help-0

[tidal solar]

WHAT?!?! there's a proof for 2+2?

[alpine sable]

Here we go

[paper oar]

Quantitative

[stable grail]

a 2,-3 b 6,7 C - 8,5 find all sides <@&286206848099549185>

[fallow jasper]

Proofs*

[alpine sable]

theta_1 is the one that needs to be found, A and theta_1 should be linked but I'm struggling with how

[stable grail]

PLZ help

<@&286206848099549185>

[alpine sable]

Corrected diagram

how to solve this

over a Sphere with radius R

the easiest way

[tawdry saffron]

how to calculate the surface area of a circle only knowing the length of 2 cords and in between the 2 cords and that the 2 cords are parallel

don't know if they are opposite of the centre or not, one cord is 8cm, other is 12cm and the distance between them is 1

[red phoenix]

Must easier, 90-Theta 1 = phi = 42

Then use the refraction equation for theta 2

.

[crisp grove]

depends on which of the center the chords are, if on the same side area will be larger

[alpine sable]

I don't think that's correct....

[tawdry saffron]

I guess they are on the same side since they differ 4 cms in length but only 1 cm between them

[red phoenix]

Ah yes 🙂 brain fart

I meant 90-theta 1 + phi = 90

Phi = theta 1

[tawdry saffron]

In a circle [AB] and [CD] are two parallel chords with lengths 8 and 12. The distance between AB and CD is 1. What is the area of ​​that circle? @crisp grove this is all I got

but I don't really know the properties of chords in a circle

so idk how to solve this

I tried with triangles but didn't work out

[alpine sable]

How is phi and theta 1 equal? By what geometric reasoning? 🤔

[red phoenix]

Correct this is wrong

I saw the normal as orange instead of the gray one

[alpine sable]

Yup the normal is grey, I'm terrible at labeling

[red phoenix]

I did find something earlier tho

[alpine sable]

Logically there is enough there for a solution, but finding it.....

[crisp grove]

do you have the answer? Let me check if I got the correct answer

[red phoenix]

If you continue the initial orange line down, you can find another phi by alternate angles, I mingled this into something . Also if you extend the gray normal to intersect with the other one , I also found something

But I don’t have any paper around to work on this rn 😦

[crisp grove]

yup got it

[tawdry saffron]

appearantly it was possible with triangles

[crisp grove]

it is

this is the rough idea

@tawdry saffron

[tawdry saffron]

thank you!

[red phoenix]

360 = 180 - phi - theta 2 + theta 1. This and the other refraction equation is enough?

[dreamy crow]

is this open for questions?

[alpine sable]

Well that gives this....

Eldritch nightmare unlocked

[blazing sage]

Hi guys im new here. Soo

[winter hull]

Is this channel free for a quick question?

[alpine sable]

Soo the equation above gave you a heart attack? 😂

[winter hull]

Can someone please help me why (sin 2^24 * 56 degrees)/(2^24 * sin 56 degrees) = 1/2^24

[blazing sage]

No as in.. i have some qns to ask

[winter hull]

= 1/2^24

why

[blazing sage]

This is my solution. I just wanna double confirm if its correct or not.🙂

Its on laplace

[crude hazel]

how can I solve for x in sin(x) * cos(x) - sin(x) + cos(x) - 1 = 0

[blazing sage]

No idea. Whose the expert here haha

[noble sinew]

factor then use zero-product property

[crude hazel]

ty i see it now, akjdbkahdbasd

[blazing sage]

Anyone can help with my solution on laplace?

^^ doc.1

[vale wigeon]

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

[crisp grove]

SS will be appreciated

[blazing sage]

Here it is the question. And my solution

[crisp grove]

looks ok to me

[crude hazel]

what do I do to solve (cosx)^3 + (sinx)^3 = 0

would I factor, use an identity, or etc...

[crisp grove]

tan³(x)=-1

[crude hazel]

not sure where that came from, could you show me what u did

[crisp grove]

divide both side by cos³(x)

and rearrange

[crude hazel]

I don't think you can cancel cos^3(x) in cos^3(x) + sin^3(x)

[blazing sage]

Bro heres my friend solution. Its abit different. So i wanna double check here. See whose correct

[crude hazel]

they are seperate terms

[crisp grove]

@crude hazel non zero

[crude hazel]

show me your work on a notepad or paper, I think you are doing something wrong

[blazing sage]

@crisp grove u can see my friend ans above. Thanks man!

[crisp grove]

oh you ignored the wind gust term entirely

your friend is correct here

[dreamy crow]

is this correct?

[crisp grove]

cos³(x) is nonzero because x=2nπ+π/2 doesn't solve the equation to it's right to cancel both side

[dreamy crow]

oh im sry i didnt know this channel was taken

my bad

[blazing sage]

So mine was wrong? The one in green is correct?

[blazing sage]

This msg is for me right🤣

[crude hazel]

yes but sin^3(x) + cos^3(x) / cos^3(x) != sin^3(x)

you can't cancel cos^3(x) so where did you get tan^3(x)

[crisp grove]

yes

[crisp grove]

what are you saying? 👀

[blazing sage]

I guess im wrong then

[crude hazel]

I'm just wondering how dividing both terms by cos^3(x) gives you tan^3(x)

[unique tapir]

Hello

[crude hazel]

which identity is that, I don't think I learned this yet aaaaa

[unique tapir]

how do I find the equivalent fraction?

Like for the first one 2/4 do I times it by 2

4/8?

[vale wigeon]

that's one way to do it, but not the only way

you say "the" equivalent fraction as if each fraction has one and only one of those...

[unique tapir]

Oh

[vale wigeon]

also, going from $\frac{2}{4}$ to $\frac{2 \times 2}{4 \times 2}$ is not ``timesing it by 2''; if anything, you should specify that you're multiplying \textbf{the top and the bottom} by 2, so as not to make people think you're talking about $\frac{2}{4} \times 2$

[ocean seal]

Ann

[alpine sable]

U multiply it by an even number @unique tapir

[vale wigeon]

don't post misleading info, justak_.

