help-27

[drifting mauve]

"calculate" it

[idle carbon]

Is it a place holder or smth?

[solar goblet]

what's the derivative of x^2?

[drifting mauve]

YES

[idle carbon]

For?

[drifting mauve]

to account for the fact that dC/dx = 0 for any constant C

[idle carbon]

So it just has to satisfy that function?

[orchid shadow]

C can be any number you want it to, and the equation is still correct

[idle carbon]

😭 huh?

Calculus confusing 😭

[solar goblet]

recall that the derivative of f(x) is the rate of change of f(x). the rate of change does not change whatsoever where f(x) is located vertically on the graph, which is the same as adding an arbitrary variable C to the function, so x^2 and x^2 + 1 and x^2 + 69 all have the same derivative, i.e. 2x

[drifting mauve]

it's really not 😭

[idle carbon]

I need to learn algebra 1-3 and geometry still

[solar goblet]

differentiating a function yields you a function, but it's not an injective operation. there are, again, infinite functions whose derivative is the same

that is, (x^2 + C)' = 2x for all C

[devout snow]

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[orchid shadow]

can you find the derivative of

x²?
x² + 1?
x² + 100?

they are all the same.. so if you have d/dx x² + c, then the value of c doesn't matter

[orchid shadow]

uh

what

.close

[devout snow]

Channel closed

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[solar goblet]

.reopen

[devout snow]

✅

[solar goblet]

the owner deleted the og message

[orchid shadow]

no no no it has my name

i don't have a question

[idle carbon]

😮

[solar goblet]

and?

[orchid shadow]

ok fine

[misty crest]

!show

[devout snow]

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

[lethal pollen]

He accidentally made the post

[misty crest]

i’m fucking with him

[orchid shadow]

lmao

[idle carbon]

😂

[lethal pollen]

Oh mb

Can I joi-

[idle carbon]

Dont count me out

[drifting mauve]

i don't know how bro is gonna do with differential equations

[misty crest]

,w plot x^3 + 1

[woven radish]

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[misty crest]

,w plot x^3

[woven radish]

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[misty crest]

the slope/rate of change is the same at each point it’s just that the graphs differ by a vertical shift

[idle carbon]

Ohhhh

Cool

[misty crest]

so if you’re given a function f that you’re integrating, you’re finding a function with a derivative of f but since you can shift a function without changing its derivative we add the arbitrary constant C to account for this

if however you’re given some "initial condition" you can then substitute in for x and y to find what C must be

for example, if we had f’(x) = 2x and an initial condition of f(0) = 69

[woven radish]

Marshall The Gamer
Compile Error! Click the reaction for more information.
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[misty crest]

we know from integrating f’ that we get f(x) = x^2 + c

but since we have the condition that f(0) = 69 we then have 69 = (0)^2 + c hence c = 69

if you want to type infinity it’s \infty

[orchid shadow]

no, the left hand side is an indefinite integral wrt x which means its a function of x, whereas the right hand side is a definite integral with bounds, so the answer is a number (in terms of n)

[misty crest]

yep

[idle carbon]

What about -infinity to infinity?

[misty crest]

,w int_{-infinity}^{infinity} e^(-x^2)

[woven radish]

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[orchid shadow]

that's still a definite integral so still a number

[idle carbon]

😭 i should stick with algebra 1-3 and geometry then precal

[misty crest]

what’s algebra 3

[idle carbon]

Is there no algebra 3?

[misty crest]

not where i live

[idle carbon]

Oops

[misty crest]

algebra 1 —> geo —> algebra 2 —> precalc —> calc

[idle carbon]

Ok yeah, that

[misty crest]

if you like this stuff you should go get some books and learn on your own

for the fundamentals

[idle carbon]

I just spent $70 on coding books so i am broke boi

[orchid shadow]

im still so confused by the american math education system why are the levels of education named after subtopics of math

[idle carbon]

And it was right as i went from coding to math too

[misty crest]

tough

[idle carbon]

😂

[misty crest]

what else should it be

[orchid shadow]

just call it math?

[idle carbon]

My grandma should be able to, grandmas are always rich

[orchid shadow]

if you need names for each level

[idle carbon]

Too basic

[orchid shadow]

just like

for example

[misty crest]

are you european

[idle carbon]

Kneif friend me back

[orchid shadow]

you said algebra 1 -> geo -> algebra 2

does that mean there's a period of time in which you learn algebra, and then you learn geometry, and then you learn algebra again?

[misty crest]

you didn’t add me

[idle carbon]

It says pending

[misty crest]

algebra 1 is like basic inequalities, lines, quadratics, factoring etc

systems of equations

maybe some completing the square

[idle carbon]

Yeah, i think i already got that, so i need geometry and algebra 2

[misty crest]

wont take too long

[terse solar]

yes ? you cant learn everything at once

[misty crest]

i accepted it

[idle carbon]

Yippy

[idle carbon]

Says who 😤

[idle carbon]

I’m 13 and “attempting” to understand calculus

Because i really dont

😭

[orchid shadow]

wait is each one of these courses like "algebra 2" or whatever a whole year

[misty crest]

you haven’t learned the fundamentals

[idle carbon]

My science teacher said algebra more fun

[misty crest]

yes lmao

it’s dumb

[orchid shadow]

because why can't you just do multiple topics in one year and just have it be math and like

ordered by difficulty

[idle carbon]

I am trying to take it over summer

[orchid shadow]

and not by topic

it just makes more sense

[idle carbon]

Slower for less gifted peeps

[misty crest]

because american high school education is terrible and teaches to the worst students

who get left behind in elementary school

and never catch up

[idle carbon]

Fr!

