precalculus

[winter comet]

there's no description or anything lol

[terse pebble]

lmao

[half sinew]

WHAT DESCRIPTION

IM JUST SOLVINF?

[winter comet]

its a proof

[terse pebble]

explain how you get from the first to the second line

[half sinew]

That was steps 4-5

[terse pebble]

you mean from chatgpt

[winter comet]

4-5?? what?😂

[terse pebble]

Step 1:

Step 2:

Step 3:

[winter comet]

fr 🤣

[terse pebble]

lmao

[half sinew]

I can show you the front page

[terse pebble]

yes

[half sinew]

I have my search history

💀

[terse pebble]

we don't need to see that

[winter comet]

the front page of what

[half sinew]

The rest of the rook

Wait no

[terse pebble]

bro you sent the same page

[half sinew]

This one

[terse pebble]

homie did the same thing as chatgpt

😭

[half sinew]

…

There’s no other ways I could’ve done it

[half sinew]

So of course it would be similar

Give me another problem please

Geometry

This time

[terse pebble]

yuck bro

we need to iron out your solution first

can you explain

[half sinew]

Just because you suck at it doesn’t mean anything

[terse pebble]

step by step your working

[half sinew]

Let me put my shirt on

[winter comet]

whats bro doin without his shirt 💀

[terse pebble]

having too much fun

[half sinew]

Alright

What now?

Geometry?

[terse pebble]

explain the proof you just gave

[half sinew]

Binomial theorem

[terse pebble]

right..

[winter comet]

explain the binomial theorem

[half sinew]

Factoring out

N^2

Simplifying the expression

And subtracting 1

But to be exact

[terse pebble]

just explain the transition from these lines

like you've wrriten n choose 2 and all that

[half sinew]

Write out the formula and simply if ng the expression

[terse pebble]

yea seems legit

i think you might've done this one on your own

proof by induction certainly isn't the obvious route

[half sinew]

give geometry

[terse pebble]

alright let me find one

[half sinew]

I haven’t showered in 2 days

@winter comet

[winter comet]

what about it

[terse pebble]

alright

Farmer Pythagoras has a field in the shape of a right triangle. The right triangle’s legs have lengths 3 and 4 units. In the corner where those sides meet at a right angle, he leaves a small unplanted square S so that from the air it looks like the right angle symbol. The rest of the field is planted. The shortest distance from S to the hypotenuse is 2 units. What fraction of the field is planted?

@half sinew

[half sinew]

Send a picture

Jesus Christ

Nvm

Actual

Send a picture

[terse pebble]

what is there to see

a diagram?

[half sinew]

Just send the picture

[winter comet]

draw a picture if you need one lol

[half sinew]

Don’t ask questions

Im weird

Not the diagram

The question

Obviously

[winter comet]

why?

[half sinew]

I SAÏD DONT ASK QUESTIONS AND SEND THE PICTURE

sorry

[winter comet]

mighty sus 💀

[half sinew]

Good boy

[terse pebble]

dude needs to put the image into gpt

[half sinew]

If I really could I could’ve just insert your response

But im actually going to solve it

[terse pebble]

i’ve got to get ones without solutions online

😭😭

[half sinew]

I’ll send a picture

[terse pebble]

thanks

🙏🏻

[half sinew]

nice ip grab

[terse pebble]

🥱

[half sinew]

…

@rancid bluff don’t say the answer

Please

[rancid bluff]

No I was about to ask a different question on a task that I am unsure how someone comes to the conclusion 😭

[terse pebble]

ask

immanuel can probably help you

[half sinew]

145/147

D

YAY

@terse pebble @winter comet I GOT IT

[terse pebble]

you didn’t get it bro

[winter comet]

nice, howd u do it :>

[terse pebble]

be fr

[half sinew]

I mean Knief couldn’t even answer this

It took a while

But I had to use the area of a triangle

[terse pebble]

!shiw

[half sinew]

Find the hypotenuse

[terse pebble]

!show

[tender quest]

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

[winter comet]

can you be a little bit more specific 💀

[terse pebble]

king of vagueness

[half sinew]

And set my variable s

[winter comet]

[half sinew]

Ok doctor what do you want me to elaborate on

Just use show

!show

[tender quest]

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

[half sinew]

The problem

[terse pebble]

explain your work like you would to a student

[half sinew]

Just show

!show

[tender quest]

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

[half sinew]

Im learning how to use commands

[half sinew]

The same way I’m explaining it to you is the same way I’ll explain it to a student.

[terse pebble]

you’d be a horrible teacher

[terse pebble]

@lean drum bro you think he knows what he’s doing?

[winter comet]

show your steps such that each step flows logically from the last one lol

[terse pebble]

^

[lean drum]

What?

Why ping me?

[terse pebble]

because you’re a geo dude

[half sinew]

You’d also need to calculate the area of the planted region and divide it by the total area.

[winter comet]

its like if someone is trying to explain how to drive a car and you're like "ok so first i used my foot"

[lean drum]

Bruh.

[half sinew]

I mean

[half sinew]

They’re consistently

Giving me college questions

[terse pebble]

college??

[lean drum]

Oh, this AMC bullshit.

[winter comet]

its funny to watch 💀

[half sinew]

AMC questions

Are advanced level

But its fine

[winter comet]

thats more like college lel

[terse pebble]

yea

[winter comet]

analysis?

[half sinew]

A bit easier

[lean drum]

It’s not. They’re fairly doable for high schoolers or even middle schoolers.

[half sinew]

Middle Schoolers?

[lean drum]

Anyways, knief, if you don’t mind, can you copy paste it?

[half sinew]

Probably Highschool 11th

[terse pebble]

and paste what

[half sinew]

These are problems you should see on the SAT

From amc

[terse pebble]

no

[winter comet]

they're harder than the sat lol, the sat is easy

[terse pebble]

SAT is like find the area of a triangle with sides 3, 4, and 5

too difficult for me

[half sinew]

No i mean

These are problems

I want to see on the SAT

[terse pebble]

🤔

bro youd get a 400 math

[winter comet]

....what 😂

[terse pebble]

why would you want to see that shit

[half sinew]

How

💀

[lean drum]

The problem.

