help-17

[upper iron]

Therefore, we have only one equation, and with 3 variables

So, infinity of solutions!

[tall patio]

it wasnt just about solving this

they wanted a basis

of the kernel

[mellow rapids]

Damn I could have just chosen a number all along xD that's why I was lost

[tall patio]

yeah

i'm sorry

since we know the dimension

if you find 2 vectors

thats good

no need for more

[mellow rapids]

do these work?

[tall patio]

they do

they are clearly not linearly dependant

and they're part of the kernel

so jobs done

[mellow rapids]

thanks a lot

[tall patio]

(because you know the dimension)

[mellow rapids]

would the basis of the image be (3, -3, -4)?

[tall patio]

since the image is of dimension 1

any vector part of the image is a basis

but (3,-3,4) cant be part of it

look at what the vectors look like

after matrix multiplication

the outputs are in R^2

[mellow rapids]

so i need to find a basis for the columns? like (1,0)?

[mellow rapids]

oh, it should be on the original matrix right

(1, -3)

[tall patio]

yeah

for example

because thats the image of (1/3,0,0)

[mellow rapids]

what if the dimension were not 1?

[tall patio]

you would need more vectors

[mellow rapids]

the dimension of the image is equal to the rank, right?

[tall patio]

the rank is the dimension of the image

by definition

its the name we give it

[mellow rapids]

what do i need to do to find the coimage and the cokernel?

the cokernel is perpendicular to the image, correct?

[tall patio]

they are the image and kernel of the transpose right?

[mellow rapids]

oh i see

in this case, would (3, -3, -4) be a basis of the coimage?

[tall patio]

im pretty sure the coimage is of dimension 2

oh no

maybe not

[mellow rapids]

how do i find this?

[tall patio]

same as we did but for the transpose (im pretty sure there are rank nullity theorems analogues for cokernels and coimage but im not sure)

[mellow rapids]

the echelon form of the transposed matrix is this, so the rank is 1
because we have two columns, the nullity would be 1

[tall patio]

transposed matrix should be 3 rows

[mellow rapids]

for some reason i forgot to include a row while doing the echelon form lmao

but the rank and nulity are still both 1, right?

[tall patio]

they are i think

[mellow rapids]

this seems to work

[tall patio]

im pretty sure its 3,1

for the cokernel

[mellow rapids]

why?

[tall patio]

well because if you do the multiplication it works

and also

because this

y1 is 3 times bigger than y2

[mellow rapids]

oh i'm dumb

lmao

thanks

[tall patio]

for coimage

its the image of which vector,

?

[mellow rapids]

well i just chose the first one

[tall patio]

no that doesnt work with echelon form (im sure)

just take a column of the original matrix

[mellow rapids]

i did the same mistake twice xd

[vocal sleet]

@mellow rapids Has your question been resolved?

[mellow rapids]

what's the relation between the dimension of the image and the coimage? in this case they are equal, but is there a specific rule? as far as I know, the dimension of the coimage is equal to the dimension of the kernel, but idk if there's any rule regarding image and coimage

[tall patio]

just use rank nullity theorem for the transpose

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[balmy furnace]

This is d, correct? It has a negative slope from x <8 and x>8 but a zero slope exactly at 8.

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[verbal sluice]

Would somone be able to help me

[verbal sluice]

How did they get ∑ i to (n^2/2 + n/2)?

by the way i isn't imaginary

it's just a non constant

[flat whale]

https://i.ytimg.com/vi/XJkIaw2e1Pw/maxresdefault.jpg

top right

[verbal sluice]

oh okay thanks

ive been trying to get the riemann numbers for this forever

and it wont work

ive done it for the first question and it worked fine

for Un

@flat whale

I've used wolfram alpha

It gives a different asnwer

but even that is wrong

is dx 1/n?

the integral is from 0 to 1

[flat whale]

,w int 0 to 1 of 3+3x^2

[twin meteor]

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Requested by riemann#2529

[verbal sluice]

I'm not trying to calculate the integral

[verbal sluice]

I'm trying to find the upper and lower riemann sums

[flat whale]

why is this your subinterval. it doesn't even include any number between 0 and 1

[verbal sluice]

I'm trying to find a general solution

[verbal sluice]

that should be subinterval i

[flat whale]

general solution to what?

[verbal sluice]

the upper and lower riemann sums

you know

[flat whale]

i get that

[verbal sluice]

dx ∑ M

[flat whale]

but you still need to be integrating on the correct interval [0, 1]

and not some random interval of your choosing

[verbal sluice]

so what do i do

o wait

it should be 0 +

shouldnt it

[flat whale]

correct your interval to include [0, 1]

[verbal sluice]

0 + (i-1)dx

[flat whale]

yes. but you're doing 1 + (i-1) dx

[verbal sluice]

yeah okay

thank you

[verbal sluice]

how would you go about solving it for a heaviside function?

