help-10

[trim portal]

if you have a guarantee that such x exists, you could just start at x = 0 and increase x at every step

[manic moon]

Yeah natural number

[manic moon]

But that is a numerical method isn't it

Brute force

[trim portal]

it gives an exact answer in a finite amount of time, if such x exists

but yes, it is brute force

[manic moon]

Isn't there an algebraic way

[trim portal]

without knowing anything about f you cant make a better algorithm

[manic moon]

You know f

But you don't rely on specific cases of f

[kind hawk]

even knowing f, if you cant even evaluate the sum without actually summing it step by step, you are out of luck

[trim portal]

this is also a problem

[kind hawk]

sometimes you may be able to find precise asymptotic bounds which are good enough

[manic moon]

So it's impossible to have a nonpiecewise nonnumerical algorithm

[kind hawk]

but those would depend highly on f

[trim portal]

depends on f

[manic moon]

Yeah, that's a piecewise algorithm

Or whatever you call that

[trim portal]

but there isn't a general algorithm that could solve the problem for any f

[kind hawk]

I dont wanna say impossible cause maybe there is a smart way, but I would doubt it

[trim portal]

hmm

[manic moon]

Maybe something involving calculus

[trim portal]

f could be any computable function

[manic moon]

Let's say domain is reals

Just for simplicity

Oh wait there is a formula for polynomials

[trim portal]

isnt the domain naturals? since i is always gonna be a natural number

[manic moon]

Uhh yeah

[trim portal]

and you only need f(i)

[manic moon]

But domain of f

Oh righhhht

Yeah

Naturals

But let's say k is real

[kind hawk]

well, if the domain of f is the real numbers then you can do some tricks like approximating the sum with an integral

[trim portal]

You're looking for an algorithm that has K and f as inputs and returns x, right?

[manic moon]

And range is real

[manic moon]

Yeah

[kind hawk]

if that bound is good enough it does actually allow you to solve for x

but it will depend very highly on how nice f is

in general this will not work

[trim portal]

f is an input to the algorithm

[manic moon]

Yes

[trim portal]

there is no way that an alg that can solve this exists

[kind hawk]

do you realize how truly disgusting a general function f could be?

even if you assume that f is continuous or even smooth I doubt this will be possible

[trim portal]

f's domain is naturals

[manic moon]

well theres this for powers

[kind hawk]

powers are some of the nicest functions ever

and look how difficult even there the closed form is

[trim portal]

I doubt this would be any helpful to actually solve
sum = K

[kind hawk]

and then it still amounts to solving a polynomial of high degree, which is quite literally impossible in general

[manic moon]

Well I actually came up with this q just by thinking if theres a way to get such algorithm for f(x)=1/x!

[kind hawk]

maybe its possible here because of the very precise form of the polynomials but that would require quite a bit of research I would guess

[trim portal]

so the actual problem is solving

1 + 1 + 1/2! + 1/3! + ... + 1/n! = K?

[kind hawk]

that might be possible because error bounds for e are very well studied probably

[manic moon]

Yeah basically e

[manic moon]

We start with I=0 so you get 1+1+1/2+1/6...

Additional 1

[kind hawk]

well still not easy. anyway, gtg. good luck

[manic moon]

Thanks

[trim portal]

do you always have a guarantee that a solution exists?

[manic moon]

This is a specific case I wanted to come up with, yeah, but that general case is also a q I would like a response to

[trim portal]

general case is impossible

[manic moon]

For f(x)=1/x!

?

So only approach is brute force

?

[trim portal]

For this you don't need to use brute force i believe

[manic moon]

How then

Is min x so that sum is >K gonna make it easier than =k

[trim portal]

you could probably bound
$\sum_{i = n+1}^\infty \frac{1}{i!}$

[warm shale]

MæthIsAlwaysRight

[manic moon]

Bound meaning?

Find a formula for it?

[trim portal]

i meant more like finding a reasonable estimate for it

wait, i got an idea...

i just need to try it out rq

[manic moon]

😯

[trim portal]

nvm i probably dont

[manic moon]

You could maybe define a function such that it's the function that provides the solution to this

But thats not a good answer

[trim portal]

if you could find an n that's an upper bound on x, then you could make O(log(n)) algorithm

[manic moon]

Still numerical

[trim portal]

so you want O(1) algorithm?

[manic moon]

Algorithm doesn't necessarily mean a numerical one; it's a process which I can apply to said equation to find the answer.
Like solving ax=c. The algorithm is to move a to the other side (divide by a)

My goal isnt to compute a specific value of K, but find how to do it for any K. And a guess-until-found doesn't satisfy me Truly, nor, I believe, many mathematicians

Because say a geometric series has a formula for sum up to nth term

Is there such a formula for when the ratio isn't constant, but part of harmonic series

[kind hawk]

straight up, no. there are sometimes bounds but thats literally it

even for the harmonic series itself there are only bounds

[manic moon]

But wait, if harmonic series sum itself doesn't have a proper formula then a good guess is that

Yeah

[trim portal]

you could use those bounds to speed up your search, but that's pretty much it

[manic moon]

Hmm

Well the bottom of the fraction of harmonic series is n! If unsimplified

But what about the top

[trim portal]

the top would be some ugly sum

sum of i! up to n! i believe

or sth like that

no

$\frac{\sum_{i=1}^{n}\frac{n!}{i}}{n!}$

[warm shale]

MæthIsAlwaysRight

[trim portal]

or alternatively

$\frac{\sum_{i=1}^{n}\prod_{j\neq i}^{n}j}{n!}$

[warm shale]

MæthIsAlwaysRight

[trim portal]

it cant be simplified

[obtuse pebble]

@manic moon Has your question been resolved?

