help-49

[edgy garden]

idk why i thinki forgot my basics but if this is the differential equation:
x^2y" + 3xy' +10y = 0

and we make the substitution x = e^z then what will my y" and y' equal?

[edgy garden]

dy/dx = dz/dx * dy/dz

dz/dx = 1/e^z

[dawn dagger]

differentiate here both sides again

for y''

[edgy garden]

so

d^2y/dx^2 = d^2z/dx^2 *dy/dz + dz/dx * dy^2/dz^2 right

[dawn dagger]

bruh this format

[edgy garden]

wait i will latex it

[dawn dagger]

y''(x) = y''(z)z'² + y'(z)z''

,,\frac{\dd^2y}{\dd x^2} = \frac{\dd^2y}{\dd z^2} \cdot \left ( \frac{\dd z}{\dd x} \right )^2 + \frac{\dd y}{\dd z} \cdot \frac{\dd^2 z}{\dd x^2}

[grand pond]

bacc

[dawn dagger]

Here I rather prefer the other notation

,, y''(x) = y''(z) \cdot (z')^2 + y'(z) \cdot z''

[grand pond]

bacc

[edgy garden]

why is z'^2 though? wont we just apply the product rule?

[dawn dagger]

yea

If you differentitate y'(z) wrt x

you get y''(z) * z'

an additional z'

[edgy garden]

oh probably thats why i wasnt getting the right solution

will try again

[dawn dagger]

yea you need to chain rule again since z = z(x)

[edgy garden]

I tried substituting it back in this equation but somehow I am still not able to get it in the constant coefficient form.

y' = y'(z)/e^x
y" = y"(z) * 1/e^2z -y'/e^z

x^2y" = y" -y'e^z

3xy' = 3y'(z)

+10y

so we get the new equation as

y" +y'(3-e^z) + 10y = 0

[midnight plank]

@edgy garden Has your question been resolved?

[dawn dagger]

Why did you do this sub in the first place?

I just watched a mini vid, and that's a cauchy euler equation

y=x^m
y'=mx^(m-1)
y''=m(m-1)x^(m-2)

[midnight plank]

@edgy garden Has your question been resolved?

[midnight plank]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

[subtle torrent]

what's the vid

[midnight plank]

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[dawn dagger]

It's a german video

[subtle torrent]

😭

I'm German

[dawn dagger]

Wat

[subtle torrent]

Lemme see😭

[dawn dagger]

Bro stop playing

you from the UK

briish

[subtle torrent]

Wtf

With my broken English

Mods will stop us cuz we're occupying the help channel

[dawn dagger]

no

[subtle torrent]

Why is it a Cauchy Euler equation

[dawn dagger]

https://www.youtube.com/watch?v=ll-BPEx4vfI

[subtle torrent]

Good

[dawn dagger]

Are you for real German???

[subtle torrent]

Sure

Ich bin Deutscher

Ha that's the reason why they substitute with e^z

[subtle torrent]

Beautiful

[dawn dagger]

niemals

Sprichst du deutsch

[dawn dagger]

Was ist der Grund

[subtle torrent]

damn lemme open my deepl

[subtle torrent]

We want to cancel out x^n

[dawn dagger]

Lügner

you are not German

[subtle torrent]

I should pick up my German learning, darn

[dawn dagger]

bro

it's obvious

Ich Bin Deutscher

says no Deutscher

we say was geht bruder

[subtle torrent]

Learned

[midnight plank]

@dawn dagger Has your question been resolved?

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Remember:
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• Be polite and have a nice day!

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[torn mica]

is there a formula to know the diagonal length of an even 2n sided polygon?

[torn mica]

.close

[midnight plank]

Channel closed

Closed by @torn mica

Use .reopen if this was a mistake.

[midnight plank]

Available help channel!

Send your question here to claim the channel.

Remember:
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• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
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[real pivot]

For part a this is what I was thinking:

We already know that each binomial of order $k$ has $2^k$ nodes, and there can only be one binomial tree of each order in the heap. Another thing we know is that each binomial tree $B_k$ has $2^k - 1$ edges. So finally the total number of edges in a binomial heap with $n$ nodes is the sum of edges in each binomial tree in the heap:

Total number of edges: $\sum_{i=1}^{\alpha(n)} (2^{k_i} - 1) = \sum_{i=1}^{\alpha(n)} (2^{k_i}) - \sum_{i=1}^{\alpha(n)} 1 = n - \alpha(n)$

($k_i$ here refers to the position of $1$'s in the binary representation of $n$. For example $n = 13$ (Binary: ${1101}_2$), where $k_1$ refers to the index of first 1 from right $k_1 = 0$, $k_2$ refers to the second 1 from right $k_2 = 2$ and so on...)

is this good?

