help-39

[odd mauve]

@random horizon gonna ping so you know

[dapper kraken]

remember x=sqrt(2025-r^2)

[odd mauve]

yh

[odd mauve]

yeah

thats why i did

^0.5

stockholm

[odd mauve]

Im having a hard time taking the derevative

ik how to solve it

[dapper kraken]

try doing it interms of x instead of r

[odd mauve]

that would give me height?

[random horizon]

ya i will help u

[odd mauve]

i dont need it tho

[odd mauve]

ty

[random horizon]

why

[odd mauve]

if i find r

it will be mcuh faster?

[random horizon]

just a minute

[dapper kraken]

both works, if you do it interms of x the derivative is easier to get

[odd mauve]

i see

[odd mauve]

so you mean to substitute r with (45^2-x^2)^0.5

or whatever

it was

instead of x?

[random horizon]

V=1/3pir^2*x

x=sqt(45^2-r^2)=sqrt(2025-r^2)

[dapper kraken]

yes

[random horizon]

V=1/3pir^2sqrt(2025-r^2)

right?

[odd mauve]

how is pir^2 at the bottom?

should it be at the top or am i tripping

[random horizon]

sorry

pir means 3.141592

[odd mauve]

ok then what do i do after that

[odd mauve]

yeah

[random horizon]

if r= 25cm ,max volume V=1/33.1425^2*sqrt(2025-25^2)

[odd mauve]

huh

r = 25?

[odd mauve]

could you help me derevate this too

[random horizon]

please another problem

[odd mauve]

wdym

[random horizon]

complex problem

[odd mauve]

its not hard bro

i just want the derevative

[random horizon]

i know

sorry where r u from?

[odd mauve]

sweden

[random horizon]

yaaa wonderful

[odd mauve]

??

bro cmon i got a test

[random horizon]

what do u doing now?

👍

[odd mauve]

solving that problem

man

[random horizon]

are u man or woman?

[odd mauve]

bro

why u asking all these questions for

[rough forge]

interrogation

[odd mauve]

solve my question please

if ur smart

[random horizon]

I want to be close to you.

I am freelancer and I would be able to help u with my skill.

[pearl pond]

@odd mauve Has your question been resolved?

[rough forge]

waste of time

[pearl pond]

@odd mauve Has your question been resolved?

[odd mauve]

🥶

so sigma

[pearl pond]

@odd mauve Has your question been resolved?

[pearl pond]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

[pearl pond]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• 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.

[smoky cairn]

I would like to design a neural network that is the "parameterized" operator of a commutative monoid. I'm not 100% sure about the terminology, so I'll explain what I want:

I have a set of vectors of cardinality n and would like to reduce it to a single vector with a time complexity linear in n. I want that reduction process to be invariant to permutations of the set, and to be able to be done "online" / in a streaming fashion (meaning I would not have the entire set available at a given time but only the current aggregated vector and the "latest" vector).
Some example of operators that would fit are element-wise addition, maximum and mean. For those familiar with transformers, attention would not work as it has a n^2 time complexity. However, I don't know which operator is best for a given problem and would therefore like the neural network to learn one based on the data and the objective of the optimization process.

When it comes to making the operator commutative, one way would be to have the output of the system be o(x,y) = (f(x,y) + f(y,x)) / 2 with f being the learned operator (the actual neural network). That is however undesirable as we are doing twice the amount of computation (imagine the network ends up just being the addition, that would be a waste of compute).
As for associativity, I don't see a better way to get it than with some regularization on the loss we're optimizing against, and that would at best give me an approximately associative operator which is not what I want.

I don't have a precise question, but I would like any information / pointers that would help me think about this problem in the right way

[pearl pond]

@smoky cairn Has your question been resolved?

[pearl pond]

@smoky cairn Has your question been resolved?

[pearl pond]

@smoky cairn Has your question been resolved?

[pearl pond]

@smoky cairn Has your question been resolved?

[pearl pond]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• 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.

[jade moss]

is there a faster way to solve instead of plugging in and checking like my professor said

[fossil jewel]

plug and check every real between 0 and 2pi, thats what i always do

[jade moss]

damn it

i would think there is a quicker and more efficent way

[robust kraken]

let $\theta$ be this angle i think i’ll do $tan(\theta)=\sqrt{3}=\frac{\frac{\sqrt{3}}{2}}{\frac{1}{2}}$ so this angle is pi/3

uh wait

[jolly parrot]

tm

[robust kraken]

but idk if it’s correct

[compact ridge]

well you know that tan(first quadrant angle) = positive number

so applying inverse tan to both sides

$\text{1st quadrant angle} = \tan^{-1} (\text{positive number})$

[jolly parrot]

south

[compact ridge]

you should know how to solve tan(x) = sqrt(3) then

[pearl pond]

@jade moss Has your question been resolved?

[pearl pond]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

[pearl pond]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• 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.

[grave parcel]

can i get help please

[grave parcel]

its calculator assumed, casio classpad is allowed

idk how to get started

[compact ridge]

say if I have y = 2 and y = 5, what's the vertical distance between?

[grave parcel]

3??

[compact ridge]

yep

so now you have y = f(x) and y = g(x)

and also you know that g(x) is entirely above f(x), g(x) > f(x) for all real x

[grave parcel]

do we find tp

[compact ridge]

yes!

[grave parcel]

of ramp walkway

and supporting cable

[compact ridge]

the turning point would give you the minimum distance

[compact ridge]

you need to set up the right quadratic though

like before you did 5 - 2 = 3 right

[grave parcel]

yes

[compact ridge]

so now from that, what's the right function to minimise

[grave parcel]

wdym??

[compact ridge]

you're not minimising f(x) alone

you're also not minimising g(x) alone

[grave parcel]

sorry im abit confused

[grave parcel]

i understand all the way till this

[compact ridge]

yeah so you did (second function) - (first function) right

first function was y = 2, second function was y = 5

[grave parcel]

is the 5 and 2 random numbers??