[manic moon]

It can

[manic moon]

It can be simplified a d that's the problem

Take n! Outside the sum and the n! Cancel, so no progress made

[timid silo]

@manic moon hm what about taylor formula with integral rest ?

[analog rivet]

90/sin 9 = 50/sin x?

oh sorry watcheer

[manic moon]

?

[manic moon]

no problem!

[timid silo]

u know this formula ?

[manic moon]

uh which one

maybe no? idk

show it to me

[manic moon]

how will it help...?

[timid silo]

if u take f=exp , b=a=0

ah wait

[manic moon]

uh, and wheres the sum part

[timid silo]

the one with the ...

[manic moon]

ok, but here i need to find n?

so its the same as finding x in a sum from i=0 to x of f(i) that equals K?

where f(x)=exp

[timid silo]

that could be good for this

it is just an idea, idk if it will work yet

[timid silo]

n is increment

ill find an expression that use the sigma notation

i found this

[manic moon]

so we divide K by e to get n! ?

[timid silo]

uh wait, u want to solve for K or for n in this ?

[manic moon]

no

for x

[timid silo]

1 + 1 + 1/2! + 1/3! + ... + 1/n! = K

[manic moon]

yeah, find n

[timid silo]

and K is a number u choose ?

[manic moon]

take out n!

[manic moon]

yeah

[manic moon]

but then we still have n in other terms

so it doesnt help

[timid silo]

then u cant, because th sum of 1/k! tend to e, so if K>e u cant have this equality

[manic moon]

what?

[timid silo]

for example

[manic moon]

who said

K>e

K<e

[manic moon]

with your provided equation, no

but that doesnt mean its impossible generally

[timid silo]

if K<e its ok

[manic moon]

well yes

i never said K>e

by the way, can i find people in this server who are willing to teach me, i. e. not help with specific problems, or answers, but teach me in order, mathematics?

[timid silo]

i think it is very difficult to teach math without speaking

like only written

[manic moon]

i mean

you can use a whiteboard

for visuals

and text is the same as speaking except visuals

[timid silo]

anyway it is not convenient, but the main probleme is probably the time needed to teach

[manic moon]

but i bet out of all the people i could find volunteers

the question is where

[timid silo]

maybe ask the moderators

to create a channel for courses

[manic moon]

<@&268886789983436800>

[timid silo]

it would be more adapted by private message i think

[manic moon]

too late

[timid silo]

idk actually

but u can still find books, and if u daont understand u can ask here

[upbeat plinth]

you probably wont find anyone willing to teach entire math topics

[manic moon]

of the 200K people?

no one?

[timid silo]

ye

[hot hazel]

if someone is willing to do that theyll charge money for it

no one will become your free personal tutor

[manic moon]

come on, out of 200K

[timid silo]

maybe ponctual lesson

but probably not entire stuff

[manic moon]

books are ..

well i know some stuff already there

so i dont want to read i t again

but then i skip stuff i might not know, if i choose to skip those topics

[hot hazel]

we get way fewer than 200k people checking this server on any given day (closer to a couple thousand). furthermore, most of them are not qualified to help you. it is highly unlikely you will find someone willing to do charity work for you among those who remain, considering that personal tutoring is usually a (fairly well paid) job

my home city has 1 million people, but if i go into public and start asking for $100, no one's gonna give it to me

[manic moon]

i dont need extremely qualified

people

just so they understand the concept themselves

[upbeat plinth]

i think you fail to realize what a huge effort and time sink it is to be a personal tutor

[hot hazel]

i don't know how to explain to you that people usually don't work for free for people they dont know

[knotty dome]

youtube exists

youtube has great tutorials for stuf

[manic moon]

ok, like?

[knotty dome]

unless you're targeting some highly esoteric branch

[manic moon]

i would like specific examples of sources of enlightenment on YouTube

[timid silo]

for wich language ?

[manic moon]

language? english is ok

except for a few syntax differences, math is the same everywhere

say calculus

i dont know what there is to learn

i know some stuff already\

but i dont know what im missing out

[upbeat plinth]

you could try khanacademy or mit opencourseware

[timid silo]

anyway u can still ask mods for channel for courses

[manic moon]

i already pinged them

[manic moon]

so channel for courses?

[hot hazel]

i dont know what this means

[manic moon]

ask @timid silo

[hot hazel]

we have a #calculus channel for example

[manic moon]

but thats for specific problems

[timid silo]

i meant creating channels specificaly to learn stuff

not questions

[hot hazel]

like reading groups?

we consider those out of scope of the server

[manic moon]

no...

[upbeat plinth]

none of our channels are meant to teach courses

[manic moon]

and thats the reason for the existence of the suggestion

[timid silo]

yes i though of making new ones

[manic moon]

oh wait math-pedagogy is kind of that ? by the name, im figuring?

[upbeat plinth]

having such a channel requires volunteers, probably paid, to run it

which goes back to the point on effort, time, and money

[manic moon]

volunteers and paid dont go in one sentence

[upbeat plinth]

whatever

hired help

again people usually dont work for free

[hot hazel]

im not sure this is within scope of the server in any case

[manic moon]

usually is the key...\

[timid silo]

i though it would still be the same principe, like the questions channels. Pepole help for free here

[hot hazel]

we are a mathematics server, we're not trying to recreate a school

[manic moon]

math server cant have math courses?