[unique tapir]

So I can’t

[vale wigeon]

it doesn't have to be even.

[unique tapir]

.

[vale wigeon]

and machen, don't put words in my mouth.

all i did was criticize your terminology.

[unique tapir]

what

uhhh

[vale wigeon]

i pointed out the mistake you made with your word choice.

[unique tapir]

oh

My grammar sorry

[vale wigeon]

and i even told you "that's one way to do it", which means that what you did is correct. multiplying the top and bottom by 2 does give you a fraction equivalent to what you started with.

it's not the only way to generate equaivalent fractions though.

[unique tapir]

oh so it works with like 4

[vale wigeon]

if anything, you can multiply the top and bottom by any number, so long as you multiply by the same number on both.

[unique tapir]

oh

[vale wigeon]

for example, you could go from $\frac{2}{4}$ to $\frac{2 \times 42069}{4 \times 42069}$

[unique tapir]

I can use any number

[ocean seal]

Ann

[unique tapir]

OHHH

TY

ANN

I GET IT

ty

[crude hazel]

what trig identity is sin(x) + cos(x) = tan(x) + 1

[vale wigeon]

it's not a trig identity

[crude hazel]

it seems to be true though, so what is it then

[vale wigeon]

it is definitely not true lmao

just take x = pi/4

you have sqrt(2) on the left and 2 on the right

[quartz oxide]

Did you misread something?

[vale wigeon]

did you want to treat it as an equation and solve it for x?

[tranquil parcel]

Ig it should be sin^2(x) + cos^2(x) = sec^2(x) - tan^2(x)

[vale wigeon]

pretty enormous misread then innit

@crude hazel do you have a screenshot or something

[tranquil parcel]

Would you mind helping me with a problem in channel 3?

[vale wigeon]

i have looked at it and don't feel like involving myself in it

[tranquil parcel]

Lmao

Why not

[vale wigeon]

i don't have enough time or energy for riemann sum fuckery

[tranquil parcel]

Yea fair enough

[crude hazel]

when I used symbolab to solve x in sin(x) + cos(x) = 0, it said to rewrite sin(x) + cos(x) as tan(x) + 1

strange

[vale wigeon]

did it say rewrite or did it say divide both sides by cos(x)?

because it's very likely the intended move way to divide both sides by cos(x), as that takes you from sin(x)+cos(x)=0 to tan(x)+1**=0**

[crisp grove]

been telling him the same thing lol

[quartz oxide]

And the denominator does not matter (unless it is 0) since the whole fraction is 0

[crude hazel]

ok I see it now ty

[glacial tiger]

need some help lol

[crude hazel]

does PQ || ST mean line PQ is parallel to ST?

[glacial tiger]

yes

[stark trail]

Similar triangles

[glacial tiger]

how do i prove that

[stark trail]

PRQ and SRT are vertical angles

[glacial tiger]

ok

so thats an angle

[stark trail]

PR/TR=QS/SR shows that the two pairs of corresponding sides are similar

[stark trail]

Yes

[glacial tiger]

so

SAS?

[stark trail]

Yes

[glacial tiger]

ok

after i prove that

then

whats the reason why they are parallel

if they are equal

[glacial tiger]

?

[stark trail]

Lemme think :v

[stark trail]

Hmm

What I do is

I draw a new line that I assume is parralel to PQ and goes through R

Then compare both lines using this new line that I just made

By looking at the angles

[glacial tiger]

but like

whats the reason

lol

[glacial tiger]

?

[stark trail]

I kinda forgot what’s the relation of the angles called but I’m sure that the fact <PQS = <TSQ proves this a triangle

[glacial tiger]

uhh

[stark trail]

Aternate interior angles

@glacial tiger

[glacial tiger]

ah yes

[stark trail]

When alternate interior angkes are equal,then both lines are parallel

[glacial tiger]

yess

ty

[stark trail]

Sorry for not responsive

[glacial tiger]

no ur fine

[alpine sable]

how do i solve the equation

[crisp grove]

$cos(x)sin(y)=\left( sin(x+y)-sin(x-y)\right) /2$

[ocean seal]

Ryuzaki

[alpine sable]

what

[gray isle]

look up product to sum identities

[alpine sable]

okay

[dapper tendon]

n^1000000000/2^n=? ( n tends to infinity )

how do i solve this?

[wild marten]

L'hospital rule?

[clever locust]

What a monstrosity of a limit lol

Like, in what context would you ever care about $\lim_{n\to\infty}\frac{n^{1000000000}}{2^n}$?

[ocean seal]

Lorago

[wild marten]

I think its a self made question

[clever locust]

Yeah, looks like it

[wild talon]

what does this expression mean?

all values of N are greater or equal to 0?

so all values of N are positive?

or does it mean that the series of numbers is increasing

or none of those xd

[clever locust]

It's a quantifier

So what it's saying is "for all n greater than or equal to n_0"

So usually you use it to say that something is true for all n that are greater than or equal to some n_0 (in this specific case)

If I were to write something like

$$\forall n \geq 0 : \sqrt{n} \geq 0$$

what I would mean, in words, would be:

"For all $n$ that are greater than or equal to $0$, it is true that the square root of $n$ is greater than or equal to $0$."

[ocean seal]

Lorago

[clever locust]

Does that make sense @wild talon ?

In your case, n_0 is some fixed number

[wild talon]

wait what do i assume n nought to be if it isnt specified

[clever locust]

If it isn't specified, then you simply don't know what it is

Just that you can call it n_0

[wild talon]

ah ok

makes sense

thanks 👍

[clever locust]

No problem, if you're still confused, feel free to ask more

[clever locust]

Lmao I came up with a really stupid solution to this

It boils down to using L'Hôpital's rule 1000000000 times

It's actually a quite simple solution, but there are other solutions that are much better lol

If you're still interested, I can share it, but you haven't responded to anything so I'm guessing you just left it at that

[alpine sable]

looking at the denominator

|p-q|

distance of two points in R^3

represented in spherical coordinates is what i want

but this is assuming same polar angle from both points p and q?