[compact ridge]

yes

but it's easier to think of numbers first

then carry over the same logic into functions

[grave parcel]

so do we do ramp walkway - supporting cable

[compact ridge]

it's the other way around actually

supporting cable - ramp walkway

[grave parcel]

oh yeah

[compact ridge]

yeah and then find the vertex and then sub the x-coordinate in to find y

[grave parcel]

wait so how do i first start off??

[rain vessel]

Abs(Y1-Y2), find the min of this function

[compact ridge]

oh right, you need to convert this to algebra

[grave parcel]

yeah

[compact ridge]

literally, $(0.003x^2 - 0.186x + 25.18) - (-0.001x^2 + 0.062x + 18.04)$

[grave parcel]

i see

[jolly parrot]

south

[grave parcel]

@compact ridge can i ask a question rq

[compact ridge]

yea?

[grave parcel]

can we do this faster by using casio classpad??

[compact ridge]

oh yeah your GDC can absolutely find the vertex for you

[compact ridge]

you just graph this

[grave parcel]

yeah as its calculator allowed

[compact ridge]

yeah

[grave parcel]

do i just type that in

[compact ridge]

usually a lot of maths at this level is only scientific calculator allowed

[compact ridge]

yeah

[compact ridge]

cause it's better for students to practice algebra then forget it, than to never learn it properly

[grave parcel]

its high school maths so we allowed graphic calculator atm

[compact ridge]

you're lucky

[grave parcel]

ok i graphed it

how do i find vertex

[compact ridge]

I don't know your model of calculator, sorry

so go look up a YT tutorial

there should definitely be a menu item for extrema or something

[grave parcel]

wait so am i finding the vertical distance??

[compact ridge]

yeah

[compact ridge]

and from before, that's the y-value of the vertex of

[grave parcel]

then that’s all??

[compact ridge]

yep

[grave parcel]

ty

.close

[pearl pond]

Channel closed

Closed by @grave parcel

Use .reopen if this was a mistake.

[compact ridge]

a lot of maths problems are use your brain / learn this new technique

then algebra bash, or GDC bash

i.e getting to the algebra means you've done the hard part

[grave parcel]

oo

ty bro

[compact ridge]

no worries again mate

[grave parcel]

.reopen

[pearl pond]

✅

[grave parcel]

can you actually double check my answer

i. got (18.7, 3.90116)

so vertical distance would be 3.90116 right??

is that correct

[compact ridge]

should be 3.296, which rounds to 3.30 to 2 dp

[compact ridge]

https://www.desmos.com/calculator/rjt6fuxqwb

[grave parcel]

ahhh

[compact ridge]

plot and then click on the vertex

you can check it yourself! Desmos is an easier way to do the same things as on your GDC

[grave parcel]

i did 0.004x^2 - 0.248x + 7.14

[grave parcel]

from subtracting that

[compact ridge]

I don't think I typed it wrong, which is also another thing

"why is Desmos giving me the wrong answer!??"

[compact ridge]

yeah that's correct

if you really try x = -b/(2a) for the vertex Desmos tells me it gives the same

[grave parcel]

it doesn’t give me the answer u got

[compact ridge]

calculator error somehow, idk

[grave parcel]

sigh

anyway

the next question says

what is the closest distance that the ramp walkway is to the water surface

there would be 2 answers ye

we need to find the x dont we??

[compact ridge]

no, that's another y-value

[grave parcel]

oh wait nvm i’ve got it i’ll solvethat myself

ty dude

.clos

.close

[pearl pond]

Channel closed

Closed by @grave parcel

Use .reopen if this was a mistake.

[compact ridge]

appreciate the thanks

[pearl pond]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• 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.

[hasty edge]

Elaborate.

You want to expand this, or what exactly?

I'm asking because I'm confused on what exactly you're trying to do with the function.

x<-1/4, then.

🤨

How did you get that?

Ah well

To answer your question, yes you take the more restrictive inequality

1+4x

I cannot tell

[pearl pond]

@orchid ore Has your question been resolved?

Channel closed

Closed by @orchid ore

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• 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.

[grave parcel]

can i get help please i dont know how to start

[sharp smelt]

Define turning point

Also, this isn't a test, is it?

[grave parcel]

it isn’t a test.

[grave parcel]

the peak of the parabola

basically

[sharp smelt]

Do you know calculus?

[grave parcel]

i dont think i need calculus for this

[naive pond]

Don’t go there

[grave parcel]

ye i definitely dont need calculus

[sharp smelt]

It is useful

but not needed

[grave parcel]

i dont need it for this

[naive pond]

Just use the formula $\frac{-b}{2a}$

[jolly parrot]

747244351179980930

[naive pond]

That will give you the x value of the turning point

[sharp smelt]

yeah, and that is obtained using calc, is it not?

[hasty edge]

Well that's a bit misleading 💀 (relative to the question)

[grave parcel]

-b/2a = 3

[naive pond]

There’s like 5 different ways you can obtain it

[hasty edge]

Recall that this is for ax^2+bx+c.

[grave parcel]

guys one at a time

who is helping me??

[naive pond]

You can find it through the midpoint of the roots, setting the derivative to 0, using the vertex form and plugging in values from standard form

But anyways yeah

Uhh so this problem is different actually

[grave parcel]

yeah i dont get that entirely

[naive pond]

I didn’t read it all nvm

[naive pond]

Don’t worry about what I said here

So, the “turning point” in this scenario is going to be in the middle of the two roots of the equation

[fierce sky]

$$\frac{\left(a+b\right)}{2}=3,
-4 = 3^{2}-3\left(a+b\right)+ab$$

[naive pond]

So, we know that 3 is the midpoint of the line formed by the two roots

[grave parcel]

yes

[jolly parrot]

Roy

[grave parcel]

cause it’s the line of symmetry

[grave parcel]

CAN U CUT IT OUT

nvm

what do we do next??

