help-0

[lone heart]

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[grave oyster]

Whats a definite and indefinite integeral?

[grave oyster]

And whats the diffrence?

[alpine sable]

Integrals with bounds are calrd definite

Like, integrating from a to b

[grave oyster]

Bounds in the sense?

[alpine sable]

From a point to another point

[grave oyster]

Ohhhh okk. So like boundries. I get it

Alr. And inde1finite?

Google makes it so hard to understand them defination😩

[alpine sable]

Undefinite are empty, you just have that shlong the function and dx

[grave oyster]

Ohhk

[alpine sable]

It's not used to calculate the area under the curve between two points

It simply used to get the integral

[grave oyster]

I get it.

[grave oyster]

I see. Thanks

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[hollow spoke]

could anyone help me out with this? we're doing parametric curves

[hollow spoke]

im j confused as to how my teacher got their answer

[bitter vault]

It is the chain rule. Note that dy/dx = 1/(2t). Now, to find d^2y/dx^2, we differentiate again wrt x. To do this, use the fact that d/dx (dy/dx) = d/dt (dy/dx) * dt/dx.
This is the chain rule

[hollow spoke]

oh the top part is a product rule?

[bitter vault]

No. It's just the chain rule

[hollow spoke]

could u explain it in numbers terms sry ion really understand

[bitter vault]

You have a function of t that you want to differentiate wrt x. Use the chain rule to do so

Let u(t) = dy/dx.
Then d^2y/dx^2 = du/dx = du/dt * dt/dx

[hollow spoke]

sorry maybe its j the format of discord i dont rly get it

thanks for the explanation ima j watch a youtube video on it

[bitter vault]

$\dfrac{d}{dx} \dfrac{dy}{dx} = \dfrac{d}{dt} \dfrac{dy}{dx} \times \dfrac{dt}{dx}$

[ocean seal]

1345631

[hollow spoke]

aight thanks that helps a lot

wait hmm only thing is when i do that

i get

oh wait

nvm i got it thanks for the help

@bitter vault

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[paper coral]

do i just do

8.14x10^15 * 3x10^5

and thats how long it is?

then i convert that number into years cause thats in seconds?

[spark creek]

First you'll convert light years into km

And then divide it by speed of light

[vale wigeon]

no need to do something only to then later undo it

a light year is by defn the distance traveled by light in one year

[paper coral]

ye

[vale wigeon]

so in fact you do not need to do any calculation

[paper coral]

but it says how many years not light years

[vale wigeon]

lightyear/lightspeed = year

it will take light 8.4*10^15 years to cover 8.4*10^15 lightyears

[paper coral]

so 8.14x10^15/3x10^5

[vale wigeon]

no

no

no

no

no

[paper coral]

wait huh

[vale wigeon]

.

[paper coral]

oh

so we basically do nmothing?

[vale wigeon]

that said, 10^15 sounds way off. isn't that 4 orders of magnitude above the radius of the observable universe?

but yes

[vale wigeon]

.

[paper coral]

ah okay

thanks

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[fossil sundial]

.open

[placid zinc]

Thoughts on the problem?

What would it mean if (x - a)(x - b) = 0?

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[lone heart]

Please don't occupy multiple help channels.

[edgy sand]

after grahping here, how do i find the bounds?

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@edgy sand Has your question been resolved?

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@edgy sand Has your question been resolved?

[lone heart]

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[winter moat]

dumb question how would you calculate run with rise and theta? ex: 10cm tall pipe with a 45 degree angle, trying to find the length

[winter moat]

having trouble finding a formula but i may have missed it

[open folio]

Do you know SOH CAH TOA?

[winter moat]

nah think i missed that part in hs

[open folio]

Sin = opp/hyp
Sin(45) = 10/hyp

[winter moat]

wait oh fuck me are one of those the formula

ah thank you

[open folio]

Are you in geometry class?

[winter moat]

no, electrical course rn

[open folio]

https://www.youtube.com/watch?v=PUB0TaZ7bhA

[winter moat]

thank you, will check out

[open folio]

At uni?

[winter moat]

nah some trade course, group of us were covering conduit bending rn and all of us just realized we forgot everything about trig lmfao

thanks again

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[fast cloak]

Is empty relation all reflexive identity symmetric and transitive?

[fast cloak]

.close

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[dusky elk]

1 sec

Mr. Avramenko would like to be more dashing, so he purchases a horse, a carriage, and a top hat for $11 557. The horse cost $350 less than the carriage but was more expensive than the top hat by a factor of eight hundred. How much did each item cost?

[lone heart]

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[ocean prism]

So my problem is this one

[ocean prism]

How can i find on the 2nd one $f^{n-1}(x)$

[ocean seal]

NicoA

[ocean prism]

This is my job finding $f^n(x)$

[ocean seal]

NicoA

[ocean prism]

Its correct if i put just n-1 on the exponents?

[lone heart]

@ocean prism Has your question been resolved?

[little drum]

of course. Since you evaluated f^n (x), you can always put any n in place of "n" and it has to work. but note that, from your argument when finding f^n (x), it assumes that "n" must be ≥ 1, and n must be integer

as long as those are followed, replacing n with (n - 1) does not look like an issue

[ocean prism]

Oh i see

Im trying it rn

Got it somehow

Thanks!

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[woeful ridge]

How would I start this? So I know the radius is 16cm but when making my triangle is that 16 the hypothenuse?