[grand pond]

Calc III Victim (Pt. 2)

[midnight plank]

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[gritty gorge]

If I'm given an indefinite integral like in this image, and I have a definite integral to calculate of the same form, how do I use the indefinite integral to calculate?

[summer terrace]

$\int f(x) , dx = F(x) + C \ \ \int_a^b f(x) , dx = F(x) \big|_a^b = F(b) - F(a)$

[grand pond]

Emily

[midnight plank]

@gritty gorge Has your question been resolved?

[midnight plank]

Channel closed

Closed due to timeout

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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.

[carmine hawk]

How can I simplify this fraction

[main current]

Can cancel x² from top and bottom

You'll have a leftover x on the denominator. That will always be there

[carmine hawk]

i got it

I'm assuming I have to factor t^2/3

Idk how to factor that out of 1

[barren onyx]

hi

[barren onyx]

apply l hospital

[carmine hawk]

not allowed..

[barren onyx]

?

[carmine hawk]

i need to follow the directions

i need to factor

[keen hill]

divide every term by the highest powered term

[barren onyx]

Ah

its infinity by infinity form

[carmine hawk]

so 1/t^3/2 isnt right so

[barren onyx]

so take the highest power common from numerator and denominator

I assume thats what u gotta do

[keen hill]

it isn't correct?

[carmine hawk]

no

[keen hill]

oh for that

[barren onyx]

right t as t^3/2

[keen hill]

well for the factoring

[barren onyx]

and take it common

answer should be 1/2 i believe

[keen hill]

it should be (t^(-1/2)-1)

do you understand why

[carmine hawk]

nope

i dont

[keen hill]

the left side needs to be equivalent to the right side

[carmine hawk]

but its not correct either

[keen hill]

not 1/t^(-1/2)

just t^(-1/2)

or

1/(t^(1/2))

do you understand why it would be that

[barren onyx]

take out t^3/2 common

[carmine hawk]

oh ok yeah

[carmine hawk]

idk

[barren onyx]

youre gonna have t^3/2(t/t^3/2-1) in the numerator

t/t^3/2 is just 0

so answer should be -1/2

[keen hill]

the problem calls for it to be done step by step

so im assuming every step needs to be filled in

[barren onyx]

oh

alr

[keen hill]

remember that powers add when you multiply, so when you factor out a t^(3/2), you need to make sure all the other powers add and match

[carmine hawk]

ok i get it

also

idk why this is true

[keen hill]

think about what the horizontal asymptote means

[carmine hawk]

approaches a num

[keen hill]

it just describes the end behavior

[carmine hawk]

yeah

[keen hill]

before the end

it might cross

so like

it might cross an asymptote at some finite value

but at infinities, (the ends) it will approach a number

[carmine hawk]

how do i ratioanlize?

[grand pond]

bacc

[dawn dagger]

Multiply the numerator and denominator by the conjugate of the numerator

[carmine hawk]

wouldnt that have to be on both the top and bottom?

[dawn dagger]

yes

[carmine hawk]

like what would that be?

\sqrt{x^2-2x-1}-x?

[dawn dagger]

yes

no

sqrt(x^2+2x+1)-x

only that

the conjugate of a+b is a-b

[carmine hawk]

ohh

little stuck on the next part

[carmine hawk]

idk how to factor the largest power here

[dawn dagger]

The largest power is x^2 pull that from the root

[carmine hawk]

i thought itd be

but it doesnt work

[carmine hawk]

so idk

[dawn dagger]

bro

this program is so misleading

x^2+2x+1 = (x+1)^2

yea it seems to me it wants sqrt((x+1)) twice

[carmine hawk]

oh what

[dawn dagger]

sqrt((x+1)) * sqrt((x+1)) = sqrt((x+1)^2) = sqrt(x^2+2x+1)

[carmine hawk]

nope

[dawn dagger]

i dont know

[carmine hawk]

idk either

[dawn dagger]

i mean i actually know but idfw computer program learning sites

Or is it x?

[carmine hawk]

It's not x either

[dawn dagger]

x*sqrt(1+2/x+1/x^2)

factor the highest power

sorry, i dont think this game is worth my time, wish you good luck tho

@bright shoal Yo

[bright shoal]

Yo

Lol

[dawn dagger]

can you help

[bright shoal]

No bro you goated 🐐

Yea ofc

What's the question sir

[dawn dagger]

we tried that

[dawn dagger]

.

[bright shoal]

We need to factorise?

[dawn dagger]

yes

[bright shoal]

Okok

[dawn dagger]

but this stupid site decides to do things weird

[bright shoal]

bro can you type in latex pls

Pls

[dawn dagger]

idk latex

@small jasper can you help

[small jasper]

$\sqrt{x^2} \cdot \sqrt{1+\frac{2}{x}+\frac{1}{x^2}}$?

