help-19

[manic sleet]

so we "normalize" it

[manic grail]

ok

so its the direction of tangent

but length one

[narrow crypt]

ye

[manic grail]

so now

why r'(t)/norm r'(t) times dS = dr

[manic sleet]

remember how dS is norm of r'(t) dt

the norms cancel, and this is okay bcz they're scalars

[narrow crypt]

its not norm, its size (magnitude)

[manic sleet]

I've always heard it called norm

[narrow crypt]

it is?

damn

[tidal matrix]

oh yeah, generally it'll be called the (2-)norm

but if it helps clarify across the language barrier, it is the size of the vector

[manic grail]

its the same thing

the only difference is we got different kind of norms

so magnitude is one type of norm basically

[narrow crypt]

oh

mb gang 🙏

[tidal matrix]

nah you're good

i mean, a normal vector is the perpendicular vector, so its confusing

[manic grail]

nws i was confused aswell on why they call it with 2 different types

uhm also

can someone tell me what a tensor is

[steel quarry]

its basically something that generalizes vectors and matrices and scalars

[manic sleet]

a scalar is a 0-rank tensor, vector is a 1-rank tensor, a matrix is 2-rank tensor

[manic grail]

wtf is a scalar

yall keep saying it but idk lemme translate

yea makes no sense someone explain

[steel quarry]

not getting into formal definitions, it is a number

its called a scalar, because it scales vectors

[tidal matrix]

like $3\vec{x}$ or $(0.35)\vec{y}$

[clever fjord]

haseeb

[tidal matrix]

the 3 or the 0.35 part

[manic sleet]

any real number

I called the function f:R2->R "scalar" because it took an input of two variables and outputted a real-number i.e. a scalar

[manic grail]

i dont understand

so whats a scalar

is the number 2 a scalar

[manic sleet]

so if you recall from elementary physics, a scalar has a magnitude

a vector has a magnitude and direction

the number 2 has a magnitude

it's 2 units waway from the origin

but a vector say <2,4>

is sqrt(2^2+4^2) units away from the origin

but also points in the direction of <2,4>

[south plume]

a singular number, something that is not a vector

[manic grail]

so scalar is the distance from (0,0,0....,0)

like the distance from the begining of coordinate system

[south plume]

it is just a number

[manic sleet]

that's just the magnitude yes

but not unique to a scalar

[manic grail]

so magnitude is a scalar

[south plume]

yes

[manic sleet]

right because it's a number

[manic grail]

cause it takes multiple numbers

and outputs one

ok

[manic sleet]

its not that it takes multiple numbers

it's that it outputs ONE

a real number

[manic grail]

yes

so

any function R^n -> R

is a scalar

[manic sleet]

a scalar function

[manic grail]

is R^3/2 defined?

[south plume]

it's a name we give to variables to distinguish them from vector variables. it's nothing but a real number

[south plume]

if you can define half of a cartesian product, sure, but i have personally never heard of this

[manic sleet]

there are real dimensional fractals.... but not in a traditional sense

[manic grail]

https://tenor.com/view/aww-hell-nahh-aww-hell-aww-hell-nahh-gif-9659330954843262630

nvm i think ill focus on the integral

[manic sleet]

just stick to integers 😅

[manic grail]

yes

also

why do we put dot product when multiplying F and T

[desert jolt]

As in?

[manic grail]

like we have dS times T = r'(t) dt

and we replace r'(t) dt

but it becomes like this

anyways i need to go

[manic sleet]

so what this integral (\int_C F\cdot d\vec{r}) really means is how much "work" you're doing along the path (C)

[clever fjord]

PajamaMamaLlama

[manic grail]

yes ik what it means

im examining it purely mathematically

[manic sleet]

the only way I can think it about it physically

but because if you sum up the components of work

soemthing with projections

and dot product is tied to projection

but I won't hold you much if you have to go

have a good day :)

[manic grail]

yes ik that

but forget about this specific case

why when subbing in dS T in r'(t) dt

where there is no dot product

we make T . F a dot product

why not T x F

or is that the same as multiplication of functions like when we have a sub like that its always dot product

[manic grail]

alr you too man thanks to yall for all the help i appreciate it very much

[steel quarry]

F.T can be interpreted as a sort of projection of F in the direction of T

In general if you do F.dr, you'd get work but F x dr would give you torque

[odd edge]

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[ebon island]

2x+by=10
ax+4y=15
2b=a
system has no solution what can be value of A

-2
1/2
4
8

[ebon island]

I have no clue

[narrow crypt]

what does it mean

for a system to have no solution?

hint: solution of a linear system is their intersection

[ebon island]

parallel

[narrow crypt]

exactly

[ebon island]

so how do I turn it parralel?

[narrow crypt]

same slope

how do u find slope of a linear eq?

[ebon island]

mx

[narrow crypt]

can u rearrange the two equations into y= mx+c

and then make m equal?

[ebon island]

huh

by=10-2x
4y=15-ax

[narrow crypt]

so

\begin{align}
y &= \frac{10}{b} - \frac{2}{b}x\
y &= \frac{15}{4} - \frac{a}{4}x
\end{align}

can u determine the slope?