[onyx spoke]

no, that channel is for discussions about how to teach mathematics on a broad scale

[manic moon]

yeah, i saw by this point already

[hot hazel]

i mean, if you can find a miracle group of trustworthy people willing to commit to a project like this, let us know

somehow i doubt youll have much success

[onyx spoke]

"usually" as in "you would be astronomically lucky to find one"

[hot hazel]

just because we're a mathematics server doesn't mean we facilitate literallyt everything mathematical

[manic moon]

well i like to teach people when i have the time and will stuff i know and they dont

[hot hazel]

we do not run a mathematics journal and we do not run a mathematics school

we provide a space for the broad discussion of math and for asking and answering questions

as well as some off-topic social spaces

[manic moon]

but the name is Mathematics, suggesting the broader implication of the word, that encompasses different mathematical stuff

[hot hazel]

i dont even know how to respond to that

[manic moon]

alright, whatever

thanks i guess

[hot hazel]

i'd like to think that we satisfy the most obvious implications of "general-purpose mathematics discord server"

[timid silo]

and would it be possible to try creating others channels, and after, see if it works ?

[hot hazel]

if you want to run an experiment like this you can make your own server and try it

[timid silo]

could still delete it after

[hot hazel]

i dont know why we'd host it on ours

seems like a massive amount of moderation work

[timid silo]

becaus it is already a big server

[manic moon]

experimenting is the way to perfection

[timid silo]

but ok

[manic moon]

what is the problem

[hot hazel]

so you want to leech off us for your pet project?

[timid silo]

hm yes ?

[manic moon]

alright, maybe we should resort to my previous question

[manic moon]

why not just make a channel, make a few roles, and try seeing what happens

its not like the server is gonna get hacked. .. ..

[timid silo]

he said it is a lot of work

[manic moon]

i mean, maybe there can be no rules, and the rules will be implied by the name of the channel

[onyx spoke]

this would be a nightmare to moderate

[manic moon]

except for other stuff that aplies to the server as a whole

[hot hazel]

i dont see how that would end up any different from #calculus or similar topic channels

the reason the topic channels are filled with questions is because thats the most common type of activity

you can hold general conversations in them if you want

and indeed people do frequently in the advanced channels like #foundations and #math-pedagogy

[manic moon]

eh, 1 problem vs topics, examples, ways to understand,, ,

[hot hazel]

you can already ask for that stuff in the topic channels?

[onyx spoke]

you could just ask about these things

[manic moon]

general conversations doesnt include learning a topic continuosly, or does it?

[timid silo]

i think u should elaborate more the things u want before proposing it

[hot hazel]

i dont see how you enforce that without a large moderation effort

[manic moon]

well, id argue we should get back to my previous Q because its fading away in history

[manic moon]

it was your idea, i was only helping you

[timid silo]

yes, it was for the teaching stuff

[manic moon]

alright, could you just tell me what the moderation effort mostly consists of because i might be in misunderstanding

[obtuse minnow]

hello

[manic moon]

well hello there?

[hot hazel]

by far the bulk of our moderation activity on the server is trying to corral people into using the help channels the proper way

we have spent thousands of collective manhours trying to make it as clear as possible

and we still get people posting their questions in the wrong sections

[obtuse minnow]

by chance do you know synthetic division?

[hot hazel]

after this long conversation i still dont 100% understand what distinguishes your proposal from #calculus

so i would imagine the average server user would be totally lost

[manic moon]

oh, is it not possible to use some AI bot that filters messages based on content, or does that not really exist

[hot hazel]

that would be very expensive to run and would probably not work very well

[manic moon]

a bit'

[hot hazel]

please get your own help channel, see #❓how-to-get-help

[manic moon]

this demonstrates your point very clearly i see

[manic moon]

.

[timid silo]

crunchy

[obtuse pebble]

@manic moon Has your question been resolved?

[obtuse pebble]

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[ionic oar]

what are you stuck on?

[feral parcel]

How do I check if ps is parallel to qr

[ionic oar]

try angle chasing and see the (idk what its called) but the "rules" for parallel lines

[feral parcel]

Ok

.close

[obtuse pebble]

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[stable briar]

can someone help me understand the farmat's last theorem?

[primal roost]

it only says that there is no solution $a^n + b^n = c^n$ with n > 2 and n, a, b and c are natural numbers

[warm shale]

FluxusX2

[primal roost]

@stable briar

[stable briar]

but is it still true if c^(n+1)?

and b is still b^n

[primal roost]

Im not sure but i would say it can be true for some cases but it does not count in general

[obtuse pebble]

@stable briar Has your question been resolved?

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[pallid linden]

guys

[ember frost]

...?

[frigid burrow]

@pallid linden pls ask your doubt

[obtuse pebble]

No need to ask “Can I ask…?” or “Does anyone know about…?”—it’s faster for everyone if you just ask your question! See https://dontasktoask.com/

[knotty dome]

guys!!

very hard question

i cant answer

😢

[obtuse pebble]

@pallid linden Has your question been resolved?

[obtuse pebble]

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[junior hull]

what did they do to the end? i got the ln(2)/0.06=t

i get that they are putting it in measurement of a year but how can i do it in my head

nvm

.close

[obtuse pebble]

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[hollow void]

Could someone help me with b)

[hollow void]

And explain how you got to the answer

[obtuse pebble]

@hollow void Has your question been resolved?

[hollow void]

<@&286206848099549185>

[warm jetty]

@analog vault

<@&286206848099549185>

[hollow void]

<@&286206848099549185>

[obtuse pebble]

@hollow void Has your question been resolved?

[obtuse pebble]

@hollow void Has your question been resolved?

[obtuse pebble]

@hollow void Has your question been resolved?

[solar hornet]

@hollow void what have you tried?

simple google search would tell you how to do the intervals right?

so is there a more specific problem here?

[obtuse pebble]

@hollow void Has your question been resolved?