[grand pond]

Civil Service Pigeon

[small jasper]

cause it mentions $\sqrt{x^2}$ on the next line

did you try that?

[grand pond]

Civil Service Pigeon

[dawn dagger]

yes

that makes sense

goat

[bright shoal]

Okok

[dawn dagger]

@carmine hawk

[small jasper]

this is too much scaffolding lol

just make it a 1 part numerical response

[bright shoal]

Yes so you took x inside

Getting (x+1)^2 inside the root

[carmine hawk]

What do I try?

[small jasper]

.

[bright shoal]

Which gives mod (x+1)

[dawn dagger]

what pigeon suggested

[dawn dagger]

bro

[bright shoal]

Yes bro

[dawn dagger]

😂

[carmine hawk]

Doesn't work

[dawn dagger]

i am allergic to modular arithmetic

[bright shoal]

Lol

[small jasper]

[dawn dagger]

yea your site sucks

sorry to say it

[bright shoal]

Na

[small jasper]

do we think they made a mistake lol

[bright shoal]

The site is cooked

[dawn dagger]

civil service pigeon goated fr

[bright shoal]

@carmine hawk give a good look at the question

Is the question right

[carmine hawk]

💀

Yeah I guess

[bright shoal]

Bro is goated 🐐 cz he is a civil service pigeon

The question is right?

[dawn dagger]

ye

[bright shoal]

Tf the site

[small jasper]

do my work for me 🙄

lemme ruin that "goated" opinion for you by being an entitled helpee

🙂

[dawn dagger]

i know what i say

[bright shoal]

No bro Is a 🐐

Cz bro does goated 🐐 question too

@carmine hawk

You need to find the largest power that can be taken out of

The root

Right?

[small jasper]

what if the boxes are in reverse order

[dawn dagger]

thats what it says goat

[bright shoal]

Na me no 🐐

[small jasper]

like what if they pulled a $$\sqrt{\frac{1}{x^2}+\frac{2}{x}+1} \cdot \sqrt{x^2}$$

[grand pond]

Civil Service Pigeon

[dawn dagger]

what if commutativity exists

[bright shoal]

So

[small jasper]

what's the probability that whoever wrote this was too braindead to think of that

oh wait I can't read

in the parentheses

mmmmmmmm

[bright shoal]

Wait

What if we just write

√(x+1)

[small jasper]

it says "power of x" tho

[bright shoal]

√(x+1)

[bright shoal]

You correct but brain-dead guyz

Need brain dead answers 💀☠️

[small jasper]

.

[bright shoal]

Its not even a question anymore

We need to satisfy the site guy

By giving the answers he likes

[small jasper]

can you find it in inspect element by any chance

🤔

[bright shoal]

Let's see

[small jasper]

now

did we try $\sqrt{x^2} \cdot \sqrt{\frac{1}{x^2}+\frac{2}{x}+1}$

[grand pond]

Civil Service Pigeon

[small jasper]

commutativity gone

test all six permutations of the second radicand

[carmine hawk]

Yes

[bright shoal]

Try

√x

Try once

[bright shoal]

Try √x in the left box once

[bright shoal]

√x^2

[carmine hawk]

.-.

no

[bright shoal]

What?

[carmine hawk]

its right..

i dont

understand

[bright shoal]

Have you tried it already

[dawn dagger]

bro you are comedian

[bright shoal]

Wait √x right?

[carmine hawk]

explain

[dawn dagger]

briiiiiiiiiiiiiii

[bright shoal]

See in the bottom its written

[dawn dagger]

[bright shoal]

In the left box

[dawn dagger]

ye

[bright shoal]

Write the square root of the largest power

Which can be taken

From the

Square root

Now we took x^2 common in the root

√(x^2)(1+2/x+1/x)^2

So they broke it like that

[small jasper]

didn't I legit say that earlier

[bright shoal]

√x^2 *(√(1+2/x+1/x^2))

[dawn dagger]

no

[bright shoal]

Na bro is the 🐐

Imma just his messenger

[dawn dagger]

you are an entitled helpee, pigeon

[small jasper]

🙄

y'all suck

I'm leaving this server

[bright shoal]

💀

[bright shoal]

If you leave who will bring us the messages

The letters

The gifts

[dawn dagger]

who will eat the bread crumbles huh

[bright shoal]

After all you are a civil service pigeon

[dawn dagger]

☠️

[bright shoal]

Bro write it in root

Fr

Bro is getting rooted

[dawn dagger]

fr

[small jasper]

I'm too rich for that

[carmine hawk]

oh

[small jasper]

deal with it

[bright shoal]

Bro eats the premium bread crumbles

[dawn dagger]

goated

[bright shoal]

Yay rocket science Woohoo

[small jasper]

I prefer bibimbap

[small jasper]

bruh I legit said that earlier 💀

#help-49 message

[bright shoal]

Bro is a good guy

Bro said it

But bro did not Enforce

[dawn dagger]

yea bro

it was an issue of typing it correctly

[carmine hawk]

💀

[small jasper]

._.