[ebon island]

where do you get 15/b from

[narrow crypt]

oopsie

[clever fjord]

k

[narrow crypt]

there we go

[ebon island]

ya idk what to do here

wait

[narrow crypt]

.

[ebon island]

I cross multiplied it

the answer is not looking pretty

[narrow crypt]

could u show

u should get

[ 8 = ab]

[clever fjord]

k

[narrow crypt]

right?

[ebon island]

40-8x=15b-bax

[narrow crypt]

lets think back to our objective

what a system where there is no solution, right?

so to get there we must have two parralel lines

and for that the slopes of both lines should be the same

[narrow crypt]

from this

we get

[ -\frac{2}{b} = -\frac{a}{4} \implies \frac{2}{b} = \frac{a}{4} \implies 8 = ab]

[clever fjord]

k

[narrow crypt]

or i want to follow from this

this equation has no soln when x is multiplied by 0

u will 40 = 15b and if 15b isn't 40, theres no solution

so simlarly

[ (ba - 8)x = 0 \implies 8 = ab ]

[clever fjord]

k

[narrow crypt]

ye?

[ebon island]

ok

[narrow crypt]

do u know how to proceed?

[ebon island]

nope

[narrow crypt]

hint: b = 2a is given

[ebon island]

so

2b^2=8

b=2

so a=4?

[narrow crypt]

👍

[late sinew]

Bro made the approx his status

[narrow crypt]

,w find solution to 2x + 2y = 10 and 4x + 4y = 15

[clever fjord]

Results provided by WolframAlpha

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

Requested by nuclearinteraction

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[manic grail]

hello for vector functions going to R^n with nEN and n>=2 whats the notation other than f(x,y,z) = P(x,y,z) i + Q(x,y,z) j + R(x,y,z) k
i have seen another notation without using the unit vectors i j and k

[placid wolf]

$$f(\vec x)=\langle P(\vec x),Q(\vec x),R(\vec x)\rangle$$

[clever fjord]

Rose

[placid wolf]

any notation you use for a vector you can use

[manic grail]

ok

.close

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[odd edge]

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[shrewd trellis]

Am i on the right track?

[indigo dirge]

I believe so, youre solving for x right

[shrewd trellis]

yes

[indigo dirge]

is that a 0 on the rhs

[shrewd trellis]

its a 0

[indigo dirge]

ok, so assuming x =/= sqrt8, you can just set the numerator to 0

[placid wolf]

Right, use algebra to your advantage. multiply both sides by sqrt(8-x^2)

[shrewd trellis]

Im trying to solve for C

[shrewd trellis]

did i do it incorrectly?

[indigo dirge]

you can solve for b and c using the derivative

[placid wolf]

not incorrectly, but it will be easier to solve if you do it frances/my way

right off the bat you can multiply both sides by sqrt(8-x^2), the 0 will annihilate it on the right side and you are left solving a much simpler equation

[shrewd trellis]

x =/= sqrt8, I dont understand this part

[indigo dirge]

if x was sqrt 8, then x^2=8, and that would make the denominator 0

[shrewd trellis]

x equal to 2

would make the numerator

0

[placid wolf]

there is one more solution

but yes that is the solution to get C

[shrewd trellis]

x = -2

[indigo dirge]

yep

[shrewd trellis]

so

the coordinate of C is

(2,2√ 4)

[indigo dirge]

yes

[tidal matrix]

$f(x)$ should be $x\sqrt{8-x^2}$, not $\sqrt{x(8-x^2)}$

[clever fjord]

haseeb

[indigo dirge]

the coordinates of c are still correct though

[shrewd trellis]

which screenshot is this referring to?

[indigo dirge]

most recent one

i think

btw root 8 is 2 root 2 not 2 root 4

and it can be simplified to 2,4

[tidal matrix]

$\sqrt{8}$ is $2\sqrt{2}$, yeah, but that doesn't simplify to 4

[clever fjord]

haseeb

[tidal matrix]

so you simplified your root wrong, but that "wrong root" was the correct answer

[shrewd trellis]

so is this what u guys mean

[shrewd trellis]

is that better?

[tidal matrix]

yep, nicely done!

[indigo dirge]

yep!

[shrewd trellis]

and for the Coordinates of A and D

correct?

B is D, my bad for that

[indigo dirge]

one sec

$x=\pm\sqrt8$

[clever fjord]

Frances

[indigo dirge]

if im not wrong

[shrewd trellis]

isnt that what i did?

[indigo dirge]

wait whats d)

[shrewd trellis]

last q

[indigo dirge]

oh

range is correct

[shrewd trellis]

yes dmain i made a mistake

@indigo dirge is this better?

[indigo dirge]

yep thats right 😄

[shrewd trellis]

yay thanks

[indigo dirge]

(dont forget to close this btw)

[odd edge]

@shrewd trellis Has your question been resolved?