[half sinew]

There’s something called preparing

[lean drum]

My phone is lagging.

[terse pebble]

oh you mean the link to AOPS?

[lean drum]

A hell lot.

[half sinew]

@terse pebble you would get a 560

[terse pebble]

thanks bro

[half sinew]

And a 400 reading

[half sinew]

That’s horrible

For math

[terse pebble]

"expect youtube"

[half sinew]

☠️

[lean drum]

No, like, the picture problem they were working on.

[terse pebble]

idk what you mean

i sent the problem

[half sinew]

@lean drum just solve it

If you use a calculator you’re banned

[winter comet]

jynx

[terse pebble]

he’s a geo dude he can do it

[half sinew]

Well guess what

Once im in university

[lean drum]

I have a meeting in, like, 10 minutes. Be patient.

[half sinew]

I’ll thrive like never before

[half sinew]

Sorry

[terse pebble]

you’re going to start posting history shorts on youtube?

[lean drum]

I could probably bullshit this with calculus.

[half sinew]

Science + ENGLISH + math

[half sinew]

No you can’t

[lean drum]

I would rather you take a coord geo approach, though.

[half sinew]

I already solved it

[terse pebble]

right

[lean drum]

Okay, knief, what did you ping me for again?

Are they trying to check their work?

$\frac{|Ax_0+By_0+C|}{\sqrt{A^2+B^2}}$

[terse pebble]

you can go now lol it’s ok i just pinged you because you do geo a lot and i was giving this guy problems after he said he was a great problem solver

[obsidian monolith]

;(

[terse pebble]

and he’s been cheating on them

😭

[lean drum]

XD

[terse pebble]

giving vague answers

[lean drum]

Ok, I guess I’ll show my working here.

[half sinew]

Dude plays Football Fusion

[lean drum]

Let us denote the uppermost corner of S (s, s), and the origin the lowermost corner. Then we have that the equation of the line that forms the right triangle is $y-3=-\frac34x$. Simplifying further we have $y+\frac34x=3\implies 3x+4y=12$.

[obsidian monolith]

;(

[lean drum]

(Used to.)

[half sinew]

Easy

@terse pebble

Cant even solve it

[half sinew]

Cheating @terse pebble

[half sinew]

Straight from GPT

[lean drum]

From here, we can use the formula presented above and show that $\frac{|3s+4s+12|}{5}=2$.

[obsidian monolith]

;(

[lean drum]

No?

[winter comet]

you should know that doesn't look like a GPT answer 💀

[half sinew]

That does

“Lets denote”.

[winter comet]

GPT never says taht 💀

[terse pebble]

that’s not gpt

[lean drum]

I think I’m having a brain fart.

[half sinew]

Let me guess

Snapchat ai

[terse pebble]

my ai

[winter comet]

me 24/7

[half sinew]

Continue solving

Don’t stop

You should be done by now

[lean drum]

No, not tripping.

[lean drum]

Do realize that I’m doing this on an iPhone 6 with less than 20% battery.

[half sinew]

Oh

[lean drum]

It’s laggy as fuck.

[half sinew]

iPhone 6

Buy a new phone

[lean drum]

Can’t.

[winter comet]

ion even have a phone 💀

[terse pebble]

your parents hate you bro

[winter comet]

😭

[half sinew]

You’re a university student.

And you can’t buy a phone.

…

[winter comet]

i am not 💀

[winter comet]

indeed i cannot 💀

[terse pebble]

bro what if you need a ride home or some shit

[lean drum]

$s=\frac27$

[obsidian monolith]

;(

[terse pebble]

🔥

[half sinew]

“Undergraduate”

[winter comet]

they know when my classes end lol, also sometimes i borrow my dads phone

[lean drum]

mathematics.

[winter comet]

if my classes end early then... i wait

[lean drum]

Undergraduate mathematics.

[winter comet]

💀

or borrow someone elses phone but like i hardly do that cuz social anxiety

[terse pebble]

viper has done all of engineering math before his senior year

[half sinew]

Guys should I have my parents confiscate my phone

And only use a laptop for school?

[winter comet]

i haven't done discrete

[terse pebble]

do engineers even do discrete

[winter comet]

if that counts

[terse pebble]

cs majors do

[half sinew]

Dude thinks he’s special because he’s advanced.

[lean drum]

I should learn complex analysis.

[winter comet]

not sure 💀

[half sinew]

He’s still in college

[terse pebble]

churchill is a soft intro

just need mv calc

[half sinew]

Im in alg 2 going to aim for pre calc and calc 1 in Summer.

Churchill is the goat

[lean drum]

I’m using YouTube. I’m going to absolutely annihilate all of my sanity.

[terse pebble]

not winston

[terse pebble]

michael penn series is good

bright side of math

but you need a book tbh

[lean drum]

Maths 505?

[terse pebble]

oh he does videos for that?

[half sinew]

I think we shall make a study group

[terse pebble]

i thought he just did integrals

[lean drum]

Yes.

[winter comet]

yeah but i mean don't some/(most maybe?) engineers do use programming to an extent...

[half sinew]

Only to help each other with mathematics

[terse pebble]

yea fair

[half sinew]

Im a CS major

[terse pebble]

discrete is a snooze fest

[terse pebble]

bro you’re in algebra 2

[lean drum]

You know what is actually hilarious

[half sinew]

Sophomore*

[winter comet]

i didnt know you could have a major in high school

[half sinew]

I mean I’m going to major in CS

We all make errors

Calm down

[winter comet]

ah

[terse pebble]

mcdonald’s is a good career

[lean drum]

I saw someone using $drdsdt$ for spherical coordinates instead of $drd\varphi d\theta$, they said class was mathematica based 😭

[obsidian monolith]

;(

[terse pebble]

😟

[half sinew]

I’m not working at Mcdonalds

I’m considering switching my school.