[flat whale]

what is the full question

[verbal sluice]

Same thing

just different function

that function being a heaviside

[flat whale]

what do you mean "same thing"

i can't read your mind

[verbal sluice]

∫H(x+3) {0≤x≤2}

find U_n and L_n

like general solutions to them

[flat whale]

where's your work for the previous problem

just use that and replace f(x) with H(x+3)

[verbal sluice]

not working sadly

wait

hold on

lets say

∫H(x-5) {0≤x≤5}

and you had to find U_n and L_n right

L_n would be 0 obviously right

but what about U_n

would that be 0

or like infinitesimally small

[flat whale]

.

either show that

[flat whale]

or show why it's not working

[verbal sluice]

ignore that

I dont care about that

could you answer that one

[verbal sluice]

this one

[flat whale]

same answer

[verbal sluice]

how?

[flat whale]

.

[flat whale]

.

[verbal sluice]

the function only begins at x = 5

[verbal sluice]

I read the question wrong

could you please answer this?

[flat whale]

then try again.

show your attempt on the correct problem

[verbal sluice]

this is the correct problem

[verbal sluice]

this one right here

you cant work it out right?

because the function doesnt exist till x = 5

which is the end of the interval

[flat whale]

the heaviside function is defined for the entire real line

[verbal sluice]

but it's just 0 till 5 right?

[flat whale]

yes

[verbal sluice]

so how would you even do that

surely it's just 0

[flat whale]

probably have to show that both upper and lower are 0

[verbal sluice]

but 0 isn't the answer for the U_n

it is for L_n

[flat whale]

okay?

you have the answer so just follow it?

[verbal sluice]

no i dont have the answer

but it lets you see if your answer is correct

[flat whale]

show what you mean

[verbal sluice]

It's an online quiz thing

so if I write an answer

[flat whale]

probably shouldn't be cheating on quizzes

[verbal sluice]

and can press a button to see if its correct

[verbal sluice]

we have weeks to do them and we are meant to find resources online and stuff to find out how to do it

because we dont get taught it

its like an initiative thing

ive finished the whole thing

im just struggling on this one thing

[flat whale]

so why can't you show what you mean then

just screenshot is fine

[flat whale]

show the question verbatim

and your answer for upper sum

[verbal sluice]

bra please

[verbal sluice]

because thats cheating

idk if youre trolling me or not

I'm just tryna get a guide on how to approach it

not show my actual questions

[flat whale]

lol you are cheating

[flat whale]

typing this doesn't make it any less cheating

<@&268886789983436800>

[verbal sluice]

fine bra

idk why you hate me so much

i'll just leave

[flat whale]

.close

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[tulip nebula]

,rotate

[obsidian root]

Is this right?

Someone?

[twin meteor]

The following error occured while calculating:
Error: Parenthesis ) expected (char 64)

The following error occured while calculating:
Error: Parenthesis ) expected (char 64)

[viral copper]

,calc (2^(-2^(1000000000+1))+ 2^(-2^(1000000000-1)))^(2^(-1000000000))

[twin meteor]

Result:

1

[viral copper]

Well clearly not

[obsidian root]

Thanx

.close

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[viral copper]

I think you need to use the natural logarithm to solve it btw

0^0

[modern ledge]

they gone xd

[obsidian root]

No I'm here

[vast shale]

75

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[misty dragon]

hello

[misty dragon]

i am stuck on this question, where i need to collect all the stars by constructing some lines

however i am stuck on the last line

ik how to make it start at x=6 but idk how to end it at x=10

[river minnow]

6 < x < 10

[misty dragon]

ah i see

[river minnow]

Inside the {}

[misty dragon]

ty

[misty dragon]

yup

.close

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[vast shale]

hey

[vast shale]

trying to improve my understanding of the chain rule

want to differentiate 2^x

but i don't know how to

my first step was to find the "outer function"

which I thought was alrady 2^x

and the inner function was x

if you differneitate x you get 1

so the derivative would be 2^x * 1

which it isn't

[outer warren]

because you didn't differentiate the outer function

[sudden compass]

uhm u dont use chain rule for this..? cant u do limit definition?

[outer warren]

consider that 2 = e^ln(2)

[vast shale]

ah ok

so 2^X = e^ln(2)^x

[floral seal]

for me i just take log for both sides

[vast shale]

Can you show me how exactly that would be done

[vast shale]

thank you. can you explain the third step

I see you're differentiating in terms of x, so x becomes 1

[floral seal]

Yes

[vast shale]

I'm guessing the 1/y comes from differentiating lny

[floral seal]

yes

[vast shale]

but I don't understand why you differentiate that

I thought in dy/dx, you differentiate the x terms

[floral seal]

i just derive both sides

[vast shale]

right but why is that

[floral seal]

what do you mean why

[vast shale]

if it's dy/dx, don't you differentiate the x terms, I don't see why you differentiate the y terms

like for example if y = x and then you differentiate, from my understanding you differentiate the x, not the y

[floral seal]

its chain rule

[vast shale]

or wait hold is dy/dx for y just equal to dy/dx

[floral seal]

yes

[vast shale]

ah okay gotcha

thank you

[floral seal]

no problem

[vast shale]

enjoy your day

.close

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[tender sand]

yo can anyone help

[river minnow]

Considered using the law of sines?

