help-49

[mighty tree]

i meant

times 1

thats a times

[buoyant yoke]

what?

[mighty tree]

its times 1 right?

or did i made a mistake differnatining it

[buoyant yoke]

$\dv{(x\sqrt{x+4})}{x}=\sqrt{x+4}+\frac{x}{2\sqrt{x+4}}$

[grizzled mirage]

your picture is blurry, how can anyone understand

[grand pond]

Bonk

[buoyant yoke]

i can understand just fine

[mighty tree]

OHHH

alright my bad

so we set it=0 right

den we get 3x+8=0 x=-8/3

[buoyant yoke]

yup

[mighty tree]

err sub that into eqn of rectangle and we are done?

[buoyant yoke]

yup

[mighty tree]

erm

i got -area

[buoyant yoke]

yeah

[mighty tree]

did i mess up or smth

er wat

[buoyant yoke]

take the absolute value of that

[mighty tree]

oh

[buoyant yoke]

its because our width is actually -x

because our x is negative

[buoyant yoke]

(or |x|)

[mighty tree]

oh wait

the ans is

x2

so its 6.16 as ans rounded up

[mighty tree]

ohh

13 ye

[buoyant yoke]

boom

[mighty tree]

erm wat

its also possible ans key might be wrong

it was wrong once in a qn

[buoyant yoke]

hm?

you got it right tho

[mighty tree]

huh

i got

using mod

8/3

but ans is

16/3

[buoyant yoke]

??

[mighty tree]

no wait

6.16 is ans

[buoyant yoke]

,w 8/3*sqrt(-8/3+4)

[grand pond]

Results provided by WolframAlpha

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

Requested by .bonk__

[mighty tree]

ah yes ans is

twice that value

that long decimal place

[buoyant yoke]

ohhh, right

look at the height

[mighty tree]

uh huh

[buoyant yoke]

remember at the very start, i said its symmetric around x-axis?

[mighty tree]

hmm yes

[buoyant yoke]

we only have the top half of the rectangle

[mighty tree]

hmm why

didint we set length as sqrt(x+4)?

[buoyant yoke]

yes

[mighty tree]

which shld be the whole length right

[buoyant yoke]

but its length is actually 2sqrt(x+4)

[mighty tree]

oh

wait wat why

[buoyant yoke]

sqrt(x+4) is only from x-axis to the curve

[mighty tree]

ohhh

hmm i understand tyty!!

i do have another qn

can i post here

or do i js make a new one

[buoyant yoke]

up to you

idm

[mighty tree]

aight qn 12 er all ik is that h+r= radius of sphere

from info of wn

qn

i guess i need to express h in terms of r before i can differenatite it

but i kinda sub in and yea im stuck

[buoyant yoke]

first look at the 2d case

[mighty tree]

hmm triangle and circle?

[mighty tree]

hmm yes

[buoyant yoke]

and then you need to find a relation between h and r

obviously, we want the triangle to always hit the circle

[mighty tree]

i have no idea how to find the relation 💀

[buoyant yoke]

i tihnk its better to start a new channel

get some fresh minds

[mighty tree]

hmm sure np np

thanks still!

.close

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[wintry palm]

Im not really sure how to solve this, any tip would be very appreciated. the instructions are: "Write the size of the angles <IJE and <FEJ"

[buoyant yoke]

is HI a straight line?

[wintry palm]

yes

[buoyant yoke]

are you familiar with the inscribed angle theorem?

[wintry palm]

yes

[buoyant yoke]

so then can you find angle EFG?

[wintry palm]

its 63 isn't it?

[buoyant yoke]

yup

[wintry palm]

well i came this far already, i just dont know how to get ije and fej

[midnight plank]

@wintry palm Has your question been resolved?

[lethal owl]

Is D the center of the circle
Like why are there no information for the question?

[wintry palm]

Yeah D is the center, I don't know what information to add, the only information i have is the picture and the instructions

[heady plume]

If EFG = 63°, then EJG = ??

Remember, opposite angles in a cyclic quadrilateral are supplementary

[wintry palm]

so 117?

so thats mean IJE is 63

[lethal owl]

You can check that via the properties of the cyclic quadrilateral
What properties do you know about the cyclic quadrilateral

You know what's a cyclic quadrilateral is right?

[heady plume]

Yep

Can you similarly do FEJ?

You have FGJ given

[wintry palm]

so that means FEJ is 92

i get it now

thanks for your help

.close

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[ionic thicket]

for a one-tailed test how do i know if i should use the left or right tail?

[lavish venture]

what’s the context

[ionic thicket]

i want to know when to reject critical value and when to not

the inequalities are confusing to me

i'm also self learning this

[lavish venture]

ok but again it depends on what the context of the problem is

what is your alternative hypothesis

[ionic thicket]

,rotate

[ionic thicket]

H1: mean of differences > 0

[lavish venture]

sure but what difference before - after or after - before

[ionic thicket]

After - before

[lavish venture]

so since $\delta > 0$ we consider a rejection region of $t \geq t_{0.05}$

[grand pond]

knief

[ionic thicket]

why is that?

