help-13

[fair mortar]

?

[wraith dagger]

bettim

[tame wraith]

the differentiation of sinx log2, yh

i meant from the very beggining

[fair mortar]

this will be the only term inside the last parenthesis right?

[tame wraith]

yh

[fair mortar]

we were told to use logarithmic differentiation

[tame wraith]

oh right

[fair mortar]

thanks

[gray blade]

yo

how’d you change your tex color

[fair mortar]

preamble

[gray blade]

?

[fair mortar]

.close

[cedar kiln]

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[fair mortar]

preamble edit

[cedar kiln]

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[coral valley]

test

[foggy merlin]

bro wat

[coral valley]

this is not looking right

is there a better way to write this down?

[foggy merlin]

?

I saw what you wrote btw

[coral valley]

what I wrote?

how do you even take an exam at home?

how do i screenshot the exam paper perfectly like that?

[foggy merlin]

im not debating tho, is it a test or not

[coral valley]

it's not

[foggy merlin]

then, what does it mean ?

[coral valley]

I just don't want the image goes too further up the chat

that's all

[foggy merlin]

sound like cap

[coral valley]

??

[foggy merlin]

im not buying it

[grand forge]

???

[coral valley]

ur wasting my time holy shit

[grand forge]

You have 348 previous messages

You knew it works

[coral valley]

???

I've always done it as the screenshot is more visible

so people are more likely to help

thats all

[cosmic steppe]

Yeah don't say "test" though next time

[grand forge]

It’s literally less visible

Surley having it pinned is more visible

[cosmic steppe]

What does d.p. Mean. Decimal points?

What have you done

[coral valley]

yes

[cosmic steppe]

So far

[coral valley]

the screenshot above

im trying to do question a

[cosmic steppe]

Your handwriting's a bit hard to read

[coral valley]

that doesn't look correct as examples given in the material is way more simple

im just wondering if there is a way to simplify what I wrote

my lecturer previously used factorial

[cosmic steppe]

Mmhm so evaluate each of those derivatives at x = 8

Uh

[coral valley]

is 4 derivatives enough/

?

[cosmic steppe]

I mean. The denominator is just 3^n

But

Yeah

[coral valley]

from examples online usually ppl go for 4 derivatives

[cosmic steppe]

Yeah but now you need to evaluate each derivative at x = 8

[coral valley]

aight, so seems correct already

thanks

.close

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[vocal raptor]

from A to B point tourist gone with car. for t1 hour he moved 60km/h, for other t2 he moved 80km/h. find t1/t2, if the tourist travel average speed was 68 km/h

[vocal raptor]

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[somber otter]

What are the 3 equations within the system of equations for this problem?

[cedar kiln]

@somber otter Has your question been resolved?

[somber otter]

<@&286206848099549185>

[obtuse grail]

First equation: Sum of # of shares times price of each share = Total lottery amount
Second equation: 3 times as many Macy's stock than GameStop stock
Third equation: Growth over the year should = amount problem wants you to gain in a year

Do you think you could turn those three sentences into equations using the conditions?

[somber otter]

1. 45.1g + 26.3b + 14.2m = 28324
2. 3m = g
3. 48.257g + 27.352b + 14.484m = 29572.19

Does this looks right? @obtuse grail

[obtuse grail]

Equation #2 is incorrect, switch the coefficient

[somber otter]

The one im most confused about is the 3rd equation

2 would be 3g = m?

[obtuse grail]

Yes, since you have 3 times as many Macy's stock, increasing gamestop share amount 3 fold will give you the same amount of shares as Macy's

But the 3rd equation is correct I believe, you are just looking at how much money you would have next year with the expected growth

[somber otter]

ohhhh I see what you are saying

[obtuse grail]

Can you handle the system from here?

[somber otter]

yeah I think I should be able to

thank you I appreciate the help

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[obtuse grail]

Always

[cedar kiln]

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[wide scaffold]

question: prove that for every whole number n and natural number d, there exists a whole number r that satisfies the follow:
n = t * d + r, where t is a whole number

[wide scaffold]

I am really not sure how to do this need some starting points

(discrete mathematics)

[mighty drift]

Is that really it ? No other conditions such as 0 < r < d ?

[wide scaffold]

Yes that is a condition my bad

0<=r<d

[mighty drift]

It's euclidian division

[wide scaffold]

I am not sure we can use that yet

[crimson delta]

what can you say about n-d

[mighty drift]

You can prove it by induction

[wide scaffold]

n-d=t*d+r-d
n-d= d(t-1)+r
?

[wide scaffold]

we cant use that as well I think XD

[mighty drift]

Then you should be able to use the fact that any bounded part of N has a maximum

[wide scaffold]

Why should i use bounds here?

Bare with me I am a bit slow😀

[mighty drift]

You need to use a property of N at some point

You said no induction

[wide scaffold]

Correct

So how do I bounds in my case

[mighty drift]

I'm telling you there's a way of proving it using this other property of N

You need to find a set to which you can apply this property meaningfully

Since d is fixed, maybe use it to find t ?