[ornate peak]

I'm not getting this one, pls can anyone help me

[alpine sable]

<@&286206848099549185>

i have an idea if you could ping me i'd present you my answer and wait for an approval lol

ping me then

[alpine sable]

How do I determine where this cosine function = 0? - https://imgur.com/a/jlwrpei. I'm a bit confused looking at this on what the easiest way to determine where 2cos(2x) = 0. First I would divide both sides by 2 but then what number do I plug in as the x? I know that a standard cosine function is equal to 0 with either pi/2 or -pi/2. I'm not sure if there's something I can do with that information.

[austere bridge]

if you know that $\cos\left(\frac{\pi}{2}\right)=0$, then you want $2x=\frac{\pi}{2}$ so $x=\frac{\pi}{4}$. Same for the negative case

[ocean seal]

cgodfrey

[alpine sable]

Ah, it was that simple.

Thanks.

[austere bridge]

np!

[swift peak]

how is (x1/2)^2 + (x2/2)^2 + (x3/2)^2 = x3^2?

what happened to 1/2?

[vale wigeon]

that's chi, not x

[swift peak]

ye

[vale wigeon]

chi-squared variable with three degrees of freedom

[swift peak]

but what happened to 1/2?

[vale wigeon]

what 1/2?

[swift peak]

the one with the normal rvs

[vale wigeon]

you gave no info about the distribution of X_1, X_2 and X_3. are they N(0,4)?

[swift peak]

its mean = 0 and sd = 2

is that it?

[vale wigeon]

aha

so X_k/2 are all standard normal

so the sum of their squares is chi-square

[swift peak]

this is confusing

i thought snd was with standard dev = 1

[alpine sable]

hi all

how could i set up this integral

[gaunt magnet]

https://tenor.com/view/cat-leaving-leave-oops-bye-gif-17519616

[alpine sable]

lmao :/

[alpine sable]

pls ping if anyone knows ❤️

[crisp grove]

normal double integral

[alpine sable]

right but im a bit confused :/

[crisp grove]

$\int_0^1 \int_0^1 f(x,y) dx dy$

[ocean seal]

Ryuzaki

[alpine sable]

so

why from 0 1

[solar cradle]

You're calculating the probability

[alpine sable]

and not like 2 to swrt 3

[crisp grove]

sub f(x,y)=⅓xy

[alpine sable]

ah ok i got 1/12

tysm

i kept putting sqwrt 3

and 2

for the inner one

so i kept getting it wrong

[crisp grove]

👍

[alpine sable]

can i ask u one more question

how could i set up this integral

[crisp grove]

cylindrical coordinate

[solar cradle]

Here's a short source on calculating surface area

https://tutorial.math.lamar.edu/Classes/CalcIII/SurfaceArea.aspx

note the notation $f_{x} = \frac{\partial{f}}{\partial{x}}$

[ocean seal]

Billy Clintorus

[astral patrol]

hey guys, I don't understand how (s+3) was cancelled

[vague coral]

(s+3-3)/(s+3)² = (s+3)/(s+3)² - 3/(s+3)²

[astral patrol]

I meant, why is it allowed to put +3 -3 to cancel (s+3)

because it was originally s/(s+3)^2

[vague coral]

because +3 - 3 = 0

we basically did nothing

[alpine sable]

Does anybody know how this is true?

I feel like it's simple but I really can't think today.

[astral patrol]

ohhhhh okay makes sense, thanks!

[vague coral]

what is g by the way ?

[alpine sable]

Underived version here.

I guess if I do 3x^2 + 2x = -1. Divide by the constants. There's no x^2 + x that'll equal the result?

[vague coral]

oh, then it's simple, since g'(x) has no real solution, nothing can cancel it

you are overthinking it

[alpine sable]

I don't get what you mean exactly.

[vague coral]

Ok, I'll ask you, you know what is the point of finding the solution of an equation like this : ax²+bx+c=0 ? right ?

[alpine sable]

The point? Erm...

To solve for x?

[vague coral]

to solve for x such as the values of x cancel out ax² + bx + c

and since 3x² +2x + 1 = 0 has no real solution, that means nothing can cancel out 3x²+2x+1

that's why g' is never equal to 0

you can graph it, you will see

[alpine sable]

i think i get it...

[vague coral]

it's really simple, you are just overthinking it

[alpine sable]

im going to take a nap and then relook at it. thanks :p

you're right

[vague coral]

ok take your time

[alpine sable]

👋

[zenith dawn]

Wassup, what is a mathematical operation to gradually turn a square wave into a sine wave?

Hopefully that makes sense to someone

Pretty much something like this, by a configurable amount

[glass lichen]

Fourier stuff

[zenith dawn]

you'll have to explain in english as I have no idea what that means

[limpid spade]

exactly

Fourier series

You have Sum x=1 to inf sinx

nvm 5hat won't turn to a square

dunno what the capital pi represents

[glass lichen]

product, however I think that's just regular pi fucked up

[limpid spade]

lol

[glass lichen]

$f(n)=\sum_{i=1}^n \frac{\sin((2i-1)x)}{2i-1}$ will give a function of x

as n goes to infinity you get a more and more square wave

[ocean seal]

Mosh

[zenith dawn]

I'm not a maths expert so I don't really know what any of this means. Perhaps I didn't mean "operation", and I was using the sine wave as an example. Basically I need to do what I said for each value for x.

[glass lichen]

you didnt say anything to an individual x

you just asked how to make a wave square

which was answered

[limpid spade]

also

,w plot floor((sin(x))

nvm

[zenith dawn]

yeah so I said maybe "operation" is the wrong word. I'm not a maths wizard like everyone here so I don't know the correct terminology.

[celest anvil]

pls thx

[glass lichen]

what have you tried?

