help-19

[junior iron]

?

[spice geyser]

they meant you should just post your problem here'

[junior iron]

oh

i thought we go vc ans tuff lol

*and

*stuff

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[clever edge]

I need help with a calculator question

[clever edge]

It's given that f'(x) = sinx+ xcosx, under the interval 0<=x<=pi

I need to find where the function f is increasing

[worn sandal]

what can you say about f'(x) when f is increasing

[clever edge]

it's positive

[worn sandal]

mhm so sinx + xcosx > 0

[clever edge]

Yes

[worn sandal]

i'm not sure if there's a good way to solve this

you want to find the roots basically and I was thinking divide by cos to get
tan(x) = -x

by desmos it's around 2.02876

[clever edge]

so I'm guessing the interval would be either [0, 2.029] or [2.029, pi]

I guess I just have to plug in a value of x in between

[desert prism]

careful, since it's not increasing at the points where it's equal to zero, so you'd want to use parentheses on your intervals to indicate that it's not inclusive of the endpoints

[clever edge]

Yeah, I know I'm guessing the person who made this question made a small mistake

Also I just plugged in 2.5 and 1.5 and got that B is the correct option

Thank you guys for the help

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[soft terrace]

Is the symbol $\exists !$ common in mathematical texts to denote "exists exactly one"?

[ember oak]

$\exists!$

[clever fjord]

SWR

Shuba

[ember oak]

and yes. It is common syntax

[soft terrace]

thank you, I forgot the "s" on the end XD

[quasi sparrow]

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

[soft terrace]

interesting. I've never seen that before

[ember oak]

I first encountered it in my intro to formal set theory class

[soft terrace]

or, maybe I have and I've not seen the ! on the end

[ember oak]

Not sure where you are on your math journey, but that's where I first saw it

[soft terrace]

I did my MMath masters 2 years ago, and I've only just seen it while *re-*reading linear spaces

[ember oak]

I see I see

perhaps you simply forgot it then

The human memory will always betray you

[soft terrace]

very true

I must have come accross it before, but not really taken not of it

thanks 🙂

[ember oak]

!done

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[steady tide]

is this further reducible given the set's restriction?

ah wait i see now

c.lose

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[dense jackal]

i need help with question 9c only please

[ionic spoke]

haBOOB😂

[dense jackal]

hi can you help me out please?

<@&286206848099549185>

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[strange oxide]

https://i.gyazo.com/5048a342ac292bccbffa9ab584e67fce.png

Help me solve this polynomial multiply

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[willow jolt]

could anyone suggest a playlist/notes for the above topics to prepare for my exam this weekend 🙂 (mathematics- real analysis)

[quasi sparrow]

Just read a real analysis book

#book-recommendations

This is too broad for a help channel

[odd edge]

@willow jolt Has your question been resolved?

[fringe solstice]

indeed this sounds like standard contents in a calc 2 course for math majors

so I would look for playlists about that, or the standard books like Spivak

[fringe solstice]

either way

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[dense stone]

What is chance of the area of shape being greater than 6 and under 8 while there are 9 circles that has all equal areas and number written on it. And the two arrows will be fired

[charred spindle]

That makes no sense.

!original

[odd edge]

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.

[dense stone]

It was too complex

[charred spindle]

That's helpful. It exposes several mistranslations.

But I still don't know what the question is.

[dense stone]

It means the shape with x - chug and the two line l,m which is x jeolpyeon and y jeolpyeon that is defined by number written on circle

[nimble blaze]

korean/hangul

[odd edge]

@dense stone Has your question been resolved?

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@dense stone Has your question been resolved?

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@dense stone Has your question been resolved?

[odd edge]

@dense stone Has your question been resolved?

[mystic saffron]

You need to use a translator or ChatGPT.

[odd edge]

@dense stone Has your question been resolved?

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@dense stone Has your question been resolved?

[quiet kettle]

1 to 9 are written in the circle split to 9 parts as the figure. Shoot an arrow twice, and let p be the first targeted number and q be the second targeted number.
A line l’s x intercept is p and y intercept is q, and another line m’s x intercept and y intercept are both q, find the probability that the area enclosed by l, m, and x-axis is greater than or equal to 6 and less than 8.

[grand mural]

일단 도형이 삼각형이니까 높이랑 밑변이 뭔지 찾아보고 확률 구하면 끝

[river spindle]

Have you tried anything?

[odd edge]

@dense stone Has your question been resolved?

[dense stone]

I did

[pseudo narwhal]

do you know the answer?

[dense stone]

Obviously, no

[pseudo narwhal]

ok i thought i could verify my answer

[pseudo narwhal]

i think this is the approach ,lmk if i made a mistake

[pseudo narwhal]

lmk when you find out the answer

[river spindle]

I think total cases would be 9*9.
Also we need to find the equation of those lines and their intersection points to get the area of the triangle

I get, 12<= (p-q)(q) < 16

choose p and q such that the inequality holds true.

[river spindle]

I've miscalculated area here.
I'll get back after recalculating.

