dec 3, 2024, 8:30 AM

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ty

limpid pilot Dec 3, 2024, 8:30 AM

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.close

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calm coralBOT Dec 3, 2024, 1:35 PM

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amber wedge Dec 3, 2024, 1:52 PM

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How do i determine which is bigger wothout the calculator?

calm coralBOT Dec 3, 2024, 1:52 PM

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amber wedge How do i determine which is bigger wothout the calculator?

amber wedge Dec 3, 2024, 1:52 PM

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e^pi and pi^e

onyx plinth Dec 3, 2024, 1:53 PM

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Generally the one with the larger exponent is greater

remote mural Dec 3, 2024, 1:53 PM

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No

onyx plinth Dec 3, 2024, 1:53 PM

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remote mural No

Yes?

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I'm sure e^pi is greater

remote mural Dec 3, 2024, 1:54 PM

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The maxima of the function x^(1/x) occurs at x = e.

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So e^(1/e) > π^(1/π)

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Hint: After this, you may just do some algebraic manipulation to this inequality.

mortal orbit Dec 3, 2024, 2:04 PM

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onyx plinth Generally the one with the larger exponent is greater

so 2^3 bigger than 3^2

onyx plinth Dec 3, 2024, 2:07 PM

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My bad ,not always true i guess

calm coralBOT Dec 3, 2024, 2:12 PM

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@amber wedge Has your question been resolved?

calm coralBOT Dec 3, 2024, 2:28 PM

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remote mural Dec 3, 2024, 3:41 PM

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calm coralBOT Dec 3, 2024, 3:41 PM

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remote mural

remote mural Dec 3, 2024, 3:42 PM

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Prove that:
[UA1V] + [A1ZW] = [UA1Z] + [WA1V] = 1/2 [UVWZ]

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Given that UVWZ is a rectangle.

jolly pilot Dec 3, 2024, 3:47 PM

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area of triangle = 1/2 * base * height?

remote mural Dec 3, 2024, 3:48 PM

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Yes

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jolly pilot Dec 3, 2024, 3:48 PM

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remote mural Yes

I mean, use that here...

remote mural Dec 3, 2024, 3:49 PM

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ok

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i will tell the progress

calm coralBOT Dec 3, 2024, 4:04 PM

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@remote mural Has your question been resolved?

remote mural Dec 3, 2024, 4:04 PM

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Z26W26 = B27A27
For triangle V26P26Q26, area = 1/2 * V26W26 * P26Q26
For triangle S26V26R26, area = Z26V26 * 1/2 * S26R26
Right? And now the sum = 1/2 (Z26W26)(P26Q26 + S26R26) = 1/2 (B27A27) (S26P26 + R26Q26) right?

remote mural Dec 3, 2024, 4:34 PM

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.close

calm coralBOT Dec 3, 2024, 4:35 PM

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Channel closed

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remote mural Dec 3, 2024, 4:35 PM

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Ok bro

calm coralBOT Dec 3, 2024, 4:35 PM

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vagrant oak Dec 3, 2024, 5:26 PM

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How do I calculate how many arrangements of n objects are there, if k of them need not to be used

calm coralBOT Dec 3, 2024, 5:26 PM

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vagrant oak How do I calculate how many arrangements of n objects are there, if k of them ne...

vagrant oak Dec 3, 2024, 5:27 PM

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Take e.g. a, b, c, d, e, f and say e and f dont need to be used

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so valid arrangements are e.g.:
abcd
abedcf
efabcd
eabcd
bfadc

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I need something efficient

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currently the only way I have is summing up some stuff

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nvm, i optimized something else instead so i might not need this

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yep

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I was calculating all binomial coefficients (n choose i) with 0 < n < some bound and 0 < i < another bound instead of just using pascals triangle. Silly me

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.close

calm coralBOT Dec 3, 2024, 5:38 PM

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Channel closed

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exotic cosmos Dec 3, 2024, 5:45 PM

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x * sqrt(25 - x^2)

calm coralBOT Dec 3, 2024, 5:45 PM

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exotic cosmos x * sqrt(25 - x^2)

exotic cosmos Dec 3, 2024, 5:45 PM

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to maximize this geometrically we are maximizing the inscribed rectangle in a circle?

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is that true?

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well idk in my mind it kinda makes sense but can someone explain regardless

manic hawk Dec 3, 2024, 5:46 PM

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Yeah, that's right. You can draw the picture to see it

exotic cosmos Dec 3, 2024, 5:46 PM

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how?

manic hawk Dec 3, 2024, 5:46 PM

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Draw a circle

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Draw a rectangle

exotic cosmos Dec 3, 2024, 5:47 PM

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well that part i get

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i mean sqrt(25 - x^2) is a circle with radius 5

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well only the positive branch

manic hawk Dec 3, 2024, 5:47 PM

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Maximizing a function and twice the function is the same anyway

exotic cosmos Dec 3, 2024, 5:47 PM

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and where does the rectangle come into play here

manic hawk Dec 3, 2024, 5:48 PM

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I don't understand your question

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Are you asking how to maximise it?

exotic cosmos Dec 3, 2024, 5:49 PM

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no i'm asking how maximizing x * sqrt(25 - x^2) translates to maximizing the rea of a rectangle in a circle

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what's the reasoning for that

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i kinda know that it is the case

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but i can't justify it

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or explain it

manic hawk Dec 3, 2024, 5:50 PM

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Draw the circle. Draw the rectangle. Label the lengths of the rectangle

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If you write the expression for the area, it's the same function

exotic cosmos Dec 3, 2024, 5:53 PM

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manic hawk Draw the circle. Draw the rectangle. Label the lengths of the rectangle

the diagonal is 10?

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let x be the width and y be the length then x^2 + y^2 = 25

manic hawk Dec 3, 2024, 5:54 PM

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Not 100

exotic cosmos Dec 3, 2024, 5:54 PM

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i mean 25

manic hawk Dec 3, 2024, 5:54 PM

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exotic cosmos i mean sqrt(25 - x^2) is a circle with radius 5

This

exotic cosmos Dec 3, 2024, 5:54 PM

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wait what

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the diameter is 10 though?

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so we have a right triangle with hypotenuse of 10

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thinkies

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no?

manic hawk Dec 3, 2024, 5:55 PM

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Okay, there are several ways to draw this.

exotic cosmos Dec 3, 2024, 5:56 PM

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manic hawk Dec 3, 2024, 5:56 PM

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Right triangle with hypotenuse of 10 is fine

exotic cosmos Dec 3, 2024, 5:56 PM

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yeah so what i wrote before was okay?

