help-26

[rancid tulip]

is it 3x - 2y - z = 3 ?

or im not sure if its -2y or - 8y

.close

[topaz sinew]

Channel closed

Closed by @rancid tulip

Use .reopen if this was a mistake.

[topaz sinew]

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.

[tawny chasm]

hey there, fun little problem from my pre-calc course, except I don't know where to start

[tawny chasm]

any help is appreciated /:p

[raven sparrow]

Can you find the side lengths of the triangle on the right?

Using trigonometric ratios

[tawny chasm]

cos theta as (5 - x) / 5?

[raven sparrow]

The hypotenuse of the triangle is 5

[tawny chasm]

if x is the remaining portion between the rectangle and the circle

[raven sparrow]

Since it's a ray

[tawny chasm]

mhm

and I take that where?

[raven sparrow]

If you have a right triangle with it's hypotenuse you should be able to find it's sidelengths just in terms of theta

[craggy haven]

,tex .sohcahtoa

[thorny flame]

hayley, who shakes the world

[tawny chasm]

.close

[topaz sinew]

Channel closed

Closed by @tawny chasm

Use .reopen if this was a mistake.

[topaz sinew]

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.

[pseudo sonnet]

I'm having great difficulty proving the only if part of this problem

so the underlined assumption tells us that f o F: M -> R is smooth, yeah? but what would a reasonable approach to take to prove that F is smooth? I've tried messing around with taking coordinate representations but it doesn't seem to get me anywhere

[pseudo sonnet]

the most straightforwards approach I tried was as follows:

take any f and note that the assumption tells us that f o F is smooth. then for any fixed p in M, there is a coord chart (U, phi) containing p such that f o F o phi^-1 is smooth. since f is also smooth, there's a coord chart (V, psi) containing F(p) such that f o psi^-1 is smooth. then the composition f o F o phi^-1 = (f o psi^-1) o (psi o F o phi^-1) is smooth. but now I can't see a way to conclude that psi o F o phi^-1 is smooth (which would finish the proof, I think), so I'm stuck

[topaz sinew]

@pseudo sonnet Has your question been resolved?

[topaz sinew]

@pseudo sonnet Has your question been resolved?

Channel closed

Closed by @pseudo sonnet

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.

[latent forum]

Would solve this question? I think I have a start but am unsure if my work is correct. Please let me know

[latent forum]

<@&286206848099549185>

[sweet shard]

, rotate

[sweet shard]

you simplified b wrong and your claim in e about half a triangle is also wrong

[latent forum]

ok but everything else is good right

[sweet shard]

From x equal to 3 to 4 the shape is a trapezoid

[latent forum]

yeah but we dont know the base 2 height

b1 is 3 right

so what would be 2 be

[sweet shard]

Two points determine the equation of a line

Or just use that 4 is the midpoint of 3 and 5

[latent forum]

no i get that

[sweet shard]

So the height must also be the midpoint between the two y values

[latent forum]

oh

so most likely 1.5?

[sweet shard]

But if you don't believe me use this

[latent forum]

ok so b would be (12 + pi)/2

and e would be pi/4 + 3 + 2.25?

b1 is 3 b2 is 1.5 and h is 1 for e

@sweet shard sorry for tagging my hw is due soon

<@&286206848099549185> im really sorry but my stuff is due

[steady flint]

Oh are these Riemann sums 🗿

Or like adding up geometric shapes

[topaz sinew]

@latent forum Has your question been resolved?

[latent forum]

they are supposed to be like an intro to definite integrals

[steady flint]

Huh I see

[latent forum]

i jsut want to know if my new ans is right lol

[steady flint]

Wait which one

[latent forum]

the rieman guy said everything right except b and e

[latent forum]

this is what I think it is

[steady flint]

(12+pi)/2 is correct

You would need to do

Um trapezoid

So

I think formula for trapezoid is

[latent forum]

i tried that

i think

[steady flint]

Um

Huh it’s a slanted one

Or maybe not

Hm

No it’s not

[latent forum]

im so cooked on this assignment

[steady flint]

I think you can find the area of trapezoid

[latent forum]

yeah i tried that

[steady flint]

Then subtract (12+pi)/2

And the little small 4,5

Thing

[latent forum]

why subtract

[steady flint]

I think you can argue that it’s a triangle

[steady flint]

Gimme sec

[latent forum]

ok

What I was thinking

[latent forum]

yeah

the bottom of the semi and triangle are connected btw

[steady flint]

Hm actually it kinda renders it obsolete…. Cause you gotta add a pi/4

[steady flint]

Epic

So you can use the formula

[latent forum]

would it not be this then?

[steady flint]

Subtract (12+pi)/4

[latent forum]

im confused on why we subtract

[steady flint]

How would I represent this…. Um so your shape

Consists of

A semi circle

A rectangle

And I think a traingle

[latent forum]

i mean trapizoid?

[steady flint]

Well trapezoid and semi circle

If you wanna be like that

We know semi circle is pi/2

[latent forum]

wait

what

its pi/4

[steady flint]

r=1

Pi is circle

So pi/2 semi

[latent forum]

yeah pi^2 is circle semi is pi/2 but 1/4 circle is pi/4

[steady flint]

Yes

Quarter circle is indeed pi/4

So in our problem

[latent forum]

im so confused

oh wait i got what ur saying

[steady flint]

Notice how a pi/4 is in the bounds

Like

The thing we solving for

[latent forum]

ye

[steady flint]

2 to 4

So it would be pi/4+3

[latent forum]

ok...

