help-0

[unique kayak]

yea, just put it in there

theta is a variable like any other

also theta includes the units, so that's nice

the wave equation is essentially what you wrote, but shifted by pi/4

[jovial violet]

vertical shift is 0 magnitude?

[unique kayak]

yea

[jovial violet]

alright

[unique kayak]

magnitude 0, direction +

there's two ways you can address that, either you use a phase shift, but that's honestly more complex or you just use cosine instead of sine and use exactly the things you wrote

[unique kayak]

i specifically told you the periodic time my guy

write it in there

[jovial violet]

6pi/theta

[unique kayak]

yea, then put it there

you still have theta over 10 pi

[jovial violet]

fixed it

[unique kayak]

the wave equation is 4cos(x)

[jovial violet]

oh alright

[unique kayak]

or rather y=4cos(x)

[jovial violet]

put it in

did it

1:40 Seconds left and as for the one with the steps imma just put what u suggested and call it a day...

[unique kayak]

If you get it back and you know the solutions, please message me, I'm genuinely curious what the hell they mean

[alpine sable]

Question- If both x+1 and x+2 are factors of ax^3+x^2-ab+b find the value of a and b. Pls help me.

[jovial violet]

alright T-T

[unique kayak]

Good luck

[jovial violet]

ITS DONE

I put the cos thingyy

[jovial violet]

for that

im send u the thing once it's all corrected

[unique kayak]

👍

[unique kayak]

@alpine sable well, you can start by multiplying the factors you know together

And then maybe you can see what a and b need to be

[alpine sable]

Like for x+1=0
We get x=-1
So can we substitute -1 to p(x)?

[plush bear]

this is No Solution correct?

because cos cant be greater then 1

[glass lichen]

yeah, just use factor theorem on both factors and you get 2 equations 2 unknowns

[glass lichen]

that's true.. but irrelevant for that question

[plush bear]

hm

omg

for some reason i subtracted 5

instead of dividing

[glass lichen]

yeah..

[alpine sable]

Shall I send you my solution I am stuck

[glass lichen]

sure I guess

plugging in -1 and -2 into the poly both give 0, so you have 2 equations in a and b

[alpine sable]

(sorry for bad handwriting)

[glass lichen]

everything above the scribble looks right

then no fucking clue what you did after that

[alpine sable]

By scribble u mean the bad cutting?

[glass lichen]

no the ellipse of scribble

[alpine sable]

Then pls guide me what should I have done?

[glacial hedge]

could someoen help with this

https://math.stackexchange.com/questions/4174771/volume-of-a-solid-in-region

<@&286206848099549185> ?

[remote heron]

i suck at multivar calc, but are you sure this is bounded

[obtuse yoke]

does anyone know what the formula to find the number on any row on pascal's triangle

[remote heron]

@glacial hedge

[gentle flame]

It's bounded

[gentle flame]

If I did it right, I think your formula is correct,

[remote heron]

isnt this just choose?

[gentle flame]

But it should be dx dy

[gentle flame]

Not the other way around

[obtuse yoke]

?

[remote heron]

binomial coefficient

[obtuse yoke]

(x-1)^n is it that equation

[glacial hedge]

@gentle flame why is it the otherway around?

[obtuse yoke]

or is it x+1

[quick fiber]

I’m traveling 11 mph, I travel for 2 hours, how many miles have I traveled?

[wild viper]

22

[obtuse yoke]

22

if it is a constant speed

[remote heron]

https://brilliant.org/wiki/pascals-triangle/ theres some more information here

[quick fiber]

It’s goes like 9- 11

[obtuse yoke]

ok thanks 🙂

[quick fiber]

I would say 1and a half hours to play it safe

[gentle flame]

Because if x + y = 1, then x = 1 - y, so you expressed x as a function of y, so the integral wrt x needs to be done first

[obtuse yoke]

(n+1) ^n so... now I am gonna plug in -1 and see where it takes me

[gentle flame]

lol I know that's a garbage explanation, but I can't think of a better way to say it 😅

[obtuse yoke]

even though it is then theoretical math

[gentle flame]

It's (x + 1)^n

[glacial hedge]

@obtuse yoke i dont know where the heck you got that for um pascal's triangle?

[quick fiber]

@obtuse yoke check dms

[gentle flame]

The coefficients form the n'th row of the Triangle

[glacial hedge]

um

its

the binomial coeffecient?

[obtuse yoke]

ok

[obtuse yoke]

yah lol it is (x+1)^n

so if we plug in -1... for x it should be infinite

[gentle flame]

?

No

[gentle flame]

You're expressing x in terms of y so x is dependent on y and it needs to be integrated first

I genuinely don't know how to explain it. We called them type 1 and type 2 integrals and stuff

[glacial hedge]

r u trying to get the -1'th row of pascal's triangle?

[obtuse yoke]

yes but it would be infinite because if you expanded it it would be...

[glacial hedge]

@obtuse yoke think about it... does that make sense

[obtuse yoke]

yah

[gentle flame]

Wait whose math.stackexchange post am I looking at 😅

[glacial hedge]

mine

[gentle flame]

I thought it was yours @glacial hedge

[glacial hedge]

it is

[glacial hedge]

how does that make sense, each row you go up you get less collumns. so going up from the 1st row, you um get.... infinity rows???

[gentle flame]

We can easily show that the way you have it is wrong

If you integrate wrt y first, you'll have a y at the end, and integrating wrt x won't make the y go away

[glacial hedge]

yeah

[gentle flame]

So you'll have a y in the final answer if you do it the way you wrote it

[glacial hedge]

thats why i was confused

[junior spindle]

how do I solve the area of the triangle here?

[glacial hedge]

@junior spindle you no <MNL to be 120

you also no

[junior spindle]

what

[glacial hedge]

LN = 9, because thats the radius

[gentle flame]

Hint: Isosceles triangle

[glacial hedge]

you can then use

[gentle flame]

Which doesn't make any sense

[glacial hedge]

A = 1/2 * MNLNsin(MNL)

[junior spindle]

i dont get it

[glacial hedge]

@junior spindle wanna go to #help-2 because this is sorta being used

[junior spindle]

Yea

[gleaming warren]

occupied or not

[gentle flame]

@glacial hedge do you get it now

[obtuse yoke]

The formula is based on a positive numbers and eventually the x to the power will catch up to the positive number and all the remaining numbers will be 0+0+0... but when it is negative it is 1-1x+x^2-x^3-x^4+x^5...

