help-13

[wintry jackal]

A is vertical stretch/ compression

Yea, 0,0 1,3 2,8 and so on

[dire geode]

I can't follow all your typos

[wintry jackal]

That’s the general formula

D is how much it goes left or right, c is up and down

<@&286206848099549185>

[vernal basin]

What does A change

What would the difference be between a parent function’s values and the function vertically stretched by a factor of 2

[wintry jackal]

It stretches it vertically

I think it affects the y values only, I’m not sure as I usally am given the a

[vernal basin]

if you have all the other values just use algebra to solve for a by selecting a point

[wintry jackal]

Yea but the problem is K is also unknown

And that would be your horizontal stretch or compression

[dire geode]

Their suggestion solves for k.

[wintry jackal]

Wym by suggestion?

[dire geode]

.

[wintry jackal]

Ye but a and k are missing

[dire geode]

Your a and k are doing the same thing

If that's your general formula, it looks wrong

[wintry jackal]

Wait I js figured it out, thanks!

.claoe

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[normal shore]

How to know the order of vector in cross product

[normal shore]

If there's a diagram, ik to use right hand grip rule

But what if it is juz two random vectors without diagram

[dire geode]

Do you have an example of a cross product you don't know how to take

[cedar kiln]

@normal shore Has your question been resolved?

[normal shore]

Meaning?

Ok lemme rephrase

How can I make sure my normal component is facing upwards

Or the direction I want

[pastel vault]

you can multiply the cross product you get by -1

if it's facing in the wrong direction

[normal shore]

If question ask the plane of equation

And all my answer is differed by -1

[pastel vault]

doesn't matter then

you can use any scalar multiple of the normal vector you get

e.g if you have 12x + 4y + 8z = d1, then the d1 you get will be different with the same (x, y, z) on the plane

compared to 3x + y + 2z = d2

in fact, $d_1 = 3d_2$

[wraith dagger]

south's secret twin brother

[normal shore]

So what matters is the d

For plane equation

[pastel vault]

so they represent the exact same plane, if all the coefficients are the scalar multiple

$12x + 4y + 8z = 24$ is the same as $3x + y + 2z = 6$

[wraith dagger]

south's secret twin brother

[pastel vault]

yeah

[normal shore]

If it is -3x-y-2z=-6?

[pastel vault]

exact same plane

we multiplied both sides of the = by -1

so it's the same

[normal shore]

Oh ok

Cuz answer give only positive

Idk if negative would work

Thank u

[pastel vault]

ah then it's just what the question wants you to write

np!

[normal shore]

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[tame mural]

where is it best to learn university math online

[pastel vault]

you can't learn all of university maths online, unless you pay for an online degree or something

[tame mural]

is it worth watching youtube tutorials?

[modest cairn]

books

lots of books

you can learn number theory from a fields medalist

in a more compiled, organized way than attending their class

[pastel vault]

yeah online is the wrong approach I feel, if you mean something other than books

[tame mural]

do you have any specific books in mind?

[pastel vault]

there are nice university open textbooks also

[tame mural]

but like any specific single book that you liked?

[pastel vault]

I was going to ask which course

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[lilac totem]

Given that
$$ \vec{p}\cross\vec{q} = \vec{r} $$ , and $$ \vec{p}\dot\vec{q}=c $$, then $$ \vec{q}=? $$

[wraith dagger]

therealtdp

[lilac totem]

@lilac totem

bruh

<@&286206848099549185>

help

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[cinder crystal]

can anyone help me how to solve on how to find the variance and calulating cronbach alpha
item 1: 3.44
item 2: 3.22
item 3: 2.89

[cinder crystal]

heres the table

<@&286206848099549185>

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[rotund cloak]

how in the world is this wrong

[past wave]

!show

[cedar kiln]

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

[past wave]

show your work

[rotund cloak]

x^2 - 8= -36

we get -28

[round geode]

That is the question +- your ans

[rotund cloak]

square root it

make into smaller factors

[rotund cloak]

how do i do that

[round geode]

No clue I've never seen the software you're working on

[round geode]

It's in the blue rows

Row 3 col 3

Almost said row 2 col 2 -- too much programming

[past wave]

lmao

[rotund cloak]

oh okay

alright thanks

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[crimson sedge]

I have a question concerning an exercise about fourier's series, the question ive been stuck on is the last one because I can't seem to understand where did the (-1)^k came from

[crimson sedge]

my work is as follows, the minus that comes from partial integration will also be recurring and create another (-1)^k, cancelling the (-1)k out on the other side yet the answer seems to contain it

id like any sort of help pls and thanks

[crimson sedge]

translation :
let's consider the series of polynomials of bernoulli __ defined by : (the following 3 lines)

last question is : prove that (that relation)

oh and f_k(x) = B_k(x) and 1-periodic too

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[coarse thicket]

im doing the sum of an arithmetic series

and my answer isnt right and i dont know why

the right answer is 620

I think its because i turned 40 into 80/2, since thats where the answer on the site goes a different direction but it seemed right to me

[open pebble]

You're supposed to sum 5k-87 from 1 to 40 ?