It'd be area of the triangle made by red and blue lines(limit would be p and q instead of 2 and 3)

[pseudo narwhal]

no cause they can’t be the same number right so its 98 theres no div by 2 but i don’t think it is 99

[pseudo narwhal]

it should be 7/72

[mystic saffron]

can anyone help me with calc 1

[fringe solstice]

send your questions in an available channel:

or #calculus

[frosty parcel]

What do u need

[sly prawn]

can i get help with question b and c please?

[odd edge]

@dense stone Has your question been resolved?

[dense stone]

Is there a formula that could get area of shape using input of two random numbers

[fleet pollen]

There is the universal formula of equilateral triangles

But the shape's sides need to be known

If you know all the sides, you can calculate any shape's area

For ex, the area of an hexagon is the one of the 6 equilateral triangles it is made of

It becomes harder for irregular shapes because you need to strech them, but it becomes easy when you get used to it (Just as calculating vectors geometrically)

Was this helpful?

[fleet pollen]

@odd edge GET OUT!

[quiet oracle]

!done

[odd edge]

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

[noble solstice]

is someone capable of providing an accurate translation? If we have the question in english more people will be able to help

[regal girder]

@grand mural(?)

[dense stone]

There is a circle and numbers written on it.
And it will generate two random numbers which is between 1 and 9.
The first number is p, which is x - jeolpyeon of line l.
And the second number is q, which is y jeolpyeon of line l, and also x - jeolpyeon and y - jeolpyeon of line m.

Then what is chance of the area of shape that is formed by x - chug, line l,m being greater than 6 and lower than 8?

[grand mural]

직선 l과 m 그려봤나요?

[dense stone]

네

[grand mural]

어떤 도형이 나와요?

[dense stone]

삼각형이나 직선 두개만 있는 도형만 나와요

[grand mural]

근데 직선 l,m과 x축으로 둘러싸인 도형의 넓이가 6이상이 8미만이 되어야 하니까

삼각형 넓이를 알면 되겠죠?

[fringe solstice]

Non-English conversations are allowed in the help channels

from #rules :

tf you mean "tribe" language

[rich wasp]

why is this channel still open

[dense stone]

What do you mean by that?

[proper lake]

have you solved your problem?

[mystic saffron]

This channel has always been open. And it will stay open unless the universe dies

[fringe solstice]

.close

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[frank tide]

2log(x)-log(x+2)=0

[frank tide]

so

when you solve this wit hthe properties of logs

you get x = -1 and 2

so you test

2 is valid so 2 is a solution

however -1...

so 2log(x) cannot be 2log(-1)

bc yk the number between the () cannot be negative

BUT

if we turn 2log(x) to log(x^2)

this wouldnt be a problem

so what the heck?

[tacit wasp]

The issue is the domain

[tepid hornet]

the domain of solutions will be the original one

of 2logx

you can then convert it to logx^2, but the domain restriction will remain the same

[frank tide]

oh... yeah x > 0 and thus you cant really input -1 even if you turn it into x^2

alright ty

[tepid hornet]

yes you can

the thing is that from the start you set the domain >0

[frank tide]

mhm yeah

i understand

ty

[tepid hornet]

no matter what you do in the next steps, like moving the 2 in the log, the domain wont change

it ll still be >0

you're welcome

[frank tide]

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[wintry heart]

(727.29 - 248.50) + x <= 500

this right

[wintry heart]

So you take the initial value (727.29) and then minus the amount that Evelyn took out (248.50)

(727.29 - 248.50)

in order to see how much she needs to put in you need to add to that equation with x

(727.29 - 248.50) + x

and to make sure that the amount isnt below 500 you need to make sure the entire value is more than or equal to 500

(727.29 - 248.50) + x ≤ 500

is this correct?

<@&286206848099549185>

[tall plover]

you mixed the sign

you wrote less than or equal

but other than that yea it's correct

[wintry heart]

it has to be below (less than) 500?

it should be right, no?

the paper initially is 1.75

1.75

plus tax

1.75 + y

it has to be less than 25

(1.75 + y) ≤ 25

the number of packs he can purchase
x = (1.75 + y) ≤ 25

so x = (1.75 + y) ≤ 25 where x is the number of packs purchased and y is the tax

idk if this is correct or not

<@&286206848099549185>

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[noble perch]

is this correct? 😭

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[warm ore]

where did this sinx come from? should it not be the derivative of xsinx which is cosx?

[nimble blaze]

derivative of xsin(x) isn't cos(x)

[warm ore]

ah right, f'g+fg'

i assume?

[nimble blaze]

shouldn't be assuming

but yes, that's what you should be doing to differentiate a product

[warm ore]

gotcha, lastly the

is this due to (1/f)' = f'/f^2?

[nimble blaze]

no

[f(g(x))] = f'(g(x)) * g'(x)

[warm ore]

i thought composite functions need something like e or a trig function, can a square root be a composite function on its own?

[nimble blaze]

you have a square root of another function

going to use a different letter instead of f

h(x) = sqrt(x)
g(x) = x^2 + e^x

h(x) can pretty much be any function

[warm ore]

gotcha, ty

appreciate the help

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[tribal fossil]

this is bounded and increasing right?

when I try to calculate the limit I get something negative for some reason

what am I missing?