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[shrewd trellis]

did i fumble

[quasi sparrow]

Yes

Putting something over a common denominator means you need multiply by the denominator

[shrewd trellis]

I dont understand, what line did i mess up

[quasi sparrow]

Line after y'

[pastel orbit]

this = is where the mistake lies

[quasi sparrow]

You did
$2 - \frac35 = \frac{2-3}{5}$

[shrewd trellis]

so i meant to say 2/16x^3?

[clever fjord]

riemann

[shrewd trellis]

ok i get it

so basically 16x^-3 is

a fraction

@quasi sparrow @pastel orbit so is this better

?

[quasi sparrow]

What are you doing

[shrewd trellis]

my answer was (2,9)

[manic sleet]

i'd check that y-coordinate again

oh wait

nvm I am tweaking lmao

(2,9) looks right :)

[shrewd trellis]

thank u thank u

.close

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[oblique meadow]

(I need a ratio or a percentage for these values. Trying to win an argument with my mom, lol) 9 deaths out of 3.88 million skydives in 2024 and 40,990 deaths out of 248.6 million cars in the US registered in 2023.

[amber schooner]

,calc 9/38800

[clever fjord]

Result:

2.319587628866e-4

[amber schooner]

,calc 40990/2486000

[clever fjord]

Result:

0.016488334674175

[amber schooner]

there are your percentages

[oblique meadow]

The 38800 stands for million? Seems like 38 thousand to me

[amber schooner]

larger proportion of people driving cars die than in skydiving

[amber schooner]

no i got rid of two 0s because of the percent

you multiply it by 100 for %

[oblique meadow]

I was trying to do that but it kept giving me decimals and I had no idea where if at all I needed to move it

[amber schooner]

just a small percentage

[amber schooner]

like this means 0.0002319…. %

very few

[oblique meadow]

I suck at math and this is confusing . THANK YOU KIND AND SMART STRANGER

.close

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[soft wharf]

We

[soft wharf]

can y’all help mee

[atomic void]

what do u not understand (specifically)? All?

[bitter folio]

Which questions you need help

[soft wharf]

All

Step by step

Let’s start with no.1

[wooden python]

have you done things with arithmetic progressions before at all

[soft wharf]

I HATE THIS YK WHAT WAS THOUGHT TO US IS DIFFERENT

[soft wharf]

Progression?no

[wooden python]

arithmetic sequence

[soft wharf]

but the assignment is liek that

[wooden python]

whatever they called it in your class

[bitter folio]

(3i-1) when is it maximised?

[soft wharf]

we were all shocked and disappointed when the tescher showed that assignment

[bitter folio]

when is it minimised?

The constraints are 1 <= i <= 25 from the question

[soft wharf]

I don’t know that

😭

[wooden python]

overcomp.

[atomic void]

@soft wharf, try to type out the first 3 terms of the first question

[bitter folio]

hm okay ig

try to list the sequence

[soft wharf]

helloo

[soft wharf]

huh

Can someone pls explain on how to do this

I dont understand on how to use it

Huhu

<@&286206848099549185>

[somber remnant]

Maybe this will help?

[somber remnant]

Basically it just means the summation of u1 to uk

[lethal spoke]

Firstly you need a sequence(U) with the nth term U_n
n = 1 means we start adding from the first term (of the sequence)
And k (on top) means we stop at the kth term(of the sequence)

[somber remnant]

It doesnt need to start with 1 btw it can start with 2 or 3 or .... (if i dont remembered wrong)

[lethal spoke]

Some texts may use n=0 for the first term

[somber remnant]

If n = 2 it just mean that n2 is the starting point instead of n1

[soft wharf]

Guys how can I add this quickly?

I get the process now but how to add it hawhha

should I do it one by one

Do yall have any technique

[lethal spoke]

,rccw

[somber remnant]

Damn

[soft wharf]

Why damn

😭

is it wrong

Look

[soft wharf]

This is what the teacher said to us

and the activity is so shtty

[soft wharf]

Like wth why 25 terms

[somber remnant]

Hold up did u learn function yet?

[soft wharf]

no

Our topic rn is Arithmetic Series

[somber remnant]

Its not wrong its just that theres a way to do it a lot quicker

[soft wharf]

Is this wrong?

[soft wharf]

WHAAT

😭

[somber remnant]

Lemme find an easier formula rq

[soft wharf]

Teach me

[somber remnant]

Hopefully my handwriting isnt too shitty

[soft wharf]

u there

is this sigmas notation thing rlly related or that important to arithmetic series?

If yes why

😭

[somber remnant]

Thats ur question right?

[soft wharf]

I still don’t understand

[somber remnant]

Try to apply the first formula on this

[soft wharf]

why did u put a lot of parenthesis

[somber remnant]

The top one

[somber remnant]

To make it easier(?) For u to see

[somber remnant]

@soft wharf can u tell me which part of this is a and b

[tacit wasp]

Actually, I believe she needs another formula, which she should have been taught if they're learning arithmetic series

Which is $$\sum_{k=1}^n \ a_n = n\cdot \frac{a_1 + a_n}{2}$$

(where $a_k$ is an arithmetic progression)

[clever fjord]

Alberto Z.

