help-36

[wintry kindle]

The answer is π

[hybrid heath]

!did you have a question?

[deft kayak]

yes im trying to screen shot it

i dont know how to screen shot

[wintry kindle]

on pc you can Win+Shift+S for screencap

[deft kayak]

yea but it sends it on the xbox thingy

oh

need help <@&286206848099549185>

[pallid spoke]

hey man

this is pretty easy do you mind if i help

[deft kayak]

yea

[tranquil pine]

I’ll let you help lol

[pallid spoke]

ok so we are going up my my looks 3

3-6-9

[deft kayak]

ok

[pallid spoke]

sorry back

ok so then we have 14 and 28

[deft kayak]

7?

[pallid spoke]

actually did you fill in the top right

[deft kayak]

yea

[pallid spoke]

because its wrong

[deft kayak]

oh

what is it

[pallid spoke]

ok

so 14 is half of 28

[deft kayak]

7

[pallid spoke]

yes that order would make sense

[deft kayak]

OH

ok

[pallid spoke]

but the top right

[deft kayak]

the top right

or divide

[pallid spoke]

is the same as the bottom

its just multiplying by two

so 3*2 = 6

6*2 =?

[deft kayak]

12

[pallid spoke]

yup!

then those would be equivalent

do you understand how we got that?

[deft kayak]

no

how

[topaz bone]

2/8 is 4

3/12 is 4

i mean 1/4

so that might be the logic

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[weak ridge]

I’m stuck on this step

[cyan kayak]

@weak ridge what are the prime factors of 117?

[weak ridge]

3x3x13

[signal vector]

So can you simplify √117 now?

[weak ridge]

Yeah

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[spare glacier]

dont know if my work is correct

[lyric summit]

The answer is correct, and so is the way, but you write very chaotically there

[spare glacier]

Sorry, tried simulating timed pressure

[lyric summit]

ok then

[spare glacier]

But thats it?

Its correct?

[lyric summit]

yes, you want to see the book style?

[spare glacier]

Yes please

[lyric summit]

ok 2 minutes i write fo royu

[spare glacier]

Sure sure i can wait

[spare glacier]

Limit as x approaches 0+ btw

[lyric summit]

y must be

becasue

[spare glacier]

or maybe you already did the transform

[lyric summit]

if you use x an dy

that it is constant

so or only x o ronly y

[lyric summit]

you understand ?

[spare glacier]

Wait, come again?

[lyric summit]

x or y,

but not together

so if you rliimt function depends on y, then you shud write y >0+

[spare glacier]

oh okay

So its okay to really do let x = y, then since both approach the same value, then y -> 0 is alright to do

yes?

[lyric summit]

yes because if you write x but function depends on y, then it is constant function

and then the limit = constant

froamlly saying

[spare glacier]

Ahhhhhhhhhhh

I get it

Alright alright

Thanks so much @lyric summit

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[quick cave]

I don't get a or c. I thought you have to multiply all of the numbers and get 60 for a and for c I don't lnow where you get that 3! from

[barren crescent]

12 books in total

finding how many ways to arrange all books is 12!

[quick cave]

but then

why do you multiply here

[magic sparrow]

because you can't wear jeans as a shirt

or shoes as jeans

or a shirt as shoes

etc..

it gets rid of a lot of the options

[quick cave]

ohhh

so you multiply for combinations but do the ! for permutations right?

i mean no

but yea I get what you mean

thanks!

[quick cave]

what about c tho

hm i see

thans a lot!

*thanks

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[slim shale]

Linear alegebra, specifically starting the vector space topic

[slim shale]

for a1

i said let x and y be rational numbers part of the set Q

then if x and y is a rational number they can be expressed as a ratio of two whole numbers
x = a/b
y = c/d

When I sum x and y
x + y = a/b + c/d = (ad + bc)/bd
they are still a ratio of two whole numbers which means that are still rational numbers part of the set Q

@magic sparrow
sorry I was the same guy asking for help previously

this is what I have now

i just learned how to use cramer's rule for finding the determinant and then we jump to vector spaces and doing proofs for the first time in my life 💀

[wintry kindle]

ys that's correct

ad+bc e Z

bd e N

===> x+y e Q

[wintry kindle]

you might get thrown into cold water in math from time to time but if you accept the freezing you'll love it 🦇

do you have an approach for showing that it's not closed under scalar multiplication?

say x e Q, y e R

x * y may not be in Q?

[slim shale]

i'm probably gonna choose a random irrational number like pi or a radical 2 for k but not sure how to start it but looking at my textbook rn

since I already know those aren't rational

[wintry kindle]

hm let's see

may I suggest x = 1/1?