[forest sky]

how are you calculating the limit?

[tribal fossil]

subbing L in a_n and a_n+1

[forest sky]

that shouldn't result in a negative number. can you show your working on that?

[tribal fossil]

oh my god

I've been staring at it for 15 minutes

thanks lol

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[misty plover]

hello, i'm just a bit stuck with this question, a simple diagram of the weight split into its components should help hopefully. Normally i should be ableto do this but i'm just having one of those times where my mind is being tangled up on such an easy question (just question i should suffice)

[misty plover]

nvm found this

.close

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[snow solar]

hi! i need to learn all trig identities/solving-related precalc content by tomorrow...what's the best way to go about doing this?

[meager juniper]

Build a time machine

[snow solar]

hey wait i know most basic trig

• i can pick up most things fast, just need an order to go in

[meager juniper]

Well, hmm...

I would recommend powering through Khan Academy's course on trig then

https://www.khanacademy.org/math/precalculus/x9e81a4f98389efdf:trig

[snow solar]

okay! do u think it will be useful to try deriving most of the identities?

[meager juniper]

The most useful identities are the Pythagorean identity and the tan and cot cousins of it. And the sine and cosine angle addition formulas.

Pretty much everything else can be found using those two. (Double, half, triple angle formulas and so on)

At least imo

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[atomic pilot]

i have like

it's confusing

like I have the answer key

and it is completely different from what I get

[tardy pawn]

Is the answer 13

[tardy pawn]

Is it 13?

[atomic pilot]

yes

[tardy pawn]

Show your work ill help you

[atomic pilot]

i think i got it nowq

now

basically

[tardy pawn]

Ok bye

[atomic pilot]

the 6 parts comes later right?

like i just do f(3) * g(3) - f(0)- g(0) -6

[tardy pawn]

Yes

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[cursive sigil]

I don’t understand how I got this wrong. If you extend it you get - -3•- -3. Two negative signs cancel out. So it’s 3•3 which equals 9

[forest sky]

-x^2 = -(-3)(-3) so there are 3 negative signs

[cursive sigil]

Where is the third one?

Oh wait

Is it like this

[forest sky]

,, -x^2 = \overset{1}{-}(\overset{2}{-}3)(\overset{3}{-}3)

[clever fjord]

cloud

[forest sky]

3 * (-3) ≠ 9

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[hoary halo]

1-sin^(2)x=1-(1+cos^(2)x)

[hoary halo]

how would i solve this

sine/cosine functions are squared

[quasi sparrow]

The left side is cos^2(x)

[hoary halo]

oh u can cancel the ones

ok nvm

so its 1-sin^2 x = cos^2 x

which is derived from sin^2 x + cos^2 x = 1

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[ashen thistle]

Can someone solve this by taking the center of mass as the pivot

[odd edge]

@ashen thistle Has your question been resolved?

[ember oak]

!status

[odd edge]

What step are you on?
1. I don't know where to begin.
2. I have begun but got stuck midway.
3. I got an answer but I was told that it's wrong.
4. I got an answer and would like my work checked.
5. I have a question about someone else's work/solution.
6. I have completed the problem and don't need help anymore. Thank you.
7. None of the above

[ashen thistle]

well my status is weird i have done it by taking the point of contact of ladder with the rough surface as pivot

and ans correct

but i cant get it

from center of mass of ladder

so yeah

[ember oak]

!show

[odd edge]

Show your work, and if possible, explain where you are stuck.

[ashen thistle]

this is for the rough surface one

let me find the ugh center of mass one wait a minute

Okay so the problem here was

The friction and normal reactions' moments just cancelled each other

So how would I find the ugh

Point of slipping

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[viscid crane]

wouldnt this be 0 = 10 instead of n = 10

[viscid crane]

does n matter

[autumn bolt]

n indeed does not matter

thats why it's a trick

but I don't see how you conclude 0 = 10

[odd edge]

@viscid crane Has your question been resolved?

[viscid crane]

cuz n - n = 10

wait no

oh

oh i see

there is no equal sign

ok

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[scenic summit]

How do you put this in a form to use Laplace's method
I've tried to take everything into the exponent
and got e^[xln(t/t²+1)+t]
But now I need to find the maximum and so I differentiated
xln(t/t²+1)
but I can't get t on its own, i.e. I can't get t=f(z)

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<@&286206848099549185>

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@scenic summit Has your question been resolved?

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@scenic summit Has your question been resolved?

[scenic summit]

Anybody ?

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[dense stone]

What is the size of angle ADP+BQP when P is the midpoint of line AB in rectangle ABCD, BQ:QC=2:1

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@dense stone Has your question been resolved?

[green glen]

whats Q

[dense stone]

BQ:QC=2:1

[green glen]

no like P is the midpoint of AB, what is Q?

Is Q lying on BC?

[odd edge]

@dense stone Has your question been resolved?

[half sleet]

Have you already drawn a picture or started work with anything?
If you have, please send it here

I agree with the question previously asked, we have no idea what Q is, where it lies on ABCD the rectangle

[proper lake]

음..

