precalculus

[visual plaza]

there would be a commo factor in all these cases right?

so i would first fifferentiate with chain rule and then do the product rule? and then the result of the product rule would allow me to common factor?

[ancient inlet]

yeah

[uncut mulch]

Show your attempt

actually this would belong in
#calculus , or even better claim your own personal channel #❓how-to-get-help

[west thistle]

I'm currently in 10th grade, what are the main things you learn in percalc 11 and 12?

[undone pumice]

um, so im in precalc but im not sure why yours is like split into two grades

im in an ap class so its got a standardized curicullum for one year long... um, but i guess i can give you the list of units we're learning. though im not sure if its different?

[west thistle]

What country r u in?

[undone pumice]

US

[west thistle]

Im in canada

[undone pumice]

ohh

maybe thats it

[west thistle]

The list would be great

[undone pumice]

okay! our ap precalc course has 4 units

which are these

so the first one is like... graphing polynomials (quadratics and cubics and such. sketches, based on zeroes and multiciplity, same with rationals, graphing. as well as finding zeroes. a bunch of algebra work)

inverses as well i think? which carried into unit 2 where we learned about graphing exponentials, finding key features of them

and unit 2 was also learningabout the inverse of exponential which is a type of graph called log. so also learning properties of how to manipualte it

[west thistle]

Wait i have to wait till precalc to be taught logarithms?

[undone pumice]

and my class is right at the start of unit 3 which is trig work. eg: modeling with functions, key features, graphing, transforms of them, unit circle (kind of review of past course tbh)

[undone pumice]

uhhh it might be taught in earlier courses

[west thistle]

O alr

[undone pumice]

the way ap precalc works at my school is you can skip integrated 3 (progression is 1 is lowest, up to 3) if you take integrated 2 and get an A, so its just review. log was a integrated 3 topic but not everyone in my class learned it because some skipped rom int 2 to precalc

but i remember learning it in 8th grade when i took int3

cus they're pretty simple. and precalc kinda expands on logs with like, quadratics inside, extraneous, u substitution, and such

and, i dont reallllyyy know whats in unit4, cus we haven't learned that yet

[west thistle]

Oh alr

[undone pumice]

oh unit 2 was also like sequences like arithimetic and geometric

seems to cover most of the same topics (BASED ON GOOGLE AI OVERVIEW THO)

[west thistle]

What are transformations?

Idk if thats a stupid question

[undone pumice]

like algebraic manipulations of functions basically

like f(x-3) shifts 3 to the right, f(x)+3 shifts up 3

so sin(2x) makes graph dilate by 1/2

and such

stuff like that

not too bad

[west thistle]

So just changing the numbers around?

[undone pumice]

uhh yeah

[west thistle]

As a barebones explanation ofc

[undone pumice]

dilating and moving left, right, up, down

as well as maybe the asymptote changes. its kind of just a fundamental thing to keep in the back of ur mind

[west thistle]

This is not what i thought it was

Ty for informing me!

[undone pumice]

ah xd youre welcome

lwk idrk either im kinda just winging this class

so i can take calc 🥀

[west thistle]

Well gl!

[undone pumice]

thx igs

got calc ab then bc then idk what to do my senior year but

[west thistle]

Is there a difference?

[undone pumice]

ab is like first semester of college calc (roughly)

bc is like second semester of college calc (roughly)

[west thistle]

O

[undone pumice]

but bc covers all the ab stuff and more

but, if i skip to BC, ill only have precalc and BC and i need 3 years of math to go to a decent college 😔

soooo AB and BC it is

[west thistle]

I dont think i can reasonably go to a decent college

[undone pumice]

lol

nooo its okayyy

[west thistle]

At least thats close

[undone pumice]

im just aiming for like the UCs which is ah like public university in my state

so i need 3 yrs of math by their reqs

[west thistle]

I wanna go into theoretical physics or pure math but my local university's classes are ass💔

[undone pumice]

oh 🥀

i wanna go into applied math

or cs

[west thistle]

Cs?