[merry depot]

hypotenuse of what?

[woeful ridge]

Honestly idk how to even start this, the drawing of the picture is too confusing

Is this correct? And I just find x?

Sec

[merry depot]

draw a circle with a chord

[merry depot]

,rotate

[merry depot]

yes

[woeful ridge]

Ty just bad at figuring out how to draw it

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[lone heart]

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[toxic meadow]

may i have some guidance please

[toxic meadow]

how do i get 4 subdivisions if the interval is only [1,3]

[alpine sable]

what's the length of the interval?

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[loud oriole]

can someone explain the bottom step, how does y equal to Ae^kt / 1 + Ae^kt

[prime badge]

first they turn everything upside down
(1-y) / y = 1 / Ae^kt
then they add 1 to everything
(y+1-y) / y = (1 + Ae^kt) / Ae^kt
and turn it again
y = Ae^kt / (1 + Ae^kt)

it's pretty strange

[loud oriole]

why does y=1

[prime badge]

1 + (1-y) / y

(y/y) + (1-y) / y

(y+1-y) / y

[loud oriole]

the problem is that i dont even know where you got 1 + (1-y)...

[prime badge]

it's the second step

[loud oriole]

i just see y/y-1 =Ae^kt

[prime badge]

add 1 to each part

[loud oriole]

but like why and how is that even legal

if we start with y/y-1 = Ae^kt

how do i isolate y

[prime badge]

we know y is not 0

so it's legal to divide 1 by y/(1-y)

we divide 1 by both parts

this turns it upside down

(1-y) / y = 1 / Ae^kt

right?

[loud oriole]

oh i see

ok then

keep going so whats after

[prime badge]

then we can add 1

it will add denominator to the numerator

and then we can rotate it back

they said "add numerator to denominator" i guess that's how

[loud oriole]

ok so we have (1-y)+y / y = 1+Aekt / Aekt, i still dont see how i can isolate y from this

[prime badge]

1-y+y = 1

[loud oriole]

ooh

sheesh thats big brain

i would have never gotten that

math is too hard bruh, my iq too low for this

thx for the help bro

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[prime badge]

yeah i would think so too if i saw that

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[chrome jewel]

I'm trying to calculate the limit as x approaches 0 of a function and am confused about a chain rule outcome.

[chrome jewel]

I'm confused as to how "-1" ends up at the end of the 4th = sign and stays. I thought it became 0?

[buoyant kayak]

that's a different -1

[chrome jewel]

Where does it come from? I feel sort of dumb.

[elder grail]

check the first term

[chrome jewel]

...

Why am I allowed to be in this class. lmao.

Thank you.

[elder grail]

xD happens

[chrome jewel]

.close

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[rich basin]

How do we find a plane that is tangent to a sphere

[cursive badger]

the equation of a plane with normal vector <a,b,c> is a(x-x1)+b(y-y1)+c(z-z1)=0, yes?

[rich basin]

yeah

[cursive badger]

and the vector from the center of a sphere to a given point on its surface is normal to that surface, yes?

so a tangent plane to a point on the surface would be normal to the radius vector

[rich basin]

what I don't know that

[cursive badger]

thus, that radius vector is the <a,b,c>

and the location is the <x1,y1,z1> on the sphere's surface

[rich basin]

yeah

[cursive badger]

if it's centered around 0,0,0, then x1=a, y1=b and z1=c

otherwise you have to do a bit of math (oh no!)

make sense, or -?

[rich basin]

if it is centered wouldn't it be that x1 = a?

[rich basin]

How is that possible?

[cursive badger]

pretty sure that's what I said, I don't think I made a typo

[cursive badger]

I'm sure there's a bunch of math to prove it but

the radius vector, from the center of the sphere to a given point on its surface, is normal to that surface/right angle/normal to the associated tangent plane

[rich basin]

I remember seeing that in

https://www.youtube.com/watch?v=pQa_tWZmlGs&t=537s&ab_channel=3Blue1Brown

[cursive badger]

it's a useful concept

I think it has to do with the trig

[rich basin]

yeah

[cursive badger]

but this is two variable trig, that is two angles

and I'm too tired for that

anyways, other than that, does knowing the equation of a plane at a point & the normality of the radius vector the sphere surface give you everything you need for your problem?

or do you want to discuss something else

[rich basin]

I'm confused on he normality of the radius vector the sphere surface

[cursive badger]

ohhhh I know

it's because of you draw the sphere

I think? maybe.

since we use x=rcosthetasinphi, y=rsinthetasinphi, z=rcosphi, etc...

but idk how to do greek letters on this keyboard

anyways, that is the radius vector for any given theta and phi

the r is fixed, since it's just the surface of the sphere

[rich basin]

costhetasinphi?