[crimson delta]

discrete mathematics course without induction?

what kinda cursed stuff is that

the natural numbers are essentially defined with induction. you have to use it or something equivalent for most stuff

[mighty drift]

Agreed

[wide scaffold]

I'll check and come back because language barrier might be the issue

although I still think we cant use induction

gimme a few mins

[cedar kiln]

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[lone garden]

Let $\mathbb{C}[z]$ be the algebra of complex-valued polynomials. Is the ideal $I = { f \in \mathbb{C}[z] : f(2i) = f'(2i) = 0 }$ maximal?

[wraith dagger]

Joy!

[lone garden]

I started by assuming $I$ was not maximal, and hence there exists a different maximal ideal $J$ which contained it. Since $I$ is a proper subset of $J$, there exists a polynomial $f \in J$ such that $f(2i) \neq 0$ or $f'(2i) \neq 0$. I don't really know where to go from there, but it feels like this is the right direction, it feels like $J = \mathbb{C}[z]$ (and hence I would have my contradiction) but I don't quite know how to write that

[wraith dagger]

Joy!

[tropic oxide]

doesn't the ideal {f ∈ C[z] : f(2i)=0} contain yours strictly?

[lone garden]

oh i didn't even think about that, I thought $I$ was maximal already

[crimson delta]

as a general remark, if you have more than one restriction on a set, think about what happens if you ignore one of them

[lone garden]

yeah you're right. i was being stupid

[crimson delta]

happens ¯_(ツ)_/¯

[lone garden]

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[oak venture]

Any idea on what to do?

[oak venture]

This is what I got so far

[clear berry]

try simplifying that by shifting root to one side and rest to other then squaring

[oak venture]

okay chill

Now what

[abstract pollen]

uh, can you simplify it? factorise it?

You've done what you've been told to do, and now and try see how else you can manipulate it yourself

[oak venture]

thank you

I got this but I don't think I'm right because X and y are meant to integers so both of them have to be 1

[cedar kiln]

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[oak venture]

.close

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[loud hornet]

why is arctan(tan(7pi/4)) undefined?

[south tundra]

,w arctan(tan(7pi/4))

[wraith dagger]

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Requested by A Lonely Bean#7998

[loud hornet]

oops i said the wrong problem

sin(arccos(-1/2)) that is undefined

[south tundra]

,w sin(arccos(-1/2))

[wraith dagger]

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Requested by A Lonely Bean#7998

[loud hornet]

tan(arcsin(-1)) I need more sleep lmfao

[lyric narwhal]

,w tan(arcsin(-1))

[wraith dagger]

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[loud hornet]

well i know the answer, I want to know why that is the answer

[south tundra]

arcsin(-1) is -pi/2

And tan is undefined at -pi/2

[loud hornet]

ah

[south tundra]

Because cos(-pi/2) = 0

[loud hornet]

i see

thanks

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[median jolt]

hello, can someone help me? i need calc a and b

[median jolt]

i've tried solve it, my first attempt i get a=1 and b = 3 but doesnt verify :c

[vast pike]

its equivalent to $a+i=(3-bi)3\pi$ right?

[wraith dagger]

everg

[median jolt]

i don't know that property

[vast pike]

if you can solve problem by just put random value ..

try going to the casino 😅

[median jolt]

lol

[vast pike]

do you know that $\frac{x}{y}=z\iff x=yz$

?

[wraith dagger]

everg

[median jolt]

yes

[vast pike]

i just multiplied by $(3-bi)$

[wraith dagger]

everg

[vast pike]

lhs and rhs

ok?

[median jolt]

ok

[vast pike]

you can rewrite this $a+i=(3-bi)3\pi$ like this: $$a+i=9\pi-i3b\pi$$

[wraith dagger]

everg

[vast pike]

right?

[median jolt]

i don't know where you get 3 pi

[vast pike]

this one?

[median jolt]

yes

[median jolt]

dam

big brain

[vast pike]

maybe i read wrong the fraction

[median jolt]

is not a fraction

its a complex number

[vast pike]

yes i m pretty sure that its wrong

[vast pike]

however from this (maybe you have to change 3\pi with another constant) you can solve easily the problem

[median jolt]

wait, can i take this complex number in polar form like a fraction? really?

[vast pike]

????

you have no polar form

a polar form its $e^{i\pi/2}$ for example

[wraith dagger]

everg

[vast pike]

in your image you have no exponential

[median jolt]

is in spanish my book

[vast pike]

what a notation .....

okk

[median jolt]

yes, i never see that notation in my life

[vast pike]

i never see that..so my solution its wrong

its equivalent to $\frac{a+i}{(3-bi)}=2e^{i\frac{3}{2}\pi}$

[wraith dagger]

everg

[median jolt]

ok

[vast pike]

now $e^{i\frac{3}{2}\pi}=cos (\frac{3}{2}\pi})+i sin (\frac{3}{2}\pi})$

[wraith dagger]

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

[median jolt]

yes

[vast pike]

so

$e^{i\frac{3}{2}\pi}=-i$

[wraith dagger]

everg

[vast pike]

right?

