help-33

[dim wasp]

and e^x increases exponentially

[proud ice]

basically, $e^x$ is the frequency, so the frequency is increasing exponentially

[elfin berry]

SWR

[dim wasp]

but how do you figure what it looks like at the beginning?

the straight line

[limber hearth]

Frequency being the number of repetition of a certain motiv

[dim wasp]

straightish

[limber hearth]

e^negative is little

[dim wasp]

same for x being frequency of sinx?

[limber hearth]

Yup

[dim wasp]

ah yes

[limber hearth]

But its a linear increase

So its not sus as e^x

[dim wasp]

and then sub x=0 for y intercept

[limber hearth]

Yeah

[dim wasp]

and differentiate for turning points?

okay awesome tyvm

[limber hearth]

Sure

[dim wasp]

.close

[marsh citrus]

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[marsh citrus]

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[lament yacht]

Calculate the integral of a complex number using the residue theorem

[lament yacht]

one of the derivate in the calculation of the residue (pole z=1) is kinda hard to solve so i’m stuck in that part

there’s another way to solve the problem?

[marsh citrus]

@lament yacht Has your question been resolved?

[marsh citrus]

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[sleek fern]

We're given the matrix A, a,b in R

[limber hearth]

What is col ?

[sleek fern]

a) if b=/=2a is it correct to say Col(A) = Fil(A)

[limber hearth]

Colinear ?

[sleek fern]

Column space

sorry no

[limber hearth]

Ah

[sleek fern]

i forgot to translate

[fervent rampart]

and what is Fil?

[limber hearth]

Ok ok

[sleek fern]

Col is column space Fil is row space

my bad

so i've found both are LI when b=2a

[limber hearth]

Gen is generator right ?

[sleek fern]

span yes

[fervent rampart]

in that case what are the row and column space?

[sleek fern]

oh

dumb

let me work that out

uhh

i'm not sure where to go from here with the row space

i mean

clearly the other vector is of the same form

since a is any R i suppose when a is 2 it's LI

but is i

yeah no its LD

so 2 4 is LD to a 2a i suppose

[fervent rampart]

how did you conclude that (4, 2a) should be removed?

[sleek fern]

well 4,2a is just a linear combination of 2,a

[fervent rampart]

but how did you get that a spanning set for the column space is {(2, a), (4, 2a)}?

[sleek fern]

i replaced 2a in 4,b

[fervent rampart]

but the question is asking for the case where b ≠ 2a

[sleek fern]

okay

okay i may be confused here

let's go back a bit

we're here

we're interested in knowing if when b ≠ 2a, Row and Col are spanned by the same vectors

i've determined that these vectors are LI when b=2a

just one problem though

col is a 2x1 space

row is 1x2

is that relevant in any way

[fervent rampart]

what larger vector space are the column and row space subspaces of?

[sleek fern]

R2X2

[fervent rampart]

well the matrix itself is in R 2x2, but what vector space are the row vectors and column vectors in?

[sleek fern]

col is in R2

in fact

looking at it

i believe if a=/2b then col is a basis for R2

Row is not in R2... right?

R2 is 2x1, col is 1x2

[fervent rampart]

well in both cases we are treating them as vectors with two entries, just arranged differently

[sleek fern]

okay

so if a=/2b for the col space it's a basis for R2

as for the row space...

if b were to be 2a

we'd have

(2 4), (a,2a)

which we can express as

c(2,4) + a(1,2) a,c in R

which would be LD

so it would not form a basis for R2

but if b is not 2a

then they're LI

which means they would both be basis vectors for R2

assuming we're taking the transpose of the row space

so yes, in summary

if b ≠ 2a then Row(A) = Col(A)

i suppose i haven't arrived at a 'proper' answer though but through observation i think thats ok

[fervent rampart]

well if we can conclude that if they are both individually R^2 then that it's valid to conclude that they are equal

[marsh citrus]

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[sleek fern]

alright thanks!

[marsh citrus]

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[arctic flame]

What is the slope of the roof in degrees and
What is the total length of the roof surface?

[marsh citrus]

Please don't occupy multiple help channels.

[arctic flame]

when they mean "slope" what does that mean?

in degrees

can anyone mark it?

which angle

[cloud iron]

Probably these ones

[arctic flame]

yeah, thought so!

[stoic slate]

Gradient

[arctic flame]

the base of the triangles is 4,5m?

9:2= 4,5 m?

ok ill now use trigonometry

[main idol]

i guess we assume the roof is symmetric so that the triangles are congruent?

[arctic flame]

yeah and it wont help

[main idol]

what won't help

[arctic flame]

im using tg here

inv of tg

[main idol]

yes that gives you the angle you marked in red

still don't know what you think it won't help with

[arctic flame]

18,43 °

What is the total length of the roof surface?

so

a*h

[cloud iron]

Think about the trig again

[elfin berry]

Zbigniew Ziobro

[arctic flame]

@cloud iron

[cloud iron]

How are you getting that?

[arctic flame]

surface

so the area of two triangles

[cloud iron]

Is that what it's asking for?

[arctic flame]

What is the total length of the roof surface?

