help-0

[rigid smelt]

yes, it's a quadratic

[split cloud]

x^2-14x+29

[rigid smelt]

dont forget the rhs

[split cloud]

rhs?

[rigid smelt]

right hand side

x^2-14x+29=0

[split cloud]

its 0, kinda irrelevant

[rigid smelt]

it is...

[split cloud]

:/

sure

now wut

[rigid smelt]

just solve the quadratic like how you normally do

and dont try to factor it, it doesnt help

[split cloud]

i search up (#) factor

google didnt find a perfect factor

so i didnt bother doing it :/

[rigid smelt]

yes, not everything is perfect

like i have said, dont try to factor it

[split cloud]

quadratic equation?

[rigid smelt]

quadratic formula you meant

sure

[split cloud]

same thing :/

[rigid smelt]

or you can complete the square

it doesnt matter

[split cloud]

EW

[rigid smelt]

again, those are not the same thing

[split cloud]

dont ever mention that method again

ok 1s

[rigid smelt]

im free to mention whatever i want, im just listing out what you can do to get to the answer

if you dont feel like doing so, you dont have to tell me to not mention it

[split cloud]

im just kiddin, i appreciate the help

i got

11.5 and 2.5

?

was i supposed to get decimals?

[rigid smelt]

write them as their exact forms

and also dont forget the conditions for x

[split cloud]

like still in quadratic formula form?

[rigid smelt]

remember that x-1>=0 and 2x-5>=0

yes, in the form of a+bsqrt(c)

[split cloud]

14+_sqrt80 all over 2?

7+_ sqrt80?

[rigid smelt]

80=16*5

[split cloud]

oh!!!!!

i see

but

what about plus or minus

no minus?

[rigid smelt]

check it with the given conditions

[split cloud]

whered u get 2x-5

oh ncm

nvm*

[rigid smelt]

also you forget the 1/2 in front of sqrt(80)

[split cloud]

the 2a?

i get the quadratic way..

[split cloud]

but i still dont get .

oh nvm i got it

thanks 👍

.close

[lone heart]

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[verbal kayak]

Good day! Need help with discrete math

[verbal kayak]

(x~y)(y~z) -> (x~z)

i try simplify

((not x and not y) or (x and y))((not y and not z) or (y and z)) => (( not x and not z) or (x and z))

Honestly I don't know how to solve

[lone heart]

@verbal kayak Has your question been resolved?

[lone heart]

@verbal kayak Has your question been resolved?

[lone heart]

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[alpine sable]

I Domt understand 1 thing , I have exams after tommrow and I really wanna know how to do it
Pls note I could be pain trying to understand and be able to do work

[alpine sable]

I’m sorry but the text is really blurry

[alpine sable]

How will this help me ?

[limpid spade]

by looking up what they mean

[alpine sable]

No no I mean I need to find the missing angles bro

[limpid spade]

:/

[alpine sable]

pls don’t kill me

[limpid spade]

did u 3ven look them up

[shadow hamlet]

His internet died bro

[limpid spade]

??

[quick raven]

use the image and apply it to your work

[alpine sable]

Babe I told u to wash the dishes

[shadow hamlet]

Istg plz don’t mute me I spent my whole life in the dungeon tryna make it out

[alpine sable]

I will now

[shadow hamlet]

Yes

Smart

[quick raven]

i thought those were obvious

[shadow hamlet]

They are but the girl is too stupid to comprehend 😭😭

[shadow hamlet]

Bro

Woman

[alpine sable]

Guys?

[limpid spade]

?

[alpine sable]

I don’t understand bro

like I’m actually gonna turn emo if I don’t understand this

[limpid spade]

instead of looking at images look at definition

[alpine sable]

Ohh ok

[shadow hamlet]

U already are 💀

[alpine sable]

Shut up bro and stop sending me feet pics it’s annoying

[limpid spade]

report him

[alpine sable]

I’m jk up

*uo

*yo

[shadow hamlet]

He sends me pictures of his mom bombing my grandparents house

[alpine sable]

Okay so I finshed seeing the definition

[alpine sable]

…

Now

What do I do🥺

[limpid spade]

u read the definition

so u know the angle

[lone heart]

@alpine sable Has your question been resolved?

[lone heart]

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[fast oak]

Find the derivatives
Differentiate f(×)= /×^2-1

[calm grove]

What's this /

What's the Numerator if any?

[fast oak]

√

√x^2-1

[lone heart]

@fast oak Has your question been resolved?