[naive pond]

You can use the vertex form of a quadratic to solve this actually

[grave parcel]

yes, but they want it in factored form i think

[naive pond]

True, but you can use it to solve for the roots

We know the vertex and the “a” value

And from there we can set it equal to 0

[grave parcel]

a(x-3) - 4

[naive pond]

Yes. In this case, a=1

[grave parcel]

how do we know a =1??

[naive pond]

If you multiply this out, you will get an x^2 term with a coefficient of 1

[grave parcel]

ah gotchu

so now do i find the zeros??

[naive pond]

Set $(x-3)^2-4$ equal to 0

[jolly parrot]

747244351179980930

[grave parcel]

yes

x = 5

or

[naive pond]

Because that will give you the roots of the equation

[grave parcel]

x = 1

[naive pond]

Exactly

[grave parcel]

oh shoot that easy

wait that’s wrong i think

[naive pond]

Oh I know why

[grave parcel]

nvm its correct

a and b can be either 1 or 5

[naive pond]

Wait nvm

[grave parcel]

cause it doesn’t state if b or a is bigger

[naive pond]

I forgot it’s (x-a)(x-b) instead of (x+a)(x+b)

[naive pond]

Yeah

[grave parcel]

answer will still be 5 and 1

since (x-5)(x-1)
= x-5 = 0
x-1 = 0

x=5
x=1

[naive pond]

And by the communitive property of multiplication $(x-5)(x-1)=(x-1)(x-5)$

[jolly parrot]

747244351179980930

[grave parcel]

what’s this

[naive pond]

Basically if you multiply two numbers together, you can flip them around and their product will be the same

[grave parcel]

oh yeah i see

[naive pond]

$a\cdot b=b \cdot a$

[jolly parrot]

747244351179980930

[naive pond]

But yeah that should be the right answer

[grave parcel]

ty dude

i appreciate it

[naive pond]

Yw

[grave parcel]

idk why we would have needed calculus

.close

[pearl pond]

Channel closed

Closed by @grave parcel

Use .reopen if this was a mistake.

[pearl pond]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• 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.

[sharp smelt]

To prove it's conservative, I have to prove it's the gradient of some continuous function

so

[inland ivy]

just take the integral of both pieces I'd imagine

[sharp smelt]

$f(x,y) = \begin{cases} yx & (x,y) \in R \ x^2 & (x,y) \in L \end{cases}$

does that work

[inland ivy]

try taking the gradient

do you retrieve F?

[sharp smelt]

I did

oops

This gives (x,y) in R

[jolly parrot]

What a wonderful world !

[sharp smelt]

Does this work?

[pearl pond]

@sharp smelt Has your question been resolved?

[sharp smelt]

<@&286206848099549185>

Can I please have my answer verified

.close

[pearl pond]

Channel closed

Closed by @sharp smelt

Use .reopen if this was a mistake.

[lilac jackal]

.reopen

[pearl pond]

✅

[lilac jackal]

@sharp smelt yes

tbh u can check ur own work by gradient

its just like differentiating in calc1 to check integral results

[sharp smelt]

fair

thanks

[lilac jackal]

np

[sharp smelt]

I'll close this now

[lilac jackal]

.close

[pearl pond]

Channel closed

Closed by @lilac jackal

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• 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.

[wise burrow]

help im bad at trigonometry

[toxic lichen]

interesting problem...

[lilac jackal]

IVP with 7 initial conditions

[crude nexus]

Bruh

[toxic lichen]

i have what i believe to be a pretty elegant but also kinda complicated solution

well

conceptually complicated

given it involves a good deal of linalg...

[pearl pond]

@wise burrow Has your question been resolved?

[toxic lichen]

ok so in case anyone's interested in what im cooking, ive sorta reduced this problem to finding the -7th power of a particular 3x3 complex matrix that turns out to be upper triangular and with unit diagonal

im actually cooking

[fierce sky]

i integrated it 7 times

[toxic lichen]

ain't nobody got time for that

[vagrant briar]

i think a pattern should emerge after integrating a few times right?

then we can figure out f(x)

[pearl pond]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

[toxic lichen]

.reopen

[pearl pond]

✅

[toxic lichen]

hold on i am thoroughly nerdsniped by this shit

im not gonna dump the answer out

but istg i am almost there

oh i am way more cooked than i realized

💀

i was inverting the wrong fucking matrix

dear lord

[pearl pond]

@wise burrow Has your question been resolved?

[toxic lichen]

dear lord ok

this was TOUGH

but i think i finally fucking got it

after like 2+ pages of matrix arithmetic

but honestly? what i did beats having to do 7 integrations by a LONG shot.

[pearl pond]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• 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.

[little spear]

is there a way to turn this into an integral? i wanna check if the limit exists

[little spear]

or if you have a better way to find if the limit exists then please enlighten me

[pearl pond]

@little spear Has your question been resolved?