[ionic thicket]

wait what does the first part mean

delta > 0

[lavish venture]

delta is the mean difference

after - before

[ionic thicket]

true

it is bigger than zero

why do we consider a rejection region of t>=critical value of 0.05

[lavish venture]

i’m not sure i know what you mean?

are you confused about what a rejection region is?

or what a critical value is?

[ionic thicket]

i know what those two are but im not sure about when to do t>= or t<= ,sorry

[lavish venture]

because our alternate hypothesis is delta > 0 which corresponds to that region for the t distribution

if it were delta < 0 then it would be t <= -t_alpha

[ionic thicket]

oh so we retain the sign

hmm that's interesting, i never knew it mattered

[lavish venture]

well what do you think hypothesis testing really is?

[ionic thicket]

i am not sure

[lavish venture]

all we’re doing in this example is considering the probability distribution (which is a t distribution assuming the null hypothesis is true) and testing to see if our test statistic falls within a region that we determine to be statistically significant according to whichever significance level you use

and the significance level is just the probability of what’s called a type 1 error or just the probability of falsely rejecting the null hypothesis

[ionic thicket]

😭 this is quite complicated

[ionic thicket]

can i say that the t distribution which assumes the null hypothesis only holds within the non-critical region?

[lavish venture]

i recommend you go watch some videos by "very normal"

to help build the intuition

[lavish venture]

wdym "only holds"

[ionic thicket]

uhhhh

[ionic thicket]

thank you

[ionic thicket]

since we are assuming something for null hypothesis

[lavish venture]

the t distribution we use is a probability distribution which assumes the null hypothesis is true

[ionic thicket]

why does a critical region exist then?

[lavish venture]

did you read what i said earlier?

[ionic thicket]

sorry

ill watch some videos on this

thanks for your time

[lavish venture]

you’re welcome

go down the rabbit hole with this

https://youtu.be/FZ2_hzMyJpY?si=4POWFyKFqwfTZPS2

it should recommend others after this too

[ionic thicket]

thx 🙏

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[dusty aspen]

I want to find the 'asimptote'

How?

[lavish venture]

vertical asymptote?

[dreamy lichen]

maybe both

[lavish venture]

do you know what this is

[dusty aspen]

I know that I need to use these formulas

[dusty aspen]

yes, all

what are the nullpoints of the f(x) ?

[lavish venture]

to find the vertical asymptotes find values of x such that the denominator is zero while the numerator is nonzero

[dusty aspen]

This gives me 2 and -2

the null points

[lavish venture]

those are the zeros of the function

[dusty aspen]

I have some sort of solution here

but why did we use 1 and -1 when our null points are 2 and -2

So I am confused by that

[prime sequoia]

1 and -1 are the null points of x^2 - 1, that is, the denominator of the rational function

[dusty aspen]

I know that, yes

So, how do I know which null points to use, numerator's or denominator's?

@lavish venture @prime sequoia @dreamy lichen

[lavish venture]

!noping

[midnight plank]

Please do not ping individual helpers unprompted.

[lavish venture]

i told you

[lavish venture]

^

[dusty aspen]

Okay, so we use 1 and -1 here for vertical asymptotes.

.solved

[midnight plank]

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[pulsar plover]

someone pls provide me a method to solve this logicalllogically

i got the answer but i feel like iit ""skipped steps"

or from luck

pprobably only ggot the answer sisince i was working with the answer on the book

[midnight plank]

@pulsar plover Has your question been resolved?

[autumn canopy]

Does that say X^t (X transposed)?

If you can diagonalize a matrix (orthogonally or not), it will always have the eigenvalues on the diagonal

So basically, you just orthogonally diagonalize it and get X as transformation matrix

But it seems that the matrix does not have 1, 2, 3 as eigenvalues, so this is not possible

A brute-force way would be to set X = ((a, b, c), (d, e, f), (g, h, i)), but that would be nasty

[midnight plank]

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[orchid grove]

How to expand the function (1+1/sinx)^x

[fallow scarab]

expand for what purpose

[orchid grove]

So that I can find limit at x tends to 0+

[fallow scarab]

yea that has better context

next time just state the original problem

you don't actually do what you originally askedto solve this problem

you use $a^b = \exp^{b \log(a)}$

[grand pond]

riemann

[orchid grove]

Actually i was on the same path

But no clue

[fallow scarab]

,rccw

[fallow scarab]

you can probably just l'hopital from here

[orchid grove]

I'm lost somewhere

[midnight plank]

@orchid grove Has your question been resolved?

[orchid grove]

@fallow scarab

[fallow scarab]

did you do what i suggested

[fallow scarab]

here

[orchid grove]

...

[fallow scarab]

that doesn't look anything like l'hopital

[orchid grove]

u.v differentiation

Did I make mostake?

[fallow scarab]

https://math.libretexts.org/Bookshelves/Calculus/Calculus_(OpenStax)/04%3A_Applications_of_Derivatives/4.08%3A_LHopitals_Rule

$x = \frac{1}{\tfrac{1}{x}}$

[grand pond]

riemann

[surreal moon]

(for nonzero x)

[midnight plank]

@orchid grove Has your question been resolved?