@slim shale

lemme guess, one hour later another channel pops up where you ask the second part

[slim shale]

bro this is hard 💀

the only reason i thought of splitting x and y to a fraction was cuz of the sub note 😭

[wintry kindle]

sub note?

if x, y e Q then their only representation is via a fraction a/b with a e Z and b e N

that's rather how you'd define a rational

but regarding the second part:

if you use x = 1/1

and y = pi

somewhat similar to what you mentioned

then x * y = pi

but pi is not in Q

[slim shale]

The floating 1 above numbers, let me reading that subnote saying a rational number is a ratio of two whole numbers

[wintry kindle]

thereby Q is not closed under scalar multiplication with real numbers

[wintry kindle]

but this part is clear right

that we can find a pair which multiplies to a number that's not in Q

[slim shale]

yeah because pi is not an irrational number, and Q is the set of all rational numbers

[slim shale]

bro it was this simple 😭 ☠️ 🔥

[wintry kindle]

(pi is irrational :3)

[slim shale]

OOF

[wintry kindle]

nw

[slim shale]

goodnight, thanks for helping me, but imma see how to make the proof with more words and incorporating more vocabulary

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[vale bane]

isnt 11pi/6 out of the range

9a btw

omfg im dumb

nvm

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[granite tapir]

Prove P(B)=P(AB)+P(A'B)

Is this a coherent, good proof?

[granite tapir]

On the image, and drawing.

[wintry kindle]

well I see an image but yeah

it depicts that B = AB + -AB

and because these two sets are disjoint, P(B) = P(AB) + P(-AB)

[granite tapir]

Thanks @wintry kindle

[wintry kindle]

np :)

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[tranquil pine]

is this correct

[obsidian lake]

Someone please help me answer question 1a and 3a questions with working out!

[tranquil pine]

or this idk

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[spare glacier]

How to do 2 and 3?

I’ve tried them both, it involves lim x -> -inf sinx, or lim x -> -inf cosx

for number 2 since there’s an e^x and as x approaches -inf, then e^x becomes 0

So it it becomes 0/-inf which is 0

As for number 3, idk

<@&286206848099549185>

[trim crown]

it's actually not that hard

for 2 use -2<sinx+cosx<2

for 3 use -1 < sinxcosx < 1

[spare glacier]

Wait why

Where’d u get those

[trim crown]

-1<=sinx<=1 and -1<=cosx<=1

you just add them

[spare glacier]

Damn what the fk u can do that?

Okok

[spare glacier]

How about this tho

If u multiply them

And the lower bounds being (-1)

it can become 1?

Or do u do like (-1,1) x (1,1) = (-1, -1, 1, 1) = -1 <= x <= 1

[spare glacier]

Number 2 becomes 0/infinity

Is that alright??

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[spare bone]

let's say I hate a matrix, 4x4, already defined. and the result vector length 4, already defined. how do I know what vector I multiplied the matrix by to get the result? Also is it possible to implement this in a program?

[torpid sequoia]

so you have a matrix M and a vector b and you know that Ma = b (or possibly aM =b), and you want to find a?

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[spare bone]

Yes
I think that's what it means
This is what I saw, ξn and f(ξn) are things that I know

[torpid sequoia]

ah you're doing computer graphics aren't you

no, wait, this is siomething different

so you have an equation of the form Ax = b, where A is a matrx and x and b are vectors

and you want to solve this equation for x

right?

[spare bone]

It's about approximation functions :)
I haven't taught enough linear algebra (?) at school
And yes I want x from defined A and b if that's possible at all.

[torpid sequoia]

this is linear algebra, yes

so if this was a "regular" algebra problem you'd just divide both sides by A. but you can't really divide by a matrix. but you can multiply both sides by the inverse of A, called A^-1

so if you left-multiply both sides of that equation by (A^-1), you get (A^-1)Ax = (A^-1)b. (A^-1)A = I, by definiiton, and Ix = x, so you get x = (A^-1)b.

(thjis is basic linear algebra, which you don't know yet, but you can learn it on your own if you want)

so your question comes down to "how do i find the inverse of A and can i write a program for this"

[spare bone]

This seems understandable

[torpid sequoia]

while i could try to teach yuou how to mechanically compute the inverse of A (there are many algorithms) if you're doing this in a programming context you may actually havce access to code to do this already

that matrix in particular is fairly easy to invert by hand (because of all the 1s) but it would take me at least an hour to teach you since you're starting from scratch in linear algebra

[spare bone]

Yea... I'm willing to learn, I mean I'm going to graduate from hs next month which didn't really teach me that except arrow shaped vectors
I'm maybe going to join university next year but working on this problem after that seems too late

Also links to resources on how to compute inverses might be helpful, it doesn't need to be performant and making it or at least understanding myself is not gonna be bad anyways.

[torpid sequoia]

https://www.youtube.com/watch?v=Y4HCnVNl8xQ&ab_channel=Mulkek may help

there are a numbe rof other videos laong this line on youtube if that one doesn't do it for you

is this iin connection with a particular programming project, and if so using what languages and systems?

finding inverses by hand is very grindy and error prone

[spare bone]

Yes, it's connected to my personal project which needs minimax approximation of some function which needs to have a precision more than double precision floats (~= 16 digits)
So, for example 20 or 30 digits, or something like that
And I'm implementing a program that builds the polynomial with some degree to approximate that function so that I can regenerate any time or adjust any configuration as needed

[torpid sequoia]

so are you looking to solve that euqaiton numerically or symbolically?

(i'm a software engineer, ydon't worry about going over my head)

[spare bone]

What does numerically or symbolically mean?

