help-0

[tidal zealot]

why cant i tho

[knotty spire]

Because reality says otherwise

[real gazelle]

so if you try that, you are missing the x

try taking the derivative of the thing you have

[tidal zealot]

my whole life is a lie

im sad now

[real gazelle]

and you'll see why the derivative isn't equal to the thing you want

[knotty spire]

$\int(3x-4)^4\dd x = \frac{1}{3} \int (3x-4)^4 \dd (3x-4) = \frac{1}{3} \frac{(3x-4)^5}{5} + C$

[ocean seal]

Remavas

[tidal zealot]

so ur saying i cant do what i did if my x is to the power of 2 or grater

[knotty spire]

this is what you did

it won't work with your new integral, exactly because the derivative of x^2 is 2x

instead of 3 like here

[tidal zealot]

ok

so

i either do u-sub or expand brackets

sad life

[knotty spire]

I very highly doubt u-sub will work

[abstract fractal]

Not in this case, but expanding brackets works

[tidal zealot]

ok :/

[knotty spire]

if you see an obvious way to do an integral, just do it

You'll miss these times

[tidal zealot]

thanks guys

.close

[lone heart]

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[alpine sable]

original question

cuz i kinda rushed

[finite flax]

Your question statement also looks very rushed

Please repost and make it more clear

[finite flax]

Nobody can understand that

[slender gull]

LMAO

[alpine sable]

?

why not

[finite flax]

I dont know why you decided to write the question you were given this way

It is a mystery to me.

[alpine sable]

wdym

[karmic rapids]

send a screenshot of the actual question

[alpine sable]

i dont have it rn

also whats the part thats confusing

[karmic rapids]

everything

[alpine sable]

huh

[finite flax]

Sir, if ypu are unwilling to restate your math question, I will be forced to close your posting

[karmic rapids]

no

you are not

[alpine sable]

when (m=-1,m>=3), g(x) and y=m has 2 intersection points

[karmic rapids]

and you will not

you are not the one to decide whether this channel gets closed

[finite flax]

and report you for child abuse

[alpine sable]

whats the confusing part here

[karmic rapids]

<@&268886789983436800> troll

[karmic rapids]

just send a screenshot of the actual question please

[finite flax]

He isnt going to

[alpine sable]

(I feel like someone asks you to post an image of the original question every time lmao)

[karmic rapids]

oh isn't this like the 4th time already

[finite flax]

This is the only way he can get off 😂

[alpine sable]

i dont have the image, and the original image is in chinese

[night geyser]

it seems clear enough to me, although i dont know whether the "m=-1, m>=3" is meant to have an "or"

im assuming it does since otherwise i dont know how to parse it

[finite flax]

You have fun figuring out what parts of his math problem belong to the math problem he "rushed" writing down and can't find now

[alpine sable]

aight ykw

im asking yall to help me on this question

This is my attempt to interpret the question:\

Let $f$ be a monic cubic given by $f(x)=x^3+ax^2+bx+c$ with coefficients $a,b,c\in \mathbb{R}$. Suppose that $f(2)=3$.\

Define $g$ piecewise as $$g(x)=\begin{cases}\frac{ax-9}{x-1}&\text{if } x<1,\ f(x)&\text{if} x\geq 1\end{cases}.$$

Furthermore, $g(x)=m$ has 2 distinct solutions for all $m\in{-1}\cup [3,\infty)$.\

Find $g\circ g(-1)$.

is that good enough

[ocean seal]

Toby

[alpine sable]

did I interpret it correctly?

pretty much ye

[night geyser]

my interpretation of the question is:

Define [f(x) = x^3 + ax^2 + bx + c].

Let [g(x) = \begin{cases}\frac{ax-9}{x-1}&x<1\f(x)&x\geq 1\end{cases}.] For any $m \geq 3$, there exist precisely two values of $x$ such that $g(x) = m$; and similarly there exists precisely two values of $x$ such that $g(x) = -1$.

If $f(2) = 3$, compute $(g \circ g)(-1)$

[ocean seal]

Namington

[night geyser]

damn i was slower

[alpine sable]

btw for u guys

this is gx

ignore the circle

and i want you guys to help me get the answer

(compare the answer)

at least you guys can save ur time by getting gx instantly

lo

fr drawing g(x) took longer than getting fx

[earnest tiger]

I would start by finding the range of $$ \frac{ax-9}{x-1} for x<1$$

[ocean seal]

D3VC

[alpine sable]

thats pretty much what i did

[earnest tiger]

So you assume it to be y

[alpine sable]

here

[earnest tiger]

Then get a quadratic in x

Then make discriminant positive

You get the set of values of Y

[alpine sable]

what are you talking about

[earnest tiger]

Finding range of $ \frac{ax-9}{x-1}$

[alpine sable]

how do you go from that to getting a quad

[earnest tiger]

Finding range of $ \frac{ax-9}{x-1}$

[alpine sable]

well from this diagram, you can get b wrt a by looking at f'. Thus you can also get c wrt a

holy shit

wait

not the same a

im sorry

lmao

[earnest tiger]

@alpine sable would you just once share the original question

[alpine sable]

no

a=-9, b=24, c=-17

aight

gg

.close

[lone heart]

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[sonic egret]

If $r \in R$ and $m \in M$, where $M$ is an $R$-module, is $r \cdot m \in M$?