[tender sand]

yes

[river minnow]

What did you get?

[tender sand]

7.041

[river minnow]

,w 8 * sin(62)/sin(51)

[twin meteor]

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[tender sand]

alright thanks

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[dreamy dagger]

solve inequality

[dreamy dagger]

the red is what I'm supposed to get and so far my first part isn't close

[gentle totem]

first multiply both sides by -3 and switch the inequality operators

[dreamy dagger]

the whole line or bit by bit so splitting it into two - 4<-x+2/3 and the other one?

[split bloom]

r u sure u copied the correct answer, isnt this question v) and the red is for iv?

[dreamy dagger]

ah that's the problem

[split bloom]

u can split it into two and combine if thats easier for you

[dreamy dagger]

i just looked at the answers wrong

.close

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[pliant eagle]

Assuming we have a fair sided coin and the probability of getting heads is P(heads) = 0.5, what is the standard deviation?

[split bloom]

u mean fair sided coin?

[vocal sleet]

@pliant eagle Has your question been resolved?

[pliant eagle]

Mb yeah

[vocal sleet]

@pliant eagle Has your question been resolved?

[vocal sleet]

@pliant eagle Has your question been resolved?

[vocal sleet]

@pliant eagle Has your question been resolved?

[pliant eagle]

Nvm wrong question

.close

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[sage stump]

"An item is manufactured by three machines A, B and C. Out of the total number of items manufactured
during a specified period, 50% are manufactured on A, 30% on B and 20% on C. 2% of the items produced
on A and 2% of items produced on B are defective, and 3% of these produced on C are defective."

I would say 2% is P(D & A) a buddy says P(D|A) is what is meant here. How can I differentiate that from the wording? (D means defective)

[paper depot]

P(D&A) is the percentage of the entire production that is both defective and made by A

[wraith venture]

2% of items produced by A are defective
i.e. if an item is produced by A, it has a 2% chance of being defective
So P(D|A) = 2%

[sage stump]

how i understand it, this it what is written in the statement.

[paper depot]

no

"2% of the items produced on A are defective"

not "2% of all items are defects produced on A"

[sage stump]

okay, well thank you

[vocal sleet]

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[violet fox]

hi

[violet fox]

what is wrong with this?

I want to check if f(x) is diffren. at x = 1

(btw I forgot to write down prime in the second line)

<@&286206848099549185>

[flat whale]

,w diff sin^2(pi x) * sin(pi * x)

[twin meteor]

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[flat whale]

Simplify first

[violet fox]

what do you mean?

[flat whale]

z = sin(pi x). You have z^2 * z

[violet fox]

no no

its z^2 * bracket of z

[flat whale]

What does bracket of z mean

sin^2 already has an argument

pi x

[violet fox]

I don't get it

why did you remove the bracket?

[flat whale]

That's just how this notation is interpreted

If you meant something else, use more brackets and parentheses

[violet fox]

is this function differen at x = 1

[flat whale]

Yes

[flat whale]

The derivative is here

[violet fox]

but this is the graph

[flat whale]

You graphed some other function

[flat whale]

.

Or just screenshot the function and save us all some time

[violet fox]

here is the funtion

I solved it a million times but I dont get it

and I still do not know with did you remove the bracket
bracket of sin(pi x) is different at x=1+ and x=1-

[flat whale]

The definition, not the graph

You're plotting something different from what you've differentiated

[flat whale]

...

[flat whale]

You should have said brackets meant floor

[violet fox]

Sorry I thought you know what I mean

[flat whale]

There is no floor here

[violet fox]

yeah and I asked how did you remove the bracket

mb mb

[flat whale]

Just compute the left hand right hand limits of f' at x=1

[violet fox]

can I rewrite it as some sort of piecewise function and then compute f'+(x) and f'-(x)?

[flat whale]

Yes

[violet fox]

so what is wrong with this?

[violet fox]

f'+(1) is also zero but according to this It should be something else

cuz its undefined

[flat whale]

Your derivative doesn't take floor into account

[violet fox]

bracket or sin(pi x) x approaches 1 from right, is -1
so if I in the piecewise function I wrote it as -sin^2(pi x)

[flat whale]

,w plot floor(sin(pi x))

[twin meteor]

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[violet fox]

so its correct?

[flat whale]

On 0<x<1, the function is 0. Did you get that somewhere

And 1<x<2, f(x) is not zero.

[violet fox]

yes
and also f'-(1)=0

[violet fox]

yes f(x) = -sin^2(pi x)

[flat whale]

,w plot -sin^2(pi x)

[twin meteor]

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[flat whale]

,w diff floor(sin(pi x))

[twin meteor]

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[flat whale]

,w diff -sin^2(pi x)

[twin meteor]

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[flat whale]

,w -2 pi sin(pi)cos(pi)

[twin meteor]

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[violet fox]

Everything is correct
I am just worried about the piecewise function

[flat whale]

Looks fine

[vocal sleet]

@violet fox Has your question been resolved?