[undone pumice]

we have a locak university but its just a community college (so its highk buns)

[undone pumice]

comp sci

[west thistle]

What does comp mean cuz what i think it means makes no sense for the context

[undone pumice]

Oh. Sorry. Stands for computer

[west thistle]

Oh

[undone pumice]

Basically just coding and like how a computer works type stuff

[west thistle]

Isnt the job market for that dying

[undone pumice]

Yupppppp

it isssss

sighhhhh

thats why im considering applied math tho idk if the job market for that is cooked too

welp igs i gotta lock in or sum shi

i have a precalc quiz tmrw and i have pe (running the mile) too sob

[west thistle]

What timezone are you in😭

[undone pumice]

uhhh

west coast us

is 9pm here

[west thistle]

O

Its like 1 am here

[undone pumice]

oh xd

wow

well

i usually go to bed at like midnight xd cus else ik its not worth studying if im gonna fall asleep halfway thru a test

[west thistle]

I js dont study

Too lazy

[undone pumice]

oh lol

i only study

for precalc

mostly

my other classes i dont really needa cus freshie classes are easy ash icl

[west thistle]

I mean i technically study

But only for stuff like beyond the curriculum

[undone pumice]

ah

thats cool

always good to be ahead

[west thistle]

We're doing slop for the rest of gr10 math so at least i can 7se that to do my physics work

[undone pumice]

lolll

i see

my math teacher says we gotta lock in for the ap exam 😔 but my bio class is easy so i use that time to do my hw whenever she gives us free time lmao

[west thistle]

O

[undone pumice]

yeah lol tho i heard gr10 science is kinda hard (like chem or smt)

[west thistle]

I wasnt in gr10 science!

Apparently from what ive heard its slop anyways from ppl around here

[undone pumice]

our school is kinda weird too like bio then chem then physics igs

which other ppl told me is weird lol

[west thistle]

I was put into bio 11 1st semester cuz norm sci 10 was full

[undone pumice]

oop wow

uh

thats crazy

[west thistle]

And now im in phys 11

[undone pumice]

damn

um good for you i guess lol

our school tells us not to do physics until 11th cus like of the math not being taught lmao (ones algebra based the other is calculus based) not that it matters to me but i gues to the regular track kids who r failing

[west thistle]

Thats odd

[undone pumice]

yeah we can't take physics till 11th

like a no exceptions thing

[west thistle]

Most advanced thing i saw on the full course formula sheet was the quadratic formula

[undone pumice]

lol wild

i heard ap physics 1 (the algebra one) is like really easy tho

here the regular track takes like integrated 2 in 10th grade which ik covers quadratic formula lol and then 11th can take physics

[west thistle]

Lowkey

Quadratic formula easy af

[undone pumice]

frfr

the hardest part was deriving it

all you need to know is

memorize ts

[west thistle]

What

[undone pumice]

like i learned ts in like 7th grade

[undone pumice]

my course made us watch this like 15 minute long video

about how to go from completing the square

to the quadratic formula

and i took online math in 8th grade so uh it was highkey impossible to skip it i js sat thru it like "i dont understand ts"

but alr lol

[west thistle]

Oh i thought they made u derive it from scratch for a second😭

[undone pumice]

lol no thank god

i never rlly paid attention so that would have been erm

soooo fun and greatttt for my grade (at least they never saw me cus it was online so i could like gpt here and there)

[west thistle]

Did u do the complex plane yet

[undone pumice]

yeah

like all that

a+bi stuff

learned ts in 8th grade as well

online

yawn

[west thistle]

Wtf

[undone pumice]

no like i took online math

like thru my district

[west thistle]

All i learned in gr8 was pythag theorem😭

[undone pumice]

i took integrated 2 and 3 online

[west thistle]

Amyways i gtg cya

[undone pumice]

cya glgl

[ancient inlet]

💀

[undone pumice]

Lwk that’s what the “advanced” 8th grade track at my school got taught too. Integrated 1 was like slope intercept form and pythag theorem type shi … no quadratics or nothing … glad I got out of it lol

[ancient inlet]

I see

[knotty slate]

Can I ask a que like this here?

<@&286206848099549185>

[fading cobalt]

that goes better under #calculus

[dim reef]

Very advanced

[civic moon]

Thats too advanced

We learn pythag in england when we are 12-14

[neon flare]

yeah so 8TH grade 12 yo

[honest hornet]

isnt 8th grade 13

[neon flare]

Yh depends ig

Whether ur born early or latly and when

[honest hornet]

i suppose

[hard pilot]

@knotty slate @honest hornet
Welcome to Mathcord, new nerds

[next moat]

Why did you ping HELPERS

[undone pumice]

It was like the highest u could take (int1 = 9th grade) in 8th and the other track was js math 8 which was regular

[barren burrow]

Ahoy ladies and gentlemen

I am taking MIT OCW Single variable

Calc

So I find it doable but my pre calc is weak any tips?

[rough leaf]

practice uour trig stuff

your identities and stuff

it’s very important in calc

[barren burrow]

Any lecture for good base?

