help-0

[odd obsidian]

round

apologies

[raw shard]

wouldn’t it be ceiling?

[stark matrix]

would it be cieling for rounding up

yeah

lmao

[odd obsidian]

ceiling rounds up

[stark matrix]

ah ok

[odd obsidian]

if you just want to round to the nearest whole integer you use round

[raw shard]

or is round just ceiling if the fractional part of the number is above 0.5

[odd obsidian]

for example:

floor(1.8) = 1

round(1.8) = 2, round(1.2) = 1

ceiling(1.2) = 2

[stark matrix]

[odd obsidian]

yeah

[stark matrix]

ty

[pulsar aspen]

@silver tangle Have your question been answered? If so, please close this channel.

[sinful monolith]

need help

[vocal hawk]

where is the function? @sinful monolith

[wary stream]

One, don't asked in an occupied channel

[vocal hawk]

this channel has been occupied since yesterday btw

[wary stream]

And two, you have to determine the parent function given the end behavior

[wary stream]

So what? Rules are, don't asked in an occupied channel

[elder sedge]

again, your chances of getting an answer in #advanced-analysis is much higher for this caliber

[ocean seal]

shoury

[noble sinew]

#❓how-to-get-help (find a free channel)

[lone heart]

@silver tangle Has your question been resolved?

[past glade]

someone help me with this sums Dont mind the Line

;)

[pallid trout]

You have ot open your own channel, can't jump into someone elses

[past glade]

t

nani

[cold thorn]

@toxic gate what was the exercise?

[thorn kindle]

Round(x) = Int(x+0.5)

[stuck jolt]

Do you still need help

[grizzled sundial]

Yes plz

I just found theta bu doing tan^-1 (cos theta / sin theta) and got theta as my angle

I don’t know why you have to convert sin to cos and cos to sin

[elder sedge]

your question disappeared at least post it again

[raw shard]

the second i see the name fourier i know it’s too advanced to get an answer here

you’re more likely to get an answer in the advanced channels

yes

fourier stuff is really advanced i think

stuff with his name on it

[tranquil blade]

The function f(x) = kx⁴ + 8x² has three turning points, an absolute (global) maximum value of 8 and a zero at x = 2 .
Determine the value of k as well as the other zero(s) of f. Then sketch the graph of y = f(x).

[rotund fox]

given that y = 0 at x = 2, you can find out the k value, and then you plug in the k value to the original equation to find all the values of x which satisfy y = 0.

[placid zinc]

This channel is not your channel

[thorn kindle]

[thorn kindle]

16B+23Y+26G+32R=1000
2B = Y
G/2 = R
R = Y

4 equations

4 variables.

Now this can be easily solved.

[magic geyser]

gaussian elimination

[thorn kindle]

https://tenor.com/view/thealexera-soyjak-surprised-amazed-wojak-gif-19919803

[magic geyser]

yes

[alpine sable]

what's your question

oh

the question wants to see if it's convergent

so create Fourier integrals for each of the intervals of sigma and see if the resulting answer is a defined number

no this is lower div stuff

[pure thistle]

For infinite series, why is this wrong?

[wary stream]

Why is it divided by 6?

[pure thistle]

ah

see

that is because I am dumb

and copied my previous anser

lmfao

[raw shard]

understandable

[sonic ridge]

for future reference, please dont ask for help in an occupied channel -> #❓how-to-get-help

[wary stream]

This channel has been occupied for ages

[raw shard]

like 7 hours lol

[wary stream]

Needs to be reset

[wary stream]

I think since like yesterday

[pure thistle]

I didn't even see the open help channels, I just saw that this one was unused for more than an hour from what I can see

[wary stream]

Unused for more than an hour doesn't matter

It's under occupied

[raw shard]

didn’t you just contradict yourself

open for ages, still occupied

lol

[wary stream]

Fixed

[alpine sable]

can you send Theorem 3.8 @silver tangle

[alpine sable]

For this problem, $\tilde{\sigma}$ represents the result of integrating $\sigma$, the Fourier series of the step function, at certain intervals; i.e., if you integrate $\sigma$ in the interval $(2m-1)\pi < x < 2m\pi$, then the result should be 0, on the interval $2m\pi < x < (2m+1)\pi$, the result should be 1, etc. you want to integrate $\sigma$ on all three intervals, by literally doing \
[\int_{\text{lower bound}}^{\text{upper bound}} \sigma dx ]
You'd use $b_k$ when integrating the parts with $\sin(x)$ and $a_0$ when integrating the parts without $\cos(x)$ or $\sin(x)$. The goal of the problem is to get the values for $\tilde{\sigma}$ shown in the problem. Since the values for $\tilde{\sigma}$ hold true for all $m$, you can set $m$ to any number (e.g. 1), and use those intervals in your integrals. When integrating, make sure to consider Theorem 3.8, which states rules when integrating if the function on the interval is continuous or if there's a jump discontinuity somewhere on the interval.

[ocean seal]

bertaunth

[alpine sable]

Here's how you'd start your integration on the first interval:

**sorry for the late response—had to let the problem simmer in my head for a bit

[alpine sable]

I should clarify: it holds true for all integer values of m

[ebon wasp]

if I have a price: 500
and I want to get the price after a 5% discount, I can do 500 * 0.95 to get the discounted price
but what should I multiply the discounted price by to get back to the original value?

[alpine sable]

By 1.05

but as a reminder, next time use an unoccupied channel (one without a name associated with it)

as in from this section

[ebon wasp]

oh, sorry, and thanks!

[strange raven]

Hi

Anyone familiar with proofs.

?

Proofs of contrapositive?

