help-38

[trim lichen]

no, that's the sum of two monomials (x and 3)

[gaunt rain]

no a monomial is in the form ax^n no?

[trim lichen]

so it is called a binomial

[gaunt rain]

is 3 a monomial? isnt it a constant?

[trim lichen]

both

3x^0

[gaunt rain]

oh yeah

[violet gust]

monomial means a single term

[gaunt rain]

thats a monic quadratic

[gaunt rain]

yes i know

but x+3 is also sorta in the form a+bi in complex numbers

except there is no i

i feel so targeted

💀

did you really have to disapprove of it in 5 different ways

[trim lichen]

yes.

[gaunt rain]

i thought i cooked gng we started complex numbers today 😔

[trim lichen]

you burned it

not to the point where you became cooked yourself but

still

[gaunt rain]

bruh

ive only done a+bi and conjugates

ima rookie

and operations

[late flume]

Complex numbers are much more similar to vectors

That comparison can work

[gaunt rain]

i wish i were a vector

with direction and magnitude

[trim jolt]

@blazing geode Has your question been resolved?

Channel closed

Closed by @blazing geode

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.

[vast egret]

Question 2 - a-

[trim jolt]

@vast egret Has your question been resolved?

[vast egret]

<@&286206848099549185>

[trim jolt]

@vast egret Has your question been resolved?

[simple haven]

@vast egret the AI auto translation completely mangles the problem.

!show

[trim jolt]

Show your work, and if possible, explain where you are stuck.

[vast egret]

EXERCISE 12

The space is given with respect to a direct orthonormal coordinate system (O; i, j, k).

1. Consider the points A(0, 1, 1), B(1, 0, 1), and C(1, 1, 0).

a. Verify that the points A, B, and C are not aligned.

b. Show that the equation x + y + z - 2 = 0 is a Cartesian equation of the plane (ABC).

c. Determine a Cartesian equation of the sphere S centered at O and tangent to the plane (ABC).

We denote by I the point of contact between the sphere S and the plane (ABC).

---

2. Let α be a real number. We consider the points
   E(−α, 2/√3, α) and F(−α, −2/√3, α).

Let Sα be the set of points M(x, y, z) such that:
ME² + ME · EF = 0

a. Show that Sα is a sphere with diameter [EF].

b. Show that for any real α, the sphere Sα is tangent to the plane (ABC).

c. Let J be the point of contact between Sα and the plane (ABC).
Determine the value of α such that the distance IJ = √2.

[vast egret]

I haven't seen anything like this before, so I don't know what the text means in question 2)

[nimble stone]

write the ME and EF vectors first

[vast egret]

I had solved ME . EF

And I solved ME²

And I got something like the equation of sphere

[nimble stone]

which was?

[vast egret]

$\Vec{ME} \cdot \vec{EF} = -\frac83 +\frac{4y}{\sqrt{3}}$

[solid kiln]

╰ 𝕃 𝕌 ℂ 𝕀 𝔽 𝔼 ℝ ╮

[vast egret]

$ME^2 = x^2 + y^2 + z^2 + 2\alpha x -\frac{4y}{\sqrt{3}} - 2\alpha z + 2\alpha^2 +\frac43$

[nimble stone]

should be +4/3 no?

[vast egret]

$ME^2 + \vec{ME} \cdot \vec{EF} = 0 \leftrightarrow (x+ \alpha)^2 + (y - 0)^2 + (z-\alpha)^2 = \frac43 + 2\alpha^2$

[solid kiln]

╰ 𝕃 𝕌 ℂ 𝕀 𝔽 𝔼 ℝ ╮

╰ 𝕃 𝕌 ℂ 𝕀 𝔽 𝔼 ℝ ╮

[nimble stone]

seems good at a glance

[vast egret]

Is this supposed to be S_α?

[nimble stone]

S alpha is the set of the points M that have this property

[nimble stone]

so all the (x,y,z) for which the equation on the right holds for some alpha

ie, the sphere

[vast egret]

$(x+ \alpha)^2 + (y - 0)^2 + (z-\alpha)^2 - \frac43 - 2\alpha^2 = 0$

[solid kiln]

╰ 𝕃 𝕌 ℂ 𝕀 𝔽 𝔼 ℝ ╮

[vast egret]

We can write it like this

[nimble stone]

sure

[vast egret]

Wait

Is E the midpoint of the sphere?

[nimble stone]

the center of the sphere is (-a,0,a)

[vast egret]

Should I assume this is the answer?

[nimble stone]

its the showing its a sphere part yeah

but you havent shown the diameter is |EF|

[vast egret]

We need to prove [EF] is diameter now

We can calcul distance between EF

And see it it's 2R

Is this the way?

[nimble stone]

yup

[vast egret]

Owh

Then we substitute x_F, y_F, z_F on Sα equation

$2\alpha^2 = 0$

[solid kiln]

╰ 𝕃 𝕌 ℂ 𝕀 𝔽 𝔼 ℝ ╮

[vast egret]

[vast egret]

Substituting F here, I found that 2α² = 0

All evidence points to α = 0.

$EF = \frac{4}{\sqrt{3}}$ and $R^2 = \frac43 + 2\alpha^2$

[solid kiln]

╰ 𝕃 𝕌 ℂ 𝕀 𝔽 𝔼 ℝ ╮

[vast egret]

I think we need another way to prove that [EF] is diameter

@nimble stone

<@&286206848099549185>

I think I'll just count $\vec{EM} \cdot \vec{FM} = 0$

[solid kiln]

╰ 𝕃 𝕌 ℂ 𝕀 𝔽 𝔼 ℝ ╮

[vast egret]

Ty

.close

[trim jolt]

Channel closed

Closed by @vast egret

Use .reopen if this was a mistake.