[somber remnant]

Ye thats a must formula

But i think her teacher is trying to get her to be familar with sigma first i think?

[soft wharf]

What does arithmetic progression means

[tacit wasp]

The thing you are doing 😅

[soft wharf]

I only heard of quadratic progession

What is the word progression huhu

[tacit wasp]

Maybe you call it arithmetic sequence

[soft wharf]

Yep

[somber remnant]

@soft wharf

[soft wharf]

a is 3n

[somber remnant]

Yes?

And b?

[soft wharf]

b is 1

?

[somber remnant]

Mmm -1 might be better

I kinda place the blanket wrong

Gimme a sec

There

U get it? @soft wharf

[soft wharf]

Uh

it should be (-1)

why did u put only -(1)

[somber remnant]

Its the same ngl -(1) and (-1)

U dont even need the bracket in this case

So now back to the question

@soft wharf u can see that a = 3n and b = -1 right?

[soft wharf]

yea

[somber remnant]

Good

Now use the first formula on ur question

And send me what u get

[soft wharf]

Oki

[odd edge]

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[short topaz]

how 2nd part

[frigid isle]

Use sin c + sin d

And cos c + cos d

And divide

[short topaz]

ok thanks

lemme try that

yep that works

thanks

[short topaz]

how do I do the 3rd part?

.close

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[signal oar]

Which one?

[solid fox]

maybe the first one

[signal oar]

Have you tried anything?

[solid fox]

i have tried figuring out the price of 1 pen for each of the shops

and thats all

[signal oar]

Yes, but did you have any idea on how to do that?

[solid fox]

uhhh

i did 7 divided by 3 which gave me an approximate 2.3 dollars and for shop b i did 9 divided by 5 which is 1.8 dollars

[scenic aurora]

hi

[rough steeple]

so you dont know fractions yet?

[signal oar]

Ok, that looks good

[scenic aurora]

who the fuck doesnt know fractions

[signal oar]

But keep it 7/3

[solid fox]

okay

[signal oar]

So let's try working with that: call x the number of pens bought. Then for the first shop, you pay 7/3 * x and in the second shop, you pay 9/5 * x, right?

[rough steeple]

this problem can be solved without fractions if you didnt learn them yet, simply calculate cost of 15 pens in each shop

[solid fox]

yup

[signal oar]

Now you pay 104 dollars more in shop A than in B, can you now arrive at an equation?

[solid fox]

uhhhh

i think?

[wooden python]

ok first off, you know how to work with fractions, right?

[solid fox]

yes

[wooden python]

ok right

so the prices for 1 pencil at the two shops are 7/3 and 9/5 -- and you should NOT convert these to decimals

now can you write down the equation based on what Kepe has already said?

amount spent at shop A: 7/3 * x
amount spent at shop B: 9/5 * x

mrs tan spent $104 more at A than at B

@solid fox

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[woven mauve]

hei

[woven mauve]

i need help with this

[manic sleet]

,rccw

[toxic rose]

wrong way

[manic sleet]

whoops

[indigo dirge]

there we go

[indigo dirge]

now just expand both sides

im assuming you are solving for x?

[woven mauve]

yes

but isn t there a simpler method?

[nimble blaze]

not really
what were you expecting?

ok there is an algebraic trick that can make stuff slightly less tedious

but first focus on getting the basic approach

[odd edge]

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[graceful viper]

what about it?

[manic grail]

how do you take derivative with respect to parameter of a 3 variable function

[sand horizon]

Whats r(t) and f

[manic grail]

can someone tell me what is the total derivative

of a function f(x,y,z)

basically this

whats d f(x(t),y(t),z(t))/ dt

[green elm]

chain rule

(gradient of f at r(t)) dot r'(t)

[manic grail]

yes

how

[green elm]

which part do you not know how to do?

[manic grail]

whats the formula

how is a f(x,y,z) derivative defined

like full derivative

[placid willow]

Are there letters in maths

[manic grail]

in pure math there is probably only letters and no numbers

[leaden widget]

m, a, t, h, and s

[manic grail]

someone tell me pls about the derivative

nvm

chat gpt came in clutch

[manic sleet]

that is exactly this btw

[manic grail]

oh yea sure

i meant this formula though

[quasi sparrow]

How are people supposed to know what dot means in terms of formulas /s

[manic grail]

wdym

dot product no?

with x*x' defintion

...

.close

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[tidal matrix]

<@&268886789983436800>

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[strange aspen]

sniped

[tidal matrix]

im sorry i saw you typing 😔🥀

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[real shore]

hello, wanted to know the odds of breaking even after placing 25 billion dollars in bets total, with a house edge of 1%. The bets are in increments of 2.5m (so 10,000 bets) and the game has a 2/10 chance to pay 0, a 7/10 chance to pay 1.2x, and a 1/10 chance to pay 1.5x (this is where the 99% rtp comes from), I want to know the odds of being break even or better, with this low volatility and high number of bets

[odd edge]

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[real shore]

.reopen

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✅

@real shore Has your question been resolved?

