help-0

[marble knot]

Oh yeah, it does

[minor needle]

No no, you assume it's true for each k = m and then you prove it's true for k = m + 1.

[marble knot]

Oh ok, I'm a bit stuck on that part though

[minor needle]

Let's see

So, firstly we assume this is true for some positive integers n and k

aka inductive step

Then we'll show it holds also for k = k + 1 (or m+1, doesn't matter if k is m)

[marble knot]

yep

[ocean seal]

Modus

[marble knot]

Yes

[minor needle]

Recall that in this sequence every term is the sum of the two previous terms

In other words:

[ocean seal]

Modus

[minor needle]

How do you think we can use this statement?

[marble knot]

substitute Fn+k with what we assumed ?

[minor needle]

Might be, but I think it'll be better to use this later, but who knows

You can try it

My suggestion is to write down (based on the assumption) what is F_(n+k-1)

Then we'll add them i.e. F_(n+k) and F_(n+k-1) and then we'll be able to use the above fact

[marble knot]

How do you find F(n+k-1)?

[grizzled mauve]

you should write down the definition of Fn in the first place, will help you think

[lone heart]

@marble knot Has your question been resolved?

[grizzled mauve]

@marble knot what course is this for

[lone heart]

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[scenic stream]

is it just me or are the bases of these switched?

a) Write the mapping matrix of A*B (* being compositum) in standard basis of R^3.

[grizzled mauve]

can you zoom in more

on the part youre asking

[grizzled mauve]

also, don't use asterisk, that means lots of other things, use A o B

if outside of latex

\circ in LaTeX

[scenic stream]

ignore the slovenian, its mostly just explanation

[scenic stream]

ik

[scenic stream]

didnt know this, thanks \circ

\circ

wait what

[grizzled mauve]

dollar signs

[scenic stream]

$\circ$

[grizzled mauve]

#latex-testing to play around

[ocean seal]

N1cK

[scenic stream]

mb

[grizzled mauve]

oh that didnt render nicely

okay there we go

your question is....

[scenic stream]

is it just me or are the bases of these switched?

[grizzled mauve]

not sure which way you think it is suppsoed to be but

matrix multiplies on vectors from the left

[scenic stream]

I guess I get it now that I read the assignment multiple times

ok what if

[grizzled mauve]

if that helps

[scenic stream]

we had to find the matrix of the composition in the basis (1,1,1),(1,0,1),(0,1,1), what would the mapping graph look like then?

[scenic stream]

ok, what if we had to find the matrix of the composition in the basis pi=((1,1,1),(1,0,1),(0,1,1)), what would the mapping graph look like then?
lets call the base pi, then we would go from pi --S--> standard base --B--> standard base --A--> standard base --S^(-1)--> pi?

[grizzled mauve]

you can ignore the part about rings and modules and just trea tthis as vector spaces over fields, regular linear algebra

the notation here is
$\mathbf M_{f, \mathcal B, \mathcal A}$ in the notation of this website means

[ocean seal]

gfauxpas

[scenic stream]

this is too advanced for me

[grizzled mauve]

matrix for the function f, assuming the codomain is written with respect to the basis B, assuming the domain is written with respect to the basis A

I'll traqnslate for you

[scenic stream]

wait before you do, am I right about this?

[grizzled mauve]

Let R be a scalar field
Let M, N be vector spaces over R, finite dimensional.
Let A, B be ordered bases of M, N respectively.
Let f: M to N be a linear transformation.

im not sure what you mean when you ask about a matrix without giving me THREE Ingredients

the mapping, the basis for the codomain, the basis for the domain

[grizzled mauve]

there you go, now it's in English

[scenic stream]

the mapping from my original task

[scenic stream]

everything from the original task, the only things that are changed are written here

[grizzled mauve]

I dunno can you ask your question without referring to the picture please? or just crop oiut just the part of the picture relevant? lots of stuff going on

and its hard for me to read the small print

[scenic stream]

ok, gimme a sec

Assignment: Write the mapping matrix of A*B (* being compositum here and not multiplication) in the basis pi = ((1,1,1),(1,0,1),(0,1,1))

Would the mapping graph (in the style of the one in the second screenshot) be the following:
pi --(S)--> standard base --(B)--> standard base --(A)--> standard base --(S^(-1))--> pi?

[grizzled mauve]

im just writing up the theorem in linear algebra language because i have to go soon

[scenic stream]

can I tag some other helper?

[scenic stream]

I guess so, <@&286206848099549185>

[grizzled mauve]

of course, i just want to leave you with something before I leave

happy birthday

[toxic verge]

Happy Birthday!

[scenic stream]

oh, thought you were writing somethins outside of this

[grizzled mauve]

now with more bullet points

[scenic stream]

yea this is just too much for me to currently understand since I'm focusing just on the practical part of linear algebra, sorry

plus I only have 1 more day until my exam

[toxic verge]

bombaclat

[scenic stream]

Ill save it and read it when I go attend the theoretical part, thank you

.close

[lone heart]

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[grizzled mauve]

k im profreading it for errors

theres a lot of places where i could have made a mistake so... hopefully ig o t it right

[toxic verge]

reopen?

[scenic stream]

the question is a bit lost since there is a lot that happened in between, thats why I openeda new help channel

[scenic stream]

also 31h of vsc is crazy

[toxic verge]

0_0

gotta grind

(not fr tho lol, it just stays open as long as the laptop is open)

cant do 31h of code

[scenic stream]

youre pre uni and youre coding and doing linear algebra? thats crazy

[toxic verge]

It's not anything extra lol what i talk about here is just whatever was taught to me

the coding too is just from school

i mean i learned it in school

and then started stuff myself

[scenic stream]

nice

[toxic verge]

[lone heart]

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[alpine sable]

alright

[alpine sable]

somebody help

wtf is this

[scenic stream]

wtf is what?

the answer is 8/7

[alpine sable]

yes

but

how is it

8/7

im gonna choke myself i promise u

[toxic verge]

The working is right there

[toxic verge]

Don't threaten suicide.

[scenic stream]

ayo chill

[alpine sable]

👍

[scenic stream]

24/3, 21/3, what do you get?

also there is no way you are undergrad in math, youre pre grad

[alpine sable]

helping me would be a lost case 4 you

[scenic stream]

wdym

[toxic verge]

You're the one who asked for help.

[alpine sable]

damnnnnn

[toxic verge]

,tex.alg manip

[ocean seal]

Executor (ask on server b4 DM)

[toxic verge]

Read this once.

[scenic stream]

so you can write it as 8*3/7*3, cancel out the threes and you get 8/7

[toxic verge]

Won't work for you nick

Need to have the preamble uploaded

Come to #latex-help can walk you through it if you want

[lone heart]

@alpine sable Has your question been resolved?