I can do calc easily but pre calc kills me

[rough leaf]

i js found khans trig course helps a lot

it’s really short too

[barren burrow]

Covers everything?

[rough leaf]

what do you struggle with in precalc

[barren burrow]

Especially trigonometry

[gray osprey]

!help

[tender quest]

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

[rough leaf]

wverythjng except the hyperbolic trig functions

you may need to find yt vids

for that

[barren burrow]

Sure buddy,

Once trigono is done then it wont take long to finish other stuff

Appreciate for your help

[rough leaf]

trig is lile the main important thing

and probably like

polar coordinates

[barren burrow]

sinx as y coord and cosx as x coord of a unit circle?

[rough leaf]

nah it’s like

z=cosx + isinx

[barren burrow]

Well can you also suggest me a course for like geometry as well. Mine geometry is very weak

[barren burrow]

Oh yeah I get it then we eqaute it to e^itheta

[rough leaf]

mine is too i don’t really have a course for that

[rough leaf]

yeah

[barren burrow]

I will keep that in mind

[rough leaf]

it comes up in the later parts of calc

[barren burrow]

Well let me seek help on other places then I can suggest it to you

[rough leaf]

i have a book i’m reading maybe it helps

[barren burrow]

Like I am planning to give SAT in three months so Geometry is one of the,

[barren burrow]

Which one?

[rough leaf]

i kinda forgot the name i’ll get back to you on that

but it covers everything in amc aime and stuff

[barren burrow]

Calculus to gain expertise so I can get into good uni

[barren burrow]

No problem.

[rough leaf]

it has geomtry number theory combinatorics

[rough leaf]

if you know your basics for geomtry

[barren burrow]

Sounds to be pretty advance

[rough leaf]

like

triangle stuff

anf uh

circle stuff

you should be fine

[barren burrow]

Triangle and circles are the problem everything else still works fine

[rough leaf]

oh

just search up sat geometry on yt and watxh a couple vids

[barren burrow]

Sure buddy thanks again

[undone pumice]

Key word basic… at the level yes it is simple to understand differentiation and integration when you’re older you may learn derivations and formulas and deeper concepts… also vro y r u on discord…

[verbal kelp]

Because I’m mature enough

[undone pumice]

…. okay igs

Well anyway good luck on your math journey I suppose..

[valid topaz]

calc is a notoriously "algebra-easy" course, atleast for 1 and 2 (3 gets a bit more complex computation-wise). the real difficult part is understanding why or how the formulas and idea work.

[willow wraith]

I mean concepts are the most important thing to understand

[west thistle]

Do u learn abt the taylor series in hs

[undone pumice]

not in precalc

if u take calc probably

[west thistle]

I hope my school has calc

[undone pumice]

glgl

mines has calc ab and bc in american system so thats what im taking after precalc

[west thistle]

Dang

[undone pumice]

yeah, calc ab 10th, then calcc bc 11th

then i can chill senior year :3

[narrow wolf]

How to master calculus ( no one can master kd but still any tips )

[ancient inlet]

practice

[narrow wolf]

In which part

[ancient inlet]

the one u are weak at

[haughty fox]

Practice is important but for me it's like when learning a particular theorem or way of solving I just refer some advanced reference problems and examples and revise the core of solving for that particular part from it repeatedly

[undone pumice]

look into the logic of why something is true like the derivation of a rule and such and yeah just grind sets of diff problems until ur pretty comfortable…

[fluid fjord]

I can agree even though I’m in calc 1 pay attention to the derivatives rules the most

Power, constant, trig, quotient, exponential, even the derivative definition which is the formula of the slope

If you can master these everything else should fall into place

[strong helm]

1+1 is 2 guys just you know

[vital dagger]

Yes!! And 4+4=ATE

[strong helm]

Suiii

It’s right

[exotic saddle]

e

[fossil kindle]

is bro a flat earther

[willow wraith]

no

[hollow widget]

It can b 0 too

[regal tree]

yo, if i put x=1 and y=0 in this functional equation, i get f(1)=0, but its given that f(1)=16. where am i going wrong lol

[copper ledge]

Did you assume f(0) to be equal to zero?

That's not always the case

[regal tree]

no

Here's my working. I have a feeling I'm making a very stupid mistake somewhere

[copper ledge]

How is this possible

Wait then it must mean that f(0) doesn't exist right?

