help-17

[vocal sleet]

@heavy nova Has your question been resolved?

[heavy nova]

are these my intervals?
(-inf , -1/√3) (-1/√3 , -1/√6) (-1/√6 , 1/√6) (1/√6 , 1/√3) (1/√3 , inf)

but there are four 0's...

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[muted idol]

So to find derivative of y = ln|x^2-1|/x i used quotient rule and got that

But photomath is giving me this monstrosity, did i do something wrong or?

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[muted idol]

<@&286206848099549185>

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[lime linden]

u should think the (x^2 -1) whether > 0

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[lavish ferry]

Can someone help me do this problem (I attempted BUT it’s wrong)

[flat whale]

how do you know it's wrong?

[lavish ferry]

Cuz I guessed

[flat whale]

which part did you guess

[lavish ferry]

I lost track of the negatives and stuff after I did the u sub

I also don’t know if I was meant to do it that way

[flat whale]

,w solve dy/dx = x-2xy

[twin meteor]

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[flat whale]

you just wrote your constant in the exponent

[flat whale]

your answer is equivalent to this

[lavish ferry]

Why would it not be there

[flat whale]

$e^{a+b} = e^a e^b$

[twin meteor]

riemann

[lavish ferry]

Evil

[lavish ferry]

How would you take the derivative of this to get it to match the original? Like how I was trying to earlier

[flat whale]

do you know chain rule?

[lavish ferry]

Yes

[flat whale]

then what's stopping you from calculating dy/dx?

[lavish ferry]

Skill issue ig

Is it not just 2e^2x

But with negatives bc I forgot

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[lone niche]

plugging in x = 0, 1... into the pdf?

(p(x))

[vast shale]

im not sure what p(x) is

[lone niche]

they give you p(x)

[vast shale]

oh so p(x) is the entire chunk on top

[lone niche]

mhm

[vast shale]

n is the largest final number

and x is dependent on which one you're doing

that's a lot of items to key into the calculator 😓

[lone niche]

it's very weird that they use π

π = 0.8
π is rational!!!

[vast shale]

hmm i'd have less of an idea why

oh

thanks i get it now 🙂

[lone niche]

is there a way to define a function on your calculator

desmos >

[vast shale]

oh it defines functions? thats handy

[hushed willow]

using pi as the symbol for probability

pretty cursed

couldve just used p

[vast shale]

probably to confuse us

[lone niche]

pretty convenient

[vast shale]

realised questions like to do that

[lone niche]

agreed

well they already used p as the function

[hushed willow]

thats whhy

usually

caapital P

is used

[vast shale]

are you guys math majors

just curious of the demograhic

[thin vale]

I think there's a good mix, probably more math/physics majors than most other subjects

[vast shale]

thats cool

[thin vale]

from my observations

[vast shale]

i wish i majored in math 😞

[lone niche]

physics majors are just math majors

(real)

[vast shale]

i'll close this i guess, since the question is answered

thanks you guys

.close

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[polar zealot]

Why is the formula surface of a hemisphere: 3 * pi * r^2 and not 2 * pi * r^2 because its a half of the ball?

[polar zealot]

A ball is 4 * pi * r^2

Hemisphere is but 3 * pi * r^2 but how?

[lone niche]

because the circle on the bottom is pi*r^2

this is if you cut a ball in half, the cut area counts

[peak matrix]

it also includes this, which is pi*r^2

[polar zealot]

Bug why times 3?

[peak matrix]

the hemisphere without that is 2 * pi * r^2

but when you add that circle inside, its 2 * pi * r^2 + pi * r^2

[polar zealot]

no is surface= 3 * pi * r^2

[peak matrix]

which is same as 3 * pi * r^2

[polar zealot]

oh

let me think of that

Ah k

Its the same

[peak matrix]

Without the red area it's 2 * pi *r^2. When you include it, it's 2pi*r^2 + p*r^2 which is smae as 3pi*r^2

[polar zealot]

Ah kkkkkkk I got it. Okey thanks for answering

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[crude zealot]

I need to proof that the Wirtinger derivatives $\frac{\partial}{\partial z}$ and $\frac{\partial}{\partial \overline{z}}$ are $\mathbb{C}-linear$ maps. I know that I need to show they are additive and homogeneous, but im not able to come up with a formal proof. Thank you!

[twin meteor]

schubdroide

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[orchid jewel]

Any tips on solving this problem quickly?

[vast shale]

g is a quadratic in x^2

so you can use the quadratic formula

it also factors nicely

[orchid jewel]

huh?

[vast shale]

make a substitution u=x^2

[astral pilot]

g(x^(1/2))

[paper depot]

meh.

[orchid jewel]

Yall are insane

Too much math!

Thank you

.solve

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[astral pilot]

how to find sqrt(16818.125) by hand? (approx.)

[vast shale]

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

[astral pilot]

i dont understand any of that

[vast shale]

choose an algorithm, follow the steps

[astral pilot]

i dont understand

😭

[vast shale]

which part don't you understand

[astral pilot]

i dont know where to start

[vast shale]

choose a method to read through

this one seems the shortest https://en.wikipedia.org/wiki/Methods_of_computing_square_roots#Heron's_method

[astral pilot]

bro i am 9th grader

i don't know this

[vast shale]

it's an iterative algorthim

have you seen sequences yet?