합동인 삼각형 찾아서 하던 문제였나

DQ를 보조선 그어보고

삼각형 DPQ가 어떤 삼각형인지 보세요

[proper lake]

이해 안되면 ping하세요.

[dense stone]

삼각형 DPQ 가지고 알수있는게 안보여요

[proper lake]

어짜피 변의 길이가 하나의 문자로 다 표현됩니다.

그러면 합동 관계를 찾을 수 있어요.

물론, 구하려는 값이 각 DPQ와 같다는 건, 평행선을 그어보면 알 수 있는 사실이고..

$\bar{AP}=a$라 합시다.

[clever fjord]

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

[proper lake]

그러면.. 삼각형 PBQ과 삼각형 DQC의 변의 길이들도 얼추 표현이 되고..

그러면 보이죠

[dense stone]

그걸로 AB:BC=2:3 인걸 이용해서 BQ=2a,QC=a 인걸 찾았는데 합동은 없지않나요?

[proper lake]

합동이 정말로 없나요

[proper lake]

이 두 삼각형을 집중해서 보세요.

합동에는 SSS만 있는게 아니죠.

그래도 모르겠다면.. 직사각형의 기본적인 특징인 네 각의 크기가 어떠한가..

[dense stone]

피타고라스의 정리로 인해 합동인건가요?

[proper lake]

피타고라스의 정리로 봐서 SSS 합동으로 봐도 되고

직각이 있으므로 SAS 합동으로 봐도 됩니다.

[dense stone]

합동인걸 찾아도 ADP+BQP를 찾기에는 부족한데요

[proper lake]

변 AD와 평행한 선 하나를 점 P에서 그어보면

엇각 관계로 구하는 값이 각 DPQ가 됩니다.

합동 관계를 찾았기에, 삼각형 DPQ는 직각이등변삼각형이 되는데

그 이유는 직접 찾아보세요.

[dense stone]

이등변삼각형은 맞는데 직각은 못찾았어요

[proper lake]

합동인 삼각형의 특징을 보면

각 PQD가 직각임을 알 수 있어요.

정 모르겠으면, 각 같은 거 표시해보고 관계를 확인해보세요.

[dense stone]

아직도 못찾음

[proper lake]

각 BPQ는 각 DQC와 같고 (합동)

각 BQC+각 PQB=90도

따라서 삼각형 DPQ는 직각이등변삼각형이 되므로

45도.

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[zealous rain]

Can anyone help me with the algebra here?

[quasi sparrow]

Did you check if your rdot and theta dot were correct

[zealous rain]

yes i have, and they are correct

this to me seems like a dead end...

[quasi sparrow]

Did you use $\omega = \dot{\theta}$ anywhere

[clever fjord]

riemann

[tough portal]

ldk man

[zealous rain]

this equality isn't true though right?

[quasi sparrow]

that's the definition of omega
https://phys.libretexts.org/Bookshelves/Classical_Mechanics/Classical_Mechanics_(Dourmashkin)/06%3A_Circular_Motion/6.03%3A_Circular_Motion-_Tangential_and_Radial_Acceleration
unless you're using omega for something else

[odd edge]

@zealous rain Has your question been resolved?

[zealous rain]

yeah, that is the definition of omega in circular motion, unfortunately, in this case, i don't have a circular motion: y=Asin(omega t) and y=Bsin(omega t + alpha) defines a "2D harmonic oscilator" and theta dot = (-ABomega sin(alpha))/r^2

as an example, I can imagine an extreme case where alpha = 0 and then theta = arctan (sin(wt)/sin(wt)) = pi/4 and then dtheta/dt = 0

i think my only option is to chew through the algebra but it just seems impossibly chewy D:

[quasi sparrow]

did you check a_r and a_theta were correct

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[hexed cargo]

Please help me with this please

[amber schooner]

it’s C

[sand horizon]

Id have say B but i see why you answer this

Smart

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[hexed cargo]

Any idea

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[random stirrup]

I need help

[pastel dew]

out of context: the picture seems a bow

[random stirrup]

Huh

Oh lol

[main sonnet]

Alright, you’ve had two very similar problems earlier, what do you think you should do first

[random stirrup]

I know that but its confusing me cause its not like on the triangle its above it

[main sonnet]

Do you know if the triangles are congruent?

[random stirrup]

Yes they are

[cerulean vortex]

i find it's useful to label the diagram

[random stirrup]

Yea same

It confuses me when its above the triangle

[main sonnet]

So now that it’s been established that the two triangles are congruent, what equation can now be put together to solve for u?

[random stirrup]

u+19 + 8u−51 = 8u − 51

?

[main sonnet]

Just u + 19 on the left side

[random stirrup]

Okay

Do I just simplify from there?

And combine like terms

[main sonnet]

Yes

[random stirrup]

9u − 32 = 8u − 51

And then subtract

8u from both sides

and then add 32 both sides

[main sonnet]

No, the equation you’re trying to simplify is
u + 19 = 8u - 51

[random stirrup]

19 = 7u − 51

?