[gleaming warren]

occupied or not

before any one says i cannot get help in test i just want to say that this is my hw

[glass lichen]

are you asked to determine the co-efficient matrix

[gleaming warren]

what is that

[obtuse yoke]

complex system of equations 🙂 I think

[gleaming warren]

xy?

[glass lichen]

well im asking you cause it's your questioin

[gleaming warren]

they dont say that

they just say find $A_x$

[ocean seal]

TheGameBot

[glass lichen]

Yeah... that's most likely the co-efficient matrix for the system

[gleaming warren]

ok

[glass lichen]

so by the name on the tin.. just take the co-efficients of the system

and put them in the matrix

[gleaming warren]

oooh

i get it now

thx

[gentle flame]

Pascal's Triangle doesn't care about negative values of n

It's only defined for nonnegative integral n

[gleaming warren]

i dont get it actually

the answer is A

but the next question is same but in the end the say $a_y$

[ocean seal]

TheGameBot

[obtuse yoke]

but the equation will never theoreticly end

[glacial hedge]

wait dafuk? since when is pascal's triangle defined as an integral

[gentle flame]

integral = adjective, "being an integer"

[glacial hedge]

😤 PASCAL's TRIANGLE IS ONLY DEFINED FOR POSITIVE VALUES, SJDKLFJSFJLDSJFLSJDLF

[gentle flame]

I'm not using "integral" as a noun here

[gentle flame]

Is this related to some hw question?

[glass lichen]

you typically say "non-neg integers"

[gentle flame]

Do you know about Taylor Series and radii of convergence?

[glacial hedge]

yep

[obtuse yoke]

lol it is but you can plug in any negative value and you will end up with infinity

[glacial hedge]

YES BUT IT DOESN't APly

your no longer solving for the pascal triangle

since its only defined for positive integers

[gentle flame]

"Integral" as an adjective is a perfectly reasonable (and common) construction, but yes, I should have used that

[gentle flame]

I was asking @obtuse yoke

[glass lichen]

yeah you can do that, im just telling you the typical phrase is non-neg integers

[obtuse yoke]

but it is still theoretically possible when you get to theoretical math

[gentle flame]

What is "infinity"?

[gentle flame]

What are we on right now?

[glacial hedge]

that statement makes 0 sense xDD

[obtuse yoke]

an undefined amount but it still has value

[glass lichen]

inf doesnt have a value

[glacial hedge]

what no? its a concept... it doesnt have value

[gentle flame]

So "infinity" is undefined?

[obtuse yoke]

a chunk of rock surrounded by dark matter that is flying through space

[patent python]

mhm

[obtuse yoke]

It is a concept that has a theoretical value

[patent python]

infinity can be anything and nothing at the same time

[glass lichen]

it has no value

[obtuse yoke]

but not a solid stated value

[patent python]

it doesn’t have a value

[glacial hedge]

yall are kinda stupid

INFINITY IS A CONCEPT JUST LIKE I

i doesnt have value...

[glass lichen]

no need for an ad hominum

[gentle flame]

Then I agree, if you put in negative values, you get something that is indeed "infinity" (or "undefined", as you so kindly explained to me just now)

[glacial hedge]

yeah... I am very frustrated with this guy tho

[gentle flame]

What state, then? Plasma? Bose-Einstein Condensate?

[obtuse yoke]

It is considered "undefined: in regular math because there is no end to infinity and no set value just as x/0

[obtuse yoke]

ok... this is not science

There is no set value for infinity

[gentle flame]

Then what does "infinity" mean? Is it a variable, like x?

[glacial hedge]

@obtuse yoke have you taken calculus?

[obtuse yoke]

x could equal infinity

[glass lichen]

no it cant

[obtuse yoke]

yes

x=infinity

[glass lichen]

infinity cannot equal anything

[obtuse yoke]

could be tru

[glass lichen]

as it has no value

[obtuse yoke]

so then x= nothing

[glacial hedge]

@obtuse yoke may i ask how you passed calculus without knowing what infinity is?

[glass lichen]

you can approach infinity via limits

$\lim_{x\to\infty}x=\infty$

[ocean seal]

Mosh

[gentle flame]

How do you know he did

[gentle flame]

Even this is non-sensical

[glacial hedge]

he said he took calculus

[glass lichen]

but that's different than saying x=inf

[obtuse yoke]

infinity is a number that has no set value which is considered undefined which is sometimes considered as a non-value number because there is no set value to its name

[glacial hedge]

you cannot set a variable to infinity...... because infinity is not defined

[obtuse yoke]

then can you set x=5/0

[glacial hedge]

DUDE

[obtuse yoke]

you technically can but it is "undefined"

[gentle flame]

No

[ionic jewel]

maf

[glacial hedge]

https://tenor.com/view/buzz-lightyear-no-sign-of-intelligent-life-dumb-toy-story-gif-11489315

[gentle flame]

"Undefined" means "not defined", meaning one cannot set equal to 5/0

[obtuse yoke]

but then x is useless mostly when solving other things

[ionic jewel]

Lim x to infinity of x

is how you do what you want

[obtuse yoke]

yes so if x=5/0 x= undefined

[gentle flame]

Yes, but my point still stands

[ionic jewel]

you can't just yeet infinity whenever you want into equations

[glass lichen]

I never did that.

[glacial hedge]

i meant to tag al123

[obtuse yoke]

tru

[gentle flame]

Guys, leave it

Not worth the effort

[ionic jewel]

you could use some topological definitely of infinity

[obtuse yoke]

lol infinity = (no value) that is what you are saying

[glacial hedge]

@obtuse yoke did you pass calculus... because with the things your saying im not entirely sure you understand the notion of infinitely small values or infinitely large values

[glass lichen]

yes

[ionic jewel]

saw some cool definition of it before

with a 2D sphere

[glacial hedge]

@obtuse yoke yes thats the dictionary

[obtuse yoke]

definition #2

[glacial hedge]

not a math definition

[gentle flame]

Can you elaborate?