[ocean seal]

Mr.Brawler

[novel night]

Yes. That's a pretty important part of what it means to be an R-module.

[lone heart]

@sonic egret Has your question been resolved?

[ocean seal]

VincentBH

[lone heart]

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[echo pond]

What is the antiderivative of 5/sqrt(256-x^2).

[echo pond]

And how would we get there

[urban pine]

well denominator is difference of squares under a sqrt

[crisp grail]

do you know substitutions in integrals

[crisp grail]

that doesnt really help

[echo pond]

No i havent gotten that far

[urban pine]

its a trig sub

[echo pond]

Im using the fundamental theorem rn

[knotty spire]

$\int \frac{5\dd x}{\sqrt{256 - x^2}}$

[ocean seal]

Remavas

[knotty spire]

just so it's nice to look at

[echo pond]

Ty

[fresh parcel]

looks like derivative of arcsin

[knotty spire]

$5\int \frac{\dd x}{\sqrt{256 - x^2}}$

[ocean seal]

Remavas

[knotty spire]

my thought too

[crisp grail]

ye

with some numbers

[echo pond]

Yeah

[knotty spire]

arcsin's derivative is 1/sqrt(1-x^2)

[fresh parcel]

derivative sorry

[knotty spire]

so pull out 256

[crisp grail]

he cant substitute yet so thats kinda a problem at the end

[fresh parcel]

nah thats okay, as long as they know arcsin derivative

[knotty spire]

$5\int \frac{\dd x}{16\sqrt{1 - \left(\frac{x}{16}\right)^2}}$

[crisp grail]

arent you gonna have to substitute x/16

[ocean seal]

Remavas

[fresh parcel]

oh yeah u sub

bruh

XD

[knotty spire]

well unless

[echo pond]

Huh

[knotty spire]

he can change the differential

which is what I'd do 🤷

[fresh parcel]

u should know u sub

[crisp grail]

ye thats substituting

[fresh parcel]

u substitution

[knotty spire]

more refined, gentlemanly u-sub

[echo pond]

Hmm alright

[crisp grail]

@echo pond you didnt learn how to say for example y=x/16 right?

and than find dy = 1/16 * dx

[echo pond]

Not yet my teacher gave us the assingment saying we just had to use the fundamental theorem of calculus and we would learn substitution in the next lesson

[knotty spire]

well

can't do this without u-sub

[crisp grail]

you can

I would just find the derivative of arcsin(x/16) and it will be what you got there except for maybe a constant

[knotty spire]

That's like saying "Of course you can solve ODEs"

"Just guess and check the answer"

🤷

my opinion anyway

[crisp grail]

"Just smart guess and check the answer"

[knotty spire]

well it's an option

[crisp grail]

by knowing your derivative of arcsin, you can find that this way

[knotty spire]

@echo pond We know the derivative of arcsin(x) is $\frac{1}{\sqrt{1-x^2}}$

[ocean seal]

Remavas

[echo pond]

Yes

[ocean seal]

VincentBH

[echo pond]

I'll probably just learn the substitution method and solve it later

[knotty spire]

we have also gotten this far

so, as Vincent said

[knotty spire]

we know this to be true

[echo pond]

Yeah we do

[knotty spire]

we must now only find out c

[crisp grail]

if you differentiate that you find that c = 5

[knotty spire]

aw, what a spoiler

but yes, you differentiate that

equate to our known function

and solve for c

And you get $5\arcsin{\frac{x}{16}} + C$

[crisp grail]

cus you get $\frac{1}{16}\cdot\frac{1}{\sqrt{1-(\frac{x}{16})^2}}$ by differentiating

[ocean seal]

Remavas

VincentBH

[crisp grail]

sry mb

[echo pond]

Yes I see it

[crisp grail]

but like you have to smart guess a bit here

if you learn substitution next week this will be a bit easier and more "consistent"

[echo pond]

I see

[knotty spire]

just remember that changing the differential will make you look badass and it's way cooler anyway

[echo pond]

Alright well thank you so much

[knotty spire]

(joke) ||or is it||

[crisp grail]

.close

[lone heart]

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[inner halo]

Help with question one

[inner halo]

A

Sorry idk math im bad

[languid bolt]

ok so

if there is 20% chance of a hurricane happening, what is the chance of a hurricane not happening

[inner halo]

80

[languid bolt]

80% yes

[inner halo]

But my teacher said

130/5 is the ans and i was like wtf

[languid bolt]

wait what

how does it have 2600% chance of not happening...

[inner halo]

She said is the probability

[languid bolt]

did she say 130/5 % or just 130/5

[inner halo]

Not possibility

[lapis ingot]

a probability has to be between 0 and 1 lol

[languid bolt]

^

ikr

[knotty spire]

I'm sorry but wtf

[inner halo]

This teacher got problem ikr

[languid bolt]

2600% is just way too high of a number

[lapis ingot]

you can’t have a probability of 200% chance

[knotty spire]

Isn't this like the first probability axiom?