[hollow void]

i havent tried anything simply because Im not sure what it is

[solar hornet]

well what you have to put in the box are properties

you can google for examples and see how to measure them

there are so many youtube tutorials for measuring sign and slope too

it's all out there

maybe try something and come back, we can see how you did

[hollow void]

alright, its pretty late where I am could I close the ticket and dm u in the morning my results?

or, ill keep it open whichever u want

[solar hornet]

I think you can leave it open

[hollow void]

okay

[obtuse pebble]

@hollow void Has your question been resolved?

[obtuse pebble]

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[golden basalt]

More in depth
Quotient rule + Chain rule + product rule

[golden basalt]

Using logarithmic differentiation (I didn’t do it that way) is the one closest to my answer my best is that they factored out (3x-1)^4 ?

[crimson pike]

Looks like the calculator expanded the final expression
and logarithmic differentiation would be faster and easier

[golden basalt]

yup, havent dont logarithmic diff yet and isnt in the scope for the midterm

so my answer is correct then..... simplifying that would take a long time

[crimson pike]

yup but just recheck if you think you messed up something

[golden basalt]

checked multiple times, even did the chain rule part seperately lol thrice should be good i believe

[crimson pike]

Then yup you should be all set

[golden basalt]

ty

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[cinder relic]

need help with a math question pleaseeee

[cinder relic]

if x is an element of Z

when is x^2 ~2x +6 also an element of Z

how do you do this lol 😭

[craggy osprey]

Im not really sure what are you asking. What is ~?

[cinder relic]

ouh sory

it's meant to be a minus sign

I'm trying to translate from french and I have problems sometimes inputting symbols

[craggy osprey]

So if you have a number from Z abd you put it in the quadratic, what do you get?

[cinder relic]

wdym?

[craggy osprey]

Z as in the set of whole numbers right?

[cinder relic]

yesss

this is the question basically, I hope you can read french ehhehe

[craggy osprey]

Okay I see

[cinder relic]

determine the following sets in extension

I can't find how to do A tho 😭

[craggy osprey]

Basically, if you take a whole number and you plug it in this, you need to figure out when is the fraction a whole number

[cinder relic]

yeah but how do you do that, aren't you not supposed to just plug in each number over and over?

[craggy osprey]

So what I would do is set this equation equal for some whole y, and then try to get to a quadratic equation when one of the parameters is y

[cinder relic]

ouuuuh

I'll try that

thanks!

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[obtuse pebble]

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[tardy epoch]

,rccw

[misty meteor]

can someone check if I got it right

[tardy epoch]

yes, but 3/3 can be simplified

[misty meteor]

to 1

alr thanks

,close

.close

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[ivory trout]

Can anybody tell me if this is correct?

[obtuse pebble]

@ivory trout Has your question been resolved?

[obtuse pebble]

@ivory trout Has your question been resolved?

[obtuse pebble]

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[bright bobcat]

how to solve

[bright bobcat]

i am not sure where to start with this

[vestal carbon]

What are you solving for

[bright bobcat]

I suppose I can simplify the second and third one firsy

I am just simplifying

[vestal carbon]

You want to put all the y terms and x term’s together

So you can change the roots into y to the power of something

Then add the powers

[bright bobcat]

how do i write the radicand power

like i know i type y^3 for the power

[vestal carbon]

Yes

[bright bobcat]

but how do i express that on discord for the radicand

[vestal carbon]

What do you mean

[bright bobcat]

this thing

[vestal carbon]

its y^(5/4)

[bright bobcat]

that's how you write it? and it means the same as

[vestal carbon]

Yes

[bright bobcat]

okay

[vestal carbon]

The root is in denominator of exponent and power is in numerator of exponent

Always

And another property of roots is that rt(ab) = rt(a) * rt(b)

So you can separate the third term into x^(10/4) times y^(15/4)

Then lastly you add the powers y

So the simplified term is y^(3 + 5/4 + 15/4) times x^(10/4)

Or y^8 times x^5/2

[bright bobcat]

test

i am sorry i had to go for a second

am I going in the right direction?

<@&286206848099549185>

[mossy walrus]

yes

you are

[bright bobcat]

okay i am not sure where i go from here

[mossy walrus]

y^3*y=y^4

y^4sqrt(y)*x^2y^3sqrt(x^2)(y^3)

sorry that looks confusing

[bright bobcat]

yeah its a bit confusing

.close

[obtuse pebble]

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[obtuse pebble]

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[forest roost]

im really stuck and not sure what to do. can someone help me go step by step for this question? thanks

[forest roost]

<@&286206848099549185>

oh sorry i didnt see the after 15 minutes

[sonic rover]

So we can already kinda prove this

Wait i misread nvm. It just takes a couple steps though

[forest roost]

ok so far ive gotten this

AC congruent to BC

[sonic rover]

I think that can work i just need to think

I did it a different way though

[forest roost]

ok, thanks

[sonic rover]

The way I did it, was that because CAB and CBA are congruent, and a part of each of theirs are congruent, the other part of each must be congrunt to each other

[forest roost]

ok, i have to show every single step to make it work

are there only 3?, i feel like there is more

[sonic rover]

Only 3 steps?

What are the reasons for if you put in angle DAB=DBA

[obtuse pebble]

@forest roost Has your question been resolved?

[obtuse pebble]

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[warm depot]

Help?