[coarse thicket]

yes

the part with the formula is the same as on the site answer so its right until there

also now that i look into it, is this how i was meant to solve this?

because before i just did (31*80)/2

nvm i solved it

got the right answer

thanks for your time tho

[open pebble]

well, you're welcome I guess

[coarse thicket]

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[tired crystal]

Can someone verify my partial derivatives?

[tired crystal]

Just want to make sure they’re correct

[dreamy void]

should all be correct

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[rapid flax]

hey, i am really confused

[rapid flax]

So apparantely, the inverse of this matrix doesn't exist

This can be confirmed using this theory:

However, when doing the Gaussian Elimiation, it does work, as so:

And online calculators agree with me

why?

which one is correct

THIS IS EASY FOR THOSE WONDERING IF THEY WANT TO HELP ‼️🚨

[dawn junco]

you typo'd the matrix at the start of your gaussian elim

-41 not 41

@rapid flax

[rapid flax]

i'm gonna do horrible things in minecraft

thanks @dawn junco

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[rapid flax]

unsure what do after

[dire geode]

,rccw

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[hexed vortex]

I believe I know how to solve this

[hexed vortex]

Find 3 vectors in the null space of A and make them the columns of B

however I was confused on why exactly does matrix multiplicatino with this matrix B equals 0?

couldn't wrap my head on why that is true

[dire geode]

Do you know what null space means

[hexed vortex]

The null space is the set of vectors x, such that Ax = 0

[dire geode]

The 0 vector yes

So if you do that for 3 different x in the null space, you get the 0 vector 3 times

Say x1, x2, x3

Then just put them into B

[hexed vortex]

oh ok

so Ax1 = 0, Ax2 = 0, and Ax3 = 0

and that means Ax1 + Ax2 + Ax3 = 0

hmm how could you sepearte x1 and x2 and x3 into a seperate matrix

oh

[dire geode]

"put them in B"

I'm being vague. You should figure out how to make it concrete

[hexed vortex]

hm I'm still stuck

or hmm no nvm

I think I got it

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[livid trellis]

aren't both of them in reduced echelon form?

[livid trellis]

<@&286206848099549185>

[hard whale]

i think neither

[clever lintel]

first one is not

[hard whale]

hello

[clever lintel]

second one is ok

[livid trellis]

the last 3 are not in reduced echelon

so the first 2 must be

[clever lintel]

there's only one correct one here

that's the second one

[livid trellis]

yep

why?

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[tired crystal]

I need help solving a simple integral. We just learnt them and I’m trying to get ahead and wrap my head around them

[tired crystal]

Can anyone walk me through it

I have the answer but want to know the process to get to it

[modest cairn]

bro is Gon

[modest cairn]

u sub

[dusk goblet]

bro is Gon

[tired crystal]

Wdym gon lmao

[modest cairn]

ur pfp

[tired crystal]

I use substitution?

[modest cairn]

mhm

u = 2theta/5

[tired crystal]

Okay

One second I didn’t know id use it for this one

I thought you were tryna spell gone lmao totally forgot about my pfp

Du=2/5dx?

Or dtheta

[modest cairn]

perf

[tired crystal]

This substitution shit confuses me on sex

[modest cairn]

sex???

[tired crystal]

Where to from here

One sec lmao

🤣

[dusk goblet]

sorry i’m straight

[tired crystal]

The fraction is just messing w me

[dusk goblet]

$dx = \frac{5}{2} du$

[wraith dagger]

knief

[dusk goblet]

you’re missing the factor of 5/2

[tired crystal]

Why does the 5/2 come infront of the sin like I said just trying to teach myself this over my study week

[dusk goblet]

$\int \cos(\frac{2}{5}\theta) d\theta = \int \cos(u) (\frac{5}{2} du)$

[wraith dagger]

knief

[tired crystal]

So why does the 5/2 come infront of sin for the final answer

[dusk goblet]

$\int cf(x) dx = c \int f(x) dx$

[wraith dagger]

knief

[tired crystal]

So the c is 5/2?

