help-36

[hazy laurel]

then im kinda stuck tbh

[solar glade]

Do you know how to integrate sech^2x?

[hazy laurel]

no

[solar glade]

Do you know the derivative of tanh?

[hazy laurel]

yeah

[solar glade]

What is it?

[hazy laurel]

sechx squared

[solar glade]

Then

[hazy laurel]

ohh

alr calm

i think i get it

[solar glade]

You tell me then

[hazy laurel]

x- tanhx

[solar glade]

+C

[patent sleet]

cant forget the constant matey

[hazy laurel]

my bad guys

im done goofing around

[solar glade]

!done

[final saddle]

If you are done with this channel, please mark your problem as solved by typing .close

[hazy laurel]

.close

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[gleaming bluff]

Can someone explain the solution of 10.7 ?

[gleaming bluff]

I was able to get 1/4 sin^2 2xcosx but couldnt continue

I tried redoing it again but idk where im doing wrong. Check out the part written in black

[lavish surge]

Why did you cancel 2 and 4 u should have multiplied them

[gleaming bluff]

which part are you talking about

oh okay now i got you

what changes anyways i still cant continue lol

[lavish surge]

Actually u would have gotten it

[gleaming bluff]

i got cos5x - cos3x - cosx over 8

<@&286206848099549185>

[final saddle]

@gleaming bluff Has your question been resolved?

[gleaming bluff]

<@&286206848099549185>

[final saddle]

@gleaming bluff Has your question been resolved?

[gleaming bluff]

<@&286206848099549185>

[versed jewel]

(cos θ + i sin θ)4 / (sin θ + i cos θ)5 is equal to . can anyone help

[gleaming bluff]

?

this is my channel

#❓how-to-get-help

<@&286206848099549185>

<@&286206848099549185>

[latent jasper]

@gleaming bluff@gleaming bluff@gleaming bluff

[stoic star]

Only ping once

[latent jasper]

@gleaming bluff

@gleaming bluff

@gleaming bluff

@gleaming bluff

[digital steeple]

what is the question?

[latent jasper]

what happened?

@gleaming bluff

[gleaming bluff]

ok but no one came this is why

[latent jasper]

@gleaming bluff

@gleaming bluff

what happened?>

@gleaming bluffwhats maths probelm

[gleaming bluff]

.

[latent jasper]

@gleaming bluff

ok

[gleaming bluff]

this is the last i did

[latent jasper]

@gleaming bluffgot it

[digital steeple]

i have seen this, but i still dont know whats your question is.

[gleaming bluff]

how do i prove it i dont understand the solution

i did some work but idk where did i do wrong

[digital steeple]

which step of the solution (which is on your picture) do you not understand?

[gleaming bluff]

after 1/4 sin^2 2x cos x

[digital steeple]

this?

[gleaming bluff]

i only pinged twice within a minute. the other ones were pinged within 30min to hour. go mind your business if ur not gonna help.

[gleaming bluff]

yes

no okay

i actually saw it now

[gleaming bluff]

can you review this

[latent jasper]

?

[latent jasper]

?

[latent jasper]

?

[latent jasper]

I was actually doing my business but got irritated from your mass pings

[gleaming bluff]

okay leave then go back doing your business

as if i am the only one doing it

[latent jasper]

It's my business, my ownership. you are no one to give order to me

[gleaming bluff]

yeah right that helpers tag gives you the right, right?

[latent jasper]

But that does not mean you mass ping helpers

[latent jasper]

No!

It never gave you the right to give order

[gleaming bluff]

i do not usually ping helpers more than two times. i did not get any help so this is why i did it. i already explained it and it already happened so why not move on ?

what are you trying to prove here you're literally wasting time

[latent jasper]

If you get no reply and mass ping, you'll get nothing

[digital steeple]

where does this come from?

[gleaming bluff]

okay you can leave after this very important fact

[latent jasper]

Again, it's my business

[gleaming bluff]

can you leave?

[digital steeple]

<@&268886789983436800> @latent jasper is spamming this channel

[gleaming bluff]

you see there it is written as sin^2 2x

[gleaming bluff]

thank you.

[latent jasper]

Pings helpers
No reply
Pings again
Tells helpers to leave

[latent jasper]

HuH??

[gleaming bluff]

i am not telling helpers to leave i am telling you to leave

ThM is trying to help and you're spamming this channel rn

which causes a waste of time for both of us.

[latent jasper]

Spamming?

[gleaming bluff]

LMAO

yeah you're so funny yea yea

[digital steeple]

are you sure?

[gleaming bluff]

i actually expanded sin^2 2x there

[digital steeple]

if I draw it its not the same

[gleaming bluff]

oh

must have done it wrong

wait i did it based on a formula

hold on

[barren hound]

(modding on mobile is so annoying but I muted for a bit, nikky please don't spam like that when you're not helping)

[gleaming bluff]

thank you

[gleaming bluff]

isnt this right?

[barren hound]

but also ghio consider whether repeated Helper pings are useful

[gleaming bluff]

yeah i apologize for it but even it already happened and someone is helping me he is disturbing the channel for no reason

still, i am sorry for that.

what is the maximum amount of time i can ping helpers? Consider that at first i did it and someone came but they left without answering my question. Can I tag helpers again?