[cursive badger]

it's ugh

[x=\rho\cos\theta\sin\phi]
[y=\rho\sin\theta\sin\phi]
[z=\rho\cos\phi]

but I don't have the patience to draw that out

since it's spherical coordinates, we transform x y and z in terms of other variables

[ocean seal]

Scythe

[cursive badger]

this is the full set though

rho is constant, the weird p thing, that's the radius

since we're only dealing with the surface

and so the normal vector has trigonometric proportions at any given angle from the center

[rich basin]

I don't get how x can represent as cos(theta)sin(theta)

[cursive badger]

oh that's just parametricization

https://mathworld.wolfram.com/images/eps-svg/SphericalCoordinates_1201.svg

we don't like cartesian, square coordinates when doing some math

so we transform it

uhhh if that image'll load

wrong format just a sec

[rich basin]

okay i get it

[cursive badger]

https://upload.wikimedia.org/wikipedia/commons/thumb/4/4f/3D_Spherical.svg/240px-3D_Spherical.svg.png

acceptable, but too dark

the idea is you describe your coordinate in terms of r, theta and phi instead of x y and z

[rich basin]

yeah okay

[cursive badger]

same way you can describe a semicircle with y=sqrt(1-x^2) for -1≤x≤1 or y=sint and x=cost for 0≤t≤π

just on a higher dimension

anyways, with the same logic that tanø is ***the slope of the normal line to the unit circle at the point (cosø, sinø), you can prove that the radius vector of a sphere is normal to its surface

it's just... more

since we have more angles and dimensions

[rich basin]

yeah okay

[cursive badger]

those folks over at #multivariable-calculus can probably help explain it more if you need

I would do so myself, but my eyes are literally closing and as such my answers are growing noticeably more incoherent

[rich basin]

yeah okay

[cursive badger]

gl! and good evening, or good morning, etc...

[rich basin]

thanks

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[past sundial]

When doing scale factors, do I need to make both sides like inches if one is feet and one is inches

Cause while doing that the picture seemed weird

[lone heart]

@past sundial Has your question been resolved?

[tacit arch]

do you have an actual equation to solve

[past sundial]

Like for example if x feet is length and y feet is width and n inches is length and m inches is width do I have to do conversion to both x and y to be inches?

[tacit arch]

convert one length at a time

[past sundial]

So like
X*12 N
— = ———
Y. M
If I wanna find x?

[tacit arch]

No idea what you're trying to do

1 feet = 12 inches

2 feet = 24 inches

so if something has length and width in feet, and you want its dimensions in inches, you convert length to inches, then you convert width to inches

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[lone heart]

@orchid radish Has your question been resolved?

[orchid radish]

<@&286206848099549185>

[tacit arch]

show what you've tried

[orchid radish]

i tried doing

30000 - 3x9x9x9x9

over 30000

soo 10316/30000

but apparently its not right

[gray isle]

30000 - 3x9x9x9x9
where's that coming from

[tight locust]

At least a 2?

As in at least one 2?

Or as in at least one digit greater than or equal to 2?

[orchid radish]

its like

the possible number of numbers in each blank

first number (3) has 3 possible ones

0 1 and 3

next ones have everything besides 2

so 9 in each

[gray isle]

you're overcounting

[orchid radish]

then multiply each and thats how many 2's there arent

i am why

[gray isle]

that counts stuff like
30409
which isn't between 1 and 30000

[orchid radish]

wait what

how

i mean idk how to do it

thats how my teacher did it which i think is wrong

how do i do it

[gray isle]

you could separate this into cases

and consider 30000, the only number that can start with 3 separately

[orchid radish]

oh yea

[gray isle]

and also be careful of 00000, i.e. 0
which is also counted with that approach

[orchid radish]

thats true

but like

besides that how do i get the rest

[gray isle]

you can use a similar approach to what you had

just with the proper values

[orchid radish]

uhh

sooo 0 and 1

for the first one

[gray isle]

yes

[orchid radish]

then do i eliminate the 00000 possibility

then im ok?

[gray isle]

subtract 1

because that's only 1 possibility

and then +1 for the 30000

[orchid radish]

so then i just do nothing

-1 and +1

oh so i can just do

2 x 9 x 9 x 9 x 9

and thats the answer over 30000

?

[gray isle]

not quite

you still need to first subtract from 30000 to determine the number with a two

[orchid radish]

oh yeah

thats what i meant

i already did that oos

ps

[orchid radish]

here but instead 2

that should be correct?

over 30000

ya

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[storm ridge]

how do you graph this

[near hollow]

Determine where any asymptotes (vertical, horizontal and oblique are) and any axis intersections

And then draw the lines so that we get all these features

/ making sure it makes sense

[gray isle]

you can consider starting with long division

[storm ridge]

Am I right

[lone heart]

@storm ridge Has your question been resolved?

[gray isle]

if you entered the function into the graphical program properly
then yeh, it should give you the correct graph

[sand salmon]

i know this is more of a physics question but which one has more pressure if their depth is the same (and they are all water). i say all of them have the same pressure cause they have the same depth but my friends are saying its 2 cause it has more than the others so idk whos right

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@storm ridge Has your question been resolved?

[lone heart]

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[cinder sundial]

Is it possible to get the R?