[astral pilot]

nope

[vast shale]

hmm

a sequence is a list of numbers

start with a guess eg 120

[astral pilot]

is it like arthmetic progression?

[vast shale]

yes

an arithmetic progression is a sequence

[vast shale]

S= 16818.125

[vast shale]

then $x_1$, the second thing in the sequence is $\frac12 \left(120+\frac{S}{120}\right)$

[twin meteor]

Toby

[vast shale]

keep going until you get a number that you are happy with

[astral pilot]

whats x_1

[vast shale]

its the next number in your sequence

[astral pilot]

we have to add it?

[vast shale]

no

you just calculate it

[wraith venture]

16000 = 400^2
401^2 = 16000 + 800 + 1 = 16801

So something like 401.02

[astral pilot]

,w sqrt(16818.125)

[astral pilot]

tooo far

[wraith venture]

400^2 = 160 000
1 too many zeroes

Nvm

[twin meteor]

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[wraith venture]

But 13^2 = 169 so 130^2 = 16900

So you can guess 129 quite easily still

[astral pilot]

ik

i wqant it accurate till 3rd place

[wraith venture]

Oof

Yeah good luck with that

Either a calculator or a square root computing algorithm

[wraith venture]

Technically dichotomy is always possible, but that makes you compute quite a few squares

Like a dozen squares

Of numbers with up to 3 decimal places

[astral pilot]

dichotomy?

confused noises

[wraith venture]

I think according to theory, this is faster though

But no matter what, you'll need some sort of algorithm

[wraith venture]

Or at least it's not significantly worse

The problem is it involves division

Dichotomy doesn't

So actually dichotomy might be the fastest

Especially with the ease of computation of the sort of consecutive squares that you get

[wraith venture]

(They both exhibit quadratic convergence so it's up to the details)

<@&268886789983436800>
Spamming none everywhere

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@astral pilot Has your question been resolved?

[astral pilot]

😭

[wraith venture]

Look up dichotomy

It's about making increasingly good estimates

It's a very general method that can be applied to a lot of things

[astral pilot]

this all is going over my head

.close

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[orchid jewel]

Is this correct?

[paper depot]

no

[orchid jewel]

oh yeah

[paper depot]

even if we fix the notation issue that you are looking for roots rather than a factorization, x^3 - 1 = 0 does not have -1 as a solution, while x^3 + 1 = 0 has neither i nor -i

[orchid jewel]

true ture

[paper depot]

"what is this madwoman saying?" or "is that really so? cause i think you're wrong"

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[vast shale]

im not sure where to start

[dark kiln]

it's obvious

[vast shale]

[dark kiln]

you find the probability that 2 brothers are injured, which is the sum of three case wher that happens

same with 1 brother

and 3

and the larget is the largest

[vast shale]

why would it be the sum

also how would u find the probability of one brother

what would you sum there

[dark kiln]

e.g. Paul is injured and only paul

has the probabilitiy of 0.4×0.7×0.8

[vast shale]

why paul

how do we consider the other brothers

nvm

I get it

.close

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[hoary slate]

By proportionality theorem

[hoary slate]

Isnt it just 47/10x = BG/2x

Or what

[glad furnace]

Yes I got 23.5 for BG

However I’m not sure how to get CF

[hoary slate]

And for CF its 47/10x = CF/5X?

[glad furnace]

Oof wait

[hoary slate]

But uh why is AH greater than BG and CF

[glad furnace]

Wouldn’t that make BG 94/10 or only 9.4?

[hoary slate]

But is 23.5 and 9.4 still the answer

What will you do with AH

[glad furnace]

BG and CF are the only ones needed

I’ll try it out, thanks for the help!!!

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[waxen vine]

Hello, can someone help me understand what is the diffreence between $$ \leq $$ and $$ \prec $$. I currently study discrete math and it is something about "order relation" (idk if this is a good translation for "relation d'ordre" in french)

[twin meteor]

Tonitch

[waxen vine]

I meant \preccurlyeq

[paper depot]

$\preceq$ is just a symbol that looks different than $\leq$ but evokes the same vibe.

[twin meteor]

Ann

[paper depot]

usually it's used when you want to talk about an arbitrary order relation and wish to distinguish it from the standard one on the real numbers.

it'll always be defined in-context.

[waxen vine]

okay so I can see $(A, \leq)$ and $(A, \preceq)$ as the same thing ?

[twin meteor]

Tonitch

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[vast shale]

nevermind it clicked me i got it

2cot(x/2)sin^2(x/2) = 2sin(x/2).cos(x/2)=sinx

then we differentiate and solve lol

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[wooden mountain]

how to calculate the perimeter if 1 box is 0.5 cm

[loud walrus]

what is 0.5 cm?

[wooden mountain]

1 box

[loud walrus]

the blue line?

[tulip bridge]

What box?

