help-0

[visual nest]

but i failed

so i went -2 down and went to the closets point

which was (2.5, -2)

and so i put for one of them a(2.5)/a(#) = -2

but then I used desmos and got # = -1.25

and then when i go to point-

wait

nvmn

@alpine sable

i got it

[alpine sable]

yeah

you could

[visual nest]

its a(2.5)/a(-1.25) = -2

[alpine sable]

literally just look at the y values

and find

an a(x) that is -2

and another that is 1

[visual nest]

its dividing

[alpine sable]

yeah

-2 /1 = -2

[visual nest]

does this work?

$ \frac{2.5}{-1.25}$

uh

why did it work?

[alpine sable]

space

[visual nest]

$$\frac{2.5}{-1.25}$$

[alpine sable]

$\frac{2.5}{-1.25}$

[ocean seal]

Umbra

[visual nest]

k

so

[alpine sable]

you tell me

should be obvious

[visual nest]

yes?

since that makes -2

and its in the graph

[alpine sable]

but the

question

is asking

$$\frac{a(a)}{a(b)}$$ not $$\frac{a}{b} $$

[ocean seal]

One person

[visual nest]

so a(a)/a(b) isnt a/b?

[alpine sable]

$$f(x) = 10x$$

is

[ocean seal]

One person

[alpine sable]

$$f(10) = 10$$ ???

[ocean seal]

One person

[visual nest]

no

-2 / 1 = -2

hmm

it works

does a(-3) + a(2) work?

[alpine sable]

why are you asking

you should know

[visual nest]

ohhh

i was doing the wrong thing

a(x) = the amount of steps (y) to get to a point

k

i see

k yes it works

a(-3) + a(2) worksa

works*

@alpine sable

I GOT IT!

the answer to number 14 is

$$ \frac{a(2.5)}{a(2)} = -2 $$

[ocean seal]

Umbra

[visual nest]

Am I right?

[alpine sable]

no

[visual nest]

uh

why?

[alpine sable]

what is a(2.5)

[visual nest]

2

[alpine sable]

no

[visual nest]

what??

[visual nest]

oh wait..

-2.

bruh

so that makes positive

omgg

this stupid graph

$$ \frac{a(2.5)}{a(-2)} = -2 $$

[ocean seal]

Umbra

[visual nest]

@alpine sable

this is the final answer

[alpine sable]

correct

[visual nest]

YES

FINALLY

ty

anyway im done

see ya and ty for the help

.close

[lone heart]

Channel closed

Closed by @visual nest

Use .reopen if this was a mistake.

[alpine sable]

Good job

[visual nest]

ty

[alpine sable]

bye bey

[visual nest]

bye

[lone heart]

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[merry arch]

from my answer book: How'd they get the -k/2 i always get a k or something like that

[lone heart]

@merry arch Has your question been resolved?

[merry arch]

<@&286206848099549185>

[visual nest]

is that kumon?

just wondering and also i cant help you with this because i havent gotten that far in math srry

you can always ask someone whos experienced with this

[merry arch]

yeah itis

[merry arch]

don't have time 😭 i have to try in two days if i want help (that's why im also asking here lol)

<@&286206848099549185> that can plz help me this time? (no offense umbra)

[visual nest]

uhm

cant your kumon instructors help you?

cuz i have been to kumon before but quit like 2 years after

[merry arch]

i can't go there rn for two days im too busy

[visual nest]

bru

k

its fine

ig

[lone heart]

@merry arch Has your question been resolved?

[merry arch]

i got it solved lol

[lone heart]

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[mighty crypt]

yo i need help

[mighty crypt]

so i got two lines

one that goes from 0-1

another that goes from 0.4-0.6

however there is a scale line which makes 0.4 into 0 and 0.6 into 1

and now i got two points

0.2 raw (aka from line 1) and 0.8 raw
it converts into the scale line of line 2 as -0.2 and 1.2
my question what is the math for this conversation

[lone heart]

@mighty crypt Has your question been resolved?

[lone heart]

@mighty crypt Has your question been resolved?

[mighty crypt]

If you didn't understand I am looking for a forumla that translates a point from Line 1 (0 to 1) to Line 2 (0.4 to 0.6), but in such a way that 0.2 in Line 1 becomes -0.2 in Line 2, and 0.8 in Line 1 becomes 1.2 in Line 2. This forumla must include the 0.4 and 0.6 which are sizes of line 2!

[lone heart]

@mighty crypt Has your question been resolved?

[lone heart]

@mighty crypt Has your question been resolved?

[maiden glen]

your transformation isn't very clear

or at least isn't linear

because the interval between 0.4 and 0.6 (which has length 0.2) is transformed into a region of length 1

but you're also saying that 0.2 should be sent to -0.2, which means that the interval between 0.2 and 0.4 (which has length 0.2) is transformed into an interval of length 0.2

[mighty crypt]

back

i found the issue

and i got it working

using chatgpt

bro told me i got it wrong, it knows what doing and i tried in my code and it worked

[upbeat eagle]

Also chat gpt can be wrong

It’s wrong with me 70% of the time

For whatever reason maybe it hates me

Like the thought process is probably correct but the math sometimes does not math

[left isle]

chat gpt is terrible at math, i would not recommend using it for specific problems

it may be able to explain concepts in math, but it sucks at doing the actual arithmetic

[lone heart]

@mighty crypt Has your question been resolved?

[tacit arch]

don't use chatgpt for math. waste of time

[tight inlet]

So what to use??

@tacit arch

[tacit arch]

Your brain????

Read a book?????