[steady flint]

Which is, literally what just 12+pi/4

That’s half

2 to 3

3 to 4 is a bit more tricky

[latent forum]

oh ok

[steady flint]

As we need to subtract off the 4 and 5 thing

[latent forum]

ok

i get it

ur getting the whole triangle area

[steady flint]

I think you would subtract 1/2

Mhm

[latent forum]

ok alr

[steady flint]

Area is 3

so 3-1/2

5/2

5/2+3+pi/4

[latent forum]

OHHHH

[steady flint]

At least I’m pretty sure

It’s 12:07 am for me here

I’m sleep deprived

[latent forum]

i think bro might be cooking

same

[steady flint]

You like 15-16?

[latent forum]

my hw overdue 😭

nah 17

[steady flint]

Make sure to verify it

[steady flint]

Clac ab or bc?

[latent forum]

i gotta wait till tmmrw cus its overdue and I need a code to unlock it

ab

[steady flint]

Mhm

Oh mice

I’m 16

[latent forum]

wby

[steady flint]

Multivarible and odes

[latent forum]

bro is a d1 sweat

[steady flint]

Should be on real aand complex before 17

I learned this when I was 14-15

[latent forum]

damn lol

[steady flint]

So it’s been awhile I’m sorry if it’s incorrect. But ideally speaking for solving these problems….

You need to find a bunch of areas of shapes

That you ALREADY KNOW

[latent forum]

nah all g

yea

[steady flint]

It should be accurate

Idk where you got that 1.5 from

In your e answer before hand

[steady flint]

Nah 🗿

[latent forum]

the last dude kept saying that the second base is the midpoint dist from from first base (3-0)/2

[steady flint]

I’m nothing compared to my friend lol

[steady flint]

It probably could work tbh

[latent forum]

not a single number💀

[steady flint]

He’s using the trapezoid thing….

And then subtracting out like 3

And 1/2

[latent forum]

oh alr

[steady flint]

Yeah

And pi/4

Well technically

[latent forum]

now i gotta cook with summation and sigma notation and limit def

[steady flint]

He’s adding pi/4

[steady flint]

You learn l hopital?

[latent forum]

no we just started integrals

[steady flint]

Riemann sums yet?

[latent forum]

ye kinda

[steady flint]

They fun trust

[latent forum]

like r hand l hand and middle

[steady flint]

Remember for a descending slope a right Riemann sum is underestimation

[latent forum]

ye

[steady flint]

Left is over

Mhm

I forgot how to do trapezoid Riemann sums

[latent forum]

we didnt do that yet

[steady flint]

I reccomend you memorize the formulas just for the unit…

[latent forum]

and no simpsons rule either

[steady flint]

And then forget about it

[latent forum]

yea i will

[steady flint]

Wha is that

[steady flint]

This was a joke

[latent forum]

idk it was on my lecture 2 days from now

[steady flint]

Oh it’s quanfying a series

In like a integral

I’ll have to memorize it

Don’t quote me on it

I haven’t used that at all in calc ab or bc

[latent forum]

oh

[steady flint]

I’d also reccomend another website that you can use for math

Math stack exchange : )

Like this

[latent forum]

oh yeah

[steady flint]

I’d say similar but I think math stack exchange is for more…. Sweaty people

As it’s a no bs environment and no drama should go on in the forums

[latent forum]

ye i saw that 💀

[steady flint]

You learning series…?

Harmonic….?

Power…?

[latent forum]

nah

[steady flint]

Maclaurin?

[latent forum]

idk what a series is lol

[steady flint]

Taylor? 🥺

[latent forum]

no 😭

[steady flint]

Oh these are infinite series

Calc bc 👍

[latent forum]

oh

[steady flint]

Love them man….

[latent forum]

i know shell method and newton method

from phyics c 💀

[steady flint]

x^n/n! is e^x if I recall

Yeah I was planning on taking ap phys c and cm

After I take ap phys one, and maybe ap bio and ap chem

[latent forum]

its pretty hard for me since idk any calc really

nice

[steady flint]

🗿

[latent forum]

whats ur current sheduele

[steady flint]

Um

[latent forum]

5 aps?

[steady flint]

Well school or self study

School I’m taking ap lang

Self study im taking like 10 aps

[latent forum]

bro is a mega sweat 😭

[steady flint]

Ap phys, ap bio, ap chem definitely….

That’s like 5 aps

Ap macro and micro

Like 6

[latent forum]

i did like 14

i think

including this year

[steady flint]

Imma finish them in a year

[steady flint]

Yeah I’m taking 5 next yr

[latent forum]

why are you doing this to ur self

[steady flint]

Wdym?