[midnight plank]

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[mental lodge]

A family wants to build an extension to their current house. It is estimated that the extension will cost 500,000 DKK.

3a) Calculate the monthly payment on the annuity loan if the family borrows 500,000 DKK at an interest rate of 1% per month and repays the loan over 60 months (5 years).
Since the family pays both interest and principal on the loan, their total expense over the 5 years is greater than 500,000 DKK.

3b) What is the family's total expense for the loan (interest + principal) over the 5 years?

Interest expenses on loans are particularly important because they can be deducted from taxes. Therefore, the family needs to know the total interest expense on the loan to plan their budget.

3c) How much does the family pay in total interest on the loan over the 5 years?

[mental lodge]

How do I caculate these questions using this formula?

I´m kinda dumb and really don´t know this and I´m trying to explain this to my kid

This is my work but I know I did it wrong somewhere

only did 3a until I came to this conclusion and kinda figured I´m out of my debt here

and also, I have these follow up questions:

Instead of borrowing the money, the family mentioned earlier can choose to save the entire amount before starting the construction. The family has a savings account in the bank that offers an interest rate of 0.5% per month.

4a) How much can the family save in 36 months (3 years) if they deposit 2,000 DKK into the savings account each month?

4b) How long will it take the family to save 500,000 DKK if they follow the above savings plan?

4c) How much does the family need to deposit into the savings account each month to save 500,000 DKK in 4 years?

4d) If the family succeeds in saving the amount in 4 years, how much cheaper is this for them compared to taking the loan mentioned in question 3b?

where I´m supposed to use this formula

I kinda need someone to hold my hand and guide me through this so I can explain it to my kid, or maybe just give me the correct numbers and I can figure it out by myself

<@&286206848099549185>

<@&286206848099549185>

anyone online?

[wicked oak]

I am!

Just give me a second!

[mental lodge]

hey ami

sry

amy

thank you sooo much

I just feel dumb at this point

[wicked oak]

No worries

Shall I do 3a too

[mental lodge]

at this point I´m asking for all the help I can get

I´m kinda in a time crunch and I told my daughter I would teach her that in the morning

but I havent done math in over 20 years like this

tried youtube, tried google

[wicked oak]

It’s fine!

[mental lodge]

but I need a person to actually help me

[wicked oak]

There’s this app called Gauth math that is shows like how to work it out

[mental lodge]

ok

[cedar coral]

you're not supposed to just give away the answers, Amy

[mental lodge]

ok, awesome, no idea how you got 3a

I see, I´m sorry, I´m new in this channel, mostly because of my daughter, I need to get smart agin somehow

[cedar coral]

well then, the first step would be looking at what each term of the formula means

Can you tell me what A, b, r, and n are?

[mental lodge]

r is the interest rate right, n is the amount of time, b shoukld be the amount they put in... how am I doing this far?

and a should be my answer

right?

also, please dont give amy any grief if she helped me wrong, I´m new here and dont really know what I´m doing

[cedar coral]

okay, so in your problem statement, can you tell me each of these?

basically, the only difficulty of this problem is being very careful in which term is what in each formula and the problem statement

[mental lodge]

b= 2000, r= 0,5, n= 36

right?

[cedar coral]

r is not correct

0.5 =/= 0.5%

[mental lodge]

yeah ok, fair, but I´m curious in that case, how does that diffrence alter the outcome?

[cedar coral]

if you put 0.5, that's the same as 50%

[mental lodge]

oh shit

[cedar coral]

remember that the % symbol means "divided by 100%"

[mental lodge]

yeah of course

Im dumb

sorry

[cedar coral]

details like that are like 99% of the mistakes. Maths are mostly "do this exactly"

and if you deviate on something that "looks" the same, it's usually a fuckup

[mental lodge]

haha, yeah, thats true

[cedar coral]

that's why you want to pay as much attention to details as you're capable of

and why you want to do shit slowly, but guarantee they are right when you actually write them

[mental lodge]

so its 0,05

[cedar coral]

that would be 5%

[mental lodge]

right?

no

0,005

there

[cedar coral]

correct

[mental lodge]

right?

thank you for holding my hand

but n is still 36

and b is 2000

right?

Got this far, but now I’m just uncertain of what it is I actually calculated…😕

am I in the realm of being right?

[midnight plank]

@mental lodge Has your question been resolved?

[midnight plank]

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[smoky bronze]

can anyone help me in this pls

[hearty rune]

i do not like this diagram

just gotta say

but ill try work with it

what do you think so far

[smoky bronze]

im confused on number 1 2 and 3

[hearty rune]

in what way?

[smoky bronze]

Does the figure have 3 planes??

[dapper yoke]

Yes

It is 3D

[smoky bronze]

oh

in total it has 6??

[dapper yoke]

No just 3 for each dimension in this case

[hearty rune]

we cant really assume that, only 3 are visible

[dapper yoke]

If you look at the excercise, 1. is asking you to find a line that intersects the planes r and p

Can you find it?