[solemn grove]

chain rule it my guy

that’s just (x^2-1)^(1/2)

treat the bracket like you’d treat x
times by differential of what’s in the bracket

[fast oak]

f= u/v using quotient rule

[solemn grove]

what

[solemn grove]

no, chain rule

there is no denominator

[fast oak]

What is the quotient rule for the derivative of f=u/v

[fast oak]

Ty

[solemn grove]

nws

[solemn grove]

don’t forget to close

.close

@fast oak

[fast oak]

.close

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[magic fiber]

Hi! I’m working on a question where I’m supposed to find exact solutions (in interval 0 til 2pi) for the equation:

2sin^2(x) - sin(x) - 1 = 0

I couldn’t solve it on my own (attempted to substitute sin(x) as T and solve it as a quadratic) and noticed through wolframalpha the expression could be factorized into:

(sin(x) - 1)(2sin(x) +1) = 0

The factorization is perfectly logical and I understand how it works, but is nothing I could get to on my own and would see instinctively. Hence I ask, are there any other possible approaches to this question or if not, methods and tricks to see such factorizations in the future?

[glass lichen]

t=sin(x)

You get a quadratic I t

[gray isle]

substitution can help make stuff look simpler

you don't necessarily need to factorise, if you're unable to factorise and/or can't be bothered you can always use the quadratic formula

recognising whether stuff is likely to have a nice factorisation comes with practice

[magic fiber]

I can only imagine😄 in that case, I’ll send some screenshots because I attempted a substitution both with completing the square and the formula and didn’t get viable answers in either one.

[tight locust]

it might be a very simple thing to say but remember that sin^2(x) is just a fancy way of writing (sin(x))^2

[magic fiber]

I can’t find the notes of my attempts, but as mentioned, I remember both of my attempts at performing a substitution of sin(x) failed (tried formula and completing the square). I’d really appreciate if someone shows their step by step here to see if I can catch what I did wrong.

[tight locust]

sure

let sin(x) = t

then we have:
2t^2 - t - 1 = 0

now find factors of ac that add to equal b

[magic fiber]

well -2 and 1

[tight locust]

yep

now let's split the linear term. -2t + t = -t

so we have

2t^2 - 2t + t - 1 = 0

factor by grouping

2t(t-1) + (t-1) = (2t+1)(t-1)

[magic fiber]

And that is completely correct. I’m however completely unfamiliar with the method you used. How did you rewrite 2t(t-1) + t-1 as the following expression?

[tight locust]

2(5) + 5 = 5(2+1) = 5(3)

if it helps you we can make another substitution

let (t-1) = A

then:
2tA + A = A(2t+1)

[magic fiber]

Ahh now I see

Thank you

I’ll have to look a bit deeper into factoring by grouping, splitting the linear term etc. completely unfamiliar with these terms. Thanks a lot for the help!

[tight locust]

yeah i'd say it's the easiest way going about factoring non monic quadratics

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[plucky lynx]

what are you thinking of to approach this problem?

Multiplication is associative, so you can each part of it anyway you like.

wdym? I meant it as (-8a^2b^4)(3a^-5b^-3) can be group up as (-8)(3)(a^2a^-5)(b^4b^-3).

sorry if I confused you, lets backtrack. You said do all the powers first, what do you mean by that?

yes if you mean -8.

when you multiply a^n and a^k what do you do?

I meant in general.

if you have a^n and a^k, what is a^na^k? If you can do it, all that is left in your problem is to apply that for a and b.

How did you get -24^10?

It shouldn't have a power.

a^na^k = a^(n+k).

Apply that for a and b in your question.

your not distributing, I think that is what is confusing you.

[regal acorn]

To format it better, $$a^na^k = a^{n+k}$$

[plucky lynx]

I know, did not want to use it.

[ocean seal]

hiro

[raven rover]

Just laws of exponents (you can look these up)

[plucky lynx]

,rotate

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@alpine sable Has your question been resolved?

[lone heart]

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[alpine sable]

Hello

[alpine sable]

Guys I am really bad with probabilities and thus I do not even know where to start

Can someone spare me some time and patience to explain it thoroughly

👍

[lone heart]

@alpine sable Has your question been resolved?

[alpine sable]

<@&286206848099549185>

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@alpine sable Has your question been resolved?

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[gritty wave]

I've done a.) already and sketched the first part of b, I'm just not sure what the bounds are supposed to be for this integral?

[tacit arch]

.close

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[weary oxide]

Can someone help me with Q40

[sudden hinge]

@weary oxide what does the red text say lol

[weary oxide]

Ignore

[sudden hinge]

so what did you try

[sleek osprey]

This is the national talent hunt Program?

[weary oxide]

Idk I’m just helping my friend

I don’t think so

[sleek osprey]

<@&268886789983436800> Can someone check this please not sure if it's an exam. Just making sure.

[sly mantle]

this is a past test which is available online

[meager snow]

if you are worried he might be cheating don't worry it's the 2018 version

[sly mantle]

https://nthp.iba.edu.pk/pdfs/NTHPBatch2018PastSamplePaper.pdf

[meager snow]

probably just practicing

yeah exactly

[sleek osprey]

ah thanks

Anyways

[weary oxide]

i still didnt get an answer

He prob did it by now

[tacit arch]

feel free to .close

[weary oxide]

Wait

[weary oxide]

so cant help?