[wooden mountain]

1 square is 0,5cm

[loud walrus]

you mean 1 square from that book? like the little one?

[wooden mountain]

Yeah I don’t know what are these called

[loud walrus]

but that's area, i think u mean one side

or the perimeter of 1 square

the square can't be 0.5 cm

it could be 0.5 cm^2 in anycase

try to use translator to know the original question

[loud walrus]

No, you are wrong

They are saying the lenght of each side of the square is 0.5

[queen wolf]

since it says 0.5 cm and not 0.5 cm^2 then I also think it would be the side length

[loud walrus]

and if I'm not wrong (i don't understand your language), is talking about the big square

it's the only one that makes sense to me

so you have a big square 0,5 cm side

[wooden mountain]

I’m 11 and I’m bad at English how do I explain

[loud walrus]

i think this is the information

each side of that big square is 0,5 cm

[wooden mountain]

Nono

Does it make sense now

[loud walrus]

well, u know your language better than me xD, if that's the case, then you should only add up

[wooden mountain]

But how, do I separate them?

[loud walrus]

if each side of that small square is 0,5 cm, you only need to count the number of squares that touches the border and divide by 2

no

divide by 2, or multiply by 0.5

is the same, but not divide by 0.5

25 * 0.5cm = 12.5cm

[wooden mountain]

I get it

[loud walrus]

cool

[wooden mountain]

Thank you

[wooden mountain]

So 12,5cm is the perimeter?

Hello?

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[digital zephyr]

You know where it says solve simutanous equation which type of simutqnous equation is it taking about

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[digital zephyr]

hello

<@&286206848099549185>

[crystal garnet]

Hi

So here they gave 2 equations right

Both of which equal to y

[digital zephyr]

i just what to know what type it is

liner quadratic?

[crystal garnet]

The only way I think this sum can be solved is by equating both of them together and solving as a quadratic

[digital zephyr]

so this is a quadratic simutaneous equation question

[crystal garnet]

X=-5 or x=2

[crystal garnet]

Yes just equate both eqns

[digital zephyr]

ok

[digital zephyr]

.close

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[digital zephyr]

are u sure its a quadratic

[crystal garnet]

Yes

You can use the quadratic equation too

[digital zephyr]

Why is the question like this then

<@&286206848099549185>

[karmic imp]

What exactly are you stuck on?

[digital zephyr]

Scroll down from this message

Bruh

[crystal garnet]

This is not the same question right?

What grade math is this?

[digital zephyr]

Grade 9

[digital zephyr]

9

[crystal garnet]

Okay

Its quadratic

[digital zephyr]

What do you mean

Is it foundation

[crystal garnet]

Substitute x=y-5 in the first equation

[digital zephyr]

Send me a link where I can learn this

Because I can't find it

[crystal garnet]

I don't really have a link or anything I'll explain?

If you notice in these kind of questions they're giving you 2 equations and asking you to solve them right

And there's two variables

Now if you can manipulate one of this equation by equating one variable with the whole equation and thus substituting the part you manipulated in the 2nd equation, one variable is eliminated and you have to solve for the other

usually this ends up as a linear equation or a quadratic. You will not have anything further in 9th grade.

if it's a liner you've to just shift the numbers from LHS to RHS and solve

If it's a quadratic you either use factorization or the quadratic formula

[digital zephyr]

Is this it

[crystal garnet]

And you can find the other variable by substituting the first variable you found in the original eqaution

[crystal garnet]

Now this one is different

These kind are simultaneous equations

You solve both these equations together

[digital zephyr]

This?

[crystal garnet]

Yes here equate both the equations

and solve for c

X***

[digital zephyr]

So is this the right one

[crystal garnet]

Familiarize yourself with these quations you'll be good

[crystal garnet]

Even the question just before this is right the way of solving is different

Solve all of the sums in your textbook

[digital zephyr]

I don't understand the other one doesn't have y =
though

[crystal garnet]

This is basics and are essential for all the upcoming topics even in 10th, 11th and 12th

[crystal garnet]

Yes because those are simulanious equations

[digital zephyr]

So this is what you was talking about

[crystal garnet]

the way you solve them is you put one equation below other and chose one variable. Make the constant of that variable same for both the equations. That means you will have to multiply the entire equation with a number that will make one constant before a variable equal. Then you can cancel the variable you just equated

[crystal garnet]

YES!

That's right

[digital zephyr]

Ok

Thanks

.close

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[robust iris]

Hey there

[robust iris]

So I just wrote an exam and there was one question that I wanted to make sure of the answer

They provided a statement, if it's true prove it, if it is false provide a counter example to prove why it is false.

Statement: If (v1,v2,v3) is linearly independent, and (w1, w2,w3) is linearly independent, (v1,v2,v3,w1,w2,w3) is linearly independent.

[lapis marten]

What was your answer?

[robust iris]

False

[lapis marten]

and your counterexample?

[regal bane]

Youch you really have to make a counter example from R³ that's kind of a pain

[robust iris]

I wrote false, as you could use examples of closure under addition (e.g., v1 + w1 may be equal to some v or w), also used some examples of scalar multiplication and 0 vector

[regal bane]

Did you give 3 specific vectors for v, and 3 specific vectors for w?