[tough hatch]

read #❓how-to-get-help

@silver tangle .close if you have no immediate questions

[tough hatch]

is the bot malfunctioning on this channel?

[fading zephyr]

.close

[lone heart]

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[mint bronze]

using the standard defibitions of convergence show that the sequence 1/n converges to 0.

my apologies if this is really trivial to do.
im just struggling with it conceptually and maybe going through an example with someone would help me

[mint bronze]

i think ive got a solution.
but im not sure if its a good solution

[chrome salmon]

You have to write that N>= 1/epsilon
Then for n > N , (1/n) -> 0

[mint bronze]

so aside from that does it make sense?

[chrome salmon]

Yeah it does

[mint bronze]

awesome

.close

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[mint bronze]

@chrome salmon thanks

[lone heart]

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[alpine sable]

The sum of the areas of two circle, which touch each other externally, is 153 * pi. If the sum of their
radii is 15, then the ratio of the larger to the smaller radius is
(a) 4: 1 (b) 2: 1 (c) 3: 1 (d) None of these

[alpine sable]

please help

[chrome salmon]

What do you think this will look like

[alpine sable]

can you help me

[chrome salmon]

Yes I'm asking how the figure will be

[alpine sable]

there is no need to actually know the figure tho

it is from a question bank and they gave no figure

i am practicing stuff

[chrome salmon]

Yes but can you imagine it

You won't get it until you know how it looks

[alpine sable]

well i actually did it before without a diagram

but i forgot it right now

[chrome salmon]

Ok anyway the sum of radius of both circle is 15

[alpine sable]

yeah

[chrome salmon]

If r is radius of first circle then other circle is 15-r

[alpine sable]

yes

[chrome salmon]

Then the area will be pi(r²)+ pi(15-r)²

[alpine sable]

so should i substitute it in the equation R^2+r^2=153

[chrome salmon]

Nope

Cuz the circle is not inside circle

That's why I'm telling you to make a figure

[alpine sable]

oops sorry it is +

[chrome salmon]

Yes

[alpine sable]

yeah ig i will get an equation to solve

.close

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[royal meadow]

is the covariance just 0?

[lone heart]

@royal meadow Has your question been resolved?

[crisp grove]

yes

[royal meadow]

sick

they don't look independent, is all

oh wait

i made an amateur mistake

independent -> cov = 0, but not the reverse

[crisp grove]

yeah

[royal meadow]

.close

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[jaunty onyx]

hi! i need help with proving this statement in mathematical statistics

if Y is a random continuous variable and E[Y^k] exists, then E[Y^n] also exists for all natural number n < k.

[vale wigeon]

since Y is continuous, it admits a PDF. express E[Y^k] as an integral involving the PDF. consider the integral separately on [-1,1] and outside [-1,1]

[frigid coyote]

can i get help pls???

[wary stream]

Read #❓how-to-get-help

[jaunty onyx]

sorry i did not understand "consider the integral separately on [-1,1] and outside [-1,1]" really sorry, does that mean i'll have to look at the pdf with those bounds? sorry

[vale wigeon]

to prove x^n p(x) is integrable over the real line, you will want to prove that it is bounded above (in absolute value) by x^k p(x)

but this only works for |x| >= 1

there are some wrinkles in this argument that i am leaving to you

[jaunty onyx]

alright alright thank you so much @vale wigeon !!

.close

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[spring shard]

Hello

[spring shard]

i just begginer with algebra programming

[lone heart]

@spring shard Has your question been resolved?

[spring shard]

Huh

[glass lichen]

<@&268886789983436800>

[spring shard]

<@&268886789983436800>

Help

Please

<@&268886789983436800>

<@&268886789983436800>

[fading zephyr]

sorry, done

[spring shard]

thx

[spring shard]

my laptop was about to explode but thx

[topaz scaffold]

What's the question, @spring shard

[lone heart]

@spring shard Has your question been resolved?

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[chilly garden]

hi

[chilly garden]

i need help generalizing the following

(1), (1+x), (2+2x+x^2), (6+6x+3x^2+x^3)

there is a pattern here that i am not seeing

n = 0, 1, 2, 3....

[royal meadow]

it's $\sum_{i=0}^n \frac{n!}{i!}x^{i}$

it's just the sum of all the derivatives of x^n, right?

that's what you were doing?

[chilly garden]

that looks wrong somehow. when i = 0, and n = 3, you get 6x^3

[royal meadow]

no

wait

[ocean seal]

Kaisheng21

[royal meadow]

ok how about this

but yeah you're just summing the derivatives right

[chilly garden]

yep

looks right

yeah

summing derivatives

its an induction problem

[royal meadow]

hmm

ah i think i see

[chilly garden]

prove integration((x^n)(e^-x)) = n!

limits infinity and 0

[royal meadow]

hah

[chilly garden]

i proved for n = 0, so i am assuming true for n = k, i will try n = k+1 now

wait

once you show the sigma notation

how do you show that it equals n!

@royal meadow i was able to prove that the sigma function somehow equals -n!/k!

[lone heart]

@chilly garden Has your question been resolved?

[lone heart]

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[sterile vale]

Hello, we are given these tan values and we are asked to find the precise angle of phi in the interval given

[sterile vale]

So we have solved the equations, we have found that tan(phi)=1

and now we are trying to find an appropriate interval to find the phi value

For example we have done this

But then, to actually find the tan value, we set this condition

Why? where does it come from and what does it imply?

[alpine sable]

Your tan(x) = 1/3

Between 0 and 1

If x is between -pi/2 and pi/2, that means quadrant I and IV

In quadrant IV tan is negative

[sterile vale]

Ah, of course, thanks a bunch

[alpine sable]

No problem

[sterile vale]

But... Why wouldn't we just set it to 1/3 in the first place?