[torpid sequoia]

did yuou want to get a formula that will give you the vector in terms of your ξ values or are you looking for specific numerical solutions for a given input

there's some techniques in (fairly advanced) linear algebra that can be used to rewrite that euqation but it would take a while to learn them

it's probably easier if you want a symbolic solution to solve it using row reductions, but you'll end up with a fairly ugly mess

if you want a numeric solution, i'd just prep a matrix and use a standard linear algebra library (like the one in NumPy, if you use python) to find the inverse

[spare bone]

Preferably a formula, because I want to run the program each time I want to generate the polynomial with different number of terms for example

If that's not what you meant sorry
Not good at math terms :(

[cyan kayak]

Here's an explicit solution, but it's pretty long and ugly: https://semath.info/src/inverse-cofactor-ex4.html

[torpid sequoia]

yeah exactly

like i said, linear algebra problems tend to get grindy with even relatively low dimension

[cyan kayak]

Up to you if you want to copy this into your program. There is probably a way to group adjugates to reduce the number of calculations, but be ready to massage a lot of code.

[torpid sequoia]

if yuo're looking for numerical solutions i'd use a numerical inversion routine, like numpy.linalg.inv

[cyan kayak]

Well, it sounds as if he is using an arbitrary precision arithmetic library, so he probably can't also use numpy

Though, a lot of libraries will provide helpful functions.

[torpid sequoia]

yeah, in that situation i'd probably use sagemath (and in fact just did)

the thing is, it's brutal

[cyan kayak]

Maybe Flint? https://github.com/flintlib/flint/

Flint has the added benefit of having a very high quality arbitrary precision arithmetic core based on ball arithmetic.

[torpid sequoia]

the upper left element in the inverse is ((zeta_0^2 - zeta_3^2 - (zeta_0^2 - zeta_1^2)*(zeta_0 - zeta_3)/(zeta_0 - zeta_1))*(zeta_0 - zeta_2)/((zeta_0^2 - zeta_2^2 - (zeta_0^2 - zeta_1^2)*(zeta_0 - zeta_2)/(zeta_0 - zeta_1))*(zeta_0 - zeta_1)) - (zeta_0 - zeta_3)/(zeta_0 - zeta_1))*(1/(zeta_0 - zeta_1) + (zeta_0^2 - zeta_1^2)*(zeta_0 - zeta_2)/((zeta_0^2 - zeta_2^2 - (zeta_0^2 - zeta_1^2)*(zeta_0 - zeta_2)/(zeta_0 - zeta_1))*(zeta_0 - zeta_1)^2))/((zeta_0^2 - zeta_3^2 - (zeta_0^2 - zeta_1^2)*(zeta_0 - zeta_3)/(zeta_0 - zeta_1))*(zeta_0 - zeta_2)/((zeta_0^2 - zeta_2^2 - (zeta_0^2 - zeta_1^2)*(zeta_0 - zeta_2)/(zeta_0 - zeta_1))*(zeta_0 - zeta_1)) - (zeta_0 - zeta_3)/(zeta_0 - zeta_1) + 1) - 1/(zeta_0 - zeta_1) - (zeta_0^2 - zeta_1^2)*(zeta_0 - zeta_2)/((zeta_0^2 - zeta_2^2 - (zeta_0^2 - zeta_1^2)*(zeta_0 - zeta_2)/(zeta_0 - zeta_1))*(zeta_0 - zeta_1)^2)

and the others are no better

[spare bone]

I don't know python, but in the language I used, Go, there is gonum which doesn't go beyond float64 precision
But the number of calculations is not a problem for now, I'll thinking hardcoding the solution in the article
Might be ugly, but not bad for the starting point imo 🤔

[torpid sequoia]

ah go

i'm admittedly not aware of any extended precision libraries for Go

[cyan kayak]

I am not either, but I have avoided Golang

I'm more of a Rust guy

[torpid sequoia]

there is math/big apparently

https://pkg.go.dev/math/big

arbitrary precision

[spare bone]

oh yes there is, it's not that... big though, it definitely lacks many features

[cyan kayak]

Well, if you can find CFFI bindings to Flint, that's what all the big boys use.

[spare bone]

big as in library, not the number

[torpid sequoia]

yeah, largely this is because people doing this sort of work are more liekly to use python or julia in my experience

[spare bone]

I'd agree for that, sadly

[torpid sequoia]

go is great if you're writing microservices in google's ecosystem... otherwise, not so much

[spare bone]

I have been writing it for a year it's been great for me

[cyan kayak]

I won't speak to Golang's strengths and weaknesses because I lack the hands on experience to make it appropriate, other than to say I don't really agree with some of the design choices.

[torpid sequoia]

i've been a software engineer for nearly 40 years, so i am in a position to have opinions :)

[cyan kayak]

Oh gosh, someone actually older than I am in this server

I've only been doing this professionally for about 20

[spare bone]

I'm getting bit offtopic, It definitely sounds cool tho
Like I was born 17 years ago

Can't imagine me coding since -3 yo

[torpid sequoia]

i'm being a bit loose with the help channel format because you're clearly working on a personal project rather than a homework assignment

the ... unusual structure of the matrix in this problem makes me think ther emight be a way to get it to a more-easily invertible form using a change of basis or some other manipulation, especially if the zetas are not arbitrary

but my linear algebra isn't strong enough for that

[spare bone]

Thank you for the information tho you two
I definitely learned a ton
I gotta go take a bath, sorry if the channel closes on timeout, it happened multiple times in the past xD

[torpid sequoia]

i took linear algebra in 1990 (1989? hard to remember at this point) and have forgotten almost all of it

good luck on your project

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[lapis atlas]

how can I calculate the matrix element for this interaction?