[lapis marten]

Well if w1 = v1, w2 = v2 and w3 = v3, the system isn't linearly independent right?

[robust iris]

That's also true

The question counted 4 marks, do you think I will at least get some of them?

[regal bane]

If you gave specific vectors, and used them to break linear independence, then full marks.

If you didn't, maybe you'll get some marks for showing you understand how linear independence might have been broken

[robust iris]

I just generalized, there wasn't a lot of writing space

[regal bane]

But yeah, counter example = give me a specific case

[robust iris]

Alright, thanks so much, another question was: T is a linear map R^2->R^1, T([4 5]) = 20 and T([1 2]) = 2. What is T([1 1])?

For this I set up systems of equations and got values for x1 and x2 and then subbed them into T([1 1]) to get the final answer

[regal bane]

Yeah that sounds about right. You really just have to display that you understand T is linear.

[vocal sleet]

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[karmic imp]

Use a calculator

It does say to use a calculator to approximate

[regal bane]

Putting an x and arrows is a little strange. There's no algebra here

[eager walrus]

they were thinking of like

turning it into exponential form

[onyx spade]

No like how do i put it into calculator

To find x

[karmic imp]

What kind of calc do you have?

Because there's normally a log button on there

That button there

You can type in whatever base you want

[vocal sleet]

@onyx spade Has your question been resolved?

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[fierce badge]

Do I go here for help?

[fierce badge]

Pls

@everyone

[peak matrix]

That's against server rules

[fierce badge]

Oh sorry

Could you please help me as a friend then pls

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[solemn spear]

Is anyone available to voice chat for 5 mins to explain what is happening here?

[flat whale]

just ask your question

[solemn spear]

I just dont understand what its saying here

I barely understand the notation

[flat whale]

https://math.libretexts.org/Bookshelves/Calculus/Calculus_(OpenStax)/05%3A_Integration/5.03%3A_The_Fundamental_Theorem_of_Calculus

https://math.libretexts.org/Bookshelves/Calculus/Calculus_3e_(Apex)/05%3A_Integration/5.04%3A_The_Fundamental_Theorem_of_Calculus

[solemn spear]

yes that is what im trying to learn

[solemn spear]

what should I try to understand first?

[flat whale]

read one sentence at a time and ask a question when you don't understand

[solemn spear]

what is a definite integral?

[flat whale]

an integral with bounds

$\int_a^b$ definite integral

[twin meteor]

riemann

[flat whale]

$\int$ indefinite integral

[twin meteor]

riemann

[flat whale]

this one gives you a number

[flat whale]

this one gives you a function

[solemn spear]

what is that symbol called?

what does dx mean?

[flat whale]

welp you should go back a few pages

https://math.libretexts.org/Bookshelves/Calculus/Calculus_3e_(Apex)/05%3A_Integration/5.01%3A_Antiderivatives_and_Indefinite_Integration

[solemn spear]

what is this saying? the derivative = function? that doesnt seem right thats like saying 4 = 7

[flat whale]

nope

the derivative changes the function

If e.g. F(x) = x^2, f(x) = 2x

What's F'(x) = ?

[solemn spear]

2x. so the capitalization of f is just because its a different function? why is there F and f?

[flat whale]

F and f are different symbols in math yes

so they represent different things, in general

in the context of antiderivatives, typically F relates to f through F' = f

Similarly for G' = g

[solemn spear]

so capital letters means its antiderivative?

[flat whale]

typically

nobody can control what symbols authors choose to use

you always have to infer from context

[solemn spear]

i'm used to regular derivatives being notated as f(x) = and f'(x)

[flat whale]

this is also a regular derivative

[flat whale]

it just relates to f via this eqn

[solemn spear]

so F = antiderivative and F' = derivative of antiderivative ?

[flat whale]

read this entire sentence

[solemn spear]

im confused what F' means

[flat whale]

F = a function

[flat whale]

like F(x) = x^2

[flat whale]

the prime on F is the same as prime on any other function

[solemn spear]

so for some reason the derivative of F = another function?

[flat whale]

Do you agree that f(x) = 2x another function?

[solemn spear]

I don't know what to believe now. but i'll say no

[flat whale]

Both x^2 and 2x are functions of x

[flat whale]

The derivative of a function is a function yes

if you haven't learned derivatives, i suggest doing that before learning integrals

[solemn spear]

I understand derivatives

isnt that the same as f' = f

[flat whale]

https://math.libretexts.org/Bookshelves/Calculus/Calculus_(OpenStax)/03%3A_Derivatives/3.01%3A_Defining_the_Derivative

[flat whale]

i don't think you do

[flat whale]

if you're unsure about this

[flat whale]

how did you conclude f' = f?

[flat whale]

Reminder that F(x) = x^2 and f(x) = 2x

[solemn spear]

what you said the derivative = a function

[flat whale]

what's f'(x) = ?