[winter comet]

ngl I don't have a problem with that

[terse pebble]

$d\rho$

[obsidian monolith]

knief

[lean drum]

Hmm

[river drift]

spherical coordinates probably have the least standardization out of any "standard" coordinate system

[winter comet]

actually i don't like the letter "s"

[lean drum]

I don’t like the letter t

[winter comet]

t is good

[terse pebble]

yea

[winter comet]

just write it with a curve at the end

[lean drum]

$\rho$ vs $\varphi$ I guess

[obsidian monolith]

;(

[terse pebble]

nah rho for r

[lean drum]

Why bro

[terse pebble]

isn’t rho standard

[lean drum]

Don’t be like Task Bot

[terse pebble]

it’s spherical not cylindrical

[winter comet]

the first one can get confused with a plus

i used to hate t for that reason

[terse pebble]

r is for cylindrical

[winter comet]

but now its fine i just changed how i write it

s though

[terse pebble]

(r, theta, z)

[river drift]

radial coordinate: r, R, or rho
polar angle: theta or phi
azimuthal angle: phi or theta
not even getting into phi vs varphi, and which axis is the polar axis

[lean drum]

Oh shit my bad

[winter comet]

my s always somewhat resembles a 5 😭

[terse pebble]

varphi is so much better

$\phi, \quad \varphi$

[lean drum]

It looks cleaner

[obsidian monolith]

knief

[terse pebble]

phi looks like a music note

or empty set

$\emptyset$

[obsidian monolith]

knief

[river drift]

people love to call anything which involves a line through a circle "phi"

e.g. empty set, diameter symbol

[winter comet]

hey look, its saturn!
no, its phi :)

[lean drum]

The fuck is a diameter symbol

[river drift]

$\diameter$

[lean drum]

$\diameter$

[obsidian monolith]

cloud

;(

[river drift]

it's used in technical drawings

[winter comet]

its saturn

i'm not wrong

[terse pebble]

low-key

[lean drum]

I can see it

I see the rotations

[half sinew]

Im back

[winter comet]

hi back

[lean drum]

Hi back, I’m blow

[half sinew]

This is why you don’t own a phone.

[winter comet]

why 😐

[lean drum]

!offtopic

[half sinew]

At senior year I’ll be taking calc 3

[winter comet]

epic

[half sinew]

Wait no

[lean drum]

I’m doing that shit at junior year

[terse pebble]

you’re in 10th grade taking algebra 2

[lean drum]

Get better

[half sinew]

Whats after calc 3

Linear Algebra

Yeah

[lean drum]

Your death

[terse pebble]

differential equations or linear algebra

[winter comet]

🗿

[river drift]

example (i had to make this in machine shop)

[half sinew]

Cool

You’re struggling

[lean drum]

?!

Knief knows I’m dropping a 5 on the exam

[winter comet]

i'm cringing

[terse pebble]

engineering is hard

[half sinew]

There’s no calc 3

for ap

[winter comet]

a 5 on the ap multi exam? 💀💀

[half sinew]

Unless you’re in BC

[lean drum]

Talking about BC

[winter comet]

oh 💀

[half sinew]

Rookie class

I did some BC problems

[lean drum]

There should be AP linalg

[river drift]

can't wait for AP differential equations

[half sinew]

I’ll be doing that next year

@lean drum

Im right there

[winter comet]

nah fr

[lean drum]

Ok

[winter comet]

probably actually coming eventually

[terse pebble]

15 years

[river drift]

they have a little linear algebra in the AP precalc curriculum but it's optional (not on the test)

[terse pebble]

ap precalc is such a waste

[lean drum]

They’re edging it in BC right now

They only do seperate

[half sinew]

Ap precalc is a waste

Self study it

[terse pebble]

they should’ve made a more advanced class

[winter comet]

precalc is a waste

[half sinew]

…

[lean drum]

Yes

[half sinew]

We need AP CALC 3

AP CALC CB

[lean drum]

Yeah, they’re edging it but they won’t do it for some reason (apparently optional in classes too?!)

[terse pebble]

you mean CD

but i don’t think colleges even have calculus D lmao

i’ve seen

A B and C

[half sinew]

@lean drum I’ll be taking BC next year

[lean drum]

If you take AB that’s sad

[half sinew]

If I get rid of Precalc

[lean drum]

“Rid of precalc”

[river drift]

to be fair they taught separable DE's in my uni calc class, as part of the "applications of integrals" section

[half sinew]

Nah BC IS. Both calc 1 and calc 2

[half sinew]

This summer

[winter comet]

ohh is that why they're called AB and BC? because colleges on the quarter system or smthn have calc A, calc B, calc C?

[half sinew]

Precalc credits

[terse pebble]

i think so?

not sure

[winter comet]

that would actually make sense 💀

[terse pebble]

cloud would probably know

[winter comet]

i always thought the naming system was a bit weird

[river drift]

my school is on the quarter system and we do have calculus ABC (and D but a lot fewer people take it)

[winter comet]

what's D?

[terse pebble]

probably vector

[half sinew]

I know kids that take pre calc for Senior year

[winter comet]

what about multi though lol

[terse pebble]

yep

[terse pebble]

maybe that’s C?

[winter comet]

it's not reallly in BC though to my knowledge

[terse pebble]

no it’s not

BC ends at sequences and series

[river drift]

A is limits and derivatives
B is integration
C is series + intro multivar
D is the rest of multivar

[terse pebble]

polar

[winter comet]

i mean i guess they do have vector stuff but calc 2 also 💀

[terse pebble]

and parametric

[winter comet]

ah

then E is vector calculus

[half sinew]

CALC BC covers everything besides calc III and up…

💀

[river drift]

no D is vector calculus (among other things)

[winter comet]

oh

[river drift]

technically ABC are called "calculus" and D is "vector analysis" (whatever that means)

[half sinew]

Hmmm

@lean drum phone died

Anyways

@terse pebble just

Make a Mathematics

Group chat

[terse pebble]

what

[half sinew]

Private for help

[terse pebble]

how much are you paying

[half sinew]

$0

We discuss and solve math questions

Let’s make an alliance

[terse pebble]

https://discord.gg/math

[winter comet]

already exists and you're in it
and its upgraded to server status

[half sinew]

Will become the phantom forces.