[celest anvil]

dont know how to solve

[glass lichen]

well it tells you how to

[limpid spade]

https://www.chegg.com/homework-help/questions-and-answers/use-power-sums-evaluate-n-3s2-2s-3-n3-n00-s-1-give-answer-whole-exact-number-lim-n-00-2s-3-q54316549

lol

[glass lichen]

chegg

[celest anvil]

i dont have chegg

[limpid spade]

it's from chegg

[celest anvil]

no the answer is on chegg

you need to sign up to see it

[glass lichen]

yeah and you shouldnt use chegg to begin with

[carmine lion]

hmm

how to solve this

$\sin^2{x}=\sin{2x}$

[ocean seal]

abe

[carmine lion]

apart from x=0

[lofty gorge]

sin(2x)=2sin(x)cos(x), and now you have a common factor.

[carmine lion]

oh yea

sorry

didnt see that

[carmine lion]

because i want to solve this inequality

$\frac{\sin{2x}}{2}> \frac{1}{\sqrt{3}}\sin^2{x}$

[ocean seal]

abe

[carmine lion]

because the maximum of sin function is 1

so i wanna find where both of them are one

[lofty gorge]

Why? You would want to find where the two sides are equal, to find boundary points.

[carmine lion]

oh yea

so i do the same?

[lofty gorge]

So you would want to solve with those coefficients, which isn't harder (and makes the solution nicer)

yes

[carmine lion]

ok

ty for helping

[alpine sable]

hi all why is this incorrect

[median tendon]

Could you show your working out? I'll try and see if I can pick up on any mistakes

[alpine sable]

i think its the integral i set up thats wrong

im not entirely sure how to set it up but the first one was from -9 to 9

then -sqrt(9-x^2 ) to positive sqrt(9-x^2)

and then

integrate over the f(x,y)

[median tendon]

do u know what the actual answer is supposed to be? i havent done this in a while and i dont want to teach u the wrong thin

but basically this is that u want to find the surface area of

$x^2+y^2=z^2$

[ocean seal]

_Youssef_

[alpine sable]

i dont ;/

[median tendon]

the perimiter of a circle is 2 pi r

that is the surface area of the function you want at one instance of the z value

does that make sense?

[alpine sable]

somewhat

i guess my question is how do i set up the integral exactly in this case

[median tendon]

ok, so pretty much its integrate the perimeter equation from z=0 to 9

and you know that the radius of a circle in this case is z, right?

[alpine sable]

yeah

[placid zinc]

Take a quick look through your book/internet, there is a "surface area by integration" formula

[median tendon]

are u still confused on how to proceed?

[alpine sable]

yh im not that good at setting up the integrals :/

[median tendon]

integrate 2 * pi * z from 0 to 9

integration is pretty much the same as addition over an infinitely small steps between two intervals

if u think about the graph at the top, you have infinite amount of circle perimters that you want to add up

since the graph is made up of infinite amount of circles that are insreasing in raduis

[alpine sable]

so its not a double integral then?

[median tendon]

not with this setup

but u could definitely do it in the x y coordinates and have two integrals

[alpine sable]

i get 81pi

but thats not right ;/

[median tendon]

why do u think thats not right?

[alpine sable]

i submitted it and it marked it wrong 😛

[median tendon]

huh

im sorry lmao

[alpine sable]

its ok

[median tendon]

idk

[alpine sable]

the integral gave me 81pi

https://www.symbolab.com/solver/double-integrals-calculator/\int_{0}^{9}2\pi z dz

i tested it in symbolab also to make sure i was right

heres the link

[median tendon]

i know, that method was wrong for some reason, not sure why though

[alpine sable]

its not a test its homework, u have 10 submissions

and i cant enter that bc it wants exact numbers, not decimals

so like fractions or ints

[median tendon]

ok just post question again and ping the helpers i think

[alpine sable]

thank u so much though for ur help

[alpine sable]

if anyone knows this pls ping ❤️

[placid zinc]

@alpine sable

You don't seem to be aware of the formula you're expected to use

[glass lichen]

dont ping random users, and what have you tried?

[hasty nacelle]

oh sorry and I got the answer its y=2x-1

[glass lichen]

ok

[alpine sable]

yeah i dont think so :/

this?

[median tendon]

@alpine sable

[median tendon]

if u use those formulas, you end up with the same answer as the google tool in the pic I'm replying to without the r term in the brackets (the r term in the brackets takes into account the closed end of the cone which is not what you are after I think)

[alpine sable]

what is that value as a fraction?

[median tendon]

$\frac{81}{}

ops

$81\sqrt{2}*\pi$

[ocean seal]

_Youssef_

[alpine sable]

ah tysmm ❤️

that worked

[median tendon]

np

im sorry if i confused u before

[sterile gust]

Pls help me find a way to do it

(using Fourier series)

[placid zinc]

Note that you get the left when x = pi/2

Is there any closed form for f(x)?

[alpine sable]

noo ur awesome!

[sterile gust]

The range is 0 to 2pi

[crisp grove]

differentiate both side u get a sum of cosines, use AP sum formula for cosines

[sterile gust]

It is a clever way but, I need to prove it with Fourier series only

[crisp grove]

well then it's easier

bn = 1, ½, ⅓, ...

u just have to calculate inverse of this

[sterile gust]

How is bn=1, 1/2, 1/3,.... (Iam quiet a newbie)

[crisp grove]

f(x) = a0/ +a1 cosx + a2 cos2x + ... + b1 sinx + b2 sin2x + ...

compare both sides

[sterile gust]

Ok.... Thank you!