0<tan<1/3

Why do we gradually "shrink" the interval and how do we know when the interval is too small?

[alpine sable]

Im guessing because it says in question part a) to check on that interval. I dont know french though

[sterile vale]

It says to find phi knowing that x and y are on the interval -pi/2 to pi/2. those are the only conditions given

But we dont find a solution on this interval, it is too broad and contains multiple values

[sterile vale]

Then we try again with this condition

then we try a third time and only then do we find the condition but it seems like a total waste of time to try it three times when we could have just set it as 0=<tanx=<1/3 in the first place and same for tany

[lone heart]

@sterile vale Has your question been resolved?

[alpine sable]

It could have skipped some stuff sure.

If you start from the fact that tan(x)=1/3

We have two places where it is that value: in the first and third quadrant

We then take into account our interval, -pi/2 to pi/2 and this gives us quadrant 1

@sterile vale

[sterile vale]

Yes, that is true. That is an easier way to do it

thank you, I appreciate the help

[alpine sable]

Same steps for y basically

.close

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[sterile vale]

Wait sorry I have another question :S Am I correct in assuming that there are behind the scenes steps here that were skipped or is it really so obvious to pass from one to the other?

[sterile vale]

Because I dont really see any easy way to do it except to factorise, using a^2-b^2=0 and then solve each part separately so how can we jump to sin(6x)sin(4x) right away?

[lone heart]

@sterile vale Has your question been resolved?

[sterile vale]

@jovial hemlock

oh

sorry

<@&286206848099549185>

[rocky atlas]

I don't understand

Is there anything given about x

[sterile vale]

Hey bro #❓how-to-get-help

Oh

Oh

i am sorry

fdsjhdfshhsdf

i thought you were gonna ask your own thing

Sorry lmao

[rocky atlas]

no

[sterile vale]

Nothing is given except that equatio

[rocky atlas]

I don't understand how that happen, your question

[sterile vale]

I dont either

There is...nothing else

nothing given

and it goes from one to the other

I know that you could pass through it by the identity a^2-b^2=0

but I dont know how they jump to it so quickly so im wondering if there's an easy trick Im missing?

or they just assume because we know how to use this formula that they wont give details

[rocky atlas]

It would be interesting if there is a particular step/formula to jump

[sterile vale]

yea it would be very convienient

[rocky atlas]

Btw sin^2x=sin^2y is only possible when x and y are periods of each other

[surreal abyss]

Hi, I would like to ask why there is a vertical asymptote in this function ?

[rocky atlas]

Dark Angel this channel is busy

[sterile vale]

That would make sense but that condition too isnt given

this is the entire solution given

[surreal abyss]

Oh sorry

[rocky atlas]

No I mean if sinx=siny shouldn't that only be possible when x and y periodic angles?

But that doesn't make any difference

[sterile vale]

I gotta be honest with you I dont know what I am doing, I only have some slight trig intuition and I just follow the formulas and learn them by heart. So I cannot tell you why but what you are saying sounds wrong

Like technically we could bring the x and y to one side and solve the equation for a given value and it should spit out a solution

I really dont know how to explain it but I dont think what you say is a necessary condition

[rocky atlas]

Yh youre right

[sterile vale]

x and y values in trig are so abstract though

sigh

[sacred terrace]

we are asked to find the fourier series of the function f(x) , how do we find the fourier series from a graph ?

[sterile vale]

.close

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[thorn kindle]

asymptotic equivalence. sin(0)/0 = 1

that's an abuse of notation but you should understand what that means

[lone heart]

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[mild snow]

Trying to convert this spherical equation to rectangular but i'm not quite sure what to do

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@mild snow Has your question been resolved?

[mild snow]

<@&286206848099549185>

[mild snow]

oh boy i do love getting help on this server

.close

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[hybrid owl]

Hey! I know the coefficient of restitution formula but I just don't know where to start with this massive question :/

[lone heart]

@hybrid owl Has your question been resolved?

[hybrid owl]

<@&286206848099549185>

Here’s what I’ve done so far, I have no idea what to do from here

[bleak ridge]

Would you have to prove that the speed of A is >= to the speed of B a after the first second collisions?

[hybrid owl]

I think so but I'm not sure how to do that

[bleak ridge]

You'd prob just prove it numerically

Lemme see if I remember physics

[hybrid owl]

ty!

[bleak ridge]

So uhh

[rigid oyster]

so ez

[bleak ridge]

Conservation of momentum and stuff

It's perfectly elastic that means KE is conserved too right

[hybrid owl]

cool, so you mind helping if you know haha?

[hybrid owl]

yep

that's what I've done so far

[rigid oyster]

jk dont know what sgoing on only doing A levle

[bleak ridge]

Did you try factoring it

[hybrid owl]

I did this, but now I’m lost again what to do next

[bleak ridge]

Wait why'd you solve for μ

Or am I misunderstanding

[hybrid owl]

I just ended up with an equation relating the velocity of A and B after the first collision

I thought that could be useful

[lone heart]

@hybrid owl Has your question been resolved?

[hybrid owl]

<@&286206848099549185>

[mortal mantle]

Isn't this a physics question with the elastic collisions ? So I think it would be better to ask in a physics discord for a better understanding of concept rather then just to do it

[hybrid owl]

It's in my maths course

[mortal mantle]

Oh, I'm not sure how I would do it mathematically, but If you are interested, you can look up linear momentum and elastic collisions and solve it through physics

They set you up with formulas and it's just substitution and algebra from there

[hybrid owl]

yeah I'll try

[pallid trout]

I mean the first part is fairly simply, it's perfectly elastic, B is at rest, so it's just VaMa + VbMb = (after impact) VaMa + VbMb
You know that Vb is initially 0 and you know that Va will be 0 after.