[vast egret]

.reopen

[trim jolt]

✅

[vast egret]

I got another way

We have centre is $(-\alpha; 0; \alpha)$
$$\text{We can calcul} \frac{x_E + x_F}{2}$$

[solid kiln]

╰ 𝕃 𝕌 ℂ 𝕀 𝔽 𝔼 ℝ ╮

[vast egret]

And look if xE + xF/2 = -α or not

(-α + α)/2 = 0

I kept proving α = 0

I think there is a shortage of assistants at the moment.

.close

[trim jolt]

Channel closed

Closed by @vast egret

Use .reopen if this was a mistake.

[trim jolt]

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.

[next vapor]

guys i have the double integral of sinx siny with D (-pi,0) (pi,0) (pi,pi/2) I need to find the volume

[trim jolt]

Please don't occupy multiple help channels.

[next vapor]

.close

[trim jolt]

Channel closed

Closed by @next vapor

Use .reopen if this was a mistake.

[manic lagoon]

bruh hwhat?

[trim jolt]

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.

[mystic iris]

good question

[drowsy trench]

The center of the circle is point O. The radius of this circle is 10 cm. The length of the chord AB is 16 cm. Based on the given diagram, calculate the length of CM.

[wet lintel]

love me some chord-chord theorems

[wet lintel]

you can also just use pythagoras if you don't know the theorems

[drowsy trench]

so 8x8=x*(10-x)

?

[wet lintel]

yeah

[drowsy trench]

thanks

.close

[trim jolt]

Channel closed

Closed by @drowsy trench

Use .reopen if this was a mistake.

[trim jolt]

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.

[boreal shuttle]

$f_n(x)=x^ne^{-x}$ prove that $C_n$ passes par 2 points fix

[solid kiln]

<rajel />

[boreal shuttle]

i did $f_n(x) = f_{n+1}(x)$ and then i got
$x^{n+1}e^{-x}=x^ne^{-x}$ and by simplfying both sides with $x^n$ we get that
$x=1$

[solid kiln]

<rajel />

[boreal shuttle]

but that just .... , one point

it says it passes by two :(

<@&286206848099549185>

[stark sandal]

how did you simplify?

[trim jolt]

@boreal shuttle Has your question been resolved?

[trim jolt]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

[trim jolt]

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.

[languid spade]

This is from geometry I am helping a freshman with, I feel like I’m missing information. It’s a similar triangles problem but I am stuck on how to relate three different sides of three differently scaled triangles

[verbal stream]

try to set up an equation to find x

what similar triangles do yo usee

[languid spade]

ABC, ABD, and BDC

[verbal stream]

right, or more precisely
ABC ~ ADB ~ BDC

[languid spade]

Yess

[verbal stream]

so try to set up an equation for x

[languid spade]

I was only able to come up with constant times x = constant times x or couldn’t get rid of the other variables

Like x/6 = 9/x

Or am i comparing the wrong sides?

[verbal stream]

no this is good

x/6 = 9/x so what is x

[dense grove]

It can be solve using pythagoras theorem

[languid spade]

How 🙏

[languid spade]

Thank you!

It works out yay

[dense grove]

,🥳

[languid spade]

🎉

.close

[trim jolt]

Channel closed

Closed by @languid spade

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.

[leaden nebula]

how do i do this

[trim lichen]

do you know how to solve DEs like this one

like do you know what form the solutions take

[leaden nebula]

it depends if its real, complex or repeated right?

[trim lichen]

yes

well

"it"

[leaden nebula]

ye but generally it's y=e^(λt)

what does bounded on all R mean in this case

like only the real ones?

[trim lichen]

it means the same thing as the word "bounded" means in general

informally: does not blow up to infinity

when is the function e^(lambda t) like that?

[leaden nebula]

ohh so I should see which values a,b cause the solution to not blow up to +/- inf?

[trim lichen]

yes

[trim jolt]

@leaden nebula Has your question been resolved?

[trim lichen]

note that a function like sin(t)e^t still blows up to infinity even though it oscillates from positive to negative

[leaden nebula]

idk theres a lot of cases...

@trim lichen

[thorn bay]

soooo

just, to get a sense of how you should know intuitively this is wrong

there should be a combination of the form
$y=K_1 \sin(K_2 t) + K_3 \cos (K_4 t)$
for some real constants $K_1, ... , K_4$

[solid kiln]

gfauxpas

[thorn bay]

do you have that intuition

[leaden nebula]

yeah

[thorn bay]

so, you missed those

[leaden nebula]

wait uh wut

[thorn bay]

gotta figure out what went wrong

[leaden nebula]

this is for the complex case right?

[trim lichen]

well really only the oscillation case matters from the ones youve written because you want nonzero bounded sols

so you get a = 0, b > 0 and thats correct

[thorn bay]

all I'm saying is that you should look at the original problem statement and think "there should be some solution of y=K_1 cos(K_2 t) + K_3 sin( K_4 t)$ based on examples of odes youve seen before

complex, real , whatever

[trim lichen]

actually any a ≠ 0 will mean your solutions have a factor of e^(-a/2 * t) which is not bounded nmw

well

no sorry i lied

[thorn bay]

btw how you doin Ann, havent talked in a few years

[leaden nebula]

cuz if a neq 0 it would be unbounded ye

[trim lichen]

theres one case you didnt consider

a=0, b ≠ 0

y'' + ay' = 0

then you get e^(-at) and 1 as basis solutions

[thorn bay]

also

[thorn bay]

you did:

repeated roots
real and distinct

there are other possibilities

do you see what case you missed

you STARTED along the right lines

in part 1

but then you didnt follow through

you said if the roots are complex, for a bounded solution, you need a=0, b>0

and then you stopped

aah I found the mistake

sorry id idnt notice sooner

lambda=0 is sufficient but not necessary

so, actually, since you're not required to find the solution

you technically got the right answer for the wrong reason

so, dont know if that merits full points or not

[leaden nebula]

ohh i got it now

ty

.close

[trim jolt]

Channel closed

Closed by @leaden nebula

Use .reopen if this was a mistake.