[violet fox]

I thought a lot but I could spot the mistake. Rn, I gtg
Thanks for you help

[vocal sleet]

@violet fox Has your question been resolved?

[vocal sleet]

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[vast shale]

.close

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[vocal sleet]

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[amber blaze]

Hey I need help solving this

[soft walrus]

First solve $\int_{\sqrt{y}}^{4}\frac{x^2}{1+y\sqrt{x}}\mathrm{d}x$

[twin meteor]

XxMrFancyu2xX

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@amber blaze Has your question been resolved?

[amber blaze]

No

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[pallid zenith]

what have you tried?

[wicked ice]

alright here's my work

[pallid zenith]

looks like you get an answer?

[wicked ice]

from what I saw my teacher doing I feel like I need something along the lines of a decimal

[pallid zenith]

i mean your answer involves a root so it should be a decimal?

is that the only reason youre doubting your answer?

[wicked ice]

yeah pretty much

[pallid zenith]

well your answer will be a decimal

[wicked ice]

i tried turning 22016 into a decimal and came out with 148.37789592793

[pallid zenith]

it looks like its sqrt(86)/2?

[wicked ice]

wym?

[pallid zenith]

you have two time answers

one of them is sqrt(86)/2

[wicked ice]

oh no those were the two answers apart I thought I would have to commbine them to get my answer

its in the top right

[pallid zenith]

? theyre roots of the polynomial right

[wicked ice]

yup

[pallid zenith]

hold on i gotta go to the bathroom, i wanna see what i get

[wicked ice]

oh never mind apperciate it i had found my answer

[pallid zenith]

oh

okay

[wicked ice]

.close

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[cunning saddle]

help

[cunning saddle]

why this?

[worthy citrus]

Why what?

[flat whale]

What part don't you understand

[vocal sleet]

@cunning saddle Has your question been resolved?

[cunning saddle]

converts to trigometric functions

x-1 = tanq why

[flat whale]

Standard trig sub you try

More practice I guess

1 + something ^2

something = trig function

[vocal sleet]

@cunning saddle Has your question been resolved?

[cunning saddle]

Excuse me, I'll ask later, thanks

.close

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[supple silo]

does this work?

[supple silo]

the question is to determine if the points make a right angle triangle

[vocal sleet]

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@supple silo Has your question been resolved?

[supple silo]

<@&286206848099549185>

[spiral inlet]

You've got the right idea, but it looks like you assumed sqrt(11) would be the hypotenuse

@supple silo

[supple silo]

oh my bad that was a dumb mistake

thanks

/close

.close

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[mild raven]

isnt the equation 60(1+r/24)^2*12= 5000 solve for r

[mild raven]

wits wrong w this work

seems perfect 2 me

[vocal sleet]

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[bitter ridge]

How do I start this?

[bitter ridge]

I started but doesnt = 0 for the proof

[vocal sleet]

@bitter ridge Has your question been resolved?

[eternal dune]

I dont think I explained it well before

lets start with this

can you see how this is true?

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.reopen

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[foggy mantle]

why do you integrate the sin and not the cos

why not k*sin^2cos rather than kcos^3

[vocal sleet]

@foggy mantle Has your question been resolved?

[strange oak]

Why not just Let u = cos(t) du = -sin(t)dt

Which makes it a nice ∫-60udu |(1,0) after doing u(0), u(π/2)
And canceling out the sin(x)

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[fluid obsidian]

-60u²

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[vapid marlin]

can anyone help me prove this?

[timber orchid]

What if you try drawing the line segment BD?

[north cobalt]

I think then it will be an equilateral triangle

I think

[vapid marlin]

yep

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[raven bough]

Join BD

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[steady moth]

Pre Calc 2 but I can't seem to conceptualize this

[steady moth]

I understand that 4 in front of cos is the amplitude, and -pi/2 is the phase shift but has no C

The equation im using is Y = Asin(B(X-D)) + C
And y = Acos(B(X-D)) + C

[left crest]

Express $\cos(x - \frac{\pi}{2})$ in terms of $\sin(x)$

[twin meteor]

Encrpyt

[left crest]

If needed use unit circle

[steady moth]

what?

[vocal sleet]

@steady moth Has your question been resolved?

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@steady moth Has your question been resolved?

[steady moth]

Without further explaination I have no clue what's going on

[vocal sleet]

@steady moth Has your question been resolved?

[steady moth]

.close

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[maiden trellis]

i had this question, and Im guessing the name of this is an ambiguous case.
For this case it told me that it was an ambiguos case, so i could solve it. however is it possible to tell if this is an ambiguous case without knowing? And if so how?

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[ionic relic]

.

[worn fulcrum]

just a small question about fields

[worn fulcrum]

is 1 needed in every field as the neutral?

so instead of the regular neutral element it has to be 1 in a field?