[raven rover]

Do you know how to find f(-x)?

[weary oxide]

I’m slightly younger than my friend, not in that class yet so no

[sleek osprey]

oh.

[weary oxide]

the oldest friend hates this kind of math so he also doesn’t know

Its been more than an hour i dont think he needs help anymore lmao

[sleek osprey]

ok

[tacit arch]

.close

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[alpine sable]

.close

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[alpine sable]

sumone help me find out the X and help me understand this equation (would be good if u speak georgian)

[lone heart]

@alpine sable Has your question been resolved?

[obsidian crane]

you know what tan is equal to ?

[alpine sable]

no bruh its just X there

all this stuff is so confusing

oml

[obsidian crane]

I mean the formula of tangent

[alpine sable]

imma cry for real i hate math

[alpine sable]

oh yeah sin:cos

[obsidian crane]

tan x = sinx / cosx , correct, it's also equal to something else

tan x = perpendicular / base

x here is the angle

[alpine sable]

uhh

[obsidian crane]

wait x might confuse you sec

[alpine sable]

this why there is no help for me dawg i dont understand what you are saying in english

[obsidian crane]

tanΘ = perpendicular / base

Θ here is the angle

look at the diagram

what's the perpendicular

and what's the base

and whats the angle

plug in the values that's it

[alpine sable]

bru

bruh oh nah

whats a prrpendicular

and tf is a base

how do i discard this i aint gon get no help

.close

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[lean wraith]

is part c of this asking for the area of a semi circle or the area of the curved surface of the cylinder

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.close

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[wet spindle]

this implies that P(x) has roots > 3

[wet spindle]

but we're only given 2 roots

is that it?

hmm wait I confuse it with factors

#help-1 message why? @tacit arch

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[alpine sable]

i'm given a problem i currently have no knowledge of how to solve, it's to do with defined integrals:
A parabola whose branches are pointing downwards crosses the X axis at x = 0 and x = 1. The area, once limited by the parabola and X axis is equal to 2. Find the parabola's equation.
how would i go about solving such a problem?

[knotty spire]

A parabola whose branches are pointing downwards crosses the X axis at x = 0 and x = 1.

Just from this info, what would the equation of the parabola be?

(with unknown parameters)

[alpine sable]

y=-ax^2+b?

[knotty spire]

where's the x term

Do you remember the equation for a parabola in terms of its roots?

[alpine sable]

i don't

unless i do

if it's crossing at x=1, doesn't that make the x term 1x?

y=-ax^2+x+b

[knotty spire]

not necessarily

Well, hm, I don't know how to make you remember or derive the form easily

so here it is

$y = a(x-x_1)(x-x_2)$ is the general form.

[ocean seal]

Remavas

[knotty spire]

where x_1 and x_2 are the parabola's real roots

(of course this only works if the parabola has real solutions)

[knotty spire]

Now, plug in our known info into this equation

[alpine sable]

ax^2-ax if i didn't mess it up

[knotty spire]

not quite

We know our parabola is pointing downwards

I mean

[knotty spire]

We could probably have it in this form

and then get a negative value for a

Or we can do -a in front

And get a positive value for a

no difference really

[alpine sable]

so knowing that the parabola is pointing downwards, am i supposed to just write y=-a(x-x1)(x-x2)?

[knotty spire]

I think that is the better option

[alpine sable]

i assume this suffices for an answer, then

[knotty spire]

nope

We didn't use the other piece of information.

Which will help us determine the value of a

[alpine sable]

oh right the area

[knotty spire]

So how would you find the area of your parabola and the x axis

$y = -ax^2 + ax$ (once expanded)

[ocean seal]

Remavas

[alpine sable]

defined integral

[knotty spire]

Yup

Try integrating it yourself

You will get an expression in terms of a

[alpine sable]

i get a = -2.4

plugging it into my calculator confirms it

.close

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[knotty spire]

,w integrate -2.4x(x-1) from 0 to 1

[ocean seal]

Results provided by WolframAlpha

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

Requested by Remavas#3737

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[compact drift]

Can somebody please explain what this describes?

[compact drift]

I don't understand the left part

[knotty spire]

,w binomial coefficient

[ocean seal]

Results provided by WolframAlpha

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Requested by Remavas#3737

[compact drift]

Thanks' I'll read more on it

How do I release the channel?

.close

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[compact drift]

.close

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[honest cypress]

I need help on the second problem

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[hazy cairn]

I have made a start on this and got 1 proved

but how would I go about doing parts b and c

like

i have an idea for b but im not fully sure

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[alpine sable]

I'm not sure I understand this

[knotty spire]

What do you not understand?