[toxic lichen]

ok so like

[lilac jackal]

approximate the sum as $\int_0^{n^2}f(k)dk$ where $f(k)$ is the summand

[jolly parrot]

ロケットジャンプ

[toxic lichen]

if you squint hard enough

[little spear]

not allowed

no approximation

[toxic lichen]

the general term of the sum looks like 1/n^2

so you can try and look at the difference between the actual general term and 1/n^2

[lilac jackal]

i mean if u ask about integrals then u can only approximate

[toxic lichen]

i cooked something

actually it is even simpler

[little spear]

would you suggest doing the limit convergence test between this and 1/n^2 ? do i show that the sum behaves like 1/n^2 so if it goes to +- inf then the limit goes to inf, if the sum goes to a finite value then the limit too?

hang on i cant know if the sum goes to a finite value we didnt learn that

well we did we didnt learn which finite vlaue

[lilac jackal]

maybe just do a change of var and integral comparison

[toxic lichen]

no im suggesting purely algebraic machinations

no integration at all even

[little spear]

i meant the integral test

so like i can do all the convergence tests

i just cant say "this behaves like this"

or cant i

hmm its harder but not impossible if i do it via the limit comparison test

[lilac jackal]

id wait for anns thing

[lilac jackal]

but i need to die now. i have to wake up early

[little spear]

sweet dreams :>

[lilac jackal]

[hazy pilot]

litteraly what I meant with "taking the n's" out

[little spear]

why can we take the n^2/n^4+sqrt(n) out

[toxic lichen]

brackets

[little spear]

also how did n^2 become n^4

[toxic lichen]

but also wdym

n is constant wrt k

[little spear]

oh

true

[hazy pilot]

btw, since this is a limit, you can only split it into 2 terms if they converge

both converge

[toxic lichen]

we are adding up n^2 terms all of which equal n^2/(n^4+sqrt(n))

[toxic lichen]

nope i am doing purely algebraic manipulation WITHIN the limit

[little spear]

the bounds, you can split the bounds not the integrand

[toxic lichen]

finite summations etc

[little spear]

i dont think i understand

[toxic lichen]

$\sum_{k=1}^{420} 69 = 420\cdot 69$

[jolly parrot]

Ann

[little spear]

that i do understand

OH

[toxic lichen]

$\sum_{k=1}^n n = n^2$

[jolly parrot]

Ann

[little spear]

yes yes yes

[toxic lichen]

$\sum_{k=1}^n f(n) = nf(n)$

[jolly parrot]

Ann

[toxic lichen]

yaeh

thats the idea here

[little spear]

ok we didnt learn this but its not hard. thanks !

[toxic lichen]

do you need me to also explain how to handle the other sum

cause i cooked something up for that as well

[little spear]

isnt it a geometric series up to n^2?

[toxic lichen]

it is not

nowhere near a geometric series

[little spear]

wait

i didnt say that

[toxic lichen]

if it were (number)^k inside the sum then yes, but it's k^(number) instead -- very different

anyway

[little spear]

i know i know im bluffing right now haha

[little spear]

can we say that the value of a sum is the same as the value of an integral of the function of the series in that sum

[toxic lichen]

mmmmmmmm

what.

[little spear]

wait actually

how do we evalue the k one

[toxic lichen]

i have no idea what you tried to ask there genuinely

[little spear]

yeah ignore that

[hazy pilot]

answer is 1

[toxic lichen]

i just showed how i squeezed a riemann sum out of $\frac{1}{n^4+\sqrt{n}} \sum_{k=1}^{n^2} \sqrt{k}$

[jolly parrot]

Ann

[toxic lichen]

@little spear do you understand this image?

[little spear]

im processing it

[little spear]

okay, so a riemann sum is the sum up to n (in this case n^2) of f(xi)dx where dx is b-a/n^2. b-a here is 1 since its from 0 to 1 and thats the 1/n^2 part?

[toxic lichen]

(b-a)/n^2 but yes

im integrating from 0 to 1

1/n^2 is the subinterval width

and x_k = k/n^2

[little spear]

the one in the root right?

if so, shouldnt it be n^4? so that sqrt(n^4) = n^2 ? then we have dx = b-a/n^2?

[toxic lichen]

no, the subinterval width appears outside the function -- and i put it outside the summation entirely

$\int_0^1 g(x) \dd{x} = \lim_{n\to\infty} \frac{1}{n^2} \sum_{k=1}^{n^2} g\paren{\frac{k}{n^2}}$

[jolly parrot]

Ann

[toxic lichen]

g(x) = sqrt(x) in this case

[little spear]

oh

i see what you mean. this wasnt covered in depth in lectures nor is it relevant for the exams but doesnt hurt to know 😂

thank you and sorry if i BSed too much 🙏🏻

[toxic lichen]

i mean this is just riemann sums

only you've got n^2 subdivisions instead of n, which is a bit of a complicating factor but not impossible to handle

[little spear]

we did go over them but we didnt manipulate them or anything, we just had them quickly skimmed so that we know the definition of an integral

[toxic lichen]

...right

yeah i mean the stuff i cooked up is like

i wanna say surgically precise

but maybe thats not the best way to describe it

but it did take some know-how for me to find this solution

[hazy pilot]

what is the solution then?

[toxic lichen]

well i can repost the same thing that i did but in full if you and/or @little spear want it

[hazy pilot]

I mean, what is the limit equal to? That is what I was interested in 😅

You don't have to repost the whole thing

[toxic lichen]

well the first summation goes to 1 and the second goes to 0

[hazy pilot]

yeah so it is equal to 1

[toxic lichen]

yes

[hazy pilot]

great then my solution was also correct, I was a bit stressed XD

[toxic lichen]

the reason i 'd you earlier is because it was too early to share that

[hazy pilot]

My apologies

[little spear]

i found an official solution

[toxic lichen]

interesting

they went an entirely different route

with bounding and shit

[stuck knoll]

its the tringineer

[little spear]

yeah this is calculus 1 and were engineers haha

[toxic lichen]

tringineer?

[stuck knoll]

trinity

[little spear]

oh hello

[stuck knoll]

hello

are u ib

or is it like iib

idk how engineering works

[little spear]

wait lets move to general

[stuck knoll]

ok

[toxic lichen]

close this then?

or what

[little spear]

.close

[pearl pond]

Channel closed

Closed by @little spear

Use .reopen if this was a mistake.

[pearl pond]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• 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.

