help-10

[nova vale]

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[round pewter]

So I understand the 52!/49!

But I'm so confused on the order matter part

[river falcon]

a set of 3 cards

[round pewter]

Yes

[river falcon]

in how many ways u can arrange those 3 cards in a line

[round pewter]

Wym line

[river falcon]

like put them down

how many ways

[round pewter]

Like 1 2 3

How does that work

[river falcon]

yes

[round pewter]

So it has to increase by 1 each time?

[river falcon]

no i mean

in how many ways u can arrange the 3 cards

or in how many ways u can permute them

like if u have 2 things a and b then you can either a,b or b,a

[round pewter]

Yuh

[river falcon]

like that but for 3 things

so how many times?

[round pewter]

Uh 6

[river falcon]

right

[round pewter]

Cus 3!

[river falcon]

now

if order matters

[river falcon]

then every 6 of those arrangements are unique

but its asking for when order doesnt matter

[round pewter]

What does it mean order doesn't matter

[river falcon]

like

the order in which u arrange things

a,b and b,a

[round pewter]

Oh but when order matters it has to be what

[river falcon]

in the first one i have a at first, in the second one i have at first

wdym

[round pewter]

So like when it doesn't matter it can be like a c b but when it does, does it mean like abc?

[river falcon]

when order matters, every arrangement is counted as unique

so if order matters then a,b and b,a are two different

but if order doesnt matter then its 1

[round pewter]

😭

So when order matters you count like a jack queen king different as jack king queen?

[river falcon]

yes

[round pewter]

Okay that makes sense

[river falcon]

so here

[round pewter]

Because then there are less arrangements

[river falcon]

u basically have 6 arrangements of a set of 3 cards

[round pewter]

Why is that

[river falcon]

because the number of ways u can permute 3 things is 6?

3!

[round pewter]

Alright thanks I gotta go though

Cya later alligator

[river falcon]

okay

cya

[round pewter]

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[timid silo]

help, tried a lot of attempts

tried differentiatiing on both sides

tried e^x(f(x)+f'(x)) form

not reaching anywhere]

[stone vortex]

pw?

[timid silo]

i reached quite far with differentiating on both sides but it looks ugly

[timid silo]

ye

[stone vortex]

oh ok

[timid silo]

anyone?

[junior granite]

what did you got with this?

[timid silo]

too ugly i lost track

ive just been scribbling in my notebook

applied by parts like twice too

[junior granite]

lol
but I think that's the best way

[junior granite]

what

why?

[timid silo]

because i integrated again

[timid silo]

ye

can you sjhow me your working once?

[junior granite]

damn

[junior granite]

erm I didn't solved it

but if you differentiate the xg(x)/{e^x+1)
you can compare it with the function that is being integrated

from there you can find what g(x) will be

[junior granite]

(completely*)

[timid silo]

ye thats the tough part...

ill gibve it a shot once again later]

[junior granite]

I mean the {e^x+1}^2 could be eliminated afterwards
then it is not that difficult

[timid silo]

i cant understand maths typed 😭

[junior granite]

huh?

[unreal musk]

Do you mean you can’t understand it written at all, or that e.g. you’d rather see it with the equation bot?

[timid silo]

yes this

i cant understand it typed in chat basically

dont help me yet tho please i wanna give it a shot myself

i can come back later right if i still dont get it?

[junior granite]

${(e^{x}+1)}^{2}$

[warm shale]

77²

[timid silo]

thank you :)

[junior granite]

this thing in the denominator

[timid silo]

ye this wilkl get cancelled

[junior granite]

yup

[obtuse pebble]

@timid silo Has your question been resolved?

[timid silo]

got it

stupid calculation error

thanks tho @junior granite

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[dreamy shuttle]

someone pls help

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[stoic anchor]

how can I find out what digit does the product end with

[gilded needle]

is this the product of the numbers 71 through 79? it's kinda hard to read

[stoic anchor]

yea

[gilded needle]

ok

do you know about modular arithmetic?

[stoic anchor]

nope

[obtuse pebble]

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[dull heath]

help pls

[tardy epoch]

multiply top and bottom by rational conjugate

[dull heath]

what's next

[tardy epoch]

divide all terms by the largest one

[dull heath]

n*6?

[manic chasm]

for these type of limits, normally it is easiest to check the rate of change of the terms, so if the bottom term grows faster then it goes to 0, since you are dividing by infinity.

[dull heath]

i think thats difficult now. and right answer is not 0

[tardy epoch]

largest term being the one that grows the fastest as n goes to infinity

[manic chasm]

well, it seems to diverge since the top is so dominate

[tardy epoch]

in your case it's n^(3/2)

[manic chasm]

riemann help me in #help-35 😭

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[fallow dust]

can somebody confirm my definitions:

[fallow dust]

one to one: every y has at most one x

onto: every y has at least one x

[shadow dagger]

yeah they're fine

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[crisp spruce]

I don't get how I'm supposed to calculate the average acceleration

[obtuse pebble]

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[severe pasture]

do you know how to find acceleration at a specific point in time

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[jagged isle]

hii

[jagged isle]

I want to calculate the Eigenvector for the Eigenvalue λ = 3 of a matrix A \begin{bmatrix} 1 & -1 & 2 \ 0 & 3 & 3 \ 0 & 0 & 9 \end{bmatrix}.

[warm shale]

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

[jagged isle]

Right now I want to calculate Ker(A - λ!)