[analog sage]

help me out

im mad stuck

[tacit arch]

!help

[lone heart]

Please read #❓how-to-get-help

[lone heart]

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[tidal bane]

I am following this paper: https://arxiv.org/pdf/2008.07669.pdf

Background:
The gist of it is that they initialize the weight matrices of an discretized ODE with a orthogonal polynomial basis which behaves recurrently, in the form of c' = Ac + Bu, where A and B are weight matrices (N x N) and (N x C) respectably (N is a hyperparameter and C is the number of channels) , c are coefficients that describe the orthogonal polynomial at each time step (this behaves as the state that is passed between time steps) and u is the input at each time step.

I have been trying to, for fun, create a modified form of the chebyshev polynomial that behaves in a similar way to LegS (Scaled Legendre). I will put all the latex for this below. What I am having a question on is this:

Question:
I have been trying to understand the derivations more thoroughly as I have been going through this myself. I am wondering how, within section B.1.3, specifically section Derivatives of Chebyshev polynomials how the author goes from the first equation defined as:

\begin{align}
    2T_n(x) = \frac{1}{n+1}\frac{d}{dx}T_{n+1}(x) - \frac{1}{n-1}\frac{d}{dx}T_{n-1}(x) \qquad \text{for } n \geq 2
\end{align}

to the equation 11 also descibed in the same subsection.

Again, I will provide the derivations below

[ocean seal]

BeeGass

[tidal bane]

I could only get this far:

[tacit arch]

it's better to copy paste pieces at a time

and practice in #latex-testing

[tidal bane]

yeah I made a post here so that way I can reference the question better

[tidal bane]

https://discord.com/channels/268882317391429632/1142158143623807086

[lone heart]

@tidal bane Has your question been resolved?

[lone heart]

@tidal bane Has your question been resolved?

[lone heart]

@tidal bane Has your question been resolved?

[lone heart]

@tidal bane Has your question been resolved?

[tacit arch]

try to just stick to one place. adv-analysis is more apt than here since all your details are already there

.close

[lone heart]

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[alpine sable]

Hello, I think I have easy to solve problem but its kinda unclear for me and I can't find 100% clear answer anywhere, I roll a dice twice, I need probability A- that in 1st roll it would be "4" , B - there is only one "4" , my results are that P(A)=1/6 and P(B)=10/36, but now I need to get P(B|A) and i have no idea how to solve this problem, I get reult more than 1 so it's obv wrong

[azure swan]

The definition $P(B|A) = \frac{P(A \cap B)}{P(A)}$ is useful here

[ocean seal]

Jangler

[alpine sable]

I used exacly this definition

and i get 16 i dont know how

[azure swan]

What is your result for $P(A \cap B)$?

[ocean seal]

Jangler

[alpine sable]

16/36

[azure swan]

How did you get that?

[alpine sable]

in this you use P(a)+P(B)?

i did so

[azure swan]

No you don't

[alpine sable]

oh

so that's wrong

[azure swan]

You use that to calculate $P(A \cup B)$ IF A and B are disjoint

[ocean seal]

Jangler

[alpine sable]

it's unclear for me to be honest

[azure swan]

$A \cap B$ means, that A and B happen simultaneously

[ocean seal]

Jangler

[alpine sable]

i have 1st A than B

[azure swan]

Which results fit to die description: "The first number is 1 and there is only one 4?"

[azure swan]

What do you mean with that?

[alpine sable]

I roll 2 dices, in 1st roll I want to roll 4 P(A)=1/6, and second roll I want to have only one "4" P(B)=10/36 (but now im confused if its not wrong also)

[azure swan]

No. A is the set of all results, where the first of the two dice is 1 (and the second one can be any value)

B is the set of all results of the form (4, x) or (x, 4) with x≠4

$A \cap B$ is the set of results, which are both in A and in B

[ocean seal]

Jangler

[alpine sable]

set you mean amount of this possibilites ?

[azure swan]

No with set I mean a collection of results

[alpine sable]

so for A(4,1 4,2 4,3 4,5 4,6)

for B(1,4 2,4, 3,4 ,5,4 ,6,4 and that from A)

is it correct?

[azure swan]

Oh wait why did I read that the first result has to be 1, I'm dumb

Your notation is not correct

[alpine sable]

so what i should change?

[azure swan]

You should write $A = { (4,1), (4,2), (4,3), (4,4), (4,5), (4,6)}$

[ocean seal]

Jangler

[alpine sable]

yea thats right

[azure swan]

Also, (4,4) is in A

[alpine sable]

ohhh okay!

[azure swan]

B contains all the pairs of A without (4,4) , and the flipped pairs

So what is $A \cap B$?

[ocean seal]

Jangler

[alpine sable]

$B = {(1,4), (2,4), (3,4), (5,4), (6,4), (4,1), (4,2), (4,3), (4,4), (4,5), (4,6)}$

[ocean seal]

Thic

[alpine sable]

thats B right?

[azure swan]

No, (4,4) should not be there

[alpine sable]

$B = {(1,4), (2,4), (3,4), (5,4), (6,4), (4,1), (4,2), (4,3), (4,5), (4,6)}$

[ocean seal]

Thic

[azure swan]

(there should be exactly one 4)

Yes, that's correct

[alpine sable]

$A \cap B$? is what is diffrence between right?

[ocean seal]

Thic

[azure swan]

(you need to write \ before { and } because otherwise they won't be shown)

[alpine sable]

oh oki doki

[azure swan]

No that is the intersection of A and B

So the set of all elements, which are in A and in B

[alpine sable]

so its A without (4,4) $A \cap B = { (4,1), (4,2), (4,3), , (4,5), (4,6)}$

[ocean seal]

Thic

[azure swan]

Correct

[alpine sable]

how i use it now?