Like the very first one

it's been some time

[languid bolt]

answer shouldve been 0.8 or 80%

[inner halo]

Cant possibly be 130/5

[lapis ingot]

the probability of something not happening is 1-(the probability of it happening)

so like going back to the hurricane example

[inner halo]

Yea?

[lapis ingot]

1-20/100 is 80/100

so the chance of the hurricane not happening is 80%

[knotty spire]

why si that you might ask?

Well, the chance of a hurricane happening or it not happening must be 1

0.2 + 0.8 = 1

[languid bolt]

are you sure you asked your teacher about number 1 a?

and not another question?

[inner halo]

What other question can possibly get 130/5

[lapis ingot]

none of them because this is probability

lol

[languid bolt]

unless your teacher meant (130/5)%

which is 26%

could be one of the answers of the other questions

[inner halo]

Nope

My teacher wrong

Thanks for helping anyways

Thats why everyone in yr 10 failed add maths

[knotty spire]

I somehow doubt a teacher could get the axioms of probability theory wrong

🤷

[lone heart]

@inner halo Has your question been resolved?

[lone heart]

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[dire cargo]

I must prove that they are equal, using trigonometric identities, but I'm stuck with this one

[vale wigeon]

expand on the left?

see what falls out

[dire cargo]

:/ thank you so much

I'm so bad with this topic

.close

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[native wigeon]

2*\root m divided by 3p+2b partial derivativ for b. I solved it to be - 2 \root m divided by (3p+2b)^2 . The right awenser is -4 \root m divided by (3p+2b)^2 . My question is how do i change my math so my -"2" will end up just right and be a -"4"

[native wigeon]

I do the following steps

2Root m / 3p+2b <=> 2Root m * 1/(3p+2b) <=> 2*Root m *(3p+2b)^-1 derivativ

2*Root m * (-1) * (3p+2b)^-2

[urban pine]

don't forget chain rule for the interior of (3p + 2b)^-2

[lone heart]

@native wigeon Has your question been resolved?

[lone heart]

@native wigeon Has your question been resolved?

[urban pine]

@native wigeon just saw you said this wasn't resolved. did you not check your chain-rule work and find the error?

[lone heart]

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[hot bison]

ive got the equation 2 sin(3x) = 1

[hot bison]

and I divided both sides by 2 to get sin(3x) =1/2

how do I remove the sin?

[uncut torrent]

arcsin of both sides

aka inverse sin function

[hot bison]

wait so

that removes the sin

[uncut torrent]

yeah

[hot bison]

and if I arcsin 1/2

ok

thanks

that was helpful

.close

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[wary escarp]

apparently this is wrong

idk why

also I didn't put a + 18 at the end

[marsh rapids]

Forgot+18

,w expand (x-3)(x-1)(x+6)

[ocean seal]

Results provided by WolframAlpha

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

Requested by themateo713#5303

[wary escarp]

why is my answer wrong tho

[marsh rapids]

There's also x^2 * 6

Then you get (-4+6)x^2 and it matches

[wary escarp]

ohhhhhhhhh

thanks

.close

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[sharp moth]

Is this a trig identity?

[vernal thunder]

Yes

[prisma elbow]

yes, specifically it's a double angle identity

https://www.khanacademy.org/math/precalculus/x9e81a4f98389efdf:trig/x9e81a4f98389efdf:angle-addition/v/trigonometry-identity-review-fun

@sharp moth

this video basically shows how to get them

from the basic trig addition formulas

[sharp moth]

Ah okay sweet, thank you

.close

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[sharp moth]

Is this just a different way of finding the answer, and is there multiple answers?

[mystic dew]

Bro, this seems way too complex for the question

[vernal thunder]

I thought you can directly substitute it in the equation

[sharp moth]

I believe that you need to get the second derivate to get the acceleration

Sorry I meant to include this in the picture

My derivate was not going to be that equation

It was going to be something with cos and sin, not sec and tan

[mystic dew]

That's fine

You could do it that way too

Like conventionally derivative of sec x is secx*tanx

So, they probably differentiated that to get the double derivative

[sharp moth]

But cos and sin also is a correct answer? Is it in simplest form when only using sin and cos?

[mystic dew]

Yeah yeah, cos and sin is correct too

So did you substitute the value in?

[sharp moth]

Yes and I got the value of -sqrt(2)

This is the incorrect answer still

[mystic dew]

No, it is +sin pi/4 * sin(2*pi/4)

It is -(sinx)(-sin2x)

So it is +(sinx)(sin2x) right?

The last step in your calculation?

[sharp moth]

Yes

It's - on the first term

-(sinx)(sin2x)

[mystic dew]

Did you get the correct answer?

[sharp moth]

No when I typed in the above in the image I got -sqrt(2) which is incorrect

the correct answer is 3√2

[mystic dew]

.

[sharp moth]

You mean to say that this portion is incorrect right?

[mystic dew]

yeah

it should be added

not subtracted

[sharp moth]

I'm reviewing my work to see if I can find where I mistakenly forgot or misplaced a sign

[mystic dew]

.

[sharp moth]

That must be it my bad

[mystic dew]

yeahh

👍

[sharp moth]

Yep that's it

@mystic dew Thank you so much for your help I really appreciate it

.close

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[thin urchin]

what power of n is nlogn?