Kids still stuck in elementary at my middle school

😂

[orchid shadow]

💀

[terse solar]

you have to go through the intermediate stages first, you really shouldn't just skip to calculus
dont push it, you will get there in due time

[idle carbon]

I was bored and thought calculus would be fun, i am planning on learning intermediate before i start really looking into it

What does

[woven radish]

Marshall The Gamer

[idle carbon]

Do?

[terse solar]

its two integrals, one inside another

[idle carbon]

😮

😭

[misty crest]

it’s used in multivariable contexts

[idle carbon]

Ohh

Kool

Aid

[misty crest]

there are a lot of things you can do

$\iint$

[woven radish]

knief

[idle carbon]

Oh

[misty crest]

you can do that btw

$\iiint$

[woven radish]

knief

[idle carbon]

$\iiiint$

[woven radish]

Marshall The Gamer

[idle carbon]

😱

$\iiiiiiint$

[woven radish]

Marshall The Gamer
Compile Error! Click the reaction for more information.
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[idle carbon]

I broke it

[misty crest]

https://youtube.com/playlist?list=PLHXZ9OQGMqxc_CvEy7xBKRQr6I214QJcd&si=IByRF6HvTgv2UfIl

[terse solar]

if you really want to understand calculus, start at sequences, series and limits, knowing what a double integral symbol is won't be useful to you until later

[misty crest]

this is a good playlist

[idle carbon]

Ik

[misty crest]

but yes you need single variable beforehand

and before that you need algebra

[idle carbon]

Yeah

My mommy says I’m special

[restive river]

man I skipped my entire sequence chapter in my precalc class and got away with it in final exams, i hope i wont run into any issues in calc 1

[idle carbon]

💀

[misty crest]

you won’t

[restive river]

👍

[misty crest]

calc 2 has sequences

and series

[restive river]

calculus 1 seems easier than precalc

[idle carbon]

I love sigmas

[restive river]

at least the limits look easy

[idle carbon]

$\sum$

[woven radish]

Marshall The Gamer

[restive river]

the hell is that symbol

[idle carbon]

I am Σ

[misty crest]

summation

[restive river]

do yall use it in calc

[misty crest]

yep

[restive river]

i think i skipped that shit too

[misty crest]

you’ll see it in riemann sums

[idle carbon]

A sum of a series increasing in value by set intervals

[terse solar]

please dont skip this stuff lol it will be important

[idle carbon]

I am so Σ

[terse solar]

you dont want to encounter it at a point when your teachers or professors bring it up and assume you already know what it means

[idle carbon]

I wrote a formula with it, took me an hour but it works

[restive river]

👍

my initial plan was to major in computer science, then I decided to switch to computer engineering

i skipped my entire discrete math class too

[restive river]

i hope i wont run into any issues in comp eng classes

discrete math is the worst bs i ever seen

[idle carbon]

Good luck 💀

[misty crest]

nope

[idle carbon]

I’ve tested it

[terse solar]

your notation is wrong

[idle carbon]

Wdym

[misty crest]

k is the index

[idle carbon]

Can you adjust my variables?

[misty crest]

you can’t go from k = 1 to k = k -1

that makes no sense

[terse solar]

the first summation also has no lower bound given

[restive river]

slap a couple variables there it should fix it 👍

[misty crest]

yep

[idle carbon]

You set the lower boundry, the first one is the input

[misty crest]

you have to write that?

[idle carbon]

It is a formula for solving summations where K ≠ 1

[misty crest]

you’re confused

look up a video on summation notation

[idle carbon]

I have tested with a summation calculator and it evaluates properly

K-1 is just saying that the N value for the summation is equal to K-1

[terse solar]

that is definitely not how the notation works

[idle carbon]

It is just representing a variable

It holds no value on it’s own

[misty crest]

if you’re trying to represent some other quantity then you can’t use k since it’s the index variable

[idle carbon]

So how would I represent that the N in the third summation is equivalent to the lower bound of the original summation - 1?

[terse solar]

the original summation doesnt have a lower bound 😭

[idle carbon]

You set the lower bound yourself, plug in the values

[misty crest]

$\sum_{k=1}^n k$

[woven radish]

knief

[idle carbon]

The rest of it is just a way to solve for it

[orchid shadow]

sorry

[misty crest]

lmao

[terse solar]

again, that's not how the notation works, you can't just leave part of an equation blank to fill in, use a variable instead

[idle carbon]

💀

[idle carbon]

So it would be K = g or smth

[terse solar]

yes

[orchid shadow]

do you want two nested summations? like $\sum_{k=1}^n\sum_{j=1}^{k+1}x$

[woven radish]

DiamondPanda16

[terse solar]

it doesnt seem that way since all the summations are isolated in parentheses

and i dont think he's at the point where he can apply nested summations yet

[idle carbon]

Like this?

[idle carbon]

I cant

[misty crest]

why N = Z?

[idle carbon]

A placeholder variable

[misty crest]

$\sum_{k=1}^n k = 1 + 2 + 3 + \dots + (n-1) + n$

[woven radish]

knief

[idle carbon]

Ik

[misty crest]

what use is there in saying n = z

[idle carbon]

Z is the input variable

[misty crest]

no

[idle carbon]

Its just saying that you set the value of Z and the upper limit of the summation is equal to that

[misty crest]

just leave it as N then if you want it to be a variable

[terse solar]

the notation on the upper bound doesn't work that way either;
in this kind of summation, both the top and bottom should have a value that represents the lowest value and highest value of the index k; and the notation k=1 on the lowest bound is only using the equality sign to indicate that k is the index of that summation

[idle carbon]

Whats an index?