[cloud iron]

I would take that to mean this length

Unless the true question is lost in translation and it really is asking for area

[arctic flame]

ok pytagoras

,calc sqrt4,5^2+1,5^2

[elfin berry]

The following error occured while calculating:
Error: Unexpected operator , (char 6)

[arctic flame]

idiot

[cloud iron]

Do it with . as the decimal point

wolfram is coded to NA format

[arctic flame]

,calc (sqrt4.5^2+1.5^2) * 2

[elfin berry]

The following error occured while calculating:
Error: Undefined symbol sqrt4

[arctic flame]

is he acoustic

[cloud iron]

sqrt(stuff)

sqrt should be outside

[wide citrus]

,w sqrt(4.5^2+1.5^2) * 2

[elfin berry]

Results provided by WolframAlpha

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

Requested by jandro0103

[arctic flame]

voila

[wide citrus]

Did you have to do this?

[arctic flame]

?

[wide citrus]

,calc sqrt(4.5^2+1.5^2) * 2

[elfin berry]

Result:

9.4868329805051

[arctic flame]

i think my teacher doesnt know how to round up

he gave 9,48 m as an answer

which should be 9,49 m if he wants to round it

[wide citrus]

https://tenor.com/view/thumbs-up-double-thumbs-up-like-agreed-yup-gif-16109683157885754862

[arctic flame]

@cloud iron ty sir

[elfin berry]

Result:

4.7445630918967

[arctic flame]

u can close this channel

[cloud iron]

.close

[marsh citrus]

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[marsh citrus]

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[worn musk]

Hi, I am going through the book Concrete Maths and I was introduced to the repoitore method and having some trouble understanding it... I was reading the first answer to this maths stack exchange post to understand it more:

https://math.stackexchange.com/questions/1017498/mathematical-explanation-for-the-repertoire-method

And I was confused by the lines shown in thes screenshot, what exactly does linearity mean in this context? ... I don't understand how this is true

[main idol]

did you understand the next few sentences?

[worn musk]

No I did not, I thought it looked like basic substituation but its not whats going on

I understand how to use the repertoire method after I watched some youtube videos but what I don't understand is the word "linearity" and how they are able to say this? The screenshot I posted above is stated like some kind of intuitive mathematical law -- but I am just not seeing it

[marsh citrus]

@worn musk Has your question been resolved?

[marsh citrus]

@worn musk Has your question been resolved?

[marsh citrus]

@worn musk Has your question been resolved?

[marsh citrus]

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[tepid hound]

Prove that, (AB)^2 is not equal to XY where X= AxA and Y=BxB. A and B are n×n matrix.

[main idol]

Make up any random matrices for n=2

[marsh citrus]

@tepid hound Has your question been resolved?

[tepid hound]

An example is not a proof right?

[brave marsh]

Proving that (AB)^2 != A^2 B^2 in general amounts to showing that in some matrices A,B you have the inequality

[marsh citrus]

@tepid hound Has your question been resolved?

[tepid hound]

Can u elaborate?

[brave marsh]

You are asked to show that $(AB)^2 = A^2 B^2$ does not always hold.

[elfin berry]

Azyrashacorki

[brave marsh]

So it's sufficient to show one case where it doesnt'

[marsh citrus]

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[arctic flame]

Let’s say I have 83 dm in radius.

What’s the formula for circumference?

[arctic flame]

Pi+r^2?

[grizzled sonnet]

2pi * r

pi is just the ratio of circumference to diameter

[elfin berry]

Pro_Hecker

[grizzled sonnet]

so C/D = pi
D = 2r

C/2r = pi
C = 2pi*r

[marsh citrus]

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[marsh citrus]

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[timid osprey]

In a fairground lottery, you can bet on one of the numbers 1.2,...,6. If the selected number appears exactly k times (k=1,2,3) when rolling three dice, you may keep your bet and also receive k times your bet. If the selected number does not appear, the bet is lost. Calculate the expected value and variance of the profit.

[timid osprey]

how do we get to this formula?

[marsh citrus]

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[solemn thunder]

hi

[solemn thunder]

does anyone know how to get the last one

i tried using combination and i got 0.03 or smth

[marsh citrus]

@solemn thunder Has your question been resolved?

[solemn thunder]

No

[marsh citrus]

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[terse basin]

can someone explain how to do 2a for me

[terse basin]

is Sn = n/2 (T1+Tn) the only formula we can use here?

since we don't know what n is

[spare oasis]

You can easily find what n is

an = a + (n-1)d

[terse basin]

do we use Sn = n/2 (2a+(n-1)d)?

[spare oasis]

Doesn't really matter

[spare oasis]

Use this for n

We know the first and last terms

And the common difference

[terse basin]

n=1?

wait wth

a is first term right?

[spare oasis]

Do you know

Ap general term

[spare oasis]

Yes

[terse basin]

Tn = f(n) or smth like that?'

[spare oasis]

Formula

[terse basin]

ohh

[spare oasis]

No 😭

[terse basin]

yea

i do

[spare oasis]

This one

[terse basin]

oh yea

[spare oasis]

We know An which is...?

It's 396 ;-;

A is 204

D is 6

Find n

That's it

[terse basin]

my brains not functioning rn

n=33

[spare oasis]

Ok

Let's start from the BASICS

[spare oasis]

Probably

I didn't check

Yes it's correct

[terse basin]

would i plug into this?

[spare oasis]

That's it

[terse basin]

n=33?