It looks like I can’t

[gray isle]

what's the original question

[cinder sundial]

Triangle ABC has three height

Those lengths are 2,3,4

Ask for the triangle’s area and perimeter

[cinder sundial]

Ramonov could you check this out for me

I found the area will be equals to 1/2(sqrt455)

The ratio I found for a : b : c is 3:4:6

The correct answer is 144(sqrt455)/455

It’s been 3 days, it’s seems like I will never get the correct answer

[gray isle]

what's R

[cinder sundial]

a : b : c= 3R:4R:6R

[vale wigeon]

i have an idea about this but i need to get home and put it on paper before saying it

[cinder sundial]

Here’s how I find the ratio a : b : c= 3R:4R:6R

[gray isle]

I found the area will be equals to 1/2(sqrt455)
note that your work doesn't actually say that is the area

considering the two different formula for Area, you reached the same result of
R^2/2 sqrt(455)

which doesn't give you the numerical value of area without knowing R

[cinder sundial]

but sqrt[s(s-a)(s-b)(s-c) stands for the area of triangle

[gray isle]

yes

[cinder sundial]

i dont have to get the value of R cuz they cancels each other out

[gray isle]

and simplifying that gets you

R^2/2 sqrt(455)

using 1/2 ab sin(C) also simplifies to R^2/2 sqrt(455)

indicating that both formulas for area result in the same expression

R^2/2 sqrt(455) = R^2/2 sqrt(455)
which is true

[cinder sundial]

but those Rs cancel each other out at the end of my equation

ohhh

i got it

i got it

[gray isle]

cancelling those R^2 gets you
1/2 sqrt(455) = 1/2 sqrt(455)
which is true

[cinder sundial]

then i have to get the R

[gray isle]

https://www.quora.com/How-do-I-find-the-area-of-a-triangle-given-three-altitudes
will be useful

[cinder sundial]

put the R's value in, i will get the correct answer

[cinder sundial]

am i right?

[gray isle]

if you are able to determine R then yes, that'll work

[cinder sundial]

damn, do you have any idea about how to get the R

[gray isle]

tedious algebra

https://math.stackexchange.com/questions/55440/find-the-perimeter-of-any-triangle-given-the-three-altitude-lengths

[cinder sundial]

wiat

wait

[cinder sundial]

in the second line, b* sinC will be equal to the height

i think R=24/sqrt455

i dont know

its solved

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[astral pawn]

these are 2 separate equations

[astral pawn]

My question is: Is the value of x and y I got wrong?

Okay nevermind, my value are correct but I noted the question wrongly 😅

.cloe

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[desert pollen]

I am so confused with linearity why is A non-linear and B linear? Is it because in A the dependent variable u is multiplied w/ the derivative???

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.reopen

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✅

[desert pollen]

<@&286206848099549185>

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[vale wigeon]

fuck it gonna post this problem here, since someone chose to post right over it in #competition-math before i got any responses at all:

Is it possible to place a finite number of non-overlapping unit disks on the plane such that each disk touches exactly 3 others?

so far i have only arrived at the obvious conclusion that if it's possible then it's only possible with an even number of disks (because handshake lemma)
and of course you could try arranging the disks in a hexagonal grid but that'd require infinitely many

[vale wigeon]

in the original problem statement the disks were coins but that's only because it's a problem for kids. and the coins are intended to be identical to each other in size

[shut fox]

Can someone please say me what this theta function/notation represents in this formula and how it affects my calculation, my usage of formula?

[vale wigeon]

@shut fox this channel is occupied, please post in an available channel

[shut fox]

Which one is available?

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@vale wigeon Has your question been resolved?

[vale wigeon]

god no of course it fucking hasn't everyone keeps posting the fuck over me

i mean, i got the answer from elsewhere so whatever

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[boreal kernel]

is this able to be factorised further?

[lament glen]

perhaps it means a^nb^n = (ab)^n

[boreal kernel]

so its just x^5 + (yz)^10?

[vale wigeon]

sum of fifth powers can be factored actually

[lament glen]

oh yea there's also that

[boreal kernel]

can you explain how this is factored? im not sure how

[opaque inlet]

That depends entirely on what you’re doing

Have you learnt the sum of fifth powers?

What grade are you in?

[boreal kernel]

uh no and year 9

[opaque inlet]

Yeah that should be the factorised form then

[boreal kernel]

ok! tysm for your help

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[wet spindle]

you can write that as $\frac{1}{12}$ or $\frac{12}{1}$ and it wouldn't matter right?

[wet spindle]

as long as you don't confuse the confetti for the dollars

[ocean seal]

Hyperlix

[vale wigeon]

what do you mean by "that"?

[wet spindle]

a pound of confetti for $12

[vale wigeon]

you can write whatever you want but if you don't make it clear how the numbers you write relate to the problem then there's no point in it

[torn forge]

^

[vale wigeon]

there's no point in writing 1/12 if you don't write that it's actually (1 lb)/(12 usd)

[wet spindle]

alright

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[hot hamlet]

so im practicing sketching curves and im struggling with figuring out the limits when x goes towards an undefined part of the function.
the method for graph drawing that we're using is something like:

1. identify where the function is undefined
2. calculate the derivative to find the critical points
3. take the left and right limit of the function when x goes towards undefined point from 1.
   ...

i keep getting 3 wrong because apparently i suck at one sided limits.
but i was wondering why i cant just check the value of the derivative in two points close to the undefined x, one right and one left, instead?
wouldn't a positive value of the derivative tell me that the function is growing and a negative tell me that its decreasing? im probably missing something here but i have a hard time understanding what.

also, writing this question made me realise that i might have misunderstood something.
when i check lim -> -2+, i get negative infinity. does it go towards negative inf because in the one sided limit calculation im moving to the left on the x-axis? which would mean drawing it out would actually result in a positive slope, growing from negative infinity?
i think i really managed to properly mindfuck myself with this

[hot hamlet]

https://cdn.discordapp.com/attachments/771323241302196234/964502300859187240/image.png

[lone heart]

@hot hamlet Has your question been resolved?

[lone heart]

@hot hamlet Has your question been resolved?