[winter comet]

LOL FR

[winter comet]

cringe

[terse pebble]

🤣

[half sinew]

we’ll unite to form khaos

And destruction

[half sinew]

And dominate competitions

Ultimate Shinobi

You guys ever seen the 2017 Warriors

We’re going to transform

And rise

[terse pebble]

yea

[half sinew]

Well we need privacy

[terse pebble]

you were like 8 bro

that’s crazy

[half sinew]

So create a Discord Group chat.

It’s like going to a public gym and a random guy joins the conversation.

[winter comet]

the first time i remember knowing the date was like 2012

[terse pebble]

probably about when you’re 4 or so

[winter comet]

i remember thinking 2014 randomly was like especially new lol

[half sinew]

You didn’t even accept my request Knief

[winter comet]

probably because years felt so long 😔

[terse pebble]

from what

[half sinew]

ACCEPT MY REquest

[half sinew]

Randoms

Intervening within our conversation.

[winter comet]

we are all randoms wdym 💀

[half sinew]

What if we want to do

😉

😉

In our private GC

[terse pebble]

yea i’m not accepting your request bro

[winter comet]

[half sinew]

Alright im sorry

I wont make a GC

if I do you can block me

[half sinew]

So

Ummm

I guess

We just go our separate ways.

You can do it

YAYY

Wow

https://tenor.com/view/nikola-jokic-jokic-job-the-job-is-done-job-done-job-is-done-gif-5273907227416172086

Umm

Yeah

[pulsar patrol]

👴

[faint barn]

@subtle nymph nerddd

[viscid thistle]

https://media.discordapp.net/stickers/1263773888316440617.gif?size=160&name=Attention+Seeker

[exotic barn]

this is kinds pointing to yourself

[willow bear]

!redir

[tender quest]

This channel is only for on-topic discussion. Please take casual conversation to #discussion or #chill.

[viscid thistle]

Just jokes dw I don't mean it

[random flax]

Hello guys u clean wondering if anyone could help not sure which 2 i got wrong

[feral raft]

Guys I am having a very silly doubt
My doubt is shouldn't a mod should came there in the eighth formula

Because as we know the differentiation of sec inverse x has mod x

[river drift]

,rccw

[river drift]

the formula as it stands only applies for positive x, yes

[karmic karma]

i love integration

[rocky wind]

Please don't cross-post the same question in multiple channels
#geometry-and-trigonometry message

[rocky wind]

A mod may come if you post sth off-topic. Your integral calculus questions suits #calculus better than this precalculus channel.

[formal sorrel]

hey

i have a very stupid qn

if f and g are onto then is gof or fog **always **onto?

[rocky wind]

!showwork

[tender quest]

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

[formal sorrel]

its not part of a question im just asking whether this property is valid or not????

[rocky wind]

You're asking a question.
That's why you have to show us your efforts and thoughts on your question, so as to provide context.
In this way, we know where you're stuck, and helpers can reply more quickly by avoiding repetition of concepts, facts and steps that you've already known, and they can give guides/hints that adapt to your level and understanding

[willow bear]

eighth formula?

i don't see formula (viii) in your image

[willow bear]

"If f and g are functions such that they are individually onto and their compositions both ways (fog and gof) are defined, is it always the case that at least one of said compositions is onto as well?"

is this what you are asking?

[formal sorrel]

precisely yes

[willow bear]

f: X -> Y and g: Y -> X

try proving that f o g is surjective, preparing yourself for the possibility that your proof may fail

[formal sorrel]

im getting the result is true?

is it correct

[willow bear]

show your proof

[formal sorrel]

i drew some function mappinps and tried to make an example in which this result is not followed

do u want those?

and a little bit of thinking

[willow bear]

sure but your description makes it sound like you don't really yet have a proper proof

[formal sorrel]

i mean if every element in C has a preimage in B and every element in B has a preimage in A then a element in A must be connected to every element in C via B?

ukw il just check with my mentor

ty for trying to help me tho

[viscid thistle]

Does anyone know if d is correct too? I don't rlly think its 100% correct but my friend says d is correct too?

[willow bear]

,rccw

[tribal gate]

U guys have such easy question

Jk

[raw hill]

d would be right if it said f’’ instead of f’

[viscid thistle]

I dont understand why

[viscid thistle]

Yeah we know, we just have shitty teachers

[raw hill]

Inflection -> concavity changes -> f’’ changes from positive to negative (concave up to concave down) or vice versa -> aka f’’ changing sign

???

Consider x^2 at x=0 as a counterexample

[viscid thistle]

Nvm i was looking at it the other way wround

Thanks

[opal sapphire]

Hello I need help in solving this question. I've tried solving it by 1+y^2 = t^2 as well .

[half sinew]

Wow…

[rocky wind]

you've posted your question in a wrong channel. Please try #calculus or #math-discussion

[opal sapphire]

Oh thank you

[scarlet wyvern]

Can someone tell me how to solve these problems or link me to a video that teaches it?

i thought of a method that works but it's time consuming so it wouldnt be that good on tests and quizzes

[scarlet wyvern]

Also will the shape of parabolas, ellipses and hyperbolas ever be affected by the restriction of t or whatever the parameter is?

[hardy peak]

i need help 😭

[willow bear]

incorrect. there is a closed-form solution, it's just extremely torturous to get to

[half sinew]

Oh

But

[river drift]

if nothing else you can brute force it with double angle/angle sums to get rid of the 3x and power reduction to get rid of the ^4

[half sinew]

Well thanks for the info, I’ll correct myself.