[dawn dagger]

like dozens times

[dawn dagger]

we know you great and stuff

[carmine hawk]

idk what to do here btw

[bright shoal]

Fr I tho6

thought*

[small jasper]

Recall that $$|x|=\begin{cases} x, x \geq 0 \ -x, x<0 \end{cases}$$

[bright shoal]

Bro is asking the proof of Riemann's theorem

[dawn dagger]

pigeon will fly you through these

[grand pond]

Civil Service Pigeon

[small jasper]

I'm in bed rn 💀

I'm just waiting until I can take my pill and then I'm sleeping

[bright shoal]

Cz bro was not able to get help even after having civil service pigeon and bacc

[dawn dagger]

oh damn

[bright shoal]

Pill

💊

Take it now

And sleep

[small jasper]

no u

[bright shoal]

Bro's brain needs rest

[small jasper]

if ygs did my work for me

then that wouldn't be an issue

[bright shoal]

Bro is so goated

[small jasper]

smh

[bright shoal]

Bro's brain produces hp

[carmine hawk]

idk

[bright shoal]

💀☠️

Na

Na

Hell na

[small jasper]

r u ok

x approaches -infty -> x < 0 -> |x| = -x

[carmine hawk]

oh they meant

literally -x

ok

[bright shoal]

Lol

[dawn dagger]

damn

[bright shoal]

Spare him lord pigeon

[carmine hawk]

pls spare me

[bright shoal]

He will not be able to face thou torments

[small jasper]

you don't want to see what happens when I mark proofs then

[carmine hawk]

💀

[dawn dagger]

the "r u ok" killed me

[bright shoal]

Hail lord pigeon 🐦

[bright shoal]

Fr bro sounded like a true prof.

[small jasper]

yeah I'm the math friend of my group and I pull it on them all the time lol

[dawn dagger]

if you get helpful then it's over

[bright shoal]

That's the problem

I am not able to get helpful

[small jasper]

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

[grand pond]

Civil Service Pigeon

[small jasper]

throw the +x in there, factor, and run with it

[dawn dagger]

you should honestly

[bright shoal]

Time issue bro

[dawn dagger]

you will get it (trust the process)

[bright shoal]

Today's my off

So I cane

came*

[bright shoal]

What ? Helpful role 💀☠️

[dawn dagger]

fly with it*

[bright shoal]

Lol

[bright shoal]

Fr run you wasted too much time on a question

And you have several left my guy

[carmine hawk]

wdym

[bright shoal]

Lol

[carmine hawk]

a few 😭

[bright shoal]

Type +x in the box

My guy

Factor

And run

You need to do other questions my guy

[carmine hawk]

oh ok thats right

[small jasper]

Help me

[bright shoal]

💀☠️

Ok let's try

[small jasper]

$x+\sqrt{x^2+2x+1}=x \left(\cdots)$

[grand pond]

Civil Service Pigeon
Compile Error! Click the reaction for more information.
(You may edit your message to recompile.)

[small jasper]

Most of it is already factored from earlier

[carmine hawk]

im lost

[bright shoal]

We tryin it fr

Wish me good luck

[small jasper]

@dawn dagger ^

[dawn dagger]

found you now you are not lost

[carmine hawk]

not sure what im supposed to do with the

[dawn dagger]

Out of all math I hate geometry

[bright shoal]

let's try

[carmine hawk]

so

idk

[dawn dagger]

idk either

you say you are lost

you dont even say what specifically is the issue

@bright shoal

[bright shoal]

Me?

[dawn dagger]

yo

[bright shoal]

Yo

[dawn dagger]

can you help

[bright shoal]

Sure

[carmine hawk]

idk how to simplify after what we have

to actually compute the limit

[dawn dagger]

what are we havign

[bright shoal]

Just trying pigeon's question

[dawn dagger]

this?

[carmine hawk]

yeah

well no this

[dawn dagger]

this is like

-xb+x

factor x

x(-b+1)

[dawn dagger]

also post the whole

[carmine hawk]

well yeah ik how factoriazton works

[dawn dagger]

you send everything but the bottom

[bright shoal]

Ok so now

We need

[carmine hawk]

theres nothing else

[dawn dagger]

apparently not lol

[bright shoal]

No cap but can I say something

Pls

[dawn dagger]

this is all about factorization

[carmine hawk]

did you want the submission button

[bright shoal]

What you have inside the square root is nothing but (1/x +1)^2

[dawn dagger]

yea you should submit

[carmine hawk]

factorizing that weird expression

[carmine hawk]

this

[dawn dagger]

if you factor x and let it go -inf you will get your answer

[carmine hawk]

i have it like that

[dawn dagger]

the terms that are divide by x go to 0

[bright shoal]

Now if you take the root

-x(1/x+1)+x

-1-x+x

-1

Done

Simple as it looks

[carmine hawk]

howd you get to this

take the root?