(because sin=-1 and cos=0)

[median jolt]

yes

[vast pike]

now its like before

its equivalent to $\frac{a+i}{(3-bi)}=-2i$

[wraith dagger]

everg

[vast pike]

hence

[median jolt]

oh

[vast pike]

${a+i}=-2i(3-bi)=-6i-2b$

[wraith dagger]

everg

[median jolt]

yes

[vast pike]

mh.. i think that a and b are reals?

[median jolt]

mmm, i don't know but i think i can go alone

[vast pike]

...if i do all correct i think the are no soulution xD

[median jolt]

ok, im gonna try, thank youu

[vast pike]

np

[median jolt]

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[jade stag]

can you walk me through find prime of (lnx)^8

[jade stag]

says to use extended power rule

[long arrow]

you mean derivative ye?

[jade stag]

ye

[long arrow]

use chain rule

[jade stag]

i got 8/x times lnx

[long arrow]

times (lnx)^7

[jade stag]

oh

i got 8/x times (lnx)^7

[long arrow]

yea

[jade stag]

thats all she wrote?

[long arrow]

who's she, anyway that's all

[jade stag]

just a sayin

for "thats all"

do i have to put parenthesis

is it more formal

[long arrow]

you can rewrite it in two ways

[jade stag]

(8(lnx)^7)/x

like on paper

not caclulator

you know

on a test

[wraith dagger]

Modus

[cedar kiln]

@jade stag Has your question been resolved?

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[unborn night]

Is this right?

[unborn night]

So far

Integrating it isn't always my favourite 🙃

[velvet mortar]

So this is linear 1st order ODE solved by integrant factor. I can't remember the formula

[unborn night]

Yep. Pretty sure the integrating factor is just e^int(P(x))

I'm just not 100% convinced by the last couple of lines

[violet night]

this looks completely correct

[unborn night]

Alright thanks. Just didn't want to do integration by parts with a substitution because it would've been long but was being an idiot and realise I can just substitute u=x+4 anyway. Cheers

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[west silo]

i dont really understand how to solve for it

[unborn night]

Have you drawn a diagram?

[west silo]

i have the points marked out on a graph

but i dont know what to do with the 5:1

[unborn night]

Not 100% sure but I think you can do the x value and the y value separately. If u have smt drawn like this u can try it out

as in you take the 5/6 of the x and y value

Sorry it;s not very clear.

Like this

[cedar kiln]

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[cedar kiln]

@west silo Has your question been resolved?

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[upbeat frigate]

'

[digital spade]

You'll need to find local minima

And take the first one

[cedar kiln]

@upbeat frigate Has your question been resolved?

[upbeat frigate]

the first local minima?

[digital spade]

Yeah exactly

Since it's a trigonometric function it will have infinite minima

[upbeat frigate]

yep

12pi?

[digital spade]

Yupp

[upbeat frigate]

thxx

i have another problem im trying to figure out

[upbeat frigate]

im trying to figure out how to write the equation for this to find the y-intercept by setting x=0

is it

3sin(x/2 + pi/4)?

well no that's wrong

idk how to do it

if it was 3sin2(x/2 +pi/4) it would work but it seems wrong

well i have no idea if it's right

[digital spade]

The phase shift goes outside of the sine function

[upbeat frigate]

o hhhhhhhhhhhhhhhhhhhhhhhhhhhhhh

ur sure?

i thought vertical was outside?

[upbeat frigate]

yeah phase shift is inside

vertical is outside

[digital spade]

Oh right my bad

So that would be $f(x)=3\sin(2(x+\pi/4))$

[upbeat frigate]

why is there an 8?

[digital spade]

For the period

Wait

Got them mixed up

[upbeat frigate]

idk

[digital spade]

Should be 2 not 8

Because period is 2π/t

[wraith dagger]

midy

[digital spade]

Then solve for x=0

[upbeat frigate]

it says the period is pi

[digital spade]

Yeah

If you divide 2π by 2 you get a period of π

That's what the 2 is for

[upbeat frigate]

I don't really understand how periods work in the equation

I understand sin(x) period is 2pi normally

[digital spade]

Yeah exactly

Imagine if sin(x) was sin(1*x)

That would make the period 2π/1

So 2π

[upbeat frigate]

ohh the parantheses confuse me a bit cuz its outside the x +pi/4

but it doesn't matter what order it's multiplied right i mean they all get multiplied anyway

[digital spade]

Yeah exactly

[upbeat frigate]

wait no im still confused

[digital spade]

Haha shoot

[upbeat frigate]

like 3sin(2x+pi/4)

is different from 3sin2(x+pi/4)

which is the same as 3sin(2x+pi/2)

3sin(pi/2) = 3

[digital spade]

By 3sin2(...) do you mean 3sin^2(...)?

[upbeat frigate]

i mean this

[digital spade]

No yeah you got it right

[upbeat frigate]

yeah what im saying is that i dont think or know if thats right

[digital spade]

But yeah 3sin(2x+pi/4) is different

[upbeat frigate]

i should watch this video but

a= amplitude b= part of period of that equation c= phase shift d= vertical shift

so shouldn't it be?