[vernal lynx]

what is sen^4 (3x) in your questions ??

is it sec^4 (3x) or sin^4 (3x)

am assuming its a sine function

[willow bear]

sin

but in Spanish

[vernal lynx]

oh i see

you need to use trigo identities to simplify the expression

since the power is 4 take the poser 2 outside

hint 1 : sin(3x) = 3sinx - 4sin^4 x

hint 2 : cos^2x = 1 + cos(2x) /2

hint 3: sin^2 (3x) = 1 - cos(6x) / 2

after substituting identities you should be getting integral (sin^3 (x) cos(x)dx

in that case take sinx = t

then derivate it to simplify it in an algebraic form of integral

hence cosx dx = dt

then it should be integral ( t^3dt)

after integrating just put the value of t

i think this question was decent since its an integral of sin^m (ax) cos^n (bx)

where a is 3

[wispy valley]

What's wrong in my method

[raw hill]

Sign error

Also x changed to theta but you kept dx

Btw this is calculus, not precalc

Just put in the correct channel next time

Oh you double posted

Yeah pls don’t do that

Cause it’s inconsiderate to have two people answer the same thing

[wispy valley]

+1

[wispy valley]

By mistake

[wispy valley]

Where?

Oh

Mb

Sorry man

Stull @raw hill it won't affect much

Method is still the same

Just +1 this time

[raw hill]

r u sure about that

Because $\cos^2 \theta+2\cos \theta+1$ is a perfect square

[obsidian monolith]

Civil Service Pigeon

[raw hill]

Also this should be 1/sin(theta), not sin(theta)

[wispy valley]

Man

So many mistakes

Thanks man

What's the diff between pre Calc and calc

[raw hill]

Pre calc: before calculus (usually preparatory skills for calculus, so stuff like algebra)

Calculus is

Calculus

It’s mostly an American thing

[wispy valley]

Guys got another doubt

In q 3

What's wrong with my method

[willow bear]

something seems to have gone wrong while executing your substitution

[wispy valley]

What exactly?

I seem to have done it correctly

[willow bear]

also what is integration doing in the PREcalc channel anyway.

you should go to #calculus

[wispy valley]

Man

This stuff confusing

[river jungle]

How do I find the value of an inverse trig ratio?

Ohhhhhh wait hold on never mind

I can just graph the inverse of the sine function and find y = -1, right?

$x = \sin y$

[obsidian monolith]

TheBacons

[latent veldt]

help

,help

[obsidian monolith]

A brief description and guide on how to use me was sent to your DMs!
Please use ,list to see a list of all my commands, and ,help cmd to get detailed help on a command!

[severe flicker]

hi im trying to figure out what im supposed to do to reach the answer of x is undefined on pi/4 + pi/4 * k

i know that a regular tan is undefined on pi/2 + pi*k but i dont know how to find where its undefined on a manipulated graph

[willow skiff]

$4(x - \pi/2) = \pi/2 + \pi k$

[obsidian monolith]

south

[tulip zenith]

3tan(4(x-(pi)/2))=3tan(4x-2pi)=3tan(4x)

which basically means that the domain will be ->
(set of all real numbers)-(integral multiples of pi/8) ie.
R - n*(pi)/8 where n belongs to integers

[winter comet]

<@&268886789983436800>

[formal wren]

Help

[lost sundial]

(x - sqrt(6))^2 >= 0 so x^2 + 6 >= 2x sqrt(6) with equality when x = sqrt6
that means g(x) = 2.5x/(x^2 + 6) <= 2.5x/(2x sqrt(6)) = 1.25/sqrt(6)
and we have that g(sqrt6) = 2.5 sqrt6 / 12 = 1.25/sqrt6
so the max of g is 1.25/sqrt6

[rapid thunder]

There you go

[rocky wind]

!nosols

[tender quest]

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

[rocky wind]

this is a #precalculus channel, so please guide OP without using #calculus

[rocky wind]

!nosols

[tender quest]

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

[rapid thunder]

I don't even really know how to do calculus

My friend sent me that when I sent them the image

[slow stream]

Any tips on learning math for someone who only knows primary school math like addition multiplication division subtraction

Im doing a cs degree

[formal wren]

Did u use derivatives to answer it?

[formal wren]

Sorry are u able to write it out in struggling to read it?

[tulip zenith]

is it 2.5 or is it 2*5?

[formal wren]

2.5

[tulip zenith]

just differentiate it once with respect to x

and then equate it with 0

to get the critical points of the initial fnc

and once you find them, u can see that where the slope of the graph is positive and negative and according to that u get the points which will have zero slope thereby giving local maxima or local minima, the points u get, just put them in g(x)

for local maxima point u will get g(x) max value and vice versa

[unreal osprey]

I don’t understand precalculus…

[solid cypress]

I love ts tho

especially the piecewise functions bro

they're so easy

[unreal osprey]

I don’t know a thing about it…

[echo sinew]

Well, you will learn them I believe

What don't you understand of precalculus? Typically it is because you don't know/remember enough prealgebra

[flat stratus]

What is the fastest way to learn precalculus? I have a book on it (as well as calculus) though I kinda have focus issues.

[unreal osprey]

Ohh… then I will learn more pre algebra..

[sly narwhal]

Just got to continuity and I'm a bit confused. It was stated that a function that has a point with no limit is not continuous, but sin and cosine are continuous, yet they have no limit at infinity. Why?

Is infinity just not counted when considering function continuity?

[terse pebble]

infinity is not a number

[sly narwhal]

Ik

But you can still find limits a function approaches it

[terse pebble]

basically, a function f : X —> Y is continuous if and only if for every open set V in Y, f^-1(V) is open

[sly narwhal]

Ok

[river drift]

a function is continuous if for every point in its domain the function value is equal to its limit

infinity is not a point in any function's domain because it's not a number

[sturdy hound]

I want to find vector AB, so I subtract A from B
(5-(-2)), (4-3) = < 7, 1 >

but when I graph it it is in a different position than the purple line which is the vector I want to find.