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x^2 + y^2 = 100

manic hawk Dec 3, 2024, 5:57 PM

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No, because that has diameter 20

exotic cosmos Dec 3, 2024, 5:57 PM

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i'm confused 😭

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am i being dumb

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10^2 = 100

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wait

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okay i'm dumb

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lol

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no

manic hawk Dec 3, 2024, 5:57 PM

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Radius and diameter are different

exotic cosmos Dec 3, 2024, 5:57 PM

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i'm talking about the triangle though

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😭

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just the triangle alone

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it's just pythag

manic hawk Dec 3, 2024, 5:58 PM

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Draw it on coordinate axes

exotic cosmos Dec 3, 2024, 5:58 PM

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manic hawk Dec 3, 2024, 5:58 PM

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That's not your x and y

exotic cosmos Dec 3, 2024, 5:59 PM

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uhhh i just gave it some labels

manic hawk Dec 3, 2024, 5:59 PM

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exotic cosmos let x be the width and y be the length then x^2 + y^2 = 25

Draw this equation, but not those labels

exotic cosmos Dec 3, 2024, 5:59 PM

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like coordinate geometry free

manic hawk Dec 3, 2024, 6:01 PM

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exotic cosmos

Until this picture, I had no idea why you were talking about hypotenuses or triangles. You really don't want either in this question.

exotic cosmos Dec 3, 2024, 6:02 PM

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yeah i was confused too

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i think u were talking about a circle

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and i was talking about pythag lol

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manic hawk Dec 3, 2024, 6:04 PM

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Now you can find the area of that

exotic cosmos Dec 3, 2024, 6:05 PM

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uhhh i don't know what i'm going for

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the diagonal is again of length 10

manic hawk Dec 3, 2024, 6:05 PM

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Don't use the diagonal

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Label the positive x-intercept x

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Then find the y-intercept in terms of x

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Then find base and height

exotic cosmos Dec 3, 2024, 6:08 PM

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okay but then i use half the diagonal

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hmm

manic hawk Dec 3, 2024, 6:08 PM

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exotic cosmos x^2 + y^2 = 100

Okay, after further review, this will work, but it takes some algebraic cleverness to see why.

manic hawk Dec 3, 2024, 6:08 PM

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exotic cosmos okay but then i use half the diagonal

Yeah, or you can just use the equation of the circle

manic hawk Dec 3, 2024, 6:08 PM

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exotic cosmos i mean sqrt(25 - x^2) is a circle with radius 5

This here

exotic cosmos Dec 3, 2024, 6:08 PM

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yeah that's the height

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the base is x

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but we have 8 of those triangles

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thinkies

manic hawk Dec 3, 2024, 6:09 PM

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Stop using triangles

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You have 4 of those rectangles

exotic cosmos Dec 3, 2024, 6:09 PM

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sure if radius is one diagonal of a rectangle

manic hawk Dec 3, 2024, 6:09 PM

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Maximizing a function is the same as maximizing four times that function

exotic cosmos Dec 3, 2024, 6:09 PM

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then there's 4 such rectangles

exotic cosmos Dec 3, 2024, 6:13 PM

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manic hawk Maximizing a function is the same as maximizing four times that function

sure makes sense

exotic cosmos Dec 3, 2024, 6:13 PM

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manic hawk Okay, after further review, this will work, but it takes some algebraic cleverne...

how would i do it via this

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h^2 + b^2 = 100

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100 - b^2 = h^2 -> h = sqrt(100 - b^2)

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area of rectangle is b * sqrt(100 - b^2)

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hmm i need a scaling factor and maybe some factorization

manic hawk Dec 3, 2024, 6:14 PM

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Replace b=2k

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Yeah, scaling factor

exotic cosmos Dec 3, 2024, 6:16 PM

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manic hawk Replace b=2k

okay

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yeah that should work

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2k * sqrt(100 - 4k^2)

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2k * sqrt(4) * sqrt(25 - k^2) = 4k * sqrt(25 - k^2)

exotic cosmos Dec 3, 2024, 6:18 PM

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manic hawk Okay, after further review, this will work, but it takes some algebraic cleverne...

alright thanks for the help!

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kannawave

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.close

calm coralBOT Dec 3, 2024, 6:18 PM

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Channel closed

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calm coralBOT Dec 3, 2024, 7:33 PM

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red locust Dec 3, 2024, 7:39 PM

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i just need help here

calm coralBOT Dec 3, 2024, 7:39 PM

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red locust i just need help here

red locust Dec 3, 2024, 7:40 PM

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would my c stay as square root of 217

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or do i make it 14.73

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i know it cant be simplified further

manic sandal Dec 3, 2024, 7:41 PM

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both are correct, i was always taught to keep a square root but it is your choice

red locust Dec 3, 2024, 7:41 PM

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would i do it like this: (7+√217, -10) or (7+14.73, -10)

red locust Dec 3, 2024, 7:41 PM

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manic sandal both are correct, i was always taught to keep a square root but it is your choic...

oh okay

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so when i calculate it

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its same answers right

manic sandal Dec 3, 2024, 7:41 PM

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yep

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well slightly different because of rounding

red locust Dec 3, 2024, 7:42 PM

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okay was just confused

manic sandal Dec 3, 2024, 7:42 PM

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but very very similar

red locust Dec 3, 2024, 7:42 PM

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this is what i got with 14.73

red locust Dec 3, 2024, 7:42 PM

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manic sandal but very very similar

okay thank you

solid pollen Dec 3, 2024, 7:42 PM

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keep it as sqrt, as further calculating after approximating won't give you the correct result (if you have to use the 'c' after calculating it). Supposing it's a theoretical math class.

red locust Dec 3, 2024, 7:43 PM

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thank you so mch

calm coralBOT Dec 3, 2024, 7:58 PM

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@red locust Has your question been resolved?

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noble crane Dec 3, 2024, 8:08 PM

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calm coralBOT Dec 3, 2024, 8:08 PM

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noble crane

mortal orbit Dec 3, 2024, 8:08 PM

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noble crane

!status

calm coralBOT Dec 3, 2024, 8:08 PM

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noble crane

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 was told that it's wrong.
4. I got an answer and would like my work checked.
5. I have a question about someone else's work/solution.
6. I have completed the problem and don't need help anymore. Thank you.
7. None of the above

noble crane Dec 3, 2024, 8:08 PM

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my fault

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im stuck on why its not zero

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4.) I guess

mortal orbit Dec 3, 2024, 8:12 PM

#

wdym it's not 0

#

you did the ratio test

#

you found that 1/R = 0

noble crane Dec 3, 2024, 8:13 PM

#

it is zero right?