[warm depot]

Hola

[sonic rover]

What with

[warm depot]

I got a question about linear equations

[sonic rover]

Ok

[warm depot]

y = mx + b

i need to give an example to show you what I am confused with

lets make two plots on a graph

y = 3x + 5

y = 3(1) + 5 = 8

y = 3(2) + 5 = 11

my question is about the slope

[sonic rover]

Ok

[warm depot]

The plot gives us 3/1

[sonic rover]

Yeah

[warm depot]

I want to understand how the y-intercept and slope connect with the graph. When I do the work I can verify that it is the slope, I want to understand why.

i had a hard time formulating this question

Its like, how would I make sense of y = mx + b

[sonic rover]

No problem.

The y intercept is what the value for Y is when x=0. If x = 0 in the question you sent, then we have

y=3×(0)+5, or y=5

[warm depot]

Its like I know the how I really didn’t grasp the why yet if you don’t know what i’m saying lol

When x is zero, looking at the origin, its where it touches in the y axis right? Its why its called an intercept.

But what I didn’t really understand is the slope

[sonic rover]

The slope is how much y changes when x increases by 1

In your equation, when x increases by 1, y increases by 3

[warm depot]

What about the (+ 5), the y-intercept

It affects y as well, don’t it?

[wary badger]

dude snatches purses

[sonic rover]

It does yes, but you can think of it like an initial value. Kinda like where the function begins

Notice how

y=3x+5 and

y=3x+2 have the same slope of 3. But they're at different locations on the graph because of that y intercept

[warm depot]

I feel as though you are about to help me make a groundbreaking moment

[sonic rover]

About to

[warm depot]

So the y-intercept doesn’t necessarily impact the rate of change, all it does it as you said place it somewhere else on the graph

[sonic rover]

Exactly

[warm depot]

DoC I am in your debt

Thank you so much

[sonic rover]

You are very welcome

[warm depot]

Is there a way to say that with more clarity for my notes?

Its so that if I forget I can relearn easily

[sonic rover]

The best way I can think to say it is that the y intercept is where the graph is located when x=0

[sonic rover]

The graph itself will go up or down, based on what the y intercept is. The bigger that +b value, the higher on an x-y plane it is. Vice versa for the more negative that plus b value

[warm depot]

Oh another question, how do you know if the rate of change is increasing or decreasing

Based on the function

[wary badger]

second derivative

[warm depot]

for example going up and down a graph

[wary badger]

concavity

[warm depot]

second derivative being?

[wary badger]

the derivative of the first derivative

[sonic rover]

Are you in calculus

[wary badger]

oh you’re in algebra

[wary badger]

^

[warm depot]

I get concavity, i’m in algebra 1 lol

Concavity is the curvature, no?

[sonic rover]

Yeah don't worry about derivative rn haha

[wary badger]

concave up -> rate is increasing, concave down -> rate is decreasing

[warm depot]

Oh I might need that for stocks

Determining whether it is bullish or bearish

[sonic rover]

Definitely useful for that

[warm depot]

Analyzing the data, but thats irrelevant to this

So slope is determined by the coefficient of x because it directly impacts y.

y = 3x

3 / 1 = 3

[sonic rover]

Correct

[warm depot]

slope = 3

the y-intercept only impacts the position of the “line”

[sonic rover]

Correct

[warm depot]

I have one more question if you have the time

[sonic rover]

Yes

[warm depot]

So I know linear functions are constant but what about different types of functions. Ones that make a U shape etc

[sonic rover]

You'll actually learn about this in calculus if you decided to take it. Let's look at a "U shaped" graph, being a quadratic equation. I'll just go simple with y=x^2

[warm depot]

Exponential graph?

[sonic rover]

One thing about non linear equations is that they have something called a "tangent line" at each specific point

[warm depot]

at the origin?

[sonic rover]

A tangent line is a line that touches a graph at exactly one spot

It could be anywhere, including the origin

[warm depot]

the same spot on the y axis?

[sonic rover]

Here's an example

You can kinda see how the linear equation only ever touches the quadratic at that one spot

[warm depot]

Theres a term for that

I forgot what it was

[sonic rover]

Yep tangent

[warm depot]

Oh its tangent

What about when it never touches it and it seems as though it is the same as a linear graph

It started with an A I believe

Asymdote something like that

[sonic rover]

Asymptote?

[warm depot]

There it is

But whenever I hear about these different types of functions i’m just lost

I don’t know what I’m looking at basically lol

[sonic rover]

Yeah lemme finish my rant rq

[warm depot]

Ofc

Stage js urs

[sonic rover]

So anyway

What we would say here, is that at that point of x=1, we would say that the graph has a slope of positive 2, as given by the equation. But that slope of 2 will never be seen again anywhere else on the graph, because it's only ever tangent at x=1

Here's a different point with a different slope

At x=-1, the graph has a slope of -2

Hopefully this isn't too much

[warm depot]

Is it because when x is squared it can never have more than one similar point with a linear graph. Say x is 10 it’d be 100. It follows a pattern indifferent to a linear one.

[warm depot]

I guess I can understand, I haven’t grasped the basics all that much yet other than y = mx + b

[sonic rover]

Yeah this kind of stuff is what you would learn in calculus

[sonic rover]

Not quite. It's actually what we mentioned earlier, finding the derivative

The main point I'm getting at is that non linear equations, like quadratic or exponential, have different slopes at each point on the graph

[warm depot]

This is where cos, cosign, tan etc come in?

Thats trigonometry, no?

[warm depot]

Can you elaborate on the different slopes?

[sonic rover]

Those are trigonometric functions and they could potentially be related, but those are functions mainly used with triangles and the unit circle

[warm depot]

The angles of a triangle I think

[sonic rover]

Yeah. Remember what I showed up above, when x=-1, the slope of the equation of y=x^2 was -2. Because that's what the slope of the tangent line was. But when x=2, the slope was +2, again because that's what the slope of the tangent line was

[warm depot]

And the reason why it’s tangent is it’s derivative

Its*

[sonic rover]

Yeah

[warm depot]

So in algebra 1 i’d just use a calculator for those functions

As long as I understand what it is i’m doing

[sonic rover]

I highly doubt they will ask you to find the slope of a non linear equation

Because this is higher level high school math

[warm depot]

AP precalculus?