[grave parcel]

how do this

i dont know how to get started

i’ve looked at y=a(x-2)^2+1

and know that the turning point is (2,1)

[toxic lichen]

so you know that y=a(x-2)^2 + 1 is parabola C, yes?

[vernal iron]

You can identify the graphs with calculating their turning points

For example, for the first equation, the turning point is -0.5 ( -b/2a => -2/2(2) = -0.5 )

After identifying the graphs, you can create the equations with this formula: a(x²-Sx+P) with S being the sum of roots and P being the product of multiplying the roots, and in order to get a, you can use the coordinates of the turning point

Then after creating the equation yourself, you can compare it with the given equation and get the values

[pearl pond]

@grave parcel Has your question been resolved?

[pearl pond]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

[pearl pond]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• 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.

[pulsar stump]

is $0 \neq 1$ in integral domains a requirement? i cant find it mentioned in wikipedia

[jolly parrot]

Regulus

[proper dove]

I think

Its convention

[unkempt yacht]

can you elaborate?

[proper dove]

Is zero ring an integral domain

[pearl pond]

@pulsar stump Has your question been resolved?

[rose robin]

0*a = 1*a, 1 is the multiplicative identity, so 0*a = a

because an integral domain is a ring, a*(b+c) = a*b + a*c
letting c=0, a be non-zero, and b be the inverse of a
a*(b+0) = a*b + a*0
0 is the additive identity, so on the LHS, a*(b+0) = a*b = 1
but on the RHS, it's 1 + a
so 1 = 1+a
but 1 = 0, so 1 = 1+a = 0+a = a
so 1 = 0 = a, which contradicts that a is non zero```

I just looked up the definition of integral domains, so someone else correct me please

[pearl pond]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• 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.

Channel closed

Channel closed due to the original message being deleted.
If you did not intend to do this, please open a new help channel,
as this action is irreversible, and this channel may abruptly lock.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• 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.

[cobalt hinge]

Let $a_0, a_1, a_2\ldots$ be the sequence defined by $a_0=\frac{2025}{9999}$ and $a_n=a_{n-1}+9\qty{a_{n-1}}$ for integers $n\ge 1$, where $\qty{x}=x-\floor{x}$. What is the last digit of $\floor{a_{2025}}$?

[jolly parrot]

;(

[cobalt hinge]

I have no clue

Like absolutely zero clue

[karmic forge]

First start with the recurrence relation

[cobalt hinge]

How so?

[karmic forge]

A hint you would find useful

$a{n-1} = \floor{a{n-1}} + \qty{a{n-1}}$

[jolly parrot]

WizzyGeek

[karmic forge]

Yah I have no idea how to typeset

Substitute that in the recurrence relation

[cobalt hinge]

The hints already said that but I'm confused

Ah, I guess I'll try it

$a_n=\floor{a_{n-1}}+10\qty{a_{n-1}}$, like this?

[jolly parrot]

;(

[karmic forge]

Yep

[cobalt hinge]

Oh shit

[karmic forge]

It's much easier now

[cobalt hinge]

So that's where I messed up

I kept on plugging it in for a_n

Le tme try

[pearl pond]

@cobalt hinge Has your question been resolved?

[pearl pond]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• 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.

[still dirge]

What am I doing wrong?

[tall flint]

i'm having trouble following what you're doing in general

you have t = x^3 + 1 which is fine, but why are you solving for x after?

[still dirge]

dx = dt/3x^2

so how do I write x^2

I have to use t

right?

[tall flint]

perhaps it would help if you instead had it arranged as x^2 dx = 1/3 dt

x^2 dx is already present in your starting integral

[still dirge]

oh

yeah, that makes sense

god this is frustrating, I am okayish at math but these integrals are super hard just because I'm bad at noticing things like this...

[tall flint]

valid

[still dirge]

thanks

.solved

[pearl pond]

Channel closed

Closed by @still dirge

Use .reopen if this was a mistake.

[pearl pond]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• 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.

[hoary nacelle]

Help

[hoary nacelle]

Is my little simple la done right I never took LA course so maybe there are inconsistencies in notion or not rigorous

[prime bramble]

seems good to me

[hoary nacelle]

I must say this is too easy to self study

[tropic saddle]

wouldnt hurt to actually write out what Lbeta1 etc are

[hoary nacelle]

This is probably exponentially easier than that torturing analysis

[hoary nacelle]

True 🥰🥰

[hoary nacelle]

What is the study of basic algebra why the book seems to be so abstract? Isn’t linear algebra harder but this is actually easy

The basic algebra seems to be different set and discussion of preserved structures and I don’t know what it is all about

[tardy bay]

algebra (abstract algebra) is generally very abstract and undertaken after linear algebra. It is conserned with much more general spaces than vector spaces, so the theory can get pretty messy

[hoary nacelle]

I bought a book and it discusses different homomorphism and weird lemma it looks fun but I feel my foundation isn’t good enough for it

[hoary nacelle]

Is category an ordinary set?

[tardy bay]

no

categories are even more abstract and can generally not be contained in sets

[hoary nacelle]

With what knowledge I can understand this book, it’s called algebra chapter 0

I bought it already and it looks actually down to earth I wonder if I may study it

[tardy bay]

you can probably tackle it head on

everything you need to know is contained in the book

it will just be difficult

[hoary nacelle]

I will try it, I thought it’s more of general algebra.. I found it fun 🥰

[tardy bay]

look up some guide for it

[hoary nacelle]

With time and patience, I have always been the dumb one at class but I try hard so🥰🥰 as long as I am patient enough will be fine 🥰

Hopefully

[tardy bay]

it's not structured in an order i would recommend learning algebra

[hoary nacelle]

Should I know a bit of other things?