[dusk goblet]

yea

[dusk goblet]

this is true for any constant c

[tired crystal]

So everytime I have something du i should take it out of the integral and then integrate?

[dusk goblet]

the du stays

but the constant can be pulled out if you’d like

[tired crystal]

Tbh I have no idea what the du even means

[dusk goblet]

go to khan academy

[tired crystal]

Okay lol

Like why does it just get dropped when integrating

This correct the way I showed it?

Nvm

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[rapid flax]

what is an implicit equation for a plane?

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[dense grove]

I dont understand what i need to do to solve this

[modest cairn]

yeah me neither

what kinda q is this 😭

[dense grove]

Exactly 😭 its apparently grade 5 level??

[queen ice]

Let’s assume that you can buy n nuggets. In what ways can you change the order such that you end up with n+1 nuggets instead? (Assuming your order of n nuggets has enough boxes of 4 and 7 nuggets)

@dense grove

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[queen ice]

@dense grove this channel will close soon btw

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[fossil coral]

I need hlep with this.

[fossil coral]

help*

the (y+10)^2 is what Im unsure about

<@&286206848099549185>

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[fossil coral]

oh

not even bing ai can save me now (on helping me with this problem)

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@fossil coral Has your question been resolved?

[crimson sedge]

You can write it in another form

It's stay like that

You question is kind of unclear

[crimson sedge]

You are having troubles simplifying it

?

[fossil coral]

eh. yeah

[crimson sedge]

!status

[cedar kiln]

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 was told that it's wrong.
4. I got an answer and would like my work checked.
5. I have a question about someone else's work/solution.
6. I have completed the problem and don't need help anymore. Thank you.
7. None of the above

[fossil coral]

ok. I got stuck on the (y+10)^2

Not sure what to do with it

[crimson sedge]

You just keep it like that?

[fossil coral]

huh.

its correct as it is rn?

nope thhat was wrong

[crimson sedge]

You have cancelled the y-3 term from the numerator and the denominator right ?

[fossil coral]

yes

wait no

i cancelled the y+3

[crimson sedge]

Mb

Yeah

y+3

So now you have left with sqrt(y-3)(y+10)^2

[fossil coral]

hmm

[fossil coral]

so cancel the sqrt and the ^2

[crimson sedge]

This can't be written as sqrt(y-3) sqrt[(y+10)^2]

[crimson sedge]

Yes

[fossil coral]

(y-3)(y+10)

[crimson sedge]

Yes

No

[fossil coral]

so I write it as ln(y-3)+ln(y+10)

[crimson sedge]

Sqrt still exists for y-3 since it does it doesn't have any squre

Squaee

Square

Get it?

[fossil coral]

oh

yeah

[fossil coral]

so I write it as lnsqrt(y-3)+ln(y+10)

[crimson sedge]

Yes

But that can be simplified furthur

[fossil coral]

do i need that 1/2 at the start?

[fossil coral]

how?

[crimson sedge]

What is ln(a^b)?

[fossil coral]

b * ln(a)

[crimson sedge]

Yes

What we have here is, a as y-3 and b as 1/2 since it's sqrt

[fossil coral]

ah. So still need that 1/2

1/2ln(y-3)+ln(y+10)

[fossil coral]

So is 1/2ln(y-3)+ln(y+10) my answer now?

[crimson sedge]

Yes

[fossil coral]

tysm

.close

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[glacial tendon]

hello

[glacial tendon]

I cant seem to figure these out

[nocturne pulsar]

if u draw a straight line like this you get a triangle inside

these would both be right angles

so the measurement of the inside angles of the triangle would be 7x+35º, 100-90 and 120-90

and all inside angles in a triangle have to add up to 180

do u think u can take it from there?

@glacial tendon

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[glacial tendon]

yes thanks

[modest cairn]

yes

[nocturne pulsar]

awesome

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[manic hedge]

erm howd they get /4

[idle crystal]

theres this length

[manic hedge]

so just 3x+2y=39

got it

i thought that wasnt included

thanks!

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[ocean robin]

where did the x^2 go?

[ocean robin]

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[hot crag]

yes

just replace sqrt -4 with 2i and sqrt -49 with 7i

in complex numbers, weirdly enough, sqrt(-a) times sqrt(-b) is -sqrt(ab)

oh it's plus mb

i was wondering why there was no 96i

yeah, checks out

??

no, your answer is correct

[crimson sedge]

k thx

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[idle crystal]

this is what i drew

yeah i have completely no clue

[cedar kiln]

@idle crystal Has your question been resolved?