[lone heart]

@alpine sable Has your question been resolved?

[toxic verge]

Just clicking the cross doesnt help.

Tell us whats troubling you.

[lone heart]

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as this action is irreversible, and this channel may abruptly lock.

[lone heart]

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[balmy slate]

How could I simplify this expression? I know that sin^2 + cos^2 = 1 but I don’t know how to separate it from e^x.

[balmy slate]

It is also possible that it can't be simplified, there are no instructions stating otherwise.

[remote heron]

i dont see how anything nice can happen here

you might be able to reduce the number of terms a small amount but i dont think any magical cancellations happen

i could be wrong though

[balmy slate]

alright, thank you

[remote heron]

actually i guess just distributing is nicest, maybe

np

[balmy slate]

.close

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[scenic stream]

Why did we get the following matrix for b) and not the transposed version of it?

[sly mantle]

first column of matrix is the coordinates of F(a) in the basis (a,b,c), second column is coordinates of F(b) etc

[lone heart]

@scenic stream Has your question been resolved?

[lone heart]

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[untold flower]

any help would be greatly appreciated 🙏 i dont know where to go from this

[winter light]

Replace √x with another variable

[untold flower]

aweh

[winter light]

Such as u = √x

[untold flower]

ahhh i think that makes sense wait

gimme a second

[winter light]

But first write down that x must be ≥ 0 for the sqrt to exist

Otherwise you might forget it later

[untold flower]

im stuck again

[lavish cave]

it's not the cube root of x!

it's 3 * sqrt(x)

[untold flower]

wati what

[lavish cave]

yeah

$3 \sqrt{x}, \sqrt[3] {x}$

[ocean seal]

south

[untold flower]

ohhhhhh

damn i been struggling on this for like 30 minutes

mb

[lavish cave]

no worries

[untold flower]

how did you know to do this ?

then it becomes this ?

[lavish cave]

practice

you'll find you get a hidden quadratic

[lavish cave]

indeed!

[untold flower]

i dont even know any of these names i dropped out of 2nd grade

this is hard af

[lavish cave]

what matters isn't the exact name but knowing the technique

the problem-solving approach

[untold flower]

alr i got the answer

thank you

.close

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[untold flower]

thanks for the advice

[lavish cave]

np!

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[hot basin]

any advices for when i should use 2^n, (n r), n^r and n! / m!

[hot basin]

these are my notes

but is a little hard to identify each case

[placid zinc]

A bit more thorough and has examples:
https://www.mathsisfun.com/combinatorics/combinations-permutations.html

[hot basin]

that's really helpful, thanks

it looks like my teachers learned from this lol, because they told that you should rethink the problem to another similar, like "balls" like the website

but well, thanks

.close

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[velvet finch]

i do not know how to do this

[mossy reef]

,w 13/8 - 3/5

[ocean seal]

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[mossy reef]

Good luck

[velvet finch]

what are the steps for you to get that answer

[mossy reef]

That’s not even the answer

Wait @velvet finch are you allowed a calculator

[velvet finch]

yeah

but i ain even know the steps

[mossy reef]

What calculator is it

[velvet finch]

sharp EL 510

cuz canadian

[mossy reef]

Aaand we’re back to good luck

,w 3/5 - 3/8

[ocean seal]

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[mossy reef]

,w 3/10 - 13/8

[ocean seal]

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[winter light]

Use the fact that $\sin\left(\frac{\pi}{2} - \alpha\right) = \cos(\alpha)$ or, if you prefer, $\cos\left(\frac{\pi}{2} - \alpha\right) = \sin(\alpha)$

[velvet finch]

but you gotta show steps for the question to get marks ykwim

[proven leaf]

actually no, this is doable?

[ocean seal]

Alberto Z.

[velvet finch]

this is doable this is grade 12 advanced functions

it was on a test

.close

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[quiet hemlock]

https://youtu.be/NJdhrS0SLG8?si=trl9stpQhO3fhOud

Could anyone fact check this video if it's true? I doubt that the 1.5th root of 4 is 3

[sturdy blade]

.........

[quiet hemlock]

I know i know

[lunar saddle]

The 1.5th root of 4 is not 3

[quiet hemlock]

Then tf is this video saying then

[sturdy blade]

💀 💀 💀

[lunar saddle]

-# didnt watch the vid yet

[quiet hemlock]

Ah

[sturdy blade]

Don't watch it

Please

[lunar saddle]

idk

But 1.5th root of 4 is 3 is equivalent to saying that

[quiet hemlock]

Has to be incorrect right?

[sturdy blade]

Okay now

Prove that 1.5th root of 4 is irrational

[lunar saddle]

what?

[lunar saddle]

$4^{\frac{2}{3}} = 3$

[ocean seal]

Carbonite

[lunar saddle]

that is kinda bullshit

[quiet hemlock]

It's obviously irrational what number wouldn't become irrational after that torture of 1.5√

[lunar saddle]

!occupied

[lone heart]

Someone else is already using this help channel. If you need help with a question, please open your own help channel/thread (see #❓how-to-get-help for instructions).

[umbral mountain]

ok np @lunar saddle

[quiet hemlock]

So like

[lunar saddle]

and welcome to mathcord @quiet hemlock @umbral mountain

but you understand why the vid is wrong right

proving it is irrational is a fun next excercise

[quiet hemlock]

Is this actually inaccurate

https://youtu.be/NJdhrS0SLG8?si=trl9stpQhO3fhOud

It says 1.5√1 is 1.5

WAIT

It's actually 1.5 x √1

Not 1.5√1

!solved

!solve

solved

[lunar saddle]

well $4^{\frac{2}{3}} = 2^{\frac{4}{3}} = \sqrt[3]{2}^4$

[lunar saddle]

its .close btw

what

aiya

[ocean seal]

Carbonite

[lunar saddle]

@quiet hemlock this is clearly not 3

[quiet hemlock]

According to the vid 1.5√8 ≈ 4.1

It's either 4 or 4.24

What is this kid smoking

And 1.5√7 is EXACTLY 4

[lunar saddle]

,w 1.5*sqrt(7)

[ocean seal]

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[lunar saddle]

...

[quiet hemlock]

Radaca where are you getting these measurements from

That block is shorter than that one

It IS 3.96

Radaca isn't dumb

.close

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[tidal palm]

Hello 👋 could someone verify this question ? The answer key says it’s B) but isn’t A) also false?

[rigid tree]

yeah a is obviously false

[tidal palm]

So both A & B are false right?