[quasi sparrow]

Try to use the multinomial theorem

[odd edge]

@real shore Has your question been resolved?

[edgy holly]

@real shore Could you confirm if the answer is around 2.33 %?

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[ivory grove]

@drifting zealot

Hint: ||Can you find angle DEA?||

[drifting zealot]

I'm new to the subject since the class is at its own pace, the last time I've worked with something similar was a while ago

[ivory grove]

OK. Can you find angle DEA then?

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[pastel orbit]

how does this argument look?

here's 1-7, if needed

[pastel orbit]

oops, these aren't supposed to have partials

that's a typo

I suppose here's a TLDR

I'm only really looking for if the overarching idea behind my proof is correct

I don't mind if nobody is willing to check details

[odd edge]

@pastel orbit Has your question been resolved?

[tidal matrix]

i just wanna say your custom QED is adorable

[pastel orbit]

the credit belongs @rotund ginkgo for making it

(another reminder that we love you, det )
(let me know if you're tired of getting these pings though )

[tidal matrix]

omg det like the hit homormorphism from GL_n(K) to K

[pastel orbit]

yeah!

[rotund ginkgo]

(det loves higher too )
(and it okie to ping ><)

[pastel orbit]

https://tenor.com/view/kristigocouple2024-gif-11331379229047422940

I love det c:

[pastel orbit]

also I got this verified elsewhere, so I can close the channel now

.solved

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[rotund ginkgo]

det is staring at that cute ear moving for too long now

[pastel orbit]

[rotund ginkgo]

:giggwe:

[pastel orbit]

[sick plaza]

Hairy ball theorem

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[dusky pilot]

find f(x), given a•f(x)+b•f(3-x) = -3x+5, a=-3/7, b=4/7
the first step would be to replace 3-x with t, but then the answer key continues and says that after we have a•f(3-t)+b•f(t) = 3t-4, we should return to the variable x and find f(x) through a system of equations. i don't understand what "returning to x" means and how it's possible.

[low locust]

the name of the variable doesnt matter

whether its af(3-t)+bf(t)=3t-4, or af(3-x)+bf(x)=3x-4, same thing

[dusky pilot]

so if i put t = x nothing changes

[tidal matrix]

could you post the answer key, so we could see what they mean by "returning to x"?

[dusky pilot]

it's in another language

[wooden python]

in what language

[dusky pilot]

it' s only one line and it only says we return to x and replace a and b

that's all

and it shows the system

[wooden python]

this is not what i asked

[dusky pilot]

romanian, i'll show you the picture

[rose coral]

$$\begin{aligned}
&a f(x) + bf(3 - x) = -3x + 5 \
&a = -\frac{3}{7} \
&b = \frac{4}{7}
\end{aligned}$$

Texit are you is are be have stupid

[rose coral]

@dusky pilot i'll assume you know how they got to here

From this equation, hopefully you also know how we replaced a and b with their respective numerical values

When we return to the variable x, we simply change the input again. we also accordingly change the output

[dusky pilot]

yes, i did every step

[dusky pilot]

it stays the same then ?

[rose coral]

Hey wait a second

[dusky pilot]

i mean, first x = 3-t and then we conveniently say x = t

[rose coral]

Im convinced they did something wrong

$$a f(x) + bf(3 - x) = -3x + 5$$
$$3 - x = t \iff x = 3 - t$$
$$af(3 - t) + bf(t) = -3(3 - t) + 5$$
So far, I agree with this.
$$af(3 - x) + bf(x) = 3x - 4$$

[rose coral]

Ok so we changed x -> 3 - x

[dusky pilot]

how am i supposed to learn from this if it's wrong ??

[rose coral]

I don't think its wrong

Sorry for that

-3(3 - x) + 5
-9 + 3x + 5
3x - 4

Ok in my opinion, the substitution they made was unnecessarily complicated

I'll try to rewrite this, see if you understand:

$$af(x) + bf(3 - x) = -3x + 5$$
Change the input \textit{and} output $x \implies 3 - x$:
$$af(3 - x) + bf(3 - (3 - x)) = -3(3 - x) + 5$$
Simplify:
$$af(3 - x) + bf(x) = -9 + 3x + 5$$
$$af(3 - x) + bf(x) = 3x - 4$$

[rose coral]

@dusky pilot do you understand this?

[dusky pilot]

just a second

oh

so no jumping back and forth with t

i got it, actually it was simple

[rose coral]

The substitution with t may or may not be easier to understand

It's up to you decide your preferred method

[rose coral]

!done

[odd edge]

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[dusky pilot]

thank you!

.close

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[dusk juniper]

How to do Linear Equations 2

[opaque eagle]

Context?

[dusk juniper]

Here

[clever fjord]

dyxn

[low locust]

given that its called linear equations 2, what was linear equations 1 ?

[opaque eagle]

You want to try and solve this?