[regal tree]

why?

wait also, wouldnt this be the same for any x

[copper ledge]

This is obviously a contradiction that f(1)=16 and so 16 cannot be zero so the only conclusion is f(0) ain't a finite real number

[regal tree]

lmao im wondering what the maker of the problem was thinking

[neon flare]

how can u even get 16 when we don't have the formula of F(x) or F(y)

we cant input

[copper ledge]

Why not?

[neon flare]

no equation

[regal tree]

its given that its 16

[copper ledge]

The function is probably 1/x kinda function

[regal tree]

you can a lot of times formulate the function from a functional equation(not true here prob)

[neon flare]

daym how

so lets say an easy example is 2 f(x) = f(y) we can say f(x) = x and f(y) = 2x ?

but there are many solutions to that one

infinite ig

[regal tree]

for example here

[neon flare]

howd u get rid of 6/5 and f(x) ?

oh bc derivative of f(x) is 0 right

[regal tree]

yee

[neon flare]

howd u also get rid of 5 and 1/5

[regal tree]

also by trial and error i got the function of the previous question as 16/x

[regal tree]

replace x with 5x

[neon flare]

how show us

[regal tree]

using this ig

[neon flare]

too high lvl for me

[regal tree]

just put in x=5t and ull get f(t)

[neon flare]

why is f'(2)=f'(0) not equal to 0

[regal tree]

why would it be zero?

[neon flare]

bc the derivative of a number is zero right

[regal tree]

this is given btw

[regal tree]

yes, but f'(2) basically means is, what value does the derivative take when i put x=2? i do the differentiation then i put x=2

[neon flare]

how do u get F(0) = 2 ?

[regal tree]

put x=y=0 in the og equation

[neon flare]

What now

[regal tree]

solve for f(0) from here

[neon flare]

Oh like that

Daymm thx

nvm

i changed the 5 into 6

[regal tree]

you messed up the second step, you can cross multiply like that

[neon flare]

so i can cross multiply f(0)/2f(0) with 1/5 plus 6/5 ?

[regal tree]

oops i meant you cant*

[neon flare]

i didnt

i divide by 2f(0) to get rid of it on the right

[regal tree]

see what you did in the right hand side, f(0) only gets cancelled in the first term, the second term(ie 6/5) will now have a f(0) in the denominator too

[neon flare]

damnn

both terms

[regal tree]

dont over think this, just let f(0) be some x and solve the linear eqn in one variable

[neon flare]

wdym

[regal tree]

you know how to solve a linear equation in one variable? like 3x+5=14 type?

[neon flare]

yeah

3x = 9 x = 3

[regal tree]

we have the same thing but f(0) is our variable (f(0) is not actually are 'variable' since its a constant, but it is an unknown thing just like x)

[neon flare]

i dont have the vision

[regal tree]

wdym?

[neon flare]

i dont see what to do

[regal tree]

your know how you solved x here? do the same thing for this

[neon flare]

i didnt solve shi

[tardy birch]

lolll

[tardy birch]

this is easyyyyyy chatt

[neon flare]

show us

[tardy birch]

kk hold up

I can’t clearly read the exact problem 😭

It looks like something like:

f\left(\frac{c+6}{5}\right) = \frac{f(c) + 6}{5}

or maybe

f(c) = \frac{2f(c)}{5} + \frac{6}{5}

[neon flare]

its f(0)

[tardy birch]

oooo

well then jst replace the 'c' for a '0'

[neon flare]

well i used gpt he just multiplied by 5 and substracted 2f(0)

to get 3f(0) = 6

so f(0) = 2

[tardy birch]

hmmm let my try gpt to see ok?

okk yeaa my says that too

[neon flare]

thats the bigger picture btw ..

[tardy birch]

ooh ok tyyy

[tardy birch]

nvmm gpt gave me 8

[regal tree]

dont use ai for maths its unreliable as hell

[tardy birch]

heyy im not the only oneee..honeyy

[neon flare]

it was easy maths

so its fine i was just slow for sum reason

tried to simplify with f(0) but multiplying by 5 is easier for sure

[tardy birch]

hmmmmm

[valid topaz]

hey emu

[rough leaf]

first one is like

yo isn’t there rwo values

wait i might be geeked

[fossil kindle]

unless you give it simple af questions like 6+3

[round geyser]

What about this

[valid topaz]

raise it to the 5th power

[round geyser]

We know 100 can be 10^2

[round geyser]

You mean 1/5

[valid topaz]

no, if we raise to the 5th, we get (x^5)^(x^5)=100^5=10^10

so x^5=10

[round geyser]

Oh

Okay

x=5th root of 10 or (10)^(1/5)