I know a bit of field bcs of linear algebra

[tardy bay]

for example, learning about universal objects before groups seems very strange to me

usually one picks up several examples from abstract algebra which help make sense of category theory

learning category theory first is like studying organic chemistry to bake a cake

the canonical introduction to algebra is the textbook by dummit and foote

it gives a much more natural, in my mind, introduction to the field

[hoary nacelle]

Group theory, is it very hard what material should I use it always sound too fancy too me :😭

[tardy bay]

either way it will likely take years to learn the book you have

[hoary nacelle]

I got dedication

[tardy bay]

group theory is as hard as you make it

it's a very general field. there is currently active research in group theory

however

the group theory that is typically included in a undergrad course is not too difficult

it's a bit weird and unfamiliar, but not too difficult

[hoary nacelle]

Wow that sounds super exciting though I am studying economics and I’m pretty sure it’s not in my curriculum but I will try to enroll one as minor next year just like analysis

It had been so enlightening than boring study I currently have

Group theory I can just learn hands on right?

[tardy bay]

yes

but I wouldn't use the book you sent me

the chapter 0 one

[hoary nacelle]

The book I got it for a discount, since I got a bit too addicted to learn different analysis for Folland’s book. And I felt I need to engulf gaps for everything

So I got it

[tardy bay]

i would also be surprised if you learn group theory in economics

ok

[hoary nacelle]

Yes my study is super super boring

Like i actually feel like i hate it

[tardy bay]

keep in mind that that book seems closer to being a useful book to look stuff up in rather than learning from

consider switchin major, maybe? I am personally studying applied mathematics in finance which is fun and has advanced math

and economics

[hoary nacelle]

I am actually thinking of it, since I then need to prepare a lot of different subjects probably but since most of students pick courses of their wishes it’s gonna be fine

I am kinda addicted to different topology introduced in introductory analysis and but I am not sure though I heard math is very hard

I mean I only study one thing I am good at it, it is probably gonna be way worse than now if I compete with those who genuinely study mathematics

And many self doubt

[tardy bay]

i went from engineering mathematics to pure mathematics

it was difficult, but doable

if you put your mind to it, it wont be that bad

[hoary nacelle]

I have been thinking this as well which had been the reason I started to do linear algebra self study, alongside my preparation for comb of intro an analysis and advanced analysis Folland’s

I feel like if I do well with both I definitely switch

I feel Econ is just weird

[tardy bay]

follow your heart my guy

[hoary nacelle]

I hope it won’t be that awful though

[tardy bay]

you can't stop yourself from doing something just because it's hard. where would it lead us if we only did easy things?

[hoary nacelle]

To be honest I was quite of that type of person showing off, I told my friend that I would be passing a gradual course of analysis

And I had been preparing analysis since December lasy year

[hoary nacelle]

Exactly

And that is precisely the reason I felt addicted to mathematics

Analysis has been so addictive

Like so addictive

And I had been quite irritated and upset since the book of follands was so abstract but now I felt it is not like excruciatingly hard but maybe potentially in the spring next year I can do it

However I do find linear algebra almost impressively straightforward and easy though

Like the proof of subspaces and linear transformation, inner product spaces

[rough forge]

i think you will love it

[hoary nacelle]

Though some semi positive defined matrix is a bit abstract

[hoary nacelle]

Yes it’s fun

And set theory is also fun, naive set theory had been so fun to read

[tardy bay]

Linear algebra is generally intuitive and ”nice”

[hoary nacelle]

Yes that is very very true

[hoary nacelle]

It contrasts very sharply of the analysis I did

Though self study made thing hard but in general it had been hard

If I could genuinely switch majors then I would be very happy that I could dump this study Econ study

[hoary nacelle]

Only part I felt hard is when the Fourier transformation is introduced

[pearl pond]

@hoary nacelle Has your question been resolved?

Channel closed

Closed by @hoary nacelle

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• 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.

[calm roost]

hi guys, are the following correct?

[calm roost]

thats all thanks

[fierce jewel]

This is

[calm roost]

are the rest?

[pearl pond]

@calm roost Has your question been resolved?

[pearl pond]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• 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.

[prime hedge]

For the love of God, can someone tell me if I am just dumb, or if he is

This is on a TikTok of a parent and child, who both ended up coming out as trans. For variables, the exact reasons why it happens are unknown, so all we have to calculate probability is the fact that 0.6% of the population is transgender

[hasty edge]

[prime hedge]

Actually I think I am the dumb one

[midnight haven]

https://cdn.discordapp.com/attachments/1175225230281674792/1290474060027006997/attachment.gif

[prime hedge]

I mean either way my argument stands that it's a statistically improbability, not a statistical impossibility. We were both just dumb

.close

[pearl pond]

Channel closed

Closed by @prime hedge

Use .reopen if this was a mistake.

[broken fossil]

first world ahh problem

[flint zenith]

real

[unborn abyss]

0.6% * 0.6% is like 0.0036% (1 / 200 times 1 / 200)
buuuuut that's only 1 / 40k which... there's a lot more than 40k families in the world

[prime hedge]

Ja, I redid my calculations

My dumba** did 0.6x0.6 instead of 0.006x0.006

[unborn abyss]

ye

[prime hedge]

I would say he was wrong, I was right and wrong

Right about it being a statistical improbability, wrong about the exact probability

[plush moss]

Maybe wrong in debating about math on tiktok

[prime hedge]

I'm definitely less wrong than him

[pearl pond]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• 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.

[midnight haven]

I just wanted to check in to see if i set this problem up correctly. calculus 2 - finding volume using integration. (question b)

[midnight haven]

I get the concept but setting up the integral is still confusing

[earnest sphinx]

Yep you got it

[flint basalt]

looks right to me, but just make sure you put the entire inside of the integral in parentheses.

[midnight haven]

Alright

awesome thanks

.close

[pearl pond]

Channel closed

Closed by @plain lance

Use .reopen if this was a mistake.

[pearl pond]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• 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.