[digital steeple]

as my drawing shows you obviously missed the "-" in using this formula:

[gleaming bluff]

oh right i am actually solving it again and i think i am close to the answer

let me share my progress

i think i got it but i only need to make it positive

make the -2

positive

i dont know why i got the answer like this though

i think i did another error while using the formula

[digital steeple]

you do it now step by step the same way as in the "original" solution. why dont you compare it with this - you will see your error.

you again missed some "-", if i see it the right way.

[gleaming bluff]

alright found it. thanks a lot

.close

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[flat pewter]

for the function f the equation becomes -2^2+6 but idk if the answer will be 10 or 2

[smoky narwhal]

(-2)^2 = 4

there

solve :)

[flat pewter]

i don't get it it's 4?

wait lemme think and use my brain

so it's 10 then

[mental roost]

(-2)^2 = (-2) * (-2) = 4
negative times negative = positive

[flat pewter]

i put it in desmos and it said -4 so i was confused

[surreal vault]

-2^2 = -4
(-2)^2 = 4

[flat pewter]

ok

how do i know if parentheses are around it

or when they're not around it

[surreal vault]

whats the full question

[surreal vault]

when substituting stuff in put it in parentheses

ex. when subsituting for a in a^2
a = -5, a^2 = (-5)^2

[flat pewter]

ok

[surreal vault]

but if the thing is sort of like

2x^3 - x^2
then follow order of operations

ex.
x = -1
2(-1)^3 - (-1)^2
2(-1) - (1)
-2 - 1
-3

[flat pewter]

those numbers are confusing me

[surreal vault]

which numbers

[flat pewter]

just the whole thing

[flat pewter]

this whole example

but i think i'm good for now

[surreal vault]

btw for the first thing

im pretty sure the answer isnt 10

[flat pewter]

why

oh i didn't fully solve it

it's 68

that was just for one

can u help with this one

what does it mean when it says f(-1) does it mean the coordinates of when y=-1?

[surreal vault]

i think it means to substitute -1 into it

[flat pewter]

it's just a graph tho

[surreal vault]

basically what is the value of y when x = -1

[flat pewter]

oh

wait

so -3

[surreal vault]

i guess

[flat pewter]

and the second one would be -1

what about f(x)=0

[surreal vault]

it means to find the values of x such that f(x) = 0

in your case its just the values of x such that y = 0

[flat pewter]

ohhh

so the x intercepts

[surreal vault]

yea i guess

[flat pewter]

do u know how to do end behavior cause i forgot

[surreal vault]

nop but i seaeched it on google

just look what happens when x goes to positive and negative infinity

[flat pewter]

oh i remeber now

when x goes to negative infinity y goes to infinity

type shi

when x goes to infinity y goes to infinity

@surreal vault are you still here

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[woven galleon]

Can someone find the volume and surface area of all 4 of these please

[final saddle]

@woven galleon Has your question been resolved?

[woven galleon]

Can someone help

Uhh

Wait

For 1.

?

Idk Bru

So just multiply them together for volume

So 196

Then how do I do surface area

Alr

So what would that be

7x4x2 7x7x2?

Like that for the first bit

so 210 for the SA right?

for 3 V=336

is SA 208?

if not lk what i did wrong

@glass beacon

How I did 8x7x2

Uh alr

196?

@glass beacon

Wait nvm

292 right

Is the SA for 2 97?

@glass beacon can you help with just 3 more

If you can just give me 4 and 2 then that’s all I need please

B and h is 5 and 4 so I don’t get it 5 n 4 / 2?

[soft zealot]

faiyrose

[woven galleon]

So it’s 50 right

Was that volume

Alr

R is 8 and h is 6

Diameter

[hearty harbor]

let him cook now

[woven galleon]

2r=d 2 r = d

[soft zealot]

faiyrose

[hearty harbor]

why use the formula if you can just integrate over it

jkjk

[woven galleon]

What does the $ mean

Oh alr

[hearty harbor]

or you can just do $\int_{0}^{6} \int_{0}^{2\pi} \int_{0}^{4} r dr d\theta dz$

[soft zealot]

N(μ,σ²)

[hearty harbor]

: >

[woven galleon]

😭

[hearty harbor]

dont listen to me

do u still have any questions @woven galleon ?

[woven galleon]

Yes uh I got 301

[soft zealot]

Result:

301.59289474462

[woven galleon]

Yes

6

[soft zealot]

faiyrose

[woven galleon]

Alr

Lemme solve rq

wait im comfused on how to solve it

[soft zealot]

faiyrose

[woven galleon]

i got 96

is that right

πr² I’m just bad at this bro mb

What is that

πr²

Yo I got class in like 5 mins can you just plz tell me what the volume and surface area is😭

[soft zealot]

faiyrose

[woven galleon]

10

[soft zealot]

faiyrose

[woven galleon]

80

[soft zealot]

faiyrose

[woven galleon]

So 80x3.14?

251.2

[final saddle]

If you are done with this channel, please mark your problem as solved by typing .close

[woven galleon]

But if I do that it’s to big

ohh

[soft zealot]

faiyrose

[woven galleon]

alr

wait is that the volume

or sa

alr

wat was the volume btw

oh alr ty bro

u saved me

God Bless You😁

.close

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[cursive spoke]

how to solve problem by creating equations

[final saddle]

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.