[azure swan]

So what is $P(A \cap B)$?

[ocean seal]

Jangler

[alpine sable]

5/36

[azure swan]

Yes

[azure swan]

Now you have to plug everything in and you are done

[alpine sable]

plug where ?

[azure swan]

In the definition of the conditional probability

[alpine sable]

$P(B|A) = \frac{P(A \cap B)}{P(A)}$

[ocean seal]

Thic

[alpine sable]

to this but written correctly

[azure swan]

Yes

[alpine sable]

because $A \cap B $ = $B \cap A $

right?

[azure swan]

Yes

[alpine sable]

so it 5/36/1/6 = 5/35 * 6/1 = 5/6

[azure swan]

Yes (but with 36 instead of 35)

[alpine sable]

yes yes missclick

great, thanks a lot I'm so dumb with this stuff

diffrent question should be posted in diffrent topic right ?

[tacit arch]

.close

[lone heart]

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• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
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[heady pollen]

!status

[lone heart]

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

[frank ridge]

1

[heady pollen]

may i ask what grade of school you are in?

[frank ridge]

10th

why

[heady pollen]

just curious

[frank ridge]

is this a very simple problem that a first grader can solve 😭

[heady pollen]

what i would do is get a function for the x value of the dot and a function for the y value of the dot

it is not easy if i am reading it correctly

[frank ridge]

do you know how to do it

[frank ridge]

i don't understand that

well i do

but how

[heady pollen]

that is the difficult part

we can solve this in two/three steps

first, we ignore the rotation

then the x value will just be 20(mi/h)*t

and y will be 0

then we ignore the velocity and only look at the rotation

that is the difficult part

[frank ridge]

that would be like

a sine

wave thingy

right

[heady pollen]

yes

[frank ridge]

because the dot goes up and down up and down

ok

keep going pls

[heady pollen]

we are looking at a wheel spinning without moving here

the dot starts at the bottom

so to easier discribe it we can rotate the whole thing (including the axes) so that the dot starts on the right side and moves counterclockwise

we want the x value, which after the rotation is the y value

so we use r*sin(omega t)

where omega is the angular velocity

which we will get later

try to get the y value with a similar approach

[frank ridge]

this part doesn't make sense

how did you get that

[heady pollen]

hmm

that is what you would write in physics

so i just used that here

usually we have something like sin(theta)

where theta is the angle

[desert cairn]

How do I get help

[heady pollen]

now we can rewrite this

#❓how-to-get-help

[frank ridge]

#❓how-to-get-help

[heady pollen]

$\theta=\frac{\theta}{t}t=\omega t$

[ocean seal]

Martin

[heady pollen]

so we get

$r\cdot\sin\theta=r\cdot\sin \omega t$

[ocean seal]

Martin

[heady pollen]

omega is what we call a angular velocity

it's units are radians/time

[frank ridge]

whattt

ok where does the r come from

[heady pollen]

radius

sin only ranges from -1 to 1

but we want it to range from -r to r

so we scale it up with a factor r

[frank ridge]

ok and i don't understand this either

[heady pollen]

here we just divide and multiplied by t, that is legal if t is not 0
then we call this theta/t to be omega

which is the angular velocity

it is like saying

$x=\frac{x}{t}t=vt$

[ocean seal]

Martin

[heady pollen]

this works because our velocity is constant btw, otherwise we would have to use diferentiation

so in total, the idea is:
-get x and y functions
-then notice that distance will be sqrt(x^2+y^2)
to get x and y:
-get the x and y of the entire wheel
-then go into the reference frame of the wheel where it stands on one point and rotates
-get x and y there as well
-combine what we get
to get x and y in the rotation:
-know that we pretty much always have x = r cos(theta), y = r sin(theta)
-however notice that we dont start on the right and instead on the bottom so we change it up a bit
(a drawing helps here a lot)
-feel pain by converting feet and miles into one unit

[frank ridge]

yeah

i dont understand a single word

[lone heart]

@frank ridge Has your question been resolved?

[heady pollen]

btw i think this is not what you are meant to do

this doesnt sound like something i did in 10th grade

that is what got me confused

[frank ridge]

as a tenth grader i definitely can't understand anything

is there a way to say what you said in a kindergartener level way

[heady pollen]

lets say we look at a car that moves

on the tire of the car is a dot

to describe the movement of that dot, we can say
the movement of the dot is the movement of the car plus the movement of the dot relative to the car

that is the idea

[frank ridge]

yeah...

ok

i understand the idea

i don't understand the functions stuf

[nova zephyr]

can someone verify if this is correct?

[frank ridge]

what

is this

[nova zephyr]

wdym

im just determining what value the vertical stretch and other stuff are

is this correct?

[civic stream]

this is an occupied channel

https://discord.com/channels/268882317391429632/488120190538743810

[lone heart]

@frank ridge Has your question been resolved?

[frank ridge]

…

[median oar]

Have you tried anything since

[chrome flower]

$\theta

[frank ridge]

Not really

I think I’ll just give up

[median oar]

Well it’s hard to help you if you don’t try

[lone heart]

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[lone heart]

Please don't occupy multiple help channels.

@real shore Has your question been resolved?

[real gazelle]

!status

[lone heart]

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

[real gazelle]

@real shore which one are you at

[lone heart]

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Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[daring totem]

!status

[lone heart]

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

[daring totem]

1

which one is it guuys? with justification ofc ;w;

<@&286206848099549185>

please guys send help

[plucky river]

I think number 1

[daring totem]

reason and motives?

please also tell the name of the waifu in your profile pic . . .