I haven’t learned it yet

[terse solar]

the value inside the summation that changes in each term of the sum. here it's k

[idle carbon]

Ohhh

[terse solar]

if you want to understand summation notation, you should start again and maybe watch some youtube videos that properly explain it

[woven radish]

Marshall The Gamer
Compile Error! Click the reaction for more information.
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[terse solar]

its correct now

[idle carbon]

I know how summation works

[idle carbon]

Index variables hurt my brain

[terse solar]

it feels like you're trying to skip ahead and get to more complex topics without having fully done the learning and practice required to fully understand the concepts that surround them

[idle carbon]

I spent a good chunk of time focusing on summation, so i understand the general concept, i cant calculate large summations by hands though as i do not know the proper way to convert sigma notation into algebraic notation

[terse solar]

the sums you're working with are called arithmetic series and have a closed form that doesn't involve any summations, but you do have to understand that summations can be very general and the expressions inside of them can be arbitrarily complex, which is the thing that makes them so useful in the first place

[idle carbon]

Ok

Yippy!

Google forgot my parentheses!

😤

[terse solar]

have you seen that $\frac{n\cdot(n+1)}2=\sum_{k=1}^n k$

[woven radish]

lava

[idle carbon]

Yeah, that formula is actually what led me to finding sigma notation

[terse solar]

if you wanted to move on from here, you could search up something like the geometric series

[idle carbon]

Would khan academy be a good source?

[terse solar]

idk anything about khan academy but theyre probably reliable

[idle carbon]

I need textbooks 😭

[terse solar]

you could wait until your school curriculum covers this material, lol

[idle carbon]

That is gonna take like 5 years…

7+5=12

12 is high school graduation

[terse solar]

summation is covered before 12th grade

[idle carbon]

So prob 2-3 years

[terse solar]

at least it should be

if you think you should be in a higher level math course why don't you propose it to your teacher

[idle carbon]

I dont want to skip grades, and i am already in the honors program

I have to wait until high school to be able to take way higher level classes

Lava I sent you a friend request

[terse solar]

then what's the hurry

[idle carbon]

I get bored, and i love math

[devout snow]

@orchid shadow Has your question been resolved?

[orchid shadow]

its not my question

.close

[devout snow]

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[jolly cave]

Can someone help understand how to do restrictions?

[jolly cave]

For example,

[terse solar]

with the square root function, everything inside the square root has to evaluate to a number that's not negative, right?

the restriction on a square root is that the value inside should always be at least 0

so you can say $18x^4y\geq0$

[woven radish]

lava

[terse solar]

the restrictions on the individual variables are the inequalities that you can choose so that this restriction will always be true

i think you can just leave it in this form for this question

[jolly cave]

I don’t get it

[terse solar]

well you can't take the square root of a negative number, therefore the number inside any square root has to be at least 0

[jolly cave]

Ok

So we will always know that

Greater or equal to 0

[terse solar]

yes

[jolly cave]

And how about

Figuring it out

Fixing out if the number that has to equal to 0 or higher

Figuring*

[terse solar]

in this problem the expression is $3\sqrt{18x^4y}$, and the number inside the square root is $18x^4y$. So you know that there must be the following restriction: $18x^4y\geq0$. You can simplify this by dividing both sides by 18: $x^4y\geq0$. And because $x^4\geq0$ for all values of $x$, the restriction on the variables must be that $x=0$ (so that the whole expression is equal to zero), or $y\geq0$ (when x is nonzero, you can divide both sides of the equation by $x^4$ to find this)

[woven radish]

lava

[jolly cave]

Hm ok

My teacher does it quite differently I can show you an example

[terse solar]

sure

[terse solar]

i see

[jolly cave]

Wait I think I understand it now

[terse solar]

instead of using an inequality, your teacher finds the point where it equals zero, and tests each side to determine whether that side causes the inside of the square root to be negative or positive

The result is the same though

[jolly cave]

Yeah he uses 2 cases to show and prove that anything lower is incorrect

So when stating a restriction

Do I state the answer of what X equals?

[terse solar]

well you have to figure out when the inside of the square root is equal to zero, and then you have to figure out whether to use a less than or greater than sign, etc, by your teacher's method

[jolly cave]

Hm

I’m not sure if the case proving is necessary I’ll have to ask him

Finally I figured it out though I was just missing a little bit of information

Thanks lava

[terse solar]

no problem

[jolly cave]

But how would you say

Find a restriction for a question with no variable

For example

Square root of 108

[terse solar]

i mean there's not really a restriction

[orchid shadow]

there's no restriction if there's no variable

[terse solar]

108 > 0 is always true

[orchid shadow]

the restriction is on the values the variable can take

[terse solar]

its either just true or not true

[jolly cave]

Hm okay

[terse solar]

if you were asked a question like that, with no variables, you could either say "there is no restriction" whenever it's a positive number inside the square root, or "DNE (does not exist)" whenever it's a negative number inside the square root

[jolly cave]

Oh yeah your right

He mentioned that briefly

.close

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[devout snow]

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[mortal pendant]

Where am I going wrong? I'm trying to do 675 / 15

You divide the 675 by the 5

And then the 3

Then u have ur answer

Yes?

Or should it be 3, and then 5?

[devout snow]

@mortal pendant Has your question been resolved?

[solid osprey]

(you should probably cover up your name) the division of 5 is correct, im not quite sure what you did on your division of 3?

also yes you can do that, either doing 3 and 5 or 5 then 3 both works and would yield the same result

[mortal pendant]

3 goes onto 135, 1, 0 times, remainder 3, and 3 goes into 33 11 times

And 3 goes into 5

0 times

Wel

Once

And so on

What went wrong here?

@proper kindle

@solid osprey

[solid osprey]

it should be remainder 1 no?

[mortal pendant]

Which?

[mortal pendant]

Which

@solid osprey

Which?