[cursive spoke]

bruh

[torpid igloo]

What problem do you want to solve?

[cursive spoke]

any example of solve problem by creating equations math

let me try to find the thing

[static pier]

Yeah, it’s not really procedural thing, depends case to case

[torpid igloo]

Say you have a problem like: Tom's mother was thrice the age of Tom at that time 10 years ago. What are their ages now

Are you talking about problems like these?

[cursive spoke]

nope

Two faucets flowing into a tank without water will fill it in 6 hours. If hose 1 is left alone to fill the tank, it will burn faster than hose 2 running alone, which is 9 hours. How long does it take each faucet to fill the tank?

here

i took some time translating since im asian 👽

i only know that we find how long does fauncet 1 take to fill the tank

and fauncet 2 too

[torpid igloo]

So you need to find 2 variables, lets assume they are a and b. (The time taken by faucet 1/2 to fill the tank)

[cursive spoke]

alr

[torpid igloo]

Let the rate of filling of each be r1 and r2 (So by r1, I mean that in 1 hour, it can fill r1 litres). And the volume of tank be V litres

So we can write r1 * a = V = r2 * b

And (r1 + r2)*6 = V

[cursive spoke]

what the sigma..

in here first we call the time it take for fauncet 1

and fauncet 2

to fill the tank

then we start making things up that somehow makes sense and create equations

[cursive spoke]

x and y or smth

[torpid igloo]

How do you start thinking about this?
You need to find the time it takes to fill for both the faucets. Lets say t1 and t2.
Now you assume, that in 1 hour, faucet 1 fills r1 Litres and faucet 2 fills r2 Litres.
So how many Litres would say, faucet 1 fill in t time? r1 * t. But you know that r1 * t1 = volume of the tank in litres and similarly r2 * t2

18 hours is the answer

[cursive spoke]

thank you

[torpid igloo]

😆

You can ask if you have any confusion

Its very easy if you take time to understand

It won't take you time once you get it

[cursive spoke]

you are trully a hero mr bean

😭

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[ruby lake]

i am having some diffiuclty with finding variance of Y

i built this table

so E[y]= 9/16

VAR = E[X^2] - E[X]

isn't E[X^2] also 9/16?

so var=0

[ruby lake]

E[X^2] = 0^2 * 7/16 + 1^2 * 9/16

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@ruby lake Has your question been resolved?

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@ruby lake Has your question been resolved?

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[mortal berry]

is correct?

[ivory vessel]

no

far from correct

[mortal berry]

what is the error?

[ivory vessel]

the first is you are missing dx

the second, more prominently, is you took the x out in the numerator wrongly

$\frac53x -\frac73\neq\frac13(5-7)x$

[mortal berry]

ah... you're right

now is correct?

i have missed a dx in the final integral🤦

[ivory vessel]

yes, thats correct

[ivory vessel]

from there just do partial fraction

[mortal berry]

ok

i found a better way to solve

[sharp goblet]

?

Solved ?

[mortal berry]

yes

.close

[final saddle]

Channel closed

Closed by @mortal berry

Use .reopen if this was a mistake.

[scenic pendant]

Its wrong

[mortal berry]

.reopen

[final saddle]

✅

[mortal berry]

they told me it's right

[scenic pendant]

Its not

[mortal berry]

@sharp goblet told me it was well done🤦

[scenic pendant]

Multiply fractions

[mortal berry]

ok

now?

[scenic pendant]

🤦‍♂️🤦‍♂️🤦‍♂️🤦‍♂️

Im done

[mortal berry]

<@&286206848099549185>

[wild rover]

where is the question

[mortal berry]

the integral above

[wild rover]

ok bye

man not calculus ☠️

im still learning limits so…

[manic flame]

Did you just

Split the integrals

integral of f(x)g(x) isn’t equal to the integral of f(x) times the integral of g(x)

[mortal berry]

wdym

oh right, that only applies with + and -

🤦

Now?

I try to expand with Taylor

is right?

[final saddle]

@mortal berry Has your question been resolved?

[final saddle]

@mortal berry Has your question been resolved?

[final saddle]

@mortal berry Has your question been resolved?

[wild stirrup]

Heyy

I got a better way to solve it

Then split it

[mortal berry]

thanks

.close

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[winged tulip]

can you please explain me what a cylinder set is? I read it's definition n-th time, and I still don't get it

[hybrid heath]

can you share definition?

[winged tulip]

my prof told me that cylinder sets are sets made like this, but it makes no sense (as T is a set, then R^T is a set of function from T to R, therefor X is a function which belongs to borel set)

[winged tulip]

i get to the moment when projection is defined, and then I get lost

[hybrid heath]

#proofs-and-logic might be able to help.

[winged tulip]

.close

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[fleet grove]

hello everyone! just wondering how i get a system of vectors as a linear combination

[fleet grove]

as in I have vectors a = (1, 2, 3), vector b = (2, -3, -4), vector c = (1, 0, -2)

can i just set this up and eliminate variables and avoid a matrix?