But I am currently stuck, because I obtained a zero row

Does that mean, that I can use any number for that variable??

First I got \begin{bmatrix} -2 & -1 & 2 \ 0 & 0 & 3 \ 0 & 0 & 6 \end{bmatrix}.

[warm shale]

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

[jagged isle]

And now I have \begin{bmatrix} -2 & -1 & 2 \ 0 & 0 & 3 \ 0 & 0 & 0 \end{bmatrix}

[warm shale]

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

[unreal musk]

Yep, you ideally should get zero rows, considering you want the kernel of (A - 3I) to be nontrivial and contain items other than the zero vector

[jagged isle]

thanks !!

!close

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[steady venture]

i will find you be careful ange

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[bitter terrace]

does my solution to part b look ok

[bitter terrace]

Also if a bases has 2 linearly independent elements we say it has 2 dimensions but what does the amount of elements in the basis tell us?

for example W bases has 2 elements but the vector in the bases has 3 elements

does that mean its a 2 dimensional space in a 3 dimensional space?

[minor nova]

It would be a subspace isomorphic to R2

So yeah basically that

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[bitter terrace]

Im allowed to say W is a sub space of R3 if it spans R3 right

[gilded needle]

W is all of R^3, right?

a vector space is a subspace of itself, so what you said is correct

[bitter terrace]

oh ok

Also idk if this a typo because I heard this book has tons of typo but he is interchangeably using basis and bases

[gilded needle]

where do you see bases?

[bitter terrace]

the reason its dimension 4 is because its bases has 4 elements?

earlier he would use bases I believe to represent the set of basis vectors

let me find it

[gilded needle]

if used properly, "bases" is the plural of "basis"

but to answer your question yea, if a basis (any basis) of a vector space has N vectors, then the vector space has dimension N

(every basis of a given vector space has the same number of vectors)

[bitter terrace]

oh ok I see

[bitter terrace]

what do we call the elements inside the basis?

if im understanding right

if a and b are vectors

[gilded needle]

typically just call them basis vectors

[bitter terrace]

oh ok

so a, b are basis vectors of the basis {a,b}

where a and b are linearly independent

[gilded needle]

yea, assuming they actually form a basis

(i.e. they are linearly independent and span the whole space)

[bitter terrace]

span the whole space?

so if I had

a basis in R3

ohhh

the second part

is saying that like

[gilded needle]

you would need 3 linearly independent vectors

in R^3

[bitter terrace]

oh ok

[gilded needle]

any 3 linearly independent vectors in R^3 are a basis of R^3

[bitter terrace]

oh ok I see

thanks for the clarification

[obtuse pebble]

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[meager vapor]

Hi

[meager vapor]

I’m confused on how to do find the points to find the graph and the domain and range

[stiff leaf]

Do yk what they are?

Domain and range?

Oh I gtg so can't help if you reply

But domain is just every x point of the function and range is every y value

Like in a x^2 function (-infinity, infinity) is the domain

And (0,infinity) is the range

Here in the piece wise function you use these brackets '-> [ when you have an equal to operator for a number

[obtuse pebble]

@meager vapor Has your question been resolved?

[meager vapor]

Yes I know that

But I can’t seem to figure it out

[meager vapor]

Ohhh

[meager vapor]

Wait like you mean [-8]

[obtuse pebble]

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[violet timber]

Okay so I want to 4d

I haven't done this since last year so I'm rusty but

Do I find something that multiplies to -72 and adds? to -21

I forgot if that's correct

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[cloud ibex]

. Caleb is trying to bake a pie for his grandma. The pie crust costs $6 and apples cost $3 per pound. He has $33 to spend.

a) Write an inequality to represent this scenario.

b) What is the most pounds of apples he can get

how would i slove this???

[unreal musk]

"he can't spend more money than he has..."

[cloud ibex]

how would i write the inequality??

i know minus the crust he has 27 to spend divide by three he can get 9 pounds of apples

but how would i write that into a inequality??

x3-6<33???

3x*

3x+6<33??

[fathom light]

Yep

≤

He can spend all 33$ if he wants

[cloud ibex]

ok thanks

have a goodnight!!!

[fathom light]

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[cloud ibex]

Yes

[obtuse pebble]

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[heady turtle]

"when finding extrema, it is important to consider saddle points along with local maxima and minima." Why? we already know that saddle point is not an extrema, isn't it? (since they are points where the function has critical points but they are neither local maxima nor minima) Then why should we consider it when finding extrema?

[errant basin]

I think if its more like, when you find critical points, it falls into either local max/mins, but not all critical points are local max/mins but can be saddle points instead

It might just be warning you to check your critical points and not jump to assumptions of solely max/min

[heady turtle]

I mean like, if we want to find the extrema of a function, we need to check its interior critical points and boundary points, right?