[sonic rover]

They might, that's a fairly new class but I wouldn't be surprised if they talked about this kind of stuff in it

[warm depot]

Thanks for the help DoC

[sonic rover]

Of course

[warm depot]

Thanks to you I have a somewhat better understanding

[sonic rover]

W

[warm depot]

y + mx + b

b is the y-intercept (essentially the position of the line)

y and x are coordinate points that have a relationship with each other known as rate of change.

m is the slope because it determines the relationship between y and x.

Y / X
m affects y

Could you repeat how m is the reason for rate of change, or in other words is the rate of change

[sonic rover]

Hm

To be more specific i would say m is the slope and it determines the relationship between y and x

[warm depot]

I see that

[sonic rover]

But m is the rate of change because it tells us how much y is changing whenever x increases

[warm depot]

To put it figuratively, theres some fog and I can only see 4 miles through and I want to be able to see very clearly.

And y / x is the rate of change.

Kind of like distance/time

[sonic rover]

Yeah

[warm depot]

30 mph

[sonic rover]

Mhm. That per is where the divisor is. M/h, miles divided by hours

[warm depot]

Oh also, what if there is no y-intercept in the equation

its like y = 9x

[sonic rover]

In that case the graph goes straight through the origin

When x is 0, y is also 0

[warm depot]

so we’d substitute b for 0

[sonic rover]

Yea

[warm depot]

What if there is no slope but there is a y intercept

Its not a function then?

y = x + 10

[sonic rover]

Well in that case there's an invisible 1 in front of the x

So the slope is 1

[warm depot]

1/1

Kind of like the linear equation you showed to exemplify the tangent

[sonic rover]

But it is possible for lines to be in the form

y=10

[warm depot]

Oh nvm I’m wrong there

2 is the slope

[sonic rover]

In this case, we'd say there's a 0 slope

y=0x+10, but since 0× anything is 0, we just get rid of 0x

[warm depot]

We can’t graph y = 10

we only have the y axis

[sonic rover]

Whenever there is a 0 slope, the line just goes completely horizontal

[warm depot]

so x is 0

[warm depot]

ohhhh so y = 10 infinitely

[sonic rover]

X can be whatever it wants, but it will always end up becoming 0

[sonic rover]

Yeah essentially

[warm depot]

Technically there is no slope here

[sonic rover]

If x=4, y=10. If x=16, y=10. If x=193759504, y=10

[sonic rover]

Correct

[warm depot]

How would a real life example result in that

[sonic rover]

Let's say you give away fliers for free. If you give away 50 fliers, how much money did you make

[warm depot]

0

[sonic rover]

Yeah

So in this case, a product being free is represented by the slope being 0

You made 0 dollars per flier given away

[warm depot]

When there is no slope in the equation is there an invisible 1 or 0?

Or is 0 the value of c

X*

y = x + 10

y = 1(x) + 10 or y = 0(x) + 10

[sonic rover]

When there's no slope in the equation there's an invisible x

No slope will always result in the form

y=b

If you at all see an x, that means there is a slope

[sonic rover]

This is when there's a slope of 1

[warm depot]

slope determines the relation between x and y and where there is no slope there is no relation between them

its a horizontal line

[sonic rover]

Yeah that seems to work actually

[warm depot]

Doesnt go up or down

[sonic rover]

Y is not dependant on x, we could say

[warm depot]

Yep, on the y-intercept because it determines the position of the horizontal line

But i’m not quite sure why theres an invisible x

what if the prompt says x = 2

would that make it not a function?

[sonic rover]

Correct

[warm depot]

How so?

[sonic rover]

I like to think about it this way

Let's say we have 5 people from ages 12-16, and we are measuring their heights.

Would you expect the 14 year old, for example, to have 2 different heights?

@warm depot sorry i was writing something else then realized it's too convoluted haha

[warm depot]

No since there is only one 14 year old and he can not possibly have two heights simultaneously

[sonic rover]

Correct

[warm depot]

Is this the climax towards the answer of the question, “So if there is no slope and x has a value is not a function why?”

[sonic rover]

So that's a sort of real world example.

In the math world, we could say that in every function, there should be exactly one output for each given input

[sonic rover]

Uh maybe

[warm depot]

In order for it to be linear that is, or more importantly a function

[sonic rover]

Yep. For every single function, including quadratic, exponential, etc

[warm depot]

That equation would exemplify a real-world scenario but it does not have a rate of change allowing for it to be graphed as a function

[sonic rover]

Yep

Certain applications such as desmos still allow these functions to be Graphed though

[warm depot]

I think i’ll be using demos pretty soon

[sonic rover]

But we wouldn't necessarily call this a graph. It's just a bunch of ordered pairs put together

[warm depot]

if x equals 4 wouldnt that mean y is equal to 4.

That shouldn’t be possible

Also y would be whatever b is plus x but that isn’t a function

Its just data outside of which can be used as a function

[sonic rover]

Yep, at one specific spot

But y is also equal to 5, 17, -32, -2747

[warm depot]

Which is why it isnt a function

My algebra teacher can’t teach

[sonic rover]

Mhm

[warm depot]

I don’t know what to say other than telling you the statistics. Nobody in my class learnt anything from him. He simply shows us the problem, assigns it, and grades it.