So you can get Vb in the unit u, unless they used that u to mean micro?

[hybrid owl]

ok, ty!

[hybrid owl]

.close

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[rich rose]

Hello, I am not exactly sure how the inhomogeneous part of s'(t) becomes divided by -15

<@&286206848099549185>

[lone heart]

@rich rose Has your question been resolved?

[distant socket]

math

me is so good at math

[lone heart]

@rich rose Has your question been resolved?

[zealous adder]

<@&286206848099549185>

How do I answer b

11 b

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@rich rose Has your question been resolved?

[hallow topaz]

are rearragements allowed?

are [car model A, car model B] and [car model B, car model A] considered different combinations?

[zealous adder]

No I think they're the same

And rearrangements are allowed

[woven mango]

f(x) = (3x4 - 3x3 - 9x2 + 5x - 2)
d(x) = (x - 2)
Solve for the REMAINDER and determine if d(x) is a factor of f(x)

I don't understand remainder theorem

[coarse sparrow]

#❓how-to-get-help

[somber gust]

Help

[hallow topaz]

hey isn't this Lina's channel?

[somber gust]

Idk i just joined i need some one to help with my math

[hallow topaz]

there are available channels higher

[hallow topaz]

Ok, so what you want is (car combos length 2)*(truck combos length 2)

There are two scenarios when looking at a combo: it could have happened that we sold two same models of vehicle (we have [number of vehicle models — let's call that N from now on] chance of that, or it could be a formal combination

if it's a formal combination, then we have N variants for the first pick, N-1 variants for the second and so on, only two things for our length of two

So we just multiply: N*(N-1)

Then we must divide that by the number of possible rearrangements

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.reopen

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[hallow topaz]

cause otherwise our table is full of rearrangements

[hallow topaz]

for length of 2, you have 2 possible rearrangements: AB and BA. for length of three, it's 3 possible places of C * possible rearrangements of 2 left letters, so !3

if you don't know what that ! is, it's factorial — when you multiply some integer by a previous integer and so on until you reach 1

anyway, generalized formula for number of "combos" with N variants and Length L is this:

@zealous adder Has your question been resolved?

[lone heart]

@hallow topaz Has your question been resolved?

[zealous adder]

So do I do it twice? Or do I put all the numbers in the same equation? I know for a it's 11!/4! But how can we do 2 cars and 2 trucks with this

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[hallow topaz]

you do it twice, cause you got two combos of length 2 and N 5 and 6

[zealous adder]

Do I just add up what I find after

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[hallow topaz]

then you should think of combos as new letters

so you just multiply firsth number of combos by second number of combos

[brittle scaffold]

.close

[zealous adder]

Ohhhh oki

[hallow topaz]

because first/second number of combos are number of variants on first/second place in your new, final sequence

[zealous adder]

Thank U :))))

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[harsh belfry]

Could use a hand understanding how asymptotes work.

[harsh belfry]

To my understanding, to find a horizontal asymptote,

I need to compare the degrees of the numerator and denominator.

brother this channel literally has my name on it

[charred flint]

@gaunt summit respost in an available channel above like #help-15

yeah vn only the largest exponents matter for h asymptotes

[gaunt summit]

ahh shit mb

[harsh belfry]

Does this somewhat make sense? @charred flint

[charred flint]

some of it yeah

lesser/greater means there's a y=0 asymptote

greater/lesser means there are no asymptotes, the function just goes up or down to infinity instead

same/same means there's a horizontal asymptote at c1/c2

like the coefficients in front of the largest exponents

[harsh belfry]

ah so greater/lesser is DNE (do not exist)

So for instance

[charred flint]

yup

[harsh belfry]

will make up a random fraction so sorry if it doesnt make sense

Here its

same/same

however

it tends to slightly go away from 0

[buoyant kayak]

horizontal asymptotes to not exist when this is true, but there could be an oblique asymptote

[harsh belfry]

ah gotcha, dont think im there yet

[buoyant kayak]

eventually :)

[harsh belfry]

im scared....

in this instance

would y=+75?

[charred flint]

1x^2/1x^2 right

so 1/1 is the horizontal asymptote

[harsh belfry]

yep

1/1

ohhhhh

y=1/1

is my horizontal asymptote

However there would be no vertical asymptotes

because x^2+75

[charred flint]

right

[harsh belfry]

does not equal 0

right

[charred flint]

ya

[harsh belfry]

Got it!

Thanks

.close

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[keen mulch]

Could someone help explain how they go from cos(4pi x t/3)=1/2 to getting two solutions in part e

[coarse sparrow]

Because there are 2 x that sastify cos(x) = 1/2

cos(4πt/3) = cos(π/3) = cos(5π/3) = 1/2

[wintry sage]

cosine is positive in quadrant 1 & 4

[keen mulch]

Oh yes

[wintry sage]

Quadrant 1 is Pi/3 and quadrant 4 is 2pi - Pi /3

[keen mulch]

yep that makes sense

[wintry sage]

From symmetry

[keen mulch]

Is there worded questions that might ask where you find in a negative quadrant?

Or would that mean negative time? (Which I don’t deal with atm)

[wintry sage]

Like cos(4pi x t/3)=-1/2?

[keen mulch]

Yeah

[wintry sage]

Yes, then in this case cos is negative in quadrant 2&3

So you get pi-Pi/3 and pi+Pi/3

[keen mulch]

Oh so time is still going to be positive

[wintry sage]

Yes you just use symmetry

[keen mulch]

Yep

Okay

That helps

Picturing it as quadrants

Also

It the equation is just sin(n)=n or cos(n) where n is any number, will it always just be two answers in worded problem?