[torn forge]

I mean

As the absolute value of the denominator becomes smaller than 1

the fraction will either grow to a large negative or positive value

Oh wait

wiat

I’m getting mindfucked too

Oh right

It’ll just grow when x -> -2^-

and then

When it’s 2.0000….1

it’ll start at negative inf

[hot hamlet]

my issue is that im not getting the correct answer (cause i probably did it wrong) from lim x-> -2+
when x > -2 but moving towards -2, i get that the numerator is negative (which is obvious), but the denominator is positive since x > -2 🤔 => negative result
but when i graph it in desmos its growing on the rhs of -2

idk im so fkin confused

[torn forge]

when -2>x>-1 it’ll start growing

[torn forge]

yeah

[hot hamlet]

i guess its the one sided limit that's making me confused. because in my mind a negative limit would mean that its decreasing towards infinity, which is obviously not the case looking at the derivative or the actual graph

[torn forge]

yh

i mean

I’m having trouble figuring out the problem you need help with 😅

[hot hamlet]

ok, so the problem im trying to solve is
"sketch the curve of
f(x) = 1/9*x^3/(x+2) " (idk how to make it look all fancy)
so i

1. identified undefined part of the function (x = -2)
2. calculated the derivative in order to find critical points (f'(x) = 0 which is x=0 or x = -3)
3. one sided limit from left and right to see what happens in the curve around x=-2
   with all this information i should be able to sketch the graph (might have to check lim x -> +- inf too, but i didnt get that far yet)
   the issue is that the one sided limit x-> -2+ is giving me info that would make me draw the graph incorrectly. so im trying to figure out what im doing wrong 🙂

[torn forge]

Okay

[hot hamlet]

oh shit, i think i might have figured it out. im an idiot

[torn forge]

oh okay

[placid zinc]

Can do polynomial division to get a better form

This is basically a quadratic with an asymptote forced in

[torn forge]

yh

[hot hamlet]

-inf in the one sided limit from the right means that it is growing from -inf... right?

[torn forge]

no….

You should check the left limit too

[hot hamlet]

i did

and its positive

properly mindfucked

thanks a lot

[torn forge]

wiat

💀

[hot hamlet]

hahaw hat=

[torn forge]

I’m getting confused

[hot hamlet]

about?

[torn forge]

wait wiat

Well you need both left limit and it’s derivative

at that point

[placid zinc]

lim [x → 2-] = infinity

[torn forge]

mhm

[placid zinc]

Judging by that graph above

[hot hamlet]

yes

[torn forge]

If right limit is +inf

then most likely left limit is -inf

and is growing

[hot hamlet]

right limit is -inf

[torn forge]

and if right is +inf

[placid zinc]

,w graph 1/x^2

[ocean seal]

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[torn forge]

or dat :(

[hot hamlet]

yeah, but you can tell from checking both left and right limit, so thats not an issue?

or im not following

[torn forge]

Do you mean like it’s approaches to -inf?

[placid zinc]

Can you tell what the limits are, from checking the limits? Yes.

[hot hamlet]

i really mindfucked myself with this stupid thing and now it seems like i managed to mindfuck you too @torn forge . im sorry

[torn forge]

I’m crying, cause I can’t help you 😭

[hot hamlet]

haha you already helped me 🙂 thanks a lot

[torn forge]

somehow

[placid zinc]

Let's walk through it. Have you been able to algebraically prove the left/right limits at x = -2?

[hot hamlet]

um, no... im too bad for proofs 😦

[placid zinc]

Sorry, I didn't mean "prove" so much as "check"

Oh wait, yeah you've got them in your picture

[torn forge]

yeah…

[hot hamlet]

idk if "-/+" is a proper way of expressing that shit but in my book they say stuff like "we can apply l'hopital on a limit that is "0/0"" so im just rolling with it 😦

[torn forge]

I mean, it’s a good way to express it.

[hot hamlet]

its just first years engineering math so hopefully they wont kick me out over it on the exam

thanks for the help guys, youre amazing

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[torn forge]

sheesh okay

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[edgy cape]

When I integrate to find R how do I know which way round the t limits are

when y = 0 t=π/3 and 5π/3

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@edgy cape Has your question been resolved?

[edgy cape]

<@&286206848099549185>

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@edgy cape Has your question been resolved?

[quiet wagon]

Do you mean, you dont know which one is left and which one is right?

[edgy cape]

ye

like which is upper limit and which is bottom

like because it isn’t an x value it doesn’t have to mean bigger is upper

[quiet wagon]

x=t-2sin t

Try putting both t's in that formula

And then you have 2 x's

[edgy cape]

But then I have to convert the parametric equations to cartesian to integrate and thats long

otherwise i cant use the x limits

is there any other way of knowing specifically for t

unless whatever t value gives the bigger x value is can also be used as the upper limit for t?

I have to show this,

but how do I 'show' that 5π /3 is the upper limit

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[tacit arch]

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[balmy star]

help

[lone heart]

Please don't occupy multiple help channels.

[near hollow]

$10=x+y \Rightarrow y=10-x$

[ocean seal]

Max..

[near hollow]

Go with these questions is creating a function that satisfies the first question but is only of one variable. Because if it's of one variable we can differentiate and locate min and maximums

$f(x) = 2x^2+xy, y=10-x$

[ocean seal]

Max..