[smoky bronze]

is it line l

[dapper yoke]

Yes

Now 2. is asking you which plane contains the points Q, Y and V

Do you see it?

[smoky bronze]

wait

[dapper yoke]

In the picture, the plane R contains no points

[smoky bronze]

is it plane or a line

[dapper yoke]

It may be both i guess

[smoky bronze]

plane p??

[dapper yoke]

Yes

But the plane P contains the line m right?

so i guess both are correct

[smoky bronze]

you said there is 3 planes so their names was r and p what is the other??

[dapper yoke]

The other one is at the top

It has no name, but it contains W

[smoky bronze]

ooh

[dapper yoke]

Probably if it has no name it will not be the answer to any question

[smoky bronze]

they are collinear so its line m

[dapper yoke]

Now in 3. coplanar points are the ones contained in the same plane

[smoky bronze]

a, b and c?

[dapper yoke]

Yes

Now keep going by your own

[smoky bronze]

am i correct in this

[dapper yoke]

The question asks for something that contains Q, Y and V, but it doesn't specify if it should be collinear or coplanar

But I think your answer is better

[smoky bronze]

Last one please the number 5

[dapper yoke]

Do you know what parallel means?

[smoky bronze]

idk

[dapper yoke]

Lines that will never cross each other

[smoky bronze]

line k and m?

[dapper yoke]

If you were to extend them, they will never touch

Yes

That is the answer

You should learn this

[smoky bronze]

Thank you

[dapper yoke]

No problem

[smoky bronze]

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[granite cipher]

Does this proof count?

This is what the answer sheet did

[surreal moon]

No.

[granite cipher]

What's wrong with it

[surreal moon]

Why does $\sup X\le\sup Y$ imply $\sup(X\cup Y)=\sup Y$?

[grand pond]

SWR

[granite cipher]

Surely if the sup y is greater than sup x then, y has the largest upper bound which means a set with x u y , y is still the upper bound?

[surreal moon]

The argument is a little weak, but i get what you're saying.

But, at best, all you have done is show that sup Y is an upper bound. But not the least

[granite cipher]

How do I make it more thorough

[surreal moon]

Use the definition of supremum and upper bound

[granite cipher]

Does it matter that both sets are bounded above?

[surreal moon]

If a set is bounded above, then it has a supremum

[granite cipher]

Ah okay

I'm looking at their proof

Why did they not prove max(supY,supX) part?

[surreal moon]

They looked at just the case where supX<=supY. The opposite case is just the same idea so the proof is implicit

They explain the reasoning in the first paragraph

[granite cipher]

I understand that

But isn't the proof meant to prove sup(X u Y)= max ( Sup X, Sup Y)?

[surreal moon]

Yes. What is making you think it doesn't do that?

[granite cipher]

Nevermind I see it

I find proofs confusing in terms of what needs to be said

[surreal moon]

Yeah it takes time to learn it all

[granite cipher]

Yea thanks tho

.close

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[graceful ferry]

how to prove if $f: [a,b] \rightarrow \mathbb{R}$ is continous and injective then it's stirctly monotone?

[grand pond]

prograce

[brazen palm]

On first thought, proof by contradiction

[midnight plank]

@graceful ferry Has your question been resolved?

[graceful ferry]

Do I assume it's monotone or not monotone at all ?

Like weakly monotone or not monotone

[brazen palm]

should assume:
non-"strictly monotone"

[cedar mason]

as in, a monotonic function?

ive never heard the word monotone before

but apparently its used

[graceful ferry]

Ok will try

[odd solar]

So you’ve heard of monotonic functions but not monotone?

[brazen palm]

and IVT (for reference)

[cedar mason]

i would definitely try contradiction yes

[graceful ferry]

I've done it

Thx

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[hearty island]

oh what

whasta a monotone

never heard of it

[midnight plank]

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[viral dagger]

if $p$ is a prime in the form of $a^3-b^3$, then prove it is also in the form $c^2+3d^2$ (a,b,c,d are pos integers obv)

[grand pond]

skissue.in.a.teacup

[viral dagger]

so $a^3-b^3=(a-b)(a^2+ab+b^2)$ and since $a^2+ab+b^2>1$ then $a-b=1\implies a=1+b$

[thorn sorrel]

factor a^3 - b^3

[grand pond]

skissue.in.a.teacup

[viral dagger]

subbing back gives $3b^2+3b+1$

[grand pond]

skissue.in.a.teacup

[viral dagger]

im not sure how to continue this

[midnight plank]

@viral dagger Has your question been resolved?

[heady plume]

Suppose b is odd, then b = 2k + 1 => 3(4k² + 4k + 1) + 3(2k + 1) + 1 = 12k² + 18k + 7 = 3(k+1)² + (3k+2)²

Can you work it out for b even?

T'is easy

[viral dagger]

12k^2+6k+1=3k^2+(3k+1)^2?

[heady plume]

Ahaan ✓

[viral dagger]

oo thank you!