mortal orbit Dec 3, 2024, 8:13 PM

#

the multiplicative inverse of the radius is 0

noble crane Dec 3, 2024, 8:13 PM

#

the computer homework program is marking 0 wrong

mortal orbit Dec 3, 2024, 8:13 PM

#

because they want the radius itself

#

not 1/radius

noble crane Dec 3, 2024, 8:14 PM

#

wouldn't still be zero

#

0/2

mortal orbit Dec 3, 2024, 8:14 PM

#

huh

#

1/radius = 0

#

radius = infinity

noble crane Dec 3, 2024, 8:14 PM

#

how is it infinity

mortal orbit Dec 3, 2024, 8:15 PM

#

1/infinity = 0

#

"1/0" = infinity

noble crane Dec 3, 2024, 8:15 PM

#

oh ok

#

i see thanks for clearing it up for me

mortal orbit Dec 3, 2024, 8:15 PM

#

Just to help you for next times

#

instead of computing $\frac 1R = \lim_{n\to \infty} \left |\frac{a_{n+1}}{a_n} \right |$

potent lotusBOT Dec 3, 2024, 8:16 PM

#

rafilou is not not born in 2003

mortal orbit Dec 3, 2024, 8:16 PM

#

directly compute $R = \lim_{n\to \infty} \left |\frac{a_{n}}{a_{n+1}} \right |$

potent lotusBOT Dec 3, 2024, 8:16 PM

#

rafilou is not not born in 2003

mortal orbit Dec 3, 2024, 8:17 PM

#

if you wanna use the ratio test

mortal orbit Dec 3, 2024, 8:17 PM

#

potent lotus **rafilou is not not born in 2003**

this is easier

mortal orbit Dec 3, 2024, 8:17 PM

#

potent lotus **rafilou is not not born in 2003**

then you won't forget to input 1/(what you got) with this method

noble crane Dec 3, 2024, 8:17 PM

#

how is 1/0 infinity

#

if were not taking the limit of r

#

its infinity when you take the limit of 1/infinity

mortal orbit Dec 3, 2024, 8:18 PM

#

?

noble crane Dec 3, 2024, 8:18 PM

#

though R is just a constant

#

yea because you set it equall to lim n ---> oo etc..

mortal orbit Dec 3, 2024, 8:19 PM

#

if you don't like 1/0

#

think of 0 as limit of 1/n as n-> infinity

#

then 1/(1/n) = n

#

so when n-> infinity

#

goes to infinity

noble crane Dec 3, 2024, 8:19 PM

#

ohhh ok ok I think I get it

#

I see thanks

#

.close

calm coralBOT Dec 3, 2024, 8:20 PM

#

Channel closed

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calm coralBOT Dec 3, 2024, 8:35 PM

#

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wintry echo Dec 3, 2024, 9:21 PM

#

$\lim_{x\to+\infty} \frac{x+1}{\sqrt{x^2+x}-\sqrt{x^2+1}}\cdot\ln(\frac{x+2}{x+3})$

calm coralBOT Dec 3, 2024, 9:21 PM

#

wintry echo $\lim_{x\to+\infty} \frac{x+1}{\sqrt{x^2+x}-\sqrt{x^2+1}}\cdot\ln(\frac{x+2}{x+3...

potent smelt Dec 3, 2024, 9:22 PM

#

you don't need a \ before your +

#

$\lim_{x\to+\infty} \frac{x+1}{\sqrt{x^2+x}-\sqrt{x^2+1}}\cdot\ln(\frac{x+2}{x+3})$

potent lotusBOT Dec 3, 2024, 9:23 PM

#

OmnipotentEntity

#

Wobble

wintry echo Dec 3, 2024, 9:24 PM

#

Can someone help me

atomic quarry Dec 3, 2024, 9:25 PM

#

potent smelt Dec 3, 2024, 9:25 PM

#

Have you given this a crack yet?

wintry echo Dec 3, 2024, 9:25 PM

#

For me it's +∞

#

I just plug infinity in

atomic quarry Dec 3, 2024, 9:26 PM

#

wintry echo Dec 3, 2024, 9:26 PM

#

What

fleet verge Dec 3, 2024, 9:27 PM

#

kirbyFF

wintry echo Dec 3, 2024, 9:27 PM

#

What f mean

fleet verge Dec 3, 2024, 9:27 PM

#

You have to show your work. “For you it is inf” but in reality is not

wintry echo Dec 3, 2024, 9:28 PM

#

,w lim_{x\to+\infty} \frac{x+1}{\sqrt{x^2+x}-\sqrt{x^2+1}}\cdot\ln(\frac{x+2}{x+3})

#

What

#

It's very heavy

potent lotusBOT Dec 3, 2024, 9:29 PM

#

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fleet verge Dec 3, 2024, 9:29 PM

#

monkey

wintry echo Dec 3, 2024, 9:29 PM

#

Heavy blow

#

Mmm

#

Lemme think

#

But if x goes to infinity how does it come out as a negative number

hollow totem Dec 3, 2024, 9:31 PM

#

the stuff in the log is negative

wintry echo Dec 3, 2024, 9:31 PM

#

If the functions are positive

hollow totem Dec 3, 2024, 9:31 PM

#

They aren't

wintry echo Dec 3, 2024, 9:32 PM

#

The logarithm is defined for x>0 so it is positive

#

Like √x

#

It has no negative values

hollow totem Dec 3, 2024, 9:33 PM

#

,w log(1/2)

potent lotusBOT Dec 3, 2024, 9:33 PM

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wintry echo Dec 3, 2024, 9:33 PM

#

Oh

#

But here we are talking about limits

#

The limit of the log is in positive numbers

hollow totem Dec 3, 2024, 9:34 PM

#

No it isn't

#

It's 0

wintry echo Dec 3, 2024, 9:35 PM

#

Wdym

#

,w graph ln(x)

potent lotusBOT Dec 3, 2024, 9:36 PM

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hollow totem Dec 3, 2024, 9:36 PM

#

The limit of log(x) as x approaches infinity is infinity

#

That's not what you have though

wintry echo Dec 3, 2024, 9:37 PM

#

Why

hollow totem Dec 3, 2024, 9:38 PM

#

Because... it's... not there?

#

Nowhere in your problem is there a log(x)

wintry echo Dec 3, 2024, 9:38 PM

#

,w graph ln((x+2)/(x+3))

potent lotusBOT Dec 3, 2024, 9:39 PM

#

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fleet verge Dec 3, 2024, 9:39 PM

#

Replace

#

(x+2) in the numerator

#

With (x+3 -1)

#

And split in 2 fractions

#

(x+3)/(x+3) -1/(x+3)

wintry echo Dec 3, 2024, 9:40 PM

#

Mmm

#

Can you be more clear?

#

Oh no its clear

fleet verge Dec 3, 2024, 9:42 PM

#

You have 1-1/(x+3)

wintry echo Dec 3, 2024, 9:42 PM

#

$\ln(1-\frac{1}{x+3})$

potent lotusBOT Dec 3, 2024, 9:42 PM

#

Wobble

fleet verge Dec 3, 2024, 9:42 PM

#

This is between 0 and 1

wintry echo Dec 3, 2024, 9:42 PM

#

Its 0

fleet verge Dec 3, 2024, 9:42 PM

#

So it will be negative

#

Close to 0

#

But negative

wintry echo Dec 3, 2024, 9:43 PM

#

0^-

fleet verge Dec 3, 2024, 9:43 PM

#

That is why the limit is negative

wintry echo Dec 3, 2024, 9:43 PM

#

Mmm

#

So it wouldn't be 0?