[lapis atlas]

i know that the propagator for quarks is $\frac{i}{\gamma^{\mu} q_{\mu} - m}$
and the propagator for the gluon quark quark vertex is $-i\frac{g_{s}}{2} \lambda^a \gamma^{mu}$

[soft zealot]

Sneha Joshi

[mental roost]

!15m

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[mental roost]

Might wanna check #old-network , if you haven't

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@lapis atlas Has your question been resolved?

[lapis atlas]

ok

<@&286206848099549185>

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[pale hatch]

the statement is
$$
\prod_{k=1}^{n-1} \frac{1}{k(k+1)} = \frac{3}{2} - \frac{1}{n}
$$
so I think the fallacy is in the base case itself since the LHS is undefined for n = 1 and what's written in the question is actually for n = 2
is that reasoning correct?

[soft zealot]

Frisk17

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@pale hatch Has your question been resolved?

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@pale hatch Has your question been resolved?

[midnight sparrow]

Yes the initialisation is not correct for n = 1 even for n = 2 and after

The correct formula is 1-1/n for n>= 2

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[robust oyster]

I do not understand how the equations for,

revenue (0.19-0.000002x)
& cost (0.098x-0.0000005x^2)

equal (0.092x-0.0000015x^2)

When the equation says,
Profit= revenue - cost

Why is it not,
(0.19-0.000002x)-(0.092x-0.00000015x^2)?

<@&286206848099549185>

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[robust oyster]

<@&286206848099549185>

[robust oyster]

My bad

Should I open a new channel?

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[tidal stirrup]

How do I solve this

[ivory vessel]

,rccw

[tidal stirrup]

I tried corresponding angles dae and cbf using parallel lines da and cb but I don’t know if they are actually corresponding angles

Even if they are I won’t fill in all the boxes

I also tried dae congruent cba but I don’t know what to go from there

[ivory vessel]

prove triangle DAE and CBF are both congruent

its a right triangle hyp-angle case

[tidal stirrup]

Idk how to prove the legs

I assume u mean hyp-leg theorem cuz I haven’t learned hyp-angle if that is a thing

@ivory vessel sorry for ping me still need help

<@&286206848099549185>

(idk if this ping break rules since someone did help partially but I did wait 15 minutes)

[final saddle]

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[lapis knot]

did i do something wrong here? because this is the actual answer

[shut gazelle]

Look at the variables

You have x1, x2, x3, and x4

Not x1, x2, and x3

[lapis knot]

oh right

[lapis knot]

thx

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[warm ether]

these are percentages in decimal form right?

[strong widget]

yes

[warm ether]

what other info is there

[warm ether]

so youre having an issue with d?

[strong widget]

d and f

[warm ether]

any ideas

[strong widget]

nope

[warm ether]

how would you find the percentage of a total

[strong widget]

its 100%

[warm ether]

say i had x of a total y, how would i find the percentage x is of y

[strong widget]

divide x by y

[warm ether]

thatll give you the decimal sure
so if x/y=D then x=y*D

[strong widget]

yeah

?

[warm ether]

so just multiply the total by the percentage of boys?

[strong widget]

so like 0.56(1.00)

[warm ether]

no

the actual total number of students

[strong widget]

0.56(200)

i didnt see the 200

thx\

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[stark apex]

what is this rule?

[warm ether]

chain rule

[stark apex]

how?

[warm ether]

wdym by how?

[warm ether]

the chain rule is stated there

[stark apex]

i thought the chain rule was when the exponent goes to the front and utake teh derivative out

[warm ether]

thats just an application of the chain rule

[stark apex]

oh

[warm ether]

this is the generalised chain rule

[stark apex]

howd they get -1 ?

and how were they able to plug in f'(3) into f'(u) because i thought 3 = x

[warm ether]

the argument of f here is g(x) and g(2)=3 so youre doing f'(3) *g'(2)

g'(2)=-1, f'(3)=6 so -6 is the product

[stark apex]

ohhhhhhhhhhh

Ok ty

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[warm ether]

np

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[stark apex]

Is this right?

this is the teachers and this is mine

Oh shoot when you multiply two terms with an exponent you add the exponent

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[stark apex]

Oops

.reopen

[final saddle]

✅

[hard spire]

yes, yes you do lol

[stark apex]

😢

[hard spire]

do you still need help?

[stark apex]

U can help me with another question?

[hard spire]

absolutely!

[stark apex]

😄

[hard spire]

its what im here for lol

[stark apex]

Ok one sec theres this one question

What does it mean to find the rate of change ?

[hard spire]

rate of change is slope

[stark apex]

Ohhhhhhhhhhh

So I find the derivative?