[latent forum]

bro is not going to go outside

[steady flint]

I go outside ;-;

I play chess

Honestly

I have so much free time

[latent forum]

no way u have time for that

how

[steady flint]

I skipped studying today

to busy scrolling

[latent forum]

shocked

[steady flint]

Like 3-5 hrs a day just studying concepts

And testing those concepts

And rinse and repeat

During school

Funny story

I actually haven’t learned anything

At all

[latent forum]

damn 3-5 a day MindBlow

[steady flint]

Besides history and English

[steady flint]

Hrs

[latent forum]

thats like my weeks studying lol

[steady flint]

Don’t have hw ;-;

Well you study for school

I don’t

[latent forum]

i mean

[steady flint]

But like a typical schedule would be

From 5am-3:15pm absolute brain rot

4:00pm-6pm gymnastics and working out and fun stuff

[latent forum]

5am???

bro

[steady flint]

9 pm-12 am is studying

[steady flint]

Wdym

I just scroll lol

Look at math animations

Watch 3b1b

Manim animations

[latent forum]

bro is math embodiment

[steady flint]

Close the channel we can talk in DMs

.close

[latent forum]

yea

.close

[topaz sinew]

Channel closed

Closed by @latent forum

Use .reopen if this was a mistake.

[steady flint]

If your done

[topaz sinew]

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 zinc]

I need clarification for which angle is the angle of elevation in the picture:

[pearl zinc]

Is the angle of elevation also parallel to the 32 degrees, meaning that the angle BPQ (B being balloon) is 30 degrees (since 62-32=30)

or is the angle of elevation also factoring in the 32 degrees, meaning BPQ is 62 degrees

[pearl zinc]

never mind, it's this. i checked with the answer key

.close

[topaz sinew]

Channel closed

Closed by @pearl zinc

Use .reopen if this was a mistake.

[topaz sinew]

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.

[inland crypt]

How should I solve this question

[topaz sinew]

@inland crypt Has your question been resolved?

[mystic jay]

do you know all primes other then 2 and 3 and of the form 6n+/-1

use that

assume p and q are are not 2 or 3

[inland crypt]

6n+/-1

What does that mean

6n/-1

[whole geode]

6n ± 1

[inland crypt]

Ooh

Ty

Ty I can solve it now

It both contradict where p= 6n+1 or 6n-1

So I only need to check for p = 2,3

.close

[topaz sinew]

Channel closed

Closed by @inland crypt

Use .reopen if this was a mistake.

[topaz sinew]

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.

[urban wasp]

can someone help me please

i used the formula and got λ^3 - λ + 1/2

how do i use that for the eigen values and eigen vectors

[lethal anchor]

Do you know Cramer's rule

[urban wasp]

no sorry

it might be too advanced for me 😭

[strange whale]

What's your issue here with lambda^3 + ... ?

You can't get the roots ?

[urban wasp]

yes

[strange whale]

That doesn't seem correct in the first place

[urban wasp]

i used the formula λ^3 -s1λ^2 + s2λ - s3

where s1 is the trace , s2 is coefficients of the diagonals and s3 is the determinant

[strange whale]

Well idk how you got your determinant but it's certainly not -1/2

[urban wasp]

oh yeah

it is 0?

[strange whale]

Yea

[urban wasp]

λ(λ^2-1) = 0

so i got 3 values right

for part b could i just plug it in

but its 10 marks

[strange whale]

Well you need to find the eigenvectors also ^^

[urban wasp]

oh yes

but for part b do you need to know the eigen vectors?

i seen somewhere you can just put the eigen values as the diagonals right?

[strange whale]

When I hear diagonalize I understand give both some P and D such that E = P D P^-1

[urban wasp]

p is just the eigen values right

[strange whale]

No

[urban wasp]

sorry

[strange whale]

D is the eigenvalues

[urban wasp]

i meant eigen vectors

[strange whale]

P has eigenvectors yes

[urban wasp]

ah i see

[strange whale]

And also they want you to diagonalize E

Be careful

But you can use the one for S to get the one for E

Actually they tell you to find the eigenvectors already in a)

How is that a goddamn 10 marker

[urban wasp]

that's what i was thinking 😭

i did the past paper and i kept using little tricks to do 10 markers under a few mins

[topaz sinew]

@urban wasp Has your question been resolved?

Channel closed

Closed by @urban wasp

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.

[potent night]

Guys is there a problem with the question? It is not solveable

[potent night]

I've calculated B^T B

And it's inverse doesn't exist

So what do I do

[strange whale]

Have you checked that these 4 vectors aren't linearly dependent somehow

[potent night]

Yes

The basis is linearly independent

[pseudo jetty]

,w rref {{0,1,-3,-1},{-1,-3,4,-3},{2,1,1,5},{0,-1,2,0},{2,2,1,7}}

[thorny flame]

Results provided by WolframAlpha

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

Requested by tearfox

[pseudo jetty]

doesn't look like it

[potent night]

I got caught lacking damn

Thanks

[potent night]

Sry

.close

[topaz sinew]

Channel closed

Closed by @potent night

Use .reopen if this was a mistake.

[topaz sinew]

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.

[placid token]

$\text{If the focus, centre, and eccentricity of an ellipse are respectively } (3,4), (2,3), \text{ and } \frac{1}{2}. \text{ Find its equation and standard terms.}$

[thorny flame]

riddle

[placid token]

tried this

[mortal thunder]

✓✓ will get b² = 6, a² =8

@placid token write the equation now

[placid token]

how do i get the coords for other focus

ae distance down

[mortal thunder]

Hmm? Why do you need the second focus

[placid token]

bcz the question asks for it

[mortal thunder]

You have center don't you

[placid token]

yes

but question asks for all standard terms

[mortal thunder]

Oh

[placid token]

extremities of latus rectum, vertices and fociis

And eqn of parabola

i don't understand which slope to use in parametric

[mortal thunder]

Center is midpoint of both focii => use midpoint formula

[placid token]

oh

external

[mortal thunder]

(h + 3) = 4, (k + 4) = 6

[mortal thunder]

XD

[placid token]

?