[heavy spear]

6000 dollars is invested in a bank account at an interest rate of 6 per cent per year, compounded continuously. Meanwhile, 12000 dollars is invested in a bank account at an interest rate of 5 percent compounded annually.

i keep getting 73.1

years but it says that is wrong

can someone help me with this

[gray isle]

what's 73.1 supposed to be.
what's the actual question

[heavy spear]

ok

1 sec

uh k

[gray isle]

<@&268886789983436800>

[heavy spear]

nice

[gray isle]

show your work

[tall wing]

o

is this an exam

or wait did the thing already get dealt with

[gray isle]

some questionable vid

[tall wing]

oh ok

[heavy spear]

i do 6000 * 1.06^x = 12000 * 1.05^x then solved for x\

i am on pc cant send pics

[heavy spear]

no it is homeworkfor ap calc i dont understand why i keep getting it wrong though

[wanton vortex]

maybe the "compounded continuously" (in the first sentence) and "compounded annually" (in the second sentence) have to do with it

[gray isle]

^

[heavy spear]

oh

thx

lol completly missed that

[wanton vortex]

i did too as i was initially reading the problem

[heavy spear]

thx i got it right

i know i am asking a lot of question but im full on raging cause i dontt understand what im doing wrong here

[rigid island]

@heavy spear

[gray isle]

it looks like you're omitting important signs when separating and grouping terms sidd

[heavy spear]

oh ok

you see im dumb

since i learned nothing during online schooling xd

[fallow karma]

hello, can someone teach me how to do this question??

1. A map has a scale of 4cm to 1 km. if the distance two towns is 8 km, calculate the corresponding distance on the
   map

[vale wigeon]

1 kilometer in real life corresponds to 4 cm on the map
8 kilometers in real life correspond to how many cm on the map?

@fallow karma do the words "map distance is proportional to real distance" ring any bells to you?

[heavy spear]

ye it is a converstion so 4cm on map/1km real life or the other way around so 8km in real world * 4cm on map / 1 km in real world so the km in real world caancel out and you get 32

cm

[alpine sable]

The angle of elevation from question 5 is 76 degrees and the answer for a is 14 degrees, but I’m not sure where I’m going wrong in 7b

[glacial hedge]

Is the answer all except a? because the derivatives of all of them are continuous, except for g(x) there shouldnt be a 1??? Or am I missing something very obvious???

[vale wigeon]

the range of T consists of those functions g which are continuously differentiable and satisfy g(0) = 0

[glacial hedge]

Oh, may I ask why? I am a little confused

[vale wigeon]

let g(x) = int[0,x] f(t) dt

then g(0) is forced to be 0

and of course g' = f

[glacial hedge]

Oh i see

ty

[warm cipher]

what are derivatives?

[vale wigeon]

to put it very briefly and in one sentence, the derivative measures a function's rate of change.

for a more complete description, take a calculus course or read an online resource like paul's online math notes.

[warm cipher]

ok ty

[snow nest]

can someone explain how to derive x^-2 using first principles?

everytime i do it i seem to get -2x-1/x^4

[vale wigeon]

differentiate, not derive.

$\frac{1}{h}\paren{\frac{1}{(x+h)^2} - \frac{1}{x^2}}$ is what you're starting with, yes?

[ocean seal]

Ann

[snow nest]

yup

[snow nest]

mb

[vale wigeon]

okay, so what do you do next?

do you rewrite 1/(x+h)^2 - 1/x^2 as a single fraction?

as in, is this what you specifically tried to do?

[snow nest]

yeah, x^2 - (x+h)^2 / x^2 * (x + h)^2

[vale wigeon]

in plaintext you need parentheses

(x^2 - (x+h)^2)/(x^2(x+h)^2)

anyway, ok

[snow nest]

wait multiply? where's the slash?

[vale wigeon]

typo

[snow nest]

ah okay

[vale wigeon]

so what you have here is $\frac{x^2 - (x+h)^2}{hx^2(x+h)^2}$

[ocean seal]

Ann

[vale wigeon]

because let's not forget the 1/h out front

what did you do after this?

[snow nest]

yeah i got to here

then you expand the (x+h)^2 at the top, cancel the 2 x^2s

so i get (-2hx - h^2)/hx^2(x+h)^2

[vale wigeon]

uh huh, so far so good

what do you do next?

[snow nest]

cancel the h out

[vale wigeon]

mhm

[snow nest]

and i get (-2x - h )/x^2(x+h)^2

[vale wigeon]

uh huh

[snow nest]

make h zero, kind of?

[vale wigeon]

let h approach zero, yes.

[snow nest]

-2x - 1/ x^2 * x^2

[vale wigeon]

and since we've done all the necessary work to avoid division by zero, we can just set h = 0

[snow nest]

so -2x-1/x^4

[vale wigeon]

no, set h = 0, not 1.

why are you setting it to 1 in the numerator

also parentheses

[snow nest]

oh shit

i keep getting confused

because when you cancel out variables, you set the value to one

ahh damn it

i see where i was wrong

as in, if i had the (x - h)/h, it becomes x - 1, right?

and i keep forgetting to set it to 1 instead of zero

[ionic jewel]

interesting way to think about it

[snow nest]

wait, is it wrong?

[vale wigeon]

no

(x-h)/h becomes a division-by-zero error upon setting h to 0

also yeah like, this

because when you cancel out variables, you set the value to one
is kinda flawed

[snow nest]

right, so when i cancel out h, i set it to 1, but when i'm left with h after canceling the h at the bottom, it becomes zero

[vale wigeon]

1 is what happens when you divide something by itself.

you don't set h to 1. at no point was that actually happening in your work.

[snow nest]

not in this question but say i somehow got (x-h)/h, in this case i would slash out both h's and make the top h 1

[alpine sable]

hi all how can i set up this integral

[snow nest]

anyway i figured it out so yeah, help out xoxo if you can

[vale wigeon]

no you would not

[snow nest]

cause i sure have no idea how to

[vale wigeon]

you cannot cancel out the h's in (x-h)/h

[snow nest]

wait what

[vale wigeon]

by your logic, 7/3 = 10

[vale wigeon]

@alpine sable @tawdry pawn this channel is still busy sorry

[vale wigeon]

no this is illegal

[snow nest]

nani

what

[alpine sable]

u cant cancel out a term when its being subtracted

[vale wigeon]

again

[short turtle]

cannot cancel

[vale wigeon]

$\frac{10-3}{3} \wtfeq 10 - 1$

[snow nest]

oh god tell me i haven't fucked my entire life up

[ocean seal]

Ann

[snow nest]

oh i'm an idiot

wait so

wait

[alpine sable]

if the channel is not busy and someone knows how to solve this pls ping me ❤️

[snow nest]

still busy sry

[alpine sable]

i meant for after hehe

[snow nest]

how do you do the bot thingy

it's cool

[vale wigeon]

@alpine sable you can and should move to another channel. there are 10 of them for a reason.