[glass lichen]

infinity has no value because if we define it to have a value A, then A=A+1 is true which means 0=1 which is clearly false

easy proof by contradiction

[obtuse yoke]

it said mathematics on top the definition -___-

but infinity has no set value so we assunme it has no value

[gentle flame]

Ah yes, Google is never wrong, right

[glacial hedge]

guys i give up... I'm not being mean to AL123, but he seriously doesn't understand infinity

[glass lichen]

Assume $\infty$ does in fact have a value, A. Then that means $A=A+1\implies 0=1$ which is clearly false. Hence $\infty$ cannot have a concrete value $\qed$

[ocean seal]

Mosh

[ionic jewel]

yeah actually i don't remember exactly but you can define a plane as someyhing like R^2 union infinity. If you place a 2d sphere centered at the origin of the plane you can map any point on the plane to a point on the sphere by drawing a line from the point to the top of the sphere, and mapping it to where it itercepts with the sphere. infinity is the value that maps to the very top of the sphere

[obtuse yoke]

lol but it is theoreticly correct

[ionic jewel]

called a point of compactness

[glass lichen]

At this point it's just a finitist in the wild

[obtuse yoke]

greater than any assignable quantity or countable number

[gentle flame]

Ah, the extended real line

[ionic jewel]

yea I suppose

[obtuse yoke]

yes

[glass lichen]

yes, so if you assign it a value, it will be bigger than it's value you just assigned it

[ionic jewel]

came up in a complex analysis class so we did $\bC \cup {\infty}$

[ocean seal]

bunny

[obtuse yoke]

so it is assumed as no value

[glass lichen]

why am I just learning about \b

[ionic jewel]

no

it doesn't exist

[ionic jewel]

custom server preamble

infinity is not a number

[glass lichen]

In english?

[ionic jewel]

it's not on the real number line

it doesn't exist

[obtuse yoke]

Then why do we use it in math in theoretical math physics astronomy astrology quantum physics

[ionic jewel]

you can't assign it to a value

[ionic jewel]

you dont

you don't use it anywhere as a number

just becuase the concept exists doesn't make it a number

[obtuse yoke]

yes but it is considered as a non usable number but still used as a variable for an amount that goes on forever without an end

[soft ruin]

guys can someone tell me how do I go like this in calculator

123
456

[ionic jewel]

,w largest number

[ocean seal]

Results provided by WolframAlpha

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

Requested by 兔子#6562

[ionic jewel]

notice it says incorrect

[undone dock]

Just because you use it doesn't mean it's a number. Saying something like Lim x->infinity doesn't mean that we're using infinity as a number

[gentle flame]

Ah I see

[obtuse yoke]

It is used as a consept or term to represent a number that is uncountable

[gentle flame]

The Riemann sphere

[ionic jewel]

it's not a number stop it

[obtuse yoke]

how did we get into this conversation

[gentle flame]

Gonna take Complex Analysis next to next sem

[ionic jewel]

yessir, thought it was a cool concept

[gentle flame]

Very cool

[obtuse yoke]

not a number but not a value then?

[ionic jewel]

it's a concept

[gentle flame]

Can't wait to learn about Cauchy's Residue Theorem

[ionic jewel]

i haven't gotten there yet

just doing cauchy-Reimann thm now

no residue

[obtuse yoke]

yes let us end this conversation

[gentle flame]

Interesting

Are you a math major?

[ionic jewel]

honestly complex analysis feels like the most "ah it's all coming together" class I've taken so far

yes

[gentle flame]

Same 🤩

What year are you currently in

I'm a freshman

[ionic jewel]

same

still got plenty of time for more cool math

abstract algebra looks fun but can't first it in next semester

[gentle flame]

Damn

What college, if you dont mind me asking

I have algebra next sem and them complex analysis in my 4th sem

[ionic jewel]

rather not dox myself

[gentle flame]

With real analysis and a 2nd course in linear algebra

[ionic jewel]

ooo

yeah I'm taking the "followup" linear algebra next semester

[glacial hedge]

bruh i wish there was an online school that offered like "real" math courses

[ionic jewel]

why do you think there isnt

[glacial hedge]

well

i just cant apply

because i just graduated middle school xD

[ionic jewel]

if you want to pay you could literally take some at a college

otherwise there's lots of resources and videos online

[gentle flame]

I assume you're not from the US? I'm not either. I'm from India

[ionic jewel]

well it's not gonna be worth paying for classes if it's below calc level id imagine

[glacial hedge]

no

like i mean

[ionic jewel]

haha unfortunately I'm in the US

[ionic jewel]

Big tuotion

[junior spindle]

how do you get thhis

[glacial hedge]

something like topology

[ionic jewel]

... topology is hard

[gentle flame]

If you can self study, that's always an option

[ionic jewel]

i haven't taken a class in it but I'm pretty sure even the intro is going to have higher level math

[glacial hedge]

yeah but i kinda suck at self study xD

[gentle flame]

Use Sidney Morris for Topologu

[gentle flame]

Damn

[junior spindle]

can someone help me

[ionic jewel]

the only thing i know about topology is that coffee mugs are donuts and Mobius strips are cursed

[ionic jewel]

car stops when velocity is 0

[glacial hedge]

@junior spindle do you know inscribed angle theorem? or something like that

[junior spindle]

its like its half of any inscribed angle

or double

[glacial hedge]

yep, i feel like if i self study im not gonna understand anything xDDD

[junior spindle]

idk

[sleek jewel]

so i put v(t) as zero?

[ionic jewel]

yes

[glacial hedge]

the inscribed angle is half the measure of the intercepted arc

[foggy hound]

Help pls

[gentle flame]

Mobius strip is a non-orientable surface

[glacial hedge]

why is everyone spamming quetsions

[sleek jewel]

aihgt

[true torrent]

whats 1+1

[junior spindle]

so its 24 @glacial hedge

[ionic jewel]

cuz it's questions-0 and no one knows how to scroll to other channels

[gentle flame]

A coffee mug is homeomorphic to a torus

[glacial hedge]

yeah i tihnk so

[undone dock]

Its 24 because the measure of JL is 48, so angleJML=48/2=24

[glacial hedge]

you can cancel some things....

[junior spindle]

and this is double

so 60

right

[glacial hedge]

yeah

[undone dock]

Yea

[sly mantle]

intro topology doesn't really start 'high level'

[ionic jewel]

multiply all the numerators together, and multiply all the denominators together, but yes you can cancel some terms

[foggy hound]

Ok thaks

[junior spindle]

this is the one that always messes me up

[ionic jewel]

rokabe you were typing for like 2 minutes i was waiting for a wall of text

[glacial hedge]

@\

@junior spindle dude

its the same concept

[junior spindle]

it is??