[flat whale]

yes

2x is a function

[solemn spear]

is that not what f' = f says

[flat whale]

no

F' = a function, but nowhere did i say it was equal to f'

"a function"

you seem to think of "a function" represents f(x) specifically

it doesn't

F(x) is "a function"

[solemn spear]

ok i understand now, if f(x) = 2x , its antiderivative is F(x) = x^2 . so when differentiate F(x) = x^2 it turns back into 2x, hence F'(x) = f(x)

[flat whale]

correct

[solemn spear]

so after it says write, what is going on?

[flat whale]

do all this but with f(x) = x^2 and F(x) = (1/3) * x^3

[solemn spear]

why did you turn F(x) into that?

so it becomes F(x) = x^3 / 3

[flat whale]

they tell you

[flat whale]

the one thing that's left out is C. One possibility for C is 0, but C can be any number

[solemn spear]

but since we are getting derivative of F(x) the C goes away because you cant differentiate a normal number

[flat whale]

you can absolutely differentiate any number

[flat whale]

i thought you learned derivatives

[solemn spear]

i mean normal numbers like 55, 4, 9

e

as long as theres nothing attached

[flat whale]

C is a normal number

there's nothing attached to C

[flat whale]

.

[solemn spear]

so it goes away

so now that I have x^2 = x^2 what does that tell me?

[flat whale]

if you completely ignore the integrals and derivatives, yes

[solemn spear]

what does that tell me about the indefinite integral?

[flat whale]

do some problems and find out

https://math.libretexts.org/Bookshelves/Calculus/Calculus_3e_(Apex)/05%3A_Integration/5.03%3A_Riemann_Sums

^ shows you how to do it the hard way with sums and easy way with antiderivatives

[vocal sleet]

@solemn spear Has your question been resolved?

[solemn spear]

so the original functions are on the left

and antiderivatives on right

[flat whale]

yes

"original functions" being the integrands

[solemn spear]

is there another way to phrase that? the integrands?

[flat whale]

the left sides are read as "the antiderivative of a function"

for various functions

[solemn spear]

so i wrote this wrong?

[flat whale]

well it's vague

one interpretation by "are" is that the function appears somewhere on the left

but not the entire left side

[solemn spear]

ok what the hell is going on here

they give me the hardest thing for my first example???

[flat whale]

you probably shouldn't be doing trig subs yet

at least not before polynomials

[solemn spear]

maybe this is easier

" I am given the (blank) and need to find the (blank) "

it looks like this is a definite integral because of the 9 and 1

[flat whale]

this is enough to example 2

[solemn spear]

which one of those will i use? arent those for indefinite? ex 2 looks like definite

[flat whale]

indefinite integrals give you the formulas you need to calculate definite integrals

[flat whale]

read all these examples
https://math.libretexts.org/Bookshelves/Calculus/Calculus_3e_(Apex)/05%3A_Integration/5.04%3A_The_Fundamental_Theorem_of_Calculus

[solemn spear]

i dont see one with an x^2 on the bottom

[flat whale]

you need to simplify the fraction first

$\frac{a+b+c}{d} = \frac{a}{d} +\frac{b}{d} + \frac{c}{d}$

[twin meteor]

riemann

[solemn spear]

ok I understand how they got to the 2nd line

how did they get to the 3rd?

[flat whale]

,tex .int rules

[twin meteor]

riemann

[flat whale]

they used sum rule multiple times

[flat whale]

also this

[solemn spear]

which part should I try to understand first?

usually my teacher's slides are all you need to do examples and problems

so it's surprising I need to use these external resources

.

[flat whale]

always do simpler problems first before doing hard ones

[solemn spear]

which one is the simple one?\

[flat whale]

all the ones you can do

[flat whale]

probably these

if they're not easy, then we have to go backwards again

[vast shale]

wheres the problem?

[solemn spear]

how did they get there? the places with ?

why is the 1/4 separated with the x^4? why isnt it just x^4 / 4

[vast shale]

maybe its just for solving faster

but its the same thing

[flat whale]

you'd benefit by watching a lot of lectures
https://www.youtube.com/watch?v=Gc3QvUB0PkI

https://www.youtube.com/watch?v=rCWOdfQ3cwQ

[vast shale]

completely agree

[solemn spear]

would it be easier to try a problem from my homework?

[flat whale]

there's so much you're doing it's hard to keep up with what videos you need to watch

watch the videos i linked above first before doing any of your problems

[solemn spear]

what does 60 represent?

the area under the function x^3 between 2 and 4 ?

[flat whale]

yes that's the correct interpretation of integral

there's slightly more about "signed area" when the function is underneath the x-axis, but worry about that later

[solemn spear]

Is this the correct way to visualize this in desmos?

[vast shale]

as i know integrals are the also the opposite of a derivative, am i right?

[solemn spear]

yes I think

[vast shale]

the proper term is antiderivative

but that mostly applies to indefinite integrals

[flat whale]

https://www.desmos.com/calculator/wogqvzicfa

Adjust that to your needs

[solemn spear]

what are my f(x) and g(x) in my case?

[vocal sleet]

@solemn spear Has your question been resolved?