[mortal thunder]

Overcomplicating it

[placid token]

For extremeties of latus rectum

u need parametric

@mortal thunder hello?

[mortal thunder]

Hmm gimme a min.

[placid token]

ok

oh wait the slope is same as x+y=5 ig

U can get eqn of double ordinate passing through focus (3,4) x+y=7

so slope is -1

so x coord is 3*(b^2/a×(-1/√2)

[mortal thunder]

Ok

Yeah the slope of major axis is 1, so slope for latus rectum is -1, and pass it through 3, 4

For extremeties, you can make the parametric point of ellipse satisfy the line

[placid token]

oh

for eqn i need length from minor and major axes

[mortal thunder]

Can you try to be more specific with your sentences? Which equation do you need length for?

[placid token]

perpendicular distsnce of any point on ellipse from minor and major axes

[mortal thunder]

For which equation

[placid token]

The one i sent

It should be (x-y+1)?

And x+y=5

[mortal thunder]

X = x - y + 1, Y = x + y - 5, a² = 8, b² = 6

the ellipse is $\frac{(x-y+1)^2}{8} + \frac{(x + y - 5)^2}{6} = 1$

[thorny flame]

Arya

[mortal thunder]

both latus rectum L_1, L_2 are: x + y - 3 = 0, x + y - 7 = 0

Focii are: (1, 2), (3, 4)

Center: (2, 3)

Major axis: x - y + 1 = 0
Minor axis: x + y - 5 = 0

@placid token what else do you require ...

[topaz sinew]

@placid token Has your question been resolved?

[topaz sinew]

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.

[vivid marten]

I have to determinate the biggest positive value for δ
|x − 3| < δ ⇒ |f (x) + 2| < 1

[mortal thunder]

Start with the rhs inequality

what does that give you

[vivid marten]

-3 < f(x) < -1

Im not english

[vivid marten]

is this u asked?

[mortal thunder]

okay we'll talk math then

[mortal thunder]

Yes

[vivid marten]

oh okk

I understand english

should I isolate the x?

in the inequality

[mortal thunder]

f(x) ∈ (-3, -1) => x ∈ ???

check graph

[vivid marten]

okk gimme a sec

ohh btw

(x − 3)^2 + y^2 = 4

this the equation for this

[mortal thunder]

f(x) ∈ (-3, -1) => x ∈ ???

[vivid marten]

x ∈ [-square(3) + 3, 6]

thats the answer?

[mortal thunder]

f(x) ∈ (-3, -1) => x ∈ (3 - √3, 6) => -√3 < x - 3 < 3

[vivid marten]

wait I think thats not the final answer

[mortal thunder]

?

[vivid marten]

cause it tells me to discover the value of δ

ohh

u right

should I think like this?

[mortal thunder]

hmm

no that is not g(x) = |x - 3|

[vivid marten]

I think it is

cause is meets in the y = -3

and the m = 1

[mortal thunder]

,w plot y = |x - 3|

[thorny flame]

Results provided by WolframAlpha

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

Requested by ansh_3502

[mortal thunder]

that is g(x) = |x - 3|

[vivid marten]

yea its the same

[vivid marten]

but that graph only show y > 0

[mortal thunder]

okie

what value did you get for δ ?

[vivid marten]

-3 < δ U 3 < δ

cause I isolated the x

[mortal thunder]

asked the maximum positive value of delta

[vivid marten]

|x-3| < δ
x - 3 > -δ v x - 3 < δ

[mortal thunder]

for which it is true

determine the biggest positive value for δ: |x − 3| < δ => |f (x) + 2| < 1

[vivid marten]

the thing is that it need to be positive

thats weird

bc it has to be between y = -3 and y = -1

maybe I have to discover those poins

the y

[mortal thunder]

???? You've solved the question

0 ≤ |x - 3| < √3 so the max possible value for delta = √3

[vivid marten]

can u explain the answer?

I didnt understand

[vivid marten]

=> (x - 3) ∈ (-√3, 3) => |x - 3| ∈ [0, 3)

didnt understand this part

[mortal thunder]

I'm correcting that.. That's not correct :|

[vivid marten]

ohh okk

[mortal thunder]

Nevermind this

-√3 < x - 3 < 3

You understood this?

[vivid marten]

hmm no srry

[vivid marten]

I understood till here

[mortal thunder]

f(x) ∈ (-3, -1) => 3 - √3 < x < 6 => -√3 < x - 3 < 3

[vivid marten]

=> -√3 < x - 3 < 3

[mortal thunder]

right?

✅

[vivid marten]

didnt understand

[mortal thunder]

hmm?