[idle crystal]

<@&286206848099549185>

[idle crystal]

<@&286206848099549185>

idk where to go next

[idle crystal]

<@&286206848099549185>

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[idle crystal]

.reopen

[cedar kiln]

✅

[idle crystal]

does anyone know how to do this😭

[crimson sedge]

Ur alone with this little one bro🙏😭

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[idle crystal]

😭

[crimson sedge]

I hate geometry asf hh sry

chatgbt could help u if u

Ask it if

Ig*

[twin shoal]

Gpt is ass at doing geometry though

it's not good at visualising

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[warm garnet]

Can someone explain why b =0.25 I get why A= 50 and why a =1.15

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[onyx reef]

If the sum of the first from 0-2020 of f(n) is 0, and f(n+1)=(f(n)-1)/(f(n)+1), find f(0)

Thats the question, i dont really know how to approach it can anyone help

[cedar kiln]

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[onyx reef]

<@&286206848099549185> Can someone help please

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[uneven locust]

In the white space is supposed to be:
1, 2, 2², 2³,..., 2⁸

Logically I think the answer to b is 0 because
2⁸ = 2⁷ + 2⁶ + 2⁵...

And it's impossible that 2⁸ is in all of the sums, therefore not all sides can even add up to be 2⁸

[dire geode]

,rotate

[uneven locust]

Also I found the solution to s = 8097, if you don't mind could you also help me find the solution to s = 8104

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[lean ether]

i dont understand what to do

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[cobalt dagger]

the K value i got was -2.851 can someone verify this 4 me

[cobalt dagger]

wait nvm dumb question

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[cobalt dagger]

mb

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[rose dragon]

Could I request some assitance please? I don't really know how to approach this question

[grand shale]

but z=x+iy

in the equation

solve

[rose dragon]

im not good with complex numbers

how do i solve it

[grand shale]

like

just put the value of z=x+iy

in the second equation

and solve it

u should get the first equation

[rose dragon]

thanks

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[trail dune]

What makes us reach this conclusion? Just bc it ain't a perfect square?

[viral glade]

x^2 is always positive

So x^2+1 is always greater than 0 for any x in the real numbers

If you try to set it to 0 you will get
x^2+1=0
x^2=-1

Giving you a square root of a negative number which is not defined in the real numbers

[trail dune]

I see

Ok thank you bro, helps alot

.solved

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[viral glade]

Yw

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[tame mural]

I want to read CALCULUS by Gilbert Strang MIT. I already have knowledge in some of the topics explained there, so I don't want to read those again, only which I don't understand. But, I dont know if by omitting certain topics I won't lose important information. Are there people willing to question me on the book to help me determine which chapters I should focus on reading?
I'm attaching the publicly available PDF

[dire geode]

what

[tame mural]

Your sign of confusion is unclear to me

[pallid venture]

use chatgpt to question yourself

i dont think anyone here wants to be a private tutor..

[tame mural]

It can't access the book

Right...

[dire geode]

you want a private tutor?

[slate lintel]

the most important part is doing

[tame mural]

Eh...

[dire geode]

help channels are for specific math questions

[tame mural]

So where do I ask for such things

[pallid venture]

it can, attach it to the prompt

[carmine bronze]

This belongs in #discussion but you should at the very least skim through what you already know and make sure you actually do understand the material.

[tame mural]

I'm out of uploads...

[drowsy sage]

Do the problems in the book.. find an online derivative/integral calculator and check your work if the book lacks solutions

rinse, repeat

As has been said, nobody's going to be a free private tutor for you

Alternately, Khan Academy has some free material

[tame mural]

.solve

Eh

[carmine bronze]

--> .solved

[tame mural]

.close

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[sullen slate]

I’m supposed to solve this without using reduction formulas and I just don’t even know where to start

[dire geode]

why without reduction formulas

[sullen slate]

It’s just part of the assignment, I don’t know why. This is homework

We talked about u-sub and trig identities, mixing them together but I never really grasped it

I really struggle with trig

I was thinking maybe U-sub like this but I don’t know and Identity that would help with solving this

[dire geode]

that's a fine start. i still don't see how you can do this without using any power reduction formulas though

[sullen slate]

I don't get it either, maybe my teacher wants me to go through the root of the formula, the half angle identity?