[solid osprey]

3 goes to 1 0 times, so remainder 1

[devout snow]

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[celest grove]

help

[celest grove]

The sequence of natural numbers x,y,z forms a geometric progression whose denominator is a natural number. Find the terms of this progression if it is known that their arithmetic mean is equal to (y+9)

<@&286206848099549185>

<@&286206848099549185>

[wind mason]

!15m

[devout snow]

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.

[wind mason]

Reminder that you're pinging thousands of people at once; with great power comes great responsibility.

[wind mason]

What have you tried?

[devout snow]

@celest grove Has your question been resolved?

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[calm heron]

Is this proof correct?

[winter torrent]

i'm assuming it's rough since you're on an ipad and not paper/pencil, but you should make sure your handwriting is legible. There are some spots that are particularly difficult to read, such as isin P and the boxed section up top

instead of that purple bit up top, just put "therefore ac > bc" at the end

[wind mason]

Yeah, I'm also hallucinating a bit. I see $i\sin$ rather than just is in.

[woven radish]

;(

[calm heron]

Apologies my hand writing is pretty bad sometimes

I can re write neater if you can’t read it

[devout snow]

@calm heron Has your question been resolved?

[calm heron]

Do I have to do the since c is not in p and c not equal to 0 or is there shorter way

(It’s my first time attempting formal proofs)

[devout snow]

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[tacit crow]

Hiii

[tacit crow]

How would I draw the contour lines for z=2x^2 for 2<=z<=8

I was thinking it would be a parabolic shape but i don’t think this is right

[pseudo basin]

x = ±sqrt(z/2) is what you get as your contour line equations

[devout snow]

@tacit crow Has your question been resolved?

[tacit crow]

So will it just be straight lines?

[pseudo basin]

yup

[tacit crow]

Vertical lines

[pseudo basin]

yup

[tacit crow]

Oh okay great thanks

[tacit crow]

I don’t really understand the contour lines. Because now I’ve drawn them and if I have z=8 for example then x=+-2 but then on the z-x graph, z isn’t 8 but z is all the values if you know what i mean?

[devout snow]

@tacit crow Has your question been resolved?

[pseudo basin]

the contour lines live in the xy plane

the contour lines show you where exactly z is 2, 3, ..., 8 looking from the top

[devout snow]

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[quiet furnace]

derivative of a composite solved using chain rule and quotient/product rules. 💀 im foiling out the highlighted part and i don't think that's what im supposed to be doing. please help 🙏

[sand dove]

there is no x^2 term in foiling

two x^3 terms are what you should get

x^2 * x and x^3 * x^0

[quiet furnace]

im confused

OHHHHH

so the correct answer would be h'(x) = 45x^5 + 84x^3 + 25x / √x^2+2 ?

ok i ended up just putting the answer in to check... now im confused how i got 84 and they got 90...

<@&286206848099549185>

[sand dove]

(a+b)^2 = ?

[quiet furnace]

i did that part, 3x^2^2 + 1^2 = 9x^4 + 1

and then the x on the outside made it 9x^5 + x

[sand dove]

nope, it's wrong

you're acting like (a+b)^2 = a^2 + b^2

someone doesn't remember their quadratic identities...

if you don't remember

[quiet furnace]

oh my goodness gracious

[sand dove]

write (a+b)^2 = (a+b)(a+b)

[quiet furnace]

https://tenor.com/view/meme-anime-gif-22734101

[sand dove]

and expand

[quiet furnace]

THANKS...

🛐 LOLL THANK YOU I SEE IT NOW

HOORAY... how do i resolve the question

[sand dove]

either .close or .solved

[quiet furnace]

.solved

[devout snow]

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[devout snow]

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[hard ocean]

If f is a function that is differentiable two times on a point a, then I can conclude f is differentiable once on an open neighbourhood of the point a correct ?

[hard ocean]

Where do I see a proof of this ?

Or how it comes to be true

[muted mural]

I don't think this is true

I think you can compress a sawtooth function so that all its derivatives at 0 are 0 but it has cusps infinitely close to 0

[hard ocean]

Yes maybe if given that f is differnetiable on 0 once but you can't if it's differnetiable twice (?)

Because then $f''(x)= \lim_{x \to 0} \frac{f'(x)-f'(0)}{x-0}$ exists, and therefore (i have no idea why) it means it's differentiable once on an open neighbourhood of 0

I'm trying to figure out why

[woven radish]

prograce

[hard ocean]

Idk might be wrong tbh.... if you,could write the counterexample I would appreciate it

[muted mural]

If every neighborhood of 0 had a point of non differentiability, then this limit wouldn't exist.

Because it would always have points that are undefined no matter how close you go to 0.

Do you epsilon delta?

[hard ocean]

Yes?

I see makes sense so there has to be a neighborhood where it's differentiable in all points in the neighborhood

[muted mural]

There is more than one way to define second differentiability at a point though

If you want it to be the derivative of the derivative, then yes the derivative must exist in a neighborhood. But that isn't necessary for finding the second derivative at a point.

[hard ocean]

So the theorem is true?
Ok well, I don't want that information to find the second derivative at a point I want it to use that it's differentiable at open neighborhood of a

[muted mural]

Differentiable two times at a point is ambiguous though

[hard ocean]

Why? Isn't it straightforward?

Differentiable twice at point x => f"(x) exists

What else can you conclude from differentiable two times ?

[muted mural]

You can define it as f(x)= f(0)+ ax+bx^2+o(x^2) existing

[hard ocean]

Ohh

[hard ocean]

Could be, but usually in my course this is the default

[hard ocean]

This could be useful for another question

[muted mural]

If there's context that says the limit of the limit must exist, then I think you're good because a limit can't exist at a point which is an accumulation point of holes of the domain

[hard ocean]

Yes

[devout snow]

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[toxic spire]

I cant figure out how to do this

[pseudo basin]

break into cases according to the size of group C (it can have either 1, 2 or 3 students but no other number)

[devout snow]

@toxic spire Has your question been resolved?