[main sonnet]

Yes

[random stirrup]

And then solve it?

[main sonnet]

Yep

[random stirrup]

I got U = 10

[main sonnet]

,w u+19 = 8u-51

[clever fjord]

Results provided by WolframAlpha

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

Requested by helmfirth

[main sonnet]

All good

[random stirrup]

Thank you!

[main sonnet]

👍

[random stirrup]

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[sinful stone]

I need help with Statistics. A distribution/topic called "Weibull".

I don't understand finding the mean and the standard deviation.

I also need to learn how the "Gamma function" works for non-integer values... I guess I'm learning two areas of knowledge with this question.

[sinful stone]

The book that we are using for the curriculum does not have any pages or hints about Weibull. This just feels like new curriculum for the exam that we are just meant to know, grr.

I searched the formulas up, and the expression for the mean is different to what is used in the proposed solution. Source: Wikipedia

I don't understand how lambda is used in the proposed solution for "mean". 12.03078 is "k", not "lambda"

maybe they did a mistake?

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[simple pike]

Hello.

[simple pike]

I need to find whether this series converges or diverges and show my reasoning and test used.

I've been on this problem for two hours.... I have tried the limit comparison test but can't get past this. I'm not sure if the L.C.T. works here or if I need to use the direct comparison test.

I've went through trying the direct comparison test but I'm unsure if its valid to compare it to just a series equal to the summation from n = 1 to infinity of 1?

Any guidance here would be greatly appreciated.

[quasi sparrow]

Just use divergence test

[simple pike]

So I take the limit of the summation from n = 1 to infinity of sin((n*pi + 3)/6). This is equal to infinity and therefore divergent then?

[quasi sparrow]

No

https://tutorial.math.lamar.edu/Classes/CalcII/ConvergenceOfSeries.aspx

[pallid reef]

$\lim\limits_{n\to\infty} \sin\left(\frac{n\pi+3}{6}\right)$ does not exist, so by the divergence test the limit diverges.

[clever fjord]

如月あやみ　Kisaragi Ayami

[simple pike]

Huh I guess I didn't realize that DNE falls under the criteria of being not equal to 0.

If you don't mind can you explain how to come to the conclusion that the limit doesn't exist?

[pallid reef]

It's still a sine wave

[simple pike]

Ok yeah so the limit of either cosine or sine with nothing outside of the function always doesn't exist since it doesn't converge

If approaching infinity*

And no zeros multiplied inside the function

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[thick spindle]

im confused why you do p inverse at the end instead of the beginning

[thick spindle]

i thought the formula was p^-1 M p

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@thick spindle Has your question been resolved?

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@thick spindle Has your question been resolved?

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@thick spindle Has your question been resolved?

[warped glacier]

probably cause the question has $D \leftarrow B$

[clever fjord]

south

[warped glacier]

so the inverse would be a mapping between bases $D \to B$

[clever fjord]

south

[warped glacier]

then apply the operator in basis B, M

then apply the inverse of p^(-1), which goes from B to D, to get the result in the basis D

[thick spindle]

thanks

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[pastel orbit]

alright I'm kinda tired and not seeing things properly

why does this inequality hold?

[pastel orbit]

x_n and y_n are real valued sequences

I can see why $|x_n - y_n| \leq \sup{|x_k - y_k| : k \in \N}$ holds, but somehow not this

[clever fjord]

higher!

[pastel orbit]

like if |x_n - y_n| > 1, wouldn't that make this inequality false?

[stone vector]

is this in the middle of some other problem?

[pastel orbit]

yeah

[stone vector]

more context may help to see what they're trying to do

[pastel orbit]

I want to find the closure of $\R^\infty$ in $\R^\N$, where the latter is equipped with the uniform topology generated by the metric $d(x, y) = \sup{\min{1, |x_k - y_k|} : k \in \N}$

R^\infty is the set of all real sequences that have finitely many nonzero entries, R^\N is the set of all real sequences

[clever fjord]

higher!

[pastel orbit]

I already know the answer is gonna be the set of all sequences that converge to 0

I've let $x \in \overline{\R^\infty}, \varepsilon > 0$. then $B_\varepsilon(x) \cap \R^\infty \neq \varnothing$, so we can choose a $y \in B_\varepsilon(x) \cap \R^\infty$. then there's an $N \in \N$ such that $y_n = 0$ for all $n > N$, so for any $n > N$, we hopefully have
\begin{align*}
|x_n - 0| & = |x_n - y_n| \
& \leq \sup{\min{1, |x_k - y_k|} : k \in \N} \
& = d(x, y) \
& < \varepsilon
\end{align*}
since $y \in B_\varepsilon(x)$.

[clever fjord]

higher!