[dire geode]

show the exact phrasing of the question

[dire geode]

pain

,w int tan^4(2x)

[wraith dagger]

Results provided by WolframAlpha

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

Requested by rie.mann

[dire geode]

try differentiating the answer and work backwards

[sullen slate]

Got it, any other advice, cause I gotta go soon

[carmine bronze]

Numerical? Simpson's Rule?

[sullen slate]

I have no idea what that means

[carmine bronze]

Simpson's Rule or Trapezoidal Rule?

Methods for approximating an integral.

[sullen slate]

We haven’t gone over that yet, it’s a calc 2 class.

[carmine bronze]

Fairly sure both are taught in Calculus 1.

[sullen slate]

I never learned it I guess and it was never brought up in class

[carmine bronze]

High school?

[sullen slate]

AP calc 1 and community college calc 2

All things considered it has been 2 years since calc 1

[carmine bronze]

Makes sense. AP Calculus covers material similar to what is covered in Business Calculus.

[sullen slate]

Anyway, got any ideas on how to solve the problem, or just some steps to take?

[carmine bronze]

Without using a Reduction Formula, no. The only option I can think of would be Numerical Integration using the Trapezoidal Rule or Simpson's Rule. They are both fairly easy concepts which any Youtube video should cover well.

They are worthwhile techniques to learn if you are ever in need of checking your answers in Calculus.

[sullen slate]

Okay, thank you

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[random umbra]

May I please have some guidance graphing this?

[random umbra]

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[trail dune]

Why is my solution to this question: (4a * sqrt(2a)) , wrong?

[queen ice]

Because a*sqrt(a) is not the same as sqrt(a^4)

[trail dune]

Bro what I did was

sqrt(16* 2 * a^2*a^2)

[queen ice]

Sure

How did you get 4a*sqrt(2a) from that though

[trail dune]

Hmm

Da last question I got was sqrt(75y^3), and I got 5y*sqrt(3y), which was correct. So I'm following my procedure of what I did there

I guess I'm confused of where variables go if they are sqrt(y^2)

Do they stay in, go out?

[trail dune]

Now that I think about it, if we square root da a^2, n take em out, then we end up with 4a^2*sqrt(2)

Which sounds correct?

[queen ice]

Yep

[trail dune]

Ok I see I see

ty

.solved

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[crimson sedge]

yo

I posted it 3 times

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[crimson sedge]

discord is crazy

Come on discord

.open

You suck discord

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[cobalt pier]

I tried multiple times by finding the partial derivatives of the parameters and taking the cross product

then dotting that with <x-x0, y-y0, z-z0>

but it doesnt give me the correct answer

so idk what to do differently

keeps returning false

<@&286206848099549185>

[cedar kiln]

@cobalt pier Has your question been resolved?

[mellow haven]

i suggest you eliminate the parameters completely

get a clean relation between x, y, and z

then use the tangent plane equation formula

,, z = z_0 + \pdv{z}{x} \big|{(x_0,y_0)} \cdot (x-x_0)+ \pdv{z}{y} \big|{(x_0,y_0)} \cdot (y-y_0)

[wraith dagger]

Milena

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[dire thorn]

!status

[cedar kiln]

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 was told that it's wrong.
4. I got an answer and would like my work checked.
5. I have a question about someone else's work/solution.
6. I have completed the problem and don't need help anymore. Thank you.
7. None of the above

[wicked moon]

acc nvm can u help me with this one (b and d)

uhhh so far i switch them

x = -1/2y + 2

[dire thorn]

Ok from here you need to solve for y. To do this you should get rid of the 2 on the right side somehow, then get rid of the -1/2. Any ideas on how to do that?

[wicked moon]

x-2 = -1/2y

?

oooo then i divide by -1/2

is it -2x +4

[dire thorn]

Yeah

y=-2x+4

[wicked moon]

ok

and d

would it be x = 1/2y + 5??

nvm

i did it wrong

2/5x-2 = y

[dire thorn]

Yeah

[tropic pier]

hey i needed some help w integration

can i ask here?

[dire thorn]

#❓how-to-get-help

[wicked moon]

ok for d is it -5x-10=y and f is it 4x+3 = y

[dire thorn]

Yeah

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[crimson sedge]

Does anyone understand why the answer is a) -8 ??

[dusk goblet]

(-4)(2) = 8

g(0) * f(0)

[coral jewel]

given two functions $f, g$, then $(fg)(x) = f(x)g(x)$

[crimson sedge]

Thanks

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[warm hawk]

Are none of these answers correct? My teacher said that there might not be a correct answer but there also might be one.