[trim jolt]

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.

[desert pagoda]

Can someone please tell me where the heck the -2 and 3 went

[desert pagoda]

This is my answer key btw

[bright quarry]

(-2)(3) =-6

they reversed the orientation of the equal sign

they flipped it

[desert pagoda]

Oh ok

[cedar adder]

!done

[trim jolt]

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

[desert pagoda]

.close

[trim jolt]

Channel closed

Closed by @desert pagoda

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.

[vocal cobalt]

do I solve this by setting it < f^(4) (z) / 4!

[trim jolt]

@vocal cobalt Has your question been resolved?

[bright quarry]

yea you straight up just use the bound they gave you

the 4th derivative is at most 4/5

so you have 4/5 * 1/4!

when’s the ap exam

monday?

tuesday?

[vocal cobalt]

I'm taking late

regular is Monday

would it be 4/5 / 4! so it's 1/30?

B right?

[bright quarry]

yuh

[vocal cobalt]

ok thanks 😄

.close

[trim jolt]

Channel closed

Closed by @vocal cobalt

Use .reopen if this was a mistake.

[trim jolt]

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.

[light sky]

Help

[light sky]

Is my proof for fatou s lemma sufficiently rigorous

Please point out all minor issues

Like notational wise or logical wise

[trim jolt]

@light sky Has your question been resolved?

[supple copper]

Maybe I’m stupid but how does it follow for the 2nd last line

Also not a big thing but I think every integral here needs the domain X and the dmu that you’ve omitted everywhere

[light sky]

That’s because int inf f_k <= int f_k

[supple copper]

That’s just the 4th line from the bottom

I’m just wondering how the lim went inside the integral on the left

And how the <= became =

[light sky]

That’s basically from the beginning

Or hypothesis what we want to show is fatou s lemma and that’s the statement

[supple copper]

Hmm the hypothesis is only that the fn’s are measurable

[light sky]

Yes we want to show that identity

So I let g_n which is increasing

This is okay right

And then by monotone convergence theorem

[supple copper]

Is {int inf k>=n fk}_n a monotonic sequence

[light sky]

I can make the limit inside or outside

But g_n=inf_k>=n f_k

Is monotonic

[supple copper]

Ah of course

[light sky]

Since we take infimum over less value

And so is sup_k>=n f_k is decreasing as we take less supremum over the values

[supple copper]

Yeah it looks good

[light sky]

Must say this part is super counterintuitive for many 😭😭

It got quite abstract for me and got me a long time to think 😭

[supple copper]

Oh I was looking at this earlier today so it didn’t confuse me at all now

As n increases inf has less “choice” for k yeah

[light sky]

Are you studying mathematics that’s impressive… I am so jealous of people studying math

[supple copper]

It’s more about $\inf(f_k, f_{k+1}, …) \leq \inf(f_{k+1}, f_{k+2}, …)$ because the second is a subset of the first

[solid kiln]

frosst

[supple copper]

Yeah haha

[light sky]

Actually fatou lemma is strictly equivalent to monotone convergence theorem

I am studying weird Econ stuff

[supple copper]

This is pretty deep for economics

[light sky]

I am working to get into math department

Basically I almost trashed my gpa for all those math stuff

Got addicted to it

Unfortunately not good linear algebra and everything gets so hard

[supple copper]

This is not an easy proof to do! You’ve done a great job and your proof writing for the most part was easy to follow and clear

I think my hiccup on the last part was really on me and not on your working as well

[light sky]

Sometimes proof can be tedious to read yes so it’s my fault I wrote it too small since my handwriting is like that😭

[supple copper]

Nah your handwriting is really good

One of the best I’ve seen

[light sky]

🥰🥰🥰

People like to do cursive these days I mean

I literally learned all these on YouTube 🫣🫣

[supple copper]

Epic

[light sky]

I am quite proud of myself too

[supple copper]

This is probably the only critique I’d have

And its just a notation thing

[light sky]

And more determined to eventually study math

[light sky]

I will change that part 😸🐈

[trim jolt]

@light sky Has your question been resolved?

[trim jolt]

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.

[obsidian hamlet]

Help

[obsidian hamlet]

.rotate

[trim lichen]

,rccw

[obsidian hamlet]

So

[trim lichen]

which one

[obsidian hamlet]

Ex 3 last questions

Where did i mess up?

[trim lichen]

3(d)?

[obsidian hamlet]

Yes

[trim lichen]

aight let's see here...

[obsidian hamlet]

It says 3y=-4x+11 at the answer sheet

[trim lichen]

the answer sheet is wrong, 3y=-4x+11 does not pass thru A

[lunar stirrup]

by any chance do u know general eqn of tangent to a circle

[trim lichen]

in fact yours is the correct equation bc it does

[lunar stirrup]

dude how many emojis

[lunar stirrup]

is not even wrong

[obsidian hamlet]

b²-4ac =0

[trim lichen]

,rccw

[obsidian hamlet]

It's under (5,8)

[trim lichen]

wait hold up...

[obsidian hamlet]

Ex 3.2

[trim lichen]

3y=**+**4x+11 for starters

hang on tho

this is sus

lemme graph all this shit

ok

black is what you got

dashed red is the book

you're right book's wrong

[obsidian hamlet]

Bro

What kinda book is ts

[trim lichen]

...don't call me "bro" please

[obsidian hamlet]

Im trying to self learn ts

[obsidian hamlet]

Sir

[trim lichen]

if you were doing it as an interjection may i suggest "bruh" instead

[trim lichen]

no thats even worse

im a girl

[obsidian hamlet]

😨

[trim lichen]

can you not

[obsidian hamlet]

.close

[trim jolt]

Channel closed

Closed by @obsidian hamlet

Use .reopen if this was a mistake.