[bright shoal]

See

We have

[dawn dagger]

oppa

this site sucks

you know why

[bright shoal]

(1/x+1)^2

Inside the root

I took the root

It becomes mod(1/x+1)

Now According to your condition

I can take it as +ve

So I did it

So it became

[carmine hawk]

idk what mod is

ve?

[bright shoal]

-x(1/x+1)+x

So I got -1

,rotate l

[bright shoal]

See this is mod

[carmine hawk]

ok

now this question

should be simpler

f(x+h)-f(x)/h

[bright shoal]

Na

Bro they fr correct

Its derivative is -ve

[carmine hawk]

what is ve

[bright shoal]

Your smiles always decrease after doing homework for time t

They speak in facts

[carmine hawk]

true

[bright shoal]

Apply limit definition

at x=1

What I can say more

[carmine hawk]

well i just dont know how to simplify like

1/sqrtx+h - 1/sqrt x over h

[bright shoal]

rationalise

[carmine hawk]

thats like the weird thing with the conjguate right

[bright shoal]

Yes

Show me

[carmine hawk]

sqrtx-h/x-h - sqrtx/x

is that right?

@bright shoal

[bright shoal]

No

See

Imma show

Now rationalise

And now try yourself

[midnight plank]

@carmine hawk Has your question been resolved?

[midnight plank]

@carmine hawk Has your question been resolved?

[midnight plank]

@carmine hawk Has your question been resolved?

[midnight plank]

Channel closed

Closed by @carmine hawk

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.

[clear atlas]

hello! i'm stuck on how to do this simple math problem, can i please get help ?

[novel lion]

say on friday the store sold 2x vanilla cones and 3x chocolate cones (since 2:3)

if there were 4 more vanilla cones, so 2x+4, the ratio would become 3:4

so 2x+4/3x = 3/4

[worthy wing]

Wait, doesn’t that make the initial ratio impossible? Maybe i am miss reading

[novel lion]

initial ratio is 2:3

2x/3x is 2:3

[worthy wing]

Yes i meant with the ans

[novel lion]

x=16 so initial one would be 32/48 which is 2:3

if u add 4 it would be 36/48 which is 3:4

[worthy wing]

Oh it says vanilla not total

[novel lion]

yeah

[worthy wing]

I didn’t see that

Was getting weird in my mind lol

[midnight plank]

@clear atlas Has your question been resolved?

[midnight plank]

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[twilit field]

Suppose $f \circ g = g\circ f$ for all functions g prove that f(x)=x

[twilit field]

Now this is equivalent to proving $g(f(x))= g(x)$

[grand pond]

Veni, vidi, perii

[hard shard]

surely g(x)=f(x)=-x also works

[twilit field]

I'm just quoting spivak, don't shoot the messenger

[hard shard]

g(x)=1
f(x)=x^2

[grand pond]

Veni, vidi, perii

[twilit field]

so $g^{-1}(f\circ g) = f$

[grand pond]

Veni, vidi, perii

[runic hamlet]

who says that g has an inverse

[hard shard]

!original

[midnight plank]

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.

[hard shard]

i want the source

[twilit field]

27(c)

[twilit field]

Oh, I can't ssume that

okay

[hard shard]

oh all functions

[twilit field]

okay

so I have to prove $g(f(x)) = g(x)$

[grand pond]

Veni, vidi, perii

[quiet hinge]

Yes and you are given f(g(x))=g(f(x)) for all g

[twilit field]

so just to be sure, I have to solve this without inverses

[quiet hinge]

Yes

[quiet hinge]

However you shouldnt try to prove this

Just try proving that f is the identity. I.e, f(x)=x

Yes if f is the identity then g(f(x))=g(x) but that isnt a helpful reformulation

[dreamy lichen]

If you want a little nudge in a right direction, ||try starting by figuring out value of f at certain points, such as 0 and maybe 1|| ||Do that by choosing specific g||

[midnight plank]

@twilit field Has your question been resolved?