[dense coral]

wdym?

a linear combination isn't a matrix

[fleet grove]

so if i need a + b + c = (3, 4, 5) as a linear combination

[dense coral]

ah, okay

[fleet grove]

you can use a matrix as well but i quite frankly dont want to

can i just set this like

[dense coral]

this is more like a vector equation

ok

[fleet grove]

x = 1c1 + 2 c2 - 2c3

etc etc

and use elimination from there

[dense coral]

what is c1 c2 c3

[fleet grove]

variable

can switch it so like

c1 = 1x + 2y - 2z

actually thats wrong it would be uh

[dense coral]

if you're gonna use elimination, why not use a matrix?

[fleet grove]

hate matrixes

but ill use em

anyways im just confused as to what this wants me to do and how to set it up

[dense coral]

we want to find scalars x,y,z such that xa + yb + zc = (3, 4, 5)?

[fleet grove]

yes

gaussian elimination might actually be easier

[dense coral]

yes

we can write x(1, 2, 3) + y(2, -3, 4) + z(1, 0, -2) = (3, 4, 5)

then distribute the scalars in, and then add the vectors together on the LHS

[fleet grove]

hold on lemme grab phone i have this so far

i messed setting up my matrix i think

[dense coral]

yeah, the rows should be columns and vice versa

[fleet grove]

i did

hold on

im getting something irrational now

uhm

i messsed up and idk where

do i want to make this matrix verticale

vertical

uh

i mean

like (1 0 0)
(0 1 0)
(0 0 1)

identity matrix

[tranquil pine]

not necessarily

if you have free variables in the third row apart from $x_3$ then you can solve the system

[soft zealot]

45

[fleet grove]

ykw

im scrapping this and doing it as a system of linear equations

[tranquil pine]

you have $x(1, 2, 3) + y(2, -3, 4) + z(1, 0, -2) = (3, 4, 5)$. This equates to $\begin{pmatrix} 1 & 2 & 1 \ 2 & -3 & 0 \ 3 & -4 & 2 \end{pmatrix} \begin{pmatrix} x \ y \ z \end{pmatrix} = \begin{pmatrix} 3 \ 4 \ 5 \end{pmatrix}$, as you correctly stated. I suggest instead of performing row operations, you solve this through elimination or substitution, or a combination of both.

[soft zealot]

45

[fleet grove]

i was using guassian elimination and got stuck

[tranquil pine]

but row operations could be used to solve this

[fleet grove]

so

[tranquil pine]

What are you stuck on?

[fleet grove]

back to ole reliable

[fleet grove]

i messed up somewhere, ended up with third row: 0 0 0 = a weird number

[tranquil pine]

yeah then ig instead of gaussian elimination, use the normal methods

unless the question specifically asks for that

[fleet grove]

it doesnt

i got it

thank you! ill be back soon enough lol

.close

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[haughty pulsar]

Question 1.b partie 2

I can't translate

[final saddle]

@haughty pulsar Has your question been resolved?

[scarlet sequoia]

quelles sont les valeurs que peuvent prendre x^2 et y^2 mod 4?

[haughty pulsar]

jsp

att

[scarlet sequoia]

excuse moi on est passés mod p

[haughty pulsar]

mod p?

[scarlet sequoia]

oui

[haughty pulsar]

bahh ya bcp de possibilités jsp

[scarlet sequoia]

d'après la question d'avant, x^2 + 1 et y^2+1 c'est comment mod p

[haughty pulsar]

different de 0 mod p

[scarlet sequoia]

ok

[haughty pulsar]

donc?

[scarlet sequoia]

j'essaie de voir où l'exo veut en venir

[haughty pulsar]

À p/x

pttr utiliser la question d'avant

La solution c'est évidemment en utilisant l'absurde

[scarlet sequoia]

ok je pense j'ai la solution oui

si par l'absurde x n'est pas divisible par p

alors on pose u un inverse de x mod p

et donc a = uy vérifie...

[haughty pulsar]

inverse?

pas au programme

[scarlet sequoia]

alors

bézout quand même?

[haughty pulsar]

oui

[scarlet sequoia]

bah

[haughty pulsar]

même fermat

[scarlet sequoia]

donc inverse au programme

[haughty pulsar]

non

[scarlet sequoia]

bah si regarde

x et p premiers entre eux

ux + pv = 1

donc ux = 1 mod p

u inverse de x mod p

[haughty pulsar]

ouais pas au programme

[scarlet sequoia]

bof bof

[haughty pulsar]

pas de notion "inverse"

[scarlet sequoia]

bon ok

[scarlet sequoia]

alors refais ce raisonnement

on en vient à u tel que ux = 1 mod p

et regarde qu'est-ce qui se passe avec a = uy...

[haughty pulsar]

?

hmmm

[haughty pulsar]

jsp

[scarlet sequoia]

bon

x^2 + y^2 c'est quoi mod p

[haughty pulsar]

0 mod p

[scarlet sequoia]

oui

[scarlet sequoia]

bon bah comment on fait apparaître a là dedans ?

[haughty pulsar]

jsp

double bezout?

on ne peut pas car p peut diviser ou ne pas diviser y

[scarlet sequoia]

non, il suffit de multiplier

on a du y^2

comment on fait apparaître a= uy?