[errant basin]

yes

[heady turtle]

And if we find that there's only a critical point in the interior which is saddle point

Shouldn't we just ignore it cuz we shouldn't consider saddle point when finding the extrema

[normal cairn]

from what i understand, thats exactly what your original message says. the way we find maxima is by finding the critical points first. but not all critical points are maxima or minima, so it's important to always keep in mind that any critical point we find could very well be a saddle point

maybe im misunderstanding, but thats what i got

[heady turtle]

Hmmm Actually I mean, uhh

Mind that here local extrema and extrema are different

Maybe I express the terms wrongly

[heady turtle]

I mean when finding extrema, why still need to consider saddle point (global extrema, not local)

[normal cairn]

my only thought is that while you have in your mind two different steps: a) finding critical points and identifying them as maxima or minima and then b) picking the largest maxima to call the extrema.
maybe the sentence you're quoting doesn't discern those as two different steps, and simply puts all of the steps in one pile. in which case, while searching for the extrema, you would actually just have to identify the saddle points

maybe its shaky wording on the sentence you quoted or something im not getting, but as far as im concerned youre absolutely right that if you already know all the maxima of a function as well as all the saddle points, then you dont really care about the saddle points, all you care about are the maxima and which one of them is actually the largest

[heady turtle]

I made a summary, Just want to confirm : if we want to find the extrema of a function, we need to check its interior critical points and boundary points, but if we find that there's only a critical point in the interior which is saddle point, then we dont really care about the saddle points, right? all we care about are the maxima and which one of them is actually the largest, since the only point in the interior is a saddle point, so we only need to focus on the boundary points, am I understanding correctly? @normal cairn

[obtuse pebble]

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[frail crater]

How do i go about solving these proportions involving fractions, i can do it with decimals and whole numbers but I’m confused how to do this with fractions, do i need to make them all have the same denominator? Do i neeed to convert to decimals?

[wary trellis]

2 1/2 can be written as 5/2
3 3/4 can be written as 15/4
9 1/2 is 19/2
So we know
5/2 : 15/4 = 9/2 : x
Aka 5* x/2 = 15* 9/8
Therefore x = 27/4 aka 6 3/4 boxes

If my calculations arent off but that's the gist of it

[frail crater]

the answer im getting on the answer sheet is 14 1/4 boxes

but so you converted them to improper fractions, i will try that

lets start over

[wary trellis]

The idea is to find the amount of boxes per kg which you get from the fact that 2 1/2 kg fills 3 3/4
Which should be 5/2 => 15/4
To get 1kg of sugar we need to divide with 5/2
1kg => 3/2box
And then just multiply 3/2 boxes by 9 1/2

[frail crater]

for example

with this question using decimals

i do this

I use the cross method

But with fractions I’m not sure how to do that

[wary trellis]

Whenever you have Number.xyz
You can write it as Number xyz/1000

[frail crater]

right because of the decimal places

ok i understand that

[wary trellis]

So for example 1.63 is 1 63/100

[frail crater]

ok im following so far.. so how can we translate that to the question now, so for example 2 1/2 kg of sugar fills 3 3/4 boxes

do we now make those numbers decimals?

or how do i go about finding the ratio to solve for x

like would that just be 2.5 and 3.75 can i do that or no

ya so if i just convert all the fractions to decimals and solve it that way i was able to get 14.25 or in other words 14 1/4. ill try to just kep doing that

thank you

🙂

.close

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[sand meadow]

Need help evaluating the definite integral

[sand meadow]

I'll post screenshots of my solution

I successfully integrated it but can't evaluate the limits

It's leading to indeterminate forms, getting stuff like infinity - infinity

on the first screenshot, the solution starts from the second Q. I made a mistake the first time

[tardy epoch]

what

why do you have 4 pages of work

with half of it scribbled out

[sand meadow]

I made mistakes. Let me rewrite it without the mistakes

or is it even necessary? I'll just write the final answer

[tardy epoch]

showing some work would be helpful if you make mistakes

otherwise just use an online calculator

,w int 0 to inf of x^(2018/3) / (x + x^2019)

[sand meadow]

I used it to confirm that I arrived at the correct integral

[warm shale]

Wolfram Alpha doesn't understand your query!
Perhaps try rephrasing your question?
Click here to refine your query online

Requested by rie.mann

[sand meadow]

I've seen the answer to the question, I just don't understand it

[tardy epoch]

surprising wolfram can't figure this out

[sand meadow]

I understand how to integrate, but the part where you evaluate the limts, how they arrived at the answer was weird

[tardy epoch]

show

[sand meadow]

a moment, it's calculating it again

damn, lol, It also couldn't solve. What i fed it the first time was the simplified version after I had done some manipulations

let me show my workings more neatly first

after simplifying, it becomes an integration by partial fractions question

use wolfram to evaluate this

[obtuse pebble]

@sand meadow Has your question been resolved?

[tardy epoch]

i lost you here. which term x^2019 become?

[sand meadow]

Full solution re-written

[sand meadow]

I factored out an x

so it became x raised to 2018

and x raised to 2018 is u^3

it essentially simplifies to an integration by partial fraction question which I have solved, my issue is putting in infinity into the final answer

[tardy epoch]

okay assuming your antiderivative is correct

which i can't find

plugging in infinity is really taking a limit

[sand meadow]

its in the last pic, at the bottom

[tardy epoch]

$F(x) |^\y_0 = \lim_{B \to \y} F(B) - F(0)$

[warm shale]

riemann

[sand meadow]

didnt know that

[tardy epoch]

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

[sand meadow]

forgot to substitute u back to cube root of x raised to 2018

[tardy epoch]

they're called improper integrals

[sand meadow]

in this case what would t be?

[tardy epoch]

my B here

[sand meadow]

So I'm taking the limit of this as x approaches infinity?

[tardy epoch]

you could think that way yea

[sand meadow]

https://tenor.com/view/sad-smile-person-gif-3593640814102488583

[tardy epoch]

just don't forget to subtract F(0)

[sand meadow]

oh the limit is for only f(b)?

this math problem is so annoying, how do i even take the limits of that?