Or nx I mean and n is constant

[wintry sage]

It depends on the domain the question is asking about

[keen mulch]

If the domain contains one rotation there will be 2 points and if the domain contains 2 rotation there’s 4 points etc

Is that right

[wintry sage]

If the domain is [0,2pi] and the period is 2pi there will be 2 solutions, however if the period is Pi there will be 4 I believe

[keen mulch]

Yes okay

Then 0,4pi would be 4 solutions for 2 pi and if period is pi there be 8?

[wintry sage]

Yes

[keen mulch]

Okay

Exam tomorrow

3hr 15 mins

I have couple other questions if I could ask

[coarse sparrow]

They may have half a rotation or a quarter a rotation too

[keen mulch]

What does that mean

[coarse sparrow]

[0, π/2]

[keen mulch]

[0,pi/4] for domain?

Oh okay

Yeah

[coarse sparrow]

In my school we draw them out as spiral

It helps with edge cases

[keen mulch]

What’s edge cases

[coarse sparrow]

Something like this

This ensures you get the correct number of answers

[wintry sage]

That’s nice, we weren’t shown that

[keen mulch]

So if it were 0,2pi you just draw a circle from positive x axis back to same spot?

Then a line through it gives two answers

[coarse sparrow]

It depends on the brackets too, is it [0, 2π] or (0, 2π) or a mixed of both

[keen mulch]

Square brackets

You’ll get 2

Actually surely will get 2 for both

[coarse sparrow]

If it’s (0, 2π) and cos(x) = 1 you’ll get none

[keen mulch]

Oh yea nvm cos0 equals 1 and cos2pi equal 1

() means not inclusive

Could anyone explain part c please? Why is the lower limit greater than upper limit

[west bloom]

Because level decreases from 900 to 400 as t increases

[keen mulch]

I don’t understand sorry

[west bloom]

The tank has water right

And it's falling out

[keen mulch]

Yes

Isn’t that given by dv/dt

[west bloom]

So the level at one point was 900 units

Then it becomes 400 units

[keen mulch]

Ohhh

Okay

[west bloom]

Yea and it's negative

[keen mulch]

negative?

Wdym

[west bloom]

$- \frac{5}{2\root{t}}

Didn't work

Wait

-5/2√t

You see the negative sign?

[keen mulch]

Yes

So that’s the loss

[west bloom]

Right

[keen mulch]

Of water per second

[west bloom]

Yes

[keen mulch]

Okay

Why have they integrated that again in part c?

Because isn’t that rate of change of rate of change?

[west bloom]

Because as time will increase volume will vary from 900 to 400

You can imagine a discharging capacitor's response

That's what it sort of looks like

[keen mulch]

Idk what that is sorry

[west bloom]

Ok so what is a derivative

[keen mulch]

rate of change

[west bloom]

Then why does the derivative give instantaneous velocity

If it's rate of change

[keen mulch]

Rate of change at a certain point ?

Or instantaneous rate of change at a certain point?

Wait

[west bloom]

What would that mean

[keen mulch]

I’m an idiot

I thought they’re integrating was differentiating

[west bloom]

No

I am trying to see where your fundamentals are not right

If you properly visualise you'll always solve all problems

[keen mulch]

okay

So differentiating gives rate of change

[west bloom]

Yes

[keen mulch]

Integrating is the opposite

Idk what you would call it but velocity to displacement

For example

[west bloom]

So you add velocities and it becomes displacement?

[keen mulch]

add? You integrate the velocity to get displacement

[west bloom]

And why is integration different to addition

[thorn kindle]

What's the problem

@west bloom

[keen mulch]

Integrating is opposite of differentiating? Addition is opposite of subtraction? Addition and integrating aren’t related?

[vale wigeon]

this is your original question, yes?

or has that already been answered?

[keen mulch]

That is original question

[vale wigeon]

what you are looking for is V(400) - V(900), where V(t) is the volume of water at t seconds after the start of draining

$\int_{400}^{900} \paren{-\frac{5}{2\sqrt{t}}} \dd{t} = V(900)-V(400)$ by fundamental theorem of calculus

[ocean seal]

Ann

[west bloom]

I answered his question but I think (s)he has a difficulty with understanding what exactly does integrating a function mean so that's what I was asking

[vale wigeon]

integrals with bounds going 'the wrong way' are sometimes convenient to consider; if you are allergic to such integrals, you can always reverse the bounds and multiply by -1

$\int_a^b f(x) \dd{x} = -\int_b^a f(x) \dd{x}$

[ocean seal]

Ann

[keen mulch]

or I could take absolute value with 400 as lower and 900 as upper? Is that correct too

[vale wigeon]

i mean, sure...

[keen mulch]

Same thing as this

Okay

[vale wigeon]

you can do this, and you will get the change in volume from t=400 to t=900, which will be negative bc our water is draining

[keen mulch]

But do you take absolute value of that?

[vale wigeon]

do you mean "but are you required by decree from up above to specifically 'take the absolute value' instead of 'multiplying by -1'?"

if you get, say, -200 (or whatever other number)

do you need to justify bureaucratically why you can then go on to write "the amount drained is 200 liters"

[keen mulch]

Ah okay

You don’t really have to take absolute value bc you justified it with that statement? Correct?

[vale wigeon]

there is no such thing as "having to" do something

[keen mulch]

Okay but -200 means 200 litre

Is lost

[vale wigeon]

yes, that's what i'm saying.