[vivid marten]

ohh

got it

[mortal thunder]

what does it mean ???

in terms of inequality

[vivid marten]

that x is bigger than -square(3) and lower than 6

[mortal thunder]

-√3 + 3 < x < 6 [should be open interval]

that x is bigger than 3-square(3) and lower than 6

so (x - 3) is bigger than -square(3) and lower than 3

[vivid marten]

but it belongs to the graph

[mortal thunder]

Yes but f(3 - √3) = f(6) = -1 which we do not want

|f(x) + 2| < 1, remember?

[vivid marten]

ohh true

[mortal thunder]

Now, f(x) ∈ (-3, -1) => 3 - √3 < x < 6 => -√3 < x - 3 < 3

[vivid marten]

got it

[mortal thunder]

And we require max positive δ such that -δ < x - 3 < δ

[vivid marten]

yea

[mortal thunder]

so we put δ = √3

[vivid marten]

ok

[mortal thunder]

because, for $\delta > √3, |x - 3| < \delta \cancel{\implies} |f(x) + 2| < 1$

[vivid marten]

and δ = 3

[thorny flame]

Arya

[mortal thunder]

No

δ must be less than or equal to √3

[vivid marten]

why is that?

[mortal thunder]

because for δ > √3, |x - 3| < δ => x > 3 - δ does not necessarily imply |f(x) + 2| < 1, for example consider δ = 2

x > 3 - 2 = 1 does not imply -3 < f(x) < -1

[vivid marten]

hm

δ = 2 its where?

[mortal thunder]

Hm?

δ = 2 => |x - 3| < 2
And you do not want this

[vivid marten]

ok so if delta = 2 then 2 < x - 3 < 2

[mortal thunder]

-2 < x- 3 < 2

yes

so 1 < x < 5

[vivid marten]

yea

[mortal thunder]

so basically you can pick x = 1.5 but f(1.5) + 2 > 1

contradiction

[vivid marten]

hmm

lemme see

yea right

got it

I replaced in this equation
(x − 3)^2 + y^2 = 4

u right

ohh I think I understood

cause in -square(3) < x - 3 < 3, -square(3) its between y = -3 and y = -1

so it should be -square(3) < x - 3 < square(3)

idk if Im thinking right but it makes sense to me

[mortal thunder]

yes it's right

[vivid marten]

cause they symetrical

[vivid marten]

thank you very much

for the explanation and for the patience ahahahha

Im noticing one thing here

cayse we only thought for x - 3

what about for -x + 3

?

cause |x-3|

forget it

I was making a mess

[topaz sinew]

@vivid marten Has your question been resolved?

Channel closed

Closed by @vivid marten

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.

[fleet jewel]

Can someone help me with this? We are allowed to use a graph calculator. I know "most" on what to do this but not how to but all stuff in my graph calculator because everytime I put an X it automatically goes to 4.4. I'm using the Casio fx-cg50

[topaz sinew]

@fleet jewel Has your question been resolved?

[fleet jewel]

<@&286206848099549185>

[sweet shard]

.close

[topaz sinew]

Channel closed

Closed by @sweet shard

Use .reopen if this was a mistake.

[fleet jewel]

?

[topaz sinew]

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.

[topaz finch]

I'm struggling with understanding how one can calculate the smallest distance possible between two functions. Like these two functions for example. Any help is appreciated 🤍

[odd pagoda]

lets call the functions f and g

then you have points (x,f(x)) and (y,g(y))

you can compute the distance between those

and then minimize it by differentiating with respect to x and y and setting the result as zero

(if you know multivariable calc)

[neon iron]

just find the tangent that has a slope of 2

[topaz finch]

Ah, I'm clueless with multivariable calculus unfortunately

But I understand

[topaz finch]

That could work too now that I think about it 😄

[odd pagoda]

ok the other option is to go via slopes

if you have the connection line then it needs to be orthogonal on both graphs

[dim oriole]

Fuck you

[odd pagoda]

here it helps that one of the functions is linear, leading to what deepfried said

[topaz finch]

I think I could wrap my head around that

Thanks for the help :D

I forgot to close this 😅

.close

[topaz sinew]

Channel closed

Closed by @topaz finch

Use .reopen if this was a mistake.

[topaz sinew]

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.

[dapper cairn]

got -10x

and 3

i dont know what to do now

[timber crystal]

It is asking for the y-value where x=3

if y=-10x

and x=3

What would be y?

don't you see something that can maybe... Replace something else?

[dapper cairn]

i dont see any number i could replace it

13 ?

because 3 - 13 is -10

[sinful flint]

what if it was f(x)=-10x

and you were given x=3

would you know what to do?

[dapper cairn]

no i would not

[sinful flint]

okay

$f(3)=-10\cdot 3$

[thorny flame]

Bonk

[sinful flint]

does this make sense or no?

[dapper cairn]

yes

it would be -30

[sinful flint]

exactly

thats what the question is asking

[dapper cairn]

oh ok

[sinful flint]

you essentially substitute in the value 3 for x

[dapper cairn]

but i dont know what to sub it with

and how do i find it

[sinful flint]

x=3

f(x)=f(3)

-10 * x=10 * 3

do you see what happens here?

the x gets replaced with 3

because x=3

[dapper cairn]

so it would be 30?

30/-10

nah

[sinful flint]

-30

-10*3=-30

[dapper cairn]

so Y = -10(3)

[sinful flint]

yes

[dapper cairn]

thank you

.close

[topaz sinew]

Channel closed

Closed by @dapper cairn

Use .reopen if this was a mistake.