Thats where my issue is

If i directly substitute infinity, i'd be getting indeterminate forms like infinity - infinity

do you know how they got the answer, that pi over stuff

[tardy epoch]

Use log identities to combine it into one log

,tex .log rules

[warm shale]

riemann

[sand meadow]

hmm

[obtuse pebble]

@sand meadow Has your question been resolved?

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[night blaze]

I got A. to 44.98cm But i cant figure question B out without using the derivative. Can somebody help

[tawny copper]

Well, u can graph it

Then said "Base on the graph" blah blah blah but actually use derivative to get the answer

[night blaze]

But I can’t

[tawny copper]

?

[night blaze]

“Without using the derivative”

[tawny copper]

Yeah

That why u graph it

[night blaze]

So I graph A(r)

[tawny copper]

Use derivative to get the actual value (on your note), then pretend to graph it and write "base on the graph the smallest possible.... is ....." on ur paper

[night blaze]

Yeah I know you can use it but the class with this question(my brothers class haven’t even learned derivatives yet😭

[tawny copper]

LMAO

[night blaze]

So I don’t understand how to solve it

How they solve it

[tawny copper]

Then graph it then

Very slow

But it works

[night blaze]

Can’t I use limit ?? Perhaps

X->0

Yeah I don’t know

Is it possible to solve without finding the derivative????

<@&286206848099549185>

[obtuse pebble]

@night blaze Has your question been resolved?

[timid silo]

@night blaze why dont u just take the A(r) and instead of formally deriving to minimise it, just write out the limit definition of derivative and argue that if lim A(r+h)-A(r)/h is 0 as h goes to 0, then r must be an extremum of A. So you're still deriving but using limits and from first principle

[night blaze]

So there isn’t quite an exact answer?

[tawny copper]

Teach ur bro calc 1

LMAO

[night blaze]

Impossible

[tawny copper]

problem solved

[night blaze]

Bei they’re learning about quadratic polynomials

They haven’t even got to vector yet nor derivatives

[tawny copper]

Isn't there a way to get local max min in quadratic poly?

[night blaze]

-b/2a

[tawny copper]

Yeah

But 1/x aint quad poly

[night blaze]

Yeah that doesn’t work

[tawny copper]

Literally teach ur bro a little calc wont hurt

[night blaze]

But how is it solvable

[tawny copper]

Graphing ....

[wicked shadow]

Get the derivative to get the local max point and local minimum point

[wicked shadow]

First derivative only

[night blaze]

F’(x)=0

[wicked shadow]

U mean that question?

[night blaze]

Nah

Just typing

[tawny copper]

teach ur bro graphing and fx diiference

[night blaze]

Brb

[tawny copper]

mono somthing table

[wicked shadow]

So what do u need?

[tawny copper]

read this

bruh

[wicked shadow]

Lol reading??? I am lazy

[tawny copper]

Hi lazy

Im dad

[wicked shadow]

Should i laugh then?

[tawny copper]

Yes

U have my permission to laugh

[wicked shadow]

U need a doc.

U have been diagnosed as paranoia

[wicked shadow]

Question b can be solved using calculus only why don't u want to solve it using derivative?
This question is considered as
An application on minima and maxima
Derivative is the ideal way

[night blaze]

Monotoni

On my language is called monotoni forhold

[night blaze]

Mate

[wicked shadow]

What, this question cannot be solved then

[night blaze]

Yeah that was my thought lol

[wicked shadow]

What lang is that

[night blaze]

Monotoni?

[elder ingot]

1 + 1 = 3?

[night blaze]

Explaining how the graph looks based on the derivative

[wicked shadow]

Yeah

[night blaze]

Danish

[obtuse pebble]

@night blaze Has your question been resolved?

[wicked shadow]

Now I see,
Look bro long story shorts
U brother need to learn calculus basics other than it he won't be able to anything

[obtuse pebble]

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[glacial robin]

Could someone send me in the right direction

[light quarry]

Which part about it is bothering you or just where to start?

[glacial robin]

Wait, should i use the sum of identity angles for this

I really dont know where to start yeah

[light quarry]

So there are 2 formulas you need

1 is for the magnitude of complex numbers and the others is for the angle

[glacial robin]

Uhu

[light quarry]

And you either have those formulas and memorise them or you can see and derive them from drawing z in the complex plane

[glacial robin]

What are the formulas?

[light quarry]

So if $z = x+yi$ then the magnitude is $|z| = \sqrt{x^2+y^2}$ and $tan(\theta) = \frac{b}{a}$ but for the tangent you have to check if the solution is in the right quadrant

[warm shale]

Goran

[glacial robin]

Do i need the tangent tho?

[light quarry]

Oops I didn't even realise I put b/a it should be y/x

[glacial robin]

All good

[light quarry]

I am not sure what you mean

[glacial robin]

Theres a formula for the tangent but for this tangent it does not seem like i need the tangent

[light quarry]

I mean this formula just calculates the angle easily

[glacial robin]

Okay

I have no idea how to use the formula

[light quarry]

Ok so here we have that x = -5 and y = -5 right

[glacial robin]

Yes

[light quarry]

So plugging into the formula you get $|z| = \sqrt{(-5)^2+(-5)^2} = 5\sqrt{2}$

[warm shale]

Goran

[light quarry]

That's the first part

[glacial robin]

Huh

So 50 is 5sqrt2?