[vernal thunder]

do you know any log properties

[thin urchin]

yes

[vernal thunder]

Because there’s one that is used to answer that question

Which one

[thin urchin]

loga^b = bloga

[vernal thunder]

Ok

So use the original question and you’ll find the answer

[thin urchin]

what power of n is logn^n

[vernal thunder]

Do you have to convert log to exponential

[thin urchin]

n^k = logn^n so would I do e^n^k = n^n?

[vernal thunder]

Where did you get the e from?

That’s from ln

Not log

[thin urchin]

to cancel the log

oh

n^k = logn^n so 10^n^k = n^n

idk I have no idea

[vernal thunder]

Ok you’re good

[thin urchin]

so how do I find k

[vernal thunder]

Convert to log again

[thin urchin]

log(base10^n)k = n^n?

or just logn^k = n^n

if that's correct then I can solve for k

[vernal thunder]

$log_n(log(n^n))=k$

[ocean seal]

% Openglobe %

[vernal thunder]

Something like this

[thin urchin]

ok

ty

i cant do log base n on webwork

[vernal thunder]

What

[thin urchin]

i know that logn! is O(nlogn)

idk how I can put logbasen(log(n^n)) on webwork

[vernal thunder]

I have no idea because I haven’t used it before

[lone heart]

@thin urchin Has your question been resolved?

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[sour adder]

Question regarding this math problem. When working on this problem, you need to use the Pythagorean Theorem to find sin -1 (number) why would -7 of -7/25 of sin in particular be the fraction that becomes negative?

[tacit arch]

That's confusing. Can you show the original problem

[tacit arch]

r is hypotenuse and is always positive

[sour adder]

hmm really? Never knew that

[vernal thunder]

r is radius, instinct moment

[sour adder]

I get what he meant thanks tho lol

alright thanks for the help

Another Question.

How would I approach this question none of the numbers are seeming to appear on the tangent table.

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[alpine sable]

just want to know if i did this correctly

https://tenor.com/view/spider-man-forever-dance-anything-gif-23997714

[drowsy lagoon]

correct

[alpine sable]

thanks

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[ocean seal]

xihiro

[spring badger]

it looks similar to binomial formula?

no sorry

[ocean seal]

xihiro

[spring badger]

are you sure that there is simple expression for this

[tight locust]

you're using the wrong letters for everything

anyways

$(x+y)^n = \sum_{k=0}^n \binom{n}{k} x^k y^{n-k}$

lol hold on

[ocean seal]

EndTimes

[tight locust]

partial deriv wrt x:

$n(x+y)^{n-1} = \sum_{k=0}^n \binom{n}{k} k x^{k-1} y^{n-k}$

[ocean seal]

EndTimes

[tight locust]

multiply by x:

$xn(x+y)^{n-1} = \sum_{k=0}^n \binom{n}{k} k x^{k} y^{n-k}$

[ocean seal]

EndTimes

[tight locust]

so your expression just turns into:
pf

@deft willow

👍

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[slate kayak]

.close

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[knotty veldt]

am i misunderstanding something?

the top value of the sigma sum indicates the final value of n, therefore the error bound is given by 101 nth term

yet for some reason they use the 102 nd

why do i speak its adding 👀

this j turns into self help for me every time

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[slim fern]

How many numbers in the form 1!+2!+...n! are perfect squares?

[slim fern]

I think its just 2 numbers (1 and 3), but idk how to prove it

Ok i solved it msyelf

if there is an n >= 4, it is not possible
1! + 2! + 3! + 4! + 5! + ... n! mod 10
= 1 + 2 + 6 + 24 mod 10
= 33 mod 10
= 3 mod 10
3 cannot be the last digit of a perfect square, so n >= 4 is not possible
so now just check n < 4
1! = 1
1! + 2! = 3
1! + 2! + 3! = 9
2
2 is the answer

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[stable night]

hi, my thoughts on this is that every chosen relation is reflexive to itself

like out of the 65536 possible choices every relation is reflexive

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[dry flame]

Hey Guys, could you help with this problem?

[echo socket]

Try multiplying both sides by 2x

[echo socket]

How did you get 1/x + 1 = 3*2x?

[dry flame]

Multiplying both sides

confused if 3 can be multiplied into 2x

[echo socket]

You have to multiply 1/x by 2x too

[echo socket]

Ofc? 6x?

Instead you should have gotten 2 + 1 = 6x

[dry flame]

oh

i thought you only had to multiple each side

not the fraction also

to cancel the 2x

[echo socket]

When you multiply both sides by a number, every term is affected

[dry flame]

yep gotcha, thanks mate

[echo socket]

Feel free to type .close if you don't have any questions to post

[dry flame]

.close

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[sharp moth]

Is there more then one way to a function to the power of 2?

[sharp moth]

I thought it would be written like this

Though my textbook seems to show this as

[chrome plank]

writing it like f(x)² might be misleading

So instead it's written f²(x) or (f(x))²

That also applies to trig functions, sin²(x), cos²(x), ...

[prisma elbow]

^

[lost coral]

its similar to how u write powers for trigonometric functions as well

[sharp moth]

Thank you I was just about to pop in and ask.