[glacial hedge]

m<EFG isthe measure of the arc GE

[glacial hedge]

xD same

[junior spindle]

oh so its just double?

70?

[glacial hedge]

yeah

[ionic jewel]

maybe i should study some topology then

[sly mantle]

it starts off laying down definitions that are at surface level easy to parse but may make you ask why are they formulated that way til it makes sense later

[junior spindle]

you add or multiply the two sides?
like is it x+15 or x(15)

[glacial hedge]

Im a little confused how the minimum of f(x,y) on x^2+y^2<=1 helps you find the lower bound for that inetgral?

[ionic jewel]

I rather thought it would go the other way of them showing you why things work like so (like why you have to do limit def of derivatives and stuff first)

[gentle flame]

Isn't that literally linear algebra in a nutshell?

[glacial hedge]

sorta

[gentle flame]

I assumed that all courses were like that

[sly mantle]

LA defs are quite intuitive on 1st pass

[ionic jewel]

i guess conceptually it can make sense but every video (3b1b shout-out) that relates to it is quite complex and has some wack stuff

[gentle flame]

Well, except for the vector space one, yeah

[sly mantle]

a vector space is a set of stuff you can scale & add (following other rules), that's it

[ionic jewel]

i still don't know what the point of eigen-stuff is, but wow am i good at finding it all

[gentle flame]

Imo it's like LA nicely let's you wade in, and Topology throws you in the pool

[gentle flame]

🙄 I know

[sly mantle]

eigenstuff is good for instance in decomposition. eigendecomp makes matrix powers easy

[gentle flame]

But stuff like rank don't really make sense at first glance

[gentle flame]

That's not an explanation for what it is at all though

And no, before you ask

I'm still figuring it out

[ionic jewel]

this is literally the only application i know for it

[gentle flame]

QM uses eigen stuff a lot

Ditto for Mechanics (springs, anyone?)

[ionic jewel]

QM is pretty much magic as far as I'm concerned

[glacial hedge]

lol

[ionic jewel]

take a few derivatives to find the pattern

[glacial hedge]

try writing down a few derivatives and notice a pattern

[ionic jewel]

lmao

[sleek jewel]

???

[glacial hedge]

bunny you beat me to it

[ionic jewel]

derivative of e^u is du*e^u

[gentle flame]

Are you an Ivy League kid

I'm guessing yes

[glacial hedge]

where did you get that from

[gentle flame]

Just a guess

?

[strong furnace]

I thought this was chill lol

[gentle flame]

F

[glacial hedge]

wait @gentle flame how did you get ivy leage from bunny saying lol

[gentle flame]

Not from that

Just a guess based on his knowledge of mathematics

[glacial hedge]

oh

[sly mantle]

there's also reduction of quadratic forms. also since it makes matrix powers easy, it gives a nice way to solve linear systems of ODEs (assuming diagonalizable). related to normal modes of coupled oscillators in mechanics

[ionic jewel]

I'm not going to say where I go but I'll take your guess as a compliment anyways

[gentle flame]

Damn I just remembered the quadratic forms thing

[glacial hedge]

@sly mantle you are an engineering major i assume?

[gentle flame]

We went over it very quickly in our course

[ionic jewel]

thank you rokabe

[gentle flame]

Fair enough 😄 compliment indeed

[sly mantle]

phys/math

[gentle flame]

Double major?

The ODE thing blew my mind when I first saw it

[ionic jewel]

aaaaa physics

[gentle flame]

👌 GR

[foggy hound]

Find the area plssss

[ionic jewel]

area of a cuboid is length*width*height

[sly mantle]

also yeah the simultaneous diagonalization of commuting operators is often abused (though its theory is a bit glossed over) in baby qm

[wanton smelt]

wait no

yall aint seen that

[ionic jewel]

wait

[gentle flame]

Bruh

[wanton smelt]

thats volume

[gentle flame]

That's volume

[glacial hedge]

wait what? do you want surface height?

[wanton smelt]

lol

[glacial hedge]

*area

[ionic jewel]

he wants volume i imagine

i mistyped

[foggy hound]

Area

[ionic jewel]

surface area

oh

[gentle flame]

Surface area?

[foggy hound]

Yea

[ionic jewel]

there's 6 sides, find the SA od each and add them together

[gentle flame]

What year are you currently in

[undone dock]

Surface area=2(lw)+2(lh)+2(wh)

[glacial hedge]

lmao me being banned from majoring in physics or math....

[ionic jewel]

i don't want to go through it but I'm willing to bet you can just throw identities at it

[wanton smelt]

that's assuming I know what identities are

[junior spindle]

this shit looks confusing af

[strong furnace]

let me guess ? did you break the laws?

[sly mantle]

grad

[wanton smelt]

samurai shampoo

[gentle flame]

Damn

[ionic jewel]

might be able to do (cos^2(x))^2 then use pythagorean identity on that to make it sin and go somewhere from that

[gentle flame]

I am but a humble freshman 🙇‍♂️

[glacial hedge]

nah, i just wasnt allowed to because my dad was an EE and his excuse was "I almost got shipped of to china"

[wanton smelt]

oooh thanks

does that work with sin too

[ionic jewel]

a^4 = (a^2)^2 for all a

[gentle flame]

Express sin^4 + cos^4 as (sin^2 + cos^2)^2 and expand sin^2 (2x) using the double angle formula

And it falls out of that beautifully

[wanton smelt]

sin^2x=(1-cos2x)/2?

[gentle flame]

Too lazy to type it all out

[gentle flame]

Sin(2x) = 2 sin x cos x

That one

[wanton smelt]

but it's not 2x

[glass lichen]

as phrased that isnt true

[sly mantle]

note i've a trig sheet in pins

[wanton smelt]

sin^2(x)

my bad

[glacial hedge]

wait what is the lower bound of a double integral?

[ionic jewel]

no one looks at pins

[glacial hedge]

whats pins?

[sly mantle]

evidently

[gentle flame]

Are you really in middle school

[glacial hedge]

actually i just graduated xD

[gentle flame]

I didn't even know Discord was a thing in middle school

[ionic jewel]

do double integrals have a singular lower bound?