[near hollow]

Method from here is make f(x) be composed only of x. Then locate the minimum and maximums of f(x) using differentiation

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[solid bone]

hi there, i am stuck on trying to prove a statement:

[solid bone]

$\forall a \in \mathbb{Z}^{+} , 4 \nmid a^{2}+2$

[ocean seal]

django_24

[solid bone]

i tried to a proof by contradtion but it feels kind of abstract

is there a rigorous way to show it?

in my proof by contraction i basically said: a = sqrt(4k-2) for some integer k this a is not an integer

is that rigorous enough?

[noble sinew]

If you don’t give an argument for why it isn’t an integer then no

Quickest way would be to look at it mod 4

[last herald]

This

[solid bone]

yh i considered doing cases as well

but not sure how that would work tbh

[last herald]

You'll find there are only limited values a perfect square can have mod 4(or any integer greater than 1).

[solid bone]

do i just argue in every case that a is not an integer by contradiction?

[noble sinew]

look at it mod 4 like I said

[solid bone]

yh a mod 4 is either 0 or 1 or 2 or 3

[noble sinew]

and what is a^2 mod 4?

[solid bone]

same thing?

[last herald]

Nope

Check them all

[noble sinew]

how do you get a^2 mod 4 = 3 for example?

[last herald]

What is a^2 mod 4 for each integer 0-3

[solid bone]

sheesh i gotta take a minute to think about this

[noble sinew]

(its just squaring these)

[solid bone]

isn't the answer for mod bound between 0 and 3 inclusive for all integers

and a^2 is an integer

[noble sinew]

do them 1 at a time

what is 0^2 mod 4?

what is ...

[solid bone]

i see

lemme try that

thanks

[quasi scarab]

its the same concept as your last question, only not with 3, but 4

[solid bone]

yeah but that was an implication so it clicked and made sense in that case

i am seeing that the mod alternates between 0 and 1?

[noble sinew]

so is it possible for 4 to divide right hand side?

[solid bone]

no. would only be possible if we add 3 or 4

not 2

[last herald]

Bingo bango

[solid bone]

https://tenor.com/view/that70s-show-eric-foreman-light-bulb-idea-gif-4680281

light bulb moment lol

the only thing i am concerned about is i can convince myself of this but how do i express the concept that a^2 mod 4 is either 0 or 1?

+2 part can be justified with an explanation

i think i need to think about this a bit more

thanks a lot tho guys. appreciate your help :)

[quasi scarab]

list the cases, thats it

[solid bone]

ah i see

got it

tysm

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[royal grail]

I am currently trying to create a question involving De Moivre's Theorem and Volume of Revolution and one part of the question is to find the volume of solid formed when a curve with parametric equations x=cos³t and y=sin⁸t are rotated about the y-axis (the boundaries of the definite integral are not decided yet, but say we call them a and b). And this is what the initial steps should look like:

[royal grail]

And when I tried to decide the boundaries, I decided to look up on desmos on how the curve should look like after converting the parametric eqn to Cartesian eqn.
And this is what it looks like:

[royal grail]

this is the conversion btw

[royal grail]

And now I'm not sure what would happen if I try to integrate to find volume formed when rotated about the y-axis because there's 2 areas (labelled in blue and black) under the curve between y=0 and y=1; tbh I don't even know what happens if I simply try to integrate x = f(y) for this curve

very sorry for the long message

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[royal grail]

<@&286206848099549185>

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@royal grail Has your question been resolved?

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@royal grail Has your question been resolved?

[steep rover]

im not very sure since im still in calc 1 but i think honestly it will look like a disk with a tiny line/piece missing out of it where the line seperates the areas, or since its the integral it might just look like a whole disk

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[royal grail]

ye that's what I think but idk which one too

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[severe rover]

7+3m=17+m

[oblique spire]

What to do with it

[severe rover]

answer pls

just checking if i know it

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[lime bronze]

Can someone teach me how to find the degree measure of a arc when the given is the:
arc length=6.28cm
circumference=36.68cm

[oblique spire]

Like the angle of the arc?

Given the arc length and circumference

?

[lime bronze]

That works as well since angle and it intercepted arc is equal right?

[remote kettle]

i think ik

[remote kettle]

arc length/circumference * 360 = degree of the arc

not sure if its correct tho

[lime bronze]

Oh

[remote kettle]

try it

[lime bronze]

Alright

[oblique spire]

I guess u are indeed correct

[remote kettle]

thonxe

[lime bronze]

So itd be 61° right?

[remote kettle]

i dint calculate

😅

[lime bronze]

Aight thanks guys

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[arctic agate]

How to chose n0 for this series?

[arctic agate]

i need to use series because then i can change level of precision

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@arctic agate Has your question been resolved?

[noble sinew]

I don't understand what that is supposed to mean

why not use a more known series, pick whatever from here for example https://math.stackexchange.com/questions/451604/can-the-factorial-function-be-written-as-a-sum

or use the gamma function integral

[arctic agate]

thats is what i am talking about

real-valued factorial aproximation

[noble sinew]

yes? I gave you several?

[arctic agate]

on site you linked there is solution for only natural numbers

[noble sinew]

and what is the problem with this?

[oblique spire]

He wants to change the level of precision

Ig

That's why

[noble sinew]

yes you can do that?