[upbeat frigate]

this instead?

period is pi? so b is 2?

[digital spade]

Yeah B is 2

[upbeat frigate]

when i graph that the y-intercept is not one of the answer choicessss

ergheriohjgiehgioehgoiher

it's 2.121

and that is not it?!?!?

[digital spade]

I'm getting 3

[upbeat frigate]

how

[digital spade]

What function are you graphing

[upbeat frigate]

3sin(2x+pi/4)

B is 2

Asin(Bx+C)+D

[upbeat frigate]

u get 3 from ur function

[digital spade]

The formula is Asin(B(x+C))+D

[upbeat frigate]

organic chem tutor why 😭

[digital spade]

Haha give me a minute

[upbeat frigate]

no actually other places say its bx

idk

[digital spade]

Yeah

I'm guessing C is after you've multiplied B with phase shift

So Asin(B(x+G))+D = Asin(Bx+C)+D

Where C is B*G

[upbeat frigate]

really??

what trickery is this?!?!

XD

why do they do this to us

[digital spade]

Hahaha

[upbeat frigate]

idkk

is that actually how part of how its derived?

do we have to derive it ourselves to make sure aaa what do we do omg

so unfair

[digital spade]

Yup 😦

Thankfully we've got the multiple choice to verify

[upbeat frigate]

if we can rule out the other answers

i mean its not 0

cuz of the phase shift

that's about the only one i can rule out myself XD

[digital spade]

It's not pi/4 either

Cause if sin() = 1 then 3pi/4

If we shift sinx to the left by half a period the y intercept is basically the maxima

Amplitude of 3 means maxima is 3

[upbeat frigate]

alr should we take a deep breath

or try to verify

[digital spade]

https://www.mathsisfun.com/algebra/amplitude-period-frequency-phase-shift.html

That might help

[upbeat frigate]

no i looked at my lessons and it just gives me this equation

[upbeat frigate]

oh wow thats pretty

omg that website is actually so incredibly cool

alr lets take a deep breath

[digital spade]

Haha yeah one of my favorite websites for math

You got this

[upbeat frigate]

i got one question wrong on the entire exam

lets look

.-.

praying rn

fuck

its wrong

😂

gg

legit only question that stumped me

the rest were law of sines cosines, areas, unit circle, etc

[digital spade]

Oh damn

Hmmm

[upbeat frigate]

yeah i still wonder why its wrong

maybe we can get someone in here

idk

[digital spade]

Yeah I'm stumped

Oh wait

Oh god

3sin(2x-pi/2)

No

[upbeat frigate]

yeah still what?

-1*3

-3?

[digital spade]

yeah

[upbeat frigate]

thats just evil??

[digital spade]

Ikr

[upbeat frigate]

they didn't say if it was positive or negative

holy fuck

[digital spade]

Not even left or right like what

[upbeat frigate]

wow...

[gritty viper]

its annoying since you can't solve it without knowing the specific method the teacher wants you to use to understand transforming sine functions

but

assuming since it's not given that the axis of oscillation is y=0

you have your formula of Asin(Bx - C) + D

3sin(Bx - C) + 0

period pi is 2pi/B so B=2

phase shift pi/4 is C/B = C/2 so C is pi/2

3sin(2x - pi/2) + 0

then find the y-intercept

[digital spade]

So do we assume phase shift is to the right if it doesn't say otherwise?

[gritty viper]

ah wait i messed up on the phase shift calculation

yes positive phase shift means to the right

if it was to the left it would be negative

[digital spade]

Negative is right

I think

[gritty viper]

sin(x-1) is shifted one to the right

but you would say the phase shift is 1

sin(x+1) has a phase shift of -1

[digital spade]

Ahh yeah that would make sense

[cedar kiln]

@upbeat frigate Has your question been resolved?

[upbeat frigate]

Tysm I understand now

[gritty viper]

np

[cedar kiln]

@upbeat frigate Has your question been resolved?

[cedar kiln]

@upbeat frigate Has your question been resolved?

[vernal pine]

stupid nerd asses

[cedar kiln]

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[mortal musk]

Why is it that it says an not equal to 0 is divergent, yet we get a convergent value in this other one?

[tropic oxide]

first off it's lim a_n ≠ 0, not that a_n itself isn't 0.

and second, there's a difference between a_n (the terms themselves) and s_n (the partial sums)

[mortal musk]

If you take the limit of a_n, if it's not zero it's divergent, and the other one is convergent because the limit of the partial sums has a limit that exists?

if you have n=3 rather than n=1, can you still use a_n != 0 for divergence, or would you need to use partial sums for this?

[tame wraith]

if you would imagine that a_n converges to a number that isnt 0

then when you do the infinite sum

you would add that number an infinite amount of times

so it has to be divergent

[tame wraith]

wdym by n = 3 instead of n =1 ?

the limit of the partial sum already includes this.

well not always though

if you have 1/n, then a_n goes to 0, but s_n diverges. but for most other sums that i know, if s_n converges then a_n doesnt go to 0.

[mortal musk]

ahh okay, thank you!