#

$0^{-}$

potent lotusBOT Dec 3, 2024, 9:44 PM

#

Wobble

hollow totem Dec 3, 2024, 9:44 PM

#

What's "it"

wintry echo Dec 3, 2024, 9:45 PM

#

Its like -0,00000000000000001

#

This should be the notation

hollow totem Dec 3, 2024, 9:45 PM

#

thonk

wintry echo Dec 3, 2024, 9:46 PM

#

potent lotus **Wobble**

This

atomic quarry Dec 3, 2024, 9:46 PM

#

wintry echo Dec 3, 2024, 9:46 PM

#

Its the notation standard

#

I think

hollow totem Dec 3, 2024, 9:46 PM

#

Not for the output of a limit

#

But sure why not

wintry echo Dec 3, 2024, 9:47 PM

#

hollow totem Not for the output of a limit

Output , bro we are not on a PC

atomic quarry Dec 3, 2024, 9:48 PM

#

Bro rn

#

wintry echo Dec 3, 2024, 9:48 PM

#

But the limit is an inexact evaluation

#

Isn't that a swinging thing?

hollow totem Dec 3, 2024, 9:49 PM

#

no and no

wintry echo Dec 3, 2024, 9:49 PM

#

Why?

hollow totem Dec 3, 2024, 9:49 PM

#

Because those words don't even make sense

wintry echo Dec 3, 2024, 9:51 PM

#

Mmm

#

Anyway

#

I think I'm doing it all wrong

#

😓

#

With 0^- it will never come to -2

hollow totem Dec 3, 2024, 9:52 PM

#

what's the limit of -1/x

wintry echo Dec 3, 2024, 9:53 PM

#

0

#

By hopital

hollow totem Dec 3, 2024, 9:53 PM

#

what's the limit of 2x * -1/x

#

No not by lhopital

#

You can't apply lhopitals to that

wintry echo Dec 3, 2024, 9:53 PM

#

Oh okay

wintry echo Dec 3, 2024, 9:54 PM

#

hollow totem what's the limit of 2x * -1/x

-2

hollow totem Dec 3, 2024, 9:54 PM

#

even though one of the parts has limit 0

#

The limit is still -2

atomic quarry Dec 3, 2024, 9:54 PM

#

wintry echo -2

wintry echo Dec 3, 2024, 9:55 PM

#

But I have a fixed 0

hollow totem Dec 3, 2024, 9:55 PM

#

What

#

What's a "fixed" 0

wintry echo Dec 3, 2024, 9:55 PM

#

Which I have 0

#

Now anything I do will always return 0

wintry echo Dec 3, 2024, 9:56 PM

#

hollow totem But sure why not

.

hollow totem Dec 3, 2024, 9:56 PM

#

What's a fixed zero

wintry echo Dec 3, 2024, 9:56 PM

#

Oh no

#

This is not an exact 0, its like $0-\epsilon$

potent lotusBOT Dec 3, 2024, 9:57 PM

#

Wobble

hollow totem Dec 3, 2024, 9:57 PM

#

The limit is 0

#

The function itself isn't

wintry echo Dec 3, 2024, 9:57 PM

#

Wdym

hollow totem Dec 3, 2024, 9:58 PM

#

The limit is zero

#

In both cases

#

It's not "0+ε", it's not almost 0 or inexactly zero or 0^- or any of this other stuff which has no mathematical meaning which you keep making up

#

It's just zero

wintry echo Dec 3, 2024, 9:59 PM

#

What

hollow totem Dec 3, 2024, 9:59 PM

#

THE LIMIT IS ZERO

#

of -1/x and also of log((x+2)/(x+3))

wintry echo Dec 3, 2024, 10:02 PM

#

But

#

Why its 0

#

Within limits

hollow totem Dec 3, 2024, 10:03 PM

#

wdym without limits

#

without limits it's a function, not a number

wintry echo Dec 3, 2024, 10:03 PM

#

Because a limit cannot be 0^+

#

I mean why

hollow totem Dec 3, 2024, 10:05 PM

#

Ok nothing you say ever makes any mathematical sense

wintry echo Dec 3, 2024, 10:06 PM

#

https://youtu.be/h6XGsdQ-Dfs?si=oV-ODFgD9zCj_OQ7

YouTube

blackpenredpen

when we have 1^infinity limit indeterminate form

Here's an example that the limit indeterminate form 1^infinity does not approach 1.

Subscribe for more math for fun videos 👉 https://bit.ly/3o2fMNo
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▶ Play video

#

Here it seems my notation is used

atomic quarry Dec 3, 2024, 10:07 PM

#

Bros are fighting

#

wintry echo Dec 3, 2024, 10:09 PM

#

@atomic quarry

#

What fight

atomic quarry Dec 3, 2024, 10:09 PM

#

Me rn

#

wintry echo Dec 3, 2024, 10:11 PM

#

Why can't I do anything😭

calm coralBOT Dec 3, 2024, 10:26 PM

#

@wintry echo Has your question been resolved?

calm coralBOT Dec 3, 2024, 10:41 PM

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Channel closed

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radiant moss Dec 3, 2024, 10:51 PM

#

confused where to start for this

calm coralBOT Dec 3, 2024, 10:51 PM

#

radiant moss confused where to start for this

calm coralBOT Dec 3, 2024, 11:06 PM

#

@radiant moss Has your question been resolved?

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granite spade Dec 4, 2024, 2:00 AM

#

Can someone please tell me what I did wrong??

calm coralBOT Dec 4, 2024, 2:00 AM

#

granite spade Can someone please tell me what I did wrong??

#

Please don't occupy multiple help channels.

granite spade Dec 4, 2024, 2:00 AM

#

#

This was my work

kindred estuary Dec 4, 2024, 2:04 AM

#

granite spade

You messed up here

#

You went from 5 + x^3 on the left to 5x + 3

#

Somehow

granite spade Dec 4, 2024, 2:05 AM

#

kindred estuary You went from 5 + x^3 on the left to 5x + 3

yeahh I figured it out the 2dn time

#

thank you so much!!