[spare oasis]

Yes

[terse basin]

okay

9900

[spare oasis]

Yep

Congratulations

[terse basin]

thanks man

[spare oasis]

That's correct

[terse basin]

would u know how to do the previous question

the dot diagram

[spare oasis]

Lemme see

[terse basin]

i have some sort of vague idea but i cant put it into words

[spare oasis]

Uhhh

I guess because

They always form a square shape

That's what the basic definition of a square is

The power one

Algebraic proof is easier tbh

[terse basin]

yea that's what i plan on doing

[spare oasis]

Alright

Good luck on that

[terse basin]

but idk how to do it

lol

[spare oasis]

Oh

Well

[terse basin]

i think for n is larger than or equal to 2

u get 2n-1

[spare oasis]

NO

[terse basin]

oh

[spare oasis]

Why would n be greater or equal to 2 😭

First of all

If you can't figure out what to do

Write out what you need to find the expanded form

1+3+5+7+9.....

[spare oasis]

Upto n

Notice anything?

[terse basin]

uhhh each sum adds up to a square

ig??

like 1+3

is 2^2

and there are only two terms

ifykwim

[spare oasis]

I guess

That's what shown

Geometrically

[spare oasis]

In that dot diagram thing

[terse basin]

i get that

[spare oasis]

That's it

[spare oasis]

For the geometric proof

[terse basin]

why can't i write for n is greater than or equal to 2: Tn = Sn - Sn-1

where Sn = n^2

u substitute and get 2n-1

and for T1 = S1 = 1^2 = 1

[spare oasis]

Why does bro want n greater equal to 2

S0 = 0

[terse basin]

cus my teacher said u have to test S1

[spare oasis]

Sum of zero terms

[spare oasis]

So do you need to find out Sn in terms of n?

[terse basin]

idk

[spare oasis]

If you want

Use sum of Ap

a = 1

d=2

I don't understand what exactly do you want though

[terse basin]

nvm i did it

i was overcomplicating ma fault

.close

[marsh citrus]

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[hardy marsh]

Help again PLzz

[marsh citrus]

@hardy marsh Has your question been resolved?

[marsh citrus]

@hardy marsh Has your question been resolved?

[marsh citrus]

@hardy marsh Has your question been resolved?

[hardy marsh]

Help

[marsh citrus]

@hardy marsh Has your question been resolved?

[marsh citrus]

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[vagrant stag]

Not sure how to approach this

[tight kite]

draw diagram

[vagrant stag]

Yes I did

[tight kite]

send

[marsh citrus]

@vagrant stag Has your question been resolved?

[marsh citrus]

@vagrant stag Has your question been resolved?

[marsh citrus]

@vagrant stag Has your question been resolved?

[marsh citrus]

@vagrant stag Has your question been resolved?

[marsh citrus]

@vagrant stag Has your question been resolved?

[marsh citrus]

@vagrant stag Has your question been resolved?

[quiet anvil]

If we call the point AD and BE intersect F, then we have a plethora of triangles and a lot of information about the various angles.

This seems like something that you might be able to solve via angle chasing, using sum of angles in a triangle is 180 over and over again, along with vertical angles around F and the sum of supplementary angles is 180.

If this isn't enough. You might be able to prove similar triangles or something else interesting using the angle bisector theorem

The angle bisector theorem states |BD|/|DC| = |AB|/|AC|

[marsh citrus]

@vagrant stag Has your question been resolved?

[empty saffron]

@quiet anvil try askng in a new channel to get someone's atention

[quiet anvil]

That's not a question

that's an answer, or at least a suggestion

[empty saffron]

oh sorry my bad, I just say a lot of "has your question been solved" I thought someone had used the opportunity to ask for help with something they needed

my bad

[still temple]

lol

[marsh citrus]

@vagrant stag Has your question been resolved?

[quiet anvil]

<@&268886789983436800>

[quaint valley]

!original

[marsh citrus]

Please show the original problem, exactly as it was stated to you, with the entire original context. A picture or screenshot is best. If the original problem is not in English, then post it anyway! The additional context might still be helpful. Do your best to provide a translation.

[marsh citrus]

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[velvet shadow]

Hii

[velvet shadow]

solving linear equations

im stuck

[rocky shoal]

take all the x on a side and the numbers on the other

[velvet shadow]

ok so

[rocky shoal]

the negative 2 goes to the other side with positive

[velvet shadow]

5x and 3x

[rocky shoal]

and the positive 3x goes negative

[velvet shadow]

wait ur too fast what

[rocky shoal]

haha im sorry

it should look like this x=number

[rocky shoal]

yes 5x-3x

[velvet shadow]

uhm

[silent pewter]

5x - 2 = 3x + 6
5x - 3x = 6 + 2
2x = 8
X = 8/2, 4

[velvet shadow]

where did the minus come from

[lucid turret]

Transposition

[rocky shoal]

it went to the other side

goes with a minus if positive

[lucid turret]

x = 4

[velvet shadow]

yeah im trying to figure out how

[lucid turret]

prime just told

you aren't listening to us

[silent pewter]

Collect like terms, whena digit changes its position(LHS and RHS) its became completely opposite

[rocky shoal]

5x-2=3x+6
5x-3x=6+2
2x=8
x=4

[velvet shadow]

i dont need multiple people helping one person at the same time

[silent pewter]

For example
When postive 3x went to LHS its became negative 3x

[velvet shadow]

Oh

[silent pewter]

I guess i will go then

[velvet shadow]

Ty

[silent pewter]

@velvet shadow just one question are you also in 8th grade(just curious)

[velvet shadow]

where did 6+2 come from

[velvet shadow]

No im in 9th

[rocky shoal]

the -2 was with the 5x when it goes to the 6 it becomes a positive

[lucid turret]

I am in 9th too

LOL

[silent pewter]

Oh

[rocky shoal]

im in 12th

[velvet shadow]

that's besides the point, people struggle with math what are you trying to prove

[lucid turret]

damn

[rocky shoal]

did you understand?