[plucky river]

Hm...

No

I can't solve this

[foggy current]

It's not 2 since the "door" and the "window" are on opposite sides

Not 3 because there should be a window on the front

And not 4 because the window should be on the back

I mean on the front

[plucky river]

Hah

Idk

[ruby current]

!15m

[lone heart]

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

[daring totem]

;w;

[plucky river]

Fate/kaleid liner Prisma☆Illya

[plucky river]

Found this anime on the internet

[daring totem]

looks like a very sexy anime lady}

[daring totem]

thank you sir .

[daring totem]

understood capitan, tysm!

[plucky river]

Her name is 'Iriyasufīru fon Aintsuberun'

.close?

[daring totem]

||very sexy indeed||

[daring totem]

.close

[lone heart]

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Use .reopen if this was a mistake.

[plucky river]

Yeah!!!!

[lone heart]

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Remember:
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• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
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[vapid steppe]

if you know a function is differentiable does that imply that the first derivative is continuous?

[summer dirge]

differentiable everywhere?

[vapid steppe]

sure

[tacit arch]

No

[vapid steppe]

what’s the counter example

[alpine sable]

That seems intuitive but I can't think of an example. Show us dark magic, Riemann

[alpine sable]

hacks

Ooooh this is like the topologist's sine curve

[median oar]

,w integral of |x|

[ocean seal]

Results provided by WolframAlpha

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

Requested by frosst

[median oar]

oh wait

that's just not differentiable, not discontinuous

[alpine sable]

,w graph x^2sin(1/x)

[ocean seal]

Results provided by WolframAlpha

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

Requested by labyrinthsplash

[summer dirge]

since I'm now curious, is there a counterexample that is not a piecewise function?

[tacit arch]

No idea. Make one up

[alpine sable]

Using the floor function you can (probably) define any piecewise function as a non-piecewise function

I'll let you judge whether that counts

I'm not motivated enough to explain how you'd do that

The construction is kind of long

@summer dirge Anyways, unless you have more questions you can now .close this channel

[summer dirge]

this wasn't my channel lol

[real gazelle]

@vapid steppe did that answer your question ^

[alpine sable]

frick

[lone heart]

@vapid steppe Has your question been resolved?

[vapid steppe]

wait

[lone heart]

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[wooden epoch]

Why is the formula for inverse proportion y = K/x?

[real gazelle]

Because when x goes up, y goes down

[wooden epoch]

but how did they get K/x?

[real gazelle]

y = 1/x is just a relation that shows up in a lot of places, hence why people gave it a name, "inversely related"

The K is just a "proportionality constant": it affects how strong the relationship between y and x is, but it doesn't change the qualitative behavior of it

[proven leaf]

Think about what happens as x increases, this means the denominator goes up, watch what happens with numbers: $\frac{1}{2}=0.5\to\frac{1}{3}=0.33\bar{3}\to\frac{1}{4}=0.25\ldots$.

Notice, that as we increase the denominator our output decreases in value, this is what \textit{inverse} proportion is. As x increases/decreases, y decreases/increases respectively :)

[ocean seal]

MrFancy

[proven leaf]

$k$ is just some constant, it's doesn't matter what we chose, the same principle still holds:

$\frac{2}{3}=0.66\bar{6}\to\frac{2}{4}=0.5\to\frac{2}{5}=0.4\to\frac{2}{6}=0.33\bar{3}\to\ldots$

[ocean seal]

MrFancy

[wooden epoch]

oohh okay i understand, where does the K come from though and why?

[real gazelle]

usually it's something that you measure experimentally

so you collect a bunch of data and then figure out the best "K" value that fits the data

[proven leaf]

$k$ was just chosen, we can choose any variable, it could $n$ or $b$ for all we care :) but generally you choose $k$ for this stuff

[ocean seal]

MrFancy

[wooden epoch]

sorry i didn't mean the letter chosen, i mean the value for k sorry for the miscommunication

[proven leaf]

for that you are usually given a set of points and have to find the inverse proportion from those points

[wooden epoch]

it is similar to gradient?

[real gazelle]

do you mean like y = kx?

if so then yes

the k serves the same function in that equation

[wooden epoch]

but isn't the gradient in a curve not a constant?

[proven leaf]

gradient is slope

[wooden epoch]

yeah

[proven leaf]

for y=kx, k is the slope, k is the gradient

[real gazelle]

Yes, the k in y = k/x is not exactly the gradient

But it serves a similar role in determining how steep the graph is overall

[wooden epoch]

ohh okay

[real gazelle]

The higher the value of k, the steeper the graph

[proven leaf]

https://www.desmos.com/calculator/elfsjm04kz

desmos is always a good way of visualizing it

[wooden epoch]

okay thank you guys! i appreciate the help

.close

[lone heart]

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[proven leaf]

[real gazelle]

no problem at all!

[lone heart]

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[split forge]

How to prove that 10 is a solidary number?

[upbeat hornet]

what do you mean by solidary?

[split forge]

solitary

[real gazelle]

Do you mean a number that doesn't have any friendly pairs?

[upbeat hornet]

can you provide the definition?

[split forge]

It's a number that doesn't have any friends according to mathworld

[upbeat hornet]

what is a friendly pair

[upbeat hornet]

Can you define “friend”?

[proven leaf]

10 is not a solitary number...