[light quarry]

Yep

[glacial robin]

Oh

I see

Okay

[light quarry]

$\sqrt{50} = \sqrt{252} = \sqrt{25}\sqrt{2} = 5\sqrt{2}$

[warm shale]

Goran

[glacial robin]

What have i exactly calculated now

[light quarry]

Now we get that $tan(\theta) = 1$ meaning that $\theta = \frac{\pi}{4}$ but if we look at the complex plane that's the wrong quandrant so we can add $\pi$ for the final solution of $\theta = \frac{5\pi}{4}$

[warm shale]

Goran

[light quarry]

That is in radians

But I see that your solution asks for degrees so that would be $\theta = 45deg$ for the first part and adding 180deg to get $\theta = 225deg$

[warm shale]

Goran

[glacial robin]

Okay

What exactly is the format in which im answering

Because it seems kind of weird

[light quarry]

It seems to be degrees so you would get $z = 5\sqrt{2}(cos(225)+i*sin(225))$

[warm shale]

Goran

[glacial robin]

Yeah but why do i have to put those numbers in that order

I know the solution but i dont get why thats a solution

[light quarry]

I am not sure what you're asking about

The formulas we used to derive the solution?

[glacial robin]

Yes

Why do those work

[light quarry]

If you draw out a complex number like this

[glacial robin]

Sorry, i get taught in a different language then i answer questions in so it all confuses me

[light quarry]

r or the magnitude or |z| we get from pythagorean theorem

And the angle theta by the fact that it's a right triangle and that's just the definition of tan

[glacial robin]

Alright, thanks

Have a good day

.close

[obtuse pebble]

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[violet stream]

I have to use integration by parts

this is my work so far

[tardy epoch]

!ss

[obtuse pebble]

Please post images (such as PNGs or JPGs) of the question rather than other filetypes such as PDFs which have to be downloaded. Non-image downloads can potentially contain viruses or other security risks.

[violet stream]

I figured it out

.close

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[dapper patrol]

i need help i cant solve this math question…

[dapper patrol]

<@&286206848099549185>

[cold yacht]

what part are you struggling with?

[dapper patrol]

im confused on how to draw the function graphs my teacher wasn’t good at explaining this lesson

[cold yacht]

do you know what type of function a would create? parabola, linear, etcc

[dapper patrol]

a quadratic

[cold yacht]

yes !!

[fallen igloo]

a quadratic function is the same as a parabola

[cold yacht]

since 5x^2 is a quadratic equation, it will graph a parabola. what does the coefficient x^2 tell you about how the parabola will be shaped?

will it be upwards or downards?

[dapper patrol]

it would have a minimum

so downwards

[cold yacht]

close - a minimum would mean a U shape, so upwards

[fallen igloo]

If the x² of the equation is positive, the parabola would be upwards

[cold yacht]

can you identify where the vertex/atix of symmetry would be?

[dapper patrol]

would it be at 2,0?

[cold yacht]

the vertex?

[dapper patrol]

wait wouldn’t it start at 0?

[cold yacht]

or the axis of symmetry

[dapper patrol]

the vertex

[cold yacht]

in the formula, ax^2 + bx + c, bx denotes where the vertex would be

snce there is no x term or constant in our equation (its just 2x^2!), it would start at (0,0)

[dapper patrol]

because the answer for 4a) is this and im confused

[cold yacht]

see how the minimum point is at (0,0)?

[dapper patrol]

yeah

how would i determine where they are drawn on the graph?

[cold yacht]

where the vertex is drawn, or the lines pointing up to infinity?

[dapper patrol]

lines on the graph

[cold yacht]

for the second part, you can start plugging in points into your equation

its easy to start with x=-2, x=-1, x=0, x=1, x=2

once youve found the correct x value, you can plug it back into your function to find the corresponding y

can you try for -2 first?

[dapper patrol]

would it be 1?

[cold yacht]

so 2(-2)^2 = 20

[dapper patrol]

ohhh

[cold yacht]

so the point would be (x,y) = (-2, 20)

does that make sense ?

[dapper patrol]

but on the graph both equations start at 0 and dont go up as high as 20

[cold yacht]

well, they do, you just cant see it because the graph has been constrained to show only up to y= 10

in reality, those lines would go up forever

thats what the -> arrow shows at the end, that it continues on to infinity

[dapper patrol]

ohh so the graph is just showing a representation of what it would look like instead of including all the exact points

[cold yacht]

oh wait im looking at the wrong equation btw

urs is 2x^2 not 5x^2

so it would be 2(-2)^2

which is 8

and u can see on the graph it does intersect at y = -2, x = 8

sry for the confusion im in an 8am class 😢

[dapper patrol]

ohh its ojay😞

[cold yacht]

try with -1

[dapper patrol]

wait i have a question first

[cold yacht]

if the graph is correct, itll intersect at y =1

2*

i cannot read

[dapper patrol]

the substitution is always used to get the points of a function right?

[cold yacht]

yes, to get the y value

since you are plugging in random x values

[dapper patrol]

ohh okay , so even if it wont reach the point i can just draw the arrows

[cold yacht]

yeah, thats why its a good idea to kind of play around with the substition, and also just be reasonable

you could find x = 100

but its not going to really be easy to show the scale of the graph that way

thats why -2 to 2 mightbe easiest, like theyve shown

[dapper patrol]

ohh okay

yeah my teacher said to use these for the functions (i’ll send it in a second

[cold yacht]

yep, you can see how your teacher has chosen a x value, and then plugged into the formula right?

to get y?