[obsidian hamlet]

Shshsh

Never happened

[zinc ginkgo]

just block ann

[obsidian hamlet]

No cus she's good

[trim lichen]

im gonna give him one last chance to apologize

[obsidian hamlet]

Sorry

[lunar stirrup]

he was telling her to block u lmao

[trim lichen]

instead of running for the hills as soon as a trans lady such as me kindly asks him to not call her by masculine words

[obsidian hamlet]

Oo you're MTF?

[trim lichen]

i am a trans woman, yes

[obsidian hamlet]

What's your sexuality then?

[trim lichen]

...

[zinc ginkgo]

[obsidian hamlet]

I MWAN

[trim lichen]

#discussion

[zinc ginkgo]

.

[obsidian hamlet]

NO access

[lunar stirrup]

open a new help channel for this

[trim lichen]

but also thats kind of a weird question to ask anyway

and also it says in my bio.

[stoic garden]

This is one of the most interesting conversations i've seen 😂

[obsidian hamlet]

Okay bye

Watch me be back in 10min

[lunar stirrup]

looking forward to it

[trim jolt]

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 hinge]

I need help with this
https://www.desmos.com/calculator/ifhmf3cjlc

[wraith hinge]

where does the derivative equal 0 here

[wraith hinge]

🥀

@trim lichen vro...

[stoic garden]

This lags my whole computer 😭

[wraith hinge]

Hold on I can send a picture

[stoic garden]

Derivative of what?

[wraith hinge]

y = x^2(sin x)(cos y)

[stoic garden]

Do you know about implicit differentiation?

[wraith hinge]

no

like i know what it is

[wraith hinge]

but this graphs a bit weird

[stoic garden]

,w graph y = x^2 * sin(x) * cos(y)

[trim lichen]

??????????

[solid kiln]

Results provided by WolframAlpha

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

Requested by en.ratham

[trim lichen]

@wraith hinge care to explain what that was about

[wraith hinge]

what was about

[stoic garden]

Do you realize you're giving him the exact attention he's looking for?

[trim lichen]

this is what

[wraith hinge]

What is that

[trim lichen]

aight fine you're playing dumb <@&268886789983436800> deal with this please

[wraith hinge]

It was the other guy

🥀

[iron pier]

Coined by American rapper XXXTentacion in 2015 (see quotation below) as a modification of bro, referencing his group "Very Rare".
huh I acutally did not know this

(hiphop slang, Internet slang) Synonym of bro (term of address to a male friend).

src: https://en.wiktionary.org/wiki/vro

[trim lichen]

Synonym of bro (term of address to a male friend).
ayup

[wraith hinge]

sure nice power trip

[dull temple]

?

[wraith hinge]

can u help me with my issue

[iron pier]

Interjection
ayup

Alternative spelling of hey up
(New England) Alternative spelling of ayuh
im learning so many new words today 0_0

[wraith hinge]

y = x^2(sin x)(cos y)

whats the derivative of this

[trim lichen]

i used it as a somewhat drawn-out pronunciation of "yup"

[ionic pendant]

urban dictionary otoh has some support for listing it as a 'gender-neutral' version of bro

[iron pier]

are we really about to debate the connotation of "vro" rn 💀

[dull temple]

this doesn't fly here.

[iron pier]

uhhh... you'll need to do a bit of chain ruling

[wraith hinge]

how can it fly if its on my screen its a 2D dimension

you cant fly there

[iron pier]

it's figurative

[wraith hinge]

vro...

[vagrant imp]

I've heard my female classmates call each other bro, I don't think its a big deal

[wraith hinge]

exactly...

[trim lichen]

not the time for that

[dull temple]

maybe it's best if you take a nap before studying, you seem to be tired

[wraith hinge]

you have any tips for better sleep

[dull temple]

yeah i can think of one

.close

[trim jolt]

Channel closed

Closed by @dull temple

Use .reopen if this was a mistake.

[iron pier]

it's like, $2x\sin x\cos y+x^2\frac{d}{dx}(\sin x\cos y)$

oh ok nevermind I guess

[solid kiln]

00100000

[dull temple]

yea in general it's fine but in this case she specifically asked them not to

[trim jolt]

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.

[obsidian hamlet]

Hi

[obsidian hamlet]

Help

?????

[obsidian hamlet]

It says it tangent

Istg yall helpers only come when there's drama

[trim lichen]

let's see

ok

[obsidian hamlet]

I would do that same

[trim lichen]

so since your book is now proven to contain a nonzero amount of typos

it's time to go for desmos again

[obsidian hamlet]

Yes

[vagrant imp]

your work seems ryt

[obsidian hamlet]

<@&268886789983436800>

[trim lichen]

lmfaooooooooooooo

wow you are fucking rotten. <@&268886789983436800>

[obsidian hamlet]

Tweakiing

https://tenor.com/view/mods-gif-3703083771809089146

[grim sparrow]

[simple haven]

cool

[obsidian hamlet]

Ann is the best helper

[trim lichen]

get b& speedrun misgender% or something

ftr

[obsidian hamlet]

What's b

[trim lichen]

desmos is quite a wonderful tool

[obsidian hamlet]

Ahh yes for drawing

[trim lichen]

b& is a humorous abbreviation for "banned"

[obsidian hamlet]

Also

[obsidian hamlet]

Crazy

Do you prefer green grapes or purple grapes

[stoic garden]

@obsidian hamlet never bite the hand that feeds you.

[trim lichen]

offtopic...

[obsidian hamlet]

Isn't that the..

[stoic garden]

Shoot wrong person

[trim lichen]

well that's a bruh moment if i ever saw one

[obsidian hamlet]

What does vro even mean

[iron pier]

what in the world is happening here

[trim lichen]

it is apparently a variation on "bro".

[iron pier]

I see no math problem

[simple haven]

vro = bro with a different first letter

[vivid cave]

what's going on?