[dapper birch]

a better way to put it is that taking an integral is the inverse of taking a derivative

[vast shale]

yeah

[dapper birch]

and better yet: integration and differentiation are inverses of each other

[vocal sleet]

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[vital heron]

8000, 800,80.... find the 7th term

[vital heron]

uh i got r = 10

is that right

is it 0.1

[lime gorge]

the sequence goes 8000,800,800?

[vital heron]

sorry i meant 8000, 800, 80

typo

is 0.008 the answer

[lime gorge]

yea that seems right

[vital heron]

thank uu

.close

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[soft walrus]

<@&268886789983436800>

[strange crater]

<@&268886789983436800>

[soft walrus]

interesting stuff

[winter hawk]

.close

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[spring hull]

i got stuck on this one

[soft walrus]

Do you know slope-intercept form?

[spring hull]

yeah

i got

(0,6)

(-5,2)

[near forum]

can i ask an alg 2 question here?

[vocal sleet]

Please read #❓how-to-get-help

[soft walrus]

so then what is the slope?

$m=\frac{y_2-y_1}{x_2-x_1}$

[twin meteor]

XxMrFancyu2xX

[spring hull]

0 -5

6-2

[soft walrus]

be careful of your negatives

0-(-5)

[spring hull]

5

[soft walrus]

yes

so we have $\frac{0-(-5)}{6-2}$ so what is the slope, $m$?

[twin meteor]

XxMrFancyu2xX

[spring hull]

5/4

[soft walrus]

Yes

and at what point does the line cross the y-axis?

[vast shale]

Be careful, that's run/rise

[soft walrus]

oh dam

thanks

yes Alex, make sure you do your $y$ values on top

[twin meteor]

XxMrFancyu2xX

[soft walrus]

and the $x$ on bottom

[twin meteor]

XxMrFancyu2xX

[spring hull]

alr

[soft walrus]

so we have $\frac{6-2}{0-(-5)}$ so what is $m$?

[twin meteor]

XxMrFancyu2xX

[spring hull]

4/5

[soft walrus]

yes

and now at what y-value does x=0 for at what point does the line cross the y-axis?

[vestal sail]

4/5

Oh

So what was the original equation?

[spring hull]

-8

[soft walrus]

be careful that's the x-axis

[vestal sail]

The y-intercept is when x = 0, simply plug in 0 for x

[vast shale]

In case of any confusion this channel is already taken and help is already being given

[soft walrus]

yes but I think with the graph given they want them to do it visually

[spring hull]

6

[soft walrus]

yes and that is $b$

[twin meteor]

XxMrFancyu2xX

[vestal sail]

Ok I will help someone else then

[soft walrus]

so we have both $m$ and $b$, so what is the slope intercept form?

[twin meteor]

XxMrFancyu2xX

[spring hull]

y=4/5x +6

[soft walrus]

👍

[spring hull]

thanks

[soft walrus]

yw!

@spring hull im going to close the channel now, you all good?

[spring hull]

Yup

[soft walrus]

.close

[vocal sleet]

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[karmic imp]

Fyi, in my opinion, you should let the OP close their own channel

You should close if someone forgot to close it

[vast shale]

Yeah that surprised me too

[soft walrus]

👍

[vocal sleet]

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[inner patrol]

hey yall, I need some help with the second part of this question (b). the first part was fairly easy (seemed a bit too easy for a 10 mark Q tbh, I probably fucked it up) just by using IVT. But, I can't think of any functions that would satisfy part b. I thought maybe a non continuous function, but that would require for it to have infinitely many discontinuities within a defined interval (i think) which personally i dont even think is possible.

[rugged vortex]

I mean (-1)^x is a stupid ass popcorn function where it's just violently discontinuous

But I don't think it's integrable

Yes snow I said popcorn

[inner patrol]

lol true

but I think that it has to be integrable. I haven't learnt any theorems that suggest that it would be integrable

[rugged vortex]

Hm

I mean try using an odd function

And bounds such that a = -b

So for example, f(x) = x

See where that goes

[inner patrol]

f(x)=x wouldn't work if a = -b because c would just = 0

[rugged vortex]

no

if $f(x)$ is an odd function and the bounds are $a = -b$ and $b > a$, then:
$$\int_a^b f(x) \ddx = 0$$
$$\implies \int_a^0 f(x) \dd x = -\int_0^b f(x) \dd x$$

[twin meteor]

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

[rugged vortex]

And this holds true as long as the odd function is continuous [a,b] (I'm pretty sure)

and x is continuous for sure lol

[cobalt crypt]

part a requires some combination of IVT and looking at the cases where that fails

[inner patrol]

No, I don't think it should because the negative and positive areas jut cancel out.

[cobalt crypt]

[inner patrol]

I thought the same thing, but take cos(x) bewteen 0 and 2pi, then c would just equal to pi. But the integral is 0.