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[worthy ridge]

how do you compute E(X^2)?

where X is the random variable

this is the definition for E(X)

but I don't see what I need to do with $E(X^2)$

[wraith dagger]

normalAtmosphericPa=101,325

[worthy ridge]

Do I do $E(X^2)=\sum_xxPr(X^2=x^2)$?

[wraith dagger]

normalAtmosphericPa=101,325

[foggy merlin]

no

$\mathbb{E}(X²) = \sum x² \mathbb{P}(X=x)$

[wraith dagger]

Ｈｅｒｅｌｓ

[worthy ridge]

THanks!

I was also wondering how this relates to the regular population variance formula: $\frac{\sum(x_i-\mu)^2}{N}$?

[wraith dagger]

normalAtmosphericPa=101,325

[foggy merlin]

you know that :
$\operatorname{Var}(X) = \mathbb{E}((X-E(X))²)$

[wraith dagger]

Ｈｅｒｅｌｓ

[foggy merlin]

maybe it comes from this, i havent done a lot of statistics

[worthy ridge]

wait

so is there no direct way of converting E(X) --> E(X^2)

[tropic oxide]

of course there isn't

knowing only E(X) is not enough to know E(X^2)

[worthy ridge]

and just to confirm:

geometrically, the cdf is the actual "curve", and the pdf is the area under the curve?

oops

otherway around

[tropic oxide]

indeed it is the other way around.

[worthy ridge]

thanx

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[quartz salmon]

Hello everyone,

I'm currently working on a calculus problem and I came across this step-by-step solution for an integral:

$$I=\int u^2\ ln(u)\ du=\frac1{3}\int ln(u)\ du^3=\frac 1{3}[u^3\ ln(u)-\int u^3\ d(ln(u))]$$

$$I=\frac 1{3}[u^3\ ln(u)-\int u^2\ du]=\frac 1{3}[u^3\ ln(u)-\frac 1{3} u^3]+C$$

I'm having trouble understanding the reasoning behind some of the steps.

If anyone could provide some clarification or walk me through the solution, I would greatly appreciate it. Thank you in advance for your help!

[wraith dagger]

dgh

[lyric narwhal]

du^3??

[quartz salmon]

Context of the question: https://math.stackexchange.com/questions/4659910/need-help-solving-an-integral-with-substitution-method/4659934#4659934

[hearty fjord]

Probably dealing with the u^2 term in the integrand

[lyric narwhal]

but du^3 makes absolutely no sense

[hearty fjord]

But that is a weird thing to do really

I'd do by parts if I was asked to do this problem, most likely

[lyric narwhal]

i think they have tried to do it by parts as well

I just have no idea what they've written

but the answer is correct so

[hearty fjord]

fair enough I guess ¯_(ツ)_/¯

[lyric narwhal]

anyway @quartz salmon the du^3 notation makes no sense

you just have to do integration by parts

[quartz salmon]

why, is it not allowed?

[lyric narwhal]

you can learn the DI setup for integration by parts

to make it easier

[lyric narwhal]

you can say that

du^3 just makes no sense matematically

i suppose they were trying to write d/du(u^3)

[quartz salmon]

what's the DI setup?

[lyric narwhal]

just a fancier and easier way to do integration by parts

[quartz salmon]

okay so could you walk me through how i can solve it using IBP?

[lyric narwhal]

have you learned the v du setup?

[quartz salmon]

i am not familiar with these acronyms no

[lyric narwhal]

well

[quartz salmon]

i've learnt IBP briefly

[lyric narwhal]

how have you learned IBP

ah

[quartz salmon]

like 1-2 weeks

going through some of the pages

nothing i've delved into much

[lyric narwhal]

i would suggest learning IBP properly then

https://www.youtube.com/watch?v=KKg88oSUv0o

or any other video

[quartz salmon]

okay, i will have another look

thanks

[cedar kiln]

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[stone lagoon]

How to find radius

[cedar kiln]

@stone lagoon Has your question been resolved?

[stray otter]

,rotate

[cedar kiln]

@stone lagoon Has your question been resolved?

[cedar kiln]

@stone lagoon Has your question been resolved?

[mortal yarrow]

Does the triangle tangent to the circle like on the top and on the bottom ? @stone lagoon

[stone lagoon]

yes

@mortal yarrow

[crimson sedge]

r=4

@stone lagoon hope it helps...

[stone lagoon]

@crimson sedge thanks so muchh

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[heady juniper]

Factorise 8 (p-3)³ + 343

[cerulean sail]

8 and 343 are cubes; sum of cubes I would assume

[heady juniper]

Yes

But when i take it in the form of a³ + b³.
Should it be [{8(p-3)}³ + (7)³]or [{2(p-3)}³ + (7)³]

Can you tell me this

[midnight bluff]

8(p-3)^3=[2(p-3)}^3

[woven hearth]

what is the square root of -1 ?

[heady juniper]

Thanks

[heady juniper]

i

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[soft shard]

Hello, I wanted to ask that:

[soft shard]

What's an equivalence class in Relations and Functions?

[cedar kiln]

@soft shard Has your question been resolved?