[haughty pulsar]

multiplier quoi

tu me dis des consignes sans les terminer

[scarlet sequoia]

il faut bien que tu essaies de les terminer par toi même

sinon on apprend pas

[haughty pulsar]

regarde moi ce que j'ai fais

[scarlet sequoia]

trop compliqué et peut-être des erreurs dedans

just

x^2 + y^2 = 0 mod p

[haughty pulsar]

check?

[haughty pulsar]

oui

[scarlet sequoia]

donc

si on multiplie par u^2...

[haughty pulsar]

hmmm

ill get a paper

[haughty pulsar]

bahh u²x² + u²y² = 0 mod p

x = 1 - pv

ux*

I see where this is headed

oh shit

its simple

thx bro

@scarlet sequoia you tha goat

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[frail fiber]

hi i need help. could anyone come in a voice call?

[hybrid heath]

!da2a

[final saddle]

No need to ask “Can I ask…?” or “Does anyone know about…?”—it’s faster for everyone if you just ask your question! See https://dontasktoask.com/

[spiral storm]

whats the topic?

[frail fiber]

endless numbers

/values idk im not native

[hybrid heath]

If english is not your first language, VC may be an even more difficult channel of communication

[frail fiber]

1+1/3+1/5+...+1/endless shouldnt equal endless right? it should get closer and closer to a specific number right?

[frail fiber]

it should be fine i hope

[hybrid heath]

I believe it is endless

[hearty zephyr]

not necessarily

[hybrid heath]

Are you familiar with the Harmonic series?

[hybrid heath]

"Infinite series" by the way

[frail fiber]

im not sorry

[hybrid heath]

Harmonic series: $\frac{1}{1}+\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+\frac{1}{5}+...$

[soft zealot]

SWR

[frail fiber]

I ran it through a python code with really high numbers (smth like 1010000000) and i got smth around 11.35

[hybrid heath]

But that's not infinitely high

[frail fiber]

yes but from now on the value that i will add is increasingly small

[hybrid heath]

what is your native language?

[frail fiber]

german

[hybrid heath]

English proof:
https://web.williams.edu/Mathematics/lg5/harmonic.pdf

Other proof:
https://en.wikipedia.org/wiki/Harmonic_series_(mathematics)#Definition_and_divergence

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[frail fiber]

yes, okay thank you

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[hasty bear]

I need help with binomial expansions

[hasty bear]

I will fully explain myself

This question is confusing to me because when using this general equation:

the k value by the way is one less than the term

so if the sixth term is what we need to solve for, the k value is 5

anyways, I'm not sure what they mean by ascending powers of x or descending powers of x

Like, is the general term in itself based on ascending powers of x or descending

[hasty bear]

The correct answer to this question is 7/4x by the way

but im wondering what the answer would be if it was ascending powers of x instead of descending

[pseudo shoal]

youd do it in ascending powers of x and find the value for the sixth term

[hasty bear]

why did this person do it this way then

they simply took the 6th term in descnding powers of x

and it was the correct answer

wait

[hasty bear]

how would you do it in ascending powers of x though

like what does that mean in itself

whats the difference between finding the answer between descending and ascending

thats my confusion

[pseudo shoal]

ok so

[hasty bear]

and how does it apply to the equation

[pseudo shoal]

its how u arrange the powers of x

in descending or ascending order

[hasty bear]

right

[pseudo shoal]

from a quick calculation

in ascending powers itd be 7x^9

i did this quickly so it might be wrong

[tulip coyote]

(e.g. something like 1 + x + x^2 is "ordered" with the powers of x increasing [ascending powers of x], whereas x^2 + x + 1 is "ordered" with the powers of x decreasing [descending powers of x])

[pseudo shoal]

but in descending powers of x you have an x^-1

[pseudo shoal]

^

[hasty bear]

yes

i understand that part

however, what i dont understand is how i find the value of k and solve for the term and simplify

[pseudo shoal]

you just vary k

[hasty bear]

what does that mean

if k is 5 in descending terms, then k has to be another value in ascending terms right

i want to know how you would find that value

[pseudo shoal]

yh k would be 3 in ascending i think

sorry im not explaining myself very well im kinda tired

essentially every value of k corresponds to a power of x

you have to see which power of x youre looking for and use that k

[hasty bear]

heres something i did

my logic was that since in ascending order of powers we have to solve for the 5th term

in descending order of powers, naturally we'd have to solve for the 3rd term

it was the same term regardless

so i tried solving for it and got the question wrong

when expanding the binomial

we get this

[tulip coyote]

Assuming you're writing the terms as $\binom{6}{k} x^{6 - k} (-2x^2)^{k}$, you won't get the terms in decending powers of $x$ (as $k = 0$ gets you $x^6$, but $k = 6$ gets you $64x^{12}$)

[soft zealot]

@tulip coyote

[hasty bear]

so if it ever asks us a question for descending powers of x we have to turn it into ascending powers of x and find the appropriate term?

if thats the case then this person didnt solve the question properly

they simply took the 6th term from descending powers of x and got k and plugged it into the equation

instead of turning it into ascending powers of x first

wait

im so confused

when that equation got expanded it naturally turned into descending powers

of x

even though it should be ascending

meaning they purposely altered the equation so that we just look at the term and simply solve for it without thinking any further

at least thats what i am assuming

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[gray acorn]

if this point is (-3, 3)

toh nvm

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[ember creek]

hey really quick, is this a construction of a median?