[dapper patrol]

i just wasn’t sure how to completely use them

yeah

[cold yacht]

wdym? what each function graphs like?

[dapper patrol]

yeah because he didn’t specify well on how to plot the graphs

[cold yacht]

well, from the values, you can kind of see how it would look just by kind of playing connect the dots

you can put the values found on a graph, for instance for sqrt(x)

(0, 0) (1,1) (4,2) (9,3)

and kind of see what its going to draw

[dapper patrol]

ohhh okayok

[cold yacht]

also, it may be more fun to use a graphing software such as desmos

to just plug in thos ebasic equations on the board,

and play with changing it

like what happens if you change x^2 to 5x^2? what about -5x^2?

same with the others

[dapper patrol]

oooo yes

thank you so much this was very helpful im so thankful😭😭🙏🙏🙏

[cold yacht]

nws i hope its a bit clearer for u now

[dapper patrol]

i have my test tomorrow so i have to review most of the styff im confused about

yes it did thank youu!!

[obtuse pebble]

@dapper patrol Has your question been resolved?

[obtuse pebble]

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[spare prairie]

Not sure what to do now that I solved for X?

[spare prairie]

Find the points of inner section

[sturdy arch]

Can you take a full pictures

[obtuse pebble]

@spare prairie Has your question been resolved?

[obtuse pebble]

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[frigid oyster]

Intro to diff eq

Looking to solve y' + 2yx = e^{-y^2}

I've thought about using a substitution of v = y^2 which would yield the v' = 2yy' but i don't think it is quite right because of that other y'. Thoughts?

[obtuse pebble]

@frigid oyster Has your question been resolved?

[frigid oyster]

<@&286206848099549185>

[wary badger]

are you sure you copied the question correctly

[frigid oyster]

i think its like, an impossible human solve

but maybe im just delusional

[wary badger]

that says dx/dy sir

[frigid oyster]

bruh

thanks i got it from here then 💀

[wary badger]

if it was dy/dx then yes it would be impossible

as far as i know

[frigid oyster]

ok that is why i was going crazy lol

yeah i didnt see a way to solve it

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[boreal palm]

can someone explain what i did wrong here bc idk why the answer key got y/2sqrtxy

and i got just y

[restive gorge]

can you explain the 2nd line

[boreal palm]

oops i js figured it out

i forgot parentheses and so forgot to do a step

but can u explain where to start with a diff problem

[restive gorge]

sure

[boreal palm]

idk what im doing

[restive gorge]

what do you wanna do

implicit differentiation?

[boreal palm]

find dy/dx

yeah

[restive gorge]

ok

you apply 1st line d/dx ( ) on both sides

[heady turtle]

What's the website in pic2 may i ask

Looks good

[boreal palm]

quizlet

[warm shale]

bacc

bacc

[restive gorge]

Let's start with sine

[boreal palm]

cosx + -2sin2dy/dx = 0?

[restive gorge]

ok you boss

yea

[warm shale]

bacc

[restive gorge]

now solve for y'

[boreal palm]

oh

[warm shale]

bacc

[restive gorge]

last step?

[boreal palm]

just isolate the dy/dx and divide cosx/4sin2y?

wait

[restive gorge]

yea

that's it

[boreal palm]

why is it sin2y and not sin2dy/dx?

[warm shale]

bacc

[restive gorge]

You must not change the argument

It's like doing

f'(g(x)) = f'(g'(x))

this is wrong

[boreal palm]

ohhh

[restive gorge]

Chain rule was

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

[boreal palm]

i gotchu

[restive gorge]

thanks

[boreal palm]

thank you sm!

.close

[obtuse pebble]

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[normal inlet]

!help

[obtuse pebble]

To ask for mathematics help on this server, please open your own help channel or help thread. See #❓how-to-get-help for instructions.

[normal inlet]

I don’t understand the jump from sinx+ to sinx()

[raw egret]

factor out sinx

look that, 1+cot^2x is a trig identity

[normal inlet]

so i divided everything by sin x

[raw egret]

it's like this problem:

4x + 7xh + 9xc

factor out the x in this problem

x(4 + 7h + 9c)

bc

x * 4 + 7h * c + 9c * x = 4x + 7xh + 9xc

and yeah, $\frac{sinx}{sinx} = 1$

[warm shale]

tank_driver011

[normal inlet]

i think i get it because the sin infront of the cot turns into 1 making it just cot

[raw egret]

exactly bc sinx(1 + cot^x) is the same as the original which is sinx + sinxcot^x

when you're ever in doubt, just multiply it out

[normal inlet]

how is the cot untouched from the factor out

[raw egret]

i don't understand.

[normal inlet]

when i divided the sin infront of the cot its 1 but do i not divide cot by sin as well

[raw egret]

think of it, like, taking the stuff out that repeats. the stuff that repeats, you can separate the equation to 'divide' it out

[normal inlet]

okay

[raw egret]

@normal inlet better?

[normal inlet]

yeah yeah

i get it now

[raw egret]

great

also, sinx = 1/cscx

that's how they got csc^2x/cscx

[normal inlet]

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[tropic mirage]

Can I have help solving this problem

I don't think it's solvable

[teal turret]

is everything except p1 a constant?

@tropic mirage

[tropic mirage]

there are n goods

idk if you know economics or langrange

[teal turret]

ok can u answer my question lol

[tropic mirage]

but the utility function was
(sqrt(x1)) + a2(sqrt x2) + ... + an(sqrt xn)

uh

pn are various prices

[teal turret]

but are all the variables shown above independent of p1?