.close

[midnight plank]

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[heady plume]

@viral dagger quick question, where you getting these Qs from

[viral dagger]

my teacyer

[midnight plank]

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[sullen moss]

In this exericse it want us to show that M is subspace in M_3(R) or not

[sullen moss]

I know it has two condition to show it but I dont know how to write the proof make it looks correct

[dawn dagger]

on which one are you stuck?

[sullen moss]

The second exercise

[dawn dagger]

try to see if it's closed

or easier, does it contain the null matrix?

[sullen moss]

Do we have to check whether it non empty first ?

[sullen moss]

for second exercise I dont think it has null martrix

[dawn dagger]

why

[sullen moss]

because null martrix it mean everything in martix equal to zero right ?

[dawn dagger]

yes

[sullen moss]

so it doesnt matter what a b c are

[dawn dagger]

exactly

[sullen moss]

But I dont know how to write it

like make it look logic -_

[dawn dagger]

just like here

you could write: for all a,b,c in R the matrix 1 a b, a 1 c, b c 1 is never equal to the null matrix because you cannot get rid of the 1s from the diagonal

[sullen moss]

okay

[dawn dagger]

you could also say it is necessary that a=b=c=0 but that doesnt result to the nullmatrix

you end up with the identity matrix instead

[sullen moss]

Okay

but have one question related to subspace

in my class teacher said that we have to check if the set is non emply is that the same as check in null matrix ?

it has two condition to follow

first we have to check whether it non empty or not -_

[dawn dagger]

Well if it contains the null matrix then it cannot be empty since it has at least that one as element

[sullen moss]

okay i got it

[dawn dagger]

but like it's easier to show that something is not a subspace by simply showing that the zero vector is not in that set, because every subspace is also a vector space and every vector space must contain the zero vector

[sullen moss]

so for vector we have to check it has zero vector or not

so what about function ?

what did we have to check ?

like E={ f in c^o(R) , f(-x)=f(x)}

[dawn dagger]

Ok so first question is what is the null function looking like? And then to see if it's in E you need to prove/disprove whether it satisfies the constraint f(-x) = f(x)

[sullen moss]

f(0) ? -_

sorry i dont know T.T

[dawn dagger]

the null vector is simply the neutral element regarding addition

f(x) = f(x) + 0

so the null function is n(x) = 0

Now you need to see if n(x) = n(-x)

[sullen moss]

so if n(x) = n(-x) also = 0 ?

[dawn dagger]

can you show why

[sullen moss]

now if n(x)=0 so it doesnt matter inside the function n(-x)= 0 even n(1) = 0 ?

it just like f(x)=2x but if we put f(-x)= -2x instead

but here we have n(x)=0 so if we put n(-x) it still equl to zero

is that make sense ? -_

[dawn dagger]

yea

[sullen moss]

Btw here the answer i write for exercise 1

Is that make sense ?

[dawn dagger]

looks fine

now show lambda * A is also in M and you are done

[sullen moss]

yes xD

Thank bunch that's really help me a lot T.T

Now I understand more about null space and how to check it now

so basically all null thing are just neutral element right ?

[dawn dagger]

what is a null thing?

[sullen moss]

like null vector or null function xD

[dawn dagger]

yea basically, matter of fact, whether it's vectors, matrices, functions, polynomials you always call the neutral element the null element / zero vector

[sullen moss]

oh wait what is neutral element of polynomials ?

it is zero ?

Anyway Thank you again that has been really helpful to me

.close

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[dawn dagger]

yes

n(x) = 0

polynomials are also functions

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[neon rune]

maybe

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@sage elm Has your question been resolved?

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[uneven sandal]

\[
\text{let } f \in C^\infty[0, \infty) \text{ with } f(0) = 0 \text{ and for } x > 0: \quad 
f(x) = \frac{1}{x} \int_{\frac{1}{2} x}^{\frac{3}{2} x} f(y) \, dy.
\]
\[
\text{Question does this imply: } \exists c \in \mathbb{R} : \, f(x) = cx
\]

[grand pond]

tobi

[uneven sandal]

I already proofed this for analytic functions, this is easy.

If you know some theorems that could help me answering this question I would appreciate that.

[midnight plank]

@uneven sandal Has your question been resolved?

[uneven sandal]

<@&286206848099549185>

[midnight plank]

@uneven sandal Has your question been resolved?

[uneven sandal]

.close

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[nova wasp]

how would i show this

[buoyant linden]

factor

u see how the top can be rewritten as

1 - r^2 - r
= (1-r)(1+r) - r

and the bottom can be rewritten as

(r^2 + 2r + 2)(r^2 + 1)
(r^2 + 2r + 1 + 1)(r^2 + 1)
[(r+1)^2 + 1](r^2 + 1)

[nova wasp]

ohhh

i was overcomplicating it lol

[buoyant linden]

(r^2+1)(r+1)^2 + (r^2 + 1)

[nova wasp]

thanks

.close

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[minor cipher]

i got a curve on a cartseian plane, say parametrised by its arc length s, thats defined by s=0 is at (0,0) and y = s^(3/2), how do i get an equation of the curve in terms of x,y ?

[prime hornet]

welcome back to mathcord harper

unfortunately I gtg rn

but I just wanted to say hi

[pearl idol]

what's x equal to?