[keen mulch]

Okay

Thank you everyone who helped

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[grave hinge]

Question and my explanation.

Some please help

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@grave hinge Has your question been resolved?

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[grave hinge]

<@&286206848099549185>

[chrome salmon]

Will be right

And you forgot dx in integration

I hope your calculations are right cuz I didn't check all of it

[grave hinge]

The concept used us correct?

[grave hinge]

This one is like 4th or 5th try.
So yeah, i did forget dx

[chrome salmon]

Yes

Disk method

[grave hinge]

Yes
If it's a little to much to ask,
It would be help if you'd actually solve it.
Cuz, 16pi/15 is marked incorrectly on edX

[chrome salmon]

I can't do that

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@grave hinge Has your question been resolved?

[grave hinge]

No.
It isn't

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[harsh belfry]

In order to simply this could I potentially bring the square root to the denominator?

[harsh belfry]

My professor doesnt care about rationalizing the denominator, but wants us to eliminate improper fractions

[harsh belfry]

Ohh I see now

[vale wigeon]

those are called nested fractions not improper fractions

[tough hatch]

they probably have a different definition for it

[harsh belfry]

I'm extremely ||thats putting it lightly|| math literate

I see now

so this should work right

[vale wigeon]

-(x+1)

[harsh belfry]

ah yes

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[rapid verge]

Hello, does anyone know how to solve the volume?

[coarse sparrow]

you find the area and multiply it by its width

[tough hatch]

i'm going to go ahead and assume that the 8 cm is the height

maybe drawing appropriately placed extra lines would help

[coarse sparrow]

I think the 8 is the rectangle height

[rapid verge]

yeah i was confused on that

i didnt know if 8 was height or not

so would the volume be: volume of rectangle prism + volume of semi-circle

[coarse sparrow]

yeah

[rapid verge]

with the volume of the rectangle prism is it 24 x 24 x 8

[tough hatch]

more like a semi-circular prism

[rapid verge]

is that correct

about vol of rectaangle prism

[alpine sable]

yeah

[lone heart]

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[crude bridge]

anyone wanna help factoring this polynomial x^3-x^2-4x+4

[vale wigeon]

have you made any progress so far?

[crude bridge]

Yup

But I am just a little stuck

X^2 (x-1) -4(x-1)

Could I (x-1)(x^2-4)?

[fading comet]

Please helpp, got 4sqrt(2) from the second derivative but it's wrong? If the first derivative allows you to find the max/min value of the function, wouldn't the second derivative allow us to find the max/min of the first?

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[fading comet]

Please helpp, got 4sqrt(2) from the second derivative but it's wrong? If the first derivative allows you to find the max/min value of the function, wouldn't the second derivative allow us to find the max/min of the first? repost

[tacit lodge]

is it +4,-4,0?

[fading comet]

no..

<@&286206848099549185>

[frosty flint]

-4, 4

[fading comet]

thanks it's correct how? please explain

[frosty flint]

extremum of f'(x)

[fading comet]

oo ok .close

.close

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[placid wharf]

im unsure on how to solve this other than using guess and check

[placid wharf]

also i dont understand how this rule would work if x was 0

[vale wigeon]

what rule?

[placid wharf]

relationship

[vale wigeon]

y=-3x+7 is not the correct equation for the table.

[placid wharf]

oh

thats the answer sheet

[vale wigeon]

the answer sheet is wrong.

it's y = 3x - 5

[placid wharf]

how do you figuure that out?

[vale wigeon]

every time x increases by 1, y increases by 3

[placid wharf]

oh and then 0 is -5

so its minus 5

[vale wigeon]

at your level you do not yet consider anything more complicated than linear equations

[placid wharf]

thanks alot Ann

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[keen mulch]

Just got last min exam question. For the above function. Can that be considered a function since it passes vertical line test?

Or does it have to also be smooth to be considered a function

[tough hatch]

exam question?

[keen mulch]

Exam prep

[vale wigeon]

no, smoothness is not required

[keen mulch]

My exam is tomorrow morning, this is a past paper

Okay

Is it considered a function even at end points too Ann?

[vale wigeon]

wdym

are you asking whether the endpoints of that curve are part of the graph too?

[keen mulch]

is the function defined at those points yes

[vale wigeon]

they are drawn with filled circles, so yes.

[keen mulch]

Or is it considered a function inclusive of endpoints

[vale wigeon]

if they were drawn with hollow circles they would not be included in the graph

[keen mulch]

Okay thank you

And for differentiating

The function has to be smooth, otherwise undefined

At the point it’s not smooth

[vale wigeon]

yes, the derivative doesn't exist at sharp corners

[keen mulch]

Okay

Can you differentiate at end points? Or are they undefined ?

Or does it depend if inclusive or exclusive

[vale wigeon]

your function may be differentiable or not differentiable at an endpoint of its domain, but if the function itself is not even defined there, then it makes no sense to talk about whether or not it's differentiable there

[keen mulch]

What if the function was defined at the endpoint?

[vale wigeon]

...reread the first half of my sentence?

[keen mulch]

It may be or may not be?

[vale wigeon]

yes, some functions are differentiable and others are not

[tough hatch]

have you encountered left-hand and right-hand derivatives?

[keen mulch]

Is there a way of determining if the end point is differentiable?

[keen mulch]

I think so very briefly

When an equation f(x)={ multiple equations?

Is that what it’s like

[vale wigeon]

..........

[tough hatch]

if both left-hand and right-hand derivatives exist at an endpoint of the domain of f, then f is differentiable at that endpoint

[vale wigeon]

i'll let .666 take over

[tough hatch]

wdym?