Ok

[verbal pewter]

question: do you need the higher-level roles to access calc channels

(by level i mean level of schooling)

[raw hill]

You can always just manually add the channel to your list

[verbal pewter]

ic thats useful ty

[pearl ruin]

Is it just me or does pre cal lowkey make no sense

Pre cal trigonometry

[undone pumice]

i get it i think... do you want help

[rigid ore]

'trig makes sense'
also that person:
Is this calculus or english? Its very easy.

wdym csc(x) = 1/sin(x)

wdym sec(x) = 1/cos(x)

[undone pumice]

its okay they're just reciprocals

just imgine like... its not so different than 1/x ... just... now its got sin there

[true geode]

They're just functions that are defined like that, tbh

cosec(x) is defined as 1 divided by sin(x); etc.

[alpine bluff]

tbh life would be so much better if sec(x) = 1/sin(x) etc

I wonder what the person who defined that was thinking…

but it probably has something to do with the unit circle

[ionic temple]

the way i remember it is look at the third letter and itll tell you the trig function its a reciprocal of

seCant = 1/cos

coSecant = 1/sin

coTangent = 1/tan

[alpine bluff]

That’s true lol

[ionic temple]

i will admit when i first saw secant being 1/cos i was angry abt it not being 1/sin too lmao
it seems so much more intuitive that way as well

[undone pumice]

Frfr I got mixed up a lot it’s better now but I remember getting frustrated and quitting on learning any extra math js cus of having to graph those (eventually had to learn lmao)

[verbal hornet]

HI

[brazen sedge]

Whats the best way u guys memorized the unit circle? (like the cos tan sin radian angles stuff) i got like 2 hours before my pre calc assesment 💔

[pearl ruin]

I looked it up on tiktok and there’s some good ways to do it

It all repeats and it’s super easy

Won’t take ya long

[strange spire]

Learn the key angles for the first quadrant, swap + and - sign as the x and y coordinates go in different directions/quadrants

It won't take you long to memorize actually

[pearl ruin]

Also like the radians

It’s 6,4,3,2,3,4,6

For the denominators

It goes in a circle

And for each quadrant there’s a rule

The first one all the numerators are pi

Subtract, add, and prime numbers

[strange spire]

He also probably needs All Students Take Calculus, or?

[strange spire]

In a situation where you will need to identify if the trig will be ratio positive or negative according to the quadrants, you can use "All Students Take Calculus" rule

I. Quadrant: All rations are positive
II. Quadrant: Only sine and cosecant are positive
III. Quadrant: Only tangent and cotangent are positive
IV. Quadrant: Only cosine and secant are positive

[brazen sedge]

alrr

[brazen sedge]

quick question--is the tangent the hypotenuse in the unti circle?

[strange spire]

What do you mean?

Like if we build a triangle in the unit circle?

[pearl ruin]

I kinda jus memorized it like how it is on a usual graph

Quad 1, x and y r both pos

Quad 2, negative x and pos y

And so on

[strange spire]

Yeah

[strange spire]

Ik but that’s just an alternative for him

[brazen sedge]

yea

[stone hull]

no, it isn't

because it follows a tangent axis, not the radius of the circle

sorry if i drew it badly, but it goes outside

now, take a look at this one

this is some random angle x and when drawing the tangent line, it goes beyond the unit circle

the line follows the tan axis

same thing with cot

[undone pumice]

Yeah me too… my math teacher recommends we sketch a unit circle on our quiz if time allows…. Tho I have memorized fine… I try to remember in quadrant 1 y goes from 1 to 0 so decreasing and goes from 0 to 1 so increasing … and then fill in all denom of 2 and then top is sqrt 3 2 1 (simplify sqrt1 as 1) and then yeah

[willow canyon]

Hello

[round geyser]

Radius will always be positive

[sonic hill]

😉

[rigid ore]

co- means complement, so secant was named first and then, csc happened

[west thistle]

What is the sin function?

Like ik its a finction but wtf actually is it?

[undone pumice]

its just a repeating representation of how it changes as the angle changes

[pearl ruin]

Yeah

[carmine orbit]

solution to y"+y=0 at y(0),y'(0)

[stiff mist]

I didn't find a channel for mechanics so I posted this here (please tell me where I should post it instead)
Can someone solve this please?

[craggy ravine]

You can look for help in the available help channels higher in the channel list! People will answer you there in a decent timespan, typically a few minutes

Im looking for a document with exercises on proof by induction and the principle of well ordering, including strong induction.
Anyone got good references on that?