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[chrome plank]

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[uncut depot]

how do i solve this

[uncut depot]

L'Hôpital's rule doesn't work

i remember my teacher using some method to solve it

he substituted 2x for x

so it became: $\lim_{2x \to 0} \left(\frac{\tan(2x) - 2x}{(2x)^2\tan(2x)}\right)$

[ocean seal]

azorfus

[uncut depot]

then i don't remember how he solved it

do i apply this

[harsh girder]

you can use $\tan(x) = x+\frac{x^3}{3}+o(x^3)$

[ocean seal]

秋水

[tacit arch]

don't think they can use taylor series

[uncut depot]

nope

and what's o

[tacit arch]

if you don't know it, ignore it

[tacit arch]

can you, or can't you use taylor series?

[uncut depot]

i can't

[tacit arch]

try the second one

[uncut depot]

also

what's $\lim_{x \to 0}\frac{\cos(x)}{x}$

[ocean seal]

azorfus

[tacit arch]

you should be able to solve that

[uncut depot]

is it infinity

[tacit arch]

,calc cos(0)

[ocean seal]

Result:

1

[uncut depot]

what about $\lim_{x \to 0}\frac{1 - \cos(x)}{x^2}$

[ocean seal]

azorfus

[uncut depot]

\its just

0

right

1/(x->0) - 1/(x->0)

what if one infinity is bigger than the other one

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[coarse remnant]

could someone explain what I did wrong here? I can't find anything to justify getting 0/8 points on this problem, and I'm pretty sure I'm correct...

https://cdn.discordapp.com/attachments/938624840192102410/1000635291830329405/unknown.png

[coarse remnant]

teachers are supposed to give feedback and explain why they marked someone down but my teacher didn't which is nice

apologize for the amount of writing lol its supposed to be an "essay" assignment

where you explain in detail how you solve the problem

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@coarse remnant Has your question been resolved?

[coarse remnant]

<@&286206848099549185> its been 15 minutes :)

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@coarse remnant Has your question been resolved?

[novel night]

Your write-up looks mostly ok to me. I'll assume you got the correct answer in the end (your method looks right, and I'm not going to check for arithmetic mistakes). So I'll assume the teacher didn't like something about the explanation. A few possible issues: you used standard Cartesian coordinates, with east at 0° and positive angles going counterclockwise, but didn't say you were doing it until kinda hinting it at the end. Since the problem said north was 0° etc, maybe they expected you to stick with that from the beginning.

[coarse remnant]

I highly doubt that, since the platform im using has shown how to solve this kind of problem before, and they always convert afterward in their explanations.

[novel night]

If being really picky, you used the phrase "the vector of the plane". That should probably be "the velocity vector of the plane", and a few other word-choice issues like that.

[coarse remnant]

Also, I don't think that should account for a 0/8 (at most a 4/8 since I got the answer correct).

[novel night]

And probably you should say the plane starts at the origin, and maybe explain a little clearer about the "target vector" being where the plane should be after just one hour (though I understood what you meant).

[coarse remnant]

yeah no they wouldn't be that picky I think, multiple of my friends have gotten answers completely wrong and they marked it as right cuz it "looked right" (I think I asked a question based on that before)

I feel like it's just a mistake then

[novel night]

Well, the 0/8 thing -- does your teacher usually award partial credit? If so, then yeah this feels like a mistake on their part. I certainly wouldn't have given a 0.

Is this a college or high-school course?

[coarse remnant]

usually, if you get the problem wrong but the reasoning seems fine, then you get partial credit

I am doing it at a college but it is a high-school course (precalc, I'm in grade 10 and accelerating math)

[novel night]

Yeah, your reasoning looked ok to me. Ask the teacher I guess? Are they friendly and open to such things?

[coarse remnant]

I emailed them yes

I honestly have no idea

its completely online, i have never met my teacher

just have to hope

this question has brought my grade down a whole 7% which is fun!

[novel night]

Heh, I see. Ok well good luck getting the grade fixed, and keep up the good work! :)

[coarse remnant]

thanks! and thanks so much for the help and for reading my whole essay lol

.close

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[devout mirage]

How can I tell which is a function and which is not

[devout mirage]

(I function cannot have 2 of the same x of y)

[high rapids]

Vertical line test

[devout mirage]

Wdym

[tacit arch]

https://mathworld.wolfram.com/VerticalLineTest.html

[devout mirage]

Thank you

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[alpine sable]

is not a linear map basically just a function with fields of higher degree as domain/range?

[carmine shuttle]

\textbf{Linear} map $f:A \rightarrow B$ is a function that should satisfy that
$\forall x, y\in A: f(x)+f(y)=f(x+y)$ and $\forall$ scalar $c$ and $x \in A: f(cx)=cf(x)$

[ocean seal]

kelvinchan9786

[alpine sable]

let $U,V$ be vector spaces over the field $\mathbb{F}$, and let $L: U \to V$ be a function which would be called a linear map if:

1. for every $u_1,u_2 \in U$, $L(u_1+u_2) = L(u_1) + L(u_2)$
2. for every $u \in U$ and $k \in \mathbb{F}$, $L(ku) = kL(u)$

[ocean seal]

metnal

[alpine sable]

thats the definition i had

but i guess yours is probably better

wait im dumb

my definition already said that it is a function

🤦‍♂️

ty

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[strange fractal]

how am i supposed to solve question e? i need more info

[knotty spire]

can you turn the quality of that picture down?