[steep hearth]

is it zero? or do i need to solve something to show the missong Q

and when solving for seasonal index (Q1)
should i divide it to 2 or 3

[tough hatch]

read #❓how-to-get-help

[keen mulch]

Like this?

[tough hatch]

a function doesn't have to be a piecewise function for left-hand or right-hand derivatives to exist

[keen mulch]

Okay

So if I was trying to tell if an endpoint was differentiable. Do I differentiate then enter x value of endpoint, if I get undefined it’s not differentiable at that point? Otherwise how do I approach it

[tough hatch]

if these derivatives exist and are equal, then f is differentiable at x_0

[keen mulch]

equal

Like both equations return the same value

Does the 0^- means approaches 0 from negative side?

[tough hatch]

yes

[keen mulch]

Okay good

[tough hatch]

is f defined on the left of x=x_0?

if not, then the left-hand derivative doesn't exist

which implies that f is not differentiable at x_0

[keen mulch]

Okay

Thank you

I think this may be outside my course

But the info will be useful

Thanks for your help

and Ann too, sorry I couldn’t understand… 😦

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[zinc gate]

Hi, notation question: how would you denote $T=T(x,t)$ with arrow notation, explicitly showing that the variables are $x$ and $t$? I thought it was something like $T:\mathbb{R}^2\rightarrow\mathbb{R}\ [x,t]$ but i forgot

[ocean seal]

mummiedanser

[vale wigeon]

you can't

[zinc gate]

Oh hmm

Ig what i saw was something else

Thank you!!

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[solid bloom]

hello

[tough hatch]

@solid bloom stop using a different channel if your question doesn't get answered in the current one

[solid bloom]

i can't close it

[tough hatch]

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[solid bloom]

oh sorry

can you help me tho pls

do i close this now

.close

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[dusty geyser]

back with another try to get the derivation of depressed cubic equations down, this is what I already have but I'm a little stuck on how to progress
https://cdn.discordapp.com/attachments/486841106298961930/907592887229906944/2xvqNf5fI90AAAAASUVORK5CYII.png

the substitutions are based on the geometric approach as shown here:
https://cdn.discordapp.com/attachments/486841106298961930/907593266705350696/unknown.png

an example that I solved with the same method before going over to try to generalise it:
https://cdn.discordapp.com/attachments/486841106298961930/907596991989702687/unknown.png

but if I do the same in the general solution (with variables p and q), I arrive somewhere that looks nowhere near Cardano's formula
let me resketch that rq
https://cdn.discordapp.com/attachments/486841106298961930/907598620273033216/1lAgAAgOHQBQGm5fSZM5s2bnoTHHzy1Mk1a9bIqwAAADCceI5Z5A4EAAAAALAEPAsCAAAAYFnoggAAAABYFrogAAAAAJZEUf4Pww2XHgmsJwAAAAASUVORK5CYII.png

[chrome salmon]

Holy

[dusty geyser]

oh, I should also mention that I got the general idea of the proof (or rather the start of it) from Veri's video https://www.youtube.com/watch?v=cUzklzVXJwo

[lone heart]

@dusty geyser Has your question been resolved?

[alpine sable]

its occupied channel you should go and get available one

[jaunty crane]

where can i get help

[unborn summit]

A 13ft long ladder rests against a wall when its base begins to slide. When the base is 12ft from the wall, the base slides at a rate of 5ft/sec.
a. How fast is the top of the ladder sliding at that moment?
b. At what rate does the area of ​​the triangle formed by the floor, the wall, and the staircase change at the same time?
NS. How much does the angle \thetaθ between the ladder and the ground change at the same time?

[glass lichen]

#❓how-to-get-help

[lone heart]

@dusty geyser Has your question been resolved?

[unborn summit]

):

[tacit lodge]

u can equate the speed of top and bottom points along the ladder

take components of velocity

[lone heart]

@dusty geyser Has your question been resolved?

[wanton folio]

what a stupid sentence. go to a free channel it's not hard to understand how this server works.

<@&268886789983436800>

[wispy ingot]

@dusty geyser
https://cdn.discordapp.com/attachments/486841106298961930/907596991989702687/unknown.png
I believe that you swapped 27 and 1, as in 1 needs to be the negative number and 27 positive.

[fading zephyr]

banned

[wispy ingot]

(not to pry, i'm bored)

[wispy ingot]

wack

[wispy ingot]

Furthermore why did you opt for the abc-formula when the the shortcut to (p- -

Oh i see, mhmh i was mistaken, you're correct.

[waxen copper]

i need help on a) please

[dusty geyser]

What part of occupied channel did you not understand :FeelsBadMan-1:

[topaz badge]

pls pls pls

[alpine sable]

Just put it into the equation @topaz badge

[topaz badge]

it wont work

cuz log a is 7 not a=7

[alpine sable]

you can solve for a and for b and then put it

[topaz badge]

how

[alpine sable]

or you could rewrite so it would have log(b) and log(a)

[topaz badge]

Oh Ok

[lone heart]

@dusty geyser Has your question been resolved?

[trim oracle]

Anyone can help me what to do here ?

[alpine sable]

find derivative

then find zeros

then just check intervals and see where derivative is positive

[trim oracle]

Find zeros?

[glass lichen]

roots, zeroes, solutions, etc

they're all synonymous

[trim oracle]

Ah

I still don’t rlly know what to do lol

[glass lichen]

Have you ever solved a polynomial equation before...?

[trim oracle]

Yes

That is how far I got lol

[glass lichen]

ok... now solve that for the roots

[trim oracle]

When derivative = 0?

[glass lichen]

yes

so you partitioned the x axis into your 3 intervals to check the sign of f'(x) in to determine intervals of inc and dec

[trim oracle]

?