[alpine sable]

what do I understand @knotty spire

would be a better quesion

how would $a_n = 0$ be a solution

[ocean seal]

Joseph Fourier

[knotty spire]

Well, does the given $a_n$ satisfy the given recurrence relation

[ocean seal]

Remavas

[alpine sable]

I dont know

im not given a_n-1

or a_n-2

[knotty spire]

Well

You are given the general formula for $a_n$

[ocean seal]

Remavas

[knotty spire]

So you can easily compute a_n-1 and a_n-2

[alpine sable]

ok

.close

[lone heart]

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[winter tangle]

cos^2(t) = 1-sin^2(t)

try using that?

erm also what we elliminating

[knotty spire]

the parameter would be t

[ashen igloo]

Combing both equations basically

[knotty spire]

x + y^2 = 1 should work

[ashen igloo]

Could u explain

[knotty spire]

$\sin^2x + \cos^2x = 1$

[ocean seal]

Remavas

[winter tangle]

this

[ashen igloo]

Aha ic

Ty

.close

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[alpine sable]

I still dont understand

let $a_n = 4^n$

[ocean seal]

Joseph Fourier

[alpine sable]

what would I do here

[knotty spire]

Plug that into $a_n = 8a_{n-1} - 16a_{n-2}$

[ocean seal]

Remavas

[knotty spire]

And see whether it holds

[alpine sable]

ok

but

[knotty spire]

Or well, rather

Evaluate the RHS

[alpine sable]

but how

is it just $84n^{n-1}$

[ocean seal]

Joseph Fourier

[alpine sable]

...

same thing for 16

or would I plug that in for $a_n$ then re arrange for $a_{n-1}$ and $a_{n-2}$

[knotty spire]

sorry wait what, why is it suddenly n to the power of n-1

[ocean seal]

Joseph Fourier

[knotty spire]

Ok let's clear some thing up first

$a_n = 4^n$

[alpine sable]

yes

[ocean seal]

Remavas

[knotty spire]

Can you tell me what $a_{n-1}$ will be

[ocean seal]

Remavas

[alpine sable]

$4^{n-1}$?

[ocean seal]

Joseph Fourier

[alpine sable]

?

?

?

@knotty spire

[knotty spire]

Yes

[alpine sable]

ok

so next

[knotty spire]

So now, without rushing it

$8a_{n-1} - 16a_{n-2}$

[ocean seal]

Remavas

[alpine sable]

$8(4^{n-1}) - 16(4^{n-2})$

[ocean seal]

Joseph Fourier

[knotty spire]

And now you simply simplify this as much as possible

and see whether you get $4^n$ at the end

[ocean seal]

Remavas

[alpine sable]

how can u even simplify that

[knotty spire]

using exponent laws

[alpine sable]

ok mb I have down syndrome

[knotty spire]

you can express every term here as a power of 2

Then use the old and beloved exponent laws

[alpine sable]

what

[knotty spire]

to give you a hint

8 = 2^3

[alpine sable]

oh

ok

uhh

16(4^{n-2})

becomes {4^n}

@knotty spire

in order to use the exponent laws the bases have to be the same right

[knotty spire]

for most of them yes

[alpine sable]

I got

$2^{2n+1} - 4^n$

[ocean seal]

Joseph Fourier

[alpine sable]

@knotty spire

[knotty spire]

so does that equal 4^n

[alpine sable]

no

[knotty spire]

there's your answer

[alpine sable]

but the textbook says it should be right

[knotty spire]

hm

,w simplify 8(4^{n-1}) - 16(4^{n-2})

[ocean seal]

Results provided by WolframAlpha

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

Requested by Remavas#3737

[knotty spire]

well you did something wrong

[knotty spire]

$2^{2n+1} - 4^n$

[ocean seal]

Remavas

[knotty spire]

$2^{2n+1} - 2^{2n}$

[ocean seal]

Remavas

[knotty spire]

Alright you are close to the actual answer

[alpine sable]

so...?

what did I do wrong

[knotty spire]

No you're correct

I just failed to see you hadn't simplified to the end yet

[alpine sable]

how do I further simplify this

[knotty spire]

factor 2^{2n}

[alpine sable]

$4^{n+1}-4^{n}$

[ocean seal]

Joseph Fourier

[knotty spire]

nope

What I want you to do is this

$ab + ac = a(b+c)$

[ocean seal]

Remavas

[knotty spire]

Pull 2^2n "out"

[alpine sable]

$2^{2n}\left(2^{2n}-1\right)$

[ocean seal]

Joseph Fourier

[alpine sable]

@knotty spire

[knotty spire]

mhm

wait no

$2^{2n+1} = 2\cdot 2^{2n}$

[ocean seal]

Remavas

[alpine sable]

ok so

$2^n(2-1)$

[ocean seal]

Joseph Fourier

[alpine sable]

2^2n

sorry

[knotty spire]

You can probably calculate the parentheses

[alpine sable]

yeah done

I cant fucking believe I forgot exponent laws

need to sleep

thanks

.close

[lone heart]

Channel closed

Closed by @lyric arch

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[knotty spire]

👍

[lone heart]

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[alpine sable]

$In the library at Lenape Elementary School, there are
2
5
as many fiction books as there are nonfiction books. There are 56 books in the school library. How many books are fiction books?