[oblique spire]

He is using a series

[noble sinew]

its an int from 0 to inf?

change bound to 100000 or whatever

[arctic agate]

how would i compute integral?

also i provided you with series i wanna use and just asked what n0 i should use

i didnt ask for "better" solution

[noble sinew]

I said I didn't understand what it even meant with x->n_0

[arctic agate]

me too thats why i am asking

[oblique spire]

Well I am pretty sure the numerator should the kth order derivative of the factorial function

As per Taylor series

[noble sinew]

hence I gave you an alternative?

[arctic agate]

and that alternative involves me rewriting entirity of wolfram alpha

which i belive i am not capable of

[noble sinew]

what?

[oblique spire]

What does that mean

[arctic agate]

dude how to compute integrals using program?

[oblique spire]

Oh

[noble sinew]

numerically?

[arctic agate]

you still need to antiderive

[oblique spire]

The gamma function is inside the series anyways

So

U will need to compute it

Eitherway

[noble sinew]

what? you can write x! as an integral

[oblique spire]

Are you coding something?

[arctic agate]

not really because n0 CAN be hole number if its positive unless x->n0 says otherwise

[arctic agate]

yes

[noble sinew]

so look up numerical integration?

and use gamma function def

[oblique spire]

Ur question rather is how to code integrals in programming

Ig

[arctic agate]

uhh so ig i just code series i found and try difrent n0 and thats it...

[noble sinew]

what?

[oblique spire]

Generally in computers u will use gradient descent

[noble sinew]

what is your problem with using gamma function def

[oblique spire]

Not trying randomly

[oblique spire]

Same question

Lmfao

[arctic agate]

way worse computationally

if you want any sort of accuracy you need to calculate area of milions of trapezes

[noble sinew]

did you even look at what you posted?

[arctic agate]

yes

[noble sinew]

it invovles gamma function itself

like????

[arctic agate]

but if n0 can be hole number its fine..,

[noble sinew]

your series is a series and an integral

you say you wont use an integral bcs less precision

[oblique spire]

Ya then gamma is just factorial

[arctic agate]

????????

[noble sinew]

well yours is worse

[oblique spire]

Are u sure

I have been programming for quite a while

Ig series are more computationally

Expensive

Than just one integral

[noble sinew]

his is both a series and an integral

he needs kth derivative of gamma function

GAMMA FUNCTION IS BY DEF AN INTEGRAL

LIKE I HAVE SAID

[oblique spire]

If the input of gamma function is whole number

[arctic agate]

did you even look at thing i posted?

[oblique spire]

Or n0 is whole number

We can evaluate

Gamma

[noble sinew]

yes?

[oblique spire]

Without the integral

[arctic agate]

^

[noble sinew]

then use if clause?

and use even less expensive

such as one of the ones I posted

[oblique spire]

Why would he use if clause tho

He is trying to know if n0 is whole number

That's all

Because if it is

It makes computations easier

[arctic agate]

if n0 can't be hole number

this series is useless

[oblique spire]

Ya

[oblique spire]

This is all i can think of for now
Notice that the numerator is the nth order derivative of x! U can use the derivative of gamma function to compute it then u have to use trial and error to find what values of n_0 satisfy it ig

[arctic agate]

hmmm

wait derivative of gamma function

is just definition of gamma function without integral

so mayby i could compute first 8 derivatives of gamma functions

and just integrate it into my program

and use taylor series to put it all together

[lone heart]

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[smoky tangle]

hey guys not rlly a doubt but anytime I calculate the volume and total surface areas of:
Cylinders
Cones
Spheres
Hemispheres
Composite figures

I'm always off from the answer in the book, even If i take the correct pi value and if my calculations are correct.
Whenever I'm in class I get near the correct answer or sometimes even the correct answer, but when I study at home I get a huge difference between mine and the book answer.

Can someone suggest how to calculate the volume and TSA of the figures I mentioned above AND get the correct answer? (pi values are 3.14 and 22/7)

[smoky tangle]

Also, When do i use 3.14 and 22/7?

pls ping when answering

[lone heart]

@smoky tangle Has your question been resolved?

[smoky tangle]

<@&286206848099549185>

[granite imp]

pi is not 22/7

[lone heart]

@smoky tangle Has your question been resolved?

[smoky tangle]

well\

Ill clise theticket i got some ans

.close

[lone heart]

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[green hazel]

Guys

[green hazel]

When a question asks, "When does the function take on it's average value"

Do I plug in the average value answer into the original to solve for x?

What are the steps I take

Yeah from A --> B

[runic iris]

calculate average value then solve for average value

[green hazel]

Just in general

[runic iris]

I think

[green hazel]

No It would ask that after you solved the average value

The question would be

[torn forge]

yes ^^

[green hazel]

"When does a function "take on" it's average value?

[ocean seal]

WhipStreak23

[torn forge]

+/- sqrt 3 yes

😾

[green hazel]

Sorry

I'm talking about Average value calculus formula

[torn forge]

OH

💀

[green hazel]

1/ b-a ( integral f(x)

from a -> b

[runic iris]

ye that gives you the average

[green hazel]

Sometimes after they ask u

For the average value

Then they ask

When does this function take on its average value

I need to know how to do that

[runic iris]

then you find the x for which the value of f(x) is the average

[green hazel]

How do u do that

Plug in average value into original?