[toxic spire]

Hmm

What about the cases of group A and B having no students?

[pseudo basin]

well you will have to subtract those away in each case

[toxic spire]

Damn

Hmmm

Alright ill try

.close

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[normal bough]

this is the graph of the first derivative

does the function reach local extremum

the answer says No but I thought Yes becuae there are places where f`(x) = 0

but the second derivative is 0 here as well so these are inflection point not extremas yes?

sbd plz help

[normal bough]

I think that there can be an inflection point at the same time with an extrema so i dont knwo

I am stupid, there cant be an extrema and inflection point at once

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[copper prairie]

this is like my 6th time asking for help today

[copper prairie]

but here goes

$\frac{\left(2x-1\right)}{x+3}$

[woven radish]

♱

[copper prairie]

How do i find the inverse function of this

am i supposed to polynomial division

i lit dont know where to start

[faint gorge]

try to solve for y

[copper prairie]

i tried doing the graph of 1/x but that did NOT help

[wind mason]

Sure. Or note that $\frac{2x-1}{x+3}=2+\frac{A}{x-3}$.

[woven radish]

;(

[copper prairie]

right.......... Howd u get there

[faint gorge]

factor 2 then you got x-1/2 then add and subtract 3

[copper prairie]

ok hold on lemme try it on paper

Ill brb

[wind mason]

You can always just note that the the coefficients of the x should match up.

[copper prairie]

ok so that is

2 - 7/x + 3

[wind mason]

Plus?

[copper prairie]

acciden

[wind mason]

Oh, nevermind, I can’t see well cause of the glare.

[copper prairie]

Ok wait but how do i find the inverse function now

y - 2 = -7/x + 3
?

$y-2=-\frac{7}{x+3}$

[woven radish]

♱

[copper prairie]

guys literally what how r u supposed to find the inverse of fractional functions

[faint gorge]

multiply by x+3

[copper prairie]

then youd get terms like xy and stuff

and that sux

[faint gorge]

yes

the yx terms

you factor y

that's the trick

[copper prairie]

I tried

i got

(-13 -2x ) / x+3

it doesn't look right

[copper prairie]

yeah solving for y there gives u

$\frac{\left(-13-2x\right)}{x+3}$

[woven radish]

♱

[faint gorge]

hmm

[copper prairie]

It doesnt make sense why is the inverse just shifted vertically

[faint gorge]

how'd u get 13

you add 6 on both sides

[copper prairie]

i have no idea

[faint gorge]

-7+6 = -1

[copper prairie]

$\left(y-2\right)\left(x+3\right)=-7$

[woven radish]

♱

[copper prairie]

$xy+3y-2x-6=-7$

[woven radish]

♱

[copper prairie]

$y\left(x+3\right)=2x-1$

[woven radish]

♱

[copper prairie]

U just get back at the original position

chatgpt says the inverse is (-3x - 1) / (x - 2) but i dont trust it

[iron kindle]

!nogpt

[devout snow]

Please do not trust ChatGPT or similar AI tools for mathematical tasks, as they often generate output which "sounds correct" but has numerous factual or logical errors. Use of these AI tools to answer other people's help questions is strictly against server rules (see #rules).

[copper prairie]

..which is why i said i didn't trust it

h

ykw i give up

[faint gorge]

no

[copper prairie]

i lit don't get it

the next question is another "find the inverse of this fractional function"

how can u . When if u multiply u get xy terms

in class we did a method that was like

Polynomial divisiona

and then doing something with the gra[h of 1/x

I don't get that either

[faint gorge]

I know what happened and it was misleading

[faint gorge]

should have worked with that smh

[copper prairie]

what did u mean try to solve for y

[faint gorge]

x(y+3) = 2y-1
xy+3x = 2y-1
xy-2y = -1-3x

y(x-2) = -(1+3x)
y = -(1+3x)/(x-2)

When you have an equation y = f(x) and you want to compute the inverse

then first step is to flip x with y

x = f(y)

and then solve the equation for y

[copper prairie]

ok i got this

Oh

Ok the graph is shifted when its inversed bc

The asymptote at -3 just becomes an asymptote at 3

idk

I think

[faint gorge]

the inverse function of a function is basically symmetric to y = x

[copper prairie]

oh yeahhhh

we did something like that

[faint gorge]

https://www.desmos.com/calculator/9jz7mx4k2b

[copper prairie]

yeah i js did that

so i think

also

for

I am guessing it works for this too

our maths teacher also said to

try to find the inverse by restricting the domain/codomain?

But idk how that would work

i mean, i know how it would work for functions like x^2

but no idea for this

alr

whatev

I did it

I'm done w the hw and everything

so ty again for helping

.close

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[faint gorge]

.here you don't have to actually

[topaz obsidian]

Can someone explain why this ain’t the right anwser

For reference this is the right answer, but idk how they get 484 in the square root

Also ignore I didn’t square root the 484 on the bottom in the image I initially sent, I noticed that and forgot to change it bc it in pen rn

[sharp kayak]

remember $\frac{x^2}{484} + 1 \neq \frac{x^2 + 1}{484}$

[woven radish]

BuilderDolphin

[topaz obsidian]

OHHHHHH

OHHHHHHHHH

[sharp kayak]

yep

[topaz obsidian]

I have to find the like demoninator

Bruhhhh

I’m such a goofy

Thank you so much

[sharp kayak]

1 is just the number over itself lol

no

np*

[topaz obsidian]

I was worried I was wrong again😂

Have a great one, you’re amazing!