[alpine sable]

In the library at Lenape Elementary School, there are
2
5
as many fiction books as there are nonfiction books. There are 56 books in the school library. How many books are fiction books?

<@&286206848099549185>

[rose raven]

The formatting is a little wrong

Can you fix it and then people can help - hard to see what you mean

is it 25 times as many fiction books as there are non fiction?

[alpine sable]

yea I think idk lmao

[rose raven]

Well basically

Let x be the number of non fiction books

25x + x = 56

This seems wrong though

[alpine sable]

Okay thanks anyway

[rose raven]

Are you just posting your homework?

Because I think you should give it a go first

[alpine sable]

<@&286206848099549185>

<@&286206848099549185>

.close

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[fringe yoke]

X

[fringe yoke]

How come taking the integral of an area function gives you volume?

I guess I am confused because I don't understand what an area function is exactly...

[tight locust]

@fringe yoke post the problem

i can explain it much more clearly to you if you give me an example.

[fringe yoke]

My goal is to turn this curve into some sort of volume thing

If I remember correctly from AP Calc last year this is called the disc method? Not sure.

[tight locust]

ok i see what you're doing. this is a solid of revolution.

[fringe yoke]

Wait one sec

isn't solid of revolution when I rotate the function around?

[tight locust]

is there no rotation here?

[fringe yoke]

No the disc is contained under the function

[tight locust]

what does the actual question say

[fringe yoke]

No question

I asked that question to re-develop an understanding of integration

So I guess my ultimate goal would be to turn that infinite sum into a standard integral

[tight locust]

it's unclear what you're trying to do here, tbh

[fringe yoke]

Ok sorry

[tight locust]

what solid is desired

[fringe yoke]

Imagine an infinite amount of these cylinders

With width dx and radius 1/2(f(x))

I want to find the total volume of these cylinders, but I need to use calculus

<@&268886789983436800>

[sly mantle]

ty

[tight locust]

lmao

[fringe yoke]

Xd

I just need to revisit riemann integrals

[tight locust]

the area of a solid like this is the base times the height

where is the height?

[fringe yoke]

pi*radius^2*width

Those are cylinders

[tender dagger]

is this cylinder in 2d?

[fringe yoke]

Yea

[tender dagger]

that has 0 volume

[tight locust]

^

[fringe yoke]

Right but if we add them all up using calculus we can find their volume no?

[tight locust]

volumes don't exist in 2d

[fringe yoke]

We are imagining them

[tender dagger]

think about it

you have h * dr^2

[fringe yoke]

I drew it in 2d but I imagine they are in 3D

XD

[tender dagger]

you need two integrals to get non zero volume

[fringe yoke]

hmm

hmm

[tight locust]

the height of a cylinder does not lie in the same plane as its width

and the width of a cylinder is exactly twice the radius (diameter of a circle is constant). so what you're actually describing is impossible

[tender dagger]

I think by width he means height

[tight locust]

not by what he drew and wrote

[fringe yoke]

ohhh

[tender dagger]

it doesn't particularly paint a pretty picture in my head

[fringe yoke]

dude I think I get what you mean

rn

[tender dagger]

like the cylinders intersect a lot

[fringe yoke]

No no it still works

[tight locust]

a circle has the same diameter no matter how you measure it. you are simultaneously telling me that the diameter of the base of the cylinder is dx AND it is f(x) at the same time

[tender dagger]

Ok I sse

[tight locust]

that dx you just drew is actually perpendicular to the x axis

[fringe yoke]

IMagine you are looking sideways at these discs

[fringe yoke]

I am saying the diameter of the circle is f(x)

and I want to multiply that by dx

[tender dagger]

yeah so the volume is pi/3f(x)^2dx

[fringe yoke]

to get these cylinders

[fringe yoke]

1/4

?

Area of each cylinder

[tender dagger]

• 4pi/3

[fringe yoke]

and that sum is every cylinder under the curve

radius = 1/2(f(x))

Area = R^2 * pi * width = (1/4 f(x)^2) * pi * dx

So how do I convert that thing

into an integral that I can actually compute ?

[tender dagger]

just integrate over x

[fringe yoke]

Why does that work?

[tight locust]

this doesn't work.