[real gazelle]

This appears to be an open problem

It is believed that 10, 14, 15, 20, 22, 26, 33, 34, 38, 44, 46, 51, 54, 58, 62, 68, 69, 70, 72, 74, 76, 82, 86, 87, 88, 90, 91, 92, 94, 95, 99, 104, 105, 106, and many others are also solitary, although a proof appears to be extremely difficult.

[split forge]

can you prove it please

[proven leaf]

yea I was looking at math world which said it's wasn't my fault

[proven leaf]

i wouldn't even know where to begin...

[split forge]

Says I have to prove it, teacher gonna whoop me if I don't put something in the answer

[real gazelle]

Well no one here can help you with it

[vale wigeon]

whoop as in give you actual, for realzies physical punishment?

[real gazelle]

Unless you misread the problem

It appears to not be known whether 10 is a solitary number

[split forge]

Could it be a trap question where I have to say this

[real gazelle]

We cannot help you figure out the intentions of your teacher

[split forge]

He's 45 and single, if that can help

He's a math tutor

[real gazelle]

I don't think we can help you with this any further

.close

[split forge]

dang

[lone heart]

Channel closed

Closed by @real gazelle

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[vale wigeon]

.reopen

[lone heart]

✅

[vale wigeon]

you should bring it up with the higher ups if he uses corporal punishment btw

like that's not something that a teacher should be doing in this day and age

@split forge

[ruby current]

or any day and age

[split forge]

I'm a big guy, don't worry about it, I'm just not good with maths so I need a tutor even if I'm old

I can take it, thanks tho

.close

[lone heart]

Channel closed

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[ruby current]

you want to prove that there does not exist $n$ such that $$\frac{\sigma(10)}{10} = \frac{\sigma(n)}{n}$$

[ocean seal]

tushar

[ruby current]

is that correct?

oh

[real gazelle]

(This appears to be an open problem.)

[vale wigeon]

big guy or not, it's still not ok to face the risk of physical abuse from his end!!!!

[split forge]

.close

[split forge]

All good

[lone heart]

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[proven leaf]

,rotate

[brittle current]

help pls

[alpine sable]

Do you know the formula for arc length?

[brittle current]

2 π r (θ/360°)

[alpine sable]

solve for theta

that is what a is asking

[brittle current]

ohh

thanks

[alpine sable]

Idk the easy way to solve (b).
But you can do it with some basic trig

[brittle current]

k

[lone heart]

@brittle current Has your question been resolved?

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[wheat isle]

How does this work?

[echo socket]

First, try differentiating (2x - b)^a

[wheat isle]

d/dx or d/da

[real gazelle]

d/dx

[wheat isle]

whats the derivative of b

[echo socket]

a is a constant, differentiating with respect to it would not make much sense

[echo socket]

b is a constant, so d/dx [b] = 0

[wheat isle]

o

2a(2x-b)^a-1 * 2?

oops

not 2a

just a?

[echo socket]

$a(2x-b)^{a-1}\cdot2$?

[ocean seal]

A Lonely Bean

[wheat isle]

yeah

[echo socket]

Okay, and we want this to be equal to 24x^2 - 24x + 6 for all x

[echo socket]

First of all, what degree does this polynomial have?

[wheat isle]

n-1?

[echo socket]

a-1 you mean?

There's no n

[wheat isle]

yeah well i only put n because n = some number but ig makes more sense to say a

[echo socket]

Yeah, and, since we want this to be equal to 24x^2 - 24x + 6, we need to make sure the degree of this polynomial is equal to 2 as well

So a - 1 = 2 and a = 3

Okay, so $f'(x) = 6(2x - b)^2$

[ocean seal]

A Lonely Bean

[echo socket]

Can you expand this?

[wheat isle]

wait where does 6 come from

oh power rule

3 from power and * 2 from the derivative

[echo socket]

2 * a = 2 * 3 = 6

[wheat isle]

ok

[echo socket]

Yes

[echo socket]

Try expanding the right hand side

[wheat isle]

b^2 -4bx + 4x^2

[echo socket]

Yeah, and don't forget to multiply by 6 to get 24x^2 - 24bx + 6b^2

[wheat isle]

yeah

[echo socket]

We want to find the value of $b$ such that $24x^2 - 24bx + 6b^2 = 24x^2 - 24x + 6$ for all values of $x$

[ocean seal]

A Lonely Bean

[echo socket]

Do you know what condition should two polynomials satisfy in order to be equal everywhere?

[wheat isle]

not sure

[echo socket]

The corresponding coefficients must be equal

[echo socket]

So, in this case we must have -24b = -24 and 6b^2 = 6

Can you solve for $b$ here?
[ \begin{cases} -24b = -24 \ 6b^2 = 6 \end{cases} ]

[ocean seal]

A Lonely Bean

[wheat isle]

has to be 1 right?

[echo socket]

Yes, b = 1

This is it, we got a = 3 and b = 1

[wheat isle]

ah okay cool

thanks

.close

[lone heart]

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[pallid basin]

is it just me or does the first solution here seem egregiously wrong

https://math.stackexchange.com/questions/175896/finding-a-point-along-a-line-a-certain-distance-away-from-another-point

[alpine sable]

would you mind posting the first solution here?

[pallid basin]

sure

[alpine sable]

ummm

no idea what they're saying

but sounds right

Think they're just using

similar triangles

to find the x and y

[tardy stag]

that's exactly right, they're doing something called linear interpolation between points 0 and 1

[pallid basin]

here is the original post for some better context

[pallid basin]

it just doesn't add up for me, if you have points (3, 3) and (4, 4) in euclidean space. They will have a distance of root 2. The points returns from using the answer formula is about (1.4, 1.4) if d sub t is 0.2

[alpine sable]

Do you know trig?