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[granite anvil]

how come this is 1

[granite anvil]

i am getting lim x-> inf of sin(1/x) which is 0 divided by lim x-> inf of 1/x which is also 0

so 0/0 = undefined

[iron kindle]

taylor expansion

[sand dove]

or y = 1/x

and l'hôpital or whatever

[pulsar dock]

A relatively straight forward proof is to use the substitution x = 1/u and use the definition of the derivative

or I guess it's clearer to use the substitution x = 1/h

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[devout snow]

Please don't occupy multiple help channels.

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[wintry cosmos]

Hi I'm not sure how to set up this hw problem, what steps would you guys use to tackle this?

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[bold venture]

did i do this correctly? my answer is 104.142

[supple knot]

what is your work exactly

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[bold venture]

what do you mean

[bold venture]

everything in the red pen

i used the integrating factor

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[solar goblet]

i wanna check my bases

for V, it's x^3, x^2, x^1, 1

for W, it's 3x^2, 2x, 1

[heavy current]

seems good to me

[solar goblet]

by the say, x^2, x^3, x, 1 and x^3, x^2, x, 1 are the same bases right?

does order matter?

[heavy current]

yes, order matters

it matters a lot

if you take the basis {x^2, x^3, x, 1} of V instead, then D(v_1) = 2x = 0 * 3x^2 + 1 * 2x + 0 * 1

so the first column of the matrix rep of D is [0, 1, 0]

not [1, 0, 0] anymore

[acoustic leaf]

that's why axler defines bases to be lists rather than sets

[heavy current]

lists are ordered yeah

FIS and many other LA books use ordered bases

[solar goblet]

i see, thank you

btw, what does differentiation matrix look like for nonpolynomials?

[acoustic leaf]

well you have to have some subspace which is closed under differentiation to have a matrix representation

[heavy current]

the vector space of differentiable functions has uncountable dimension, iirc

so matrix rep doesn't quite work

[heavy current]

actually, it might be countable, idr

[acoustic leaf]

e.g. the subspace $\vspan{\sin x, \cos x}$ would have matrix [ \mat{0 & 1 \ -1 & 0} ]

[woven radish]

cloud

[heavy current]

but either way, matrix representations of linear maps on infinite dim spaces aren't isn't quite the same

but as cloud says, a f.d. subspace would be fine

[acoustic leaf]

a very niche integration technique is to invert the differentiation matrix for a particular subspace

[solar goblet]

is there such a thing as infinite matrix?

if axler defined the matrix using basis, how would it make sense in infdim space?

[heavy current]

I'm no expert on infinite matrices, unfortunately

they do exist though

[acoustic leaf]

i think you can do something with countable bases, but you run into hairy convergence issues

[heavy current]

your bases become sequences in infinite dim, and I'm pretty sure you need to force said sequences to have only finitely many non zero elements

or else you do indeed run into convergence issues

for matrices, the consequence is that each column of an infinite matrix must have only finitely many nonzero entries

[solar goblet]

hm, i see

alright thanks

.close

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[dire mica]

does anyone have an explanation or video or something as to why if the discriminant of a straight line and a quadratic equation being equal to zero proves that they are tangential? I get the concept and can apply it but it doesnt make 100% make sense in my head.

example Q:
prove that for all real values of m, the line x=(y/m)+m is tangential to the parabola x^(2)=4y

working:

y=(x^(2))/4
y=mx-m^(2)

(x^(2))/4=mx-m^(2)
m^(2)-m^(2)=0
therefore Δ=0, and so the lines are tangential

[dire mica]

I understand how to do this question, but I cant fully visualise how the discriminant of both lines combines being zero proves their tangentiality

[devout snow]

@dire mica Has your question been resolved?

[finite briar]

Do u understand what we did here? Like why did we equate the two?

[devout snow]

@dire mica Has your question been resolved?

[acoustic leaf]

if you equate a linear and a quadratic equation, that gives you a new quadratic equation whose solutions are the intersection of the line and parabola

there are 3 possibilities there:

• they intersect twice, so the equation has two solutions, so discriminant > 0
• they intersect once, meaning they are tangent, so the equation has one solution, so discriminant = 0
• they don't intersect, meaning the equation has no solutions, so discriminant < 0

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[restive river]

Question: You are asked to arrange 10 books titled A through J in an ordered list such that the following pairs of books are not beside each other: (A, F), (B,D), and (A, B). In how many ways can the books be ordered. Provide reasoning.

My Attempt:

Total number of ways: 10!
Number of ways (A&F) or (B&D) or (A&B) occurring with everything else being random: 3x(2x9!)

ways A&F and B&D are adjacent: 2x2x8!
ways A&F and A&B are adjacent (Only happens if FAB or BAF): 2x7!
ways B&D and A&B are adjacent (Only happens if ABD or BDA): 2x7!

Ways all 3 pairs are adjacent to each other (Only happens if DBAF or FABD): 2x6!

Where I'm stuck: Not even sure if the last three lines are correct. Can't wrap my mind around the correct way to compute the overlapping. Thank you!

[restive river]

<@&286206848099549185>

am I asking in the right place?

[devout snow]

@restive river Has your question been resolved?

[restive river]

no

[devout snow]

@restive river Has your question been resolved?

[restive river]

no

<@&286206848099549185>

[devout snow]

@restive river Has your question been resolved?

[frosty portal]

if u think abt it

the only way A,F and A,B and B,D

are arranged together

is with some permtutaion

of araning these groups

so do not consider sperete cases

[restive river]

Well it says that the pairs are next to each other, so the case where AFBCDEGHIJ is wrong as well as a case where two of the pairs are next to each other, or even all 3 of the pairs.
The question is not asking about only the case where all 3 are beside each other. From my understanding we need to consider separate cases

[devout snow]

@restive river Has your question been resolved?