[silent pewter]

No offense, but seems quiet easy compare to 9th grade book in my country

[velvet shadow]

wait

[lucid turret]

which country?

[velvet shadow]

guys can you please talk in dms or something

[silent pewter]

India

[rocky shoal]

i can help you out in vc if you want

[lucid turret]

good

same

[velvet shadow]

it's literally like 3 i cant speak

[silent pewter]

Which syllabus

[rocky shoal]

you dont have to ill speak

up to you tho

[velvet shadow]

ok

[silent pewter]

One sec

[silent pewter]

Icse/cbse (ncert or not)

[lucid turret]

cbse

you?

?

[silent pewter]

Same

[lucid turret]

which class you bro

[silent pewter]

8th grade

[lucid turret]

lol

[marsh citrus]

@velvet shadow Has your question been resolved?

[marsh citrus]

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[south goblet]

is there a program or soemthing to solve this linear equations.
I get the exact same solution but all divided by 10

[fluid pelican]

have you tried with matrices?

[south goblet]

to solve it? I solved it with linear equations.

[fluid pelican]

yeah to solve the system

[south goblet]

I haven't but with linear equations it should give the same answer I think

[fluid pelican]

ah ok

well as far as programs

symbolab a website usually does pretty good

[south goblet]

where on the site do I fill in linear equations?

[fluid pelican]

ah I usually look up linear system solver and it pops up

or system of equations solver

[south goblet]

oohh wait I see my mistkake now

[south goblet]

I see I will try that next time

[fluid pelican]

okay

[marsh citrus]

@south goblet Has your question been resolved?

[marsh citrus]

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[modern lintel]

Can someone check if this is correct please? I got the right answer but I wanna make sure I done it correctly

[worldly basin]

you have not done it correctly

you have proved sin2x + cos2x = 1

and not the original identity

to do it correctly, you should only manipulate one of the sides and prove it to be equal to the other

[modern lintel]

ah

okay thank u

.close

[marsh citrus]

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[marsh citrus]

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[short sierra]

need to simplify this

so i can differentiate 2 times

what i got first is just ((cube of x) -1)^2 on the bottom part

$\frac{x+1}{\sqrt[3]{x^2}-\sqrt[3]{x}+1}$

[elfin berry]

Yousef

[short sierra]

$\frac{x+1}{(\sqrt[3]{x}-1)^2}$

[elfin berry]

Yousef

[short sierra]

now im kinda stuck

oh wait no

$\frac{(\sqrt[3]{x}+1)(\sqrt[3]{x^2}-\sqrt[3]{x}+1)}{\sqrt[3]{x^2}-\sqrt[3]{x}+1}$

[elfin berry]

Yousef

[short sierra]

oh nice

thank you universe you've saved me once again

.close

[marsh citrus]

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[marsh citrus]

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[fathom ridge]

[ 2^{2 + \log_4 (25)} - 2^{3/\log_5 2} ]

[elfin berry]

argon

[fathom ridge]

Is that it?

[whole thorn]

why did u even post this

[burnt abyss]

fr

[marsh citrus]

@balmy birch Has your question been resolved?

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[lucid turret]

Find 1/1^2 + 1/2^2 + .................... till 1/n^2 where n = infinity

[burnt abyss]

n=infinity

[distant peak]

||pi²/6||

[lucid turret]

yes

pi^2/6

I know

I want to know how to know

[burnt abyss]

https://www.youtube.com/watch?v=d-o3eB9sfls

watch this

it's a great video

[lucid turret]

Nope

[distant peak]

there is a proof using fourier series
one with Cauchy..
welp im not doing much maths these days so i forgot

[proud ice]

,calc zeta(2)

[elfin berry]

Result:

1.6449340668483

[burnt abyss]

also one with euler's formula and l'hopital

and one with Parseval's identity

[distant peak]

kekw

[burnt abyss]

and Weil's conjecture

on Tamagawa numbers

[lucid turret]

Never mind

.close

[marsh citrus]

Channel closed

Closed by @lucid turret

Use .reopen if this was a mistake.

[lucid turret]

Thanks nonetheless

[burnt abyss]

https://en.wikipedia.org/wiki/Basel_problem

here some of the proofs

if you don't want to watch videos

you're welcome

[lucid turret]

Thank you

,w zeta(3)

[elfin berry]

Results provided by WolframAlpha

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

Requested by anshulyolo121

[marsh citrus]

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[vapid topaz]

Two separate rabbit populations are observed for 80 weeks, starting at the same time
and with the same initial populations. The growth rates of two rabbit populations are
modeled as follows, where t = 0 corresponds to the beginning of the observation period:
r1(t) = 4 sin(2πt/72) + 0.1t + 1, where r1 is rabbits per week, and t is time in weeks,
r2(t) = t^1/2, where r2 is rabbits per week, and t is time in weeks.
A.Find the first positive time t for which the rates of growth are the same (I think I got it right, t=31.718266weeks. Used calculator to find intersection.)
B.What’s the physical significance of the area between the two curves from time t = 0 until the first time where the two rates are the same? What does the area represent? (I think I got this too, area between is the total diffrerence between the rabbits populations. Area = rabbits/week * week = rabbits)
C. Suppose you want to find the first time (call it T) after the beginning of the observation period at which the two rabbit populations have identical populations. Write an equation to solve for the unknown variable T. (I thought just to set integrals from 0 to T of the two functions equal to each other, but considering my part D, im not sure.).
D. Simplify your equation from C until you can use your calculator on it. Then use your calculator to solve this equation for T. (I got 25.45, but this does not make sense when looking at the graphs. Plugging in for T also doesnt work.)