[pallid basin]

yea

[alpine sable]

hmm

[alpine sable]

you sure you aren't doing it wrong

I just did it in desmos and it's correct

If you know trig you should be able to come up with the solution yourself. (Maybe not the (1-t) part that's kinda hard :>)

[pallid basin]

I messed up yeah, the windows calculator isn't the most straight forward to use 😅 . The solution is correct

Thanks for the help!

.close

[lone heart]

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[toxic swift]

Hi I need help again

[toxic swift]

Would x3+y2+z3 be 96

Or 95

[ocean seal]

Couldn't find an attached image in the last 10 messages.

Aug 19, 2023, 7:00 AM

[mellow grail]

huh?

[vapid shuttle]

neither?

it is just a random listing of variables with no context

[gray isle]

depends

[remote heron]

sorry i was scrolled way the heck up mb

[vale wigeon]

@toxic swift please post the original question in full

[vale wigeon]

that's it?

[toxic swift]

Yes

[vale wigeon]

so no other instructions?

you have a blank sheet of paper that only has this expression on it? zero words written elsewhere?

[vapid shuttle]

Callisto can you answer this question for me?
A5-Z7+9M

[toxic swift]

No

[vale wigeon]

oh, i know.

you wanted to evaluate X^3 + Y^2 + Z^3 when X = 4, Y = 20 and Z = 69

,w 4^3 + 20^2 + 69^3

[ocean seal]

Results provided by WolframAlpha

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

Requested by ann_dec

[vale wigeon]

this will be neither 96 nor 95

[rose sigil]

wow how could we all have been so naive this whole time

[toxic swift]

Hold on theres more to the question

I forgot to take a picture of this

Would it be 97 then

[vale wigeon]

did you crop too much again

what is X^2 + Y^2 + Z^2 supposed to be

have to say you're making it very hard for us to help you

[toxic swift]

Ok lemme look

34

I think

[gray isle]

think?

[toxic swift]

Yeah

[gray isle]

is 34 written on the page or not

[vale wigeon]

conclusion:

you don't have a question.

[gray isle]

can you like take an uncropped original image, leaving nothing out nothing relevant to the question

[vale wigeon]

come back when you have a question to ask.

[toxic swift]

I do

[vale wigeon]

you've failed to show it to us, like three times now.

[vapid shuttle]

@rose sigil snow reference

[carmine reef]

Wouldn't you need a value for all three of those to constrain the variables?

Even knowing sum of squares shouldn't be sufficient

[rose sigil]

i love snow

[vale wigeon]

yeah also the first two equations are symmetric in X, Y and Z while the expression whose value we are (supposedly) asked for isn't!

but good luck getting that out of OP

[toxic swift]

The answer is 34 for the second one

[vapid shuttle]

"the answer"?

[gray isle]

where's 34 coming from?

where's this question coming from

[vale wigeon]

thin air

[gray isle]

from a book? teacher? worksheet?

[toxic swift]

It's on the page

[gray isle]

take a picture of the page

[toxic swift]

I did

[gray isle]

post the image of the page

[toxic swift]

Ok

[gray isle]

(the whole page)

[toxic swift]

Well it's on my computer

[vapid shuttle]

upload it from your computer

take a screenshot

[gray isle]

log into discord on the computer

[vapid shuttle]

like this

a screenshot

and then post it here

[gray isle]

snapshot

[vapid shuttle]

you cropped it

show the bottom line

not just the top two lines

[rose sigil]

why is the bottom equation cropped out wtf

[vapid shuttle]

bruh

[gray isle]

THE WHOLE APGE

[alpine sable]

Baby steps come on guys

[carmine reef]

Are you just typing this yourself

[alpine sable]

Don't make me want AnyDesk access bruh 😂😂

[vale wigeon]

this is a real patrick lid moment

[vapid shuttle]

this has to be intentional

I don't wish to live in a world where this is non-intentional

[alpine sable]

Last chance @toxic swift , full equation or idk mods EQUATIONS*****

[toxic swift]

Okay

[alpine sable]

Mind the 'S'

[toxic swift]

This is the full equation

[rose sigil]

🤣

[vapid shuttle]

then it is unsolvable

boohoo

[carmine reef]

Not solvable

[toxic swift]

Bruhhh

What is my math teacher giving me

[rose sigil]

what are you giving us

[vapid shuttle]

not this

[gray isle]

are you 1090% sure that you didn't omit anything?

[toxic swift]

?

[vapid shuttle]

,w omit

[gray isle]

took us asking you many times before 34 magically appeared

[ocean seal]

Results provided by WolframAlpha

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Upgrade to WolframAlpha Pro!

Requested by austinu

[subtle birch]

Are you constantly thinking so as to what to add more in the question. Like there is a high chance you would put some value for x^3+y^3+z^3 in a while (you made it yourself or your friend gave it to you)

[alpine sable]

Guide How fail someone nevertheless 101

[alpine sable]

I agree

[toxic swift]

I didn't make it myself my teacher gave it to me

[alpine sable]

Can you show us how you went to determine the answer as 97 UNLESS you put the values themselves, ie. Trial and error

[carmine reef]

Why did it take you so long to show the 34

[alpine sable]

Cuz it wasn't there

[toxic swift]

Yes it was

[vapid shuttle]

where did the 96 come from??

[alpine sable]

Only way to check if you're true bro

[alpine sable]

Show us your 96 working

silence does hit hard

[dull dove]

Isn’t this one of those solve and get one million US dollars questions?