I think they meant the second question

[dusk juniper]

like -3x+5=-2x-2

[low locust]

ok so the problem here are the fractions?

[dusk juniper]

I don't think I can I don't understand it

[dusk juniper]

ye

How do I do it

[opaque eagle]

Well, it's the exact same

Are you familiar with fraction arithmetic?

[dusk juniper]

Nope

I'm in Asia so maybe different stuffs

[low locust]

are you familiar with how to add and subtract fractions

[opaque eagle]

So you can't find $\displaystyle \frac 15 + \frac 13$ for example?

[dusk juniper]

Yeah

[clever fjord]

dyxn

[dusk juniper]

what do you mean by that

[low locust]

fraction arithmetic = doing +,-,*,/ with fractions

[dusk juniper]

Oh

Yeah I know that

[opaque eagle]

Well then it's the same

isolate x

[dusk juniper]

But the example showed in the picture it's different

so? @opaque eagle @low locust

[low locust]

how is it different

[dusk juniper]

Wait holy

[opaque eagle]

Do what you would in this case

[low locust]

how would you solve 5x+3=2x-2

[dusk juniper]

I get it now

ok thanks 👍🙏

Thanks bro

.close

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[dense star]

<@&268886789983436800>

[odd edge]

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[steep mantle]

moderators are blue what did you ping lmao huh

[dense star]

i dunno 😭

i clicked the role that showed up

[brittle beacon]

They have the new gradient colour thing

[steep mantle]

does the ping not turn gradieny

[brittle beacon]

It has for me

[turbid comet]

A slight theory whenever someone with a role pings it shows the colour

For others it doesn't

[dense star]

let me test it in a 1 person server

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[dense star]

omfg

[gritty spire]

<@&268886789983436800>

[low locust]

<@&268886789983436800>

[twin plover]

What

[odd edge]

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[turbid comet]

Yep my theory was correct

@dense star

[dense star]

yuh i dm'd you cause didn't want to talk in an open channel

[steep mantle]

it showed for me?

[dense star]

it's rng

yeah this specific instance it's a graduent for me too

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[woven mauve]

i did this, and i wanna know if i did it correctly

[strange aspen]

,rccw

[strange aspen]

You messed up the quadratic

Redo this part

[wooden python]

that part's correct, she messed up the step after this

unless i overlooked sth lol

[woven mauve]

i wrote 1 instead of 5....

😭

done

[late sinew]

,rotate

[late sinew]

i can't see the bottom part though

The range part

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@woven mauve Has your question been resolved?

[odd edge]

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[warm gulch]

hi guys, i need help with how to visualize and solve this. my brain gets really stuck during word problems sorry

[desert jolt]

Solving it in coordinate system is fairly easy

[warped glacier]

don't think about the 3D shape!

it's the same if you take the 2D parabola

[desert jolt]

Take horizontal standard form y^2 = 4ax

Or x^2 = 4ay either way it won’t matter much

[warm gulch]

ohh

so across is just the x value and deep is the y value

or am i wrong

like for the vertex

[wooden python]

it depends on how you orient your paraboloid

best to just sketch an axis-aligned parabola

[warm gulch]

sorry what does this mean this term sounds new to me T_T

[wooden python]

like y=x^2, same orientation as that

could even pass thru the origin

[rare verge]

what is your question ( what is the part you still dont know? )

[warm gulch]

like how to graph it

and how do i solve it

because i dont understand it

[rare verge]

you have to construct the function and then calculate the distance between the vertex and the focus point

[warm gulch]

ohh i see i didnt really get the lesson earlier so i guess ill just look up a video how to do that first

[rare verge]

could look like this

[warm gulch]

ohhhhhhhhhhhhh

oh my gosh its that simple

thanks guys

[odd edge]

@warm gulch Has your question been resolved?

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[umbral escarp]

On a certain page of a book, a password was written. To discover which page it is, the following information is given: the sum of the squares of three page numbers — the password page, the previous page, and the next page — is equal to a certain number k, which will be provided later.

Let n be the page number of the password.
Which expression relates n and k?

a) 3n² - 4n = k - 2
b) 3n² + 4n = k - 2
c) 3n² = k + 2
d) 3n² = k - 2
e) 3n² = k

[umbral escarp]

Idk what the letters even mean here

I know N is the page

Wait

Thst doesn’t make sense though

I don’t get the question tbh

[tepid pelican]

what about it do you not get?

[umbral escarp]

Uh

I’d say everything

Idk what to even do

It says n is the page

[tepid pelican]

you need to convert this relation given in words:

the sum of the squares of three page numbers — the password page, the previous page, and the next page — is equal to a certain number k, which will be provided later.

Into an equation

[tepid pelican]

page number of the password

[umbral escarp]

Ok

So how is the page 3n^2

[tepid pelican]

why should it be?