@snow nest the bot uses a markup language called LaTeX. there are some resources on it in #latex-help and #latex-testing if you want to learn more.

[snow nest]

i guess i'll check it out once i understand this

so when i cancel out the h at the bottom

i make the h's at the top 1s, right?

as h/h is 1

if h isn't by itself

[tawdry pawn]

is this channel free now

[snow nest]

yeah ig so

[tawdry pawn]

idk how to solve this question: Express log x-2 log x+3 log (x+1) - log (xsquare - 1) in single logarithm

[vale wigeon]

$\log(x) - 2 \log(x) + 3 \log(x+1) - \log(x^2 - 1)$

[ocean seal]

Ann

[vale wigeon]

is this what you meant? @tawdry pawn

also you really should be using this symbol: ^ for exponents. like this: x^2

[tawdry pawn]

yea

[tawdry pawn]

ok

but the brackets are wrong

[vale wigeon]

but the brackets are wrong

are you going to be hellbent on NOT writing parentheses around the input of log whenever possible, or do you ACTUALLY mean i parsed your message incorrectly and this isn't the right expression?

[tawdry pawn]

log x-2 log x+3 log (x+1) - log (x^2 - 1)

[vale wigeon]

do you have a picture of the problem?

[tawdry pawn]

nope also i m on pc

[vale wigeon]

are you going to be hellbent on NOT writing parentheses around the input of log whenever possible?

i don't get it

as far as i understand, what you have is this:

$\log(x) - 2 \log(x) + 3 \log(x+1) - \log(x^2 - 1)$

[ocean seal]

Ann

[vale wigeon]

but you are sending me mixed signals as to whether or not this is what you're starting with

[tawdry pawn]

the expression looks like this

[vale wigeon]

do you object to me writing $\log(x)$ instead of $\log x$?

[ocean seal]

Ann

[tawdry pawn]

yea

i mean no

don't write log (x) write log x

[vale wigeon]

yea
i mean no

here you go again

so you DO have an objection to it?

too bad

[tawdry pawn]

i am so confused rn

[alpine sable]

ann is saying to use parenthesis to make it clearer tldr

if u do log x - 1

[vale wigeon]

i'm pasking patrick_syco if he has an issue with it

[alpine sable]

that could be log (x) - 1 or log (x-1)

so using parenthesis clears that up

[vale wigeon]

and he can't even answer this simple yes-no question

which is a little disconcerting

[alpine sable]

haha iconic

[vale wigeon]

@tawdry pawn you are going to insist that i write log x instead of log(x). is that the case? Y/N

[alpine sable]

bad question

[vale wigeon]

answer my question

[alpine sable]

ambiguous

[vale wigeon]

it doesn't look ambiguous

[tawdry pawn]

i can't understand yours

[alpine sable]

oh wait nvm i read it wrong

[vale wigeon]

since patrick FINALLY provided a picture

but in patrick's plaintext rendition, the spacing threw me right off

patrick i am asking my question as clearly as possible

[tawdry pawn]

:(

[vale wigeon]

i want to understand whether or not this notation issue is going to be relevant!

[tawdry pawn]

its same question

[vale wigeon]

i want to understand whether or not you are okay with me putting parentheses around the x in log(x) !!!

and you're not telling me!!!!!

you're leaving me in the dark!!!!!!!!!!!

[alpine sable]

patrick say yes

put us all out of this

[tawdry pawn]

yes

you are right

[vale wigeon]

okay fine

i guess i'll have to just abandon my habit just this once

patrick, are you familiar with log laws?

such as $\log(xy) = \log x + \log y$

[ocean seal]

Ann

[vale wigeon]

and $\log \frac{x}{y} = \log x - \log y$

[ocean seal]

Ann

[vale wigeon]

and $\log(x^p) = p \log x$

[ocean seal]

Ann

[vale wigeon]

are these familiar or foreign to you?

[tawdry pawn]

foreign

nvm i solved it till you tried to understand my expression

[alpine sable]

ann if u have a minute can i show u my expression for this problem bc im almost certain its right or fairly close to right

[vale wigeon]

how did you solve it if you were unfamiliar with log laws wtf

uncooperative much

[alpine sable]

im confused abt this bc my expression looks like this and im fairly certain its right or close to it

idk how to latex on here :/

[ionic jewel]

is a torus the donut shape?

[alpine sable]

close to it, do u want me to send a pic

[vale wigeon]

$\int_0^{2\pi} \int_0^\pi \int_0^{7 \sin(\varphi)} r^2 \sin(\varphi) \dd{r} \dd{\varphi} \dd{\theta}$

[ocean seal]

Ann

[alpine sable]

it looks similar to this

[vale wigeon]

just writing out your integral in latex

[alpine sable]

oo

[tawdry pawn]

google

[vale wigeon]

great then why don't you go to google for all your math problems 😒

[misty pebble]

If 0 < a < 90 and cos a < 0.5, then which of the following is correct? A<30, A>30, A<60, A<45, A>60. How do I work this out?