[gentle flame]

Why are you doing multivariable calc

[sly mantle]

pin icon, top of chat

[strong furnace]

it probably wasn't a thing when you were in middle calculus

[glacial hedge]

cuz i wanna

[ionic jewel]

$$\iint_R$$

[ocean seal]

bunny

[ionic jewel]

middle calculus lol

hate when i do that

[gentle flame]

Bro I'm not that old

[ionic jewel]

type what ur thinking

it came out in like 2015 i think

[strong furnace]

my head hurts

[glacial hedge]

coudl you explain what a lower bound of an integral (single integral) is?

[gentle flame]

Yes

8th grade for me

[glass lichen]

it's just where the interval you're integrating over starts...

and lower bound of a definite integral*

[glacial hedge]

OH MY GOD IM A F**ING IDIOT

[ionic jewel]

$\int_a^b f(x) , dx$

[ocean seal]

bunny

[ionic jewel]

its the a ^

[glacial hedge]

I was thinking about like lower bound of an estimate

from series

im such a moron

[gentle flame]

I was in the sme boat, but I didn't get as far as multivariable calculus

Just a piece of friendly advice:

[gentle flame]

You're free to do whatever you want with it

[glacial hedge]

me being enrolled in 6 classes this summer xD

[sleek jewel]

Somebody tell me how to find the tangent to an equation

[gentle flame]

Linear Algebra, Group Theory, Knot Theory

[ionic jewel]

take the derivative at that point to find the slope (at that point)

[gentle flame]

All these are far more friendly to younger people than calculus

[sleek jewel]

how is it done

[gentle flame]

Calculus in 9th grade was a waste, and if I had known this, I would have chosen to do one of these subjects instead

[ionic jewel]

wdym calculus is fantastic

[glacial hedge]

well.. earth science, physics, multi, linear algebra, aops, and trying to squeeze in diffy q this summer

you cant do linear algebra without calculus?

[strong furnace]

set theory

[ionic jewel]

check out the derivative product rule

[gentle flame]

multivariable requires a crap ton of topology to make it rigorous

[sly mantle]

LA qs involving calc tend to be self contained

[glacial hedge]

what does that mean

[sly mantle]

you can skip such qs w/o worrying about skipping on important LA material

[gentle flame]

I got words like "diffeomorphism" and "non-orientable surface" shoved down my throat

[glacial hedge]

?? i think you mean advanced calc or sometihng like that

[gentle flame]

With multivariable calc

[glacial hedge]

whats qs?

[gentle flame]

My course notes for that still scare me

[sly mantle]

questions

[glacial hedge]

dafuq.... was your proffesor on crack xD

[gentle flame]

The way it's usually taught != necessarily the best order for a younger person

[gentle flame]

Nah

[gentle flame]

She's a great prof though

[gentle flame]

I felt the same way at first

It took me a while to realize that this is what muktivariable calc really is

Multivariable calc results depend heavily on the topology of your space

[glacial hedge]

so your proffesor was actually teaching topology...

[gentle flame]

No

She was teaching multivariable calc

[gentle flame]

Example: your space needs to be simply connected (iirc) if you want to have a conservative field

Or was it path connected

[glacial hedge]

me not understanding a single word of that starting to doubt the rigor of my course xDDDDDD

[sly mantle]

simply connected domain and irrotational field imply conservative

[gentle flame]

Thanks. I'm due for a much more rigorous course next to next sem

[gentle flame]

This is precisely what I mean

[gentle flame]

I hope to not be afraid of words like "doffeomorphism" by then

[glacial hedge]

wait what course are you taking next semester?

[gentle flame]

I assume you've come across differential forms too? Those are insane

[gentle flame]

Real Analysis, algebra, second LA course

[glacial hedge]

just 3 courses?

[gentle flame]

We'll do dual spaces and more

[sly mantle]

the insanity depends on context

[gentle flame]

Number Theory is my elective

4 total

Courses at my college tend to be pretty hard core

[sly mantle]

differential forms on R aren't exciting, elsewhere they're interesting

[glacial hedge]

when you say algebra do you mean abstract algebra?

[gentle flame]

Well, tbf, R is very very tame

[gentle flame]

Yes

[winter rock]

Hi,

Is that correct please ? And I'm not sur about the place I put a X in in total result and places where I just put a zero did I did that good?

[gentle flame]

Sylow Theorems and all that jazz

[wary stream]

What kind of physics? General physics or astrophysics, computational physics, etc?

[glacial hedge]

@gentle flame ya see i am restricted to these courses, because the program i am doing doesnt offer any other courses

unless i wanna take college courses

which quite frankly i dont

[gentle flame]

Do LA and learn to self study

The only good thing I got out of doing calc in 9th grade was the ability to self study

[winter rock]

Pls can someone help me in #help-3

[sly mantle]

mostly nuclear, some computational

[gentle flame]

Did you ever do GR

I'm trying my hand at GR

[glacial hedge]

@gentle flame these courses are self study, which is why i like them so much 🙂 because I can do a course in like 5 weeks instead of a full semester

[gentle flame]

Holy shit man

Tensors are hard

Einstein was brilliant

[gentle flame]

If you can do the course in 5 weeks, then it's a waste of your time

[glacial hedge]

wdym

[gentle flame]

I tried to bullsjit my first math course

It was the differential part of multivariable calc

[sly mantle]

insert obligatory christawful symbols meme

[gentle flame]

I got like a C

[glacial hedge]

how?

[gentle flame]

I went hard on the second half and got an A

[glacial hedge]

idk maybe im on crack, i got an a for the first half...

[gentle flame]

Yours doesn't have epsilon delta, does it

[winter rock]

#help-3 plssss high-school level

[gentle flame]

🤣

[winter rock]

Huuuuh nobody can help me ?

[wary stream]

What about math? What math are you focused on? Topology, Combinatorics, Matrices, etc?

[glacial hedge]

it has the epsilon delta definition, but I dont think we were required to use it... the only time i remeber doing epislon delta proofs was in calc bc

[gentle flame]

That's what I mean

We were expected to be familiar with epsilon delta on a level where we could use it on an exam

[glacial hedge]

but i mean i know the epsion delta definition...