[blissful sentinel]

You need 0 and 1 in a field

weil es ein Ring ist, und jeder Ring hat 0 und 1

0 und 1 sind nur Namen

[worn fulcrum]

der kleinste Ring hat doch nur die 0?

[blissful sentinel]

ja, aber in ein Körper muss 0 ≠ 1; der kleinste Ring hat 0 und 1, aber 0=1

also just for future reference you're probably more likely to get algebra help in #groups-rings-fields

[worn fulcrum]

ahh ok

[blissful sentinel]

Oh some people say that rings don't need to have 1 and that rings with 1 are called unital rings

(unitärer Ring)

but this is a rather old definition, from my understanding

Most modern texts follow the convention that rings always have 1

So it depends on your lecturer/textbook

[worn fulcrum]

but yeah i am learning the definitions of them today

so fields instead of requiring the neutral element, require 1 specifically?

[blissful sentinel]

There are two neutral elements, one for addition and one for multiplication

The additive neutral element is 0

[worn fulcrum]

i mean (K2) in this definition

[blissful sentinel]

The multiplicative neutral element is 1

1 is just a name for the multiplicative neutral element

[worn fulcrum]

ahh ok 🤔

but is (K, . , +) even a field?

[blissful sentinel]

It depends on what K, ., and + are

For example (Z, ·, +) is not a field

But (Q, ·, +) is a field

[worn fulcrum]

oh

[worn fulcrum]

and in that case the neutral of + is 0

[blissful sentinel]

Yes! But the 0 of a ring doesn't always have to be literally the number 0, just the element that "plays the role of 0"

Meaning it is the neutral of +

[worn fulcrum]

The division is not even a group because it doesn't meet the condition of a neutral element?

[blissful sentinel]

There is a neutral element for multiplication in Z (namely, 1)

But not every nonzero element has a multiplicative inverse

[worn fulcrum]

I mean (R, /) is not a group right?

[blissful sentinel]

Ohh

Yes that's correct, for multiple reasons

1. because division by zero is not defined
2. division is not associative
3. there is no identity element

[worn fulcrum]

ahh ok makes sense 👍

[blissful sentinel]

Just to give an example of this, if X is a set, then the power set of X is a ring, with "addition" being the symmetric difference of two subsets of X and "multiplication" being the intersection of two subsets of X

then "0" is the empty set and "1" is X

[worn fulcrum]

still trying to fully grasp what rings are

are they all residual classes?

or are only some of them residual classes

[blissful sentinel]

That's okay! Intuitively you should think of something where you can add, subtract, and multiply

[blissful sentinel]

By this do you mean are all of them of the form Z/nZ? If so then no

For example (Z, +, ·) is a ring

[worn fulcrum]

yeah that was the example presented in the lecture

[blissful sentinel]

Ah okay

No, there are many other examples of rings

So some of the ones I just gave are
(Z, +, ·)
(Q, +, ·)
(R, +, ·),
(Z/nZ, +, ·)
(R[x], +, ·)
(P(X), symmetric difference, intersection)

[worn fulcrum]

Ah ok 🤔 i think they show this because it's relevant for computer science

[blissful sentinel]

Of those, only Q, R, and Z/pZ (where p is prime) are fields

[blissful sentinel]

Very important for both computer science and mathematics (especially number theory)!

[worn fulcrum]

good to know

[vocal sleet]

@worn fulcrum Has your question been resolved?

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[coarse python]

It's me again yes can anyone straight up tell me what's the answer I just need the answer and I'll make the solution.

[coarse python]

: Mr. Jones wanted to tile her square-shaped bathroom, so he hired a tile setter. The tile setter said that he would be laying 144 square feet of tiles. What is the length of one side of Mr. Jones’ bathroom?

[vocal sleet]

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

[coarse python]

I got an answer and would like my work to be checked

Is it 27 feet

[vocal sleet]

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

[coarse python]

Idk but my answer is 27 feet

Wait it's wrong

I added the wrong number

.close

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[hushed atlas]

dont get why part b is 7 marks

[hushed atlas]

i thought u can find the other point and work it out straight away but thats wrong

[karmic imp]

That just depends on how people want to assign point values

[hushed atlas]

yeah

[karmic imp]

Overall, not sure what you're really asking, if you're asking about the point system, talk to your teacher

[hushed atlas]

i dont get why my method is wrong

[vocal sleet]

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

[hushed atlas]

i just equate y to zero, solved for t and subbed into x

and got the other point as (3,0)

then height of triangle from the other point i took as 8

then 1/2bh

[hushed willow]

did

you use the initial

parametric

equation

because it quite literally asks you to use the tangent equation that is done in part a

[hushed atlas]

ohhhhhh

no i didnt thats why

thanks

.close

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[oblique panther]

I need help: I was reading through my solved algebra exercises and in one them I had to find the equation for a plane knowing that it's parallel to the plane 3x-y+2z=-4, both being equidistant to P(1, 2, 1)

[silent spire]

hmm

[oblique panther]

For some reason I found the distance between the known plane and the point by dividing the dot product of the plane's normal vector and the distance between a known point (0, 4, 0) by the normal vector's versor

[rugged vortex]

There's a couple ways

[silent spire]

what dont your start by assuming this potential

[fluid obsidian]

you know the similarities in equation of plane that are parallel

[silent spire]

"equation"

what dont you assume that

[oblique panther]

but I don't know why

or how it's correct

[oblique panther]

I tried projecting the point to the plane, calculating the distance between the projected point and the point itself, multiplying it by the normal versor then adding it to the initial point

[silent spire]

i believe you can solve it using this way

maybe just some went wrong

have you checked?