[crimson delta]

an equivalence relation is a relation that is reflexive, symmetric and transitive

the equivalence class of some element a contains all elements b that are related to a for some equivalence relation

[soft shard]

UM

Ohhh

Yeaa

Kinda got it

Would it be okay for an example?

[cedar kiln]

@soft shard Has your question been resolved?

[crimson delta]

consider eg the relation aRb iff 7|b-a on Z

then the equivalence class of 0 are all numbers with 7|b-0, so all multiples of 7

the equivalence class of 1 are all integers b with 7|b-1, so all numbers one after a multiple of 7

and so on for 2,3,4,5,6

then the equivalence class of 7 is again the same as for 0

[cedar kiln]

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[tame finch]

Can someone help in this?

I've tried to find some sort of pattern but I just can't find a pattern

[tame wraith]

lmao

[dusk finch]

lol

[soft shard]

Ahh

Got it

Thankyou!!~

[tame finch]

Pls I need help

[tame wraith]

this is the only thing ive found

only thing i would know how to ddo is plug that into a calculator

[crimson delta]

partial fractions

and hope stuff telescopes

[tame finch]

Thank you

I will never forget this

[tame wraith]

,w partial fractions 1/( (3n -2)(3n+1)(3n+4) )

[wraith dagger]

Results provided by WolframAlpha

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

Requested by doctor99268#2294

[tame finch]

Thanks

My question has been resolved

[crimson delta]

then feel free to .close the channel

[tame finch]

.close

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[timber palm]

6 ÷ 2( 1 +2)

[cosmic steppe]

Aren't you hilarious

[tame wraith]

ultimately there is no right answer

[cosmic steppe]

Aren't you the brightest comedian of all time

[dusk finch]

Ambigious question. It can be interpreted as:
6/(2*(1+2))
or
(6/2)*(1+2)

[cosmic steppe]

Would you like a golden medal

For your funniness

Or would you wanna find your father

LOL

[wraith dagger]

ℝamonov

[cosmic steppe]

AYO

[cosmic steppe]

@timber palm for you G

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[cosmic steppe]

Now use the channels appropriately

[dusk finch]

.reopen

[cedar kiln]

✅

[dusk finch]

.close

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[jade stag]

this doesnt make sense to me

[jade stag]

I thought N'(45) was ( .047 * 945013 ) e ^ 0.047(45) ?

[marble root]

Looks like you plug 45 into the N function which evaluate to 945,013. Then plug that value into N’

[jade stag]

that is clear to me

however

why not -> N'(45) was ( .047 * 945013 ) e ^ 0.047(45) ?

[tropic oxide]

$N'(t) = 0.047N(t)$, not $N'(t) = 0.047 N(t) e^{0.047t}$.

[wraith dagger]

Ann

[cedar kiln]

@jade stag Has your question been resolved?

[jade stag]

ann

ignore the other stuff

just focus on this

rate of change = prime right?

derivative

ok lets back up for a second once again

start fresh

look at this

this is a similar problem

this is my progression

notice a

b and c

[tropic oxide]

ok sorry i am busy with other shit rn

[jade stag]

is it pain related

<@&286206848099549185>

ohh

i see it

[jade stag]

question a) isnt a derivative? 😮

[cedar kiln]

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[livid needle]

Small question, there are 10 yellow balls and 8 white balls in a bag, I take out a ball and don't return it to the bag what are the chances of me getting two yellow balls?

[livid needle]

I don't have a clue how to do this

[tranquil oracle]

how many ways are there to take out 2 yellow balls

[livid needle]

Wdym?

[tranquil oracle]

(assuming the order of taking out matters)

each way of taking out 2 balls is equally likely

so just need to count the number of ways to take out 2 yellow balls

[livid needle]

What do you mean by a way?

Like the chances first time would be 10/18 and second time 9/17

[tranquil oracle]

well we can also do with that

since you have that idea already, then the probability is found from multiplying them together

[livid needle]

Exactly why multiplying?

[tranquil oracle]

P(A and B) = P(B | A) P(A)

A: first ball is yellow
B: second ball is yellow

P(B | A) = probability the second ball is yellow given the first ball is yellow

[livid needle]

I see, but why?

[tranquil oracle]

tbh i'm not sure what you find unclear

[livid needle]

Why is multiplying the way to find out the answer?

Why not dividing for instance

Or subtracting

[tranquil oracle]

do you know what probabilities are

like they show the fraction of scenarios you are interested in out of all scenarios, based on what you know

so the chances for the first time being 10/18 means you are interested in 10 out of every 18 scenarios

[livid needle]

Ok

[tranquil oracle]

and out of these 10, the second time being 9/17 means out of every 17 scenarios that come out from these 10, you are interested in 9 of them

[livid needle]

Ol

Oh, I think I understand

[tranquil oracle]

so to find out all the scenarios where you are successful both times...
10 out of 18 is the same as 170 out of 306 for the first step
then i'm further interested in only 9 out of 17, so that's 90 out of 170 out of 306

[livid needle]

Yeah

Thx

[tranquil oracle]

pretty much what you are doing is multiplication

[livid needle]

I see

Thx

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[livid needle]

.reopen

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✅

[livid needle]

Well then what would be the probability of two balls being the same color

For the first one it's 18/18

[tranquil oracle]

add in those events for red

but to do the second one you'll have to... match what you had, which is not something you can specify a probability for without knowing what you had

so you have to split into cases depending on whether it's yellow or white

[livid needle]

Oh

I see

I thought it's possible to figure a single probability out

Thx

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[heady spindle]

this DE is separable?