[toxic swift]

I can't do it 😬

.close

[lone heart]

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[alpine sable]

Lmaoooo

Gotcha

[lone heart]

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[flat roost]

If im asked to prove a function ≡ another function, am i allowed to start from the RHS and convert that to the LHS or not? Thanks

[echo socket]

Surely

[flat roost]

thank you very much

.close

[lone heart]

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[alpine sable]

Do you have a question to ask

Ok

.close

[lone heart]

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[near apex]

Try removing helpers role from Roles perhaps if pinging is an issue.

[lone heart]

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[hollow vapor]

I don’t really know where to go. I can get the perpendicular distance and the gradient but i don’t know what to do with it

<@&286206848099549185>

[left isle]

maybe you could find the equation of the line that passes through the segment and use the point of intersection to find the distance between that and C, which you could then use to find the coordinates of D

there may be a simpler way, but that's what came to mind first

[hollow vapor]

AH I FORGOT ABOUT POINT OF INTERSECTION

[left isle]

lol

[hollow vapor]

THANK YOU

[left isle]

yeah then just equate the two

no problem lol

[hollow vapor]

🙏

.close

[lone heart]

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[lone heart]

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[split rose]

I have a few question about the answer.
Why answer is 4 i dont understand why D is false.

[winter light]

I don't understand what valid means

Should it be interpreted as the logic expression returning true?

[split rose]

yeah maybe

my sister study in python

[winter light]

Otherwise I would say they all are valid (for me valid = makes sense)

But are you given that the correct answer is 4?

[split rose]

yeah they said the correct is 4

[winter light]

Ok and you don't understand why it is true or why are the other answers not correct?

In other words, are you able to tell the result of the first expression?

[split rose]

I can remember a little bit about true false

like t or t = t , t or f = t

so i trying to make understanding about
A True and false = False right ?
B also false
C True
D False
E true

is that correct

[lone heart]

@split rose Has your question been resolved?

[winter light]

A and B yes, but pay attention to C, D, E

Let's start with E which is easier, ok? @split rose

[split rose]

ahhh in understand that have no false in this right ?

i mean all of them make sense.

so they can be true

[winter light]

Nope, the issue is a little more subtle

[winter light]

But yes, they all make sense, but we have to figure out which of those 5 answers gives False in output for some integers. If you look carefully at the question, they ask which of those 5 expressions is valid (i.e. returns True) for EVERY integer x we give in input @split rose

[split rose]

ahhhh

[winter light]

That's the key of all the exercise, yeah. I admit it was tricky precisely because of this

[split rose]

thank you man

you bring my brain back when i was young haha

[winter light]

The only thing now to pay attention to is answer C, because it seems to be always True, but not if x is 0 😉

[winter light]

Yeah, I feel the same lol

[lone heart]

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[late drum]

I’m struggling with Laplace transforms / partial fractions

Can someone pls help

part B of this question is what I am trying to answer:

[alpine sable]

Ur partial fractions are wrong?

Firstly

Your denominator for one of the fractions is a quadratic but your numerator is linear

[late drum]

oh yeah it should be = 1 right?

[alpine sable]

Yes

[late drum]

should they be A/(s+1) + B/(s+1) + C/(s+1)^2

[alpine sable]

No

[
\f1{(s+1)(s^2+1)} = \f A{s+1} + \f{Bs+C}{s^2 +1}
]

[alpine sable]

Also brb

[late drum]

what rule is this called?

[alpine sable]

It is how partial fractions are defined

The numerator is a degree lower than their denominator counterpart

[lone heart]

@late drum Has your question been resolved?

[late drum]

oh ok hold on im gonna give this a go

[late drum]

Is this right?

Oh wait

I didn’t sub right lol

should be (1/2)/(s+1) + (s+(1/2))/(s^2 + 1)

[alpine sable]

I think it's right

But let's verify

,w 1/((s+1)(s^2+1)) = (1/2)/(s+1) + (s+(1/2))/(s^2 + 1)

[ocean seal]

Results provided by WolframAlpha

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Requested by lexqa

[alpine sable]

Okay you fucked up somewhere

Let's see

[late drum]

i see where

when I set s =1

[alpine sable]

Ah yeah

2A

Actually it's all wrong yeah

Should be 2A + 2B + 2C = 1

[late drum]

B = -1/2

[late drum]

and then after I get A, B and C and sub back in I need to multiply by exp(-2(s+1)) right?

oh wait no

I just find the laplace transform of each of those partial fractions?

[alpine sable]

Yes

[late drum]

• the lapace transform of exp(-2(s+1))?

[alpine sable]

No hold up

First let's finish the partial fractions

We'll get to the Laplace

What did you get?

All in all

[late drum]

(1/2)/(s+1) + ((-s/2)+(1/2))/(s^2 + 1)

[alpine sable]

,w 1/((s+1)(s^2+1)) = (1/2)/(s+1) + ((-s/2)+(1/2))/(s^2 + 1)

[ocean seal]

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Requested by lexqa

[alpine sable]

Okay nice

But anyways yes

You now have

[
\cmap {\mathcal L}{\bmap{e^{-2(s+1)}}{\f1{2(s+1)} + \f{1-s}{2(s^2+1)}}}
]

[alpine sable]

This is what you are dealing with now @late drum

[late drum]

i see

i'm dealing with this rule:

right?

wait no this:

[alpine sable]

Yes

You are gonna be splitting the fractions too btw

The second one for example is just cos and sin

The first one will turn out to be e

[alpine sable]

This is after doing this

Anyways do it and show mr

[late drum]

alright ill give it a go

[late drum]

exp(-t)/2 for the first fraction and -sin(t)/2 for the second?