[stoic garden]

Misspelling of bro

[obsidian hamlet]

BRO CALLED IT

[trim lichen]

it's been solved already

[obsidian hamlet]

HELPERS ONLY COME WHEN THERES DRAMA

[iron pier]

oh. good to know

[obsidian hamlet]

💔

[stoic garden]

Helping people is boring :(

[obsidian hamlet]

Yes

[obsidian hamlet]

I was give u drama but someone will snitch

[iron pier]

??? i was in #help-18 where there was no drama

for quite a while

this is the top channel in the queue

[obsidian hamlet]

Crazy

[iron pier]

so it's natural to click here when done with another channel

[stoic garden]

@trim lichen what pronouns do you prefer though

[obsidian hamlet]

Do you guys prefer green grapes or purple grapes

[stoic garden]

Purple. It’s hardly a contest

[vivid cave]

green ofc

[obsidian hamlet]

BLOCKED

OUT

[iron pier]

^^^

[obsidian hamlet]

I HOPE YOURE PURPLE GRAPES HAVE SEED IN THEM

@stoic garden

[iron pier]

but purple ones are good too

[obsidian hamlet]

BLOCKED

[iron pier]

???

[stoic garden]

Wait ill show proof

[iron pier]

what'd i do

[obsidian hamlet]

YOURE JOKING

[vivid cave]

idk i've never tried the purple ones haha

[stoic garden]

✅
^ proved by the blood-branded tick mark

[obsidian hamlet]

Guys i have the last dights of π

I gatekeeping

They nan paying me enough

[vivid cave]

but I don't like red wine, and I assume that red wine is made with the purple ones therefore I don't like the purple ones QED

[empty orchid]

!redir

[trim jolt]

This channel is only for on-topic discussion. Please take casual conversation to #discussion or #chill.

[stoic garden]

!done also

[trim jolt]

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

[obsidian hamlet]

.close

[trim jolt]

Channel closed

Closed by @obsidian hamlet

Use .reopen if this was a mistake.

[obsidian hamlet]

💔💔💔💔💔

Bye

[iron pier]

0_o

[empty orchid]

Yall...

[wraith hinge]

Helpers here volunteer to help. Don't expect free help 24/7. There are many helpers here who even volunteer to do the good work throughout the day, so at least show some decency.

[obsidian hamlet]

Yes

[empty orchid]

!vols

[trim jolt]

Helpers are just people volunteering their time to help you. Be polite and patient.

[empty orchid]

xD

[empty orchid]

What did you do bro 😭

[obsidian hamlet]

I AM polite

[empty orchid]

Please don't incite a riot in a help thread next time 😭

[empty orchid]

I was just pulling it up for reference

[obsidian hamlet]

They come for drama

[vivid cave]

I live for the drama tbf

[obsidian hamlet]

I'm with u

[trim jolt]

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.

[lunar stirrup]

not able to start

i mean i tried factorizing stuff

but didnt get anywhere

[stoic garden]

Are you trying to use calculus for this?

[tiny elm]

hm what about yeah derivating

[lunar stirrup]

no havent learnt calculus yet (except the basics)

but i can use if it comes as a good expression

[kindred pier]

!show

[trim jolt]

Show your work, and if possible, explain where you are stuck.

[stoic garden]

Oh no. Trust me, it will not be pretty

[lunar stirrup]

i didnt get anywhere.. i just wrote (x^4-x^2) as (x^2-x)(x^2+x)

[lunar stirrup]

then i cant use calculus

can anyone help

[mystic iris]

the answer is so clean lmao

[lunar stirrup]

are you trolling

[mystic iris]

i put it on everyones souls the answers x coordinate is a nice number

[lunar stirrup]

what is everyones souls

[mystic iris]

im not sure how to solve it without calculus though

[mystic iris]

(just slang)

[lunar stirrup]

ok with calculus how would u solve it? i cant take derivative of that expression

[mystic iris]

just use quotient rule bruh

[stoic garden]

#help-38 message

[mystic iris]

oh alright but quotient rule is basic

[stoic garden]

Not for someone who is just starting calculus.

[mystic iris]

do you have a better method?

[lunar stirrup]

oh this is a functions question not calculus

that i havent started yet

[lunar stirrup]

ok yeah i know quotient rule but is that the only way to get the answer? cause idts our teacher would have given it if it was only calculus based

[mystic iris]

yeah im not sure of any better method but I guarantee there is

cause you get a nonic polynomial when you try to solve it with calculus

[lunar stirrup]

dude 💀

[lunar stirrup]

oh alr ill ping helpers then

[lunar stirrup]

<@&286206848099549185>

[tawny cradle]

how about simplifying the expression

i guess dividing by x^3 should make it better

[stoic garden]

,w simplify (x^4 - x^2)/(x^6 - 2x^3 - 1)

[solid kiln]

Results provided by WolframAlpha

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

Requested by en.ratham

[tawny cradle]

x^3 divide bro

[stoic garden]

Tamil mattum pesuna, enakku puriyuma 😭

[tawny cradle]

lol

[lunar stirrup]

wdym divide by x^3

[tawny cradle]

divide numerator and denominator by x^3

[lunar stirrup]

oh ok i get
(x-1/x)/((x^3+2)-1/x^3)

[tawny cradle]

yeaah

then u can simplify dr in terms of x-1/x

[lunar stirrup]

denominator =
(x-1/x)(x^2+1/x^2+1) + 2

[tawny cradle]

one second

ig v can simplify it in the form of (x-1/x)^3 and x-1/x

(x-1/x)^3+3(x-1/x)+2 will be denominator

Pls check if i am wrong

[main sigil]

its correct

[lunar stirrup]

no its correct

what to do now

[tawny cradle]

okk

substitute x-1/x as any variable

and carry ur derivative

[lunar stirrup]

ohh alright

thanks bro

.close

[trim jolt]

Channel closed

Closed by @lunar stirrup

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.