[main idol]

What the hell

[vapid topaz]

I guess part D hinges on part C.
Do you agree with my assessment on C?
The functions are growth rates so the area under the curves are the population. So integral from 0 to T of r1 = integral from 0 to T of r2

[quaint valley]

no way you typeed all that

[vapid topaz]

Im desperate lmao

been stuck for over an hour

[quaint valley]

oh no

for a you have to take the derivative of each as set them equal to eachother

i dont think a calculator will cut it

unless theymatch up perfectly but idk

[vapid topaz]

r1 and r2 are growth rates already, so the first time the growth rates are the same is the intersection of the growth rate functions

[quaint valley]

oh ok

yea

so that should work

[vapid topaz]

I was told to use calculator to approx

[quaint valley]

ok

you only need 3 decimal places also

[vapid topaz]

ok

[quaint valley]

can you explain how you got B

[vapid topaz]

Sure one sec

[quaint valley]

C is right just check your integrals maybe?

[vapid topaz]

These are r1 and r2. Y axis is rabbits per week, and t is time in weeks (given in question). Area between the curves from t=0 to 31.7 is the difference in rabbit population because area under r1 is the population 1 count, and area under r2 is the population 2 count. The area between is these areas subtracted

[quaint valley]

yes

so how did you get rabbits/week/week

[vapid topaz]

y axis: rabbits/week
x axis: weeks
Multiply to get area, week cancels and you get rabbits

[quaint valley]

yes thats nto what you showed tho

rabbits/week/week is rabbits/week^2

[vapid topaz]

Ahh yes forgot parentheses

[quaint valley]

which is the rate at which the rate of the population is changing

you dont need to show that you can just say rabbits

[vapid topaz]

I meant (rabbits/week)*week

[quaint valley]

you can just say rabbits

[vapid topaz]

yeha

[quaint valley]

ok

so what did you get for your integrals for c

[vapid topaz]

So A and B are good then. Do you agree that to find where the populations are equal, you would set the integral from 0 to T of both equations equal to each other

[quaint valley]

yes

[quaint valley]

you need the dx at the end also

other wise c is good

[quaint valley]

need the dx

at the beginnig

[vapid topaz]

thanks

So that is my antiderivative for the first part to find T on the left side

[quaint valley]

what did tyou get for your integral fo sin u

[vapid topaz]

i dont understand your question

[quaint valley]

nvm you showed it ig it didnt load

[vapid topaz]

k

[vapid topaz]

+C at the end, but that cancels later

[quaint valley]

you shouldnt get +c bc its a definite integral

[vapid topaz]

good point

[quaint valley]

only integrals without bounds have c

[vapid topaz]

changing to x for the sake of desmos and I get 25.45 and 37.58

[quaint valley]

whats wrong with that?

[vapid topaz]

Visually you can see it it wrong. From x=0 to x=25, the blue one (r1) is always above the green one, so the population cant be the same

and if i plug one (one sec

not equal

Should I ping backup

[quaint valley]

sure

@wary kite 🥺

[vapid topaz]

<@&286206848099549185>

[wary kite]

why are you pinging me

[quaint valley]

i miss you

[unkempt orbit]

r1(t) = 4 sin(2πt/72) + 0.1t + 1,
r2(t) = t^1/2

For C, r_1 and r_2 must be equal and we must find T

$$t^{\frac 1 2 } = 4 sin(2πt/72) + 0.1t + 1$$

simplify it and use calc on it?

[quaint valley]

no its when the population is the same not the rate

[vapid topaz]

^

[unkempt orbit]

ahh

mb

let's integrate in that case

[quaint valley]

144/pi sin (pi T/36) +.1T^2/2 +T = 2/3 T^3/2

[vapid topaz]

ignore the +Cs

[unkempt orbit]

yep, you can bring that little T on the lhs to the rhs and plot it all

[quaint valley]

lhs?

[vapid topaz]

what is lhs

[wary kite]

left hand side

[vapid topaz]

and rhs

[unkempt orbit]

*left hand side

right hand side

[quaint valley]

yea

[vapid topaz]

whar

[unkempt orbit]

$$-144/pi cos (pi T/36) = 2/3 T^3/2 -0.1T^2/2 -T$$

[elfin berry]

leoh

[wary kite]

🤔

https://www.overleaf.com/learn/latex/Learn_LaTeX_in_30_minutes

[unkempt orbit]

it's almost done gl

[unkempt orbit]

(I was lazy mb)

[quaint valley]

whats that

[wary kite]

$e^x = \sum_{n=1}^{\infty} \frac{x^n}{n!}$

[elfin berry]

knief

[quaint valley]

show me how 🥺

[wary kite]

it’s language for typing math

[wary kite]

^

[quaint valley]

no

show me

[wary kite]

😟

[vapid topaz]

what is going wrong waaaaahhh

[unkempt orbit]

Just keep the cos term on one side, get the rest to the other

So the right should have a polynomial which you can plot

on the calc

[quaint valley]

i got 221

[wary kite]

$r_1(t) = 4\sin(\frac{\pi}{36}t) + 0.1t + 1, \quad r_2(t) = t^{\frac{1}{2}}$

[elfin berry]

knief

[quaint valley]

$f(t) = help me$

[elfin berry]

ℰ𝓁𝓁𝒶

[quaint valley]

hehe

[vapid topaz]

It gets the same~25.45 and 37.5858

which is wrong

[quaint valley]

i got 221

[vapid topaz]

T=221?