[alpine sable]

You should get like

Both cos and sin

Because

[late drum]

oh I see what you mean

[alpine sable]

[
\f{1-s}{2(s^2+1)} = \f1{2(s^2+1)} -\f s{2(s^2+1)}
]

[late drum]

yeah

[alpine sable]

Also where are Ur Heaviside funcitons

[late drum]

ok so it should be sin(t)/2 - cos(t)/2

i haven't done that bit yet

[alpine sable]

Are u sure u applied this?

No

You cannot skip it

You cannot do the Laplace transform for the insides first

[alpine sable]

It's why I wrote the L behind the e and not in front

Anyways just expand the e and do it concurrently

[late drum]

hmm

[alpine sable]

Like

U r doing the same stuff

[alpine sable]

Just apply this first

[late drum]

I am not sure how to 😞

[alpine sable]

[
e^{-2}\cmap {\mathcal {L}^{-1}}{\f{e^{-2s}}{2(s+1)} + \f{e^{-2s}}{2(s^2+1)} -\f{se^{-2s}}{2(s^2+1)}}
]

Does this help you

[late drum]

I think so, so I find the laplace transform for each fraction inside the brackets now?

[alpine sable]

Inverse Laplace*

But yes

You do

[late drum]

ok I can do that but why is there still an exp(-2) out the front?

[alpine sable]

Do you see $e^{-2(s+1)}$ here

[alpine sable]

What happens when u expand the brackets

[late drum]

oh right I see

[lone heart]

@late drum Has your question been resolved?

[lone heart]

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[alpine sable]

I have decided that this is linear, but I don't know how to construct the matrix representation of T in the standard bases of P2 and P3

[oak perch]

b is a isn’t

Like he said, find images of 1,x…

[alpine sable]

what?

[oak perch]

Again a is not linear

[alpine sable]

yes A isn't linear

B is linear

[oak perch]

For b find images of 1,x,…

[alpine sable]

how do i do that

[oak perch]

For example T(x^2)=1+2x+x^2

1,2,1, 0 for the third column, see

[alpine sable]

can you be a bit more specific

what do i do exactly

[oak perch]

Find matrix such that

(T(1), T(x), T(x^2))=(1 x x^2 x^3)A

And I just gave you the last column

It’s like a Picard triangle when you finish it

[alpine sable]

$\begin{bmatrix} 0 & 0 & 1 \ 0 & 1 & 1 \ 1 & 2 & 1 \end{bmatrix}$

like this?

[ocean seal]

kyou

[oak perch]

No

[alpine sable]

P(1) = 0x^2 + 0x + 1

[oak perch]

For forgot x^3

[alpine sable]

P(x) = 0x^2 + x + 1

[oak perch]

And if it’s P2->P2 it’s still wrong

[alpine sable]

ok i think i got it thanks

[oak perch]

Okay , np

Your position of 1 in the first column is very strange

Should like this

[alpine sable]

this is the matrix representation?

[oak perch]

Yeah

[alpine sable]

why 1 1 1 in the first row

[lone heart]

@alpine sable Has your question been resolved?

[oak perch]

Because coefficient of 1 in (x+1)^k is 1

[lone heart]

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[lone heart]

Available help channel!

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Remember:
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• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
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[eternal tulip]

Help I suck at geometry

[upbeat gorge]

!status

[lone heart]

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

[eternal tulip]

1

[upbeat gorge]

Ok so I’ll explain how I would analyze this problem

So we want angle CPB, right?

What angle will help us find CPB?

[eternal tulip]

APB?

[upbeat gorge]

Yes

Now, how do we find APB?

[lone heart]

@eternal tulip Has your question been resolved?

[eternal tulip]

Idk

[upbeat gorge]

Well we have triangle APB

[eternal tulip]

Yea

[upbeat gorge]

So we can take PAB and PBA and take that away from the sum of angles of a triangle

[eternal tulip]

Isn’t PAB and PBA the same triangle

[upbeat gorge]

Angles PBA and PAB*

[eternal tulip]

Isn’t that still same

[upbeat gorge]

Why are they the same

[eternal tulip]

What’s the difference between PBA and PAB

[upbeat gorge]

You tell me in what aspect are they the same

Ok, so here’s the key observation: what can you say about AP and BP?

@eternal tulip

[eternal tulip]

Oh

They are different line

[upbeat gorge]

Yes, but they are in a circle

Where P is the center of said circle

[eternal tulip]

Right

[upbeat gorge]

And A and B are points on the circumference of that circle

So what does that make AP and BP?

[eternal tulip]

Radius?

[upbeat gorge]

Yep

[eternal tulip]

Oh

[upbeat gorge]

And so what can we conclude on their lengths

[eternal tulip]

Idk

[upbeat gorge]

Well, all radii of a particular circle have the same length

So AP=BP

[eternal tulip]

Yea

[upbeat gorge]

That means triangle ABP is isosceles, yes?

So what can we say about angle PBA and angle PAB

[eternal tulip]

Angle A = Angle B?

[lone heart]

@eternal tulip Has your question been resolved?

[paper quartz]

How do I learn the Trigonometry table like the sin 30 is equal to and all?

[eternal tulip]

idk

alr i think i got the answer

[carmine reef]

Memorize sin 30, 45, 60, do the rest by comparing with unit circle

[shut carbon]

Hello, i need help with 5(b)

[paper quartz]

No, Like can you learn it mathematically

[carmine reef]

Ok both of you open your own channels

#❓how-to-get-help