However, it still has the same direction and magnitude but it just starts from the origin. Is this still vector AB??

[willow bear]

yes it is

a vector can be shifted around wherever you want, without rotating it or changing its length, and it'll still be the same vector

[sturdy hound]

ok thank you! because i had a similar question on a test but im confuse why i got it wrong

my sketches at the bottom probably arent right but i feel like b) should be true and im confused why it isnt

[summer ruin]

(7, 1) are not it's coordinates with respect to the origin

they are with respect to the tip of A

you can see that if you make 7 steps right and 1 step up from the tip of A you'll get B

[sturdy hound]

yeah

[sturdy hound]

do you think. you could also take a look at the question i just had about b)?

[willow bear]

that scan, dear lord

[willow bear]

G + K = -F not F

the sum G+K is a vector that's like F but pointing the opposite way

[sturdy hound]

wait sory i drew it online and it is pointing the same way as F, did i draw it wrong?

[willow bear]

yeah cause the arrow that you drew isn't G+K

G+K would be pointing down and to the left

it would go from the tail of G to the tip of K

[sturdy hound]

so it should look like this then?

[hoary iris]

,, \lim_{\left(h \rightarrow 0} {\frac{\ln{\frac{\sin{(x+h)}}{\sin{(x)}}}}{h}\right)}

[obsidian monolith]

Monkey•D•Luffy
Compile Error! Click the reaction for more information.
(You may edit your message to recompile.)

[mint widget]

Can anyone help me in this question

[hoary iris]

Use properties of det

[mint widget]

What is det? Determination?

[hoary iris]

Determinant

[mint widget]

What is the properties of determinant?

[hoary iris]

Do you only know how to expand a determinant?

!status

[tender quest]

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

[mint widget]

No.

[hoary iris]

For this?

,, \lim_{h \to 0} \frac{1}{h}\ln\left(\frac{\sin(x+h)}{\sin(x)}\right)

[obsidian monolith]

Monkey•D•Luffy

[hoary iris]

Anyone help with this limit

[rapid thunder]

Who wants to teach me?

[old pollen]

Do you have questions

[rapid thunder]

Never

I will escape school

[old pollen]

!da2a

[tender quest]

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

[rapid thunder]

pure regret

[turbid skiff]

1/h × {ln(sin(x +h)) - ln(sin(x))}

$\frac{ln(sin(x+h))}{h}$

[obsidian monolith]

╰ 𝕃 𝕌 ℂ 𝕀 𝔽 𝔼 ℝ ╮

[wintry egret]

what.

did the messages just dissapear

bro what

[hoary iris]

@winter comet do you know about this?

[winter comet]

are you trying to differentiate ln(sin(x)) using the definition of a derivative?

[hoary iris]

exactly!

[half sinew]

Finally.

[terse pebble]

were you muted

lmao

[winter comet]

ofc

[terse pebble]

tough

[half sinew]

Yeah

💀

I dont even know if we have a calc channel?

[hoary iris]

but how to do that limit?

[willow skiff]

probably use $\sin(x + h) = \sin x \cos h + \cos x \sin h$

and then as $h \to 0$, the inside of the $\ln$ would become $1 + h \frac{\cos x}{\sin x}$

now use $\ln(1 + u) \approx u$ or $\lim_{u \to 0} \frac{\ln(1 + u)}{u} = 1$

[obsidian monolith]

south

[hoary iris]

,, \lim_{h \to 0} \frac{1}{h}\ln{\left(\cos(h)+\cot(x)sin(h)\right)}

[obsidian monolith]

Monkey•D•Luffy

[hoary iris]

@willow skiff what to do from here?

[willow skiff]

Read the 3rd line

[hoary iris]

how does cos(h)+cot(x)sin(h) become 1+h*cot(x)?

[willow skiff]

cos(h) goes to 1

sin(h) goes to h

[hoary iris]

how?

doesn't it goes to 0?

[willow skiff]

you can't use that because you are dividing by h in front

well cos(h) goes to 1 - h^2 / 2 and sin(h) goes to h - h^3 / 6

but you can ignore terms of h^2 or higher

since h^2 / h = h --> 0 and so on

[hoary iris]

expansion of sin and cos?

ok ok

if I take y = h cot(x)

can I take cot(x) out of the limit?

@willow skiff

[willow skiff]

yes that's the idea behind $\ln(1 + h \cot x) \approx h \cot x$

then don't forget originally you had a 1/h out in front

[obsidian monolith]

south

[lean drum]

What the fuck did I get pinged for again...

[terse pebble]

our whole conversation got purged lmao

immanuel pinged you calling you a gpt user

[lean drum]

Bruh

[terse pebble]

hayley erased our conversation

[hoary iris]

thank you

[half sinew]

😦

[heady bluff]

For this unit circle is the space highlighted in purple 30 degrees or blue 30 degrees. I know it says 30 degrees in the blue area but isn’t zero degrees not an angle?

Because I see 4 spaces..but apparently just wht appears to be only 3 (actual)angles?

[winter comet]

this angle is 30 degrees

[heady bluff]

Ohhh ok

Ok!

That makes sense now

Ty!

[random furnace]

hi

[chrome ether]

https://nohello.net/en/

[random furnace]

Do you have any guide on what concepts to learn before differential calculus?

[willow bear]

getting your algebra up to speed is the most important thing 100%

a close second in terms of importance is the concept of a function

and then also straight lines and slope

[hoary iris]

why is it bad to just say hi? lol

[willow skiff]

wastes time

instead of saying 'hi' you could ask your question directly

and receive a quicker response

[hoary iris]

'Hi' don't always mean they want some help though but also agreed with this.

[livid tide]

,w graph derivation of x^3

[obsidian monolith]

Results provided by WolframAlpha

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

Requested by sagnik3321

[livid tide]

bruh

how tf do i get the graph of ts

[echo sinew]

What do you mean with graph derivation?