[sonic rover]

Yeah that's not a great way to teach

[warm depot]

You have been very helpful, I learned a lot today

[sonic rover]

Great to hear

[warm depot]

I’d argue you are overqualified to be a teacher lol

[sonic rover]

Oh I am a teacher lol

[warm depot]

And a great one

[sonic rover]

I like tutoring for fun so I do this on the side because students rarely ask for help outside of class haha

[sonic rover]

I appreciate it

[warm depot]

Of course, thank you so much for helping me learn

You have a great rest of your week

[sonic rover]

You're welcome. You as well

[warm depot]

Know that you have a knack for this 🙂

So do I close this chat and say farewell

Goodbye 👋

.close

[obtuse pebble]

Channel closed

Closed by @warm depot

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[obtuse pebble]

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[round cosmos]

how would i go about deriving e^(x^(2)+tan(x)+x*cos(x))

[patent osprey]

chain rule

product rule

power rule

[round cosmos]

thanks!

.close

[obtuse pebble]

Channel closed

Closed by @round cosmos

Use .reopen if this was a mistake.

[wary badger]

<@&268886789983436800>

💀

ok bro

[timid silo]

Woah oh someone call the popo

[wary badger]

you’re not slick bro

[timid silo]

I only saw 1 letter then disappeared

[wary badger]

self promotion

[hot hazel]

i respect the hustle tho

dude really thought the "delete it and ping mods" scheme would work

[wary badger]

😹😹

[obtuse pebble]

Available help channel!

Send your question here to claim the channel.

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[deep marlin]

yo ;w; I'm struggling w my pre-calculus rn anybody help ;w;

[deep marlin]

here, I forgot how to use my sci-cal on this

https://tenor.com/view/tobey-maguire-sad-wah-wahh-cry-gif-15729067800335956216

[red ice]

you just need to keep adding or subtracting 360 degrees

until you get an angle between 0 and 360 deg

[frigid burrow]

and convert rad to deg

[deep marlin]

how do i conver rad to deg?

[frigid burrow]

pi rad = 180 deg

remember this imo

[red ice]

yes so 1 rad = 180/pi deg

[deep marlin]

but theres no rad in my scientific calcu

[red ice]

so you can multiply by 180/pi to convert it to degree

[frigid burrow]

can you send a pic?

[red ice]

remember your calculator doesn't think for you

[frigid burrow]

there will definitle be a rad mode

[red ice]

yeah or you don't know how to do that function on your calculator

[deep marlin]

OH! THE MODE YEA

[frigid burrow]

lol

[red ice]

yeah the mode button on your calc lol

[deep marlin]

yeah and what do I do now again? TAT

[frigid burrow]

you need help in which part?

[deep marlin]

this

I keep forgetting lmao TT

[deep marlin]

how do I know if I should subtract or add?

[red ice]

well 736 is more than 360

so subtract 360

[deep marlin]

376 still not the final answer right?

it should me below 360?

[red ice]

yes so subtract 360 again

[deep marlin]

yes! 16 is the final answer

am I right? TOT

[red ice]

yep!

[deep marlin]

what about the 2nd one ;w;

[red ice]

now you just need to convert b, c, d into degrees only

[deep marlin]

I'll go back to degree mode

[red ice]

ah can your calculator convert that to degrees?

[deep marlin]

yes

[red ice]

if not Wolfram Alpha bot can do it

ok

[deep marlin]

is this right?

a

wait

i thin

k

i clicked degree again

[red ice]

,w 28 degrees 48 minutes 65 seconds to degrees

oh yeah that looks right then

[deep marlin]

heh

but our prof told us to right everything so- I won't round it off

[red ice]

it's weird, 65 arcseconds

,calc 28 + 48/60 + 65/3600

[warm shale]

Result:

28.818055555556

[red ice]

yeah ok then

Wolfram is dumber than I thought

[deep marlin]

lmao

[red ice]

it rounds for no reason

[red ice]

great so add 360

[deep marlin]

i need to add 360?

[red ice]

yeah

cause it's not between 0 and 360 is it

[deep marlin]

alrr

so 331.18194444 final asnwer

[red ice]

yeah

[deep marlin]

what about the 13pi/2?

[red ice]

convert that to degrees first

pi radians = 180 deg

so you can replace the pi

[deep marlin]

how do I do that with my calculator?

[red ice]

!help

[obtuse pebble]

To ask for mathematics help on this server, please open your own help channel or help thread. See #❓how-to-get-help for instructions.

[red ice]

https://www.youtube.com/watch?v=kMK00O9okm0

(it's 24 secs don't worry)

[deep marlin]

I got 2340

and If I click degrees button

[red ice]

cool

now we're going to use the fact that 2pi = 360 degrees

so multiples of 360 degrees

12pi = 6 * 360 degrees

that means we can just do 2340 - 6 * 360 degrees

or 13pi - 6 * 2pi radians

[deep marlin]

I got 4500 (?)

I added 360 6 times

[red ice]

you're subtracting this time

when you have larger than 360 degrees, you subtract

when you have smaller than 0 degrees, you add

[deep marlin]

it should always below 360 right?

[red ice]

between 0 and 360

[deep marlin]

the lowest I got is 180

[red ice]

okay cool that's what I get too

okay finally for part d

[deep marlin]

D is easy

I already did it xD

[red ice]

oh nice

[deep marlin]

10- 2pi

[red ice]

,calc (10 - 2 * pi) * 180/pi

[warm shale]

Result:

212.95779513082

[red ice]

and then convert to degrees yeah

[deep marlin]

final answer? or I need to convert it again to decimals

[red ice]

no, multiply by 180 / pi

180 deg = pi radians

so (180 deg) / (pi radians) = 1

multiplying by 1 doesn't change the number

[red ice]

also you can convert to degrees

ah but you need to set your calculator to radian mode

and then use the degree symbol in ANS

[deep marlin]

212.95779513082 x 180pi?