[tawdry pawn]

you were confusing me a lot

it was a simple expression

[vale wigeon]

YOU were confusing me w/ your aversion to parentheses

[tawdry pawn]

and you could'nt understand it

[vale wigeon]

oh, i am SO sorry for paying attention to spacing.

i am so fucking sorry for being thrown off by log x-2 log x+3 log (x-1) making the x-2 and x+3 appear as single units

[ionic jewel]

find out what angles in the first quadrant cos(a) is larger than 0.5

basically find where it's equal to 1/2, and see which side (higher or lower angles) are larger

[alpine sable]

@ionic jewel does this help

w the torus clarification

[ionic jewel]

the integral looks right, assuming r starts at 0 for toruses

[alpine sable]

yeah

i even put it into symbolab

to like

verify my solving was right

and i get the same thing there but its wrong when i submit

[misty pebble]

@sonic elk is this with unit circle? how do i find where cos(a) is larger than 0.5

[alpine sable]

OMG LMAO

i submitted it /3 and not /4

im so stupid

when u cant type

[ionic jewel]

,w integral from 0 to 2pi of (integral from 0 to pi of (integral from 0 to 7sin(y) of r^2 sin(y) dx)dy)dz

[alpine sable]

omg im so sorry bunny

i got the right answer

[ocean seal]

Results provided by WolframAlpha

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

Requested by 兔子#6562

[alpine sable]

i didnt enter it properly

[ionic jewel]

yeah i wanted to see if Wolfram could parse it

well glad u got it

[alpine sable]

ahh ok

thank u !!!

[misty pebble]

If 0 < a < 90 and cos a < 0.5, then which of the following is correct? A<30, A>30, A<60, A<45, A>60. How do I work this out?

[ionic jewel]

i answered this

[ionic jewel]

read from here

[misty pebble]

How do I find where its equal to 1/2?

[ionic jewel]

do you know the unit circle?

[misty pebble]

Not very well

[ionic jewel]

well go look at it and find the abswer

[glacial hedge]

This is false correct?

because any linear transformation maps the zero vector to a zero vector

and zero vector is always zero???

[plush wagon]

Q.4, I solved the question but there is a confusion that why there is Y in numerator with {{sec^2 x +Y}}

This is answer

Why is there -y in numerator?

[rigid smelt]

can you show your work?

[plush wagon]

Ok wait

[rigid smelt]

derivative of xy wrt x is not xy'

[plush wagon]

What is it than?

[rigid smelt]

xy is a product of two functions, x and y

and not a product of function y and a constant "x"

[plush wagon]

Please tell me derivative of xy

Is it 1y'?

[rigid smelt]

no

again

what im saying is, x is also a function

and not a constant

how do you differentiate a product of 2 functions?

[plush wagon]

There is formula for that

[rigid smelt]

so apply it

[plush wagon]

U'v + ....

[rigid smelt]

theres another part

write it out clearly so i know you are right

[plush wagon]

uv' + v'u / v^2

[rigid smelt]

no

see what i mean when you dont write out the whole thing?

the formula for derivative of a product of 2 functions is (uv)'=u'v + uv'

[plush wagon]

Yes

[rigid smelt]

so apply it

u and v are representative of x and y

[plush wagon]

Okay

I got it, thank you😃

[dry berry]

xy = x * f(x); (xy)' = f(x) + x* f'(x) = y + x*y'

pretty cool

[carmine lion]

How do I approach part 4

[ocean seal]

abe

[carmine lion]

will this take me anywhere

[tight locust]

differentiate

[carmine lion]

wdym differentiate

differentiate what

[crisp grove]

sin2a = 2sin a cos a ?

[carmine lion]

yes

[crisp grove]

take out common factor ans then try maybe

[carmine lion]

from that i get a < pi/6

idk if that is correct

i remember a similar problem that did use derivative

[dry berry]

you must find the exact value of a not the domain

[crisp grove]

$sin(a)(cosa-sin(a)/\sqrt{3})>0$

[ocean seal]

Ryuzaki

[crisp grove]

so u want a general solution?

[carmine lion]

exact value

[crisp grove]

wait what was the question again? I started from the inequality

oh got it

[carmine lion]

idk if my inequality is correct

or if im supposed to use dA/da

[crisp grove]

The are is $(\cos(\pi / 3) - \cos (\alpha))\sin(\pi/3)$ ??

[carmine lion]

what?

are?

wdym

[crisp grove]

with r

nvm

it's given in the q3

u have to maximize A

you know for maximum values dA/da = 0

btw are you allowed to use caculas?

[carmine lion]

uh yea?

shouldn't it be dA/da = 0 for minimum values?

[crisp grove]

then use the fact that at max value dA/da will be 0

[crisp grove]

exactly

[carmine lion]

so why did u say max values

[crisp grove]

mistake

[carmine lion]

so shouldn't i find $\frac{d^2A}{d\alpha^2}$

[ocean seal]

abe

[carmine lion]

and then $\frac{d^2A}{d\alpha^2} < 0$

[ocean seal]

abe

[carmine lion]

?

to find max

[crisp grove]

no

after finding points for which A(a) = 0

what you are referring to is the second derivative test

[carmine lion]

yea?

oh right

[crisp grove]

we use that to check if the value is indeed max / min / saddle

[carmine lion]

it can be either min/max

with dA/da

i find nature with 2nd

my bad sorry

[crisp grove]

find value of a then put it in d2A/da2 and check ifi it's < 0

[carmine lion]

$\frac{dA}{d\alpha}=r^2(\cos{2\alpha}-\frac{\sin{2\alpha}}{\sqrt{3}})$

[ocean seal]

abe

[carmine lion]

am i right

[crisp grove]

yes seems alright

[carmine lion]

ok now i got

$\tan{2a}=\sqrt{3}$

[ocean seal]

abe

[crisp grove]

solve?

[carmine lion]

am i correct

should i expand using tan2a formula or

[crisp grove]

up until now yes

what angle given tan(x) = sqrt(3)?

[carmine lion]

pi/6

[crisp grove]

6?

[carmine lion]

wait no

thats 1/sqrt3

pi/3

[crisp grove]

so...

[carmine lion]

2a=pi/3

[crisp grove]

6 ?

...

[carmine lion]

sorry

a=pi/6

i was skipping steps in my head

[crisp grove]

rolling shutter

[carmine lion]

huh??

[crisp grove]

nvm

[carmine lion]

ok

now what do i do

since r is a constant

there should only be 1 turning point yes?

or not?