[restive river]

yo whats 1+1 ?

lol

maybe 3

[wheat pawn]

how about you stop trolling?

[devout snow]

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[pseudo basin]

!status

[devout snow]

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

[pseudo basin]

@cerulean badge

[cerulean badge]

I feel like I'm making a major mistake but I really can't tell where

[pseudo basin]

your notation is a little bit all over the place

and it's hard to work with or think about or even read

(your handwriting also doesn't really help)

but there is a clever way to do this

[cerulean badge]

😭😭😭I'm sorry

[pseudo basin]

just to set your notation straight a bit: let's write $a_n$ for the $n$'th term of the GP. (notice that the ``th'' is not written)

[woven radish]

ann.in.a.teacup

[pseudo basin]

we have two sums: $A := a_1 + a_2 + \dots + a_n$ and $B := a_{n+1} + a_{n+2} + \dots + a_{2n}$

[woven radish]

ann.in.a.teacup

[pseudo basin]

our goal is to show $\frac{A}{B} = \frac{1}{r^n}$ yes?

[woven radish]

ann.in.a.teacup

[pseudo basin]

(i have not made any calculations so far just writing what we've got in a clean way)

[cerulean badge]

Okay 👌

[pseudo basin]

ok now

the trick is you do not actually need to calculate either A or B themselves

you could but it would take a lot of work

(maybe not so much that i would say "it would take you 17 years to do that" but still)

the trick is: $a_{n+k} = a_k \cdot r^n$ for any index $k$.

[woven radish]

ann.in.a.teacup

[pseudo basin]

do you understand why this is?

[cerulean badge]

Nope, never seen this actually 🤔

[pseudo basin]

well ok you know what a GP is in general right?

[cerulean badge]

Yeah

[pseudo basin]

going from one term to the next means multiplication by r

[cerulean badge]

Yes

[pseudo basin]

$a_{n+k}$ is where you get when you take $n$ steps like that starting from $a_k$

[woven radish]

ann.in.a.teacup

[pseudo basin]

so you multiply by r a total of n times

i.e. by r^n

that make sense?

[cerulean badge]

Yeah

[pseudo basin]

yeah os

so*

$B = a_1 r^n + a_2 r^n + \dots + a_n r^n$

[woven radish]

ann.in.a.teacup

[cerulean badge]

Ohhh okay

[pseudo basin]

do you see how to continue?

[cerulean badge]

Hmm kinda, give me a sec

Ohhh

Yeah

It all just cancels out

Nice and smooth

Omg thank you, life saver 🙏🙏🙏🙏🙏

.close

[devout snow]

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[devout snow]

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[granite anvil]

is my work right

this is the question

i dont have the answer so thats why im asking

[polar chasm]

,w d/dx sin(x)/cos(2x)

[woven radish]

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Requested by methisalwaysright

[polar chasm]

,w sec(pi/3)(cos(pi/6) + 2sin(pi/6)tan(pi/3))

[woven radish]

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Requested by methisalwaysright

[polar chasm]

your slope seems to be wrong

[granite anvil]

oh

yep i forgot the negative sign in the second line after seting the deriv = pi/6

ok so i've got y = 3root3x - root3 x pi/2 + 1

$3\sqrt3x - \sqrt3\frac\pi2 + 1$

[woven radish]

gamer75431

[granite anvil]

is this right

[polar chasm]

looks better

,w sin(pi/6)/cos(pi/3)

[woven radish]

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Requested by methisalwaysright

[polar chasm]

yep

that should be right

[devout snow]

@granite anvil Has your question been resolved?

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[wet robin]

i dont get it

[jovial turtle]

hello

[solar goblet]

!occupied

[devout snow]

Someone else is already using this help channel. If you need help with a question, please open your own help channel/thread (see #❓how-to-get-help for instructions).

[jovial turtle]

oh sorry

[solar goblet]

you need to find m?

[devout snow]

@wet robin Has your question been resolved?

[devout snow]

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Remember:
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• Show your work, and if possible, explain where you are stuck.
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[solemn marten]

when im comparing coefficients here, as in cos(x), i also have to account for the sin(x)

[solemn marten]

what would the comparision be? i would have said C1 + C1*sin(x) = 2

but do you have to accuont for the cos^2(x) as well?

[solemn marten]

woops this is what i meant

anyone?

[finite briar]

Can't do comparison here

[solemn marten]

yes you can

[spring rover]

I can help you

[solemn marten]

please do

[spring rover]

what?

[solemn marten]

??

[spring rover]

what do you think?

[devout snow]

@solemn marten Has your question been resolved?

[solemn marten]

anyone

[solemn marten]

thgis was incorrect

[spring rover]

what?

I don't understand

[solemn marten]

can someone other than an ai help me

[spring rover]

what can I heip you

[solemn marten]

.close

[devout snow]

Channel closed

Closed by @solemn marten

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[devout snow]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

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

[devout snow]

Please don't occupy multiple help channels.

[olive snow]

https://discord.com/channels/268882317391429632/903430333096132618

close it or idk

else for your problem

[feral bobcat]

i need help in both

can i post both here

[olive snow]

just do one after one

[feral bobcat]

ok

ill close the other

can you help me please

[olive snow]

what's the center point of the cube

any idea ?

[feral bobcat]

the cube has a diameter of 8

[wheat pawn]

cubes dont have a diameter

[feral bobcat]

so i thought the raduis of the sphere is 4

[olive snow]

yes

it will

[feral bobcat]

i mean the diagonal line

likea like equal to the side length

[wheat pawn]

the diagonal of that cube is not 8 either. The edge is 8

[olive snow]

the edges ?