[hard spire]

pretty much, yeah

then evaluate at the given point

[stark apex]

Can U explain this like your talking to a 5th grader

Why does the prime of h'x become like that

[hard spire]

okay, so this is the best way i can explain it. derivative of the outside times derivative of the inside

so 5(x^2+4x)^3 would derive to 15(x^2+4x)^2 * (2x+4)

[stark apex]

g'x is the inside?

[hard spire]

yes

[stark apex]

ohhhhhhh

genois

genius

[hard spire]

i try lol

[stark apex]

But wheres the f(g(x) in all of this

[hard spire]

g(x) = x^2+4x

f(g(x)) = 5(g(x))^3

[stark apex]

OHHHHH

[hard spire]

for f(g(x)), look at g(x) as a variable

like 5x^3

[stark apex]

Ohhh ok

[stark apex]

and u multiply it by the derivative of the inside

I see now

[hard spire]

exactly

i think a 5th grader could understand derivatives if they were explained to them like that 😂

[stark apex]

Yeah 5th grade me would definitely not understand 😭

Can I ask one more question

[hard spire]

so lets work through your problem

yes you may

[stark apex]

Not sure how to solve this?

This is how he solved it but i dont geti t

[hard spire]

at what step are you lost

[stark apex]

when he does

[hard spire]

so you're confused about how he took the derivative?

i can help

so basicallyyyyyy

there are 2 real, non insaine, ways to do it, you will need both eventually, but lets stick with the easier one for now

[faint smelt]

just differentiate it and make it positive (ie greater or equal to zero) because differentail of a function is slope of the graph

[stark apex]

Oh so did he use the quotient rule here?

Im not that intuitive idk why he chose to differentiate it because I dont understand the wording of the question

[hard spire]

ohh okay

so you know what a tangent line is, right?

[faint smelt]

did you even read my text bro ?

[stark apex]

Yea its when the tangent line only touches one point

[hard spire]

correct

do you know how to find said line

[stark apex]

Yes sorry im still confused tho

[stark apex]

Find the derivative

[hard spire]

and thennnn

[faint smelt]

slope of the curve = differential of the given function

function represents curve

[stark apex]

So what is all that nonsense about "what condition on a b c and d ensures that each tangent to the graph has a positive slope"

[faint smelt]

question is telling you to find the condition on which graph has a positive slope meaning positive differential

[stark apex]

Ohh ok

So how do we prove that the derivative is positive

[hard spire]

critical numbers

[faint smelt]

basically the differential has a,b,c so when youll make it positive youll get an inequality relating a,b,c and that is the conditon the question needs you to find

[faint smelt]

you dont need to prove that, the question states that graph has a positive slope, it wants you to find the relation between, a,b,c for it

[stark apex]

Oh ok

How do i find the relationship

The inequality

[hard spire]

with your critical numbers

[stark apex]

I will use my critical thinking

[hard spire]

so basically, you are going to set the derivative of the function equal to zero, and solve for all x's

[stark apex]

Wtf even is thsi answer

[hard spire]

thats step one

[stark apex]

Oko

[hard spire]

yes.

now this question is mega dumb, because it gives no real values

so you cant actually find where it is

but that is how you would do it

[stark apex]

oh ok if its dumb im not wasting the little brainpower i have left on it

[faint smelt]

my boy, (cx+d)^2 is always positive since square of any variable or number is always positive

[stark apex]

Screw that question

[stark apex]

Oh Wait ur right

[faint smelt]

so you just need teh numerator to be positive so the whole differentail becomes positive

[stark apex]

Oh

[faint smelt]

numerator IS ad-bc , you need it to be greater than zero ie positive and that is the final answer

[stark apex]

Oh ok

Thank u guys

[hard spire]

but you cant find the actual interval, because the denominator is a big part in the actual interval

but that is technically right

[faint smelt]

dosent matter

we dont need interval

nor the values of x

[stark apex]

Guy s why tf is physics in my calculus homework 😭 😢

[faint smelt]

denominator is positive thats all we care about

[hard spire]

oh, we bout to cook

[faint smelt]

that was math not physics

[faint smelt]

frfr ong

[hard spire]

so basically, do exactly what i said before. we do need intervals for this one babyyy

[stark apex]

my brains alr cooked :/

[hard spire]

derive it

then set equal to zero

solve for x

[stark apex]

ooh

[hard spire]

or, t rather

[stark apex]

thats why he set it equal to 0

[hard spire]

ohh, that was his work. i was about to say, dang that was pretty fast

[stark apex]

yea thats the teachers he gives answers to the homework

[faint smelt]

so look, differentail of s (ds/dt) is velocity, and when velocity becomes negative is less than zero thats when the object changes direction

[stark apex]

can you explain like your talking to a 3rd grader

[faint smelt]

just differentiate the function s and put it less than zero

[hard spire]

f'(x) is velocity, f''(x) is acceleration. its a good thing to know

[stark apex]

Is that why they say second derivative

[faint smelt]

rate of change of position is velocity

when velocity is positive that means it is moving in the same direction it was always moving ie it hasnt changed direction

[stark apex]

oh ok

[faint smelt]

when it becomes negative it means direction is reversed

[faint smelt]

usually right side is positive direction and left is negative direction

because x axis

[stark apex]

so when we set the equation to 0 we are seeing the number of time in seconds when the position is 0?