[oblique panther]

I'm checking but I cna't find where it went wrong

[silent spire]

hmmmmm

WELP then you can check the ans i think

to see the precise progress if you are sure that you know the method XD

[oblique panther]

found the error

let's try this again,,,

[silent spire]

https://tenor.com/view/stranger-things-smile-satisfied-happy-content-gif-10634374

[oblique panther]

I got the projection right this time

[oblique panther]

and it gave me that the distance between the planes is 7, which is what I got when I did this

so again I must ask

why does that work?

[rugged vortex]

Usually I just find the distance from the plane to the point using the normal vector

[oblique panther]

how?

[rugged vortex]

Create a line

I haven't done shit like this in a while but I know the process lol

But yeah

Parametrize the normal line

Plug it into the plane, solve for the parameter

You can find distance

[oblique panther]

alright, I solved it

thanks for the help

.close

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[vocal sleet]

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[placid kite]

How can I solve for X algebraically:
x*sqrt(16+(9-x)^2) = -(x-9)*sqrt(64+x^2)

[charred charm]

squaring both sides?

[placid kite]

How would that work? Wouldn’t that break the equality

[charred charm]

Then at last check which solution Satsfies the equation

[hushed pewter]

You may get an extra solution which won't actually work in your original equation, so just be sure to check your solutions when you get them

[white acorn]

$x\sqrt{16+(9-x)^2}=-(x-9)\sqrt{64+x^2}$

[twin meteor]

Kai The Doge

[white acorn]

This? ^

$x^2[16+(9-x)^2]=[-(x-9)]^2(64+x^2)$

If u square both sides ^

[hushed pewter]

$(-(x-9))^2$

[twin meteor]

SWR

[white acorn]

Oh yeah my bad

Forgor signs

[hushed pewter]

Looks good

[twin meteor]

Kai The Doge

[white acorn]

There

Then u get

[hushed pewter]

This solution may get messy

[white acorn]

Yeah lmao

[hushed pewter]

Where did you get this problem from

[white acorn]

I'm gonna expand (9-x)^2

(-x+9)^2

x^2-18x+81

[desert hornet]

ni

no

[white acorn]

My brain is a bit muddled today

$x^2[16+x^2-18x+81]=[-(x-9)]^2(64+x^2)$

[twin meteor]

Kai The Doge

[white acorn]

$x^2(x^2-18x+97)=(x^2-18x+81)(64+x^2)$

[twin meteor]

Kai The Doge

[white acorn]

(x^2-18x+97) has to be positive right?

So

[white acorn]

Wait this doesn't matter wtf am I doing

$x^2=(64+x^2)$

[twin meteor]

Kai The Doge

[white acorn]

This seems very wrong

[empty frigate]

wait how is $[-(x-9)]^2 = x^2-18x+97$?

[twin meteor]

bee

[white acorn]

( -x+9)^2

,ask x^2[16+x^2-18x+81]=[-(x-9)]^2(64+x^2)

Okay I suck

[twin meteor]

Results provided by WolframAlpha

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

Requested by Kai The Doge#8873

[white acorn]

Ur right it's 81, idk what I was doing

$x^2(x^2-18x+97)=(x^2-18x+81)(64+x^2)$

[twin meteor]

Kai The Doge

[white acorn]

$(x^4-18x^3+97^2)=(64x^2+x^4-18x^3-1152x+81x^2+5184)$

[twin meteor]

Kai The Doge

[white acorn]

$(97x^2)=(64x^2-1152x+81x^2+5184)$

[twin meteor]

Kai The Doge

[hushed pewter]

Oh yay it stayed quadratic

[white acorn]

This is taking forever

,ask (97x^2)=(64x^2-1152x+81x^2+5184)

[twin meteor]

Results provided by WolframAlpha

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

Requested by Kai The Doge#8873

[white acorn]

I'm on the right track

[vast shale]

isnt that middle term factor?