[rigid tree]

yes

[tidal palm]

Oki thank you

.close

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[indigo tapir]

Ik this is a silly doubt but i need help, in this question pulley is moving with acceleration a so wouldn't the blocks also move with the same acceleration a both of them in the upward direction and in relative acceleration it will just cancel out and we will be left with acceleration of block with mass m as g/3

[wind cloak]

You're working in a non-inertial frame so the laws don't work normally

[indigo tapir]

Please help 😭

[wind cloak]

,rotate

[indigo tapir]

Im getting acceleration of block as g/3 if there was no acceleration in pulley

[wind cloak]

Do you understand fictitious or pseudo forces?

[indigo tapir]

Yes

[wind cloak]

Well then just use that

Then it's a standard atwood machine

[indigo tapir]

I understand that there would a force in the negative x direction equal to (mass of block)(acceleration of pulley)

[wind cloak]

yep

[indigo tapir]

But i don't understand the theoretical part if pulley is moving with some acceleration so block should have that acceleration also and in relative acceleration shouldn't they cancel out ??

[wind cloak]

The pulley isn't affected by gravity (assumed massless) so there is an imbalance here

[indigo tapir]

Ohh tysm i get it now

[lone heart]

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[high tulip]

I am trying to solve for the length of EF, I am guessing it is 14 because I just extended the EF line segment towards points D and B then found out CBF/ADE were a multiple of the 3-4-5 triangle. Which then allowed me to also see that triangle DBC is also a multiple of the 3-4-5 triangle.

[high tulip]

But what I am struggling to understand is why is it that I am able to extend EF to points B and D? I feel like it is illegal, like the EF line segment if to be extended could end up either in-between BC/AD or AB/CD...

[onyx swallow]

it is illegal. I don't think it is generally the case that DBEF will be on the same line, but the length they gave is nice so it might just so happen to work out.

[high tulip]

I am a teacher at a school in a top gov school of Bangkok (I am a CS teacher. But I am trying to help my math teachers who are also stuck)..I feel like this is some kind of complicated gifted question.

[high tulip]

So I can't assume that watsoever even tho it "works" or maybe the answer choices contain red herrings.

I have been stuck on this question pondering trying so many different things for 1+ hours now

[plush wing]

dont do that, this task purely for Pythagorean theorem
simply draw rectangle EFCK, and use diagonal of ABCD for calculations

[high tulip]

I've been going crazy haha

[minor needle]

,calc sqrt(40^2+30^2)-2*sqrt(30^2-24^2)

[ocean seal]

Result:

14

[onyx swallow]

yeah you can't assume it

try and use vinton's method

[high tulip]

This is a question for 8th graders learning Pythagorean theorem for the first time (this is a question at the end of the unit).

[high tulip]

I am trying this now

[onyx swallow]

I just computed it, in this case it doesn't even work out.

[high tulip]

Ok

Let me show you what I have understood so far

Or is there an even easier way

[minor needle]

You can also use triangles EFC and ACB

But your reasoning is correct as well

[high tulip]

Let me try it

[minor needle]

I think you've already done it

[high tulip]

So, how does one (my students and myself) get good at this stuff? How am I just supposed to see things like how you all helped me?

[minor needle]

I'd say just by doing exercices, it comes with some practice, like almost everything

[high tulip]

My students haven't learned about congruence yet. So using only Pythagorean theorem would be the only approach.

[silver ruin]

👍

[minor needle]

Yeah, then just consider CFB instead of EFC

[high tulip]

Btw how do I explain to the students + my math teachers that it is illegal, when it feels like it is plausible? What rule am I violating? I am guessing "it is the assumption that the extension connects directly at points B/D"?

[onyx swallow]

by drawing a graph to scale

lemme do one

[minor needle]

I recommend you not to change the drawing given in any way, you can connect some vertices e.g. point E with point D and point F with point B, but you musn't change the length of EF. It's illegal because this way you change the constraints given

[high tulip]

I am struggling with this as well

[high tulip]

Would they still be 90° angles at AEF and CFE?

[onyx swallow]

yes ofc

[minor needle]

1st step:

2nd is to find BD (or AC) then subtract

[high tulip]

This is what I did initially to get my answer of 14

[plush wing]

tell us how you get right angle then

[high tulip]

But it is illegal to assume that E to F to B is a straight line, no?

[minor needle]

right, that would require showing that E and F lie on the diagonal

[high tulip]

Yea

[onyx swallow]

here

[high tulip]

That's why I was so confused and so unsure about that approach I had initially to get the answer of 14 (which ended up being the correct answer anyways 😭) poor kids

[minor needle]

and that they're collinear, so it's actually better to follow the previous solution

[high tulip]

This will help the students understand

What software is this??

[onyx swallow]

geogebra

https://www.geogebra.org/calculator

[high tulip]

So this would be the only way in terms of this unit being the Pythagorean theorem, right?

[onyx swallow]

it is also possible to construct E' and F' as the points on BD such that E'A is perpendicular to DB and F'C is perpendiculat to DB

and then show that E'=E and F'=F

but this assumes that you already know that DEFB are on the same line

but the proof would not be flawed

[high tulip]

Which in this problem's case DEFB are on the same line, but we cannot assume they are from the get go since the problem did not give us any indication of it being an assumption that we could make.

[onyx swallow]

yeah that's why I said that one way to proof this is you could assume E',F' are on the same line, and show that E'=E and F'=F

also there is another way to draw the diagram satisfying the rules:

AE = CF is wtill 24

but in this case, it is clear that DEFB are not on the same line

[high tulip]

E' and F' are just translated points of E F right?

[onyx swallow]

wdym

[high tulip]

Sorry, could I get clarification on what E' and F' are?

[onyx swallow]

perpendiculars on BD from A and from C

[onyx swallow]

^here

[high tulip]

Ohhh got it makes sense now

Btw, would you consider this as a gifted question? (8th grade math)

[onyx swallow]

idk much in that area, but i feel like these types of stuff anyone can pick up and learn in a reasonably fast pace if they are interested

[high tulip]

Nice haha, can you point me to any like resource or question bank/book to do more questions like this?

If you or anyone here knows

(I plan to be a math teacher in the future, I know this is probably not setting a good example 😅)

[onyx swallow]

there is a bunch of high school math contests where you can find the test bank of, like amc and stuff like that

[high tulip]

AMC and just search for math contest questions?

[onyx swallow]

there is a list on aops

high school contests

iirc

[high tulip]

Is it ok to show u my work for another problem to confirm my work?

[quasi rune]

wmi, amo, sasmo have alot of problems like these

[onyx swallow]

show it

[toxic verge]

Yeah correct

[high tulip]

Pls ignore problem 12, currently working on it and I found some logical mistakes lol

[onyx swallow]

looks fine

[high tulip]

Awesome

Thank you guys!