[tropic mirage]

yes

[teal turret]

ok so what makes u think its unsolvable

wanna work thru it?

[tropic mirage]

because mathway says it's so

the equation looks horrendous

[teal turret]

its not that bad

[tropic mirage]

I might've came to the wrong conclusion

[teal turret]

do u wanna do it?

[tropic mirage]

yes

[teal turret]

ok so just do what i tell u

first, in that big clump of parentheses on the left

just distribute everything

lmk what u get

[tropic mirage]

p1pn^2 + p1^2pn a^2

times u^2

[teal turret]

good

and distributing in the u^2 we get?

[tropic mirage]

u^2 times both pluses

[teal turret]

ok, let me write in latex

$p_1 \cdot u^2 p_n ^2 + p_1 ^2 \cdot p_n a^2 u^2$

[teal turret]

do u agree?

[tropic mirage]

yup

and divided by pn^2 + a(subscript n) m p1^2 a^2

[teal turret]

ok before we move on to the second group

im gonna make life a little easier

$x = u^2 p_n ^2 \newline y = p_n a^2 u^2 \newline z = p_n ^2 \newline t = a_n ma^2$

so we get

[teal turret]

yes?

[tropic mirage]

one second

let me process

yes

[teal turret]

ok, now moving onto the second group, let me make a few more constants

[tropic mirage]

so xp1 + yp1^2 / z+t?

oh

t*p1^2

[teal turret]

$\frac {xp_1 + yp_1 ^2}{z + tp_1 ^2}$

[teal turret]

agree?

[tropic mirage]

yes

[teal turret]

ok so now heres ur choice

quotient rule or product rule

[tropic mirage]

quotient? becuase it's a fraction

[teal turret]

we could use product, but since u chose quotient, we'll do that

[tropic mirage]

x+yp1^2 - xp1+2yp1 / (z+tp1^2)^2?

[teal turret]

no

do u remember the formula for quotient rule

[tropic mirage]

f'g - fg' / g(x)^2

oh

[teal turret]

the top is f and the bottom is g?

yes ok

[tropic mirage]

(x+2yp1) (g) - (f) 2p1t / (g)^2

[teal turret]

x+2y is incorrect

there u go

[tropic mirage]

is that it

[teal turret]

u have a + in the middle

[tropic mirage]

oh

[teal turret]

also, its not 2p1

good

correct now

now let me put that in latex

[tropic mirage]

Can you stay with me for a second? I need to do Pn but I think I can simplify constants and figure it out

[teal turret]

$\frac {(p_n ^2 + a_n ma^2 p_1 ^2)( u^2 p_n ^2 +2 p_n a^2 u^2 p_1) - ( u^2 p_n ^2 p_1 + p_n a^2 u^2 p_1 ^2)(2a_n ma^2 p_1)}{(p_n ^2 + a_n ma^2 p_1 ^2)^2}$

do you agree with this?

[tropic mirage]

1 second

yes

i think I can do pn

one second

[teal turret]

theres ur derivative

[tropic mirage]

Pn^2 x + Pn y / Pn^2 + z

I didn't expand it

thank you though

[teal turret]

well u cant exactly use x,y,z because they include p_n in them

u have to create new constants

[tropic mirage]

(2Pnx + y)*g - f (2Pn) / g^2

i did that\

x= u^2 P1, y= P1^2a^2u^2, z=anmp1^2a^2

so it becomes

Pn^2(x) + Pn(y) / Pn^2 + z

[teal turret]

i dont rlly feel like checking that lol, but if u feel u got the idea, then thats good

[tropic mirage]

well this has been fun

the equation looked impossible

[teal turret]

if its just a ton of constants, its not a big deal

just make new ones that are made up of the old ones

what exactly are u doing with this

ik u mentioned econ

[tropic mirage]

oh

again idk if you know constrained optimization

we have a utility function subject to a constraint

find the marshillian demand

plug back into utility function to get indirect utility

set that equal to u, solve for m, which gives expenditure function

divide by p1 and pn to get hicksian demands

which is what I just did

(2Pn(x) + y) (Pn^2 +z) - (Pn^2*x + Pny) (2Pn) / g^2

[obtuse pebble]

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[heady turtle]

A plane figure of infinite area rotated around an axis always produces a solid of revolution of infinite volume?

I'm not even sure if I understand this statement, can anyone give me an example

[worn yoke]

consider the region between the $x$ axis and some function $y = f(x)$, $x \ge a$. then we could find the area using an improper integral [ \int_a^\infty f(x) \odif x ] the area may be infinite if the integral diverges. but we can also rotate it about the $x$ axis, which using the disk method would produce a solid of volume [ \pi \int_a^\infty [f(x)]^2 \odif x ]
the volume may be infinite if this integral diverges

[warm shale]

cloud

[heady turtle]

Should depends on whether it's diverging or not?

[worn yoke]

well the area is infinite if the first integral diverges, and the volume is infinite if the second integral diverges. the question is, does the first integral diverging necessarily mean the second integral diverges?

[heady turtle]

So the statement is correct?

[worn yoke]

is it? does the improper integral of f(x) being divergent imply that the improper integral of [f(x)]^2 is divergent?

[heady turtle]

No

[worn yoke]

that function is not riemann integrable

neither of those would converge

[heady turtle]

Ooh right

Lemme rethink

Umm how can I come up with such a counterexample

[worn yoke]

do you know any families of functions whose improper integral convergence depends on the power?