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[gentle zephyr]

let $f(x)$ be a function with three continous derivatives such that $\abs{f^{(3)}(x)} \leq \frac{1}{4}$ $\forall x \in \mathbb{R}$ and let $P(x) = 3\left(x-1\right) + 5\left(x-1\right)^2$ be the second order taylor polynomial at $x_0 = 1$. Find $Q(x)$, the taylor polynomial of degree 2 of $g(x) = 4x + x^2 + f(7-3x)$ in $x_1 = 2$ and calculate the amount of error of a result of calculating $Q(2,1)$ instead of $g(2,1)$

[soft zealot]

938c2cc0dcc05f2b68c4287040cfcf71

[final saddle]

@gentle zephyr Has your question been resolved?

[soft zealot]

No roles to add or remove, nothing to do.

Jun 1, 2024, 3:09 AM

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@gentle zephyr Has your question been resolved?

[final saddle]

@gentle zephyr Has your question been resolved?

[gentle zephyr]

someone please

[gentle zephyr]

<@&286206848099549185>

[digital steeple]

do you know how to determine a taylorpolynom of degree 2?

[gentle zephyr]

ye

is just following a formula

[digital steeple]

degree 2 means, you do only the first 3 terms (up to the second derivative)

so take your g(x) and determine g(2), g'(2) and g''(2).

@gentle zephyr

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[sonic crystal]

so um how do I do the limit thing? where I evaluate the limit thing?

[sonic crystal]

hi slayla

do you like my handwriting

[chrome hemlock]

WATERBEAM]

[sonic crystal]

Hello bum chicken

[trail mango]

it’s mid

[sonic crystal]

do you like how I accounted for the flipped integral and limit because I’m Australian you guys see everything upsidedown

[sonic crystal]

Go do ur spec 👻

[trail mango]

[sonic crystal]

https://media.discordapp.net/attachments/268882317391429632/1223598233763319819/1192815796490080286.gif?ex=665bb1e8&is=665a6068&hm=8d1a33b02c2a4cc715df7b25a815565b1098e5afb0e75426618f65e5f991b142&

[chrome hemlock]

NO I FINISHED MY EXAMS

im playing games rn

[sonic crystal]

blud is flooding my help channel with valorant gameplay 💀

[chrome hemlock]

no

[sonic crystal]

stop losing ur games

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[copper chasm]

im stuck on part (ii) I end up with two times the right hand term instead of the whole expression. To start with idk where they get the 1/2 sin(t) from nor do i know where i get an extra 2 from. My phones dead so i cant send my working but if anyone can check the final answer itd be appreciated just in case the show that is wrong.

[copper chasm]

i integrated by parts twice then got to $$b_n = \frac{2}{\pi} \left(\frac{4n}{4n^2-1} \right) \cos(n \pi)$$ as the coefficient in front of the sum of sines (used limits $ - \frac{\pi}{2}$ and $\frac{\pi}{2}$ in the integration)

i didnt use the identities at the bottom in the process

[soft zealot]

I can't believe you've done this

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[final shadow]

Please help

I act. dont know how to do this 😭

[zealous stump]

are you allowed to just graph it

[karmic kindle]

Addition of ordinates it quite tricky

But

Basically

You must find the period of the sin function

And the tangent function

and find their least common mutiple

[final saddle]

@final shadow Has your question been resolved?

[final shadow]

I mean yeah but it wouldnt be helpful for a test

[final shadow]

Ah okay

I can try it

thank you

[zealous stump]

no calculator test 😢

[final shadow]

Our teacher allows calc

But no graph

[zealous stump]

f

that sucks

[final shadow]

I got 6 pi

i think it right

so thank you

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[timber pollen]

i require help brothers

nvm i big brained it

.close

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[faint locust]

#linear-algebra message

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[south lily]

Hi
when u have a stochastic variable (or random variable) does it only represent the possible outcomes or does it actually contain the data?

[south lily]

like when u google the definition its just the numbers that the observations can have

but then other times its used to find different things like the mean $\hat{\mu} = \frac{1}{n} \sum{X}$

[soft zealot]

chrelleren

[south lily]

up until now I thought the stochastic variable was a representation of a test/sample you do of a population and that it contains $x_1, x_1, ... , x_n$

[soft zealot]

chrelleren

[short talon]

well depending on how its defined, a stochastic random variable is actually many random variables indexed by time (usually)

in general, a random variable is a map $X:\Omega \to S$ where $\Omega$ is your measurement space, and $S$ is some set, usually $\mathbb{R}$

[soft zealot]

Bair

[south lily]

so the random variable doesnt actually contain any data?

its just the possible outcomes of ur samplespace?

[short talon]

what do you mean contain data? a random variable is just something which depends on an observation you made

so if i was flipping coins, a random variable might be the number of heads i get

[south lily]

like what I mean is the stochastic variable for flipping a coin is the two possible outcomes X = {1, 0} and not the actual outcomes from a test X = {1, 0, 1, 1, 1, 0, 0}

[short talon]

right

[south lily]

wait which

[short talon]

the former

it doesn't depend on any particular outcome

[south lily]

wdym by this then if it doesnt represent the sample u took?