[tender dagger]

thats kinda the definition of integral

[tight locust]

that dx you just drew is actually perpendicular to the x axis

[fringe yoke]

yeah it's a distance

[tender dagger]

its just hard to see what he drew

[tight locust]

that dx you just drew is actually perpendicular to the x axis

[tender dagger]

Normally we find volume of function rotated about x = 0 right?

[fringe yoke]

Is this better drawing?

[tender dagger]

He's just rotating about f(x)/2

[tight locust]

yes that's a lot better

[fringe yoke]

I suppose

[tight locust]

but you still don't have a height

[fringe yoke]

I suppose I am rotationg about f(x)/2

[fringe yoke]

We don't need height for volume of cylinders

[tight locust]

you do

[tender dagger]

height is dx

[tight locust]

if a solid lies within a single plane then it has no volume

[fringe yoke]

$A_C = r^2\cdot\pi\cdot dx$

[ocean seal]

Tim O'Brien

[tight locust]

the height can't be dx because dx is coplanar to the radius

[fringe yoke]

Whaaat

[tender dagger]

its not its perpendicular

[fringe yoke]

they aren't coplaner

[tight locust]

does your 'dx' lie in the xy plane?

[fringe yoke]

Oh shit

Wait...

[tender dagger]

radius is in yz plane, height is parallel to x axis

[fringe yoke]

Yeah

[tender dagger]

thats perfectly fine

[fringe yoke]

Radius is in yz plane

yeah

But anyway

So How do I get that infinite sum into an integral @tender dagger

I guess i am having trouble with the definition of integration

I learned it last year

[tender dagger]

Its actually the definition of integral

yeah

[fringe yoke]

I know it finds area under a curve

If that curve is an area function, then integrating that will get me volume

Idk

confusing 😭

I used to know all this man I swear

[tender dagger]

you think about integration wrong I think

it finds lot more than area under curve

you can cut sphere into infinite discs and integrate over that

[fringe yoke]

What do you mean by integrate over?

[tender dagger]

like imagine some disc from x to x+dx

[tight locust]

He literally said that r = 1/2 f(x) though. Are we to assume that z=f(x) instead of y=f(x)?

[fringe yoke]

right

[tender dagger]

with volume f(x)dx

[fringe yoke]

OK

[tender dagger]

f(x) = some pi * sqrt stuff

[fringe yoke]

mhm mhm

Wait I think I got it

[tender dagger]

then essentially integral f(x)dx gives you the sum over every disc you cut it into

[fringe yoke]

Right right

It's because

technically

those disks are in 2d

and integrating over area gives volume?

[tender dagger]

Don't think of area -> volume imo

[fringe yoke]

ok

[tender dagger]

I like to think of it as very small volume -> finite volume

[fringe yoke]

Got it

Yeah

perfect

[tender dagger]

each disc has very small volume because of how thin it is

yeah that makes inf more sense in my head

[fringe yoke]

So this disk thing you mention is literally what I have done

[tender dagger]

Yeah

except f(x) is arbitrary

[fringe yoke]

RIght

So that's my volume function

[tender dagger]

yes

[fringe yoke]

and I just integrate that

I have to sub n-> x

[tender dagger]

that sum is integation by definition

[fringe yoke]

Yeah

it's called a riemann integral right?

Dudeee that literally is integration by definition

holy shit

and since there is a dx

[tender dagger]

Riemann integral is just normal integral

[fringe yoke]

Alright alright

[tender dagger]

there is weird shit like lebesgue integral

[fringe yoke]

ye

ye

Ok I think I get it now, sort of

I understood it 0% now it's 70%

thanks you

[tender dagger]

np

now just hope someone answers me too

[fringe yoke]

XD gl

.close

[lone heart]

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[tight locust]

Oh I see it now

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[tight locust]

I had the cylinders sideways

[tight locust]

My bad

.close

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[nova void]

Question: Approximate ln(4) using trapezoidal rule and n=3. This is what I did: Took the derivative of lnx, to get 1/x. Then, found the area under the curve from 1-4 using trapezoidal rule, because lnx is positive beyond x=1, and ends at 4. My final solution is 35/24, which is 1.458 and ln(4) is 1.386. Is this the correct method or do I not take the derivative and simply plug in ln(4) into the trapezoidal rule and get some crazy fraction?

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@nova void Has your question been resolved?

[nova void]

<@&286206848099549185>

.close

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[alpine sable]

sssssssssssssssssssssss

[short cobalt]

Pythagorean theorem

@alpine sable are u familiar?

[alpine sable]

yeah

i think i did it

but idk if its right

x = 35.3553390593

2x has a length of 4x^2

and 6x has alength of 36x^2

is that right

@short cobalt

[short cobalt]

I just checked this number. it looks right to me.