[minor cipher]

i tried bullshitting it and calculating dy/ds = ⅔√s and then (dx/ds)² + (dy/ds)² = 1 (is this true?) and then square rooting the (dx/ds)² and integrating but 1. it gives me a hideous expression that i dont like it if its the actual answer and 2. im not confident this is even correct

[minor cipher]

thats what im trying to figure out

[pearl idol]

oh I see

[minor cipher]

oh i guess i know x is positive

[pearl idol]

are you assuming that x is strictly increasing in terms of s

because there's two possible square roots

that seems more or less correct though

dy/ds is 3/2 sqrt(s) tho

[minor cipher]

oh yea thtas typo

do i juswt have to suck it up then and deal with shit like (1-stuff^(1/3))^(3/2)

nvm wait

y = s^3/2
dy/ds = 3/2 √s
dy/ds ^2 = 9/4 s
dx/ds ^2 = 1- 9/4 s
dx/ds = sqrt(1- 9/4 s)
x = -(4/9 - s)^(3/2) + C

its not that bad

have i just been trolling all this time

oh my god

[pearl idol]

that seems right to me

,w integrate sqrt(1 - 9/4 s) ds

[grand pond]

Results provided by WolframAlpha

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Requested by erictao

[pearl idol]

uhh that's the same as what you wrote I think

[minor cipher]

yea i just used 27 = 9^3/2

[pearl idol]

👍

so assuming x is strictly increasing, I think this is the only possibility

[minor cipher]

that is still bad because s=y^2/3 so it still is
x = 4/9 - (4/9 - y^2/3)^3/2

thats annoyyyinnngggggggg

thanks eric

.close

[midnight plank]

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[pearl idol]

that doesn't seem so bad tbh

[minor cipher]

yh i just dont like it

[pearl idol]

[minor cipher]

4/9 - (4/9 - is funny tho

as is ^2/3)^3/2

[pearl idol]

you can transform coords to make it more symmetric prob

[pearl idol]

actually idk how you got that formula, idt (0,0) satisfies it?

[minor cipher]

yh i typed it wrong into the calculator

i forgot to write ^3/2

it shld be 8/27 - (4/9...)^3/2

[minor cipher]

thank u <3

[midnight plank]

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[upbeat plinth]

One message removed from a suspended account.

[upbeat plinth]

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[upbeat plinth]

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[lavish venture]

what

[upbeat plinth]

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[lavish venture]

\int?

[upbeat plinth]

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[grand pond]

Kenzo

[upbeat plinth]

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[fading ore]

Thats the integral sign

[upbeat plinth]

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[hearty rune]

look at the hint

[lavish venture]

what

[fading ore]

Well we can't integrate without a differential

We need a dy when we are integrating a function of y

[upbeat plinth]

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[grand pond]

Kenzo

[fading ore]

Hmm

[lavish venture]

no

[upbeat plinth]

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[fading ore]

But we can't multiply dy over

[lavish venture]

separate the variables first

[fading ore]

Bc its in the numerator

[lavish venture]

divide by y

[fading ore]

^

[upbeat plinth]

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[fading ore]

$\frac{\dd y}{\dd x} \frac1y= 0.7$

[upbeat plinth]

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[lavish venture]

what

[upbeat plinth]

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[fading ore]

Ignore what I wrote, latex screwed it up for me

[upbeat plinth]

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[grand pond]

Kenzo

[lavish venture]

whet

[upbeat plinth]

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[grand pond]

hiidostuff

[upbeat plinth]

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[fading ore]

Alr

[lavish venture]

there ya go

[fading ore]

Yeah lol I forgot a part

But if u want knief to handle it I'll leave yall alone

[upbeat plinth]

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[lavish venture]

guess you filled her dehn

[upbeat plinth]

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[upbeat plinth]

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[fading ore]

https://tenor.com/view/fire-writing-writing-fire-his-writing-is-fire-is-this-fire-hold-up-gif-15400153686296022809

[upbeat plinth]

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[fading ore]

Ok I'm gonna say something that's like 10% not true but 90% true

Mutliply both sides by dx

[upbeat plinth]

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[lavish venture]

for pedagogical purposes its the best thing to say

[upbeat plinth]

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[fading ore]

Yeah

[upbeat plinth]

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[lavish venture]

leave it where it is

[fading ore]

I guess kind of

But i wouldn't risk it

[upbeat plinth]

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[fading ore]

Yep

And now that we have differentials on both sides

We can integrate

[upbeat plinth]

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[lavish venture]

no power rule here

[upbeat plinth]

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[lavish venture]

the derivative of what is 1/x

[fading ore]

Well I mean we integrate but neither of these can use power rule

[grand pond]

Kenzo

[upbeat plinth]

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[lavish venture]

yes

[fading ore]

Nice

[lavish venture]

thats all indefinite integration is

reverse process

[upbeat plinth]

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[grand pond]

Kenzo

[lavish venture]

its y

not x though

on the left

[upbeat plinth]

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[lavish venture]

and do \ln

[fading ore]