#

.close

calm coralBOT Dec 4, 2024, 2:05 AM

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mossy wigeon Dec 4, 2024, 2:34 AM

#

e right?

calm coralBOT Dec 4, 2024, 2:34 AM

#

mossy wigeon e right?

swift laurel Dec 4, 2024, 2:38 AM

#

makes sense to me

mossy wigeon Dec 4, 2024, 2:39 AM

#

ok yt

#

.close

calm coralBOT Dec 4, 2024, 2:39 AM

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west horizon Dec 4, 2024, 2:54 AM

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west horizon Dec 4, 2024, 2:56 AM

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potent lotusBOT Dec 4, 2024, 2:56 AM

#

Kenzo

golden gulch Dec 4, 2024, 2:57 AM

#

suppose x and y are nonnegative such that x + y = 20, then consider f(x,y) = x^2 + y^2 and maximize/minimize this using the given

west horizon Dec 4, 2024, 2:57 AM

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golden gulch Dec 4, 2024, 2:58 AM

#

x+y = 20

west horizon Dec 4, 2024, 2:58 AM

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golden gulch Dec 4, 2024, 2:59 AM

#

golden gulch suppose x and y are nonnegative such that x + y = 20, then consider f(x,y) = x^2...

from this

west horizon Dec 4, 2024, 2:59 AM

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potent lotusBOT Dec 4, 2024, 2:59 AM

#

Kenzo

golden gulch Dec 4, 2024, 3:00 AM

#

we have two nonnegative numbers x and y

#

they tell us the sum of those is 20

#

so

west horizon Dec 4, 2024, 3:00 AM

#

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golden gulch Dec 4, 2024, 3:00 AM

#

x + y = 20

west horizon Dec 4, 2024, 3:00 AM

#

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golden gulch Dec 4, 2024, 3:00 AM

#

x^2 + y^2 = (x+y)^2 - 2xy

#

but x+y = 20

#

x^2 + y^2 = 400 - 2xy

#

hello

west horizon Dec 4, 2024, 3:01 AM

#

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golden gulch Dec 4, 2024, 3:01 AM

#

now we need to maximize it first

#

we know since x and y are nonnegative that means x>=0 and y>=0

west horizon Dec 4, 2024, 3:02 AM

#

golden gulch x^2 + y^2 = (x+y)^2 - 2xy

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golden gulch Dec 4, 2024, 3:02 AM

#

(x+y)^2 = x^2 + 2xy + y^2

#

i rearranged

#

for x^2 + y^2

west horizon Dec 4, 2024, 3:02 AM

#

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golden gulch Dec 4, 2024, 3:02 AM

#

because thats what im interested in

west horizon Dec 4, 2024, 3:03 AM

#

golden gulch x^2 + y^2 = 400 - 2xy

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golden gulch Dec 4, 2024, 3:03 AM

#

golden gulch we know since x and y are nonnegative that means x>=0 and y>=0

because of this, this means when we subtract 2xy from 400 we are subtracting a positive number

#

so the larger the product is, the smaller x^2 + y^2 will be

west horizon Dec 4, 2024, 3:03 AM

#

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golden gulch Dec 4, 2024, 3:03 AM

#

so the maximum of 400 - 2xy is 400

#

when x or y = 0

west horizon Dec 4, 2024, 3:04 AM

#

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golden gulch Dec 4, 2024, 3:04 AM

#

now for the minimum

#

well i guess we could do

#

$\frac{x^2+y^2}{2} \geq xy \implies x^2 + y^2 \geq 2xy$

potent lotusBOT Dec 4, 2024, 3:07 AM

#

syecko

west horizon Dec 4, 2024, 3:07 AM

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golden gulch Dec 4, 2024, 3:08 AM

#

and if x^2 + y^2 = 400 - 2xy we have a minimum at equality so xy = 100 or x^2 + y^2 = 200

west horizon Dec 4, 2024, 3:08 AM

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#

Channel closed

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golden gulch Dec 4, 2024, 3:09 AM

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west horizon One message removed from a suspended account.

AM-GM inequality

golden gulch Dec 4, 2024, 3:09 AM

#

golden gulch and if x^2 + y^2 = 400 - 2xy we have a minimum at equality so xy = 100 or x^2 + ...

this is your minimum

#

are you supposed to use lagrange multipliers

west horizon Dec 4, 2024, 3:10 AM

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silver quail Dec 4, 2024, 4:31 AM

#

calm coralBOT Dec 4, 2024, 4:31 AM

#

silver quail

silver quail Dec 4, 2024, 4:31 AM

#

ik the answer i dont know how to solve it

exotic cosmos Dec 4, 2024, 4:32 AM

#

silver quail ik the answer i dont know how to solve it

left side is also (x^2 + 1)/x

#

if you subtract both sides by that you’ll have 0 = 0

#

which is true for all real numbers

#

0 is excluded cuz well it’s not in the domain of (x^2 + 1)/x

silver quail Dec 4, 2024, 4:33 AM

#

exotic cosmos left side is also (x^2 + 1)/x

ohhh omg it is

#

so why isnt it 1 then

drifting seal Dec 4, 2024, 4:33 AM

#

🤔

exotic cosmos Dec 4, 2024, 4:33 AM

#

exotic cosmos if you subtract both sides by that you’ll have 0 = 0

see this

drifting seal Dec 4, 2024, 4:33 AM

#

$\frac{x^2+1}{x} = \frac{x^2+1}{x}$

potent lotusBOT Dec 4, 2024, 4:33 AM

#

knief

exotic cosmos Dec 4, 2024, 4:34 AM

#

also well they’re identical everywhere except where they’re undefined

drifting seal Dec 4, 2024, 4:34 AM

#

it’s just a true statement with the added condition that x ≠ 0

exotic cosmos Dec 4, 2024, 4:34 AM

#

so that’s that too

drifting seal Dec 4, 2024, 4:34 AM

#

potent lotus **knief**

all x values except 0 here would be true

#

x isn’t just 1

silver quail Dec 4, 2024, 4:34 AM

#

oh okay got it

drifting seal Dec 4, 2024, 4:35 AM

#

it’s 2, e, pi, sqrt(2), 10, -13748884 etc

silver quail Dec 4, 2024, 4:35 AM

#

so anything that doesnt equal 0 is all real numbers

#

got it

#

thank you!!

drifting seal Dec 4, 2024, 4:35 AM

#

silver quail so anything that doesnt equal 0 is all real numbers

well 0 is a real number, it’s just that we can’t divide by zero

drifting seal Dec 4, 2024, 4:35 AM

#

potent lotus **knief**

and x is in the denominator here

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so if x = 0 then it’s undefined

silver quail Dec 4, 2024, 4:36 AM

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ok got it

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thank u

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.close

calm coralBOT Dec 4, 2024, 4:36 AM

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Channel closed

Closed by @silver quail

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calm coralBOT Dec 4, 2024, 4:51 AM

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final scarab Dec 4, 2024, 4:52 AM

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using law of cosine must find x

calm coralBOT Dec 4, 2024, 4:52 AM

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final scarab using law of cosine must find x

final scarab Dec 4, 2024, 4:53 AM

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what i have rn is (8)^2 = (a)^2 + (9)^2 - 2(9)(a) cos 60 but idk here to go from there

marsh valley Dec 4, 2024, 4:56 AM

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Use law of sines to find the missing angles

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I guess you could even just use law of sines tbh

final scarab Dec 4, 2024, 4:58 AM

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yea but the topic we're on is law of cos so idk if i can use law of sines

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unless it was like you said where i can use cos after ? idk

marsh valley Dec 4, 2024, 4:58 AM

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But yeah I think your method works one sec

final scarab Dec 4, 2024, 4:58 AM

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okk

marsh valley Dec 4, 2024, 4:59 AM

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cos(60) you can compute yourself

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But it’s 1/2

final scarab Dec 4, 2024, 4:59 AM

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yeye

marsh valley Dec 4, 2024, 4:59 AM

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Once you’ve expanded everything it s a quadratic equation in x

final scarab Dec 4, 2024, 4:59 AM

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oh dang

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a^2 + a/2 - 17/18 ?