[cosmic steppe]

Yeah

[south tundra]

Yup, just multiply both sides by dx

[cosmic steppe]

Multiply both sides by dx

Ayo

[south tundra]

Btw is that dy/dx - y or dy/dx(-y)?

[heady spindle]

yes, but wolfram resolve it like a linear, but I don't get the same result

[south tundra]

Different story if it's the first one

[heady spindle]

oh no

[tropic oxide]

$y' - y = e^{-3x}$ is not separable i dont think

[heady spindle]

is the first one

[wraith dagger]

Ann

[heady spindle]

:(

[south tundra]

Okay, then you can multiply both sides by e^(-x)

And, if you look carefully at the left hand side of the equation after doing that, you will see something resembling product rule

[heady spindle]

yes :( I get wrong that exercise on my exam :(

[heady spindle]

but I interpret it like a multiplication :(

[south tundra]

For some reason I thought it's *(-y) as well

Probably because of the symbols standing so closely on the screenshot

[heady spindle]

that was the same on the exam :(

[south tundra]

But this equation is of the form y' + p(x)y = q(x), which can generally be solved by multiplying both sides by e^(integral of p(x) dx) and doing the same thing

The technique is called "integration factor" btw

[heady spindle]

yep :(

:( I have to wait for the grades, thank you

[south tundra]

Ight, good luck

[heady spindle]

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[high bloom]

heyyy guysss!! i've got my math board exam on tuesday......any time management tips?? :))

[cedar kiln]

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[eager crane]

Wheres my mistake?

[eager crane]

Should be ln|tanx| -(1/2)cot^2(x)

[cedar kiln]

@eager crane Has your question been resolved?

[eager crane]

<@&286206848099549185>

This one too

Should be sqrt(1-x^2)arcsinx

[cedar kiln]

@eager crane Has your question been resolved?

[eager crane]

<@&286206848099549185>

[cedar kiln]

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[jade stag]

my focus is on question d).
to find out how much they spent why are you suppose to do: 2022-2010+1 . multiply that by .27 cents then 10,000? i thought they bought a total of 10,000 stamps worth 2700 dollars total? thats what it says in the text anyway?

[cedar kiln]

@jade stag Has your question been resolved?

[jade stag]

<@&286206848099549185>

[halcyon marlin]

read the text for d) again carefully

[jade stag]

gotcha

ty

can you tell me why we added +1 each time when calculating the years?

for example 2022-2010+1 = 13

why the +1

[halcyon marlin]

2011 to 2022

• the cost for 2010

its weird might aswell just do 2010 to 2022 only but its the way the problem is worded

they bought it for 2010 first then decide to buy more

gives the same answer

[jade stag]

2022-2010 = 11

you mean the cost of 2010-2021.9999?

[jade stag]

2022-2011 = 11.

we need 2022-2010+1 = 13

why the +1

[halcyon marlin]

did they do 13

or 11

[jade stag]

yes

13

[halcyon marlin]

can see?

[jade stag]

im asking why the +1

[halcyon marlin]

where you see this

[halcyon marlin]

no but youre looking at some detailed answer?

asking why they did 2022-2010+1

[jade stag]

here is

another example

that shows

step by step

it says here

its a similar problem, with different numbers

[halcyon marlin]

yea cause if you do

0 to 11

thats 12 numbers

0,1,2,3,4,5,6,7,8,9,10,11

[jade stag]

whats 0

2010?

[halcyon marlin]

yes

[jade stag]

because it was the begining

but normally you count years

like this

2022-2010

[halcyon marlin]

its because they want enough to last for 2022 aswell

[jade stag]

2010-2011 is 1 year

so then it would be

12.99 years

[halcyon marlin]

lets say you want

to pay for 2010 and 2011

this is 2011-2010=1?

no you want both

2011-2010+1=2

[jade stag]

ah

i see

thanks koter

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[cedar kiln]

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[unreal pelican]

171. so i am getting close to the final answer but their answer has a z and that is throwing me off

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[void axle]

How does
(-2cost)(-sint)+(4sint)(cost)
result to 6sin t cost t

Like i get the 6 but why isnt the answer 6(2cost 2sint)
If i tried it would be like

(-2cost)(-sint)+(4sint)(cost)
2costsint + 4sintcost
6costsint + costsint
6(2cost 2sint)

[ancient lodge]

2costsint + 4sintcost
6costsint + costsint

This jump in logic is wrong, how did you get that?

[void axle]

4+2 is 6 and
theres a costsint left over for the right side

ohh
its like
2(x) + 4(x)
6x

thankyou

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[clear grail]

can someone please explain how to get these?