[wary kite]

$\int_0^T 4\sin(\frac{\pi}{36}t) + 0.1t + 1 - t^{\frac{1}{2}} , dt = 0$

[elfin berry]

knief

[quaint valley]

you need parentheses

[wary kite]

no

[quaint valley]

yea

[vapid topaz]

im confused

hour 3 of trying to figure this out

[quaint valley]

$\int_0^T (4\sin(\frac{\pi}{32}t) + 0.1t + 1 - t^{\frac{1}{2}}) dt = 0$

[elfin berry]

ℰ𝓁𝓁𝒶

[vapid topaz]

is that not the same thing that will lead to th same result????

[wary kite]

$\frac{144}{\pi}\cos(\frac{\pi}{36}t) + 0.05t^2 + t - \frac{2}{3}t^{\frac{3}{2}} \rvert_0^T = 0$

[quaint valley]

its just better notation

[elfin berry]

knief

[quaint valley]

im being picky

[vapid topaz]

These are different numbers now

how did you get pi/32 now

and 128?

[quaint valley]

i got 222 idk what to tell you

[vapid topaz]

As T?

[quaint valley]

yes

[wary kite]

$\frac{144}{\pi}-\cos(\frac{\pi}{36}T) + 0.05T^2 + T - \frac{2}{3}T^{\frac{3}{2}} - \frac{128}{\pi} = 0$

[elfin berry]

knief

[vapid topaz]

it is outside 80 week range too

[quaint valley]

lol

oops

well thats what i got from what leon said

;/

[wary kite]

,w solve \frac{128}{\pi}\cos(\frac{\pi}{32}T) + 0.05T^2 + T - \frac{2}{3}T^{\frac{3}{2}} - \frac{128}{\pi} = 0

ugh

[vapid topaz]

what is happening

[quaint valley]

nvm my equation was wrong

[elfin berry]

Failed to get a response from Wolfram Alpha.
If the problem persists, please contact support.

Dec 8, 2024, 8:22 PM

[quaint valley]

i still got one at 25 weeks

[vapid topaz]

i keep getting that too but it is wrong somehow

[vapid topaz]

.

im so tilted

ive been trying to figure this single thing out for 3 hours

[vapid topaz]

where are you getting that equation from?

it is pi/36

and 144/pi

[wary kite]

👆🏻

[vapid topaz]

and how did you get that

[wary kite]

oh oops pi/36

lemme fix that

[nimble flare]

i need helping factoring trionmaials

[quaint valley]

why at 37 wouldnt it work?

[quaint valley]

make a help channel #❓how-to-get-help

[nimble flare]

how

[vapid topaz]

Do I get a third helper lmap

[quaint valley]

make no sense

[unkempt orbit]

This is what you should get on your calc

[vapid topaz]

it is 144/pi, 4*36

[wary kite]

^

[vapid topaz]

That is not T

[wary kite]

🤔

then what is it

[vapid topaz]

IDK bruh

ive been trying to figure that out for over 3 hours now

[quaint valley]

........

try that?

[unkempt orbit]

Don't I used the wrong coefficient

[quaint valley]

oh

[unkempt orbit]

Here is the correct one

[vapid topaz]

Clearly not, at x=14 r1 is visually bigger than r2

it is somewhere in the hump after 31.78

[quaint valley]

yea

[unkempt orbit]

But that's just the rate

[vapid topaz]

The area

not the line

[quaint valley]

the area under the curve is the rabbits tho

[vapid topaz]

The area under r1 is bigger than the area under r2

Im gonna ask for more help lmao

<@&286206848099549185>

[wary kite]

oh lol

wait

my fault hold on

i forgot a -

$-\frac{144}{\pi}\cos(\frac{\pi}{36}T) + 0.05T^2 + T - \frac{2}{3}T^{\frac{3}{2}} + \frac{144}{\pi} = 0$

[vapid topaz]

i dont understand what you are doing. And where does 128/pi come from?

[elfin berry]

knief

[wary kite]

hush

[vapid topaz]

wtf

[unkempt orbit]

128 was a mistake

[quaint valley]

omg guys

its bc cos of 0 is 1

[vapid topaz]

no way....

hold on

[wary kite]

now be quiet

thank you

[quaint valley]

lol

[vapid topaz]

tysm im so done with this

[wary kite]

👍🏻

[vapid topaz]

So I close now?

[wary kite]

!done

[marsh citrus]

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

[vapid topaz]

thanks yall

.close

[marsh citrus]

Channel closed

Closed by @vapid topaz

Use .reopen if this was a mistake.