[pastel orbit]

the problem is that inequality

I can't see why it holds, but it'd be real nice if it did

so I'm willing to believe it does

[errant gust]

proof by delusion

[ember oak]

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[pastel orbit]

<@&286206848099549185>

[pastel orbit]

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[formal needle]

$$I=\int^{\pi}_{0}\dfrac{x|\sin 2x|}{3+\sin^2 x}dx$$

[clever fjord]

Amadeus

[formal needle]

i split it into 0 to pi/2 and then pi/2 to 0

but im not sure if thats the correct approach

[timid sky]

pi/2 to pi

but yes that works

[formal needle]

how would i do the pi/2 to pi section?

i've never learned how to deal with absolute values

[errant gust]

think about the sign of the sin

from 0 to pi/2

and pi/2 to pi

[formal needle]

well from 0 to pi/2

i dont need to abs val cuz its postiive

but for pi/2 to pi, sin2x will be negative

since its a horizontal stretch by 1/2

[errant gust]

yup so you can rewrite the initial integral into 2

and rewriete the absolute value for either

[formal needle]

yeah i did but idk how to write the second one?

just -int pi/2 to pi?

[errant gust]

|x| = -x when x is negative

[formal needle]

oh

[tacit wasp]

In general cases, I agree it's good to split the integral if there are absolute values. But in this case, you can simply use the King's property, i.e. u = π - x. You'll see there is a nice simplification

[formal needle]

oh let me try that then

[tacit wasp]

It is useful here because sin(π - x) = sinx

[formal needle]

right

[formal needle]

$$I=\frac{\pi}{2}\int^{\pi}_{0}\dfrac{|\sin 2x|}{3+\sin^2 x}dx$$

[clever fjord]

Amadeus

[formal needle]

?

and then i split it right

[green glen]

yeah its gonna become real nice after you remove the

mod

since sin2x = d/dx(sin^2x)

[formal needle]

ohh

[tacit wasp]

Exactly

[formal needle]

so now it becomes

pi/2 (ln(sin^2x+3) from 0 to pi/2 - ln(...) from pi/2 to pi)

[tacit wasp]

Awesome, yeah

[formal needle]

how come my answer is wrong

kinda confused

nvm i got it

thanks guys

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[ocean hamlet]

Is the permutation (12)(13) = (21)(13), that is 1-->3, 2-->1, 3-->1 ?

[low locust]

in a permutation it cannot be that two things are mapped to 1

3 -> 2

so its the cycle (132)

[ocean hamlet]

(12)(13) means 1 -->3, 3-->1-->2, 2-->1 and (21)(13) means 1-->3, 3-->1--->2, 2-->1 so it's (132)

so they're equal

?

[low locust]

they are obviously equal because (12) = (21)

[ocean hamlet]

um yea so is the product of cycles just a composition of functions ?

can i see it that way

[low locust]

yes

[ocean hamlet]

mk thanks !

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[muted oxide]

hey i have a question, how would i use the telescoping series to find the sum of 1/(n(n+3)) with n starting at 1?

[muted oxide]

i split the fractions but they are not in the form of b_n - b_(n+1)

its b_n - b_(n+3)

[elfin zodiac]

The terms will cancel

Except the first 3 and last 3

If u go to inf last 3 doesnt count

@muted oxide

[muted oxide]

yeah but how do i know that

its not easily visible with the eye

[elfin zodiac]

What do you mean?

I think it is easily visible

[muted oxide]

i mean even if i expand it i couldnt easily tell that only 3 of the terms dont cancel out

[elfin zodiac]

Why not?

[muted oxide]

idk i guess im not used to it yet

so wait

say i have a telescoping series with the terms b_n - b_(n+5)

would that mean that i would have 5 terms that dont cancel out ?

[elfin zodiac]

You can see expanding one above the other

And then fix liketerms

Like in a manual subtraction

[muted oxide]

what do you mean i dont get it

[elfin zodiac]

ABCDE
-BCDE

---

Like this

Each letter is a digit

[muted oxide]

oh

so that is easier to see

[elfin zodiac]

In your case u would put

Each term

As a digit

[muted oxide]

ok so there is no real method in telescoping series sums

i just have to observe and calcel out terms

[elfin zodiac]

I call this a real method

[muted oxide]

ok

thanks for the help

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[mystic saffron]

why is normal 16x..

equation of normal**

[pliant nexus]

um

you understand equation for tangent?

[sand horizon]

Product of perpendiculars lines slopes is -1

[mystic saffron]

no

[mystic saffron]

yeah I
K that

[pliant nexus]

can you calculate $\frac{dy}{dx}$?

[clever fjord]

Arnavutköy

[mystic saffron]

of what

[pliant nexus]

of the ellipse?

[sand horizon]

So tangent and normal are perpendicular

[pliant nexus]

do you know what implicit differentiation is

[pliant nexus]

he doesn't understand tangent either tho

[sand horizon]

Ah

[mystic saffron]

yes ik that too

[sand horizon]

So once you have tangent you have the normal

[mystic saffron]

No wait

[mystic saffron]

i get the first part

equation of tangent is S1=0

But what about the second part

[odd edge]

@mystic saffron Has your question been resolved?

[odd edge]

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[viscid crane]

how should i go on reattempting this

[robust wyvern]

wdym by reattempting it

oh wait

i didnt see third question

[nimble blaze]

130 + 60 isn't 180

[viscid crane]

oh yea

would the angle next to b be 90

yes

ok bye

.close

[odd edge]

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[viscid crane]

how do i go on about this

ill just ask in #geometry-and-trigonometry

.close

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[pale nest]

what seperates a normal person from a champion?