[short talon]

take some sample, say you flip 4 coins, and you call the outcome you get $\omega$, then if $X$ is a random variable that represents the number of heads i get, $X(\omega)$ is the number of heads i got in that particular sample

[soft zealot]

Bair

[short talon]

so in a sense, the random variable itself is independent of any particular sample, since it represents a mapping from your measurement space to the reals

[south lily]

so if the sample space was the outcome of a dice throw, then the random variable would be X = {1, 2, 3, 4, 5, 6}?

[short talon]

no? once again, a random variable is a function that maps your measurement space to the reals (or some other set)

[south lily]

wait hold on

https://www.youtube.com/watch?v=3v9w79NhsfI&t=245s

[south lily]

I got it from this video

[short talon]

which part of the video are you referring to

like what timestamp

[south lily]

50 seconds

[short talon]

im still confused, they are saying what i just said, in that case X is still a map from the measurement space (the value of a coin flip) to a number (1 or 0 depending on the flip)

[south lily]

ion get why it doesnt apply to X = {1, 2, 3, 4, 5, 6}

[short talon]

what you wrote down is a set of numbers, it's not a mapping

are you saying that that's the range of X?

then what is X itself

[south lily]

meant like

its the possible values X can take depending on the throw

[short talon]

but how are you defining X? just the value of the throw?

[south lily]

yea

[short talon]

then X is a function which maps from the set of possible rolls to a number which represents the value of the throw

so if $\omega_i$ is the measurement that the die roll is $i$, then $X(\omega_i)=i$

[soft zealot]

Bair

[south lily]

does this mean the stochastic variable could also be defined as a function that finds the average of a measurement sample? like the average of 6 dice throws

[short talon]

a stochastic random variable is a collection of random variables indexed by time, so they could be $X_1, X_2, X_3\dots X_t$ where $t$ represents the time

[soft zealot]

Bair

[short talon]

so sure, you could define a stochastic rv like how you said

like $X_t$ represents the average of the first $t$ dice throws?

[soft zealot]

Bair

[south lily]

wait I thought stochastic variable and random variable was the same

thing is we didnt use the word random variable only stochastic

(im not native english)

[short talon]

they are not the same thing

[short talon]

_ _

[south lily]

ok so if we got a samplespace with different outcomes (random variables) x_1, x_2, ..., x_n then the stochastic variable is the collection of those X = {x_1, x_2 ... , x_n}

[short talon]

yeah

[south lily]

and the samplespace isnt necessarily the whole population right

im just making sure my language barrier isnt causing any misunderstandings xd

[short talon]

what do you mean by population

[south lily]

ive learnt it all in a different language

[south lily]

like say

the whole population is the height of all students in america

and a samplespace may be like 10 classes that are chosen to be done statistics on

?

[short talon]

err i guess if you define it that way

i don't know much about statistics, in probability we just say that all of your random variables in a stochastic random variable map from the same sample space

[south lily]

ah ok fair

its because we got some stats on how to estimate the mean and variance from a sample within a confidence interval

just wondered if the samplespace are the same as those samples

would make sense if it was the case

@short talon but bro ty youve been a great help

[short talon]

no problem, you're welcome

[south lily]

❤️

have a good night

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[waxen jay]

Can someone help me figure out what I'm doing wrong for this optimization problem? It should be x=7745.9667 but I got x = 1290.994 somehow

[languid yoke]

I'm confused can't you just make the field really skinny and then the fence would be really small

[waxen jay]

im not really sure, the problem asks for the shortest possible fence that the rancher can use while still staying 2,500,000 sq ft in area

[languid yoke]

Yeah so I'm saying you could just make it like 2,500,000 by 1 and the fence could just be 1 foot long lol

so the problem's not very clear...

[waxen jay]

i dont think thats an acceptable answer haha

[languid yoke]

Ohh nevermind

I misunderstood the question

it's asking for the total fence not just the fence down the middle 🤦

[waxen jay]

yeah, i think it wants the perimeter

[lethal estuary]

what'd you give as the answer?

[languid yoke]

I think your work is correct you just didn't compute the perimeter

You just solved for one of the dimensions

I also got x=1291 (approximately)

so then y is 2.5 mil divided by that which is 1936.5

[waxen jay]

i gave 1290.994

[languid yoke]

Yeah I get 7745 when I calcuate the perimeter

[waxen jay]

wait what part did i not calculate?

did i only solve for x here?

[waxen jay]

even when you add those two it doesnt get 7745 tho

[languid yoke]

The perimeter is 3x+2y

not x+y

[waxen jay]

ohh

so i have to plug it into the original equation

<@&268886789983436800>

[languid yoke]

https://tenor.com/view/chloe-sideye-seriously-gif-10549810

[waxen jay]

tysm tho, that makes a lot more sense

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[elder relic]

how we we integrate this

<@&286206848099549185>

[feral ginkgo]

!15min

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[feral ginkgo]

Firstly put the minus sign outside the integral, so $-\int \frac{x}{x+1} \ dx$

[soft zealot]

lgkoo

[elder relic]

right

[feral ginkgo]

then the hint here is: x = x+1-1 (use this in the numerator)

[elder relic]

yea

[feral ginkgo]

have a think about it

[elder relic]

got it thankyou

[feral ginkgo]

nice

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[floral shadow]

Q3

[craggy plank]

!status

[final saddle]

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

[floral shadow]

1

[craggy plank]

Just see it as permutations of 3A and 3B

A stands for going right, B stands for going up

[robust mulch]

combinations*

[craggy plank]

Have you noticed that no matter which path they go, 3A and 3B is required?