[gentle flame]

Every exam had some epsilon delta proofs and shit

It wasn't a computational exam at all

It was like "prove this shit"

Like a real math exam

[glacial hedge]

i mean that doesnt sound too bad...

i would rather prove sometihng that do computation because i sorta failed adition on some tests xDDDDDDDDDDD

[gentle flame]

At the UG level, isn't it a little bit of everything

[gentle flame]

It's not bad, but you missed my point

[ionic jewel]

aaaaa epsilon delta proofs

[sly mantle]

as a grad i focus much more on phys than math, last time i did math seriously it was computational, and did a bit of geometry to deal with late undergrad phys

[junior spindle]

is this channel being "used"

[gentle flame]

I'm saying that multivariable as a whole is not a good way to spend your time because the integration part requires lots of high level stuff to do right

Anything that doesn't use topology is a diluted version of the true thing

Differentiation is much easier than integration (in general haha)

[glacial hedge]

@gentle flame i dont think i know of any course that uses topology in multivariable calculus

unless its a college course?

[gentle flame]

Your real analysis course should have some topology in it

[wary stream]

@gentle flame @glacial hedge If you/we were to continue this classes/course talk, we should take it the discussion channels, to free this help channel

[glacial hedge]

yeah

[gentle flame]

Calc without topology doesn't make much sense when you get into the good stuff in mathematics

Rudin literally defines topological terms on like page 20

[glacial hedge]

@gentle flame it doesnt make sense to learn topology first hto

*tho

[gentle flame]

Understood

[sly mantle]

topo helps with real analysis but many multi courses don't explicitly label relevant topo concepts as topo

[alpine sable]

What’s the answer for 1 and 4???!!!

[wary stream]

,rotate

[wary stream]

We don't give answers here

But for 4, combine like terms

Distribute

[alpine sable]

How do I do it?

[wary stream]

Can you send a picture of the full page? Can't see everything

[glacial hedge]

what is the lower bound of a double integral?

[alpine sable]

Nvm I got 4

What’s 1??

[wary stream]

Can't read it

[alpine sable]

I just need q1

Top left

[ionic jewel]

this doesn't mean anything

[wary stream]

I think this is an exam because you're not sending a clearer picture

[edgy drum]

can someone explain what a is here?

[ionic jewel]

$\int_a^b\int_c^d$

[ocean seal]

bunny

[edgy drum]

is a always the coefficient on the highest order polynomial term?

[alpine sable]

It’s a practice test like I told the guy earlier

[ionic jewel]

a is a standin for any constant number

[wary stream]

A is one of the factors

[edgy drum]

but which one?

they use x-1 meaning that a is 1

[ionic jewel]

it's a generic formula, it could be any

[edgy drum]

is that because the cofactor for x^4 is 1?

[ionic jewel]

yes in the example they give you a =1

no

[edgy drum]

how did they choose a?

[ionic jewel]

it's because you are dividing by (x-1)

[wary stream]

Find a root

[edgy drum]

right, they chose x-a == x-1

[ionic jewel]

they give it to you in the problem

they gave you the polynomial, and they give you what to divide it by

in the problem

otherwise it would be like asking "what's 10/a"

[edgy drum]

they use a root later on

[ionic jewel]

yes

they wanted to factor it out

they chose (x-1) becuase it's a factor, so they know it will divide out cleanly

[glacial hedge]

nvm asked proffesor and he said it was the minimum volume of that solid xD

[ionic jewel]

you could divide by (x- anything)

[edgy drum]

what causes them to divide there? is it just because of the remainder theorem?

[ionic jewel]

don't think that really makes sense but ok

[edgy drum]

if i have some polynomial, what allows me to just start dividing it by some binomial?

[ionic jewel]

hmm

you can divide it by anything you want

[gleaming warren]

is this occupied?

[edgy drum]

just because i know x-1 is a factor, what does dividing by it accomplish?

[ionic jewel]

if you want something nice to come out then you have to use a root like they did

[ionic jewel]

it's kinda like simplifying x^2-a^2 into (x-a)(x+a)

[wary stream]

Yes it is

[ionic jewel]

it's just a simpler form

[gleaming warren]

ok

[ionic jewel]

people like to pull linear terms out

[edgy drum]

i think it's this

iff f(a) = 0, then x-a is a factor

[ionic jewel]

yes

that's true

which is what I was trying to say lol

[edgy drum]

but the next step means that the polynomial is definitely 100% divisible by that factor

the confusing part is why that's useful

i know that 3 is a factor of 12

but I can't say 12/3 is some reduced form of 12

[ionic jewel]

yes you can

12/3=4

which means 4*3 = 12

[edgy drum]

the factor theorem i think is saying more than that

oh i see what you meant

yeah

if i know z/a = b, then I can say a*b = z

[glass lichen]

just a comment, but poor use of iff

[edgy drum]

so i divide by this thing, then multiple by the denominator and i have a simplified form of the original thing

[glass lichen]

x-a is a factor of f(x) iff f(a)=0

[ionic jewel]

yes and you can verify this by multiplying both sides by a

[edgy drum]

it's not for verifying though, right?

[ionic jewel]

no

[edgy drum]

the whole point is the get a reduced version of the original polynomial

[ionic jewel]

not usually

[edgy drum]

z is some complicated polynomial, that I know has a factor a

so if i divide z by a, I get some other value b

I know that b*a = z

[ionic jewel]

yeah so like for an example, lets say you have $x^3+5x^2-x-5$

[ocean seal]

bunny

[ionic jewel]

you could find 5 as a root, then divide (x-5) out with that long division

to be able to find the other two roots easier

[edgy drum]

what's the trick if you cant figure out a root?

just use the remainder theorem?

[ionic jewel]

1. try obvious things
2. calculator
3. remainder theorem i guess

i dont actually know what the remainder theorem is but if it helps thats good

[edgy drum]

yah

[ionic jewel]

,w 2x^3+3x^2+4x+5

[ocean seal]

Results provided by WolframAlpha

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

Requested by 兔子#6562

[ionic jewel]

yeah i think guess and check might not be the move

[alpine sable]

is anybody here good with pi?

[ionic jewel]

sure

[wary stream]

Making pie? No

[alpine sable]

@ionic jewel can you help me with a couple questions?

[ionic jewel]

you can post them and anyone qualified can answer

[ionic jewel]

well which ones do you think?

we can go through the ones you arent sure on

[alpine sable]

idk i dont pay attention in math tbh

[ionic jewel]

[alpine sable]

This is basic logic

well i do

What is a surface and what is area

but pi i have no clue how to do

[ionic jewel]

this has nothing to do with pi

thats my hint

pi is a constant 3.141592...