[rugged vortex]

the integrals aren't the same

,w integrate cos(x) 0 to pi

[twin meteor]

Results provided by WolframAlpha

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Requested by Umbraleviathan#3607

[rugged vortex]

Well

That's a special case

But if you try f(x) = x

[cobalt crypt]

in particular, IVT fails exactly when $\ds \int_a^b f(x) \dd x = 0$

[cobalt crypt]

to have there be no choice of $c \in (a, b)$ you just require $g(x) \ge 0$ or $g(x) \le 0$ for all $x \in [a, b]$

[cobalt crypt]

umbra's suggestions of odd functions will satisfy this requirement

there are probably other functions that will work too

[inner patrol]

I might be misinterpreting what you're saying, but since $c \in [a, b]$ is what the question is saying, so is the integral = 0, then c can just equal b or a no?

[twin meteor]

The Average Joe

[inner patrol]

Oh shit

[inner patrol]

good point.

my bad. I'm dumb.

[cobalt crypt]

that is precisely the point of identifying where the proof in part (a) requires you to include the endpoints too

[inner patrol]

Thank you so much, I would have been trying to think of this for days to find that.

.close

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[coral hedge]

uhh how do i find the ratio for X and Y for this?

[regal bane]

Factor x from the left, factor y from the right

[vocal sleet]

@coral hedge Has your question been resolved?

[vocal sleet]

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[vast shale]

can this be considered as an exponent 3x^1/2 + 2x + 3 ??

[vast shale]

sorry polynomial function

not exponent

[regal bane]

No

If that's x^(1/2)

[vast shale]

ok

tysm

.close

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[novel sinew]

I would like help with this question:

[novel sinew]

i currently have this diagram but i feel like this is really wrong:

yeah i'm here

[icy spear]

A and B ON the larger circle

[novel sinew]

how would that be drawn?

sorry if this is really obvious

[icy spear]

just shift your A and B so they are on the circumference of the large circle

[novel sinew]

like inside?

inside the big circle?

[icy spear]

idk how else to say it lol. A and B should be on the edge of the circle

[novel sinew]

do you mind drawing it? it's ok if you can't

if you can a really rough sketch is fine

[icy spear]

on second thought

i'm not sure this is a possible configuration given that ABCD has to be a square

unless "on" means something different than lying on the circumference

[novel sinew]

i'm still not sure about what lying on the circumference is

is that what my diagram is or is it not?

[icy spear]

it means that your points A and B should be on the edge of the big circle

[novel sinew]

ohhhhhhhhhh

i see what you mean

how would you construct the square tho as the small circle has to be out of the square?

[icy spear]

yeah it doesn't seem like a possible configuration

[novel sinew]

no worries thanks for your time

i will ask my teacher about this

thank you!

.close

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[formal tusk]

Hey

[formal tusk]

Can someone please

2

[split wind]

is it an exam?

[formal tusk]

No

Sample

[split wind]

i see

what have you tried?

[formal tusk]

I have no clie

I am stuck

Limits are in terms of y

[split wind]

https://tutorial.math.lamar.edu/classes/calcii/surfacearea.aspx

[formal tusk]

I know but I don’t know hot set up integral

[split wind]

well, you'll have to try

you know that 2pi x ds for rotation about y-axis

[formal tusk]

Yes but here

I do 1/x*sqruare root

Is that right

[split wind]

you'll just need
integrate 2πx ds

i don't see why there's 1/x

[formal tusk]

But its xy=-

1

[split wind]

yea

[formal tusk]

Don’t we make it y=1/x

[split wind]

well, you can

,w plot xy=1 for 0.5<y<1

[twin meteor]

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[formal tusk]

1/x*sqrt(1+1/x^4?

[split wind]

nah, just
2πx*sqrt(1+(dx/dy)²)

so, it'll be

int 2π/y*sqrt(1+(your work)²) dy

[formal tusk]

In terms of y or x

Dy or dx

[split wind]

what do you think then? dy or dx?

[formal tusk]

Dx

[split wind]

it's dy, since it's rotating about y axis

[formal tusk]

Got it thanks so much

Can you give me help about 3 d too?

[split wind]

3d, let's see

[formal tusk]

First oder so i have integrate both sides?

[split wind]

you'll have yo seperate them first

[formal tusk]

Multiply by dx?

1/dx

[split wind]

like all the terms with x to oneside, and y to the other

which becomes

dx/(√x*sin²(√x))=dy

and then integrate

[vocal sleet]

@formal tusk Has your question been resolved?

[formal tusk]

Thanks so much man

You are the best @split wind

[vocal sleet]

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[unique marsh]

supposed to find the area of the circular segments with only this information

[candid otter]

looks like the first step is to find the radius of the circle, do you have any thoughts or working on that?

[astral pilot]

EH= 1/2

let O be center
find <OEH

using trigonometry find radius

[candid otter]

so what's stopping you from doing that

[unique marsh]

is this correct for radius?