[pearl pond]

Please don't occupy multiple help channels.

[covert wolf]

Why can you just choose values for x to solve the simultaneous

[quartz rampart]

it doesnt matter we just want a starting point which point we get is irrelevant

yk how r=a+kb works yeah

[covert wolf]

Well i believe i do

But am i missing something

R=a+kb is jist gen form pf a line

Tbh i see where your getting at ngl

Okay thanks i get it its just a point on a line and u can choose ig

[quartz rampart]

maybe this diagram might help

the red part is the line

a1 and a2 are two starting vectors

b is the direction ratio, by which you can get other points on the line after multiplying by a factor of k and adding to original vector

[covert wolf]

Think i understand it but not sure what showing me a line to convey the line in vector form is gonna help w

Thanks though. I kinda had a understanding of why you can choose

I just thought the line can span a whole 3D plane ajd each x value has a unique y and z value

Idk im so use to elimination or substitution to solve

Thats why

[quartz rampart]

i see

[neat orchid]

Hi everybody, does anybody know natural deduction system in logic? It's something like the picture which I've attached

[covert wolf]

Thanks @quartz rampart

[quartz rampart]

you should get your own help channel

[covert wolf]

Wait twas my logic the correct logic

[neat orchid]

I'm new , I don't know how's it work 🥲

[quartz rampart]

#help-9

im pretty sure you can read that this is occupied

go to the ones that are available basically

[covert wolf]

@quartz rampart

[quartz rampart]

yes

its correct

[covert wolf]

How does it extend to planes

Like when considering planes ive seej the same done

But i dont think every x value is unique like a line

Tbf i thibk It was about two planes intercepting

Whcjh would form a line

Okay tysm

[neat orchid]

thanks a lot

[pearl pond]

@covert wolf Has your question been resolved?

[pearl pond]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

[pearl pond]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• 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.

[fringe flame]

I dont understand this question at all, like what would the first step be?

[sharp vigil]

find some facts about the angles inside a parallelogram and use that to set up an equation

[sullen wigeon]

if it's a parallelogram you already know that 1) the angles add up to 360 degrees and 2) there are 2 congruent angles

let's say that one angle x is the larger angle and the the other angle is 1/4x

[night fossil]

may I get help after this person?

[sullen wigeon]

this means that 2x+1/2x is = 360

[sullen wigeon]

depends how hard it is for me because i'm not that advanced

[night fossil]

I will tag you in the channel

[sullen wigeon]

the smaller angle is 36 degrees and the larger angle is 144 degrees

[fringe flame]

YAYYY

THANK YOUUU

.close

[pearl pond]

Channel closed

Closed by @fringe flame

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• 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.

[midnight haven]

i need help w solving this

[summer imp]

Use $\tan^2(x) + 1 = sec^2(x)$ and then it'll split into two integrals you can solve with reduction formula for sec.

[jolly parrot]

Azyrashacorki

[pearl pond]

@midnight haven Has your question been resolved?

[pearl pond]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• 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.

[livid karma]

how would i solve this

[livid karma]

since there is no y= or x=

substitute

[frail temple]

isolate y or x

[livid karma]

can you

go step by step

[frail temple]

ok let's look at the second equation

$x - 2y = 11$

[jolly parrot]

clair //

[frail temple]

how would you isolate x?

so that only x is on the left side?

[livid karma]

add 2y

[frail temple]

yes gj

[livid karma]

so x=11+2y

[frail temple]

yes

[livid karma]

wait

is that it

[frail temple]

yes

[livid karma]

YOOOO I LOVE YOU

YO UR ACTUALLY CRAZY

❤️❤️❤️

[frail temple]

😭 yw

[livid karma]

😭

.close

[pearl pond]

Channel closed

Closed by @livid karma

Use .reopen if this was a mistake.

[livid karma]

um

so i kinda did it wrong

wait

i did it to y

[gaunt surge]

Ok

[livid karma]

wait

how

[gaunt surge]

So uhhh

[gaunt surge]

Alr so let’s talk about the first issue

So x = 11 + 2y is correct

[livid karma]

okay

[gaunt surge]

Then you write -7(11 + 2y) - 2y = -13

Which is right

But do you see any mistakes on the next step?

Take some time here

[livid karma]

okay

no

[gaunt surge]

You sure?

[livid karma]

no

[plush moss]

Really put your eyes on it

[livid karma]

alright

ah shit

[plush moss]

Yea

[livid karma]

-7(11+2y)=-13

❤️

[gaunt surge]

Uhh

[livid karma]

what

[plush moss]

That's not

What we meant

[livid karma]

um

[plush moss]

-7(11+2y)=-77-14y

You should have expanded it like this

[gaunt surge]

Let’s go back to -7(11 + 2y) - 2y = -13

[livid karma]

WAIT

[gaunt surge]

Now focus on -7(11 + 2y)

[livid karma]

-7(11+2y)-2y=-13

[gaunt surge]

What does that expand to?

[livid karma]

-77-14y

[gaunt surge]

Alright so now we have -77 - 14y - 2y = -13

How can we simplify this further?

[livid karma]

-14y-2y=-13+77

[gaunt surge]

Yep

Let’s keep going

[livid karma]

-16y=90

[gaunt surge]

Yep

[livid karma]

-5.625

!

[gaunt surge]

And if we isolate y, we get y =?

Yes

That’s that

[livid karma]

but

[gaunt surge]

You can close the channel if you don’t need anymore help

[livid karma]

thats the sol

[gaunt surge]

?

Ummmm 💀💀💀

[livid karma]

according yo the answer key

thats the solution

[gaunt surge]

Yo am I ass?

[livid karma]

yes

yo its like 1am

[pearl pond]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• 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.