Any tips on this?

[onyx swallow]

AEF has base EF height AD, EFC has base EF height DB

[high tulip]

Man, completely forgot about the ways to calculate area of obtuse triangles, thank you 🙏

[onyx swallow]

looks fine

[high tulip]

🙏 thank you!

[lone heart]

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[lone heart]

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[civic haven]

.reopen

[crystal monolith]

just to clearify the answer is

1.For an inconsistent system of linear equations in two variables, the lines representing the equations intersect at no point.

2.In a dependent system of linear equations in two variables, the lines representing the equations intersect at infinitely many points.

3.In an independent system of linear equations in two variables, the lines representing the equations intersect at one point.

right ?

and dont i need to make a slope or soemthing for this ?

[modern sedge]

Seems right

[lone heart]

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[warm seal]

There's something wrong with my answer for this question of finding the rank for the matrix A.

[warm seal]

Here's the solution, which stated that the r(A)=3, while my answer is r(A)=4. https://www.scribd.com/document/323700526/2-1Problems-on-Rank-of-Matrix

!status

[lone heart]

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

[warm seal]

4, 5.

[leaden bobcat]

that would be 12 if I understood what you're doing

[warm seal]

Oh, right. Let me correct that real quick

Yup, I got the solution. Thanks for helping me.

.close

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[split dust]

Can anyone explain why Ln(2/0)= +infinity
While Ln(0/-2) is -infinity?

[quasi vector]

!xy

[lone heart]

Please show the original problem, exactly as it was stated to you, with the entire original context. A picture or screenshot is best. If the original problem is not in English, then post it anyway! The additional context might still be helpful. Do your best to provide a translation.

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[crystal token]

Please help

[lime jetty]

only solvable with trig

[crystal token]

So how do I do it?

[lime jetty]

can you calculate FB?

[lime jetty]

solution is quite ugly btw

[crystal token]

Do you know the solution?

[lime jetty]

yes

[lime jetty]

do this first

[crystal token]

4-2sqrt3?

[lime jetty]

so BEF is a right isoceles

and BE = 2 right?

[crystal token]

yeah

[lime jetty]

you can either use pythagoras to calculate FB

or simply divide by sqrt(2)

[crystal token]

can you tell me the answer first so I can first see if its correct

then explain to me

[lime jetty]

uhh

Approx 2.73205

[crystal token]

i need a sqrt

for the answer

[lime jetty]

exact answer is sqrt(4+2sqrt(3))

[crystal token]

its wrong....

[lime jetty]

wonder how you got 4-2sqrt(3)

can you show me your work

[lone heart]

@crystal token Has your question been resolved?

[lime jetty]

@crystal token I'm probably gonna show you the solution directly

[crystal token]

wdym directly

[lime jetty]

so FB = sqrt(2)

angle FBA = EBA - EBF = 60° - 15°= 45°

angle FBC = FBA + ABC = 15° + 90° = 105°

using cosine theorem:
FC^2 = BF^2 + BC^2 - 2.BF.BC.cos(FBC)

@crystal token got it to this part?

[crystal token]

I think so

[lime jetty]

so we have FC^2 = (sqrt(2))^2 + 2^2 - 2.sqrt(2).2.cos(105°)

= 2 + 4 - 4.sqrt(2).((-sqrt(6)+sqrt(2))/4)

@crystal token you can just evaluate this

I really don't know where you got it wrong

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[trim lava]

Can someone help me

[trim lava]

I dont really understand this problem

<@&286206848099549185>

[fair anchor]

hey @trim lava

[sly mist]

Is it D

Because b would be could it to be 10ab I think

😭

I don't know

[trim lava]

Yo

[fair anchor]

you have 2 variables right

[lavish tartan]

c

[trim lava]

Yh

[green dune]

Yes it is D, because 5 * (8a - 2b) = 40a - 10b. Remove the brackets by multiplying everything inside with 5.

[green dune]

No! 40a MINUS 10b!

[lavish tartan]

C

[trim lava]

Ty

[fair anchor]

what they are asking you to do is somehow get the constants in one place in front of the variables with mutliplying

[lavish tartan]

IT MUST BE C

[fair anchor]

now the best you can do would be 10(4a - b) right

[green dune]

think about it in peace. When you really did that, ask again.

[lavish tartan]

I agree

[craggy rose]

that can also be simplified by taking out 2 leaving us with 5*2(4a-b)=10(4a-b)

[green dune]

This is not the question. Read the problem again.

[lavish tartan]

just take common 10 from that equation

[green dune]

then it would be 10 * (4a - b)

[lavish tartan]

you'll get 4a-b

[green dune]

and c says 10 * (4a + b)

[lavish tartan]

C option yea

[craggy rose]

ohh i get it now

[green dune]

no!

[lavish tartan]

ah

[lavish tartan]

my vision

got you

[lone heart]

@trim lava Has your question been resolved?

[lone heart]

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[boreal path]

can someone help me with these two questions i need to know why before exams

[lone heart]

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

[boreal path]

step 3

3

3. I got an answer but I was told that it's wrong.

I got an answer but I was told that it's wrong.

wait am i supposed to respond to the bot

[whole adder]

No lol

[boreal path]

I dont know why the first question's answer is 6% though

[whole adder]

Well... you're supposed to answer, but the bot won't talk to you. It's just for people helping

[boreal path]

Oh

[whole adder]

,w (1.005)^12

[ocean seal]

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Requested by greeneyeswhitechick

[whole adder]

This question is worded strangely

[boreal path]

I know
the second question is even worse though i didnt even know where to start with this one except using the one equation with the negative power in it

[whole adder]

I'm not super happy with this as an answer

Because I'm not sure I'm reading this correctly

What did you put for the first one btw?

[boreal path]

I got 6%, but the answer key said 5%

[whole adder]

Did it have any explanation?

[boreal path]

Not really, thats why I'm asking

[whole adder]

Hmm

,w (1 - (1.005)^12)/(1-1.005)

[ocean seal]

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[whole adder]

I'm not sure how to get 5% tbh

I'm leaning towards it being wrong, but I'll see if anyone else can explain it first

[south raven]

If each monthly factor is r = 1.005 the monthly rate is 0.5 percent. Multiply by 12 months to get a nominal annual rate of 6 percent so pick d).

After the 150 dollar down payment 1 894 − 150 = 1 744 dollars is financed. Eighteen end of month payments of 113 dollars satisfy 113 = 1 744*i / (1 − (1+i)^(-18)) Solving gives i = 0.0167 per month so the nominal annual rate is 0.0167*12 = 20.06 percent,matching choice c

[boreal path]

thank you very much
i never thought of switching around 1744 with 113 in question 13, thats a great help

.close

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[alpine sable]

i did this integral by doing derivative (when u change variables). then i did parital differentation. but chat gpt says that it's really hard integral. have i done it right?