[quaint valley]

That’s my work

[wary kite]

so glad you could figure it out

[quaint valley]

lmao

you didnt say it so

[wary kite]

also it’s 144/pi

[quaint valley]

nice calc

mhm

[wary kite]

i gave him the answer?

[wary kite]

^

[quaint valley]

the answer

but he was missing cos (0)

which was the problem

[vapid topaz]

yeah

[wary kite]

nah i just forgot to negate cos when i took the anti derivative of sin

[quaint valley]

i didnt catch it until the end

when i did it myself

[quaint valley]

oh, well when you do the int you have to evaluate at 0 and cos of 0 isnt 0 so .......

[wary kite]

😟😟

[quaint valley]

and he didnt do that

[wary kite]

i’m not talking about his work

[quaint valley]

ik

[wary kite]

i was referring to mine

[quaint valley]

but i was helping him not you ❤️

[wary kite]

you didn’t

i did

[quaint valley]

you can make a help channel #❓how-to-get-help

[wary kite]

!help

!hekp

omg

!help

[marsh citrus]

To ask for mathematics help on this server, please open your own help channel or help thread. See #❓how-to-get-help for instructions.

[quaint valley]

i helped him find his mistake you just gave him the answer lmao

man shrug

[vapid topaz]

Thank you both for your time.

[quaint valley]

youre welcome ❤️

if your question has veen answered you can close the chat with .close

[wary kite]

it’s already closed ma’am

[vapid topaz]

.

[quaint valley]

oh yuou did

lmao

welp byeeeee

🙂

[vapid topaz]

bye

ty ty ty

[quaint valley]

stop hating knife

[vapid topaz]

lmao

[marsh citrus]

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[faint geode]

Could anyone help me with this problem? I'm unsure as to where to start

[marsh citrus]

@faint geode Has your question been resolved?

[marsh citrus]

@faint geode Has your question been resolved?

[marsh citrus]

@faint geode Has your question been resolved?

[marsh citrus]

@faint geode Has your question been resolved?

[marsh citrus]

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[pine palm]

how to solve?

[quaint valley]

Do you know how to do a reflection?

[pine palm]

no.

[quaint valley]

Ok so when you’re reflecting vertically (along the x axis) you want the opposite sign

So what would you do to f(x) to reflect jt along the x axis

[pine palm]

Make it negative

[quaint valley]

Yessss

Ok so now we have f(x) = -(2^x)

Do you know how to do a stretch?

[pine palm]

no

[quaint valley]

Ok so a stretch is multiplying a function by a factor to make it larger essentially

In this case our factor is 3

So how do we make f(x) 3 times larger?

[pine palm]

3x3

[quaint valley]

3x3?

[pine palm]

3^3?

[quaint valley]

No just 3

[pine palm]

Ok

[quaint valley]

^3 would make it 27 times larger lol

Ok so now we have f(x) = -3(2^x)

Do you know how to compress a function?

[pine palm]

replace x

by 1/4

[quaint valley]

We aren’t replacing x you keep it

We multiply x by 1/4

[pine palm]

so 4

[quaint valley]

Yea

You get f(x) = -3(2^(1/4)x)

Oh no it says 1/4

Do you understand?

[pine palm]

yes

but why do we keep the x

[quaint valley]

Yes the x is there

[pine palm]

sorry i miss typed

[quaint valley]

Because we aren’t changing the function we are manipulating it

Like we will get different values but if we get rid of x it’s no longer a function

X is there so when we input a value we get another value out

And are changing what we get out right now by using these rules

[pine palm]

Sounds good

[quaint valley]

Ok good

Do you know how to translate 1 unit to the right?

[pine palm]

no

[quaint valley]

Ok so this one goes along side x again

And to go to the right what do you think the sign needs to be on the one?

[pine palm]

negative

[quaint valley]

Yessss

Good job

Ok so when you do this you are putting it in parentheses with x btw

So then you get f(x) =-3(2^(1/4)(x-1))

Understand?

[pine palm]

Ya

[quaint valley]

Ok then do you know how to translate up and down

[pine palm]

is it -3?

f(x) =-3(2^(1/4)(x-1)) - 3

[quaint valley]

Yes

[marsh citrus]

@pine palm Has your question been resolved?

[marsh citrus]

@pine palm Has your question been resolved?

[pine palm]

@quaint valley do we add the 1/4 part in the final equation?

cuz this is diff

[marsh citrus]

@pine palm Has your question been resolved?

[cursive sierra]

Is there anyone to study with?

[marsh citrus]

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[fallow fern]

Hi guys im new here👋, I’m kiky and Sorry if im oot but is there any native teacher that willing to i interview for my assignment?

[proud arch]

Hey @fallow fern,
I would appreciate if you go read #❓how-to-get-help first so as to understand what exactly is the point of this server and how it can be useful to you.

.close

[marsh citrus]

Channel closed

Closed by @proud arch

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[marsh citrus]

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Send your question here to claim the channel.

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[gloomy merlin]

Or maybe this requires further information?

[modern sorrel]

You can simply write out the equations for V2 and I2 from the first one and move things around until you get a form suitable for the second one.

Check my math, but I got
$V_1 = -I_1Z_0\frac{sinh}{cosh}+I_2Z_0\frac{1}{cosh}$ and $V_2 = -2I_1Z_0sinh + I_2Z_0$

[elfin berry]

LooseEthics

[marsh citrus]

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[halcyon lark]

I keep screwing up the understanding of the Fundamental Theorem of Calculus. I do not mean the intuition, but rather actually computing them.