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not getting a clean answer from dat mm

marsh valley Dec 4, 2024, 5:03 AM

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It’s a^2 -9a + 17 I think

final scarab Dec 4, 2024, 5:03 AM

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yea i tried that too n im still getting a weird number

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well

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two numbers

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maybe this isnt the correct method n i should jus do law of sines tbh

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idk

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im supposed to use law of cos tho

marsh valley Dec 4, 2024, 5:05 AM

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I mean it should work are you really expecting a nice result?

final scarab Dec 4, 2024, 5:05 AM

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i mean kinda

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my professor said we shouldnt be seeing really horrendous numbers

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plus im getting two diff numbers

marsh valley Dec 4, 2024, 5:06 AM

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You’ll get different numbers but usually only one makes sense

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In either case there could be multiple answers

final scarab Dec 4, 2024, 5:09 AM

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hmm ok

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alr cool ty

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.close

calm coralBOT Dec 4, 2024, 5:09 AM

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Channel closed

Closed by @final scarab

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calm coralBOT Dec 4, 2024, 5:25 AM

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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.

west horizon Dec 4, 2024, 5:53 AM

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calm coralBOT Dec 4, 2024, 5:53 AM

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west horizon One message removed from a suspended account.

west horizon Dec 4, 2024, 5:54 AM

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drifting seal Dec 4, 2024, 5:54 AM

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yes

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west horizon Dec 4, 2024, 5:54 AM

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potent lotusBOT Dec 4, 2024, 5:54 AM

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Kenzo

west horizon Dec 4, 2024, 5:54 AM

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drifting seal Dec 4, 2024, 5:55 AM

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well, why would you start with x^2 + y^2 = 20?

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are those your two nonnegative numbers?

west horizon Dec 4, 2024, 5:55 AM

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drifting seal Dec 4, 2024, 5:55 AM

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did you make them squared so they were nonnegative

west horizon Dec 4, 2024, 5:55 AM

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drifting seal Dec 4, 2024, 5:56 AM

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west horizon One message removed from a suspended account.

well the sum of the squares would then be x^4 + y^4

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why not just use x and y

west horizon Dec 4, 2024, 5:56 AM

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drifting seal Dec 4, 2024, 5:56 AM

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it doesn’t say "the sum of the squares of two nonnegative numbers is 20"

west horizon Dec 4, 2024, 5:57 AM

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drifting seal Dec 4, 2024, 5:57 AM

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west horizon One message removed from a suspended account.

yea but this isn’t two

drifting seal Dec 4, 2024, 5:57 AM

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west horizon One message removed from a suspended account.

but it doesn’t

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it doesn’t say it’s 20

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it says make it as large as possible

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and as small as possible

west horizon Dec 4, 2024, 5:57 AM

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drifting seal Dec 4, 2024, 5:58 AM

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west horizon Dec 4, 2024, 5:58 AM

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drifting seal Dec 4, 2024, 5:58 AM

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let x and y be the two nonnegative numbers

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the sum of them is x + y

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is means =

west horizon Dec 4, 2024, 5:58 AM

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drifting seal Dec 4, 2024, 5:58 AM

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x + y = 20

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then it says find the numbers x and y if x^2 + y^2 is a maximum

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and then do the same for a minimum

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the sum of the squares is just x^2 + y^2

west horizon Dec 4, 2024, 5:59 AM

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drifting seal x + y = 20

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drifting seal Dec 4, 2024, 5:59 AM

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yes

west horizon Dec 4, 2024, 5:59 AM

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drifting seal then it says find the numbers x and y if x^2 + y^2 is a maximum

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drifting seal Dec 4, 2024, 5:59 AM

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mhm

west horizon Dec 4, 2024, 5:59 AM

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drifting seal Dec 4, 2024, 5:59 AM

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drifting seal x + y = 20

this is what’s given

west horizon Dec 4, 2024, 5:59 AM

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drifting seal Dec 4, 2024, 6:00 AM

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ok great

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now there are like 3 ways we can do this

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but seeing as you’re taking single variable calc

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i guess we’re supposed to just do differentiation

west horizon Dec 4, 2024, 6:00 AM

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drifting seal Dec 4, 2024, 6:01 AM

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this seems so easy with algebra but whatever

west horizon Dec 4, 2024, 6:01 AM

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drifting seal Dec 4, 2024, 6:01 AM

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so

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let’s consider the expression x^2 + y^2

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what do you want to call it

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s?

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for sum

west horizon Dec 4, 2024, 6:01 AM

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drifting seal Dec 4, 2024, 6:01 AM

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s = x^2 + y^2

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we want s to be a maximum

west horizon Dec 4, 2024, 6:02 AM

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drifting seal Dec 4, 2024, 6:03 AM

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hmm yea why wouldn’t we just use algebra here?

west horizon Dec 4, 2024, 6:03 AM

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drifting seal Dec 4, 2024, 6:04 AM

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$x^2+y^2 = 400 - 2xy$

potent lotusBOT Dec 4, 2024, 6:04 AM

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knief

west horizon Dec 4, 2024, 6:04 AM

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west horizon Dec 4, 2024, 6:04 AM

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potent lotus **knief**

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drifting seal Dec 4, 2024, 6:04 AM

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potent lotus **knief**

do they do this?

west horizon Dec 4, 2024, 6:04 AM

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drifting seal Dec 4, 2024, 6:04 AM

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what do they do

west horizon Dec 4, 2024, 6:04 AM

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drifting seal Dec 4, 2024, 6:04 AM

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wdym

west horizon Dec 4, 2024, 6:04 AM

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drifting seal Dec 4, 2024, 6:05 AM

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,rotate

west horizon Dec 4, 2024, 6:05 AM

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potent lotusBOT Dec 4, 2024, 6:05 AM

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west horizon Dec 4, 2024, 6:05 AM

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drifting seal Dec 4, 2024, 6:05 AM

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yea this is a completely separate problem though

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still is optimization

west horizon Dec 4, 2024, 6:05 AM

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drifting seal Dec 4, 2024, 6:06 AM

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yea

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i mean you can use multivariable calc

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🤷🏼‍♂️🤷🏼‍♂️

west horizon Dec 4, 2024, 6:06 AM

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drifting seal Dec 4, 2024, 6:07 AM