Yep

[lavish venture]

also dont forget + C

you only need it on one side

[fading ore]

^

[upbeat plinth]

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[fading ore]

Technically both sides would be integrated with an extra constant, but we can combine them into one big +C

[lavish venture]

not really

[fading ore]

Don't worry, it gets so much worse

[upbeat plinth]

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[lavish venture]

he is me

you havent figured that out by now

[upbeat plinth]

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[fading ore]

Yeah I'm swapping alts

[upbeat plinth]

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[fading ore]

Yes

And after we integrate the goal is to isolate y

[upbeat plinth]

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[fading ore]

Maybe

Ultimately integration is the opposite of differentiation

You just gotta take the derivative but in reverse

Well not always but usually

[upbeat plinth]

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[grand pond]

Kenzo

[lavish venture]

nope

[upbeat plinth]

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[fading ore]

+C lol

[upbeat plinth]

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[fading ore]

Don't worry the integrating constant annoys all of us

[lavish venture]

sal khan

[fading ore]

Most times I ignore it unless it's actually important

[upbeat plinth]

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[fading ore]

But I also study pure math in college so I don't do integrals like that super often

[lavish venture]

yes

[fading ore]

Khan academy

[upbeat plinth]

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[lavish venture]

his first name

...

[upbeat plinth]

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[lavish venture]

yep

the guy who makes the videos

[upbeat plinth]

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[lavish venture]

nah

hes trash

cant lie

[upbeat plinth]

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[lavish venture]

overrated

[lavish venture]

dont know, just never liked him

[upbeat plinth]

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[fading ore]

Infernal take

Ochem tutor aint half bad

[lavish venture]

sal clears

[upbeat plinth]

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[midnight plank]

Channel closed

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[upbeat plinth]

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[fading ore]

Np

[midnight plank]

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[obtuse totem]

i don’t think their mean is correct

I think it’s supposed to be x/3k after integration

k=5 btw

but again i just wanna make sure

oh sht

my bad

holyyy

i just can’t integrate what is wrong with me

[rough birch]

U good now?

[obtuse totem]

yea

.close

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[radiant roost]

the third one is out because it's not finite right?

seems right

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[sullen moss]

It want us to show that Whether set E is subspace of C^0(R) or not

[olive matrix]

just show that E is closed under addition and constant multiplication

[sullen moss]

I kinda stuck with number 5

don't we have to show that E is non empty first right ?

[fallow scarab]

Shouldn't need to show it's non-empty

[sullen moss]

But for number 5 i dont think it sastify unless beta equal to zero ?

From What I think is
since f(x) = 0 is neutral element of function and it in c^0(R)
so f(wx) = 0 also in c^0(R)

so 0 = alpha . 0 + beta

0 cannot equal to beta unless beta = 0

so how do we exactly show it -_

[midnight plank]

@sullen moss Has your question been resolved?

[sullen moss]

@gray widget

[midnight plank]

@sullen moss Has your question been resolved?

[fallow scarab]

Yea and you're not given beta is zero so it's not a subspace

[sullen moss]

so it means that number 5 is not subspace

[fallow scarab]

That's exactly what I said

[sullen moss]

okay ty

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[grand pond]

938c2cc0dcc05f2b68c4287040cfcf71

[tidal turret]

whats with this one? looks hard as hell

[swift hamlet]

My brain hurts looking at it.

[tidal turret]

agreed lmao

😂

however let's find a basis for S, a basis for T and a basis for S∩T

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@tidal turret Has your question been resolved?

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[distant pagoda]

I don’t understand how to start 4c

[hollow dome]

dV/dt is given, it asks you dA/dt

[distant pagoda]

How do I find that

Chain rule?

[hollow dome]

Chain rule

Yes

[distant pagoda]

SO I do da/dr times dr/dt ?

[fading ore]

You can find dr/dt given dV/dt and r

And then because surface area has its own formula you can find dA/dt given dr/dt and r

[distant pagoda]

Wdym ?

[hollow dome]

That works

[distant pagoda]

Idk how to find dr/dt tho

[hollow dome]

dr/dt . dV/dr = dV / dt

[fading ore]

^

[distant pagoda]

What

Im SO confused

[fading ore]

Have u done implicit differentiation before

[distant pagoda]

No

[fading ore]

Oh

Well

[distant pagoda]

Maybe I have idk

What is it?

[fading ore]

Would you agree that $\frac{\dd V}{\dd r} = 6\pi r^2$

[distant pagoda]

Îs it not 6 pi r^2

Or does the pi go

[grand pond]

hiidostuff

[fading ore]

Latex being annoying

[distant pagoda]

Ahh ok yes I agree

[fading ore]

Alright now

We can use chain rule to switch it to dV/dt

[distant pagoda]

How do we do that

[fading ore]

since dV/dr * dr/dt = dV/dt

[distant pagoda]

Oh yes okay

[fading ore]

We can think about it like the "dr" parts canceling out

In case ur gonna study math in college, just know that's not how it actually works

But its close

[distant pagoda]

No way

But ty

[fading ore]

Fair enough

[distant pagoda]

How do I find dr/dt

[fading ore]

(To be fair math looks COMPLETELY different when u study it in college but I digress)

[distant pagoda]

Really?