[stable willow]

is $\ frac {d}{dx}\ cos^2t = -sin2x$ because of a trig identity or is it some random other rule?

[solid kiln]

iisa

is $\ frac {d}{dx}\ cos^2t \= \-sin2x$ because of a trig identity or is it some random other rule?
```Compilation error:```! Please use \mathaccent for accents in math mode.
\add@accent ... \let \ignorespaces \relax \accent 
                                                  #1 #2\egroup \ifmmode \els...
l.49 is $\ frac {d}{dx}\ cos^2t \= \-
                                     sin2x$ because of a trig identity or is...
I'm changing \accent to \mathaccent here; wish me luck.
(Accents are not the same in formulas as they are in text.)```

[stable willow]

fucking hell bro

jesus christ

[main sigil]

$\frac{\text{d}}{\text{d}x} \cos^2{t} = -\sin{2x}$

[solid kiln]

MathIsAlwaysRight

[stable willow]

you saved my life

i need to learn how to use this bot

but yeah is it a trig identity pull

[main sigil]

you cant put spaces between \ and the other stuff

[stable willow]

because i don’t see it in my formula sheet

[jolly basin]

i think if u convert cos^2 to 1-sin^2 and derive

you'll get - 2 sin cos

which is -sin 2x

2sin(x)cos(x)=sin(2x) if im not mistaken

[stable willow]

oh right okay so the negative stays

can use chain rule as well right ?

[jolly basin]

yeah you could also do chain rule on the existing equation lol

[main sigil]

cos(2x) = cos^2(t) - sin^2(t) = cos^2(t) - (1 - cos^2(t)) = 2cos^2(t) - 1
This works as well

[jolly basin]

im overthinking mb

2cos(x)*-sin(x) gets to the same place as rewriting it

[stable willow]

and then that = -sin2x?

or sorry t

instead of x

[main sigil]

then d/dx cos^2(t) = cos(2t)/2 + 1/1 = -sin(2t)

[stable willow]

right i’m gonna write this shiz down because i definitely need to remember this

i remember the identity now

[jolly basin]

i mean technically d/dx of cos^2 t = 0

[stable willow]

from highschool

[jolly basin]

it would have to be d/dt cos^2 t

[main sigil]

chain rule is probably the easiest here

trig identities will be more useful with integrals

[stable willow]

they wanna go through differential equations extensively first

which is fair enough

anyway thanks guys appreciate it

.close

[trim jolt]

Channel closed

Closed by @stable willow

Use .reopen if this was a mistake.

[trim jolt]

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.

[lunar stirrup]

from that summation they are saying that
|x-2022|-|x|=f(x)

idk how to find number of real roots

[trim lichen]

f(pi) = 22/7 💀💀💀💀💀

[lunar stirrup]

yeah

[trim lichen]

R -> Q can only ever be continuous under really tight constraints btw.

[lunar stirrup]

oh

[trim lichen]

what a troll question 💀

[lunar stirrup]

its not a troll question 😭

my teacher gave

[trim lichen]

your teacher is a troll then

[lunar stirrup]

;/

can someone help me solve the question

[trim lichen]

[a function] R -> Q can only ever be continuous under really tight constraints btw.

like

what functions R -> Q can you think of that are continuous

and which never return any irrational values

[lunar stirrup]

uhh

cant think of anything

what if the function is constant

f(x) = pi

?

[trim lichen]

yes

[trim lichen]

well not pi 💀

[lunar stirrup]

OKAY 22/7

[trim lichen]

in fact it's ONLY constants.

the functional equation is a troll to distract you

[lunar stirrup]

oh

;/

that is something my teacher would do

so will it be |x-2022|-|x|=pi

@trim lichen

and im getting 1 soln from this

[trim lichen]

22/7

[hollow spindle]

First notice that the sum is telescopic and all terms cancel out and you're left with f(x)=|x-(2022/7)|-|x|

[trim lichen]

not pi

[lunar stirrup]

yeah sorry

[lunar stirrup]

how is it 2022/7

[thorn bay]

same thing

[trim lichen]

no

[thorn bay]

sorry was a joke

[trim lichen]

pi and 22/7 are not the same no matter how many underpaid teachers say they are

[hollow spindle]

Oh my bad I read f(pi)=22/7 and tought the sum ends in 2022/7

[lunar stirrup]

ive heard some people take pi = 3 💀

[lunar stirrup]

np

i got the answer anyway

thanks @trim lichen

.close

[trim jolt]

Channel closed

Closed by @lunar stirrup

Use .reopen if this was a mistake.

[hollow spindle]

Fundamental theorem of engineering

[trim jolt]

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.

[indigo plank]

technically not math but could someone help me w/ this circuit

[indigo plank]

how did they go from the top to the bottom circuit i cant figure out the source transofrmation they did

[trim jolt]

@indigo plank Has your question been resolved?

Channel closed

Closed by @indigo plank

Use .reopen if this was a mistake.

[trim jolt]

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.

[last mantle]

How would I even begin to solve this integral

I have no idea how to even start

[stoic garden]

,w differentiate t^3 + 9t^2 + 6t

[solid kiln]

Results provided by WolframAlpha

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

Requested by ayudham

[last mantle]

So I just can say
let u = t³ + 9t² + 6t

And that's all?

Then I solve by trig substitution or whatever

[stoic garden]

Before doing that, you must recognize that du would contain 6t, which doesn't match our 3t

[last mantle]

Hmm okay

True, I didn't notice that

Can we do some sort of factorization inside the radical?

[stoic garden]

,w factor t^3 + 9t^2 + 6t + 24

[solid kiln]

Results provided by WolframAlpha

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

Requested by ayudham

[stoic garden]

Than will likely not turn out pretty.

[fossil sedge]

Yks2025😉

[last mantle]

Huh?

[fossil sedge]

Nvm

[last mantle]

I have no idea

Do you have a hint as to how I could like proceed?

[fossil sedge]

Yk what