[twilit field]

I see

thanks

I'll think about this

[midnight plank]

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[hidden summit]

@ornate dew

[hidden summit]

Post the problem here

[ornate dew]

Ight

Question is

The question I need help with is

[hidden summit]

<@&286206848099549185>

You just wait now

[ornate dew]

Ight bro

<@&286206848099549185>

[hidden summit]

<@&286206848099549185>

If this doesn't work then you have to accept that the world is cruel and you'll just have to move on 💔

[gaunt otter]

Don't spam mention helpers

[ornate dew]

Sorry

I have been waiting for 4 Horus and really need to know how to do thsi

[hidden summit]

@ornate dew I'm sorry I failed you

.close

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[ornate dew]

It chill thanks you anyways

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[tawdry laurel]

Huh thats weird

[abstract cape]

yeah

suppose x=na
and y=ma
then it will be only true if mn| |m+n or a||m+n

then what

[feral sedge]

clear denominators

[abstract cape]

how?

[feral sedge]

multiply both sides by nxy

[abstract cape]

then

[feral sedge]

rearrange

try to factor

[abstract cape]

then

[midnight plank]

@abstract cape Has your question been resolved?

[midnight plank]

@abstract cape Has your question been resolved?

[jaunty canopy]

spot that (bracket)(bracket) = integer means that each of the brackets are integer factors of integer

[midnight plank]

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[midnight plank]

@carmine hawk Has your question been resolved?

[visual tiger]

do you recognize this as the power set of something?

[carmine hawk]

im not sure

thats a subset of the powerset of x

is what im guessing

its all kinda vague to me

[visual tiger]

a supset*

but

without thinking about x

[visual tiger]

this is the powerset of a very well defined set

find it

[carmine hawk]

power set of {1} ?

[visual tiger]

not exactly

power set of {1} is {emptyset, {1}}

hint: in a power set, the largest subset is the original set

[carmine hawk]

Well I meant like the set of the set of that

So like the power set of the set of the set of 1

[visual tiger]

still not exactly

[carmine hawk]

Is it the power set of the power set of 1?

[visual tiger]

no

[carmine hawk]

Hm

[visual tiger]

you can only take the powerset of a set

when you say 'the power set of 1' it doesn't make really sense

[visual tiger]

.

[carmine hawk]

So the power set of 1 and null?

That doesn't really make sense to me

[visual tiger]

the power set of {1, null}

it is that

[carmine hawk]

Yeah

[visual tiger]

1 and null are the elements of that set

[carmine hawk]

Yeah I see

[visual tiger]

so

[carmine hawk]

And the power set itself is this?

[visual tiger]

you're tasked to find all the sets x

[visual tiger]

you can do the math yeah

[visual tiger]

P({null,1}) is this

so you've been tasked to find all sets x

such that P(x) is a subset of P({null,1})

intuitively, which sets are gonna work?

[carmine hawk]

I'm not entirely certain of the definition of a subset

It's a little vague to me idk why

[visual tiger]

subset just means "all elements of one are in the other"

like

[carmine hawk]

Brb

[visual tiger]

I'm gonna pull out my best example

[carmine hawk]

So the power set of 1 would count here right

[visual tiger]

where exactly would it count?

[visual tiger]

like x = {1} or x = P({1})?

[carmine hawk]

x=P{1}

[carmine hawk]

In the subject of

[visual tiger]

uuuuh

in P(P({1})), {{1}} is an element

[visual tiger]

if it were a subset of this, then {{1}} would be an element that appears here

What I would suggest

is instead of writing x = P(something)

just start writing the possibilities for x as a set

like enumerate the elements of x

and then check if the set you created works

(last hint: if P(A) is a subset of P(B), what more can we say about A and B?)

[carmine hawk]

all of elements of P(A) are in P(B)?

[visual tiger]

that's the definition of P(A) subset of P(B)

but does that imply something about the SETS A and B themselves?

that doesn't talk about their powersets?

[carmine hawk]

doesnt it imply A is a subset of B?

[visual tiger]

yes!

P(A) subset of P(B) is equivalent to A being a subset of B

so

if we're looking for x such that P(x) subset of P({null, 1})...

[carmine hawk]

so X is a subset of null,1

right?

[visual tiger]

small x

x is a subset of {null,1}

[carmine hawk]

yeah

so how do i find X?

isnt x = X?

[visual tiger]

?

x is an element of X

X is the set of elements x such that x subset of {null,1}

[carmine hawk]

not sure what you mean

[visual tiger]

this

X = {the set of elements x such that...}

[carmine hawk]

yeah

its just like

[visual tiger]

so x is the notation for ELEMENTS of X

it's not the same as X

[carmine hawk]

if x is {null,1}

which is in the subset of {null,1}

[carmine hawk]

so X is the set itself

but im trying to enumerate its elements

idk im confused

[visual tiger]

ok

say A = {1,2,4} for example

if you're tasked to find A

you would look for the elements of A

so 1,2 and 4 are the elements of A

but A is the set that contains them all

so {1,2,4}

here you're telling me that x = {null,1} is one of the elements of X

which is true

so X = {{null,1}, ...}

and we just need to keep looking for all the others

but here's a last hint

X is the set of all subsets of {null,1}

does that ring any bells?