[minor needle]

What's your result?

[alpine sable]

x * e^arctgx - e^arctgx

[somber orchid]

Have you tried differentiating your result to double-check?

Also, don't trust AI assistants for this kind of stuff, they are often wrong

[alpine sable]

no i didnt. cause im not that good at it

[somber orchid]

How did you find your antiderivative? Did you recognize a familiar pattern?

[molten agate]

guys i need help in math for igcse

[minor needle]

,w d\dx (x * e^arctgx - e^arctgx)

[ocean seal]

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[lone heart]

Someone else is already using this help channel. If you need help with a question, please open your own help channel/thread (see #❓how-to-get-help for instructions).

[alpine sable]

it means that i did it rong?

wrong?

[toxic verge]

Can you show us your work?

[alpine sable]

yeah one sec then

[somber orchid]

Are you sure this is the correct exercise? Is it not this one you're willing to compute?
$$\int\frac{1}{x^2+1}e^{\arctan(x)}\mathrm{d}x$$

[ocean seal]

import matplotlib.pyplot as plt

[minor needle]

What's wrong here is that you firstly stated that u is arctan(x) and then that u is x

[toxic verge]

You can do it with the above one too (with x/(x^2+1) e^arctanx)

By parts first

Then u sub

[alpine sable]

lets see one sec

u mean i can solve it without uv-vdu

righr?

[alpine sable]

how i should solve it then

this is not working by sub

[toxic verge]

It isn't a valid integral.

[toxic verge]

Answer this.

[minor needle]

This substitution doesn't lead to anything nice, because x = tan(u) and the integral tan(u) * e^u isn't elementary I guess

[alpine sable]

should i leave it then without doing anything to it

[minor needle]

Besides, if you do a substitution, the integral after the substitution should only have the new variable in it.

[alpine sable]

my problem is this

[toxic verge]

No, show us the original question.

[minor needle]

This is how it works in general

[alpine sable]

this is the one which im solving and when u et to the pouint where u need to get answer for u

im getting this integral which sent to u

[toxic verge]

You are, or gpt is?

[minor needle]

Yea, it seems you indeed gonna obtain such an integral from the integrating factor

[alpine sable]

no

this is

differentatial equatoon

which im solving

and when u get to the point where u need to know answer for (u) im getting this complicated integral

and now im asking maybe i can leave it without solving it?

[toxic verge]

Is that the entire question?

[alpine sable]

this is apparently would be an answer

[alpine sable]

yeah

[toxic verge]

Yes, it would

[alpine sable]

but should i just leave integral

[toxic verge]

If you're just asked to solve the DE, then yes

[alpine sable]

oh

ok

ok if my

[toxic verge]

Wait 2 secs lemme just check one

[alpine sable]

v= e^ -arctgx

[toxic verge]

Ok yeah that is what you are getting

[alpine sable]

then y would be integral (e^arctgx * x / (1+x^2)) * e^arctgx

is this right?

[toxic verge]

Remember to take the IF to RHS

[toxic verge]

?

[alpine sable]

im saying about DE

[toxic verge]

Whys your e^arctgx in the numerator

[alpine sable]

my y would be this if im not solvin my integral

is this y correct?

are u here(((

[toxic verge]

How would your y be that

[toxic verge]

It would be this multiplied by 1/IF

[alpine sable]

what is f there?

what it stands for

[toxic verge]

Integrating factor

e^arctanx

[alpine sable]

u mean this would be an answer but i should multiply it by e^arctgx. right>

?

[toxic verge]

1/e^arctanx

[alpine sable]

oh yeah

but how i should find my integral then

uv-vdu?

[toxic verge]

This question is still weird. Are you 100% sure that is the complete question?

[toxic verge]

You cannot

[alpine sable]

yeah

[toxic verge]

Wanna see?

,w integrate e^(arctanx)

[alpine sable]

one sec dude i ll come back

[ocean seal]

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[toxic verge]

Does this make sense to you?

It's not something you can integrate.

[alpine sable]

actually not

[toxic verge]

Yeah

[alpine sable]

oh yeah i get it

[somber orchid]

,w solve (1+x^2)y'+y=x

[alpine sable]

but what i should do then

[ocean seal]

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[somber orchid]

You could also have looked at this too

This diff eqn is not really solvable...

[alpine sable]

oh shittt

[toxic verge]

Yeah gotta leave the integral of e^arctan in there

[alpine sable]

but this is would be on my exam paper

[somber orchid]

I mean it has solutions, but not ones that you can express easily

[toxic verge]

It's wrong

[somber orchid]

Is setting f to be an antiderivative of something and expressing the solutions in terms of f a satisfactory solution?

Without saying explicitly who f is?

[alpine sable]

should i just leave it like that?

then

[toxic verge]

Answer the question first

[alpine sable]

u mena this one

u actually dont have that deeep knowledge in these theories

[toxic verge]

That's not a deep knowledge question

[alpine sable]

.close

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[rigid tree]

Can someone please explain why the the boxed statement is true?? I alr asked for help yesterday but i dont quite understand

[south raven]

Because you already had (g(a+b)^2 – g(a)^2 – g(b)^2)^2 = 4 g(a)^2 g(b)^2 taking the square root gives g(a+b)^2 – g(a)^2 – g(b)^2 = ± 2 g(a) g(b); rearrange to g(a+b)^2 = (g(a) ± g(b))^2 and since every g(·) ≥ 0 we can drop the outer squares leaving g(a+b) = ± g(a) ± g(b)

[rigid tree]

oh yusm

tysm**

.close

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[velvet light]

Find the volume of the solid of revolution obtained by rotating the region bounded by the curves y =x^2 and y = 2-x^2 about the y axis

[velvet light]

i have a question but when ur rotating about the y axis, u use DY essentially so u flip your equations with x as the subject, so sqrt(y) and sqrt(2-y) then your integral is pi integral bounded by 2 and 0 sqrt (2-y)^2 - sqrt(y)^2 DY

the solution says its pi u^3 but im not getting that

[south raven]

I just worked out what you wrote before you edited it and it was a lot more difficult than that 😭

[velvet light]

sorry lol

[south raven]