[cedar kiln]

@warm hawk Has your question been resolved?

[warm hawk]

<@&286206848099549185>

[warm hawk]

<@&286206848099549185>

[stiff fulcrum]

So first off it says it's linear for times 0 to t_1. Which ones can you cross off

[warm hawk]

a and c

[stiff fulcrum]

Not quite, A and B. Because for the interval 0<=t<=t_1, A and B show as a quadratic function

[warm hawk]

ohh

[stiff fulcrum]

That make more sense?

So then for C or D, you just need to explain it. Is it linear first and then gets steeper, or vice versa?

[warm hawk]

D?

[stiff fulcrum]

Yes

[warm hawk]

wouldnt the explination be wrong because it says its __constant __then gets steeper

cuz its linear right?

[stiff fulcrum]

Linear means the slope is the exact same all throughout

But when it turns into a quadratic, the slope goes up a lot faster

Like if the inside were 2, the term becomes 4. 3 becomes 9, 4 becomes 16, etc

But with a linear, if t is 2 its 4. If it was 3 its 6. 4, 8, etc. It stays at a constant rate

[warm hawk]

yea so its linear then quadratic but D says its constant then quadriatc

right?

[stiff fulcrum]

Yep constant slope and linear are fairly interchangeable

They basically mean the same thing

[warm hawk]

oh i thought constant meant 0-slope

[stiff fulcrum]

Ah I see

[warm hawk]

my teacher also gave us this practice which has 5 errors in the whole worksheet so this might be one of them

there might be no correct answer

[stiff fulcrum]

Possibly but I'm like 99% positive it's D

[warm hawk]

yea maybe idk

its fine ill just check with my friend tmr

thanks for the help though

[warm hawk]

Do you know this one by chance?

[stiff fulcrum]

Pick one where the variable would have an exponent as 1

[warm hawk]

a and b?

[stiff fulcrum]

Yeah

Should be good to course either one

[warm hawk]

yea thats probably one of the errors

thx

[cedar kiln]

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[remote trail]

Why is the central limit theorem more effective than other methods of approximation?

[dire geode]

What

Do you have an example of what you're talking about

[remote trail]

.CLOSE

.close

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[abstract thicket]

hello

[abstract thicket]

I need help with this question

find the rule

<@&286206848099549185>

Sorry for pinging although it hasn't been past 15mins but it is urgent

[valid yacht]

Are you taking a test?

[abstract thicket]

no, it's just that I have to hand in my tuition hw today

and I cant be late

[cosmic cargo]

you problem

[abstract thicket]

bruv

idc

then what is the point of this server?

think b4 u speak bud

bro why is nobody helping

isn't this a maths server

find the rule

<@&286206848099549185>

<@&286206848099549185>

[cedar kiln]

@abstract thicket Has your question been resolved?

[brazen dagger]

Not everyone is good at all topics, have some patience. Someone who knows this topic will assist you

[cedar kiln]

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[orchid jewel]

why is it not the second one?

[twilit escarp]

You cant separate like this

That works for sum only

Take example

5*78/3 = 5/3 * 78 but not 5/3 * 78/3

[orchid jewel]

I dont get it

if it is for adding it can be done like the second picture?

but if it is for multiplying it cant be done like the second picture?

[twilit escarp]

Exactly

[orchid jewel]

ohh ok tysm

[twilit escarp]

Youre welcome

[orchid jewel]

!close

.close

[twilit escarp]

.

[cedar kiln]

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[cedar kiln]

@cosmic cargo Has your question been resolved?

[cosmic cargo]

hello

<@&286206848099549185>

[bleak viper]

where is the graph

[cosmic cargo]

ur supposed to draw it

mark scheme here

why is it that when it intercepts it gives the answers

[cedar kiln]

@cosmic cargo Has your question been resolved?

[lofty kraken]

rearange the equation for the blue line to get y on its own

[cedar kiln]

@cosmic cargo Has your question been resolved?

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[crimson sedge]

.close

[cedar kiln]

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[cedar kiln]

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[noble cradle]

can someone help with this prob :*)

[grand shale]

cauchy schcwarz?

[mental trail]

hint: $f(x) = \sum_{k=0}^M a_kx^k$

[wraith dagger]

rafilou is not not born in 2003

[mental trail]

and for the terms that remain, $\int_0^1x^n = \frac{1}{n+1}$

[wraith dagger]

rafilou is not not born in 2003

[grand shale]

integral f(x) ^2 * integral x^2 >= (integral xf(x))^2

[mental trail]

otherwise, I can suggest this:

find f if degree of f is smaller than 1945

[cedar kiln]

@noble cradle Has your question been resolved?