[crisp grove]

2nd derivative test?

[carmine lion]

oh yea

but i only got 1 value

for dA/da

soooo

[crisp grove]

,ask second derivative test

[ocean seal]

Results provided by WolframAlpha

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

Requested by Ryuzaki#6999

[woeful pulsar]

are you supposed to use calculus

[carmine lion]

i am allowed to yes

i think we're supposed to

cuz i used it in a similar problem

[woeful pulsar]

there's probably a method using R-forumla

but yeah you are probably allowed to

[carmine lion]

so is pi/6 my answer

[woeful pulsar]

yeah you need to check if it's a local maximum

[carmine lion]

but i only have 1 solution to dA/da=0

[woeful pulsar]

also check endpoints

[crisp grove]

nope as obvious it may seem u still need to do it

[carmine lion]

what... ok

[woeful pulsar]

Alternatively, you can plug it in at every point

every critical point and end point to make sure it's the largest there

[carmine lion]

https://cdn.discordapp.com/attachments/490557019623915520/871284853117693992/473221703418511360.png

[crisp grove]

yeah that is true

[carmine lion]

so what about this inequality

[woeful pulsar]

doesn't look very friendly tbh

it is doable by R-formula

but I think the intention is just plug in all the critical points and endpoints

[carmine lion]

ok so i have a critical point a=pi/6?

wdym by endpoints

[woeful pulsar]

like a=0 and a=pi/3 i think are the endpoints

just say the rectangle has area 0

[carmine lion]

how do you know those are endpoints

[woeful pulsar]

what's the valid range for a

[carmine lion]

uh

they don't give one

in the question

or should i know it

[woeful pulsar]

then think about it, you have the geometrical configuration

which angles of a are reasonable in this question?

[carmine lion]

positive

[woeful pulsar]

so a>0

and how big can a go?

[carmine lion]

hmm

pi/4?

[woeful pulsar]

how about pi/3

[carmine lion]

why pi/3

[woeful pulsar]

like you can get arbitrarily close to it

[carmine lion]

why pi/3

i dont get ur reasoning

also if i solve the inequality

https://cdn.discordapp.com/attachments/490557019623915520/871284853117693992/473221703418511360.png

i get $a<\frac{\pi}{6}$

[woeful pulsar]

okay can you draw a such that a is just barely less than pi/3

[ocean seal]

abe

[woeful pulsar]

we can get a very close to pi/3

and the closer to pi/3 the smaller it is until it reaches an area of 0

[carmine lion]

yea?

[woeful pulsar]

yeah so a is at most pi/3

we can plug in the endpoints of 0 and pi/3

as well as pi/6 and we should be done

[carmine lion]

ok..., but can u have a look at what i posted above

i dunno if my approach is valid or not

if a<pi/6

wouldnt that mean

thats the max

[woeful pulsar]

where do you have a<pi/6

[carmine lion]

from the inequality above that

[woeful pulsar]

something's wrong

[carmine lion]

why

[crisp grove]

where are you getting the inequality?

[woeful pulsar]

that 1. something is definitely not pi/6

[carmine lion]

from the answer

of iii

if Area has to be maximised,

[crisp grove]

why inequality?

[carmine lion]

r^2 will always be positive

so that means the other part

[crisp grove]

shouldn't that be a =

[carmine lion]

must also be positive

[woeful pulsar]

yeah that means 0<=a<=pi/3

[carmine lion]

https://cdn.discordapp.com/attachments/490557019623915520/871284853117693992/473221703418511360.png

[woeful pulsar]

something happened somewhere

[carmine lion]

,w solve sin2a/2 - sin^2(a)/sqrt(3)>0, 0<=a<=pi/3

[ocean seal]

Results provided by WolframAlpha

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

Requested by abe#8092

[carmine lion]

lol

[woeful pulsar]

nothing new

[carmine lion]

is this notation a thing?

$\frac{d^2A}{d\alpha^2}(\alpha=\frac{\pi}{6})$

[ocean seal]

abe

[woeful pulsar]

no

but this is

[carmine lion]

like i wanna say

[crisp grove]

that's definately pi/6 on the graph

and that indeed is the maxima

[woeful pulsar]

$\left.\frac{d^2A}{d\alpha^2}\right|_{\alpha=\frac{\pi}{6}}$

[ocean seal]

Element118

[carmine lion]

lol i haven't learned integration

ur evaluating the lower bound

?

[woeful pulsar]

this is the notation for the second derivative evaluated at alpha=pi/6

[carmine lion]

ah ok

because i've seen integration do that

[carmine lion]

ok, last thing

why are we evaluating at boundaries

don't we already know its a global max for 0<=a<=pi/3 after finding the nature of the turning point

i found that its negative so its concave down at that area

meaning its max

[woeful pulsar]

okay this depends on what you want to include

[carmine lion]

shouldn't that information be enough

evaluating at end points even though u know a max seems redundant

[woeful pulsar]

you can either

1. evaluate at boundary and critical points
   OR
2. determine the nature of all the turning points to figure out which local maximums to evaluate

there's two different approaches

[carmine lion]

but for both u need dA/da yes?

[woeful pulsar]

yes

but for method 1 you don't need the second derivative

[carmine lion]

alr

i think i would be able to do method 2 faster

ty for the help

[carmine lion]

thank you so much

i have a better understanding now

these type of questions are called maximising and minimising?

[crisp grove]

yes

[woeful pulsar]

well that's one way to describe it

[crisp grove]

optimization in general

[carmine lion]

alright

[jade peak]

i have this function, that accept two parameter and use 'pow' as power, not sure what it measures: cRnd(a,b)=>round(a*pow(10,b))/pow(10,b)

any idea?

[crisp grove]

Latex pls

[woeful pulsar]

looks like rounding to b decimal places

[jade peak]

round is a built in function

and pow is also

[jade peak]

so it's just a rounding function?

based on b decimals?

just dont understand why need power