[stiff mist]

Alright thanks

[stiff mist]

I got one but it's an Alevel document (further pure maths 1). I'm not sure if thats what youre looking for but ill send it anyway

[craggy ravine]

got something already!

[stiff mist]

Ah perfect

[green star]

Question, how do you simplify this

I tried It and got root35 over -2

But the answer is saying it’s root35 + 3root5 over 2

[rare linden]

firstly, move the minus in the numerator at the front of the fraction and then multiply both the numerator and denominator by sqrt(7)+3 to get a difference of squares formula from which you will have 7 - 9 in the denominator which is minus two, in the numerator you get sqrt(5)*(sqrt7+3)

with the minus at the front and the minus in the denominator the fraction becomes positive

your goal is to make the denominator of the fraction rational

[potent token]

you probably didn't fully redistribute after multiplying the square roots of 7 and 5

[ancient inlet]

Rationalise the denominator

[novel hollow]

Correct me if im wrong, but is this graph even possible?

I tried solving for it by assuming the form Asin(Bx + C) + D, and got 4sin(13x/24) - 2. However this does not line up with (-4pi , 0)

Also, there are only 3 data points given. Since there are 4 variables, wouldn't we need 4 data points?

[brisk raft]

does this fit your needs (after changing ampltiude)

wait

nvm

[novel hollow]

Yea i noticed that too

[brisk raft]

changing amplitude makes +/- 4pi no longer roots

wait no

hmm

[novel hollow]

Also another contradiction i found was that it shows from -4pi to 4pi, it travels two wavelengths

So from 0 to 4pi should be one wave

But it travels more than that

That means it cant be Asin(Bx+C) + D right?

[brisk raft]

maybe its poorly drawn and 0 is meant to be a root

idk

[novel hollow]

Man..

[storm shuttle]

is it js me or are the 4pi and -4pi not at equal distances from the origin

[zenith scarab]

this question so easy, that I dont even know the answer for it

[carmine orbit]

just you

[storm shuttle]

no like if u think abt it the number of curves on the left side b4 -4pi and no of curves on right b4 4pi are different

[carmine orbit]

y axis is not the line of symmetry in this graph which is making you think -4pi and 4pi arent at the same distance

[storm shuttle]

no ik its not the line of symmetry

wai 1 sec

[storm shuttle]

i marked the equal parts in both sides but on the right side there is still more dist left

[faint sail]

Are there any tips for Integral Calculus?

[mortal garden]

I mean well

uhh

u just gotta imagine pretty hard

[viscid thistle]

practice

[echo sinew]

Knowing derivatives very very well

And recognize them without too much effort

[round geyser]

Is the one on red the oscillation

That has to be a x sin

[deft vessel]

use the tabular method for integration by parts

also practice makes perfect

[frail lion]

First and foremost idea of what I think is that a cos graph but 4 cos(x)

We shift it by substracting 2

So 4cos(x)-2

But -4π and 4π are roots

So would probably try 4cos(x-π/3)- 2

But still there's a problem

[storm shuttle]

ehh?

[round geyser]

a times sin I mean

or a*sin

[storm shuttle]

no i was js talking about equal lengths

this graph is like a sin graph moved down and with bigger amplitude das it

[frail lion]

It's not sin at any cost

It's 4cos(x/2+π\3)-2

[round geyser]

I never did this so I guessed

[frail lion]

@novel hollow

[round geyser]

Where would u put pi, 2pi

[frail lion]

X=π
Y=-2√3-2

[frail lion]

See the function man

[round geyser]

Ok

[round geyser]

Is it good to memorize

[ancient inlet]

Yeah

[thick pumice]

maybe not all
Just memorize fundmentals liek sin^2 + cos^2 = 1, tan = sin/cos, sec = 1/cos, and structure of law of sines and cosines
others are derived instantly from them

[round geyser]

Thanks

[thick blade]

@rotund viper

practice problems today like you said

[rotund viper]

mhm

[thick blade]

What else?

That’s the full requirement

for the course

I’m starting my studying from the hardest to the easiest because easiest goes way faster

[rotund viper]

i guess you should also know how to translate from locus to affine quadratic

i mean like again it is impossible for me to know where you are and what you need to learn

[thick blade]

Oh yeah

Uhm locus?

Affine quadratic?

[rotund viper]

i haven't tried the khan academy precalculus course but maybe take a look at it

[thick blade]

Okie

[rotund viper]

i also know aops has a precalculus textbook

[thick blade]

Aops what’s that?

ohh

Wow

[glad nymph]

can someone teach me calculus?