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$\nabla f = \lambda \nabla g$

potent lotusBOT Dec 4, 2024, 6:07 AM

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knief

drifting seal Dec 4, 2024, 6:07 AM

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but you don’t know this

west horizon Dec 4, 2024, 6:07 AM

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drifting seal Dec 4, 2024, 6:07 AM

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potent lotus **knief**

i think it would be fun to do it this way

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but let’s do algebra

drifting seal Dec 4, 2024, 6:07 AM

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potent lotus **knief**

you get this right

west horizon Dec 4, 2024, 6:07 AM

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drifting seal Dec 4, 2024, 6:08 AM

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$(x+y)^2 = (20)^2$

potent lotusBOT Dec 4, 2024, 6:08 AM

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knief

west horizon Dec 4, 2024, 6:08 AM

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drifting seal Dec 4, 2024, 6:08 AM

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west horizon One message removed from a suspended account.

lol would you rather not

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i can show you all 3 ways

west horizon Dec 4, 2024, 6:09 AM

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drifting seal Dec 4, 2024, 6:09 AM

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because i squared the x+y

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i squared both sides

west horizon Dec 4, 2024, 6:09 AM

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drifting seal Dec 4, 2024, 6:09 AM

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because i want to know about the sum of the squares

west horizon Dec 4, 2024, 6:10 AM

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drifting seal Dec 4, 2024, 6:10 AM

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i’m concerned with x^2 + y^2

west horizon Dec 4, 2024, 6:10 AM

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drifting seal Dec 4, 2024, 6:10 AM

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ok the only downside of doing it this way is i don’t think you know inequalities

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do you remember

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$\frac{a+b}{2} \geq \sqrt{ab}$

potent lotusBOT Dec 4, 2024, 6:10 AM

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knief

west horizon Dec 4, 2024, 6:11 AM

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drifting seal Dec 4, 2024, 6:11 AM

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ok then we can do it another way

west horizon Dec 4, 2024, 6:11 AM

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drifting seal Dec 4, 2024, 6:11 AM

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potent lotus **knief**

no this is just algebra

west horizon Dec 4, 2024, 6:11 AM

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drifting seal ok then we can do it another way

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drifting seal Dec 4, 2024, 6:11 AM

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alright

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so

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if x+y = 20, what is either of them in terms of the other

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isolate x or y

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doesn’t matter

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this way is just boring imo

west horizon Dec 4, 2024, 6:12 AM

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drifting seal Dec 4, 2024, 6:12 AM

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but this is how you do optimization problems usually

west horizon Dec 4, 2024, 6:12 AM

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drifting seal Dec 4, 2024, 6:12 AM

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west horizon One message removed from a suspended account.

nah boring and longer imo

drifting seal Dec 4, 2024, 6:12 AM

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west horizon One message removed from a suspended account.

yep

west horizon Dec 4, 2024, 6:12 AM

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drifting seal Dec 4, 2024, 6:12 AM

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so

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then if f(x) = x^2+y^2 and y = (20-x)

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what if f(x)

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only in terms of x

west horizon Dec 4, 2024, 6:13 AM

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drifting seal Dec 4, 2024, 6:13 AM

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west horizon One message removed from a suspended account.

i mean it’s probably better for you because this technique is more relevant to future problems

west horizon Dec 4, 2024, 6:13 AM

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potent lotusBOT Dec 4, 2024, 6:13 AM

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Kenzo

drifting seal Dec 4, 2024, 6:13 AM

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mhm

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now differentiate that bitch

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i guess we called it s

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find s’

west horizon Dec 4, 2024, 6:14 AM

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drifting seal Dec 4, 2024, 6:14 AM

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potent lotus **Kenzo**

west horizon Dec 4, 2024, 6:14 AM

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drifting seal Dec 4, 2024, 6:14 AM

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it’s supposed to be + btw

west horizon Dec 4, 2024, 6:14 AM

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drifting seal Dec 4, 2024, 6:14 AM

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west horizon One message removed from a suspended account.

yea

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multiply by -1

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since -x

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and power rule of course

west horizon Dec 4, 2024, 6:15 AM

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drifting seal Dec 4, 2024, 6:15 AM

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no

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$2x -2(20-x)$

west horizon Dec 4, 2024, 6:16 AM

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drifting seal Dec 4, 2024, 6:16 AM

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yo

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ya know what

west horizon Dec 4, 2024, 6:16 AM

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potent lotusBOT Dec 4, 2024, 6:16 AM

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Kenzo

drifting seal Dec 4, 2024, 6:16 AM

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potent lotus **Kenzo**

yep power rule, bring down the 2 multiply by -1

west horizon Dec 4, 2024, 6:16 AM

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drifting seal Dec 4, 2024, 6:16 AM

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inside stays the same thouyh

potent lotusBOT Dec 4, 2024, 6:16 AM

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Kenzo

west horizon Dec 4, 2024, 6:17 AM

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potent lotusBOT Dec 4, 2024, 6:17 AM

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knief

drifting seal Dec 4, 2024, 6:17 AM

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yea i forgot the 2

west horizon Dec 4, 2024, 6:17 AM

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drifting seal Dec 4, 2024, 6:17 AM

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so 4x - 40

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s’

west horizon Dec 4, 2024, 6:17 AM

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drifting seal Dec 4, 2024, 6:18 AM

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so set it equal to zero

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x = ?

west horizon Dec 4, 2024, 6:18 AM

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drifting seal Dec 4, 2024, 6:18 AM

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s’ = 0

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s’ = 4x - 40

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4x - 40 = 0

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x = ?

west horizon Dec 4, 2024, 6:18 AM

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drifting seal so 4x - 40

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drifting seal Dec 4, 2024, 6:18 AM

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2x - 40 + 2x

west horizon Dec 4, 2024, 6:19 AM

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drifting seal Dec 4, 2024, 6:19 AM

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mhm

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which means y = ?

west horizon Dec 4, 2024, 6:19 AM

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drifting seal Dec 4, 2024, 6:19 AM

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right

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but

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we need to analyze further

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is this a min or max

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and why

west horizon Dec 4, 2024, 6:20 AM

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drifting seal Dec 4, 2024, 6:20 AM

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use second derivative test

west horizon Dec 4, 2024, 6:20 AM

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drifting seal Dec 4, 2024, 6:20 AM

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because we only care about a point

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not an interval

west horizon Dec 4, 2024, 6:20 AM

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drifting seal Dec 4, 2024, 6:20 AM

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yea

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f’’(10) = ?

west horizon Dec 4, 2024, 6:20 AM

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drifting seal Dec 4, 2024, 6:20 AM

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you can

west horizon Dec 4, 2024, 6:20 AM

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drifting seal Dec 4, 2024, 6:20 AM

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f’’(10) = 4

west horizon Dec 4, 2024, 6:21 AM

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drifting seal Dec 4, 2024, 6:21 AM

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f’’(anything) = 4

west horizon Dec 4, 2024, 6:21 AM

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drifting seal Dec 4, 2024, 6:21 AM