Would answer just be x =1/3?

[lone heart]

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[trim oracle]

Oh

[lone heart]

Available help channel!

Send your question here to claim the channel.

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[native willow]

hullo here's the bastard:

[native willow]

so, i defined u=(1,1) v=(1,-1) and u* = (t,-t) as the projection of u on the span
and i plugged those into the following: ║ u - v ║² =║ u - u* ║² + ║ u* - v ║²
i was expecting it to simplify to a t value of u* as the projection (specifically expecting t=0), but i can't get there

am i missing something in the process? is my expectation incorrect here?

to be clear i plugged the norm in and expanded it like so:
(|u1-v1|^ᵖ+|u2-v2|^ᵖ)^(²/ᵖ)

where u=(u1,u2), ( ie the elements of the vectors) and so on for RHS

[lone heart]

@native willow Has your question been resolved?

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[hybrid owl]

Hey! I need help with this, I’m unsure on how to use sinx in terms of these exponents.

[hybrid owl]

Nevermind, I figured it out

.open

.close

[lone heart]

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[austere elk]

anyone good with z scores?

[austere elk]

i just have a quick question

[lone heart]

@austere elk Has your question been resolved?

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[dark schooner]

3^a+3^b+3^c=2^d+2^e+2^f
a,b,c,d,e,f = natural numbers
A•b•c•d•e•f=?

[lean spire]

what have you tried so far

[dark schooner]

Nothing bro

I don't understand

[lean spire]

then try something

[dark schooner]

I don't understand bro

[lean spire]

what don't you understand

[dark schooner]

Nothing

[lean spire]

also I'm not male don't call me bro

[dark schooner]

oh ok

Pronouns?

[lean spire]

she

[dark schooner]

Alr

[lean spire]

anyway

[tropic axle]

Naturals as in including zero or not

[lean spire]

what do you not understand about the question

[dark schooner]

Not zero

If it would've been 0 then ez

But not p

0

I guess

3^a+b+c=2^d+e+f

But does that help

[tropic axle]

You can't do that here

[dark schooner]

Oh

[lean spire]

oh I've figured it out

[dark schooner]

What

[tropic axle]

If there were all being multiplied, then sure, but since they're being added to each other, you can't do that

[lean spire]

you have to include 0

wait

no

nvm

sorry

[night geyser]

erm

[dark schooner]

Not natural

[night geyser]

that equation has no natural number solutions

take both sides mod 2

[lean spire]

yeah i was right

it's 0

[dark schooner]

But

Alr

Ig

[tropic axle]

Classic 5th grade math

[lean spire]

me when 5th grade

[night geyser]

if 0 is allowed, then yeah, any solution will involve 0

[dark schooner]

Yeah but we learned 0 isnt

Nvm

[lean spire]

0 should be a natural number

[dark schooner]

Nvm

It is

[lean spire]

yeah

[dark schooner]

It english if I search it's no

But in romanian yes

[lean spire]

there's a discrepancy

[dark schooner]

Alr

thanks alison

[lean spire]

but it's almost always included at higher levels because then ω works properly as a formal number

[dark schooner]

Alr

Thx

.close

[lone heart]

Channel closed

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Use .reopen if this was a mistake.

[dark schooner]

One more question

[lone heart]

Available help channel!

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Remember:
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[plush trench]

I need help finding Y

[glass lichen]

similar triangles have equal angles

[plush trench]

Yes

But I need help finding out what y is

is it 9?

[chrome kite]

if you’re told that the shapes are similar then yes, y=9

angles in similar shapes are the same

so 5y + 7 = 52

and so y=9

[lone heart]

@plush trench Has your question been resolved?

[lone heart]

@plush trench Has your question been resolved?

[plush trench]

stfu

[lone heart]

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Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[real dawn]

Area between two curves

[real dawn]

$x+y=2$ and
$\ x=y^2$

[ocean seal]

RESIDGE

[real dawn]

Intersections at x = 1 and 4. i think 0 counts too

I've been reading solutions but I have no idea how to find the area still. they end up splitting hte integral in two. one goes from 0 to 1, and the other goes from 1 to 4

[royal meadow]

yeah

because you can see they intersect there

so area between two curves f(x) and g(x) assuming no crossovers in the interval is just integral of f(x) dx - integral g(x) dx

the area between two curves is just the difference between:
the area between one curve and the x-axis
and the area between the other curve and the x-axis

so integral of f(x) dx - integral g(x) dx

that simplifies to integral of f(x)-g(x) dx

[real dawn]

So I should split it in half?

Like this?

[royal meadow]

no

why

[real dawn]

Nvm, I tried doing it with respect to y

[royal meadow]

oh yeah if you do it dy it's simple

[real dawn]

$\int_{-2}^{1}2-y-y^2$

[ocean seal]

RESIDGE

[glass lichen]

your top function is x=y^2

wait no

head was wrong way lol

[real dawn]

There we go.

[glass lichen]

missing the dy though

$\int_{-2}^1 2-y-y^2\dd{y}$

[ocean seal]

Mosh

[real dawn]

I should re-learn with respect of x to but I'm trying to cramp study and this is only part of the topic, which is to find xbar and y bar or centroid

[raw shard]

if it’s more convenient to do with respect to y do respect to y

just do what’s easiest for you

[real dawn]

alright ty everyone

.close

[lone heart]

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[slow bone]

.reopen

[slow bone]

Help

please

[vernal creek]

Just put x to -2y

So you have 2(-2y) + 3y = 5

[slow bone]

-4+3y=5

What about the 45

?

oh

wrong question

this

Please help

[vernal creek]

Same principle

put -2y for x