[short cobalt]

yes

[lofty flare]

Idk if u already know this but another thing to know is that the hypotenuse (diagonal line) is always the longest in a right angle triangle

So your bigger result should always be the hypotenuse

[alpine sable]

alr

<@&286206848099549185>

[short cobalt]

how can u make an eq to find that?

[gray ingot]

use a variable for the length for the flagpole

[alpine sable]

a^2+b^2=130^2 im guessingg

[gray ingot]

now relate a and b

[alpine sable]

how

[gray ingot]

using the question

[short cobalt]

don't forget about the twice as long part

[alpine sable]

ohhhhh

hold on

is it

is a x and b x^2

i mean 2x

or somethin

like that

[short cobalt]

x and 2x

[alpine sable]

yea

so what the equation would be?

(x)^2+(2x)^2=(130)^2?

[short cobalt]

so if one side is x and another is 2x

and your hyp. is 130

you have all the pieces to make a eq with pythagorean theorem like u did in the last one

[alpine sable]

yeah

u see the boave

above

is that it

?

[gray ingot]

yes

[alpine sable]

(x)^2+(2x)^2=(130)^2?

alr

[short cobalt]

yes

try that

[alpine sable]

ok

i did it

im p sure its that

[short cobalt]

okay, assuming you did your calc right, it should be good

[alpine sable]

alr

yhhh

i did

i got it irght

[short cobalt]

great! nice job

[alpine sable]

i got the other one wrong tho

idk wtf is this LOL

no clue how to get that

[short cobalt]

hmm

tbh, im not 100% why its wrong.

[lone heart]

@alpine sable Has your question been resolved?

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[pearl pelican]

A computer selects digits at random. How many digits are needed to be chosen so
that the digit seven appears with a probability of at least 1∕2?

[pearl pelican]

how do i approach this questions?

[lone heart]

@pearl pelican Has your question been resolved?

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[next bluff]

So im in algebra btw, question is...for factoring trinomials...(I was absent for a math class) how do I know if it is "prime"

for like smaller numbers when doing split method I can see that it just doesnt work but what about like idk

[tight locust]

give an example of a problem

do you mean quadratics, like something in the form ax^2 + bx + c ?

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@next bluff Has your question been resolved?

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[waxen pendant]

how do u solve this tis

[next bluff]

3x^2-2x-6

factoring trinomials

[lone heart]

@waxen pendant Has your question been resolved?

[alpine sable]

Uh

[waxen pendant]

<@&286206848099549185>

[gusty gorge]

e^(lambda1 t) * v1 and e^(lambda2 t) * v2 didn't work?

[waxen pendant]

I figured it out

[gusty gorge]

okay so what have you tried

okay well the first thing to do with any math problem

is to figure out what they're asking

so what do you think this question is asking?

actually

wrong channel

[wary stream]

You're trying to close someone else's channel

That's why you're failing

[waxen pendant]

.close

[lone heart]

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[wary stream]

Did you calculate each of the following?

[lone heart]

@alpine sable Has your question been resolved?

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[barren thunder]

The dimensions of a pool are 25m length, and 16m breadth. If 40 ml of liquid chlorine is used for every 1000L of water, with the depth of the water being 4.5m, how much chlorine is used?

[barren thunder]

I had this question in my exam and apparently its 45L??

but i got 72L

[left citrus]

I just calculated to make sure

So basically

The volume of the pool where there’s water is 25164.5

Right?

Oh whoops i dunno why it did that

25 times 16 times 4.5

[barren thunder]

yeah

[barren thunder]

you need to put spaces in between the asteriks i think

[left citrus]

Aah yeah

[barren thunder]

So then i did times 1000 because cubic metre is 1000L

[wary stream]

Because discord formats text in between * as italicized

[left citrus]

Yeah not used to discord

But wait a minute I just did this and I got 1125000 as a number

[barren thunder]

so volume/1000(because per 1000L litres) times 0.04(chlorine per 1000 converted to litres)

72 🤨

but the teacher that set the question paper says its 45

and so do many of my classmates

[left citrus]

Wait I just got 45 lol

And now I forgot what I did im hallucinating

[barren thunder]

i asked some of them how they got 45 and they said "the question had 4.5 in it and one of the options was 45 so i just ticked 45"

.>

[left citrus]

But you should be right now that I think abt it

Because a cubic metre can hold a 1000L

The more I think abt it now the more you sound correct so I’m really confused

[lone heart]

@barren thunder Has your question been resolved?

[barren thunder]

i guess

[lone heart]

Channel closed

Closed by @barren thunder

Use .reopen if this was a mistake.

Available help channel!

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Remember:
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• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

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[weary void]

This is a combinations question (combinatorics), I was wondering how to get the answer?

How would you go about this?/How would you approach this question

I don't understand why we just do 6c3

and NOT multiply by 2

[spark creek]

Why do you want to multiply by 2?