[random furnace]

how many cases of factorization are essential for calculus?

[willow bear]

cases?

[half sinew]

100%

[random furnace]

yeah

[willow bear]

.... i don't know what you mean by "case" here

[random furnace]

common factor, perfect square trinomial}

dont they teach you that?

[random furnace]

you could understand methods to break down algebraic expressions into simpler factors

[willow bear]

yes i was just confused as to what exactly you were referring to when you said "case"

[random furnace]

uh ok

so what techniques do you recommend learning first to get into differential calculus?

[viscid thistle]

learn trig identities first

that's the best key

then after you go around, know the derivatives of each trig function, you can even prove it

[random furnace]

uh ok

the unit circle can be of great help?

[low anchor]

Hii can anyone help me solve these 2? I don't quite understand it since I skipped some classes

[low anchor]

I sort of understand j. where I basically turned the 2^x to y to make it easier but after getting y^2 - 5y - 4 =0 I couldn't find the final answer

[regal pagoda]

What do the instructions for the problem say

[low anchor]

Solve for x

Like find x

[regal pagoda]

quadratic formula

then do log both sides, only one answer will be in the domain

for i., notice 3 can be written as a power of 2

Specifically log_2 (3)

then do the same y sub

[low anchor]

Thing is were not supposed to use log bcs we havent learn that yet.. Idk what the teacher expect 😭

[regal pagoda]

maybe u were taught logarithms in the classes u skipped

u cant solve either problem without logarithms

[ebon zinc]

agreed

[low anchor]

Noo I already asked hehe oh welll

How about this one?

[ebon zinc]

huh

[regal pagoda]

...take the natural log of both sides

or your favorite log, doesnt matter

[low anchor]

Basically you have to find X too

[regal pagoda]

How are the class examples done without logarithms

[low anchor]

We replace numbers that are the same with a variabel like if there's 2 of 2^x we change it into y

[regal pagoda]

So are you solving for y?

You can't solve for x without taking a log

[ebon zinc]

3^2x = 2^x+1 + 54 ;
log(3^2x) =LOG( 2^x+1 + 54) ;
log(3^2x)-LOG( 2^x+1 + 54) =0; // log(a)-log(b)= log(a/b)??anyway;
log(3^2x / 2^x+1 + 54 ) =0;
is this kinda correct path ?

or wait i have better idea

[low anchor]

Hhh I can't use log, I understand how but since my teacher havent thought us yet we sadly cannot use it

[ebon zinc]

soo what ur teacher has gived u ?

what u guys are using

[low anchor]

The basics of exponent, thats it

Basically no log

[ebon zinc]

ln ?

even this ?

[low anchor]

Yeahh

[ebon zinc]

u teacher is built deferent

[low anchor]

Just like the basics

[low anchor]

Well my class cannot keep up well so he make things easier but complicated to those who know its easier to use something else...

[ebon zinc]

(3^x)^2 -2^x * 2 = 27*2 ;
(3^x)^2 = ((2^x + 27)(2));
(3^x)^2/((2^x + 27)(2)) = 1 ;
(3^x)^2/((2^x + 27)) = 2 ;

i was thinking this not anything

i will try another aprocch cuz its clear that the 27 wil cuz issues

i think about rahter than moving the 2^x along 27 is bitter

moving the 2^x alone

soo wi will get
(3^x)^2- 27(2); = 2^x ;
(3^x)^2/2^x- 27(2)/2^x=1

where this is gonna lead to

tbh idk but i had fun

:D

wait

(3/ 2^(1/2))^2x =(1+(27(2)^(1/2x)/2^(1/2))^2x)
(3/ 2^(1/2)) =(1+(27(2)^(1/2x)/2^(1/2))^2x) ^1/2x

i ended up making it more complicted which mean that the quadratci fourmula have somthing to do with all of this lol

what of a waster of time am

sorry

:D

[low anchor]

OHH THANK YOUU

[whole void]

never memorize this

[willow bear]

i mean memorizing it blindly is no good yeah

but committing it to memory and practicing these laws a bunch of times will help

[steep blade]

why does it say a° instead of a^0

• it should say , a≠0

[willow bear]

typographical defect

also tbh 0^0 = 1

[uncut star]

How do we solve the eqn

,tex $2 + log_{10} 2 = k + log_{10} k$

[obsidian monolith]

Triaengle

[sweet grove]

calculus

[gray magnet]

tf

sqrt pi

trust

[acoustic apex]

integration by parts

then somehow manipulate into dirichlet

[sweet grove]

?

[acoustic apex]

do you even know what integration by parts is 😭

[sweet grove]

im new to calculus

[acoustic apex]

then don't bother with this integral

because this is integration bee level stuff

[sweet grove]

seems fun though

and i also need an answer

[willow skiff]

you're only hurting yourself by skipping fundamentals

[acoustic apex]

https://www.youtube.com/watch?v=lLDiIf_BB-I

yeah this is mad

[sweet grove]

hmm

[zinc mantle]

i am not sure this result is even useful for that exact integral, though its just a rational function, maybe computer code can deal with that easily idk

[sweet grove]

damn

[acoustic apex]

where did you get that integral from

[sweet grove]

are you gonna believe me if i say it

roblox lmao

[acoustic apex]

.

[sweet grove]

ok thats a fair reaction

i mean if i want to i can post some question here but idk if anyone would want to solve

[acoustic apex]

Sure?

[sweet grove]

mk hold on

Every time t changes there is t/(10^10) chance of an event happening where (starting from t=0) t increases by 1 each second. If the event doesn't happen after the change, there is a 1/66 chance of t being divided by 2 (rounded to the lower integer). If the event automatically happens at t=1000, what is the probability of the event happening before t=1000?

and
Given a 5-cell with a hypervolume of 7744100sqrt(45), what's the largest hypervolume that an inscribed in the given 5-cell 3-ellipsoid (3-sphere deformed by an affine transformation) can have?