[alpine sable]

this one does

Reading comprehension

[ionic jewel]

well that one you need the formula for the volume of a cylinder

which is

$V = \pi r^2 h$

[ocean seal]

bunny

[ionic jewel]

where r is the radius and h is the height

also what is that question

[ionic jewel]

yeaaa i was gonna say it wasnt enough info

but with that you can do it

so lets go through it

V is volume, whats the volume?

[alpine sable]

10

[ionic jewel]

volume is the amount of 3d space it takes up

its provided in the question

[visual dew]

which one is correct

[ionic jewel]

first looks right-er

[visual dew]

i mean if you tilt the triangle

i can't decide between these two

[ionic jewel]

im not entirely sure either of them are true though

the one i think you are looking for is

$$\frac{DP}{DF} = \frac{EQ}{EF}$

[alpine sable]

PF/DF

Yeah

[ionic jewel]

wait i tped it wrong

[edgy drum]

that's the remainder theorem

[visual dew]

hey you mean EQ

[edgy drum]

so i guess you really dont even need to know any roots

and you can just get a remainder and its fine

[ocean seal]

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

[visual dew]

second one?

[ionic jewel]

this?

[visual dew]

yes

that worked in question

the first one got me wrong answer

[ionic jewel]

yeah but i dont see how remainders are fine

just that you can get one

[visual dew]

this is wrong ig

[ionic jewel]

why

is it wrong?

[visual dew]

PQ divides the sides to two equal ratios

[visual dew]

the second one is correct but idk why first is wrong

idk how to write that, that's why i asked

[night ice]

Busy channel

?

[alpine sable]

Draw the two triangles

Very busy

[wary stream]

If it's similar triangles, shouldn't it be $$\frac{DF}{PF} = \frac{EF}{QF}$$?

[ocean seal]

dldh06

[visual dew]

jus minus 1

same

[wraith cairn]

both are right

they are literally the same equation.

[visual dew]

help me with this

[wraith cairn]

both of the equations are literally the same.

and they are right.

[visual dew]

i got it lol

I'm so dumb, thanks

[buoyant scaffold]

a man is six times as his son. Twenty years later the man will be twice as old as his son. Find the age of the man when his son was born. man I can't do these algebra word problems

[ionic jewel]

man's age is m

sons age is s

m = 6s

(m+20) = 2(s+20)

[gleaming warren]

occupied or not

[buoyant scaffold]

Occupied

[gleaming warren]

ok

[buoyant scaffold]

Why is 2 multiplying in the right term

[lone cargo]

i think this:
"Twenty years later the man will be twice as old as his son"

[buoyant scaffold]

Hmm

Kinda makes sense but what will I do in the final exams, I can't make equations out of the question

[glass lichen]

practice before the exam

[buoyant scaffold]

Exam in 6 hours

It's 1 am

[glass lichen]

well then you shot yourself in the foot

[lone cargo]

read the thing carefully and try to understand what thing you do ?

[buoyant scaffold]

Yep

[glass lichen]

dont put it off till the last minute next time

[buoyant scaffold]

I'll try my best

[lost violet]

Show that x is a limit point of the interval (a, b) if and only if x in [a, b].

[ionic jewel]

i think some typesetting didn't get copied?

that doesn't seem like it makes sense as is to me

[sly mantle]

it looks fine

@lost violet just unpack definitions

[robust crow]

Y=5X+2

[lost violet]

mm I've already proven it for i mean that x is a limit point of [a,b] iff x is in [a,b] but now im confused because i used that [a,b] is a closet set

[robust crow]

this channel is busy?

[random pelican]

What I have to do to find the area of all those squares?

[lost violet]

yes

[wary stream]

Grid method and add it up

[sly mantle]

i'd prove it from 'scratch', it's not too bad

[hardy saffron]

I’m doing a review and my teacher didn’t teach me this so well

Can someone help?

[lost violet]

@sly mantle If i take the sequence $x_n=a+\frac{a}{n} \in (a,b)$ then a is a limit point of (a,b) because exists a sequence $x_n \subset (a,b)$ such that $x_n$ coverges to $a$ then if x is a limit point of (a,b) then x is in [a,b) and the same for b?

am i righ t?

[ocean seal]

alef0

[sly mantle]

@lost violet as given, (x_n) isn't actually necessarily a subset of (a,b) but the idea is there

[woven pollen]

When you divide exponents with the same base, you subtract - bottom from top.

g^10 / g^7 = g^3

e.g.

[lost violet]

@sly mantle I take $x_n= a+ \frac{b-a}{2n}$ then $x_n$ belongs to $(a,b)$ or im confused?

[sly mantle]

you mean (b-a)/n?

[lost violet]

2n sorry

[ocean seal]

alef0

[sly mantle]

sure

[alpine sable]

Anyone can help me with (5x x 65y )-( -10y +81x )

[short thorn]

Expand and simplify

[alpine sable]

I tried to but then it gave me a positive n Umber

Which is almost impossible with this

[short thorn]

Whats the ans supposed to be

[alpine sable]

Ur the madara uchiha?

[short thorn]

Ye

[alpine sable]

oh

[short thorn]

Ur Zoro Rornoro?

Yh one piece is shit

[dire wren]

based

[alpine sable]

Yes

[alpine sable]

bruh!

Did u even watch

[gray isle]

show work

[short thorn]

Yea i did like 10 eps i wanted to shoot myseld

[alpine sable]

Ye then don’t judge lol

At least complete it

[short thorn]

Still finna judge idc

Nah

[alpine sable]

U watched naruto

[short thorn]

Never

[alpine sable]

Lmfao

That’s like

[short thorn]

So naruto was good

[alpine sable]

Most of op

Overrated

[short thorn]

Naruto > one piece anydayy

[alpine sable]

Nah

They’re both good

[short thorn]

Nah but if we being fr

Boruto > every other anime

[gray isle]

#chill

[alpine sable]

Jjk or demon slayer is better than the naruto og

[dire wren]

...

[alpine sable]

This is simple algebra 1, so it will be quick. When it comes to system of equations, particularly systems of equations by elimination, is there some kind of rule list, or cheat sheet on what you can and cant do when trying to solve the equation? Because I get confused when people are eliminating variables when doing certain actions, and im not sure if what im doing is allowed or not. So how did you guys learn this?

[gray isle]

there isn't really a rule list

most of this concerns maintaining equality

[alpine sable]

as in?