[hard spire]

no, we are seeing when the particle turns around

[stark apex]

😢

[faint smelt]

no we are seeing when it stops to turn around

[hard spire]

this is the derivative function. of it were the regular function, you would be correct

[faint smelt]

ds/dt = 0 = velocity = speed zero

[stark apex]

ohh ok

[faint smelt]

just find derivative of s and put it equals zero @stark apex

then youll find a value of 't'

that t is your answer

[stark apex]

oh ok

[hard spire]

ive gots to go now, been nice helping you

[faint smelt]

is the answer 2sqr2

[stark apex]

tysm

[hard spire]

np

[stark apex]

this is the teachers answer

[faint smelt]

yeah sqr8 is same as 2sqr2

you know that right ?

[stark apex]

NO

😭

WTF?

[faint smelt]

bro

what grade are you in ?

[stark apex]

12..

[faint smelt]

what country ?

[stark apex]

Canada

[faint smelt]

alr

its basic math

[stark apex]

I know this if i take time to think

[faint smelt]

idk how you not know that

[stark apex]

Its simplifying radicals

[faint smelt]

yeah exactly

[stark apex]

But i always sucked at that

[faint smelt]

np bro i do too

[stark apex]

Anyways ty for ur help im gonna spend my night studying biology (the better subject)

[faint smelt]

haha alright

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[terse girder]

how would i do this question?

[terse girder]

ive tried expanding it

also love the otter

[magic sparrow]

What do you mean?

[terse girder]

turning it into (4x+48)^2=120

then using it to go into general

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[final saddle]

Please don't occupy multiple help channels.

[crimson cave]

I’m not

[lusty pecan]

close #help-39

[tiny gorge]

you are though

[lusty pecan]

can you show the full question?

[crimson cave]

Yeah sure

The question was “Each relation shown defines y as a function of x. Which function has the greatest rate of change?”

[lusty pecan]

yeah

do you know how rate of change is shown in the graph of lines?

[crimson cave]

No, can you explain?

[lusty pecan]

basically y depends on x, so the rate of change is how y changes when x changes

[crimson cave]

Rise over run?

[lusty pecan]

yep

it's called the slope of the line

[crimson cave]

Ah ok

[lusty pecan]

do you know how to calculate slope?

[crimson cave]

No

How

[lusty pecan]

well, like you said, it's rise over run

[crimson cave]

Yeah

I thought it was something different lol

[lusty pecan]

ah alright

slope refers to the m in y = mx + b

the last thing you need to know to solve this problem is how to find slope without a graph

[crimson cave]

How would I do it in like the “A”example?

[lusty pecan]

yeah so

you can think about it graphically or algebraically

graphically it's rise over run between two points

so you see how they give you two points

you find how much you climb upwards/downwards from the bottom point to the top point and divide that by how much you climb to the right/left from the bottom point to the top point

[crimson cave]

But in A they only said y= 1.3x + 1

[lusty pecan]

ah my bad I thought you were referring to B

rate of change, or slope, refers to the m in y = mx + b

[crimson cave]

So it would be 1.3 in that one?

[lusty pecan]

yes

[crimson cave]

And then we compare all the rate of changes and see which one is the greatest

[lusty pecan]

yes

[crimson cave]

K thanks

Wait

Nvm

I got it

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@crimson cave Has your question been resolved?

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[ivory vessel]

this is called monty hall problem

important detail you should remember that this is a television game show

[slim saddle]

what does that hv to do with math-

[tranquil pine]

it was explained

there

[ivory vessel]

because thanks to it, we can assume that the host will never choose the door with the prize

this fact can change the answer

[slim saddle]

oh

how am i meant to get to the answer

[ivory vessel]

well, analyze the problem first

whats the chance the contestant will choose the prize door?

[slim saddle]

1/3?

[ivory vessel]

yes

now lets label each door as 1, 2 and 3

lets say you choose door 2, but dont know whats in there yet

now the host opens the door 3, and reveals theres nothing in it

[slim saddle]

mhm

[ivory vessel]

based on your intuition, do you think you should change, and whats your chance of getting the prize now?

[slim saddle]

yes and chance is 1/2

[ivory vessel]

now, this would be correct if the host chose to pick the door randomly

but, this is a tv gameshow, and the host will never pick the prized door

therefore these are not 2 independent event

[slim saddle]

wait wat

so is the probability like 1 and 0?

[ivory vessel]

no

i suggest you draw a table of events

||doing so will give you the fact that if you switches, you actually have 2/3 chance of winning||

[slim saddle]

sorry i dont get how to draw the table of event

s

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[odd crane]

How would i do #9

What i got so far

Would i do answer indefinite integral?

Since only one x value is defined?

[trim crown]

We have two end points

One when 1/x = 1/x^2

[odd crane]

Oh yeah

[trim crown]

One is x = 2

[odd crane]

Would my bounds be 1, and 2

?

[trim crown]

Yep

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[magic ether]

i found the derivative

it is cot2x

but now i need to do [f(x)]^2

so what is (cot2x)^2?