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[worldly cave]

How to do this? Im supposed to "change order of sums" and use

mb its e^i not e^j

[dusk finch]

e is the constant?

[worldly cave]

yeah

[dusk finch]

and you are supposed to compute this?

[worldly cave]

This is the original

the problem says: Calculate by changing order of sums and using that identity

[worldly cave]

This is just what I did, idk if its ok

[mental trail]

thing is

you can't define sum from j = 1 to i when you haven't defined i yet

[worldly cave]

Yeah makes sense

So what to do?

[dusk finch]

I have no idea how to do this by swapping sums honestly

[mental trail]

think more about how to regroup i and j together in terms of n

if i varies from 1 to n and j varies from 1 to i

then you just have $1 \leq j\leq i \leq n$

[wraith dagger]

rafilou is not not born in 2003

[mental trail]

so if you had to make j vary first

then j would vary between 1 and n

and AFTERWARDS

[mental trail]

to respect this condition

i would have to vary between j and n

$\sum_{i=1}^n\sum_{j=1}^i... = \sum_{j=1}^n\sum_{i=j}^n...$

[wraith dagger]

rafilou is not not born in 2003

[mental trail]

triangle (quite literally)

[worldly cave]

hmm thats cool

[mental trail]

$\sum_{i=1}^n\sum_{j=1}^i e^{-i} = \sum_{j=1}^n\sum_{i=j}^n e^{-i}$

[wraith dagger]

rafilou is not not born in 2003

[worldly cave]

ok so this is just "renaming" the sums

[mental trail]

ok now geometric sum

$\sum_{i=1}^n\sum_{j=1}^i e^{-i} = \sum_{j=1}^n\frac{e^{-j}-e^{-n-1}}{1-e^{-1}}$

[wraith dagger]

rafilou is not not born in 2003

[mental trail]

and now you can figure it out

[worldly cave]

Wait this is not right

[mental trail]

why?

$\sum_{i=1}^n\sum_{j=1}^i e^{-i} = \sum_{1\leq j\leq i \leq n} e^{-i} =\sum_{j=1}^n\sum_{i=j}^n e^{-i}$

[wraith dagger]

rafilou is not not born in 2003

[mortal grove]

should be e^-j, just a typo

[mental trail]

no

[mortal grove]

oh mb

you're correct

[mental trail]

we don't swap j and i

we swapped the order in which we fix them

[worldly cave]

Oh nvm Ig its ok,

so this actually does

$e^{-1} + e^{-2} + e^{-3} + ... e^{-n} + e^{-2}+e^{-3} + ... e^{-n} + e^{-3} + ... e^{-n}$...

[wraith dagger]

OHHELLNAH

[worldly cave]

Ok I see the geometric sum

Also I can order them in any way because its finite?

[mental trail]

yes and addition is commutative

[worldly cave]

Why is there $e^{-n-1}$ and not $e^{-n-j}$

[wraith dagger]

OHHELLNAH

[worldly cave]

the formula is $e^{-j}\frac{1-(e^{-1})^n}{1-e^{-1}}$ right

[wraith dagger]

OHHELLNAH

[worldly cave]

@mental trail

So then I use geometric series formula again for e^{-j}

[cedar kiln]

@worldly cave Has your question been resolved?

[cedar kiln]

@worldly cave Has your question been resolved?

[worldly cave]

ohh cool

[cedar kiln]

@worldly cave Has your question been resolved?

[cedar kiln]

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[lean marsh]

can someone explain me this example

[lean marsh]

i dont understand how it jumps from step to step in the second image

[cedar kiln]

@lean marsh Has your question been resolved?

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@lean marsh Has your question been resolved?

[lean marsh]

.close

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[coarse atlas]

I was using this as an example for substitution

I was assuming you just plug in k+1 for i

[dire geode]

the last index is not k+1

it's at the top

[coarse atlas]

oh my!

so its (k+1)+1 * 2 ^ (k+1)+1

thats wild

[dire geode]

missing parenthesis, but yes

[coarse atlas]

wait where

should it instead be ((k+1)+1)

[dire geode]

yes

or just simplify first

[coarse atlas]

o

[dire geode]

1 + 1 = 2

[coarse atlas]

i wasnt sure if I could do that with them parathesis

so its k+2

[dire geode]

(a+b) + c = a + b + c = a + (b+c)

[coarse atlas]

ah makes sense.