[red ice]

no

it's just 212.95779513082

[deep marlin]

then?

[red ice]

that's it

that's the answer for d

[deep marlin]

what is this about?

[red ice]

converting from radians to degrees

radians cancels with radians, so the radians is on the denominator here

leaving us with an answer in degrees

[deep marlin]

letter c?

I'm still confused at letter c ;w; I'm getting lost lmao

[red ice]

c is also used for radians, correct

[deep marlin]

I'm stuck at letter C

[red ice]

c is just 180 degrees

[deep marlin]

answer?

[red ice]

yes

[deep marlin]

The other says the answer is pi/2 rad

onto the next one help

<@&286206848099549185>

https://tenor.com/view/why-tho-cute-kid-gif-17937097

I'll wait TOT

Oh I just put the letter on the table?

I don't know how to draw it in TT

so i'll just put the letter on the side?

I meant in the table

OH

mb mb I'm rlly tired rn. but thank u!

oh-

dang

[red ice]

oh wait yeah pi/2 rad is not 180 degrees my bad

it was 13pi/2 - 6pi = pi/2 rad

[deep marlin]

9th grader teaching me (I'm 11th grader)

https://tenor.com/view/the-simpsons-homer-simpson-hiding-embarrassed-bush-gif-6287489991893889017

.close

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[obtuse pebble]

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[untold mirage]

yp

[untold mirage]

yo

can anyone help for why on c u have to times it by 10C5

[wooden cipher]

the goals can be at any time

e.g. GGGGGXXXXX is scoring five goals then five not goals

or GXGXGXGXGX

alternating scoring and not scoring

the number ways to acore 5/10 goals is by choosing 5 of 10 to be goals

aka 10 choose 5

[untold mirage]

so using the 10C5 gives us the posibility of getting any of those combinations, while leaving it out only gives the posibility of only getting one combination?

[wooden cipher]

it counts all the different combinations

basically youre calculating the probability of GGGGGXXXXX then the probability of GXGXGXGXGX and so on, but since the probability of each are all the same, you can do (10C5)*probability of one case

[untold mirage]

and in d u leave it out cos u only want the probability of of one combination (all combinations have the same probability)

is that right?

[wooden cipher]

in d?

[untold mirage]

yep the question below

[wooden cipher]

you want a specific case for d

[untold mirage]

ye a specific combination

[wooden cipher]

specifically GXXXGXXXGX

so you only want the probability of that

no multiplying by some nCr

[untold mirage]

yeah

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[obtuse pebble]

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[young depot]

Hello everyone! I was learning about polar coordinates and integration. Is my way of getting the length of an arc (1) correct? And can someone explain why 2 is correct?

[obtuse pebble]

@young depot Has your question been resolved?

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@young depot Has your question been resolved?

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[broken magnet]

Please help

<@&286206848099549185>

[tardy epoch]

!15m

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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.

[velvet spoke]

Do you know the expression for the general binomial term

say for (a+b)^n

do you know the rth term?

[broken magnet]

Yes

[velvet spoke]

write the expression down

plug those variables in

set the power of x to zero

[broken magnet]

I did after simplifying it but it’s so complicated

[velvet spoke]

can you send it to me?

the general term

[broken magnet]

Yes wait

Now how should I proceed?

[velvet spoke]

Okay

so (x^k + 1)^b

yk the degree of x in this would be kb

example, (x^2 +1)^2

= x^4 + 1 + 2x^2

4 = 2*2

right?

[broken magnet]

Order?

[velvet spoke]

no not order

[broken magnet]

Yes

[velvet spoke]

degree

[broken magnet]

Ah yes

Sorry

Degree

[velvet spoke]

so what's the degree of x in this

[broken magnet]

10-r/3

[velvet spoke]

and we have x^(r/2) in the denominator

[broken magnet]

Yes

[velvet spoke]

to have a term independent of x

these degrees should be equal

i think it's 4, option a

is it?

[broken magnet]

Let me check

Nah

[velvet spoke]

:(

[broken magnet]

It’s c

[velvet spoke]

plan b

maybe try expanding (x^1/3 +1)^10-r

[broken magnet]

Wait they are asking term independent of x so ig the value

[velvet spoke]

,w 10 choose 4

[warm shale]

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Requested by _nofluxgiven

[broken magnet]

Also 1 more doubt arises if complete terms is to independent all of the components of expansion (x^1/3+1)^10-r has to be independent of x

[velvet spoke]

[broken magnet]

Can you help me with this Ik it’s silly

[velvet spoke]

well say the numerator's degree wasn't equal to the denominator's degree

they'd never divide to give an expression of degree 0

so I didn't even bother to think about that and just equated the degrees

,w (x^(1/3) + 1)^6

[warm shale]

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Requested by _nofluxgiven

[velvet spoke]

,w (x^(1/3) + 1)^6 / x^2

[warm shale]

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Requested by _nofluxgiven

[broken magnet]

I mean if numerator is greater then it’s possible one of terms may be independent as the degree of one may be equal to one in denominator

[velvet spoke]

thats true

valid point

good question

well if we expand the expression

whatever it was

[broken magnet]

also I think this ques is not meant to be expanded

[velvet spoke]

and do the same thing we did, we'd also get 4 as the answer

[broken magnet]

can you elaborate?

[velvet spoke]

write the general term (rth term) for this expansion

[velvet spoke]

is that (10 - r C z) * x^z/3