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[magic ether]

.close]=

.close

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[frosty hatch]

how would i go about solving question a?

i dont quite understand the wording and how the information provided relates to the equation

[ivory vessel]

the wording is weird

they practically gave you x interxept and y intercept

[frosty hatch]

oh ok

that cleared things up

ty

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[tranquil pine]

I am really struggling with understanding the derivation behind the surface area in (3) and (4)

[tranquil pine]

i kind of get the idea behind (2) but the rest are just very unintuitive

Can anyone mind explaining them to me or link appropriate resources regarding those two formulations/the general topic?

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@tranquil pine Has your question been resolved?

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@tranquil pine Has your question been resolved?

[tranquil pine]

.close

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[unborn sun]

what is the problem in english

[final saddle]

@thorny folio Has your question been resolved?

[deft ravine]

Ich nehme an F ist die Verteilungsfunktion?

Ok, das ist die Verteilung einer diskreten Zufallsvariable

Weißt du, wie du die Wahrscheinlichkeitsfunktion bestimmen kannst? Also P(X=3)?

Ja, das kannst du einfach ablesen

Nur ist die Frage wie du auf die 0,4 gekommen bist?

Ja, aber du springst von 0,1 auf 0,4

Also springst du ja nur um 0,3 nach oben

Verteilungsfunktionen sind rechtsseitig stetig

Das war im Bezug darauf gemeint

Wenn du eine Folge nimmst, die von oben gegen 3 geht, dann muss F(x_n) gegen F(3) gehen

D.h also F(3) = 0.4

Und F(2,999999999) = 0,1

Woher hast du das?

Ich sehe du hast einige Verständnisschwierigkeiten

P(X=x) = F(x) - F(x-)

Wobei F(x-) der linksseitige GW ist

F(3) = 0,4

F(3-) = 0,1

[deft ravine]

.

0,4-0,1 = 0,3

[deft ravine]

Das darfst du nicht vergessen

Also die Verteilungsfunktion um X= 3 sieht so aus: Falls x < 3 ist sie 0,1. Für x >= 3 ist sie 0,4

Das siehst du übrigens auch an dem Punkt

F(3) = 0,4

Siehe Graph

Du weißt, dass es einen Unterschied zwischen der Verteilung F(k) und P(X=k) gibt?

F(k) = P(X <= k)

Nicht P(X=k)

Nein, augenscheinlich gesprochen ist P(x=3) wie weit du nach oben gesprungen bist

Weil bei 3 springt du von 0,1 nach 0,4 nach oben

Genau

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[deft ravine]

Bitte. Keine Ahnung ob du es wirklich verstanden hast oder nicht. Das behaupten viele, wenn sie keinem Bock mehr haben, aber lies dir bitte nochmal die Definitionen genau durch. Wenn du dir noch nicht über den Unterschied zwischen der Verteilung und der Wahrscheinlichkeitsfunktion im klaren bist, kann ich halt auch nichts machen

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[jolly eagle]

In proof of contradiction do we only want to contradict the assumption or can we also contradict the variables that are given?

[prime mortar]

It depends what does your problem say

[jolly eagle]

Oh I don’t have a problem right now I was just wondering in general

[prime mortar]

Oh I suppose you only have to prove the assumption wrong

[warm ether]

usually the given variables would be part of your assumptions anyway if im understanding you

[final saddle]

@jolly eagle Has your question been resolved?

[jolly eagle]

I see so if there was a problem like the difference between a rational number and an irrational number is Irrational and you do algebra to show that the irrational number is rational is that also a valid contradiction even if you’re not contradicting the assumption?

[warm ether]

you assumed that number was irrational

when you define a variable youre making an assumption

if you break that then the proof fails to hold and you have a contradiction

[jolly eagle]

Ahhhh I seeee ok

Thank you very much

[warm ether]

nw

[jolly eagle]

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[final saddle]

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[tranquil pine]

isnt this wrong? Like they made the bounds be in Cartesian when the integration variable is r still?

[tranquil pine]

it would simply be from 0 to 1 if it was in polar?

a_r denotes the unit vector r in cylinderical coordinates to be clear

[vital crag]

where's the figure

[tranquil pine]

its just the path

[vital crag]

why do you think the bounds are cartesian?

[tranquil pine]

is P(1,1) supposed to be Cartesian then?

ok that makes more sense then

thanks

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[final saddle]

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[tranquil pine]

whats your confusion

[rotund portal]

i don’t know how to do the question

[tranquil pine]

lol funny phrasing

this is in the UK?

i mean

its just a set of 2 equations and 2 variables

[tranquil pine]

ok so lets label "one portion of chicken pakora" as x and "one portion of vegetable curries" as y

why cant you solve the linear system?

[fathom walrus]

yea fr is it the uk

[tranquil pine]

Now, how would you represent "three portions of chicken pakora" and "four vegetable curries" in terms of x and y (which we just defined)

[rotund portal]

nah bro i forgot

[rotund portal]

oh it’s that

[tranquil pine]

3x + 4y = 32 and 4x+3y = 31

solve for x and y

[rotund portal]

oh yeah that alright thanks

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[strange shoal]

i understand how to solve the homogenous part

but what am i meant to use for the trial function

[green ibex]

https://tutorial.math.lamar.edu/Classes/DE/UndeterminedCoefficients.aspx

[final saddle]

@strange shoal Has your question been resolved?