[topaz sinew]

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.

[solid bridge]

can anyone help with part c?

[raven sparrow]

Once you have the eigenvectors / eigenvalues, you can write the diagonalization with diagonal matrix D having the eigenvalues on its diagonal and matrix P having the eigenvectors as columns

[topaz sinew]

@solid bridge Has your question been resolved?

[topaz sinew]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

[topaz sinew]

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.

[stiff egret]

I have a very very very basic understanding of deravatives and integrals can someone in like the most baby language possible help me find how to do area under curves

[deep crow]

Area under a curve is given by the integral

[stiff egret]

Yea

How?

[deep crow]

Do u have a specific problem

Or LIEK just wondering conceptually

[rigid ivy]

Area under a curve can be approximated by a Riemann sum. Do you know what a Riemann sum is?

[stiff egret]

Nope and conceptually

[rigid ivy]

A Riemann sum is a way to approximate area under a curve using rectangles

[stiff egret]

Ive seen that before

But i dont know how to do it

[rigid ivy]

The smaller you divide the rectangles, the better your approximation will be

There are also different ways you can do a Riemann sum, where the rectangle meets the graph either at the right, or at the left

[stiff egret]

If i wanted to do the left one for a equation how would i do it

I ment right

But either is fine

[rigid ivy]

First, you need to decide over which boundary you want to find the area

Let's start with an example

Say, you want the area under $y=x^2$, and you want the area between $0$ and $1$

[thorny flame]

SWR

[stiff egret]

Ok ic

[rigid ivy]

Next, you need to decide how many rectangles you want to use for an approximation? 10? 20? 100? 1 million?

[stiff egret]

Also if i stop talking its cuz my phone died ill be back in 1 min grabbing a charger

[rigid ivy]

Let's use algebra and just decide we want $n$ rectangles

[thorny flame]

SWR

[rigid ivy]

If we want $n$ rectangles to fit between $0$ and $1$, we need to determine which width will allow us to do this. If there was just 1 rectangle, its width should be exactly 1. If it were 2 retcnalges, every width needs to be $\frac12$. In general, $n$ rectangles need to each have the width $\frac1n$ so that their widths sum to 1

[thorny flame]

SWR

[rigid ivy]

We have the width, now we need the height

We'll do a left sum for now.

[stiff egret]

Sorry im vacj

Back

Makes sense so far

I think is see where its going

[rigid ivy]

To find the height of some rectangle, we first need to find the $x$-coordinate of the left side of the rectangle. For the first rectangle, its $x$-coordinate will be $0$. The second rectangle will have $x$-coordinate $\frac1n$. The third rectangle will have $x$-coordinate, and so on...\
\
In general, the $k$th rectangle will have $x$-coordinate $\frac{k-1}n$

[thorny flame]

SWR

[rigid ivy]

Now that we have the $x$-coordinate of the left side of the $k$th rectangle, we can find that rectangle's height. Since the rectangle is touching the graph $y=x^2$ on the left side, its height will be $\left(\frac{k-1}n\right)^2$.

[thorny flame]

SWR

[rigid ivy]

So, for any $k$th rectangle, its width is $w_k=\frac1n$ and its height is $h_k=\left(x_k\right)^2=\left(\frac{k-1}n\right)^2$. So, its area is
$$A_k=w_k h_k=\frac{(k-1)^2}{n^3}$$

[thorny flame]

SWR

[rigid ivy]

Finally, to approximate the area under the curve, we must sum the areas of all $n$ rectangles:
$$A_{\text{approx}}=\sum_{k=1}^nA_k=\sum_{k=1}^n\frac{(k-1)^2}{n^3}$$

[thorny flame]

SWR

[stiff egret]

Hmm

Ic makes sense lemme try it for something else

[topaz sinew]

@stiff egret Has your question been resolved?

[rigid ivy]

@stiff egret you still here?

[topaz sinew]

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.

[obtuse ridge]

or where i can get them for free?

they are so expensive

[prisma mesa]

read #rules

[obtuse ridge]

i think my question abides by the rules

how is asking for free resources to study cheating

and i am asking for resources to source pirated content

not pirated content

is that okay?

[prisma mesa]

Im not a mod but idts

anyway this is surely not a question for a help channel

[obtuse ridge]

well where do you suggest i ask it

[prisma mesa]

try asking in #discussion or #chill

and try formulating your question in a way that doesnt include pirating stuff

and I'd be more specific, because "exam books" is quite broad

#book-recommendations and #resources might have sth helpful as well

[empty spoke]

.close

[topaz sinew]

@obtuse ridge Has your question been resolved?

[topaz sinew]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

[topaz sinew]

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.

[vague dirge]

in strugguling to prove this, if somone could help me get started i would appreciate it

[vague dirge]

well ik how it should start normally but idk how to even start making the right and left equal because ine has a summation and ikd how to make that not one or how 2 make the other one if that is even possible, so some help getting started would be greatly appreciated

thx brother u are useful actually

.close

[topaz sinew]

Channel closed

Closed by @vague dirge

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.

[novel flume]

can someone help explain this one to me

AC=8√2

AC is parallel to DF

but after that i don't see how to complete the problem

[topaz sinew]

@novel flume Has your question been resolved?