[fading ore]

We can find it knowing dV/dt and r

[distant pagoda]

Idk I feel like I’m struggling with year 12 maths how would I be able to do uni level maths

[fading ore]

Oh yeah

[distant pagoda]

Why

[fading ore]

Well knowing that $\frac{\dd V}{\dd r} \cdot \frac{\dd r}{\dd t} = \frac{\dd V}{\dd t}$

[grand pond]

hiidostuff

[fading ore]

We can just replace dV/dr with what we know it's equal to

So $\frac{\dd V}{\dd t} = 6\pi r^2 \frac{\dd r}{\dd t}$

[grand pond]

hiidostuff

[distant pagoda]

Mhm

Can I just leave it like that?

[fading ore]

Sure but we need to solve for dr/dt

We can just directly plug in the values we know

[distant pagoda]

What values do we know

[fading ore]

We were given dV/dt and r

[distant pagoda]

Mhm

[fading ore]

We can solve for r using that

[distant pagoda]

Sorry this may sound so dumb I have no idea how

[fading ore]

Just gotta rearrange

Divide both sides by 6pi r^2

And then directly plug in the values

[distant pagoda]

Rightt

Or root 1/6 ?

Is r root 1/6

[fading ore]

Nah u plugged in 5 for dr/dt

But r = 5

And ur trying to solve for dr/dt

[distant pagoda]

Oh

Im lost then

Whats dr/dt

[fading ore]

Same as u just did with r but for dr/dt instead

You need dr/dt =

[distant pagoda]

What do I do to find that!

Is there a formula

Ohhh

I get it

Maybe

Is this corect?

[fading ore]

Yep

And now plug in r^2

[distant pagoda]

SO 25

[fading ore]

For dr/dt?

Doesn't make sense for it to be above 1 if r is above 1

[distant pagoda]

No no

R^2

[fading ore]

Yes

[distant pagoda]

SO dr/dt is 1/30 ?

And so dv/dt is 6pir^2 / 30 ???

Maybe

[fading ore]

Mhm

[distant pagoda]

Ohh ok

THANK YOU

[fading ore]

Alright now we gotta find the surface area of the cylinder

No problem but we're only halfway done

[distant pagoda]

https://tenor.com/view/kermit-cheering-gif-3724183077221405325

[distant pagoda]

Oh

[fading ore]

Ok it's an open cylinder

[distant pagoda]

Omg I forgot abt that

[fading ore]

Ok so we need the part that wraps the cylinder plus the base

[distant pagoda]

SO it’s pir^2 + 2pirh

[fading ore]

Yes

And we know h is 2r

[distant pagoda]

Mhm

SO it’s pir^2 + 4pir^2

[fading ore]

Mhm

Or 5pir^2

So A = 5pir^2

[distant pagoda]

Okay

[fading ore]

Which means dA/dr = 10pi r

And then dA/dt = 10pi r dr/dt

And we know both r and dr/dt now that you've calculated it

[distant pagoda]

OMG

SO we just multiply and bam

[fading ore]

Mhm

[distant pagoda]

Yay yay yay

SO it’s

10pir /30 ?

[fading ore]

Yes

Then times 5 bc r is 5

So u should get 5/3 pi

[distant pagoda]

Why times 5

Why are we multiplying by r

[fading ore]

Bc we have 10pi r dr/dt

Which is then 10pi r/30

Which is then 10pi 1/6

Which is 5/3 pi

[distant pagoda]

Ohhhh

Ur amazing

Thanj u so much

[fading ore]

Np

This related rates stuff is useful anyways so I gotta know it

(Tho I don't do it very much at all when studying math tbh)

It's more of a science thing

[distant pagoda]

It’s horrible

Im taking further maths so we have to do all of alevel maths in one term it sucks

[fading ore]

Yeah

I mean if ur doing calc 2, then it gets a lot worse so just enjoy this while u can

I think yesterday I helped someone determine if $\sum_{n=0}^{\infty} \frac{\sin{(n)} \sqrt{n}}{(n+1)^2}$ converged or not

[grand pond]

hiidostuff

[distant pagoda]

Omg

Im gna fail

I need a tutor but I can’t find one anywhere so I just have to spend a million hours a day

[fading ore]

I mean people here will help

It's all just a matter of breaking things down into simpler parts

[distant pagoda]

They’re super helpful

[fading ore]

A lot of these things in math that seem really wild come from the simplest ideas

[distant pagoda]

It’s just spotting what to do I can never figure it out

[fading ore]

Yesterday I had to prove that if a number n has only 3 prime factors and 7 unique factorss of the form p^k where p is prime and k is a positive number, then n is divisible by a cube greater than 1

The reason is because you can't sort 7 objects into 3 boxes with only room for 2 objects and for one of them to not be overflowing

It's stuff like that where you just have to be creative

[distant pagoda]

Oh wow

[fading ore]

That's more of the type of stuff you do in college math tho

Well if you do number theory that is

There's lots of routes