[umbral escarp]

Wouldn’t the page just be n

[weary pelican]

yes it is

[tepid pelican]

yes, it is n

nobody said it's 3n^2

[weary pelican]

the question is

what links n and k

[umbral escarp]

What’s k

[weary pelican]

and that might involve n itself, or its square, or something else

[tepid pelican]

read this to find out

[weary pelican]

the sum of the squares of three page numbers — the password page, the previous page, and the next page — is equal to a certain number k

[umbral escarp]

3 page numbers? Or 3 digits

[tepid pelican]

3 page numbers

[umbral escarp]

Oh

[tepid pelican]

number of the password page, number of the previous page and n.o. the next page

[umbral escarp]

So that’s 3n cause it’s 3 pages

[tepid pelican]

can you express those 3 using n btw?

[umbral escarp]

3n

[tepid pelican]

they all have different numbers though

[umbral escarp]

Oh

I know

(1+3n)+(3n)+(1-3n)

[weary pelican]

you're getting mixed up

[tepid pelican]

what even is that

[weary pelican]

let's do things one by one

number of the password page

[umbral escarp]

The 3 pages

[weary pelican]

we know this one don't we?

[umbral escarp]

n

[weary pelican]

yes

number of the previous page

[umbral escarp]

Oh

n-1

[weary pelican]

and

number of the next page

[umbral escarp]

What’s the 3 for then

[weary pelican]

don't worry about it

[umbral escarp]

n+1

[weary pelican]

we'll get to it

[weary pelican]

yes

the sum of the squares of three page numbers — the password page, the previous page, and the next page

the sum of the squares

[umbral escarp]

So I put those 3 in squares

So

(n+1)^2 + (n)^2 + (n-1)^2

[weary pelican]

yes

[umbral escarp]

Now sum them

[weary pelican]

So can we simplify that?

[umbral escarp]

Uh

Just summing them

n^2+1 + n^2 + n^2-1

Then

Sum it up

[weary pelican]

wowowow

what did you do

(a+b)^2

[umbral escarp]

Oh

I just put the square into the parentheses

Forgot about hot

That

[weary pelican]

yeah that's not how it works 😭

[umbral escarp]

It should be smh

[quasi sparrow]

,tex .freshman

[umbral escarp]

It works like that in division and multiplication right

[clever fjord]

riemann

[umbral escarp]

Sadly

Why’s there a 1

Oh wait

It should be a 2

3n^2+2

[weary pelican]

yes that's better

[umbral escarp]

It’s cause I wasn’t doing it on paper before and I mess myself up

[weary pelican]

so

[umbral escarp]

On paper i can make out what it means better

[weary pelican]

that's equal to k

[umbral escarp]

It is?

[weary pelican]

.

[umbral escarp]

Oh ya

So

3n^2+2=k

What now cause that isn’t an answer

[weary pelican]

well rearrange it a little

[umbral escarp]

Why

[weary pelican]

just look at the answers

[umbral escarp]

Ok ik we have to pass the 2

But

I don’t get why

It makes no sense

[weary pelican]

why? to get the answer

we know k = 3n^2+2

are you confused because we just need to -2 each side?

[umbral escarp]

Ye

[weary pelican]

well...

[umbral escarp]

Why isn’t this the answer

[weary pelican]

idk what to tell you

[umbral escarp]

Did he just want to make it be an extra step

[weary pelican]

because they wanted you to do a very little extra work

I didn't think "-2 each side" would be so jarring

[umbral escarp]

Oh

Ur right

But

I just wanted to know why that wasn’t an answer I thought maybe it wasn’t finished and complete

Like maybe it wasn’t relations n and k

Idk I was just uncertain

[weary pelican]

I didn't create the question and its answer choices

[umbral escarp]

Ik

[weary pelican]

k = 3n^2 + 2 is a valid relation between k and n

but k - 2 = 3n^2 is also a valid relation between them

so is k - 3n^2 = 2

and etc...

[umbral escarp]

Yeah that’s what I was thinking too but I wasn’t sure it was a valid relation that’s why I was asking

I didn’t know he just wanted us to do thst

Ty though

What’s a Raphaelisius Maximus MMIII

And this

A 1939c Cepheus +13 fireworks galaxy

[odd edge]

@umbral escarp Has your question been resolved?

[weary pelican]

A supernova xddd anyways

[weary pelican]

my name but pompous

if your question is resolved you can close by typing .close

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[bleak current]

hello

[bleak current]

I have a small question

What do we find with the cross product?

A = a x b . 1/2 for triangle area

A = hb . 1/2

why do we use 1/2 if we use the cross product?

[sharp oak]

Well, because the cross product gets double the area made by the triangle, of course!

We often say that the cross product finds the "area of the parallelogram" made by the vectors

So the area of that trapezoid thingy

But that's just the triangle they make, twice. Feel free to think of it either way

[bleak current]

So, normally cross product is formula for parallelogram area

[strange aspen]

generally

[sharp oak]

Well, we often use the cross product to get a vector that is perpendicular to two other vectors

I suppose the cross product is many things all at once

[bleak current]

we do it 1/2 because, if we cut it from the middle its a triangle

[forest sky]

the cross product gives a vector which is perpendicular to both input vectors, with a direction according to the right hand rule, and a magnitude equal to the area of the parallelogram with the input vectors as sides

[bleak current]

what about pyramid volume with the cross product?