[trail mango]

eh, permutations is correct?

[craggy plank]

Both will do

[floral shadow]

But don't we have to account for cases when you can't go up and right

Oh wait

[craggy plank]

For example?

[floral shadow]

Like u go up 3

Oh wait

3a 3b

[jagged flare]

this is the way my teached me

[craggy plank]

This is doable as well

But it’s hard to explain

[jagged flare]

basically just make the edges 1 and sum em up

[floral shadow]

I think I get it

Does 6c3 work

[craggy plank]

Congrats

[jagged flare]

ya

[trail mango]

looking at the paths as permutations of rrruuu is my favorite way

[floral shadow]

Ohhh OK I get it now

[trail mango]

r for right and u for up

[jagged flare]

how does using paths of permutation work if theres a hole on the paths

[craggy plank]

It still works

[trail mango]

it doesn’t

[craggy plank]

While you have to separate it

You can’t simply get the solution with one step

[trail mango]

well not as simply as what i just said

[floral shadow]

Is it cases using perms

[craggy plank]

yeah

[wild pawn]

Think about it as a Pascal’s triangle

The sums on the sides would up to the diagonal or that’s how they taught it in my class

[jagged flare]

yeah but like my method i think also works if there are just paths that you cant cross

[wild pawn]

Oh ya you’ll also have different shapes it’s not always squares so doing it the way the teacher showed is helpful just in case other methods don’t work with different restrictions

[mellow axle]

a nice intuitive approach that i like is starting from Q and asking the question at a given point (x,y) how many ways can i go to (x + 1, y) and (x, y + 1) and working your way backwards

[floral shadow]

.close

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[main cobalt]

hey guys anyone know how to do this sequence question? T_n = 7 x T_n-1 - 10 x T_n-2 show that T_n = 3 x 2^n + 7 x 5^n

[vocal forge]

$T_n = 7 \cdot T_{n-1} - 10 \cdot T_{n-2} $ show that $T_n = 3 \cdot 2^n + 7 \cdot 5^n$

[soft zealot]

Pro_Hecker

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[main cobalt]

<@&286206848099549185>

[mortal helm]

)

[mortal helm]

here is an example of a sequence problem. hope it helps (source: https://t.ly/FhkTS)

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[empty tartan]

pls explain how all the signs changed?

[torpid igloo]

Multiply numerator and denominator by -1

[empty tartan]

i see

thanks

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[tulip cloud]

Not sure how to workout frequency density without class width or frequency

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[tulip cloud]

<@&286206848099549185>

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[rose raptor]

I differentiated but a very complex calculation is coming and I can't bring the dy/dx term out!

[forest ember]

Can you send your working

[rose raptor]

It's dirty but I did this.

[rose raptor]

I also swapped the direction. Note that please

[forest ember]

Let’s go over d/dx(xy) first

It looks like you know to use product rule, but used it wrong

Can you tell me the definition of product rule?

[rose raptor]

It's uv'+u'v right?

[forest ember]

Yeah

And since this is an implicit function, we have u = x, v = y(x)

[rose raptor]

Yeha

[forest ember]

Do you know what the derivative of y(x) is wrt to x?

[rose raptor]

d(y(x))/dx but what is y(x) here?

[forest ember]

You don’t know y(x), but you can still use the same method to get its derivative

By chain rule, you have
[ \dv {y(x)}{x} = \dv {y(x)}{y} \dv {y}{x} ]

[soft zealot]

shsgd

[forest ember]

And you just leave it as that

I prefer to write it as y’ dy/dx though

[forest ember]

Now try to do the product rule again on xy

[rose raptor]

could you explain whats y(x) here

[forest ember]

Usually you work with equations that look like y = [some function of x] right?
Here we take y to be the function of x that corresponds to this implicit function

So y(x) would be what the implicit function would look like if it were only composed of functions of x

But you don’t actually have to find it, sometimes you can’t even find it

[rose raptor]

Could you give an example?

[forest ember]

Ok, let C be a circle centred at the origin with radius 2.
C can be expressed implicitly as
x^2 + y^2 = 4

We can also rearrange to make y the subject, so we have
y = +- sqrt( 4 - x^2 )

Then this would be the corresponding y(x) ^

Here it was easy to isolate y, but this isn’t always the case

[forest ember]

Does this help?

[rose raptor]

Oh I got it. Thanks a lot

I got the ans.

Have a good day

.close

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[lapis kiln]

if i continue solving this i get x=1,3467 which is wrong cuz the answer is 3 but idk where i went wrong

[onyx peak]

wait sorry, it was correct

what exactly happened here though?

[lapis kiln]

aaaaa i found my mistake i was supposed to factor out 1/log4 not log4

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[cosmic zinc]

Hi I got a question on how to do part b of this