[ionic jewel]

dont do things that change the answer

if you do the same thing to both sides of a given equation you cant go wrong

[gray isle]

as long as you're adding/subtracting/multiplying/dividing each sides by equivalent amounts, you're more or less fine

[alpine sable]

what about something like
3x + 4y = 15
2x + 3y = 11

[gray isle]

area you familiar with the process of elimination?

[ionic jewel]

step 1: learn linear algebra

[alpine sable]

im kinda trying to relearn it all, I mainly cheated alot in high school

[gray isle]

multiply one or both equations by something so that the magnitude of one of the coefficients is the same

[alpine sable]

heard of it, yes a million times, know how to do it, I make 1 or 2 mistakes that mess the whole thing up

[gray isle]

so this is a basic algebra issue

not a concept issue

[alpine sable]

pretty much

mk thx ive got studying to do

[random pelican]

i didnt understand

[alpine sable]

@river rose dont just ask for help without saying what the issue is, lol

[feral apex]

That is still cheating

[glacial hedge]

HEy nOT Fair Im CallIng YouR MomY

[wary stream]

That's a lot. You should look up resources instead of spending hours on each topic. A lot of those are pretty complicated

[gleaming granite]

idk if this counts as cheating

[wary stream]

Like I said, look up some resources if you don't understand

[alpine sable]

I mean, cheating doesnt hurt you if you arent going to college and what you wanna do in life doesnt invole that subject, but im trying to do computer science so i fucked up

[glacial hedge]

um

[gleaming granite]

lmao

[sly mantle]

that was academic dishonesty. whoever sees that, please ping mods for future reference

[glacial hedge]

@alpine sable i would be slightly worried if your a computer science major who doesnt know algebra....

also

computer science is aplied phsyics and math at some level, which requires calc, linear algebra (very important), and diffyq

*physics only if ur a computer engineer

[alpine sable]

@glacial hedge I'm doing computer science, in terms of math it's calculus 1 and 2, for computer engineering it's calculus 1, 2, and 3. And both need linear algebra. Also I'm actually a junior in high school, so I got 2 more years to go and it's not as bad, but still behind.

[glacial hedge]

@alpine sable dude u need calc 3 and differential equations too... also how are you 2 years into hs without knowing alg?

[glass lichen]

dude u dont need to be condescending

so what if someone struggles?

[alpine sable]

lol idrc, I'm Asian and im used to this stuff

[glacial hedge]

hes talking to me but ok xD

[terse sorrel]

Could I please talk to a <@&268886789983436800>

[alpine sable]

yeah ik

@terse sorrel DM modmail

And don't ping roles

[terse sorrel]

are any online rn?

[sly mantle]

@terse sorrel dm me

[terse sorrel]

ok I dmed

[glacial hedge]

anyone know how to start this problem? How do I find the limits of integration for this?

😤 🤦‍♂️ wait nvm im such an idiot

[glacial hedge]

ok wait i actually cant figure it out

anyone know how to do this?

<@&286206848099549185> ?

[strong furnace]

it gives you the instruction as part of the problem have you tried using the polar coordinates?

[glacial hedge]

yeah

r=2, 2r^2+z^2=9

but what do i do with z?

[strong furnace]

you are using cylindrical / polar coordinates for 2d not 3d

in 3d polar coordinates are (r,theta,phi)

[glacial hedge]

wait so do i just ignore the eclipsoid?

[strong furnace]

no

you use the actual polar coordinate syste

[glacial hedge]

what does that mean? and what do I do for z in the second equation

I think the problem was supposed to be a double integral, not a triple integral

[strong furnace]

the problem does not even involve integrals

[glacial hedge]

wait wut?

"find the volume of the region" rings integrals

[strong furnace]

not when the given shape is a sphere

[glacial hedge]

its not a sphere tho...

[strong furnace]

or a cylinder

[glacial hedge]

$2x^2+2y^2+z^2=9$ is an eclipse

[ocean seal]

Elonmosqito96

[strong furnace]

you are not supposed to find the area of this shape

the area in both of them

[glacial hedge]

its asking for the volume in both of them

[strong furnace]

volume*

you want the intersection of their volumes

[alpine sable]

Question

[glacial hedge]

wait

[alpine sable]

if this channel is open?

ok nvm

[glacial hedge]

@strong furnace is this correct $\int _0^{2\pi }\int _0^2z:coord:of:both:of:them:$

[ocean seal]

Elonmosqito96

[glacial hedge]

$\int _0^{2\pi }\int _0^2z:coord:of:both:of:them:$

[ocean seal]

Elonmosqito96

[gleaming granite]

I think it's saying that there is an ellipsoid and a cylinder pierces through it so you want to calculate the volume of that mess

[glacial hedge]

could someone just walk me thorugh getting the limits of integration?

[gleaming granite]

I thought it was a double integral too

but idk

[glacial hedge]

it must be

[gleaming granite]

[strong furnace]

as I said intersection of their volumes or as they say it "volume inside both the ellipsoid as well as cylinder pieces"

[gleaming granite]

yee yee

[glacial hedge]

wait so any advice?

[gleaming granite]

uh

might be wrong but, $\int_{0}^{2\pi} \int_{0}^{2} \text{some cool stuff} : dr : d\theta$

[glacial hedge]

where does the sqrt(2) come from?

[gleaming granite]

r^2 = 2

[glacial hedge]

wait wha?

[gleaming granite]

hol up

r^2 = 4

srry bout that

[ocean seal]

keto11

[glacial hedge]

wait then how do i find the stuff thats gonna be integrated

wait wouldnt it be $\int _0^{2\pi }\int _0^22drd\theta :$

[ocean seal]

Elonmosqito96

[glacial hedge]

because z^2=1?

[gleaming granite]

$2x^2 + 2y^2 + z^2 = 9 \implies z = \sqrt{9-2x^{2} - 2y^{2}}$

[ocean seal]

keto11

[glacial hedge]

oh wait

lol i cant plug in x^2+y^2=4

xd

[gleaming granite]

yeye

[opal tinsel]

@gleaming granite when your done can you help me?

[glacial hedge]

we done

[gleaming granite]

what did you get?

[wary stream]

Is the bot broken? I see pngs instead of text

[gleaming granite]

same

[opal tinsel]

can someone help me with the marginal cost and marginal revenue

[wary stream]

Sounds very econ related

[opal tinsel]

calculus and im clueless

[gleaming granite]

I got 52pi/3