[strange aspen]

that needs 3 vectors if i'm not mistaken

[bleak current]

1/6 (a x b) . c

[strange aspen]

(a x b) dot c gives the volume of a parallelepiped
and 1/2 comes from the base and 1/3 comes because it's possible to divide a parallelepiped into 3 pyramids

[bleak current]

Ok, now I do understand it a little bit better.

Thank you, guys

[strange aspen]

if you are done type ".close"

[bleak current]

I have one more questin

[strange aspen]

ok

[bleak current]

what is linearly independent and dependent

is it dependent if the 3 vectors have 3 different directions?

noo

?

ok, thank you

.done

.close

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[zealous onyx]

hi, can someone help me, how to draw graph f(x) = ctg (4x - pi/4)

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@zealous onyx Has your question been resolved?

[zealous onyx]

.close

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[copper sparrow]

Given quadratic equation is x²+√6x+3=0 and has roots a, b. Find a²³+b²³+a¹⁴+b¹⁴/a¹⁵+b¹⁵+a¹⁰+b¹⁰

[copper sparrow]

someone please help me with this question

Given quadratic equation is x²+√6x+3=0 and has roots a, b. Find a²³+b²³+a¹⁴+b¹⁴/a¹⁵+b¹⁵+a¹⁰+b¹⁰

[wooden python]

you don't need to paste it twice

also is that one single fraction? or is it just b^14/a^15 and the rest is outside?

[copper sparrow]

okay my bad

[wooden python]

it may be easier to send a screenshot if you do not know how to write fractions properly

[crisp quail]

I would assume its the sum of left over the sum on the right tbh, im trying to write python code for it now😭

[wooden python]

people should always write fractions properly and not even CREATE such ambiguity.

[crisp quail]

True, either way its computationally exhaustive

[boreal crag]

Well one way the function isn't symmetric which presumably makes the question impossible

Since you'll get different answers depending on what you set a,b to

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[desert raptor]

Can someone help me with a polynomial function g(x)=(x+3)(x-2)(x+1), how do I use transformations to determine the zeros of the following function y=-3g(x)

[mystic saffron]

anything times 0 is 0

[dire surge]

In what case would -3g=0?

[desert raptor]

So is g like 0?

[dire surge]

Yeah

What are the zeros of g

[mystic saffron]

for what x values is g = 0?

[desert raptor]

Sorry what

[mystic saffron]

what do you need to plug in for x here to get g = 0

[desert raptor]

I don’t know… this is my first time doing this

[dire surge]

The reason why factorization is useful

If you have somethning times something = zero, that means one of them msut be zero

So g(x) is a product of 3 things, at least one of them must be zero

x+3=0, x-2=0, or x+1=0

Then you can move the x's around for each of those, for example x=-3, x=2, x=-1

Then you have the zeros

[desert raptor]

Ohhhh okay thank you very much

.close

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[halcyon lantern]

Hey. Can someone tell me what I did wrong here? I think i messed up with the multiplication near the end, but really dont know. Sorry yes I wrote on a calender lol, i also blcoked out some personal stuff.

[quasi sparrow]

,rotate

[dire surge]

,rotate

[halcyon lantern]

I apologise if my writing isnt the neatest

[carmine idol]

okay first mistake, not copying $15x^2$

[clever fjord]

Element118

[halcyon lantern]

Oops forgot the exponent lol

[carmine idol]

second mistake - probably an issue with product rule

[halcyon lantern]

Thank you

[carmine idol]

the chain rule... not very clear

maybe it's correct, but it's nested with another mistake for now

[halcyon lantern]

My apologies, im doing 100% self taught and I am working on perfection

I just finished freshman year

[carmine idol]

usually you can assert the derivative in one step

any course assuming basic calculus, you should be allowed to do so [except possibly in measure theory]

[halcyon lantern]

Thank you for your help, I very much appreciate it.

[carmine idol]

okay here, some points of poor presentation, main mistake is putting = between things which are not equal

also the boxed expression seems off, looks like you are trying to do chain rule but your symbols don't seem right

you can try getting it improved and get back with a fixed solution if you want more feedback

[halcyon lantern]

Yeah thank you bro

Ill try my best to improve

,close

.close

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[restive condor]

So I need continuous help on math, I don’t rly know how to multiply or anything more than that

[graceful viper]

do you have particular questions in mind?

or do you want suggestions on resources

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@restive condor Has your question been resolved?

[atomic void]

what grade are you?

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[harsh bison]

Not sure if this is a math problem or an excell/spreadsheet problem sorry.. I am trying to get the average of the numbers while attaching a value to them.. (If that makes sense!?) These are stats for volleyball and I am trying to see what the average passer rating is. This example my player passed 182 perfect passes aka 3. 248 good passes(2) , 225 average passes, and made an error on 64 attempts.

[atomic void]

what is "248" here

182 perfct passes
248 good passes
225 avg passes
64 errors / fails