[feral bobcat]

i mean any line equal to the edge inside the sphere

[wheat pawn]

that's different. The diameter of the sphere is equal to the cube edge

[wheat pawn]

which means that this is correct. But careful with naming stuff

now, what's the volume of a sphere or radius 4?

[feral bobcat]

tbh i do not know anything abt cubes execept their volume

anyways so 4/3 x 4^3 x pi

[wheat pawn]

which is...?

[feral bobcat]

85pi

85.33pi

that is why am asking what i did wrong

[wheat pawn]

nothing

if the biggest sphere is 85pi volume, which answers are not viable?

[feral bobcat]

D and C

[wheat pawn]

what about B?

[olive snow]

you can add another one

[feral bobcat]

so A

oh so the max volume is 85

[wheat pawn]

they are basically asking: with same center, can you have sphere A? and sphere B? and sphere C? and sphere D?

its not particularly well worded tbh

[feral bobcat]

bruh no way i lost 2 marks in my exam for this shit

this is what i reached

[alpine python]

that doesn't look like a tangent point to me

[feral bobcat]

is this correct

[high wedge]

U are right

that is the most primary right triangle.

nothing more?

[feral bobcat]

this

so I know that to find the average

we use slope formula

so i choose the points T, F2 and T+3 , 0

however, it did not work with me

[alpine python]

that should give F2 / 3

that's not wrong, but it's not one of the options so you have to choose different points

[feral bobcat]

let me try again

[spring rover]

answer is F1/T+3

[feral bobcat]

which points u used

[spring rover]

Do you want to explain the solution process?

[alpine python]

you can get that with (0,F1) and (T+3,0)

[feral bobcat]

F1-0/ 0 - T+3

there is a negative sign

[spring rover]

first 𝑇 hours is F1-F2,

The remaining fuel 𝐹2 is used up in 3 hours, so the fuel consumption rate during these 3 hours is F2/3

[alpine python]

negative sign is ok, you'll also get a negative sign with the other points you tried

[feral bobcat]

oh right because its decreasing

[alpine python]

yes

[feral bobcat]

line A means its not moving right?

that means constant velocity

[alpine python]

if you have constant velocity of 0 then you're not moving

if you have constant velocity of say, 10 km/h then you are moving

[feral bobcat]

oh right

so is II correct?

i mean I

II is correct but idk about I

[spring rover]

At 𝑡=0 both autos start together.

If A has a positive velocity and B has a decreasing velocity reaching zero, then A moves ahead while B slows down.

If B's velocity becomes negative, it moves in the opposite direction.
If B's velocity just decreases but stays positive, A moves faster, and they still separate.

[alpine python]

yeah imagine 2 cars driving next to each other, and one of them starts braking

[spring rover]

So, A and B move apart, making Statement I correct.

@feral bobcat do you understand?

[feral bobcat]

but negative veloctiy just means its speeding down right?

[alpine python]

no that's negative acceleration

negative velocity means driving in the opposite direction

[feral bobcat]

dang that is kinda counter intuitive

[spring rover]

yeah Axe is right

[feral bobcat]

but here its positive velocty?

[alpine python]

you don't really need to think about negative velocity for this problem

[feral bobcat]

because its above y axis

it is just decreasing

so negative acceleration

[alpine python]

yes

[spring rover]

Distance traveled is found by calculating the area under the velocity-time graph.
Since A has a constant higher velocity, the area (distance) covered by A is larger than that of B, whose velocity is decreasing.
Hence, A travels a greater distance than B, making Statement II correct.

[feral bobcat]

ok so let me just recap

while velocity is in the +y axis, this means it is moving right ( the same direction of A in this same)

when it is -y axis, it is moving the opposite direction, and the decreasing line just shows the magnitude

[high wedge]

the distance traveled by A is the area of triangle A and in case of B is the area of square B, so imagine.

[spring rover]

Um...

[high wedge]

so both are right

[feral bobcat]

is this correct

[spring rover]

[high wedge]

S=v*t, right?

@feral bobcat , isn't it?

[spring rover]

yeah both is right

[feral bobcat]

v = displacement / t

[feral bobcat]

then this means I is wrong

[high wedge]

never

[spring rover]

yes, you are wrong

[high wedge]

v * t = displacement/t * t

[spring rover]

......

[feral bobcat]

dude why is this confusing 😭

[high wedge]

what about you, @feral bobcat ?

easy boy, take it easy.

v * t = displacement/t * t , do you agree?

???

what are you doing now?

[spring rover]

Hey

[feral bobcat]

am here

i am just trying to analyze how I is correct

if they both are moving forward

how does that mean they are moving away from each other

we could say that A is moving faster or farthe

[high wedge]

Do you know Einstein's theory of relativity?

[feral bobcat]

bro how is that related

[feral bobcat]

@alpine python

is this correct

they are both moving right

so how does that mean they are moving away from each other

[spring rover]

NO you are Wrong

[alpine python]

they are both moving forward but their separation is increasing

[feral bobcat]

so does that mean they are moving away from each other?

i feel the wording is trash for that question

[alpine python]

eh

[feral bobcat]

that means they are farther from each other

[spring rover]

Hey

[high wedge]

if A moves faster than B, B looks A is away from own

[spring rover]

Yes this Johmsmith0317 is right

[feral bobcat]

ok ig i over thought

[high wedge]

good

[spring rover]

Great

[high wedge]

anymore?

[feral bobcat]

yes

can i dm you them pls

[high wedge]

of course

[devout snow]

@feral bobcat Has your question been resolved?

Channel closed

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Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

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

[restive river]

hello

[restive river]

i will post my question

1s

[iron kindle]

start the channel with the question next time pls

(then it also gets pinned)

[restive river]

sorry

im installing discord again on my phone to upload the pic

the status of the question is that i solved it but got an incorrect answer not sure why