[bitter folio]

Good question

[pale nest]

.close

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[mystic saffron]

its 190

[odd edge]

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[cold tapir]

how would I go about this

[regal leaf]

start with
$\frac{1}{1-x} = \sum_{n=0}^{\infty} x^n$ and then rewrite both sides of the equation

[clever fjord]

tobi

[cold tapir]

yeah i got it

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[echo socket]

How do I solve this problem: lim(x->1) x^(1/(1-x)). Do I have to just substitute 1 into the problem or do something else?

[pliant nexus]

im assuming you mean x^(1/(1-x))

[echo socket]

yes

[pliant nexus]

you cannot substitute one into the problem as you will get an undefined answer

[echo socket]

I have already discovered that

[sage harbor]

One moment

[narrow crypt]

${L = \lim_{x\to a} f(x) \implies \ln L = \lim_{x \to a} \ln f(x)}$

[clever fjord]

k

[narrow crypt]

if the limit converges since ln(x) is a continuous function

[weary pelican]

it's equivalent if L > 0

since you can compose with exp to the left

[narrow crypt]

idk what this theorem is but yes

[sage harbor]

Also, you can use exponential and logarithmic function to resolve this limit:

$x^{\frac{1}{1-x}} = e^{\ln{(x^{\frac{1}{1-x}})}}$

[clever fjord]

carp

[sage harbor]

So you can apply the theorem given there :p

[odd edge]

@echo socket Has your question been resolved?

[echo socket]

thank y'all on this one. Do you know by any chance any resources which can help me understand this topic better?

[odd edge]

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[rocky fossil]

I have no idea how to solve this

[rocky fossil]

That pic with triangles

I tried making some lines and ratios, but its not as precise as it should i think

[frigid canopy]

Could you share a clear image of the question

no need to translate it

[rocky fossil]

Sure

[frigid canopy]

Could you now translate what you have to do into english

Determine the ratio AD : EF

is that it?

[rocky fossil]

Kk

[rocky fossil]

Yeah

Where ab is twice as long as ac

[frigid canopy]

is this from an olympiad

[rocky fossil]

And ab is paraler with de and ad is paraler with ef

[rocky fossil]

Yeah

I want to challenge myself and its a road block for me

[frigid canopy]

Not one currently happening , right ( Just making sure)

[rocky fossil]

Ye

This is just practice

The big one will be at the start of next year

[frigid canopy]

Try using the basic propotionality theorm then

[rocky fossil]

Never heard of it

Or idk how its in my lang

[frigid canopy]

uh, one minute

Thales theorm

have you heard of that?

[rocky fossil]

Idk probably not

[frigid canopy]

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

read this please

[rocky fossil]

I see

So

|CE| / |CA| = |EF| / |AD|?

[frigid canopy]

yup

[rocky fossil]

So the answer is that?

And now just need to plug those numbers

Idk if they want it in numbers

[frigid canopy]

yes

[rocky fossil]

But how should i get them, is it stated in the theory too?

[frigid canopy]

what is

oh, you know |AB|:|AC|=1:2

yes?

hmm

I'm not too sure then

sorry

[rocky fossil]

Ye but there are 3 missing numbers if we count that AB is 2 cm

[rocky fossil]

Do u know anyone who could help?

[frigid canopy]

well

uh, not sure

but I think I see something that may help

triangle EDC looks like it may be similar to ABC

[rocky fossil]

Hmm

Oh ye

[frigid canopy]

would that help

[rocky fossil]

Probably lets see

Yup

But i need to get ratio of ab to de

[frigid canopy]

Hmm

Yeah, i don't know

ping helprs

*helpers

[rocky fossil]

Oh dude

[rocky fossil]

Ab:ad = de:ec

[frigid canopy]

you need AB/AC somewhere though

[rocky fossil]

Ik ab and ac

[frigid canopy]

btw, just ping <@&286206848099549185> after 15m if no one helps you

I don't think I can help beyond this, my geometry skills are bad now

sorry

[rocky fossil]

Ok

<@&286206848099549185>

[frozen needle]

Trigonalise la matrice de tchebychef dans la base de tcheby le neuille

[rocky fossil]

???

[frozen needle]

T pas le tibououi le plus perspicace

[rocky fossil]

Can you speak english please

[frozen needle]

Je préfère la mathématiques tcheby

[rocky fossil]

Whats Tcheby?

[frozen needle]

En gros c tibouille qui fait des maths tah x ens

[rocky fossil]

Ok

So can you help me?

[rocky fossil]

Original problem

[rocky fossil]

Translated

[frozen needle]

La vrai question c est ce que tu vise ENS ULM

[rocky fossil]

My goal is to get ratio of AD to EF

[frozen needle]

J’vais pas te dire que j'men bat le koicouneuille mais c reel j'men carre le tcheby

[rocky fossil]

I am lost...