It's too clear.

[strange fractal]

lol wut

😂😂

[knotty spire]

Just retake the photo, it's unreadable

[karmic rapids]

it's very readable

[tacit arch]

Just set the unknown to a variable and multiply

Then set coefficients to be the same on both sides

[strange fractal]

ok lemme try that

[knotty spire]

wait

ok discord

thank you

[knotty spire]

yeah no, I realized the issue

It had a width and height annotation that turned the resolution down

[tacit arch]

Pictures of monitors/screens are like 50% unreadable

[knotty spire]

but this^

[strange fractal]

hi ive never done that in my life can u set an example pls

[gray isle]

or consider sums and products and/or how you would normally factorise quadratics

[strange fractal]

im not up to that im doing that next week

[keen socket]

consider the second term of the quadratic

[gray isle]

were you able to do question d)?

[strange fractal]

yeah but i did it with common sense

[gray isle]

how did you do question d)

[tacit arch]

We're not your teacher we don't know what that is

[gray isle]

explain your thought process and don't just call it common sense

[strange fractal]

oh soz i thought it was rlly obv

ok so

[tacit arch]

e) is also really obv

[strange fractal]

since i have 9 ik its 9x and then i just took it away from 11x and got 2

and it was the rigjt answer and i was just like hm ok

[knotty spire]

the problem with using common sense as an argument is that no one can verify whether your 'common sense' is correct.

[gray isle]

wording could be better,
but same principle could be applied for e)

[strange fractal]

im very bad at english lol only good at science and math

[gray isle]

note that x = 1*x

[strange fractal]

oh ok

wait lemme see

[strange fractal]

ty

that was the thing i was missing lol

[karmic rapids]

is maths related to science

[strange fractal]

i think

ok bye guys

.close

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[rough yoke]

i need confirmation about how i think of functions

[rough yoke]

its the same as in sql right?

for example, a user has an id. and that user has a balance

f(id)=bal

[alpine sable]

yes

[rough yoke]

doesnt matter if another user has the same balance

[alpine sable]

but no two users can have the same ID

[rough yoke]

yeess

[alpine sable]

nice

[rough yoke]

thanks a lot

[alpine sable]

np

[rough yoke]

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[sour adder]

Quick question regarding this problem on Trigonometric Identities

[sour adder]

Can somebody explain why this problem is worked this way? I just copied it off the teachers slides, although I didn't know why she used it the way she did. Like I know the existence of the identities, I just don't know how she got rid of a sin and made three somehow lol . The work dosent make sense to me

[tacit arch]

Use Pythagorean theorem

[sour adder]

Can u elaborate

Like I know what that is and that there are identities for it but I have no idea how to apply it in this manner nor do I understand the work that is shown lol

[tacit arch]

$\sin^2(x) + \cos^2(x)=1$

[ocean seal]

riemann

[sour adder]

still not getting it because first of all, the sins are not combinable since one is a negative which would ultimately cancel them out

leaving only cos, which can turn into an identity but that's all there would be remaining

[tacit arch]

a - ab^2 = a(1-b^2)

Write out your work

[sour adder]

so for this

uh

mathematically, just how does -a dissapear when multiplying it by the outer one?

[tacit arch]

It's called factoring

2 - 18 = 2 - 2*9 = 2(1-9)

You can do all the arithmetic to verify

Or its called distributive property, same thing in reverse

[sour adder]

Ohhhhh

I get it now

That took too long for me to get lol

Ty

Gn

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[plucky geyser]

How can I find a slant asymptote

[plucky geyser]

for example, for this

[vale wigeon]

this one does not have any

however there is a general algorithm for it

if the line y = mx + b is a slant asymptote of the graph of y=f(x) at +infty, then
m = lim[x -> infty] f(x)/x
and
b = lim[x -> infty] (f(x)-mx)

if either of these limits does not exist or is infinite, then the function has no slant asymptote in that direction

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[plucky geyser]

thank you

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[frozen kayak]

Any idea? Pls give me some hint on this problem

For question 2

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[gilded vessel]

why is the integral of (1/x) = ln |x| + C

if you use the power rule and do x^-1 -> 0*x^0 = 0 --> C

i know this isnt really valid by why isnt it valid with my approach

[vale wigeon]

well first off

the power rule for integrals is NOT $\int x^p \dd{x} = (p+1)x^{p+1} + C$

[ocean seal]

Ann

[gilded vessel]

oh right

[vale wigeon]

it is $\int x^p \dd{x} = \frac{x^{p+1}}{p+1} + C$

[ocean seal]