Do

U²= t³+9t²+6t+24

Differantiats both sides

[last mantle]

2udu = 3t² + 18t² + 6 dt

[fossil sedge]

. dx

[last mantle]

Even if you factor that out, it won't be equal to our numerator

[last mantle]

Yes my bad

[fossil sedge]

Divide by 3 then

Both sidez

[last mantle]

t² + 6t + 2

Not 3t

[fossil sedge]

Oh

[last mantle]

This is why I am having a problem with solving this

If it were that simple of a substitution I wouldn't have asked

[vagrant imp]

maybe add and subtract 3t and apply by parts to the remaining expression?

[last mantle]

How would you solve the second integral

The one that has the only 3t on the numerator

[vagrant imp]

yeah thats what i said maybe apply by parts

not sure tho didnt try myself, but it could work

[last mantle]

like I think you're saying
Numerator:
t² + 6t - 3t + 2

[fossil sedge]

And substract 3t at the end

Yea

[last mantle]

Then if we have the
-3t/sqrt(t³ + 9t² + 6t + 24)?

How

[last mantle]

<@&286206848099549185> sorry for ping, please help

[fossil sedge]

No answers

Like i put it to integral solver

And there is no answer other than 0.687147...

[last mantle]

Do you think the question might have had a mistake?

I found it in a textbook

[fossil sedge]

Yea probably

[trim jolt]

@last mantle Has your question been resolved?

[hybrid field]

if you have u-sub and have differnt numbers but the same degree then thats fine

having 3t on top and 6t on bottom is fine, your variables still cancel out

remember that $\int{2xdx} = 2\int{xdx}$

[solid kiln]

Krish

[trim jolt]

@last mantle Has your question been resolved?

[old zinc]

update it turns out you need a SPACE in between the points so all your talk about "blaming people" and thinking that you were "helping" (lmfao) was completely wrong. next time instead of claiming incompetency on other people, you should do some deeper soul-searching. bye

[trim jolt]

Channel closed

Closed by @last mantle

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.

[jovial leaf]

how do i do this

[empty orchid]

You can assume that y is the unit vector on the x-axis to make it easier for you

[jovial leaf]

x axis….

we didn’t do vectors on Cartesian plane yet

Here’s what i did

I’m tryna figure out where i can use the 30 degree

[thorn bay]

so your vectors are just ... flying through the astral plane?

no space in which they're living?

[jovial leaf]

yea…

[lime sphinx]

do you know dot product?

[jovial leaf]

we just started learning

[thorn bay]

what does it mean that x-hat = 1, y-hat=1?

[jovial leaf]

no omg

[jovial leaf]

Isn’t that the symbol for unit vector

[thorn bay]

often it is, but, you're saying it's a number?

[jovial leaf]

huh

oh we learned

[thorn bay]

you wrote x-hat = 1

[jovial leaf]

all unit vectors

is 1

😟

[thorn bay]

that's not correct, all unit vectors have SIZE 1

okay it's fine, look

[jovial leaf]

sorry

[thorn bay]

you're intuitively using vectors by putting them on the plane

because you're drawing them on a flat surface

[jovial leaf]

oh really

[thorn bay]

yup

[jovial leaf]

uhhh

[thorn bay]

even if your class didn't get to it yet, that's what you're doing

[jovial leaf]

idk i feel like im barely grasping the concept

[thorn bay]

honestly it's not your fault, if your class is teaching you about angles between vectors before they're teaching you how to put them in a coordinate plane

[jovial leaf]

and i think my teacher DIDNT go in depth

[lime sphinx]

but you are playing with arrows on the board if i understand

[thorn bay]

anyway, the correct symbol for size of a vector is like this:
$\Vert \hat{x} \Vert = 1$

[solid kiln]

gfauxpas

[jovial leaf]

wait does vectors even belong to math?

[thorn bay]

absolutely

[jovial leaf]

Huh

[jovial leaf]

I thought it’s physics

well

welp

[thorn bay]

it's both

[jovial leaf]

9th

okay8

8

[thorn bay]

the double bars mean "size"

you're not saying x-hat is a number

you're saying the size of x-hat is 1

think of it like a weird type of absolute value

the size of a vector is the length of the arrow you're drying

drawing

[jovial leaf]

magnitude right

[thorn bay]

yes

[jovial leaf]

okay

[thorn bay]

"magnitude" and "size" are cinnamons

[jovial leaf]

i know like

some stuff

from physics

but yea

so it’s the MAGNITUDE

[thorn bay]

anyway, would you agree

[jovial leaf]

Like this?

[thorn bay]

that if you draw the two vectors with an fixed angle between them

that if you spun the double-vector around, no matter how you spun them, they would have the same angle?
and similarly if you moved them up, down, left, right?

agree or disagree?

[thorn bay]

yeah. usually people use double lines || . || but it's fine to use | . |

[thorn bay]

?

[jovial leaf]

yup

makes sense

[thorn bay]

so,

[jovial leaf]

oh..

crazy

[thorn bay]

what ;( is saying here

is you might as well draw y horizontal and and put them at the origin

of a coordinate plane

[jovial leaf]

whaatttttt

[thorn bay]

becaue rotating and moving it doesnt change the behavior of the angles

[jovial leaf]

okay

um

[thorn bay]

so, rotate it until the y vector is horizontal

[jovial leaf]

😭

[thorn bay]

and then move it up/down left/right until it's at the center of an xy-plane

does that make sense

[jovial leaf]

no

[thorn bay]

🫂

[jovial leaf]

sorry

i DONT

see it

[thorn bay]

okay no problem,

[jovial leaf]

😭

[thorn bay]

listen

let me draw a picture

[jovial leaf]

nndsjijndsjnxsjni

okay

thank you

[thorn bay]

np, working on it

[empty orchid]

It’s for simplicity purposes

Even for me, it is easier to imagine and/or calculate

[empty orchid]

For example, if y is the unit vector on the x axis, we can now calculate the actual vector of x

[thorn bay]