[heady turtle]

Wait no

[worn yoke]

you were on the right track there

[heady turtle]

Ok yes 1/x^p

P>1 & P<=1

So 1/x &1/x²

Does this example work? @worn yoke

[worn yoke]

both of those diverge

[heady turtle]

Edited edited

Not familiar with series knowledges😭

[worn yoke]

we want one of them to be the square of the other

[heady turtle]

I think this works now

Thank you

.close

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[spring fossil]

.close

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[next widget]

Is b right?

[obtuse pebble]

@next widget Has your question been resolved?

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[timid silo]

No

[timid silo]

It is 2(usintheta/g)

[next widget]

Why 2

[obtuse pebble]

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[cold brook]

is there a trig identity for A cos(b) + B cos(a)?

[kind hawk]

I think there was some sort of trick if you divide it by A^2+B^2. but I dont quite remember it

the idea being that the new coefficients x,y then satisfy x^2+y^2=1 and then other trig shenanigans

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[spring fossil]

Hello

I have no idea how to complete this. Thank you

[ruby path]

divide the top and bottom by t

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.close

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[proven narwhal]

Good night from southeast asia, i need some tips, today i feel bad when i already put my effort to learn matrix gauss, gauss jordan and cremer method for linear equation, i understand the stuff about determinant and adjacent Transpose but the thing is the teacher give me the question with big and fractional number without calculator for limited time it's just too hard, so i wanna know is this normal i struggle with this? Even though i really understand the theory of it? How can i improve this?

[obtuse pebble]

@proven narwhal Has your question been resolved?

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@proven narwhal Has your question been resolved?

[gentle steeple]

hii, do you have any examples of a problem that has you stuck so that i can see what kind of questions confuse u?

[obtuse pebble]

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[heady turtle]

how can I turn it into a triangle matrix....I'm so hopelessly silly, cant find a way out

[wary badger]

upper? lower?

[heady turtle]

upper

[kind hawk]

did A already include the t?

otherwise you arent supposed to have t in the off diagonal

is this still for computing the determinant?

[heady turtle]

yes

[kind hawk]

then dont do it

use block matrices

[heady turtle]

They said

10 SECS

I TOOK 10 HOURS

I'm indeed hopelessly silly I might just turn into a potato

[kind hawk]

no clue who they are and what they meant. but block matrices are way easier here imo

[wary badger]

wouldn’t the trick be LU decomposition

[kind hawk]

LU is ref but more fancy

[timid silo]

u can and every column to the first one and u get 1-t or 0 in all the forst column

and u factorise

[heady turtle]

The original matrix I need to ref is this one:

[heady turtle]

I'm not even sure did I do correctly here( R1-R2 and R5-R6

[heady turtle]

goddamn you're my superhero😭 Why am I soooooo stupid

[timid silo]

nono just do R1<-R1+R2
R1<-R1+R3 etc

[kind hawk]

its not like that magically solves it

[timid silo]

hmm it does tho

[kind hawk]

also should probably write C's if you want columns and not rows

[timid silo]

idk im not english

[heady turtle]

what are you 😭

wait It doesn't work😇

[heady turtle]

you're right

[kind hawk]

thanks. are you now gonna try block matrices?

[heady turtle]

Am I partition correctly? @kind hawk

seems wrong

[kind hawk]

its not wrong, just not helpful

you want to partition it in a way such that at least one of the blocks is just zero

and the two blocks on the diagonal are square

[kind hawk]

yes

and then you can partition the smaller blocks again

[heady turtle]

darn now it seems much simpler

[kind hawk]

yes

[heady turtle]

[
det = \left[ (-t\left(\frac{6}{7} - t\right) - \frac{6}{49})(\frac{1}{7}-t) \right] \left[ -t\left(\frac{6}{7} - t\right) - \frac{6}{49} \right] (1 - t)] = 0
]

@kind hawk Am i doing right

[kind hawk]

yes

dont multiply out everything

[heady turtle]

[ -t\left(\frac{6}{7} - t\right) = -t \cdot \frac{6}{7} + t^2 = -\frac{6t}{7} + t^2 ]
[-\frac{6t}{7} + t^2 - \frac{6}{49} ]

[warm shale]

ive

[heady turtle]

Darm this root doesn't looks good

Might including some irrational stuff

@kind hawk This ugly root is also included, right

Except x=1, 1/7

It has 3 roots in total

[kind hawk]

yes

well, two extra roots

[heady turtle]

Extra roots?

Anyway thanks

[timid silo]

a or a-ti?

[kind hawk]

its a quadratic

[heady turtle]

.close

[obtuse pebble]

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[kind hawk]

two roots

[heady turtle]

Ooh yes but for minimal poly it's only 3 i guess?

[kind hawk]

.reopen

[obtuse pebble]

✅

[kind hawk]

its 4 roots and two of those are double roots

you dont know what the min poly is yet

but it also has the 4 roots, the multiplicity might be different

[timid silo]

do you need a or a-ti as a triangular matrix?

[heady turtle]

I think I get your meaning

Thanks

[timid silo]

but its equated to a-ti

[heady turtle]

.close

[obtuse pebble]

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[heady turtle]

Yes what you think is correct😂

[timid silo]

if its a- ti then the question is short if you want triangular matrix of a

[timid silo]

can i use this channel now?

[heady turtle]

Hmmm i guess no

You should open another channel

Otherwise I can't open new channel myself