[cedar kiln]

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[compact epoch]

Eeerm what exactly does a derangement !12 calculate

[compact epoch]

I am confused cuz !12 = 12! / e right

but what exactly does it calculate

Cuz to solve the no fixed points problem

You need to divide that by 12! again

[mental trail]

so it's approximately 12!/e

[mental trail]

if you have numbers 1 to 12 lined up

how many ways can you arrange them so that NO digit is in its original place

[compact epoch]

What...

That alone would solve the problem though

why do you need to divide by another 12!

Or wait

[mental trail]

what?

[compact epoch]

12! is the possible outcomes

right

[mental trail]

you're asking for the probability of derangement?

[compact epoch]

because we looking for probabilities

[compact epoch]

Ahh i get it now

[mental trail]

then (!12)/12!

[compact epoch]

this calculates the possible cases

yeah i get it

[mental trail]

so in fact

!12/12! is not exactly 1/e

but it's close

very close

[compact epoch]

Ah ok

Another question

why does this not work for everything < 4

[mental trail]

?

[compact epoch]

dude in the video said it only works for numbers 4 and up. And the % to get no fixed points is always the same 37%

[cedar kiln]

@compact epoch Has your question been resolved?

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[ancient shadow]

I know it's probably got something to do w a smart colouring but i can't find it, i struggle to find the invariance, i said that oh the 50th one can't be black with the 51st one also beingw hite but it's not a sound argument help

[ancient shadow]

i have an idea on maybe you can prove that you can't ever haven an even sequence of likes 0s or 1s

saying a black stone is a 1 and a white stone is a 0

but i struggle on how to prove that

[solid juniper]

it’s starts like that, and the property is preserved on every move

[ancient shadow]

yh i figured it out i think

tell me tho

jic i messed it up

my argument was pretty much that every time u perform a move, to form a consecutive sequence, a consecutive sequence will always be odd because it starts off odd and then ur adding two stones on either side

but that still preserves parity of the sequence

idk tho

[solid juniper]

yea

that’s pretty much what i said

[ancient shadow]

aight ok

[solid juniper]

oh

no i said something wrong

gonna delete this sorry i was imagining it wrong

[ancient shadow]

aight imma close the channel cos i think i got it

.close

[cedar kiln]

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[modest cairn]

lmk if you need help formalizing it

[modest cairn]

.close

[cedar kiln]

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[fringe slate]

Back at it again, asking another stupid question!

[wheat pivot]

Algebra or just number?

[fringe slate]

just need to select two more that is equivalent

[wheat pivot]

I would say the 1/3^4

Same result as 3^-4

[fringe slate]

oh

oops

[wheat pivot]

The (1/3)^4

3^2/3^6 also equivalent

I guess that the two ur seeking

[wheat pivot]

What grade are u in?

[fringe slate]

yup

[fringe slate]

8th, i am aware we should have already learned this

im just not the brightest

[wheat pivot]

Be ready for 9th math

Hardest one

[fringe slate]

im prepared

[wheat pivot]

I hope you are

[fringe slate]

i have the doors barracaded and everything

[wheat pivot]

My class average was 67%

We needed 70% to pass

I finished with 76%

[fringe slate]

lol

im sure its difficult

we dont have much to learn because we have like 1.5k pages to cover by the end of the year

they are short but its really difficult

we have 90 minute periods

for math atleast

well im gonna keep this open until i no longer need it cuz im sure ill have a few issues

[wheat pivot]

Alr

[fringe slate]

yup.

[wheat pivot]

Do u have a calc?

[fringe slate]

i do

not a fancy one tho

[wheat pivot]

Then where the problem

[fringe slate]

those cost a bit much

[wheat pivot]

Calcul the 9^5 x 9^-9 / 9^3

Then calculate every other

Just link the one having the same result

It’s that easy

[fringe slate]

thanks

i need hepl!!!

my calculator doesnt do variables

it doesnt simplify to expressions

[fringe slate]

.

[ripe breach]

x^4 * x^5 = x^9 ( just calculate the power )

same as for the first one

then calculate

[sour mesa]

That's heinous

Where is the x

[ripe breach]

which x?

[sour mesa]

1/4

It's supposed to be 1/x^4

[ripe breach]

oh sh

sorry

you are right

[sour mesa]

Whyd you need a calc for this?

This is basic exponents rules/laws questions

[fringe slate]

im quite frankly slow

anyways i managed it