.close

[odd edge]

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[odd edge]

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[noble cypress]

hello

[noble cypress]

oh shit

mb

how i close

.close

[odd edge]

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[surreal badger]

how to do this question?

[odd edge]

@surreal badger Has your question been resolved?

[odd edge]

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[eager trail]

what does it want me to solve

[eager trail]

ikr

so confusing

[cold sage]

soh cah toa

[eager trail]

ik

but what is the question asking

[cold sage]

for tan Q and tan R

[eager trail]

I don't get it

[cold sage]

Q is the angle at Q

[eager trail]

shut up

[cold sage]

<@&268886789983436800>

[eager trail]

<@&268886789983436800>

[tepid pelican]

no need to spam it

[eager trail]

so it wants me to solve the angles?

[cold sage]

it wants you to find tan of the angles

its pretty clear

tanQ=...
tanR=...

[tepid pelican]

tan(x) = opposite / adjacent

try using that

[eager trail]

so arctan?

[cold sage]

no, just tan

using soh cah toa

[cold sage]

like here

[eager trail]

???

tanQ = r/12

like that?

tanR = r/12

?

[tepid pelican]

Q is this angle. Tan(Q) = opposite / adjacent

[eager trail]

It's so confusing

[tepid pelican]

what side is opposite to the angle Q?

[eager trail]

12

[tepid pelican]

and what side is adjacent?

[eager trail]

8

[tepid pelican]

right

so it will be...?

as in tan(Q)

[eager trail]

tanQ = 12/8

[tepid pelican]

what about tanR?

[eager trail]

tanR = 8/12

[eager trail]

what's next

[tepid pelican]

that's it

you determined tanR and tanQ

that's what the question asked for

you can simplify those fractions

but that's basically it

[eager trail]

so tanQ= 3/2

tanR= 2/3

got it thx

.close

[odd edge]

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[eager trail]

.reopen

[odd edge]

✅

[tepid pelican]

Do you have more questions?

[eager trail]

that's it for now, if I have more I'll ask u

[tepid pelican]

Alright, you can keep this channel closed then

[eager trail]

.close

[odd edge]

Channel closed

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[eager trail]

ty for ur help

[cold sage]

.close

[eager trail]

one more question

[cold sage]

oop

[eager trail]

when do I use inverse

like sin -1, cosin -1

tan -1

[cold sage]

that would be if you were asked to find the angle itself

like 'find angle Q'

[eager trail]

[tepid pelican]

e.g. to get the angle Q, we would now do

[eager trail]

[tepid pelican]

,calc arctan(3/2)

[clever fjord]

The following error occured while calculating:
Error: Undefined function arctan

[tepid pelican]

,w arctan(3/2)

this

[clever fjord]

Results provided by WolframAlpha

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

Requested by methisalwaysright

[eager trail]

so approximately 98 degrees?

[cold sage]

more about 180 (i lie)

[tepid pelican]

it's in radians

looks more like 56

[cold sage]

saved it

[tepid pelican]

,calc 180/pi * 0.98

[clever fjord]

Result:

56.149863922821

[cold sage]

brain is in the bin

[eager trail]

hmm, how do u know

[tepid pelican]

1 radian is around 57

and it's 0.98 so I guessed a bit lower

[eager trail]

should I js use the calculator in degrees

.reopen

[odd edge]

✅

[tepid pelican]

Depends

if you use it in radians, your answer will be in radians

you should always use whatever you need

if you want the angle to be in degrees, then make your calculator use degrees

[eager trail]

I like degrees more

[tepid pelican]

then use degrees

you will start liking radians later

[eager trail]

What do I use if i try to find the side length

[tepid pelican]

usually just normal trig functions

[eager trail]

k thx got it

[tepid pelican]

e.g. here tan(60) = x / 5

so x = 5tan(60)

and you can just plug that in a calculator

,calc 5tan(60 deg)

[clever fjord]

Result:

8.6602540378444

Result:

2

[eager trail]

which angle

I don't get the question

[cold sage]

its the angle between AB and BD

from A to B to D

ABD

[eager trail]

this one?

@cold sage

[cold sage]

exactly so

[eager trail]

[odd edge]

@eager trail Has your question been resolved?

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[odd edge]

Please don't occupy multiple help channels.

[cursive musk]

how do i set this upppp

plz

[olive needle]

Similar Triangles

[cursive musk]

someone just said that

but like

what ratio bru

[olive needle]

What's the ratio between BF and BA?

[cursive musk]

i dont know 1:1?

theres not a number

[olive needle]

BF is equal to some number, a. What does BA equal in terms of a?

[cursive musk]

um

no clue

2

?

huh

im confuzzled

[olive needle]

The tick marks indicatd that BF and FA are equal in length.

[digital kindle]

2a

[digital kindle]

Nope BF=FA

[cursive musk]

how can bf and ba be equal in length

[olive needle]

Typo

[cursive musk]

kk

yea

[olive needle]

That implies that BF = FA = a

[cursive musk]

okay

[olive needle]

Therefore BA must equal 2a.

[digital kindle]

So BA= 2a

[cursive musk]

okay