If cot(t^5) is f(t), and F(t) = the integral, then F'(t) is f(t).

So, calculating things normally, we'd do F(b) - F(a). Here, that'd be F(x^2) - F(2). F(x^2) is going to require the chain rule, so we need the derivative of the outer function times the derivative of the inner function.

The derivative of the outer function will be f(t). The derivative of the inner function will be 2x. F'(2) will just be 0.

[halcyon lark]

But putting these things together, I get bad answers. For example, if F'(x^2) is the outer derivative times the inner, my mind wants to do cot((x^2)^5) * 2x.

But, apparently the answer requires a cot(t^5) term as well. I cannot see where that term is coming from.

[amber birch]

it probably comes from the product rule, cause the integral is being multiplied by x

[halcyon lark]

I genuinely just ignored that x, so that's bad.

Okay, assuming the x was not out in front, would my answer and reasoning be valid?

[amber birch]

absolutely, that's beautiful reasoning

couldn't have explained it better myself

[halcyon lark]

Appreciate it! Thanks as well for having better eyes than me. It helped 🙂

.close

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[naive topaz]

Why do I get to sinx=cosx if I do integration by parts with u=sinx instead of u=e^x?

[amber birch]

now with u = cos x and dv = e^x, you have that du = -sin x

[naive topaz]

Ahh

[amber birch]

so it should be $- (-\int e^x (-\sin x))$ or that your $+$ should be $-$

[naive topaz]

Thank you so much

[elfin berry]

south

[amber birch]

np!

[naive topaz]

.close

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[slender quarry]

Alright, I've got a linear algebra question. I'm stuck trying to figure out the basis for the image of this matrix. I've taken the columns with the leading 1's in them, gone back to the original matrix and put those as my basis vectors, but the textbook is saying the basis should be { [1,0] , [0,1]}.
I get their logic, basically im T = R2, and R2 is 2D space, so a basis for 2D space is {[1.0].[0.1]}, but what's wrong with my basis?

[slender quarry]

here's my work along with the question

it might be the case that my answer is just fine too, since there are plenty of basis that can apply to a given space

[marsh citrus]

@slender quarry Has your question been resolved?

[slender quarry]

<@&286206848099549185>

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[glossy harness]

Hi, I need to differentiate f(x) with respect to x, but there are 2 variables t and x inside the integral, I thought of using the FTC, but what do I do with that x inside the integral?

[fossil tide]

ye

use leibnit'z rule

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[tulip sundial]

RELATED RATES QUESTION:

[tulip sundial]

i just want someone to confirm my work
V = 4/3 pi r^3

dV/dt = 32in^3/s, want to find dr/dt at r = 2inches

dV/dt = 4 pi r^2 dr/dt
32 = 4 pi r^2 dr/dt
rearrange for dr/dt, plug in r = 2

[marsh citrus]

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[faint geode]

Hi, could anyone help me with this problem? I'm unsure as to where to start

[regal coral]

$\mathcal{E}(x)=\begin{cases}
|x|^\delta \cos\left(1/x\right) & x\neq0 \
0 & x=0
\end{cases}$

[elfin berry]

Axe

[regal coral]

i think this would be continuous at 0 by the squeeze theorem

[marsh citrus]

@faint geode Has your question been resolved?

[faint geode]

yeah I'm guessing that too

[regal coral]

then

$f_{1}(x)=x\mathcal{E}(x)$

[elfin berry]

Axe

[faint geode]

wha

[regal coral]

that will help us show that f_1 can be expressed in the desired form

[faint geode]

but how is that the case?

[regal coral]

you can show it by considering the two cases x!=0 and x=0

[faint geode]

oh ok thanks

[regal coral]

$\text{if}\ x\neq0:\
f_{1}(x)=x|x|^{\delta}\cos(1/x) \ x\mathcal{E}(x)=x|x|^{\delta}\cos(1/x)$

[elfin berry]

Axe

[regal coral]

$\text{if}\ x=0:\
f_{1}(x)= x\mathcal{E}(x)=0$

[elfin berry]

Axe

[marsh citrus]

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[upbeat helm]

.

[upbeat helm]

I just need help with this

[main idol]

,rotate

[upbeat helm]

The domain is -1 , +infinity right?

[high trellis]

I just know. that e= 2

🙂

[marsh citrus]

Please read the channel description before posting, and stay on topic.

[upbeat helm]

that doesn't help😆

[high trellis]

My arithmethics and algebra are a bit faster 🙂

[upbeat helm]

So is this algebra channel or smh?

[main idol]

what does your class define "variations" as?

[high trellis]

Well infinity can't be less then 0

🙂

[upbeat helm]

For example this thing is called a table of variations

[main idol]

,rotate

[upbeat helm]

But not for a logarithmic function

[main idol]

yea that doesn't help

[upbeat helm]

isn't the table of g(x) the same of h(x)?

But starting from -

-1

probably should be smh like this

[main idol]

,rotate

[upbeat helm]

so do you know how to do it?

[main idol]

still don't know what "variations" is

[upbeat helm]

This over here is table of variations of f

[main idol]

that doesn't define variations

examples aren't definitions

[marsh citrus]

@upbeat helm Has your question been resolved?

[marsh citrus]

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[tough wind]

hello