We first find where the curves meet by solving x^2 = 2 - x^2 which gives x = ±1 so the region in the first quadrant runs from x = 0 to x = 1. Using the shell method take a thin vertical shell at position x: its radius is x (distance to the y axis) and its height is the upper curve minus the lower curve (2 - x^2) - x^2 = 2 - 2x^2. The volume of one shell is 2*pi*(radius)*(height)*dx so the total volume is 2*pi times the integral from 0 to 1 of x*(2 - 2x^2) dx. Expanding inside gives 2x - 2x^3; an antiderivative is x^2 - 0.5x^4. Evaluating this from 0 to 1 gives (1^2 - 0.5*1^4) - 0 = 1 - 0.5 = 0.5. Multiplying by 2*pi yields V = 2*pi*0.5 = pi. Therefore the solid of revolution has volume pi cubic units

[velvet light]

thank you

.close

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[robust oak]

Okay so my problem was to solve the differential equation and I just wanna confirm if all of the work I did in red is right or if not, where i made mistakes

[robust oak]

Wait I don't think I did the integral of e^(y+t^2) correctly

Oof

I just noticed that I assumed t was a constant

Wait but the integral on the left side is with respect to y

Hmmm

[south raven]

Write dy/dt = (e^{-y}/y)*e^{-t^2} Multiply both sides by y*e^{y} to get y*e^{y} dy/dt = e^{-t^2} Separate: (y*e^{y}) dy = e^{-t^2} dt Integrate to obtain e^{y}(y - 1) = 0.5*sqrt(pi)*erf(t) + C Your result e^{y+t^2}(y - 1) = t + C is wrong because the e^{t^2} factor belongs on the right not inside the left exponent

[robust oak]

Okay I get that process but I don't understand why mine is wrong

[south raven]

Your step kept the factor e^{t^2} inside the y integral so you ended up with e^{y+t^2}(y-1) on the left. but t is independent of y so e^{t^2} is a constant during that integration and should be pulled outside before integrating. once you do that the left side integrates to e^{y}(y-1) and the e^{t^2} factor stays on the right, giving e^{y}(y-1) = e^{t^2}(…)+C; dividing by the constant puts the correct form e^{y}(y-1) = 0.5*sqrt(pi)*erf(t)+C

[robust oak]

If that's just a constant wouldn't that still work though

I mean if you don't pull out the e^(t^2)

[south raven]

Because separation demands every y dependent term stay with dy and every t dependent term stay with dt the factor e^{t^2} (which depends on t) must be moved to the t side before integrating giving (y*e^{y}) dy = e^{-t^2} dt whose antiderivative introduces the error function erf(t) = (2/sqrt(pi))*int_0^t e^{-s^2} ds

[robust oak]

Oh wait I see now

I completely failed to separate correctly which I probably should have seen but whatever ig

Tyty

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[wild lagoon]

For this triple integral problem I'm having trouble understanding why the bounds for theta would be from 0 to pi, instead of from -pi/2 to pi/2 since the cylinder sits in the first and 4th quadrant.

[south raven]

sing cylindrical coords you can do it two equivalent ways: integrate once over the right half-plane (theta = –pi/2 .. pi/2) or integrate over just the upper half plane (theta = 0 .. pi) and then multiply by 2 to mirror the volume below the x axis which is what the worked solution does

[wild lagoon]

But when im integrating it im getting different solutions.

also I thought the 2 comes from the sqrt(36-r^2) since z = += sqrt(36-r^2)

[wild lagoon]

also if you were just integrating over upper half why would it be from 0 to pi/2 then multiplied by 2

this is an example in the textbook and the bounds are 0 to pi and this makes more sense to me since the cylinder would be in the upper quadrants

[south raven]

Since (x-3)^2 + y^2 = 9 gives r = 6 cos(theta) we need cos(theta) >= 0 so theta runs from –pi/2 to pi/2; writing it 0->pi just lets r flip sign and still traces the same circle. the front “2” merely doubles the upper hemisphere volume (z >= 0) to include the lower half; it is not coming from sqrt(36 - r^2)

[wild lagoon]

im calculating the integrals using symbolab and its giving two different solutions though.

[south raven]

Symbolab’s first set up (theta from –pi/2 to pi/2) is correct because r = 6 cos theta is non negative there so the integrand stays valid and it returns 72 pi

Thee second set up runs theta 0->pi and just multiplies by 2; over theta in (pi/2, pi) the cosine is negative which makes r negative and flips the integrand’s sign so Symbolab spits out a nonsense negative volume

[wild lagoon]

both volumes are positive tho

ok I think the textbook might be wrong. The answer its giving in the example problem doesn't match the integral given

[lavish cave]

no, the volume in the 2nd setup for theta in (pi/2, pi) becomes negative, which shouldn't happen

[wild lagoon]

evaluating the top integral doesnt give the bottom solution

[lavish cave]

yeah I think the solution forgot that that could happen to cos

I was scratching my head at what was going on too

but ash has pointed out everything really neatly, in ways which I couldn't do myself

[wild lagoon]

I think the solution and the textbook is wrong in this case.

thanks for the help. imma close it now

.close

[lone heart]

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[lone heart]

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[gloomy peak]

Question 5. Let the universe for the variables in the following statements consist of all real numbers.
In each case negate and simplify the given statement.
a) ∀x∀y[(x > y) → ∃z(x−y >z)]
b) ∀x∃y[(x < y) → ∃z(x < z <y)]
c) ∀x∀y[(|x| = |y|) → ∃z(y = ±x∧z = −1)]

I just want to check my answers, because chatgpt is not helping much

[lone heart]

@gloomy peak Has your question been resolved?

[woeful pulsar]

(a)why did the inside variable turn into x

[mint kindle]

Looks good, just a couple small nitpicks for a:
For the second to last step it should be ~∃z instead of ∃z~ on that last term.
And for the last step you accidentally wrote ∀x instead of ∀z

[gloomy peak]

oh oops

[woeful pulsar]

b double check negation of x<z<y

Remember $x<z<y$ is equivalent to $x<z\land z<y$

[ocean seal]

Element118

[gloomy peak]

whcihc rule is that?

[woeful pulsar]

Its called "syntactic sugar" in Python

[mint kindle]

Wait does python let you write conditionals like that?

[gloomy peak]

hmm how do i explain it, without knowing the rule

[woeful pulsar]

Yeah

[mint kindle]

Dang never knew that, python has so much random syntax lol

[woeful pulsar]

How do you understand x<z<y?

[gloomy peak]

I understand why its equivalent to that, but im just wondering why the way i wrote it isnt good. since wouldnt it be x>=z and z>=y ?

[woeful pulsar]

How do you negate a conjunction

[gloomy peak]

it becomes a disjunction and the statements are negations

[gloomy peak]

~∃z and ∃z~ the same? and should it be ∀z~? or just ∀z

[mint kindle]

It's not the same, since the inverse of an existential is the universal of the inverse.