Channel closed

Closed by @novel flume

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.

[willow cipher]

Im not sure how to approach the 2nd part of this question, to give an example of strict inclusion

[willow cipher]

https://i.imgur.com/WYVhWvT.png

[worthy storm]

look for a function that doesn't reach all of D

[willow cipher]

f: R --> R: f(x) = x^2 ?

[worthy storm]

perhaps, what is D?

[willow cipher]

the reals

[worthy storm]

ok, what is $f(f^{-1}(D))$ in that case?

[thorny flame]

Bungo

[willow cipher]

wouldnt it just be the non negative reals

[worthy storm]

yes

[willow cipher]

so that works?

an example of strict inclusion

is strict inclusion just another way to say subset?

or a proper subset

[worthy storm]

yes it means proper subset

and yes this example works

[willow cipher]

thank you

[worthy storm]

yw

[topaz sinew]

@willow cipher Has your question been resolved?

[topaz sinew]

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.

[merry bridge]

I understand why we change the bounds when doing u-substitution, because we're changing with respect to what we're integrating with. Following this logic, why do we not need to change the bounds when integrating by parts?

[golden wigeon]

Because eventually we replace u, v, du, and dv with their values in terms of x and dx

[loud oasis]

in substitution we change the variable of integration to a different variable. in integration by parts we keep the same variable

[merry bridge]

sorry does that answer still apply to my corrected question

[merry bridge]

oh, yes, you're right. duh, how silly of me

u and v are just placeholders

.close

[topaz sinew]

Channel closed

Closed by @merry bridge

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.

[mental sun]

Isn’t secant just 1 over -√21/5

yeah it was

.close

[topaz sinew]

Channel closed

Closed by @mental sun

Use .reopen if this was a mistake.

[topaz sinew]

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.

[golden wigeon]

!status

[topaz sinew]

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

[golden wigeon]

Ok, what did you get as your answer for them

Oh ok

Why do you believe $\lim_{x \to 4^-} f(x) = -\infty$?

[thorny flame]

King Leo

[timber crystal]

Read the "a few notes" part

[golden wigeon]

But nothing truly special happens at x = 4

No

Can you label x = 4

[timber crystal]

wait how do you know he wrote that

I thought you wrote -4- at first

[golden wigeon]

Its very faint blue text

[timber crystal]

oh I didn't see 😂

[golden wigeon]

Yes

E and F ask about what happens when x approaches 0 from one specific side

[timber crystal]

What's specific about f that it's dne

yes

Also yes

[golden wigeon]

Oh no

This entire time i thought that was x -> 4

i should be -infinity

L is correct: dne

❌

Sorry i made a mistake again

You care only about the positive side

i

[timber crystal]

It is DNE only and only if there are 2 values output from f(x) at x in this exercise

If you have let's say x+ then there will always be a limit it approaches to, from the right hand side

h is correct

i is not

yes

wait are there points at the end of the curves

like shaded/unshaded

I can't zoom in

there are

At x=3

You can see the top part ends with a. Shaded point

While the bottom one is not

do you know what that means?

Yeah

So f(0)

It has a shaded point at which value

[topaz sinew]

@kindred sandal Has your question been resolved?

[topaz sinew]

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.

[unreal summit]

Writing a formal proof, and I need help checking that what I have is rigorous enough, and if not what I can add to it,

[unreal summit]

The idea of the question is

and my greedy algorithm is basically, sort by maximum profits, and then schedule each at the latest available slot (i.e. their deadline)

[young lagoon]

This question might not be answered in a normal help chanel I'd recommend #theoretical-cs

[unreal summit]

oh ok thank you!

.close

[topaz sinew]

Channel closed

Closed by @unreal summit

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.

[stray spade]

hello I am somewhat confused by this rather simple seperable diff eq

[stray spade]

u is the bodies temperature, (medium temperature is irelvant), and alpha is the given constant

when I solve this IVP i get this equation:

BUT according to the textbooks answer key, this is the correct answer

i am very confused as I have verified my answer on desmos and i cannot find my error. is it possible the textbook is wrong???

[craggy haven]

why are both of you using x

[stray spade]

easier to use x on desmos

if i use "u" it wont plot and throws me a variable error

sorry if its confusing

[scenic flare]

bc you need to write u(t) = ...

[stray spade]

please just pretend x and t are the same thing

[stray spade]

alright ill do that

but that doesnt change my issue

[craggy haven]

$\f{du}{u^4} = -\alpha dt$

[thorny flame]

hayley, who does not have fins

[craggy haven]

$-\f1{3u^3} = -\alpha t + C$

[thorny flame]

hayley, who does not have fins

[craggy haven]

$3u^3 = \f1{\alpha t + C}$

[thorny flame]

hayley, who does not have fins

[craggy haven]

hmm

yeah i mean yours seems to make more sense

[stray spade]

this is what i get

additionally, when i plot the diff eq itself on desmos, my answers diff eq overlaps with the numeric derivative (it makes sense) whiolst theirs does not

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

(if youre interested)

is the textbook answer key just janked or smthn

[craggy haven]

probably

[stray spade]

wow

first time thats ever happened to me

will i get a cookie if i mail them

anyways thanks for the help

.close

[topaz sinew]

Channel closed

Closed by @stray spade

Use .reopen if this was a mistake.