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since there’s no input

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like if you plotted

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y = 4

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it’s a horizontal line

west horizon Dec 4, 2024, 6:21 AM

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drifting seal Dec 4, 2024, 6:21 AM

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no matter the x input it’s still 4

west horizon Dec 4, 2024, 6:21 AM

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drifting seal Dec 4, 2024, 6:21 AM

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is 4 > 0?

west horizon Dec 4, 2024, 6:21 AM

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drifting seal Dec 4, 2024, 6:22 AM

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which means x = 10 is a ?

west horizon Dec 4, 2024, 6:22 AM

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drifting seal Dec 4, 2024, 6:22 AM

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yep

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now for the maximum

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let’s go back to the algebra and common sense

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so

west horizon Dec 4, 2024, 6:22 AM

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drifting seal Dec 4, 2024, 6:22 AM

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the big thing about optimization is that we are given CONSTRAINT EQUATIONS

west horizon Dec 4, 2024, 6:22 AM

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drifting seal Dec 4, 2024, 6:22 AM

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west horizon One message removed from a suspended account.

yea

west horizon Dec 4, 2024, 6:23 AM

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drifting seal Dec 4, 2024, 6:23 AM

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all good

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didn’t sleep well

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my head feels like empty rn

west horizon Dec 4, 2024, 6:23 AM

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drifting seal the big thing about optimization is that we are given CONSTRAINT EQUATIONS

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drifting seal Dec 4, 2024, 6:23 AM

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yes like for instance x + y = 20 is considered a constraint

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like it’s something that must be satisfied

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but there’s a hidden second constraint equation

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which will give us the maximum

west horizon Dec 4, 2024, 6:24 AM

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drifting seal Dec 4, 2024, 6:24 AM

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can you tell me what it might be

west horizon Dec 4, 2024, 6:24 AM

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drifting seal Dec 4, 2024, 6:24 AM

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no

west horizon Dec 4, 2024, 6:24 AM

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drifting seal Dec 4, 2024, 6:24 AM

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so

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an added condition was that they were nonnegative yes?

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meaning

west horizon Dec 4, 2024, 6:24 AM

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drifting seal Dec 4, 2024, 6:24 AM

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$x \geq 0 \quad y \geq 0$

potent lotusBOT Dec 4, 2024, 6:24 AM

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knief

drifting seal Dec 4, 2024, 6:24 AM

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these are our added constraints

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coupled with the fact that x+y = 20

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all three must be satisfied

west horizon Dec 4, 2024, 6:25 AM

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drifting seal Dec 4, 2024, 6:25 AM

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so we look for i guess you could say critical points or boundary points whatever

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which would be when x = 0 or y = 0

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and going back to the algebra i said earlier

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$x^2 + y^2 = 400-2xy$

west horizon Dec 4, 2024, 6:26 AM

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drifting seal which would be when x = 0 or y = 0

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potent lotusBOT Dec 4, 2024, 6:26 AM

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knief

west horizon Dec 4, 2024, 6:26 AM

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drifting seal Dec 4, 2024, 6:26 AM

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west horizon One message removed from a suspended account.

well it’s just the boundary of the interval

west horizon Dec 4, 2024, 6:26 AM

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drifting seal Dec 4, 2024, 6:26 AM

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potent lotus **knief**

so here we look at the boundary

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and that yields x = 0 or y = 0

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which means

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x^2 + y^2 = 400

west horizon Dec 4, 2024, 6:27 AM

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drifting seal Dec 4, 2024, 6:27 AM

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if either is zero

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so that’s our maximum

west horizon Dec 4, 2024, 6:27 AM

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drifting seal Dec 4, 2024, 6:27 AM

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which would be when x = 20 and y = 0 or x = 0 and y = 20

west horizon Dec 4, 2024, 6:27 AM

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drifting seal Dec 4, 2024, 6:28 AM

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so we still didn’t find the minimum

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we only found where it occurred

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at x = 10

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if x = 10 what does y =

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remember x + y = 20

west horizon Dec 4, 2024, 6:28 AM

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drifting seal Dec 4, 2024, 6:28 AM

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yep

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so

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what’s x^2 + y^2

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when both x and y are 10

west horizon Dec 4, 2024, 6:29 AM

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drifting seal Dec 4, 2024, 6:29 AM

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mhm

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so minimum is 200

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maximum is 400

west horizon Dec 4, 2024, 6:29 AM

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drifting seal Dec 4, 2024, 6:29 AM

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we could’ve done this much simpler imo but this way also works

west horizon Dec 4, 2024, 6:29 AM

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drifting seal Dec 4, 2024, 6:29 AM

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well because you’re learning calculus

west horizon Dec 4, 2024, 6:30 AM

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drifting seal Dec 4, 2024, 6:30 AM

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so you’re supposed to use calculus techniques

west horizon Dec 4, 2024, 6:30 AM

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drifting seal Dec 4, 2024, 6:30 AM

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fire

west horizon Dec 4, 2024, 6:30 AM

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drifting seal Dec 4, 2024, 6:30 AM

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next week

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i’m ding chilling

west horizon Dec 4, 2024, 6:31 AM

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drifting seal Dec 4, 2024, 6:31 AM

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west horizon One message removed from a suspended account.

yea i did today

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but there isn’t that much for me to study

west horizon Dec 4, 2024, 6:31 AM

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drifting seal Dec 4, 2024, 6:31 AM

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mostly doing the last hws

drifting seal Dec 4, 2024, 6:31 AM

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west horizon One message removed from a suspended account.

in like half an hour

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i have a quiz tomorrow

west horizon Dec 4, 2024, 6:31 AM

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drifting seal Dec 4, 2024, 6:31 AM

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west horizon One message removed from a suspended account.

fun

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yo i’ll show you the other way

west horizon Dec 4, 2024, 6:32 AM

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drifting seal Dec 4, 2024, 6:32 AM

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or maybe even the calc 3 way

west horizon Dec 4, 2024, 6:32 AM

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drifting seal Dec 4, 2024, 6:32 AM

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well

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they both might hurt

west horizon Dec 4, 2024, 6:33 AM

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drifting seal Dec 4, 2024, 6:33 AM

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id do the same for maximum btw

west horizon Dec 4, 2024, 6:33 AM

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drifting seal Dec 4, 2024, 6:33 AM

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algebra way

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x^2 + y^2 = 400-2xy

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x or y = 0

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max is 400

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for minimum

west horizon Dec 4, 2024, 6:34 AM

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drifting seal Dec 4, 2024, 6:34 AM

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$\frac{x^2+y^2}{2} \geq \sqrt{x^2y^2} \implies x^2 + y^2 \geq 2xy$

potent lotusBOT Dec 4, 2024, 6:34 AM

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knief

west horizon Dec 4, 2024, 6:35 AM

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drifting seal Dec 4, 2024, 6:35 AM

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potent lotus **knief**

yes this is from^

west horizon Dec 4, 2024, 6:36 AM

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