[carmine hawk]

isnt the power set? that?

[visual tiger]

yes

X = P({null,1})

[visual tiger]

which...

[carmine hawk]

so the answer to the question is basically the question 😭

im confused

[visual tiger]

it's in the question yeah

[carmine hawk]

what is this bafoonery

[visual tiger]

X was hidden under your nose

the whole time

[carmine hawk]

;-;

so the same notation works? i dont have to change anything?

because the set itself implies that its null or set of nul not both right idk

[visual tiger]

?

X is the set that contains null, {null}, {1} and {1,null}

it's not equal to any of its elements

it's equal to the box that contains them all

[carmine hawk]

yeah

i think its right

i rly need sleep

tysm 🙏

[visual tiger]

np

[carmine hawk]

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[twilit field]

Trying to prove lcm(a,b), where a,b are co-prime is $ab$

[grand pond]

Veni, vidi, perii

[twilit field]

$so the multiples of a are
\
$a,2a \dots ba$
\
and
\
those of b are
\
b,2b, \dots ab$

[grand pond]

Veni, vidi, perii

[twilit field]

now, to prove that (na,mb) are co-prime

when n \neq b and m \neq a

consider $\frac{na}{mb}$

[grand pond]

Veni, vidi, perii

[twilit field]

The simplest case , would be na/mb=1

so $\frac{n}{m} \frac{a}{b}$

[grand pond]

Veni, vidi, perii

[twilit field]

so $n = \frac{b}{k_1}$

[grand pond]

Veni, vidi, perii

[twilit field]

$m = \frac{a}{k_2}$

[grand pond]

Veni, vidi, perii

[twilit field]

hmm

nvm

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[tepid lodge]

💀

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[chilly cobalt]

if f_n(x) = 1 + x + x^2 + x^3 + ... + x^n, and F_n(x) = [integral from t to 0 of f_n(t)dt]
then find lim n -> F_n(x)

[chilly cobalt]

is e^x correct?

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[tacit veldt]

I was solving this then I reached question three and realized I don't have n, what should I do?

[tepid lodge]

n = 13 I think

you and twelve other interns measure

[tacit veldt]

oh i see

thanks

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[tacit veldt]

.reopen

[midnight plank]

✅

[tacit veldt]

in the fourth question, should I see if the lengths are overlapping to find dependence? or the question is asking for something else?

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[alpine tundra]

Int 1/(1+e^x) from 0 to infinity

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[alpine tundra]

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[limpid citrus]

Can someone help me solve this? I'm very confused. I got that a^2 + ab + b^2 = 3 , but the other two are trickier

this is how i got the 1st one

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[cerulean arch]

how would u find domain and range of g(x) = 2arccos(1+2/x)

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[vast bone]

How do I approach this idk

[dawn dagger]

What do you know about the derivative of sine and cosine

[vast bone]

Sin is cos

And cos is negative sin

[dawn dagger]

and negative sin is negative cos

and negative cos is sine again

sin(x)
cos(x)
-sin(x)
-cos(x)
repeat

[vast bone]

Ohhh

Okay thanks yeah that makes sense😭

4th derivative

[dawn dagger]

yea

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[kindred chasm]

How do I do this, it's supposed to be simple but idk where to start. I have to check if the result of this is a rational number or not

[prime hornet]

what are you being asked to do?

[kindred chasm]

determine if that is a rational number or not

[civic scroll]

There is a tedious but straightforward way to do this

Let x be the whole thing

Square it, then it becomes a sum of square roots plus an integer

So that x^2 - n, for some n, is again a sum of square roots

And if you square that again and repeat the process, you should eventually obtain an integer

So finally you obtain a polynomial equation for x

And if that equation has no rational roots, then x is not rational

[jaunty canopy]

i think it'll be easier to consider just sqrt(4+sqrt(7)) - sqrt(4 - sqrt(7)) for now

there's lots of sqrts so it should be possible to simplify it quite a bit

[kindred chasm]

I tried letting x be the whole thing and squaring it
But then stopped there and actually threw that into an app and calculated what the entire thing is when squared, to see if it actually gets me a result, and it does! It's a long method but i get how to do it

[kindred chasm]

do u have any idea how i could simplify it...theres definitely some way because in the exercise before this thats what i did, but idk how to do anything to it here

I think im gonna close this tho since i have this method and ill ask my teacher tmrw how i couldve simplified

[feral sedge]

read here, is good advice

square that thing, and square root it

[kindred chasm]

Like letting x = sqrt(4+sqrt(7)) - sqrt(4 - sqrt(7)) and squaring it? that gets me the same answer too

I think this is good enough maybe

Ty chat

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[vast bone]

126

How would I find the derivative

If it has absolute value

[dawn dagger]

you can resolve it using the def.