[livid karma]

i am not passing ts shit

[livid karma]

WHAT

NO

[frail temple]

😭😭

[livid karma]

<@&286206848099549185>

[livid karma]

^^^

[blissful crown]

yas

finally god an easy question

[livid karma]

ikr

small number math

[gaunt surge]

I failed basic pre algebra 😭😭😭

[blissful crown]

im in honors alg 2 w/ trig rn

[gaunt surge]

I got the wrong answer helping him holyyyy

[livid karma]

😭🙏

soo uh

helper

work your magic

[blissful crown]

what is it asking you to do

[livid karma]

so

[gaunt surge]

I genuinely don’t know what I did wrong I might be autistic

[livid karma]

probability hater

got me the wrong answer

[gaunt surge]

Somehow

[livid karma]

snd the solution is this

[blissful crown]

yeah but what does it want you to do

[gaunt surge]

Check our conversation and see what I did wrong

Solve for the point of intersection

[livid karma]

^^

[gaunt surge]

YO

I found the mistake

[livid karma]

YOO

what

[blissful crown]

i lagged out

[blissful crown]

regive me the FULL equation

with the question

[gaunt surge]

Im sped how did i miss that

I forgot basic addition lol

[blissful crown]

is it a system?

[gaunt surge]

Yes

[livid karma]

yo

[blissful crown]

ok whats the system

[livid karma]

^

[blissful crown]

do you prefer substitution or elimination

[livid karma]

wait

no way i missed that

[livid karma]

elimination

[gaunt surge]

Oh elimination??

[livid karma]

but ky teacher will probably tske off points if the question asks for a specific way

[livid karma]

nono

this question was substiton

same shit

however you spell it

[gaunt surge]

Bro why 💀

The question is literally set up for elimination

[livid karma]

its a substitution worksheet

[gaunt surge]

The coefficients for y are the same who would ask for substitution

[livid bolt]

substituion is ezierr

wait actually in there elimination is easier

[livid karma]

i cant use mu graphing calculator either cause my teacher caught me and said quote “i will take your geometry honors rec if you use it on our next test”

yeah

thank you guys

appreciate

[blissful crown]

here:

flip it

[livid karma]

thank you guys

[blissful crown]

chromebook camera sucks balls

[livid karma]

use phone

[blissful crown]

ipod 🔥🔥

[livid karma]

LMAO

[blissful crown]

knockoff ipod*********

[livid karma]

no way this kid is in the site 64 discord server

im crying

and the factions hub

holy

[blissful crown]

im more of a noctum person

[livid karma]

got it

[blissful crown]

just because site-64 wasnt my first site

so i never really got into it

[livid karma]

got it

[blissful crown]

[livid karma]

.close

[pearl pond]

Channel closed

Closed by @livid karma

Use .reopen if this was a mistake.

[blissful crown]

😿

[pearl pond]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• 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.

[proper flare]

What is the coefficient of ab^(n-1) in the expansion of (a+b)^n?

[wet osprey]

use binomial theorem

[proper flare]

Okay.

The question PROIBITS the use of any theorem.

[tropic saddle]

sigh

ok then lets rederive the binomial theorem

(a+b)^n is (a+b)(a+b)(a+b)...(a+b), yes?

if you multiply it out you have to either choose an a or b for each pair

in your end result you want to get ab^(n-1), so you have to choose 1 a and n-1 b's

how many options are there for that

[pearl pond]

@proper flare Has your question been resolved?

[toxic lichen]

@proper flare expanding the product of n copies of (a+b), prior to collection of like terms, you will have one term for each possible choice of which letter to take from each parenthesis

[pearl pond]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

[toxic lichen]

.reopen

[pearl pond]

✅

[toxic lichen]

to illustrate my point with n=4, you will get:

(a+b)(a+b)(a+b)(a+b) =
aaaa + aaab + aaba + aabb

• abaa + abab + abba + abbb
• baaa + baab + baba + babb
• bbaa + bbab + bbba + bbbb

@proper flare do you understand and accept this idea?

1) I don't understand this idea. 

2) I understand this idea, but the question expressly prohibits it.

3) I understand this idea, but refuse to apply it for other reasons. 

4) I understand and accept this. 

5) Secret fifth option. I will now explain myself. 

[pearl pond]

@proper flare Has your question been resolved?

[pearl pond]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

[pearl pond]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• 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.

[brisk pike]

Taking a break from RA and trigo

https://math.stackexchange.com/q/5044130/1126252

heres the link of the post

i was thinking a contour |z| = R with R to infinity

my rationality, from the MSE post: You have poles at ±ki and p=q for the - choice and p=-q for the + choice

but OP suggests that because of the power

i dont have poles at +/- ki but instead branch cuts (and also that the powers makes them think that maybe contour integration isnt a nice approach)

can anyone confirm whos correct?

<@&286206848099549185>

Okay so apparently the weird k is a real number between 0 and 1/4 :\

[toxic lichen]

it's not "weird k", it's Greek kappa

[brisk pike]

ah new letter for me

welp obviously its a branch cut then

.close

[pearl pond]

Channel closed

Closed by @brisk pike

Use .reopen if this was a mistake.

[pearl pond]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• 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.

[fringe ice]

I don’t understand how Suvat works when a particle has a velocity that is going up. It’s confusing because the particle is dropped (like in the question)

[calm wing]

think of the particle as being thrown instead of dropped

initially the particle is actually going up due to the velocity you have

only later the acceleration downwards becomes big enough to make it go down instead

[fringe ice]

Ohhhh ok!

[fringe ice]

Ok understood. so does the suvat equation work for both up and down directions if only create one equation

[calm wing]

yes

it works regardless of direction as long as you stay consistent with signs (which direction is + and which is -)

[fringe ice]

Really like the ball can go up then down like when it is thrown but one equation still works

[calm wing]

yep!

that's the cool part about it

[fringe ice]

Wow that’s so cool but confusing