[white acorn]

$0=(48x^2-1152x+5184)$

[twin meteor]

Kai The Doge

[white acorn]

Factorise time

[vast shale]

nice

[white acorn]

Wait can I do this

[vast shale]

u can take 48 common

and it will be 0/48 = 0

[white acorn]

yeah what I was gonna do

[vast shale]

x^2-24x+108=0

[white acorn]

0=48(x^2-24x+108)

[vast shale]

ye ye

now we need two numbers which when multiplied gives us 108 and added gives us 24

[white acorn]

hey dude

Im not the guy who needs help

[vast shale]

oh lollll

[white acorn]

I'm the guy helping the guy

Lmao

[vast shale]

welp its pretty easy

6 and 18

so

x^2-(6+18)x+108=0

[white acorn]

0=48(x-6)(x-18)

Whee

[vast shale]

x^2-6x-18x+108=0

[white acorn]

x=6 or 18

[vast shale]

x(x-6)-18(x-6)

[white acorn]

I'm dead

[vast shale]

(x-18)(x-6)

[white acorn]

I'm not the best at typing this stuff

[vast shale]

x=18 or x=6

[white acorn]

It takes a while ngl

[vast shale]

ok

close the channel

[white acorn]

Not me

Dude

@placid kite hi u can look through

[vast shale]

bro asked and diasppeared lol

[white acorn]

Ikr

I'd close since he hasn't been here for the past very long time but I don't think I should do that

[vast shale]

let it be

[white acorn]

Trust me when I say I'm faster on paper

I just suck typing the stuff out

[vast shale]

yikes me too

its hard to type so much numbrs

[white acorn]

Ikr

It's maybe like a 3 min qn

[vocal sleet]

@placid kite Has your question been resolved?

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[full prairie]

A(-6,21) D(3,15) C(12,9)

[full prairie]

which method is used to find the incline of BD?

[river minnow]

There is not enough information

[jagged gorge]

not enough information

[river minnow]

Are you sure you have mentioned everything that is given?

[full prairie]

BD is parallel to OC

[jagged gorge]

okay

[river minnow]

Hm, wouldn't that be the same as the incline of OC then?

[jagged gorge]

9/12 = 3/4

[river minnow]

Right

[full prairie]

indeed

.close

[vocal sleet]

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@covert salmon Has your question been resolved?

[covert salmon]

<@&286206848099549185>

[random wave]

@covert salmon Is there any explanation on what the function f stands for ?

[covert salmon]

Not sure what u mean by that.

Mn is the midpoint riemann sum that they have defined

[random wave]

Well there is a function f used in the definition of M_n

Is it a general definition or a definition linked to a precise function f ?

[covert salmon]

General

[random wave]

Okay, so what would be your f function here ?

Adapted to that question

[covert salmon]

That isn't needed when finding Mn

[random wave]

Well show me what you did I guess

[covert salmon]

I havn't written anything as I am not sure what to do lol

[random wave]

So why do you tell me that then ?

How do you find M_n usually ?

[covert salmon]

Well I usually have to just use the right hand and left hand riemann sums

Now it's asking to use the midpoint riemann sum

which is Mn

[random wave]

If this M_n is shown as a general definition, then when you go on applying the definition to an example

You need to know what f is, otherwise you'll always find yourself with some f of something without ever being able to actually say what it is

So what would be your function f here ?

[covert salmon]

2x + x^2

[random wave]

Yeah I think so too

I'm basically asking you if you know how you would use that definition in order to find I

[covert salmon]

I would have to use a regular n partition here right?

[random wave]

Yes, but do you know how that would help you in any way ?

And most importantly, how would you use that partition for the calculation of this integral ?

https://youtu.be/kJ57S0Z4Vp8

There is this video of Khan Academy showing how Mn could be seen

It's when they talk about the mid-point part

In their case, they did a subdivision of the interval [-1,2], because they integrate on that interval.
On our side, the interval you are integrating at is [0,2].

[covert salmon]

yes

my deltaX will be 2/n

[random wave]

Why 2/n ?

DeltaX is a difference in x, based on your subdivision

You have a subdivision (x_i for i from 0 to n), let's say

[covert salmon]

Delta x is 2/n because we r using a regular n partition here.

[random wave]

Yeah simplifying our life

[random wave]

But if we consider that subdivision right here, starting at 0

Then n is the number of sub-intervals created from that subdivision

And your DeltaX is this distance from x_i to x_(i+1)

Since x_(i+1) > x_i, you get that the distance is DeltaX = x_(i+1) - x_i

Knowing that there is n subintervals, and that you want your total to be equal to 2 (the measure of the interval [0,2])

Then you want the sum of these measures to be 2

Supposing it's regular, it's 2/n

That's what I was looking for

The explanation

Sorry if I was not explicit enough

Now that this is cleared out

You want to evaluate your function between each of the sub-intervals [x_i,x_(i+1)]

More precisely, at the midpoints between them

Oh, well it has already been defined for us beforehand

The x_i bar symbol is associated to the x value, midpoint between x_i and x_(i+1)

Knowing that each subintervals have this size DeltaX = 2/n, as you told me

What value of x would be the midpoint of each subintervals, wrt i and n ?

@covert salmon

If you need vocal assistance, I can be there

Ow by the way, be careful, i goes from 1 to n here, so there is not n subintervals

So it's not 2/n

[covert salmon]

Are you in university?

[random wave]

I'm doing a master degree in teaching actually

[vocal sleet]

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[cyan bluff]

W1 is a matrix, W2 another matrix, b2, b1 and X are vectors, sigma is a function

...