[green ibex]

see this link

it demonstrates how to solve nonhomogenous ODEs like this one

[strange shoal]

yhyh

thanks for the help

[green ibex]

but wait

[strange shoal]

trial function is abt to be crazy 😭

[green ibex]

i don't think it even wants you to solve it

oh no wait it does

[strange shoal]

yhyh

[green ibex]

it says 'show' not 'verify'

[strange shoal]

yhyh

if it was verify

then u just put it into the equation

but even then

[green ibex]

well good luck with it

🫡

[strange shoal]

differentiating linear * exponential * sinosoidal 😭

[strange shoal]

appreciate it g

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[opaque rune]

Can someone please help me with this

[green ibex]

!showwork

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[green ibex]

!status

[final saddle]

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

[green ibex]

huh

.close

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[woven sentinel]

I Have a question

[woven sentinel]

The dervativee of something, and take x value will give u the slipe

Slope

What do the x value represent tho?

For example this i have to find derviative and find x value but how does that equal the answer?

[midnight crest]

could you send the full photo?

[pseudo knot]

,rotate

[woven sentinel]

S(x) equals y value at x and S'(x

[midnight crest]

,rotate

[woven sentinel]

And s'(x) at x point equals slope soo

[midnight crest]

ok so the x value after taking the first derivative in this context is what you're asking for right?

first think about the x and y values and what they mean in the original function.

[final saddle]

@woven sentinel Has your question been resolved?

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[tranquil pine]

idk what im doing, idk anything about e's

[magic sparrow]

do you know what a geometric series is

[tranquil pine]

yes

[magic sparrow]

Is this one

[tranquil pine]

so it is one if r is below 1

but

idk anything abt e

[magic sparrow]

No, it is one

[tranquil pine]

like legit nth, idk how i got this far inmath

[magic sparrow]

It is a convergent geometric series of the ratio is < 1

But this is a geometric series

Nonetheless

[fathom walrus]

,w eulers number

[soft zealot]

Results provided by WolframAlpha

Click here to refine your query online
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Requested by northsteve

[magic sparrow]

And that is e ^

[tranquil pine]

which is less than pi

ok

so it is 1 got it

[fathom walrus]

whyd it give me maserchoni...

[tranquil pine]

so a=1?

and r=e/pi

[fathom walrus]

if 'a' is first term of series yes

[tranquil pine]

i was gonna ask if i needa simplify it any further than the original equation but it doesnt seem to make me do that

thank you!

[fathom walrus]

just simplify, it looks cleaner

[tranquil pine]

idk how i would simplify it any further than this but also it js accepted the answer like that

[magic sparrow]

Looks good

could make common denominators

(Pi-e)/pi

And then flip it

pi/(pi-e)

I think is equivalent

[fathom walrus]

pi/pie pronounced is just pie/pie which is 1 so pi/pie = 1

🐺

[tranquil pine]

ohh ok

makes sense

[fathom walrus]

LOL

[magic sparrow]

Yah it’s just 1

Forget what I said

Pi(e)/pie = 🥧/ 🥧 =1

[tranquil pine]

i also need help on 1 more question

🙏

[magic sparrow]

Please tell us your doubts sir

[tranquil pine]

im a girl...

[magic sparrow]

Oh

[tranquil pine]

u

[magic sparrow]

What are your doubts

[tranquil pine]

is it just halfing each time

and i have to make a formula outta that

[magic sparrow]

I’ll have to ask my sir @rain compass

[fathom walrus]

how do u know its halving

heres what id do

find the area of the outermost corner triangle

[tranquil pine]

well, its at the midpoints no?

[fathom walrus]

idk it may not be that simple

just do this

find area of outermost corner triangle

then mutliply by 4 cuz theres 4 of them

[tranquil pine]

...

[fathom walrus]

then subtract that total area from the area of the big square

[magic sparrow]

This may be too complicated you should ask your sir if you don’t understand

[fathom walrus]

then theres the area of ur square number 2

[tranquil pine]

...

[fathom walrus]

what

[tranquil pine]

thats alot of math

what if it isnt that complicated

[fathom walrus]

cant take that chance...

or u can but

its up to you

[magic sparrow]

My sir says that math always has only 1 right answer

[fathom walrus]

ok but then why does my quadratic have two solutions...checkmate buddy

[tranquil pine]

so each side of the smaller triangle would sqrt of s^2

cuz its the hypotenuse of each triangle

[magic sparrow]

They aren’t real

[tranquil pine]

sqrt of a^2+b^2

but a=b

its a triangle

so 2s^2

but

its at the midpoint of each

so s^2

but

that makes no sense

nvm

[fathom walrus]

ok look at big square

[tranquil pine]

wait no

its the sqrt of s^4

no

[fathom walrus]

find x and y

[tranquil pine]

3

[magic sparrow]

!nosols

[final saddle]

As a helper, please do not give out answers that could be copied as a homework solution. Have the student work through the problem themselves and guide them along the way.

[fathom walrus]

OOPS!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

[fathom walrus]

yea x = 3 and y = 3

now find the area of that triangle

[tranquil pine]

why not js find the hypotenuse

and thats the side of the other square

[fathom walrus]

ok sure