[uncut mulch]

from scratch, unlikely to find someone willing

you could however try reading an introduction and ask questions about anything you don't understand

[frail lion]

What's this

[thick blade]

studying for. pre. alc

pre calc test kit

@frail lion

[frail lion]

Okay

[viscid thistle]

This class is buns

☹️

[paper fiber]

is there any precalculas book which goes through this road map ? or even near to this

[thick blade]

Aops pre calc does on internet archive

[paper fiber]

link pls

[lucid ledge]

question guys

if i take college algebra and trigonometry, did i basically take precalc?

[serene dagger]

Hi, long time no see

[undone pumice]

pr much idk what college algebra and trig covers but thats basically what precalc is

[worn orchid]

depends on what the next calc course covers. some calc courses assume you have a working understanding of limits and jump straight into epsilon-delta, while some don't.
if you're able to find a syllabus for whatever the next calc course is, that should help you understand what else you need to cover

[lucid ledge]

Calculus AB

[lucid ledge]

thank you to both of you!

[undone pumice]

hmm then you should be fine imo, ab starts with limits iirc (idk not in the class till next year)

[worn orchid]

ah then that's enough

[pale halo]

Where does precalc end?

I'm in the uk so we don't really have as easily segmented course modules pre uni

I could do with knowing what I actually know

[lucid ledge]

i think this is what they give

[river zenith]

How much time does pre calc take to finish ?

[rough leaf]

not long

took me maybe a

uh

a month?

[tired vigil]

does anybody have very hard question?

and also good explantory notes?

[lucid ledge]

how many hours a day?

[rough leaf]

idk

maybe 2

i js did a bunch in school

cuz i was bored

[lucid ledge]

ohh ok

[echo sinew]

Oh what topic(s)?

[undone pumice]

Yeah it’s a lot of review of algebra so it’s not too hard

[pliant hatch]

mainly the later topics in alg 2 id say

[fossil kindle]

what is epsilon delta

[thick blade]

Not exactly at all

[thick blade]

It’s a proof for limits that defines them in a rigorous way

[fossil kindle]

oh

[thick blade]

@river zenith definitely does not take a month.

[worthy jewel]

hello

[thick blade]

unit 1 (a+b) is 16 units
unit 2 (a+b) is 18 units
unit 3 (a+b) is 18 units
unit 4 (a+b) is 18 units

[thick blade]

@river zenith 18*3=54 +16 is 70

Definitely did not take you a month to do 70 units at full comprehension and you probably can’t recall each unit right now

[rough leaf]

idk

i js did the khan one

[thick blade]

I’ll look at that

[rough leaf]

the khan one is like 10 units

that’s def doable in a month

[thick blade]

Yeah idk khan doesn’t look as good as ap pre calc

[rough leaf]

idk i took a practice exam afyer the course

like an ap precalc practice exam

and i have no problem in it

but it’s diff for me cuz i’m doing a more extensive obline course for precalc at school as well

[thick blade]

You def had knowledge before the khan academy course then because khans doesn’t teach logs or any logarithmic manipulation

[rough leaf]

i knew like basic log rules

cuz my tiktok fyp is js stem

khan doesnt teach the trig functions as well

like graphs

of them

[thick blade]

Yeah so you had to have learned outside of that course which students usually don’t do

[rough leaf]

khan does logs in alg2

so you would really just need to do it’s precalc course the log part in alg 2

and assuming you did the trig part in precalc

rheres obly obe unit left in khans trig section

and i think it teaches the functions

idk fs tho

yup

it does

so if you do that

maybe month and a half two months

you should be good

[rough leaf]

wait

where did you get these numbers from

[thick blade]

ap pre calc

flippedmath.com

[hard kernel]

can anyone tell me how to know if there are one or two or non ssa triagnels
this is gonna be on my precal test
also hwo do i do angular momentum

[rough leaf]

ssa?

[hard kernel]

yea

[undone pumice]

side-side-angle, the ambigous case. where with the given info 0,1, or 2 triangles could be constructed

[proven mortar]

can someone tell me how to begin my calculus journey

i wan tto fimish it in 11th itself..

[uncut mulch]

first ensure you have a good understanding of algebra, functions, exponents,logs,trig,gro

[mortal garden]

calculus i to iii?

[tired vigil]

on calculus like full calculus, all the way frm basics

i need notes too

can you send it if you have

[mortal garden]

Oh

theres this really good calculus problem

infinite sum of inverse squares

but i think itll take most of ur time though

[echo sinew]

I guess you can look online, like "tough exercises calculus"

Aren't there any?