[gloomy peak]

therefore it should be ∀z~?

[mint kindle]

Yes, although I would recommend adding ~∃ before that step so you can show every step

[gloomy peak]

like this!/

[mint kindle]

Yes, except you actually wait to perform the negation of what's inside the parentheses until the next step, since your negation would cancel out with what's inside to go back to how it was before but with a universal, which isn't correct.

[mint kindle]

Yep perfect

[gloomy peak]

thank you!

[mint kindle]

np

[gloomy peak]

where can i find all those extra rules? theyre not in our current lectures

[mint kindle]

"syntactic sugar" is a computer science phrase to mean syntax that makes it easier to write certain things. So here a < b < c doesn't do anything special beyond just being a cleaner way to write a < b & b < c. So it's not really a "rule" as much as just notation.

[gloomy peak]

okay makes sense

so would the negation be x>=z and z>=y

i mean or

[mint kindle]

Yep it would be or

[gloomy peak]

alright

one last question

Question 6.) If p,q are primitive statements, use duality theorem to prove that
(p →q)∧(q∧p∨True) ≡ (p∧q)

this is what i have so far

I know ~p or p is p, but then theres still the "and" false. But im trying to get p from (p and p) or (p or p) or aP ∨False ⇔ P
P ∧True ⇔P

[mint kindle]

I'm not sure what the duality theorem is, could you paste the theorem here?

[mint kindle]

Hmm it seems like the goal is to get "p or q <-> something" so we can use duality theorem. But I'm not too sure how to get there tbh

I have to get going but hopefully someone else can help you finish up!

[gloomy peak]

ok thank you

[lone heart]

@gloomy peak Has your question been resolved?

[lone heart]

@gloomy peak Has your question been resolved?

[lone heart]

@gloomy peak Has your question been resolved?

[lone heart]

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[coarse crag]

Why is this considered incorrect?

,rotate

[sand cave]

did you cancel the h at the denominator because it's a 0 or did you do smth else?

[vale wigeon]

$\frac{2hx+h^2}{h} \neq 2hx + h$. you fumbled the fraction cancellation

[ocean seal]

Ann

[vale wigeon]

idk why the channel's not opening in any of our names

[lunar saddle]

bot down ig

[vale wigeon]

lets test it

!status

oh hm yeah she's down

[lone heart]

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[coarse crag]

hey

bot down?

[vale wigeon]

bot still struggling apparently

[coarse crag]

oh yes i did cancel it out

i cant do that?

[vale wigeon]

you can do it when the numerator is h * (something)

but like generally $\frac{ab+c}{b} \neq a+c$ yknow

[ocean seal]

Ann

[coarse crag]

why not?

[coarse crag]

can u texit it what you mean

[vale wigeon]

i can give you an example with numbers where it very clearly doesn't work

if you want

or i could tell you what the correct cancellation is

take your pick

[coarse crag]

this

[coarse crag]

is that because if the h gets canceled on the denomiator, it would be 0? or 1?

[vale wigeon]

$\frac{2hx+h^2}{h} = \frac{h \cdot (2x+h)}{h} = 2x+h$

[ocean seal]

Ann

[coarse crag]

oh yes i have the answer to that now but im just wondering why we cant do this?

[coarse crag]

,help

[ocean seal]

A brief description and guide on how to use me was sent to your DMs!
Please use ,list to see a list of all my commands, and ,help cmd to get detailed help on a command!

[coarse crag]

,ticket

[vale wigeon]

ok yknow what @coarse crag i think we should move to #precalculus or something

[ocean seal]

169 members found matching cket!

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========
1.   myyra (@pocketfullofmoonshine)
2.   pocket (@pocket4466)
3.   Cricket (@cricket3308)
4.   rocket_browser (@rocketnobrowser)
5.   pocket8476 (@pocket84762315)
6.   rocketman (@jubiden)
7.   Rocket (@just_rocket)
8.   bracket (@tekcarb)
9.   Philip_Puckett45 (@philip_puckett455768)
10.  Jacket (@xeeronull)
11.  XxJacketedSauce92xX (@nutboy7776)
12.  Rickettsia37 (@rickettsia376531)
13.  Benjaminpockett (@benjaminpockett)
14.  RockeTeK (Emile) (@rtk16)
15.  Pocket (@pocketdom)
16.  magimissatuklong? (@bucketomoleratmilk)
17.  BlasterBucket... (@blasterbucket)
18.  rocket (@rocketdc_)
19.  Bishop8 (@rocketpocket_88)
20.  Bucketz (@bucketz1712)```
Please type the number corresponding to your selection, or type `c` now to cancel.

[vale wigeon]

cause bot's down right now

and help channels are a bit borked

[coarse crag]

this bit lmao

[terse grotto]

There's so much :(

[coarse crag]

ightt

[terse grotto]

This is so sad

[coarse crag]

what is so much ?

[ocean seal]

Member selection timed out.

Jun 20, 2025, 1:40 PM

[terse grotto]

There's so much in queue

Or is this not a queue

,help

[ocean seal]

I can't DM you! Do you have DMs disabled?

Jun 20, 2025, 1:41 PM

[terse grotto]

Do i?

,help

[ocean seal]

A brief description and guide on how to use me was sent to your DMs!
Please use ,list to see a list of all my commands, and ,help cmd to get detailed help on a command!

[terse grotto]

,ticket

[ocean seal]

169 members found matching cket!

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========
1.   myyra (@pocketfullofmoonshine)
2.   pocket (@pocket4466)
3.   Cricket (@cricket3308)
4.   rocket_browser (@rocketnobrowser)
5.   pocket8476 (@pocket84762315)
6.   rocketman (@jubiden)
7.   Rocket (@just_rocket)
8.   bracket (@tekcarb)
9.   Philip_Puckett45 (@philip_puckett455768)
10.  Jacket (@xeeronull)
11.  XxJacketedSauce92xX (@nutboy7776)
12.  Rickettsia37 (@rickettsia376531)
13.  Benjaminpockett (@benjaminpockett)
14.  RockeTeK (Emile) (@rtk16)
15.  Pocket (@pocketdom)
16.  magimissatuklong? (@bucketomoleratmilk)
17.  BlasterBucket... (@blasterbucket)
18.  rocket (@rocketdc_)
19.  Bishop8 (@rocketpocket_88)
20.  Bucketz (@bucketz1712)```
Please type the number corresponding to your selection, or type `c` now to cancel.

[coarse crag]

just. dm me the bot is down atm

[terse grotto]

Thank uu

[ocean seal]

Member selection timed out.

Jun 20, 2025, 1:45 PM

[lone heart]

@jolly vortex Has your question been resolved?