lets say you started with vectors Blue1 and Blue2

[jovial leaf]

Huh

[jovial leaf]

sorry i DONT get this… 😭

[thorn bay]

and I kept its base point the same, but rotated it counter-clockwise a little, until I got purple1 and purple2

[jovial leaf]

yea

oh

[thorn bay]

so if the angle between blue1 and blue2 is 30degrees

then the angle between purple1 and purple2 is also 30 degrees, right?

[empty orchid]

The wording that I am using and the problem is is kinda shitty, but my point is that we can have actual values for each vector and then calculate the whole 3x-5y thing

To make it easy, if you have learned what without loss of generality means, it works the same way

[jovial leaf]

Ye

[thorn bay]

everything ;( is saying is correct, but im trying to show you why we can put them in a coordinate plane

so, listen to both of us ;)

[jovial leaf]

wait how

[jovial leaf]

no.. what is that

[jovial leaf]

i will

[empty orchid]

Then don’t worry about it

[jovial leaf]

so far what youre saying makes sense

idrk what ;( is tryna say im sorryyyy

😭

[empty orchid]

You know what a unit vector is, correct?

The unit vector on the x-axis is given by (1, 0)

[thorn bay]

alright

cat, the first image shows that rotating the vectors doenst change their angle and sizes

[jovial leaf]

NO

I DONT

i did not understand today..

[thorn bay]

the second image shows how shifting the angle right/left up/down doesnt change the angle and size

, following?

[jovial leaf]

Yea

[thorn bay]

so, here's the trick

[jovial leaf]

Yea

[thorn bay]

you can draw a coordinate plane on any flat surface, right?

as long as you dont mind ruining your computer monitor

so, here's the thing: draw a coordinate plane, in your mind, on the space where the arrows are living

[jovial leaf]

wait

by coordinate plane

[thorn bay]

(x,y) plane

[jovial leaf]

okay

[thorn bay]

so, these angles they have an angle between them of 30 degrees, and they're somewhere floating around

but, if we move them to the origin, nothing changes

[jovial leaf]

Yea

[thorn bay]

and if we rotate them so one arrow is horizongtal or vertical, nothing changes either

[jovial leaf]

Yea

[thorn bay]

so you might as well draw them at the origin, with one vector on the x-axis

ready for

https://tenor.com/view/guy-long-hair-mustache-magic-shia-labeouf-gif-17741293

?

[jovial leaf]

wait

Basically like purple 2?

U line it up at x aixs?

[thorn bay]

yeah. also, it looks like I made Purple 1 not long enough, it's supposed to be the same length as Blue1

so, pretend

[thorn bay]

exactly

[jovial leaf]

ooookayyyy

alright

makes sense

[thorn bay]

https://tenor.com/view/guy-long-hair-mustache-magic-shia-labeouf-gif-17741293

[jovial leaf]

whats the magic

[thorn bay]

now that they're sitting in a coordinate plane at the origin

the location of the arrowhead tells you everything about the vector

and you can just treat the vector as a point (x,y), the point at the arrowhead

[jovial leaf]

oh

[thorn bay]

because, do you remember how to write a ray between two points A=(xa,ya), B=(xb,yb) ?

it's just B-A

and here, the starting point is the origin, O=(0,0)

so it's B-O = B , just the point

[jovial leaf]

WHAT

wait whats this

Wdym ray

[thorn bay]

ray, a directed line segment

a line segment with a direction, so that, A connected to B is not the same as B connected to A

[jovial leaf]

so rn we’re treating the vectors as 2 points?

[jovial leaf]

okay

[thorn bay]

even better - one point, because, we put them at the origin O

and B-O is just B

[jovial leaf]

Oh

Okay

Kinda makes sense

I think

[thorn bay]

okay, now I'll let @empty orchid take over, because i want to cook dinner

GL

[jovial leaf]

like ur saying the 1 that lies on x axis?

[thorn bay]

you can do it

[jovial leaf]

bon appetite and ty

😟

[thorn bay]

okay so

this is actually torturous without using dot product

it's possible, but really annoying

are you sure you're supposed to do this without knowing dot product?

if you are:

let's say you draw x and y at the origin

then x has its head point where? @jovial leaf

it's actually not bad if you know how to use polar coordinates

[trim jolt]

@jovial leaf Has your question been resolved?

[trim jolt]

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.

[feral trail]

hi! i’m working with density and mass applications. would someone help identify where i went wrong in my problem solving? i got an answer of 8891.5697 but it was marked incorrect.

[supple copper]

the first step would be to write it as

$\text{total mass} = \iiint_A \rho(x, y, z),dV$

[solid kiln]

frosst

[supple copper]

i dont see this written anywhere for you

[supple copper]

what you've done here has nothing to do with the cone

[feral trail]

i’m not entirely sure how to write it like that, i don’t think i was taught that. this is just single variable calculus 😅

[supple copper]

oh okay

let's do it another way then

[feral trail]

okay!

[supple copper]

so if we slice up the cone horizontally

we get a bunch of disks yeah?

[feral trail]

yes!

[supple copper]

what would be the mass of a disk

here im looking for "it's density * volume"

[feral trail]

i learned it to be the volume * density, so volume would be pi(radius)^2 * dx in this case, and our density is rho(x) . but now i’m realizing i’m forgetting the height of the disc, right ?

[supple copper]

which means we need to find the density and volume of each slice (each disc)

[supple copper]

we can just denote that by some h

so it's just πhr^2 * rho

[feral trail]

for the mass of the slice

[supple copper]

perfect okay

the goal at the end is that we are going to "add up" the mass of all the slices together

and take the limit h -> 0