[grand pond]

bacc

[vast bone]

But wouldn’t I use quotient rule to find derivative

Omg I acc am being cooked with this lesson

[dawn dagger]

yoo acc cooked?

You will have a piecewise derivative that's all

[vast bone]

Yes I’m so cooked☠️

[dawn dagger]

no you are not

[vast bone]

Ohhh so I do one with x and one with -x

[dawn dagger]

your derivative literally differs by a minus

[nimble fog]

Notice you're only asked to find the derivative at one specific point. So you don't actually need to worry about the absolute value, because at that point, the function is the same as a function without an absolute value

[dawn dagger]

yea because that x > 0

[vast bone]

Ohhh

That makes sense thank you

[dawn dagger]

reading this but it is specifically at a point

[vast bone]

So I just find derivative when derivative of absolute value x is x

And then plug in?

[dawn dagger]

If you wanna find the derivative at a specifc point and you have an absolute value, then you need to figure whether you need the + or - version

[vast bone]

Also isn’t the derivative 1

For absolute value x

Or am I crashing out

[dawn dagger]

,w diff x/(sqrt(2-x^2))

[grand pond]

Results provided by WolframAlpha

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

Requested by adoniszgks

[dawn dagger]

How did you get there?

[vast bone]

No bc d/dx x is just 1

[dawn dagger]

yea

you need quotient rule

[vast bone]

Ughhhh😭☠️

[grand pond]

bacc

[dawn dagger]

You only need the first part

[vast bone]

Yeah ik

[dawn dagger]

because you wanna find the derivative at a specific point, where x is non-negative.

So consider now

,, \frac{x}{\sqrt{2-x^2}}

[grand pond]

bacc

[vast bone]

Our teacher assigned us like 50 problems for hw☠️

[dawn dagger]

You need quotient rule

[dawn dagger]

arent you happy about that

[vast bone]

Oh hell nahhh

[dawn dagger]

😂

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[vast bone]

My brain is like fried rn

164 please

[midnight plank]

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

[vast bone]

1🙏🙏🙏

[hearty rune]

what are the derivatives of h and s wrt x

in terms of f and g

[vast bone]

Yeah that’s what the question is asking😭

How do I find it without function

I know what it’s approaching ig

[hearty rune]

thats why i said in terms of f and g, do you know how to use the chain rule

[vast bone]

Yeah but ur given a function

Usually

[hearty rune]

sure, but you need to know what h' and s' are, and the only way you can do that here is writing them in terms of just f and g

like the derivative of fg is f'g+fg'

like that

[vast bone]

Okay then h(x)=f(g(x)

And use chain

But how

When ur just given a graph

[hearty rune]

im not even mentioning the graphs yet

just find h'

[vast bone]

Chain rule so f’(g(x)) * g’(x)

[hearty rune]

yeah
can you find
g(3), and g'(3) from the graph?

[vast bone]

I know g(3) is 5

How do I find g’(3) is it just slope at that point

Then 1

[hearty rune]

yeah exactly

and what is f'(5)

[vast bone]

5??

Ohhhh

-1/2

[hearty rune]

not quite

[vast bone]

What is it😭

[hearty rune]

is it going up or down

[vast bone]

Down

[hearty rune]

ah i see

youre looking at the wrong line

f is the black one

[vast bone]

Yea I realized😭

1/2

2.5??? Is that h’(x)

[hearty rune]

lets think about it
h'(3)=f'(g(3)) g'(3) = f'(5) * 1 = 1/2 * 1

dont lose track of your values

g'(3), not g(3)

[vast bone]

Ohhhh

Yeah I get it now

.close

[midnight plank]

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[midnight plank]

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[nova hare]

Find the equation of the plane containing the lines L1: x = 4-4t, y = 3-t, z=1+5t and L2: x=4-t, y=3-2t, z=1

[nova hare]

ok so like what i did was take the normal vectors of each and set each x, y, and z equal to each other to get a point where theyre equal, which was at the origin

then i took the cross product of the normal vectors to find smth orthogonal to both

oh oops i made a basic arithmetic error taking the cross product

my favorite!

i got the same answer as the provided solution oopsies!

.close

[midnight plank]

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[sharp coral]

are you sure they intersect at the origin? neither of them seem to even pass through the origin

[midnight plank]

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[winged wedge]

how os this right

wouldnt there be a whole at x=1 thus making it discontinuous

[cedar vortex]

x=-1, but ur right

the answer should be (a)

[winged wedge]

ye mb