[jolly vortex]

Yes

[lone heart]

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[night ruin]

.reopen

[lunar saddle]

.this is open already

[runic grove]

Hey, i need help for my Math presentation. The subject is : ‘How did the Weierstrass’ monstrosity function revolutionize the esthetics side of maths and the analysis side of maths’(Im french so i had to do my best to translate the subject im going to talk about). Right now, besides talking about the history of the function and talk about how the function is formed, i dont have much else to say.

[lone heart]

@runic grove Has your question been resolved?

[placid zinc]

Why do we care about the function? What does this tell us about functions in general?

[lone heart]

Channel closed

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[runic grove]

.reopen

[lone heart]

✅

[runic grove]

hey its like the subject i chose for my presentation

[lone heart]

@runic grove Has your question been resolved?

[lone heart]

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[nocturne marsh]

to avoid falling down which direction should the man move?

[jaunty olive]

The floor is smooth yeah?

[nocturne marsh]

yeah

[jaunty olive]

What do you think it is

[somber orchid]

Is that really a maths question?

[nocturne marsh]

maths=physics

[jaunty olive]

There's loads of physics questions asked on a daily basis

It's fine

[nocturne marsh]

to right

[somber orchid]

Well, sure, a physics question might be answered here, but does the question posed as is warrant maths?

[jaunty olive]

But if there are people who know how to solve it, why not let them help them

[jaunty olive]

Why?

[nocturne marsh]

then the trolly will move opposite?

[jaunty olive]

And why is that?

[nocturne marsh]

idk

[jaunty olive]

[nocturne marsh]

thatwhat i want to know

[jaunty olive]

Do you know about something called center of mass

[nocturne marsh]

center of gravity?

no

[jaunty olive]

Well in a lot of cases center of gravity = center of mass

So they're almost the same

[nocturne marsh]

ok then?

[jaunty olive]

So you know it or not?

[nocturne marsh]

know

[jaunty olive]

Ok then look at center of mass of man and trolly system

Since friction between man and trolly is internal, we don't include it while drawing fbd

Can you tell me what horizontal forces act on the center of mass of the system

[nocturne marsh]

the center of mass must constant?

[jaunty olive]

We're getting to that

Let's progress a bit slowly

[nocturne marsh]

man+trolly weight

[jaunty olive]

Is it horizontal though?

[nocturne marsh]

sorryy

[jaunty olive]

Np

[nocturne marsh]

friction?

[jaunty olive]

Where's the friction?

[nocturne marsh]

from foot

[jaunty olive]

Yeah but thats internal right?

[nocturne marsh]

ahh ok

[jaunty olive]

Because we're now looking at man and trolly system as a whole

[nocturne marsh]

then what?

[jaunty olive]

Not just man

[nocturne marsh]

ok

[jaunty olive]

Well since you mentioned that the floor is smooth, then there's no friction between trolly wheels and ground

So basically
No horizontal force on the system

[nocturne marsh]

ok

[jaunty olive]

Hence Fnet(horizontal) = 0

[nocturne marsh]

then it move uniform velocity

?

[jaunty olive]

No no

Position of Center of mass will always remain constant

The man and trolley however, will move

[jaunty olive]

This is because no horizontal force acts on the system

Note that this is only true for HORIZONTAL direction

[nocturne marsh]

but when move a force is excert by the foot?a push while move?

[jaunty olive]

Ahh but we're looking at man and trolley as a whole yeah?

Look at it this way

[nocturne marsh]

hehe

[jaunty olive]

The man exerts a force on the trolley

[nocturne marsh]

ok

[jaunty olive]

And trolley exerts an equal but opposite force on the man

So net it cancels out when looking at the system

[nocturne marsh]

okok

[jaunty olive]

So center of mass is conserved along x direction

So if man moves to the right, the trolley would have to move to the left, thus saving you from eternal misery

[nocturne marsh]

didnt getit

[nocturne marsh]

.

[jaunty olive]

Center of mass of system is fixed yeah?

[nocturne marsh]

yeas

[jaunty olive]

(Moves the center of mass to the right as well)

[nocturne marsh]

ahh

[jaunty olive]

So the trolley, moves to the left, to balance the change in center of mass' position

[nocturne marsh]

so trolley move same to cancel it

[jaunty olive]

Moves opposite

Not same

[nocturne marsh]

ok

[jaunty olive]

But yeah

[nocturne marsh]

thats why it go oppesite

ok

[jaunty olive]

Yes

[nocturne marsh]

is there a relation with momentum

[jaunty olive]

Yeah

If Fnet = 0, then pnet = constant since Fnet = d(pnet)/dt

So delta (pnet) = 0

So momentum is always conserved if sum of all external forces is 0

[nocturne marsh]

ok.

got it thank you

.close

[lone heart]

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[formal wren]

Even symbolab gave up idk how to proceed

[vale wigeon]

looks ugly af, where did you get this

[formal wren]

Please don't ask 💔

[daring zenith]

have you tried u = tan x

or similar

[formal wren]

Tried 1+√tanx = u

But it gets kind of even more confusing to isolate x

Then it becomes integral of ( (arctan( u² +1 -2u) )/u² ) du and I have no idea how to proceed from here

[tacit arch]

why do you think there's an answer then

[minor needle]

Wolfram did it

So it's doable

[hushed locust]

,w integrate x sec^2 x / (2 (1 + sqrt(tan x))^2 * sqrt(tan x))

[ocean seal]

Results provided by WolframAlpha

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Requested by cloudedhorizons

[dawn zephyr]

u = sqrt(tanx)
du = sec²x/(2sqrt(tanx))

[dawn zephyr]

seems easy from here

[red nacelle]

LOL

[toxic verge]

Yet another one of these people

Why can't yall stop

[dawn zephyr]

oh nvm, there's an x I didn't account for

[daring zenith]

no limits?

[toxic verge]

Like just stop saying "hardest integral pls" to gpt

[formal wren]

no

Brochacho if u don't wanna help that's alright

[dawn zephyr]

whats wrong..

[toxic verge]

Nothing nm

I just feel it's definitely a !xy

[formal wren]

yep i don't have any idea how to proceed further even if I take a substitution

[dawn zephyr]

gotta do IBP ig 🌚

Im gonna leave that up to you

tbh, it looks more like a "normal" or "standard" question without the x

[formal wren]

intuition

[minor needle]

IBP leads to integral of 1/(1+sqrt(tanx))

[tacit arch]

yea use this and FTC

[minor needle]

Which is still pretty hard to do, but doable

You have to suffer to solve it and that's all

[formal wren]

Waig i think I caught on

[lone anvil]

I think by parts

[lone heart]

@formal wren Has your question been resolved?

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