[open atlas]

for this one, surprisingly, you dont need to use logs

special case though

[heavy pewter]

why are there integrals in a precalculus channel 😔

[frank socket]

Splitting the fraction into two equations like that ^, setting the left numerator equal to the right numerator and such, looks odd to me, but it gave the right answer. How do you know if you can do that? Unsimplifying the fraction would result in a different answer right? Am I misreading what happened there?

[heavy pewter]

$\frac{5^{3x}}{2^{9x}}=\frac{25}{64}$ does not imply $5^{3x}=25$ or that $2^{9x}=64$

[obsidian monolith]

parabolicinsanity

[heavy pewter]

what i suggest is that $\frac{5^{3x}}{2^{9x}}=\left(\frac{5}{2^3}\right)^{3x}$

[obsidian monolith]

parabolicinsanity

[heavy pewter]

same for $\frac{25}{64}=\left(\frac{5}{2^3}\right)^2$

[obsidian monolith]

parabolicinsanity

[heavy pewter]

you might've gotten the answer but you can't assume that $\frac{P}{Q}=\frac{X}{Y} \implies P=X \land Q = Y$

[obsidian monolith]

parabolicinsanity

[frank socket]

Ah thanks, that clears that up

[heavy pewter]

but if you do want to do that for any other problems which can come up

you can let a value k such that

$P=kX$ and $Q=kY$

[obsidian monolith]

parabolicinsanity

[heavy pewter]

k can be 1 but that isn't always true so you have to generalise

[frank socket]

Gotcha, that's kinda cool

[open atlas]

Yeah this is an incredibly rare case and shouldn’t be generalized, it was just the only way I could solve it without using logs (as per the requirements of the question)

[heavy pewter]

exponential problem
can't use logarithms

what

[open atlas]

This is far better tbf

[open atlas]

Exactly

I thought the same

It’s much easier using logs but apparently the person who asked the question, said their teacher only wanted them to use exponent laws

[heavy pewter]

weird

[open atlas]

To which im assuming this is one of the only ways to solve that question by those parameters

Which is not very good cos students will get confused and start to make unreliable assumptions

[somber thicket]

i never bothered to look at my first session syllabus; and now i have a pretty-important-test in two weeks; how deep fried am i? (derivative stuff is excluded, only algebraic stuff for complex numbers)

[whole void]

honestly this is kinda impressive for a syllabus

that it does AM-GM-HM and also Cauchy-Schwarz

[somber thicket]

my school's specialty is its math department. so yeah, the syllabus extends quite a bit beyond the standard; but its not too big, its just i have been sitting on my ass for the last two months.

procrastination is one's worst enemy

[whole void]

what country do u live in just curious?

[somber thicket]

I would avoid doxing myself, but it's in asia. This is under the special math course you would want to call it.

[whole void]

I know exactly who u r now!

[whole void]

but seriously if u know little of most of this then u r actually screwed

[somber thicket]

its 10% of final grade; not too bad, but i'd like to pass. Polynomials and inequalities are like 40-50% of the marks;

[whole void]

polynomials are easy

wait do u have to know vietas?

[somber thicket]

yes

[whole void]

do u want me to give u some problems or something?

[somber thicket]

no; i already have my notes and problems. just wanted to ask what topics would be the most feasible to do first

[whole void]

1 5 4 2 3

if u want a challenge perhaps, try this https://cdn.discordapp.com/attachments/1211848292229582938/1352746886276190240/image.png?ex=68016a36&is=680018b6&hm=51f5cb5401d0d9019e6630c80d6dbbe3871a5c376263cdb633b3b653726222dd&

I haven’t figured it out yet

[somber thicket]

sorry; was talking to someone. i am not exactly sure i could solve this, but this would just serve well as a proof by contradiction where you cover every case for j? for j=0; that would just be using vieta's formulas.

atleats thats how i usually tend to solve such problems, my theory isnt exactly cut clear

[lone marten]

idk if this is the right place to ask this (i hope its ok) idk how its called in english but ill try to explain what you do in in

you get a graph and then they tell you to find the Max area of lets say ABC and you like replace the x with t then do some other things do you know what its called? and if yes where i can find a lot of tests of that kind?

i would send a image but its in hebrew

[willow skiff]

yeah just send the image, well it'd be good if you send the Google Translated image actually

your question is too vague to be answered right now

[lone marten]

let me try and trainsalte it rq

this is what google tranlate did i hope its correct

it ruied the function but its
f(x)=3-(6/x)

[willow skiff]

ah, so it's an application of differentiation

so you differentiate the area function, $(8 - x) f(x)$, with respect to $x$

also you must have $2 \le x \le 8$, from the definition of the graph $f(x)$

[obsidian monolith]

south

[willow skiff]

so naturally, expanding (8 - x) * f(x) then using the power rule will work

[willow skiff]

https://madasmaths.com/archive/maths_booklets/basic_topics/calculus/differentiation_optimization_problems.pdf

there's this whole sheet
the topic is named optimisation

[viscid thistle]

BROOOOO

SOUTH

IM NORTH

[heavy dagger]

Yo can anyone help rn

Trying to find the equation of a parabola with a given focus of (4,5) and a directrix of y=8, i understand most of the process but im not understanding how to determine wether it opens up or downward

If i am correct, since the 5 is less than the 8, it results in a downward parabola

[willow bear]

yes

the focus lies below the directrix

[random furnace]

hi

does anyone here know most of the basics of rationalization?

[willow bear]

!da2a

[tender quest]

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

[willow bear]

this is a server of hundreds of thousands of people. someone who knows <high school curriculum topic> is virtually guaranteed to exist

[cursive tapir]

bonjour a tous!

[willow skiff]

annyeong!

[oak ferry]

😭

[prisma oxide]

Help I’m so confused

[heavy pewter]

what's the issue? just look at the graph