Ann

[vale wigeon]

and if you tried to apply this with p=-1 you would impale yourself

[gilded vessel]

yeah

i see that

also im impressed how quickly you did that latex

[vale wigeon]

eh

[gilded vessel]

so is it the fact u get an undefined result make it an invalid approach

[vale wigeon]

well tbh like

this power rule can only be applied with p ≠ -1

specifically because of the division by zero thing

so i guess yes

[gilded vessel]

yeah gotcha

also while i got you here can i ask what \dd is in latex

i know it for #latex-help but u just used it so

[vale wigeon]

that gets you the pretty upright d in the differential

[gilded vessel]

aight thanks so much

[vale wigeon]

compare: $\int x^2 dx$ vs. $\int x^2 \dd{x}$

[ocean seal]

Ann

[vale wigeon]

years of experience + 90 wpm typing speed for non-math texts will do that to you

[gilded vessel]

very impressive

.thanks again

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[alpine sable]

if I have a vector v1 (1,2,3) and a vector v2 (0,3,4), how do I describe through mathematic notation the operation of forming a new vector in which each component is the maximum between the two components?
For example, between v1 and v2 it would be (1,3,4)

Is it simply max(v1, v2)? I don't think it is

[lean depot]

There's no specific notation for that. A good way to describe it is exactly as you have done so above; in words.

[alpine sable]

What exactly does this represent though? That's too specific, genuinely curious

Normalizing symmetry calculations @alpine sable

[alpine sable]

Alright, thank you

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[alpine sable]

ok wait, another thing lmao

What about summing each vector's components individually and then dividing over the number of components?

[alpine sable]

So for example for a vector v (1,2,2) it would be (1+2+2)/3

Is there a specific mathematical operation for this?

[crisp grail]

there is no specific notation for the numbers of components

[alpine sable]

: (

[ocean seal]

VincentBH

[gilded citrus]

the 1-norm is somewhat similar

except each component is abs'd first

[alpine sable]

perfect

that's what i would need

[crisp grail]

because the 1 norm is a summation as well

[alpine sable]

abs(1+2+2)/3

that's the 1 norm?

[gilded citrus]

wait er i think i might be wrong

[crisp grail]

ye you dont divide

[crisp grail]

x component + y component + ...

[alpine sable]

Alright, I'll go with your vectorspace then @crisp grail

[crisp grail]

in absolute value

[alpine sable]

Thank you

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[languid bolt]

anyone know a good youtube channel/ video / website to learn about vectors?

[abstract fractal]

Khan Academy

[languid bolt]

what about youtube videos

[last ether]

Probably the organic chemistry teacher guy because he teaches anything but organic chemistry

[languid bolt]

welp, i guess ima stick with those two

[gray isle]

prof. Leonard good too

[languid bolt]

ok ty guys

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[languid bolt]

ima need a good song playlist now

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[native cloud]

What's the factor

Maybe a combination of both?

Figure out the pattern

What's the pattern?

In mathematical terms?

[weary wyvern]

Call the nth term of the sequence a_n

Can you find a recurrence relation?

i.e. a_(n+1) in terms of a_n?

[languid bolt]

i found a pattern, do i just type it here or try to guide him to the pattern

[weary wyvern]

Haha true marvel. That's a bit of a lucky observation

[vale wigeon]

so y'all are claiming this to be a quadratic sequence?

[languid bolt]

it could be

[vale wigeon]

but consider: what if your rule described some sequence $a_n$, and i came up with a different rule $a'_n := a_n + 42069(n-1)(n-2)(n-3)(n-4)(n-5)$? you would be unable to detect the difference given the first 5 terms alone

[ocean seal]

Ann

[weary wyvern]

I don't think just finding the pattern like that would be well motivated tbh bc tough would have to have seen something like that before so maybe a more systematic approach is better

[languid bolt]

kk, ima just go (edit: i have urgent business and might not come back in an hour. edit 2: in the toilet)

[vale wigeon]

the correct answer is NEI

[rare verge]

um

i dont think

thats what the question means

ann

so the thing is

we have

2 9 18 29 42

the difference here

[weary wyvern]

Lol is that allowed

[rare verge]

is 7 9 11 13

and

7+2 = 9 9+2 = 11 and 11+2 = 13

[weary wyvern]

Just checked, it isn't

[rare verge]

right

[gray isle]

<@&268886789983436800> age issue

[rare verge]

so the difference between the differences are the same

[sly mantle]

ty

[languid bolt]

lmao, instantly said "jk im 17"

[rare verge]

.

[gray isle]

they shouldn't have joked

[rare verge]

..

[vale wigeon]

was that OP?

[sly mantle]

yeah thats a ban too

yes OP

.close

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[alpine sable]

Hello guys

I don't really understand how to solve this problem

[vale wigeon]

which part?

[alpine sable]

The first question

a

Is k referring to a constant

I am not sure if I know that I think I can solve it

[vale wigeon]

k is a constant yes

[echo socket]

The problem states that the particle passes through the point A at t=0 with speed 6m/s, are you able to write that as an equation using s(t)?

[alpine sable]

Oh then I know I can solve it

[vale wigeon]

s, not x

[alpine sable]

Ok guys thank you

.close

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[west harbor]

Calculate the angle between the plane ABCD and the line AH
Need some help with this

I'm confused why the answer is tan-1(24/sqrt(356)) instead of tan-1(sqrt(356)/24).