[topaz sinew]

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.

[wraith anchor]

How do I learn fractions fastest?

[wraith anchor]

Hello??

.close

[topaz sinew]

Channel closed

Closed by @wraith anchor

Use .reopen if this was a mistake.

[pseudo sonnet]

[hoary burrow]

Pay attention in class

[wraith anchor]

Real

I’m just trying be the best of the best tho as quick as I can

I already learned them but like

[hoary burrow]

That involves having much more patience

Than one minute

[topaz sinew]

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.

[wary ermine]

Not sure how to begin. Ive tried "solving" for c but im just stuck trying to use -3.

[twin pendant]

Factorize x^2-x-12

[wary ermine]

I got it, give me a min really sorry my damn dog did something stupid

(x-4)(x+3)

so then x+3 cancels

[twin pendant]

Yea

[wary ermine]

are we taking the x=-3 and making it into lim x-->-3? so then its lim x-->-3 (x-4)

then just -3-4 = -7

got it, thank you

.close

[topaz sinew]

Channel closed

Closed by @wary ermine

Use .reopen if this was a mistake.

[topaz sinew]

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.

[halcyon frost]

i asked this exercise few days ago and didnt get an answer

[halcyon frost]

PLEASEEE people who are familiar with this notation try to solve it

because i know that in some other notations this might not make sense

[wispy pier]

😭 I've got exams bro

[mortal thunder]

XOR dew itttttttt

[halcyon frost]

lmao, good luck on them bro

you dont have to help me with every exercise

you can sit this one out

[mortal thunder]

btw don't you think you have your notations upside down?

like, what is 1 choose n? that's just 0

[halcyon frost]

no, thats just the way we do the notations here

[halcyon frost]

thats why i said this

whatever, just imagine its backwards i guess

[mortal thunder]

$S_n = \sum_{i=0}^n \binom{n}{i}\binom{n}{n-i}$

[mortal thunder]

that's just 2nCn

[halcyon frost]

ummm

damn, im not used to this

so

[mortal thunder]

XD

[halcyon frost]

what is that supposed to mean

[mortal thunder]

wait I'll explain

[halcyon frost]

so like

i gotta put it in chatgpt to translate it to my notation

[halcyon frost]

oh sure

go ahead

[mortal thunder]

so you see

do you know binomial expansion?

[halcyon frost]

yea

i do

[mortal thunder]

So coefficient of $x^i$ in $(1 + x)^n$ is $\binom{n}{i}$ right?

[timber crystal]

switch their places

you the first person I've seen write kCn

😭

[halcyon frost]

i already put it in chatgpt so its ight

now i know

what the notations means

[halcyon frost]

yea

or wait

why x^i

is i supposed to be k or is i complex?

like, the i^2=-1, that ,, i ,,

[loud oasis]

no, i is just an index here

[halcyon frost]

right

so far so good

[halcyon frost]

romanians bro, not my fault they be like that

[halcyon frost]

sooooooooo, what next

[mortal thunder]

So, look at the coefficient of $x^{n}$ in $(1 + x)^n(x + 1)^n$

to make x^{n}, x^i from first bracket must club with x^{n-i} from second bracket

[halcyon frost]

...howd you even come up with that?

[strange whale]

coeff of x^n you want to look at

[mortal thunder]

right thx platypus

to make x^{n}, x^i from first bracket must club with x^{n-i} from second bracket

[halcyon frost]

how did you think of not only multiplying it by itself, but multiply it in such a way so that you have (1+x)^n*(x+1)^n

[mortal thunder]

pure genius

[halcyon frost]

lmao

alright

[halcyon frost]

well, it would be 1 right?

[mortal thunder]

wow smart

so x² from first bracket would totally not find a x^{n-2} from second

and totally not make another x^n

[halcyon frost]

oh so

theres no leftover terms?

[halcyon frost]

like, this just gives us the sum of the squared combinations straight up?

[strange whale]

yeah

[halcyon frost]

what??

hwo

how

let me write it down

[mortal thunder]

if your cogs run a bit, you'll realize your $x^n$s come from: $$\binom{n}{i}x^{i} \cdot \binom{n}{n-i}x^{n-i}$$

[halcyon frost]

damn, someones being a bit passive aressive today

[mortal thunder]

and adding them up to get coeff of x^n, you have

coeff[x^n]

[halcyon frost]

i cant see them as easily as you so i will write the expansions

[mortal thunder]

I appreciate that you're writing to understand.. Ow I see people who are no less than Newtons, pondering over thoughts as if what hit their head was instead an apple.

You can ask wherever you're stuck. I'll try to explain

[halcyon frost]

okk, just give me a minute to try to understand it by writing it down

[strange whale]

https://proofwiki.org/wiki/Sum_of_Squares_of_Binomial_Coefficients/Combinatorial_Proof another proof if you want, look at it later tho not now

[halcyon frost]

ok so i got a stupid question

when i multiply those thingys, sure, if i multiply them the first with the first, second with second, and so on

i get the sum of square multiply by x^n

but then theres a bunch of leftover terms

the ones i underlined

am i missing something important?

[strange whale]

well there's a ton of other terms other than x^n in that product yes