@astral pilot @candid otter

[candid otter]

just a second

where'd you get 54.29 from

[unique marsh]

i tried to find the angles for

wait i just realized i put the wrong number in the calculator

51,43

360/7=51,43

[astral pilot]

please don't use decimal approximation

i hate them

[unique marsh]

oh sorry that's what we use in my country

[astral pilot]

https://tenor.com/view/crycat-crying-cat-crying-cat-thumbs-up-thumbs-up-ok-gif-22851318

[unique marsh]

radius should be 1.15 then

[astral pilot]

ig should be right

ya it is right

[unique marsh]

i tried to use a formula i found online for the area of the circular segment but i think it's wrong

[twin meteor]

Result:

1.1523526043429

[astral pilot]

idk this formula

[unique marsh]

how would u find the area for the circular segment

this is what i used

wait i used the wrong radius

[candid otter]

it looks like the right radius, but your central angle was in degrees

[astral pilot]

,w 51.43deg in rad

[twin meteor]

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[astral pilot]

formula used is 180 deg = pi rads

[unique marsh]

ohhh

do i also put the one for sinus in radians

[astral pilot]

yes

shouldn't matter though

[astral pilot]

,calc 1/2 * 1.15^2 * (0.8976-sin(0.8976))

[unique marsh]

why is it different

i think my calculator does degrees

if that makes sense

yep

[twin meteor]

Result:

0.076551066848488

[unique marsh]

so is that the answer

0.08

[astral pilot]

yep

[unique marsh]

but in my country we dont use radians

can i find it for degrees

or is it the same

[astral pilot]

there some other formula for degrees but i can't remember it rn

[unique marsh]

oki thank u! but should it give the same result (0.08) just with another formula?

[astral pilot]

the idea is essentially same

[candid otter]

it would be something like Area (A) = $\frac{1}{2} * r^{2} * (\frac{\pi}{180}\theta - \sin \theta)$

[twin meteor]

Quixz

[unique marsh]

oh yes i just found this

thank u! i will try

yayy thank u i got it!

i have another question

"What is the length from E to the opposite midnormal?"

first, how do i find the midnormal with only this information?

[candid otter]

what is a "midnormal"?

[unique marsh]

oh sorry maybe it's something different in english

like the middle of all the sides

and they make a point

[candid otter]

Circumcenter?

[astral pilot]

altitude

[unique marsh]

sounds right

[astral pilot]

what do you mean by opposite midnormal

[candid otter]

I imagine

[unique marsh]

yes exactly

so how would i find the length from E to that point

[candid otter]

Hecker, does this look about right to you as well?

have you got it @unique marsh

[unique marsh]

nope

[candid otter]

i think you can use these similar triangles

[unique marsh]

is the point in the exact center of the line in the middle

[candid otter]

yes because the smaller triangle has side lengths that are each 1/2 of the bigger one

[unique marsh]

okay thank u!

so i could use trigonometry to find the length of c and then divide it by 2?

to find the length from the point to the center

[candid otter]

even better, there is a shortcut

because c is the radius of the circle

[unique marsh]

ohh

so it's just 1.15/2

or wait no

yes

[candid otter]

yes

[unique marsh]

1.15+(1.15/2)=1.725

that should be the result right

[candid otter]

looks good to me

[unique marsh]

thank u sm!

[candid otter]

don't forget to .close the channel 👍

[unique marsh]

.close

[vocal sleet]

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[rugged bear]

I neeed help understand the double Angie formula

[rugged bear]

Primarily

The coefficient part and what it makes

For example if I’m presented with a q such as 4cos(A-B)

I not it’ll be cosAcosB-SInASinB

But the value of 4

I won’t know what to do with it

And this goes for other instances like 4sin2a

[hasty pulsar]

you just multiply the whole thing by 4

[rugged bear]

Ok bcos it’s on the outside

@hasty pulsar can you help me w understanding the relationship between exact values and their place on trig graphs

Let’s say you solve a quadratic trig q like

6cos^2 - códex - 1 = 0

And cos x = -1/3 and cosx = 1/2

Why do we do cos ^-1 of -1/3

What’s that transformation called

Is it like going from the y axis to the x axis value

[vocal sleet]

@rugged bear Has your question been resolved?

[rugged bear]

Actually

How do I work backwatds

Like how do I find sin x + sin x\2

How do I find the expanded form of that sinx /2

[vocal sleet]

@rugged bear Has your question been resolved?

[vocal sleet]

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[vocal sleet]

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[viral copper]

$3 + 4 + 7 + 11 \cdots$ 49 terms

[twin meteor]

NEONPerseus

[viral copper]

This seems to be a shifted Fibonacci series, no idea how to compute it though

Oh wait nvm

.close

[vocal sleet]

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[vocal sleet]

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[tacit aurora]

One message removed from a suspended account.

[tacit aurora]

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[candid otter]

in what context? should we start from the very beginning

[tacit aurora]

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[candid otter]

ok

[tacit aurora]

One message removed from a suspended account.

[candid otter]

you know what a fraction is

[tacit aurora]

One message removed from a suspended account.

[candid otter]

and you know how place value works

[tacit aurora]

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One message removed from a suspended account.

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[candid otter]

so if I gave you a number like 1.2

it of course means 1 one and 2 tenths

so as you keep going to the right, the numbers represent smaller and smaller pieces of a whole number

1.001 is 1 one and 1 one thousandth
$1.001 = 1 + \frac{1}{1000}$