[slow thicket]

why is everything none

[toxic moat]

yea looks weird lol

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[limber hull]

what does it mean ifa function is defined as being R => R

[marble root]

It means that your inputs are all real numbers and your outputs are also real numbers

[slow thicket]

I dont think thats their question

it just means its a one variable equation

like y = f(x)

[limber hull]

so f(1) = 1?

[slow thicket]

R^2 to R would be z = f(x, y)

[marble root]

Gmail can you clarify your question?

[limber hull]

it just says

f: ℝ → ℝ

and I want to know what that means

like what is f

[slow thicket]

f is a function

that takes one variable and spits out another

[marble root]

F is just a function that takes real number values and outputs real number values

[limber hull]

how would i calc the limit of this function

[slow thicket]

what

[digital cliff]

you havent given us a defined function so we cant say

[slow thicket]

whats the function

[marble root]

^

[limber hull]

it uses the function f in another function

3f(x) + 3

and calc the limit

limit at 1

[cerulean sail]

Show the whole question please

[marble root]

Can you send a picture or screenshot of it?

[limber hull]

no 😭

thats the question

[marble root]

You are missing information for the question

[limber hull]

is there latex in this server

[limber hull]

no

[cerulean sail]

$\LaTeX$

[wraith dagger]

@cerulean sail

[limber hull]

i mean it also says lim 1 of f i= L

[slow thicket]

what

do you mean lim of f(x) as x -> 1 = L

[limber hull]

$\lim_{x \to 1} 3f(x) + 3$

[cerulean sail]

\lim_{x\to 1}

[wraith dagger]

gmail.com

[cerulean sail]

So they give you
[
\lim_{x\to 1} f(x) = L
]
then?

[wraith dagger]

@cerulean sail

[limber hull]

then calculate the limit i just stated

[marble root]

Yeah so then it’s just 3L+3

[limber hull]

surely not

[cerulean sail]

Linearity of limits

[marble root]

All you are doing is applying a vertical stretch of 3 and shifting the graph up 3

The fancy way of saying that is what chart said

[limber hull]

yeah but it seems to simple to just say the limit is L

[slow thicket]

thats the point

it doesnt matter what L is

[slow thicket]

this is still 3L + 3

[limber hull]

but its the only question on the homework 😭

[digital cliff]

dont know what to tell you man, thats all there is

[limber hull]

.close

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[crimson sedge]

help

[obtuse grail]

Do you remember the formula for area of a sector?

[crimson sedge]

r x b

?

[obtuse grail]

what would "b" be in this case?

[crimson sedge]

base

[obtuse grail]

Bases usually apply to 3d shapes, what base are you referring to?

[crimson sedge]

base of a triangle?

[obtuse grail]

Uhhh, not really, in this case the correct formula for area of a sector is: (ø/360º)(πr^2)

This is because of the 360º in the full circle, you are taking ø degrees of the total area

So if you had an angle of 180º, then that you be half the circle, so the ø/360º term would become 1/2 since ø = 180º

Can you try applying this formula to this problem?

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[vivid valley]

help! I need to evaluate this limit. a is an element of real values and is a constant. I have already tried L'Hopital's rule because it has the interdeterminate form of 0/0. But am specifically struggling with differentiating both the top and the bottom to a simpler form. Any suggestions would be great. thanks

[regal oak]

limit when x tends to ?

[vivid valley]

zero

sorry i missed that

[violet flume]

should we go through bit by bit on the differentiation

or is it the algebra on the backside thats a nightmare

[vivid valley]

that would be great if we could

[regal oak]

don't directly go for L-H rule

[vivid valley]

do i need to manipulate it a little first/

[regal oak]

it can be done without differentiation though

try using this to solve them though

[vivid valley]

i was looking at limit rules but i couldnt identify any of them that look similar

ill show the ones in my textbook

[regal oak]

if the 3rd and 5th wud help u out

[violet flume]

,rotate -90

[regal oak]

ohh kk

there are many more though

[vivid valley]

oh okay

[regal oak]

@vivid valley try with these and lemme know wt u get

[vivid valley]

okay thank you!

[cedar kiln]

@vivid valley Has your question been resolved?

[vivid valley]

@regal oak i cant seem to see any that would work in this instance. The only one that is catching my eye is the third, but im unsure as to how that would work with getting just x as the denominator. similarly with 5, does the fact that the x^2 as the indices of e change the fact that it might translate?

im thinking maybe i just do l'hopitals rule so that i know how to properly do it if it comes up in an exam

[regal oak]

give me a sec

see when x tends to 0 x^2 also tends to zero as well as ax^2 ryt ??

[vivid valley]

yep

[regal oak]

so fr numerator
multiply and divide by ax^2

u get

[vivid valley]

over / 1-e^x^2

how does that help with rule number 3?

[regal oak]

no lets operate them separately

[vivid valley]

oh okay

i see loosely what youre doing but i dont understand how to switch the x exclusively to the bottom

[regal oak]

we know that ln(1+x)/x when x tends to 0 becomes 1 ryt ?

[vivid valley]

yes

rule 3

on ur list

[regal oak]

x tends to zero
ax^2 also tends to zero ryt ?