[vale wigeon]

ok first off, sqrt()

sqrt(356)

second, are you looking at an answer key that says the answer is arctan(24/sqrt(356))?

or rather

no, the answer key is correct. angle HAC really is what the answer key claims it to be.

[west harbor]

This is the answer

The adjacent and opposite switched place which is why I'm confused

HC is the adjacent and AC is the opposite right?

[novel night]

No, angle HAC means the angle at A, between AH and AC. HC is opposite that angle, and AC is adjacent to it.

[west harbor]

ah I get it now

thankss

.close

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[desert moon]

how part b?

[worn fox]

you need to consider $(T''\circ \Lambda)(v)(\varphi)$ and $(\Lambda\circ T)(v)(\varphi)$ and show they are the same

[ocean seal]

ΣAC

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@desert moon Has your question been resolved?

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[ionic bear]

Can someone tell me please if limit of a_n is 1/3?

[vale wigeon]

,w prod[n=2,infty] (1 - 2/(n^2+n))

seems not

hm. but why does this diverge

oh wait

[ocean seal]

Results provided by WolframAlpha

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

Requested by Ann#0413

[vale wigeon]

ah

@ionic bear yes

[ionic bear]

Thanks

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[alpine sable]

Hi Im not sure if this is correct

My teacher said it’s £4840

[vale wigeon]

that sounds too high.

4840 would be for a 10% per annum return

[alpine sable]

So do u think i was right?

[vale wigeon]

,calc 4000 * 1.011^2

[ocean seal]

Result:

4088.484

[vale wigeon]

checks out

4088.48

[alpine sable]

Omg I could cry

Becasue he keeps getting things wrong

And it’s making me back peddle

Are u guys sure

Because I’m going to file a complaint I think

About my teacher

[vale wigeon]

well i just calculated the thing for you in front of you

[alpine sable]

Ok thank u x

.close

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[grand karma]

If you put -1 to the power of a fraction in its simplest form where the numerator is even will it be 1?

[last ether]

Well that depends on what the denominator is

And precisely what fraction it is

Iirc, $(-1)^x = \text{cis}(πx)$

[ocean seal]

Umbraleviathan

[last ether]

So for whatever that fraction is, you plug in x

[grand karma]

What is cis?

and Iirc?

[last ether]

iirc means "if I remember correctly"

$$\text{cis}(x) = \cos{(x)} + i\sin{(x)}$$

[ocean seal]

Umbraleviathan

[last ether]

But I hate writing out the cos + isin

So I use cis notation

[grand karma]

Would (-1)^(4/3) not be real then?

or (-1)^(1/3) is probably a better question

because to me it seems like it would be -1 as -1^3 = -1?

[last ether]

I guess, yeah. That's just -1

,calc (-1)^(1/3)

[ocean seal]

Result:

0.5 + 0.86602540378444i

[last ether]

But I also get this

Which is 0.5 + sin(π/3)i

The thing with complex numebrrs is that they get really finnicky

But @grand karma there are multiple answers

(-1)^(1/3) has 2 answers I think

One real one complex

[lone heart]

@grand karma Has your question been resolved?

[grand karma]

Last question can you put numbers to complex numbers?

[last ether]

Wdym put numbers to complex numbers

[grand karma]

Like 3^i

[last ether]

That, I'm not sure

I can try seeing what happens

,calc 3^i

[ocean seal]

Result:

0.45483242282661 + 0.89057704166775i

[last ether]

I guess there is an answer lol

Although

If you think about it

It is $3^{(-1)^{0.5}}$

[ocean seal]

Umbraleviathan

[last ether]

Which makes shit harder lol

[grand karma]

🤔

[last ether]

But when you raise to the power of i, I'm not sure.

[grand karma]

That looks similiar to cos + isin

[last ether]

I mean you can use that, supposedly. You don't get anything because now you get a nasty cis(0.5π) power instead of i

Okay so googling

And I should've known this

$$
\begin{align*}
3^i & = e^{i\ln{(3)}} \
& = \text{cis}(\ln{(3)})
\end{align*}
$$

[ocean seal]

Umbraleviathan
Compile Error! Click the reaction for more information.
(You may edit your message to recompile.)

[last ether]

@grand karma

[grand karma]

Ah

Tha ks

Thanks

[last ether]

Np

[desert moon]

I don't understand A maps from V but T'' maps from V', so idk how they can be commutative

part b

[last ether]

You might have to open a new channel

@grand karma if you're done, close it and give it to 1080p

[desert moon]

[last ether]

Same tbh

[grand karma]

.close

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[alpine sable]

so i’m using the product rule here. but should i be simplifying the denominator first so i get my f(x) and g(x)?

[alpine sable]

not sure how that would look

Try multiplying out everything and expanding everything

and simplify the fraction

while keeping in mind that the domain is R - {0}

okay, so multiply out first don’t do the parentheses derivatives first right

Yes

okay thank you

It will be simpler if you simplify the fraction first

oh wow

that made it much easier thank you

.close

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[terse oak]

what is the value of convolution with a constant

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Please don't occupy multiple help channels.

[terse oak]

.close

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[rough orbit]

Yo

My teacher said to use constructions to complete this problem

But I dont know what that is

<@&286206848099549185>