[lone heart]

@weary void Has your question been resolved?

[weary void]

cuz there are 2 groups

nvm solved it

.closed

.close

[lone heart]

Channel closed

Closed by @weary void

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

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

[verbal heart]

2nd one.

[neon ibex]

Hello, I need help with an integral, or explaining. In my book is says that

$$
\begin{array}{l}
\int_{-\infty}^{\infty} \frac{x \sin x}{1+x^{2}} d x=\int_{-\infty}^{\infty} \frac{x e^{i x}}{1+x^{2}} d x \
e^{i x}=\cos x+i \sin x
\end{array}
$$

[ocean seal]

MarcelUNilsson

[neon ibex]

I dont see how

[verbal heart]

But sir this room is already occupied by me. Could you please take any other room? That would be a lot. Thanks.

[neon ibex]

OOoh it was in available

[near lagoon]

Probably because (xcosx)/(1+x^2) is odd

[neon ibex]

ofcourse!

[verbal heart]

<@&286206848099549185>

Ping me, please.

If you can help me out.

[spark creek]

Do you know the condition for a quadratic equation to have equal roots?

[lone heart]

@verbal heart Has your question been resolved?

[verbal heart]

Is that with quadratic formula or discriminate? If not, then I have no idea. I apologise.

[spark creek]

Discriminant one

D=0

[verbal heart]

Oh yes.

I know that one

b² - 4ac = 0

[spark creek]

Yes

[verbal heart]

So, shall we start solving?

[spark creek]

Yup

[verbal heart]

Okay, so I guess first

[verbal heart]

We can multiply the kx with (x-2)?

So, it'll be, kx² - 2x

Is that what we have to do?

[slender gull]

Nope.

kx^2-2kx

[verbal heart]

OoOo

Oh yes, I forgot about the k

So, kx² - 2kx

[slender gull]

So now you have $$kx^2-2kx+6=0$$

[ocean seal]

What the hell am I doing here?

[verbal heart]

And we can put this on the formula

[slender gull]

Right.

[verbal heart]

So, it'll be

(2kx)² - 4(kx)(6)?

[slender gull]

No.

[verbal heart]

Then, possibly (2)² - 4(k)(6)?

[slender gull]

No.

Lol

[verbal heart]

Sorry sir, I am not that good at maths.

[slender gull]

$(2k)^2-4(k)(6)$\
This

[verbal heart]

I have a question, why do we put the k with the 2?

[slender gull]

It's alright lol we're good here.

Oh wait now you confused me.

My bad.

[verbal heart]

I meant, I just asked the question so I will have no doubts

[slender gull]

No it is indeed

[ocean seal]

What the hell am I doing here?

[slender gull]

This was correct.

Also you asked why do we put 2?

[verbal heart]

Indeed, but still, why do we put the k with 2? That's the place where I am a bit confused

[verbal heart]

No, k with 2.

[slender gull]

General form of a quadratic is $$ax^2+bx+c=0$$
So like the entire thing with x is b. So in this case we had -2kx so other than x we have -2k that's our b.

[ocean seal]

What the hell am I doing here?

[verbal heart]

Okay, got it. Thanks

[slender gull]

You're welcome.

[verbal heart]

Alright, now if we square 2k we will possibly get 2k²?

[slender gull]

No.

[verbal heart]

[slender gull]

It's not $2k^2$ it's $(2k)^2$ there's a difference, use laws of indices.

[ocean seal]

What the hell am I doing here?

[verbal heart]

Oh yes, I see. So, possibly 4k²? Am I right?

[slender gull]

You are.

[verbal heart]

So the equation goes like, 4k² - 16k = 0

[slender gull]

Unfortunately not.

[verbal heart]

[slender gull]

,calc 6*4

[ocean seal]

Result:

24

[slender gull]

[verbal heart]

My maths is so good. Isn't it?

[slender gull]

It is.

[verbal heart]

Nevermind, so, 4k² - 24k = 0

[slender gull]

Right.

[verbal heart]

Now, we take the -24k to 0. So, it'll be 4k² = 24k

Then, we take the square on the top of 4k to 24k. So, it'll be 4k = √24k?

[slender gull]

You could have done $4k(k-6)=0$

[ocean seal]

What the hell am I doing here?

[slender gull]

It won't be.

[verbal heart]

But how? Please explain.

[slender gull]

Factor

We had

4k^2-4(k)(6)=0

[verbal heart]

Yes

[slender gull]

Can you not factor this?

Have you learnt that?

Both of the terms have a common factor of 4k

[verbal heart]

Oh yes

We can take 4

[slender gull]

And k too.

[verbal heart]

So, 4k ( k - 6)?

[slender gull]

Correct.

=0

[verbal heart]

Oh yes

Okay, so what next?

Sir?