<@&286206848099549185>

[flat whale]

!15m

[vocal sleet]

Please only use the <@&286206848099549185> ping once if your question has not been answered for 15 minutes. Please do not ping or DM individual users about your question.

[cyan bluff]

I am waiting for more than a week

in #optimization

[cyan bluff]

yes?

ok it's a screenshot

and?

[flat whale]

good for you?

that's not this help channel

[cyan bluff]

ok cool, but I still wait

[flat whale]

yes. and the rule is to wait 15m before pinging

[cyan bluff]

everyone ignored me. A guy even told me to write it down in LaTeX. he didn't even see what I wrote :

[cyan bluff]

I wait since 09/05/23

[flat whale]

so?

[cyan bluff]

it's more than 15 minutes

[flat whale]

#❓how-to-get-help read that again

[flat whale]

.

[cyan bluff]

ok, so where do I ask this please

[cyan bluff]

.

is it university level?

@flat whale Where should I put it to get the fastest answer please

In my opinion it's a chain rule with a pre-university level

[flat whale]

pay for a tutor

[cyan bluff]

ok thanks

.close

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[vocal sleet]

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[runic tusk]

are these right

[thin vale]

, rotate

[vocal sleet]

@runic tusk Has your question been resolved?

[vocal sleet]

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@zenith orchid Has your question been resolved?

[hushed pewter]

If x men work for x hours per day, how many total hours per day is that?

yup

And if x² hours are worked for x days, how many total hours is that?

Exactly

So it takes x³ hours to produce x items. So how many hours does it take to produce one item?

Precisely.

1/x² total hours per item

So, how many total hours for y men working y hours for y days?

yup

Finally, # items = (# total hours) / (total hours per item)

because the relationship between x and number of items produced is not linear

It's cubic

Or, to be more exact, the rate at which each person works is not constant

It depends on whatever x was originally

no

Consider 2 people working 2 hours per day for two days to make 2 items. That means it take 2²=4 hours for one person to make one item

If 4 people worked 4 hours per day for 4 days, then each person works 16 hours total. That is, each person makes 4 items, so 16 items are made (4³/2²=64/4=16)

[vocal sleet]

@zenith orchid Has your question been resolved?

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[bronze pike]

where I start

[regal bane]

Find the volume of both, in terms of cubic inches

Then convert to fluid ounces.

[bronze pike]

would volume be V=BLpi/3

since cone

18.85 would be the answer?

@regal bane

.close

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[bronze pike]

.reopen

[vocal sleet]

✅

[pallid zenith]

find the volume of B

[bronze pike]

I found the answer

.close

[vocal sleet]

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[lean osprey]

"Two forces act on an object at an angle of 40° to each other. One force has a magnitude of 200 N, and the resultant has a magnitude of 600 N." is the diagram i drew correct for this?

[lean osprey]

@hushed pewter but the answer shows this

[hushed pewter]

Oh oops

I see now

the forces act on the object.

These two black arrows represents the two force acting on the object (located where both arrow tips meet)

The total force is the sum of the two vectors

The two vectors are redrawn like this to show how summing them works

And the red arrow is the resulting net force acting on the object

[tired raven]

Is this where I can ask questions about math?

[lean osprey]

i see thanks

.close

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[hushed pewter]

.Read #❓how-to-get-help. In short, ask in a channel that is available

[vocal sleet]

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[dull stratus]

where did my professor get the 2 exponent circled in red?

[hushed pewter]

It's not an exponent

It's the x-coefficient from the 2x-3 term

[vast shale]

reverse chain rule

[dull stratus]

ahhhh ty

.close

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[fresh mirage]

Where did I go wrong or should I have solved a different way?

[slate herald]

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

[twin meteor]

balls_stealer

[slate herald]

in the 3rd line just put cos^2 (x) instead of 1 - (1 - cos^2 (x)

then u r good to go

@fresh mirage

[fresh mirage]

Okay thank you, so was my expansion wrong?

[slate herald]

kinda wrong cuz in the forth line u made 2 positive and cos negative which should be -2 and cos

[fresh mirage]

Is 1-(1-cos^2x) = 1 -1 +cos^2x? I thought this would be wrong

[slate herald]

yea

[fresh mirage]

Oh okay thanks, ill do what you originally said 👍

.close

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[cerulean phoenix]

I am just really stuck when another angle is added to find the area of a triangle, I know that if it was SAS then it would be side x side x sin angle divided by 2. But my teacher didn't go over when there are two sides and two angles.

[left crest]

If you know two angles, you can find the third angle

[cerulean phoenix]

God i need sleep, thank you so so so much.

.close

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[vocal sleet]

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[sharp dust]

Need some help with this question idk where to start

[vocal sleet]

@sharp dust Has your question been resolved?

[sharp dust]

<@&286206848099549185>

[hexed estuary]

So you’re given P, n, and A in the problem

The principal investment is 3500 USD

the compounding period is annual meaning once every 12 months and it’s been 2 years so interest has been added twice meaning n = 2

And 3713.15 is the current amount