[runic iris]

set f(X)=average

then solve for x

[green hazel]

thank you thank you

Yes that's what I was looking for

I forgot

[torn forge]

💀

[green hazel]

this

[torn forge]

whipstreak feels left alone

[green hazel]

Is the answer

Bro I got my Calc BC exam soon

Im taking AP calc BC

[torn forge]

congrats

good

now do some more math

[green hazel]

thank you

I am scared

[torn forge]

💪😮‍💨👍

[green hazel]

But I think I can pull a 5

You only need like 60% of the questions correct

But it's pretty tough

It's not like straight testing you on calc it's like concepts you need to know in and out

[torn forge]

just do practice exams, gotta memorize the methods to solve the problems yk

oh

theory

i mean

analysis is my dream yk

game theory smells awful

Anyways we shouldn’t be talking here

💀

[green hazel]

Guys

Is FTOC tested a lot when they give both bounds in terms of a variable

Or just the B bound

Because usually I see B as a variable but A is a constant

That's all I've been tested on

Would they ever make a and b variables?

In FTOC questions

[lone heart]

@green hazel Has your question been resolved?

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[lone heart]

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[random blaze]

does anyone understand this?

[last herald]

What have you tried to solve this? Or if you don't know where to start, what geometry rules do you know that could apply here?

[random blaze]

i just need to start i cant find any paralel lines therefore dont know how to get a second angle

[last herald]

Okay, what about angles and chord lengths in circles? Do you know any rules about that?

[random blaze]

not really

[last herald]

Not sure how you solve this without them so I'll just tell you:

• If AB is a chord and C and D are independent points on the circle, ACB = ADB
• If AB is a chord and C is a point on the circle and O is the origin of the circle, AOB = 2*ACB
• If AB is a diameter of the circle and C is a point on the circle, ACB is a right angle

[random blaze]

there is no ab?

[last herald]

These are just general rules, not specific to this problem

[random blaze]

oh alr

[last herald]

Can you see how to apply them to the problem?

[random blaze]

no

wait yes

cd=ab cad =acb

[last herald]

Neither of those are correct, which rule were you trying to apply?

[random blaze]

2 i beleive

[last herald]

Rule to is probably the least useful here but it's saying that if you draw an angle from a chord to the perimeter, it'll be half as big as the angle drawn to the origin.

So in our problem, CAD = 28'. That means COD = 56'.

Does that make sense?

[random blaze]

yes

[last herald]

Rule 1 is saying that drawing an angle from a chord to any point on the perimeter will result in the same angle, can you see where you could use that rule?

[random blaze]

and then from that cod angle i can find the 3 around it right?

[last herald]

Which three angles are you referring to?

[random blaze]

the oposing angle and the ones adding to 180

180 degrees

[last herald]

Can you name the angles?

I still can't see which ones you mean.

[random blaze]

aob aod aoc

this is where im at atm

[last herald]

O is not the intersection of AC and BD, it's the center of the circle.

Trying going back to the start and seeing how we can apply rule 1. That's the simplest way to solve the problem.

[random blaze]

ok

what do you mean by cord

[last herald]

A chord is a line connecting 2 points on a circle.

[random blaze]

so like an angle

[last herald]

What do you mean?

[random blaze]

so if theres a cord theres an angle

[last herald]

Can you give me an example?

[random blaze]

ab is a cord

[last herald]

If you were to connect them, yes.

What is the angle?

[random blaze]

oh i think its just a langueage thing

chord is an angle

[last herald]

Chord does not mean angle.

[random blaze]

oh

[last herald]

There are related angles but a chord is a line.

[random blaze]

oh right i read it wrong sry

i understand now

so ad is a chord

[last herald]

Yes

[random blaze]

great

il try go through it with that and say if i get stuck

[last herald]

You can talk me through how you solve it, then I may be able to help better.

[random blaze]

all done tysm

.close

[lone heart]

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[fossil mason]

Hi

[fossil mason]

Could someone help with this

[fossil mason]

,rotate

[lone heart]

@fossil mason Has your question been resolved?

[lone heart]

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[alpine sable]

Hi, I was wondering what the correct approach would be to this question and the answer it

f(x)=x^5 + x^4 - 13x^2 + 19 divided by (x-k)

s(x)=k^5 - 17

what is k

[gray isle]

what's s(x)
what's the question asking for specifically

can you post the original wording

[alpine sable]

alright one sec

if its not a complete question then I'm sorry for wasting your time

[gray isle]

its not complete

there's nothing saying what the
s function
represents

[alpine sable]

ohh okay, Ill ask the person who sent it for the extra bit of the question, no wonder I couldn't do it then 😅

[alpine coral]

can

someone

help

me

?

[gray isle]

#❓how-to-get-help

[alpine sable]

.close.

wait that didn't work

[royal grail]

remove the . at the end

so .close

[alpine sable]

.close

[lone heart]

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[loud oriole]

can someone explain this summation

why are we doing c + c + c...
if the top and bottom index have nothing to do with it

[gray isle]

the summand isn't dependent on the index k

so every term being added will be c

c = c
when k=1, 2, 3... etc
(for all k)

[loud oriole]

ok so whether it is n sigma k=1 or n sigma k=2 it will give the same answer

[gray isle]

poor wording

wdym by "answer"

[loud oriole]

if we look at my og pic, would the answer change if the value of k was changed

[gray isle]

if you changed your starting value, the sum will change

if you start from k=2,
instead of k=1, you'll have 1 less term

resulting in (n-1)*c

but the individual terms being added will be the same