[native snow]

it converges to something?

[native snow]

is it 1+(root2/2) perchance

[raw hill]

No. For $n \geq 5$, we have
$$\frac{1}{n^2} \leq \int^{n}{n=1} \frac{1}{x^2} \dd{x}$$
and so
$$\sum^{\infty}{n=5} \frac{1}{n^2} \leq \int^{\infty}{4} \frac{1}{x^2} \dd{x}=\frac{1}{4}$$
Thus,
$$\sum^{\infty}{n=1} \frac{1}{n^2} \leq \left(1+\frac{1}{4}+\frac{1}{9}+\frac{1}{16} \right)+\frac{1}{4}.$$

[obsidian monolith]

Civil Service Pigeon

[raw hill]

,calc 1 +1/4 + 1/9 + 1/16 + 1/4

[obsidian monolith]

Result:

1.6736111111111

[raw hill]

,calc 1+1/sqrt(2)

[obsidian monolith]

Result:

1.7071067811865

[raw hill]

I will say that this problem (known as the Basel problem) was proposed in 1650 and wasn't solved until 1734

Chances are that you can find some questions that scaffold various proofs of this online if you want

Here is one of the ones from the high school level. There are some results that are given to you outright, but those aren't too hard to justify - I suspect they were given to reduce the number of marks that the question was worth.

You can find a laundry list of proofs here

I'll let you do more googling if you want to

[raw hill]

Yes, by the p-series test.

[native snow]

why is the first part true? and why the the integral in the second one start from 4 and not 5

[raw hill]

No. For $n \geq 5$, we have
$$\frac{1}{n^2} \leq \int^{n}{n-1} \frac{1}{x^2} \dd{x}$$
and so
$$\sum^{\infty}{n=5} \frac{1}{n^2} \leq \int^{\infty}{4} \frac{1}{x^2} \dd{x}=\frac{1}{4}$$
Thus,
$$\sum^{\infty}{n=1} \frac{1}{n^2} \leq \left(1+\frac{1}{4}+\frac{1}{9}+\frac{1}{16} \right)+\frac{1}{4}.$$

[obsidian monolith]

Civil Service Pigeon

[raw hill]

typo, my bad

[native snow]

ohhh i get everything else now

except why the first equation is true?

[raw hill]

You can compute the integal on the right hand side and it's obvious

To avoid calculation, you can also justify it by noting that $\frac{1}{x^2}$ is a decreasing function and using a Riemann sum style argument.

[obsidian monolith]

Civil Service Pigeon

[raw hill]

,w graph 1/x^2, x>0

[obsidian monolith]

Results provided by WolframAlpha

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

Requested by civil_service_pigeon

[native snow]

-1/n - (-1/n-1)

[raw hill]

You should put parentheses around the denominator if you have more than one term, but yes. I say this because in a literal sense, you wrote
$$-\frac{1}{n}-\left(-\frac{1}{n}-1\right).$$

[obsidian monolith]

Civil Service Pigeon

[native snow]

oh mb

ok wait i dont get why n has to be >= 5 tho

[raw hill]

Because smaller values of n don't give you a tight enough bound

you can verify this for yourself

You might be able to pick a smaller value of n, but I was lazy and just went with something that I knew would work

5 seemed "big enough"

(Ex. bounding at n=2 gives an upper bound of 2, which is insufficient to prove that 1.707... is not the value)

[native snow]

ok but $$\frac{1}{n^2} \leq \int^{n}{n-1} \frac{1}{x^2} \dd{x}$$ is true for $n \geq 1$ right

[obsidian monolith]

arrow

[native snow]

oh alr got it

[raw hill]

Not $n=1$. But it's true for $n>1$.

[obsidian monolith]

Civil Service Pigeon

[native snow]

mb yes

i meant > 1

[native snow]

oh alr so u were showing that it has to be less than 1.707

cool thanks

also how do u type latex so fast

[raw hill]

correct

[native snow]

lol

[raw hill]

I guess I type a lot in latex (and in general tbf)

Because I am too lazy to retype, here you go

[native snow]

hmm true

ok but for the basel problem

we cant compute the actual number it converges to?

just an arbitrarily good enough upper bound?

[native snow]

oh

[raw hill]

The reason I responded like I did was to prove that your answer was wrong without giving you the actual answer

luckily lazy bounding worked

otherwise I might have given in

the actual answer is quite surprising, which is why I didn't want to reveal it prematurely

[native snow]

hmm alright dont tell me then

[native snow]

but tbh i genuinely dont understand most of this

even one bit

so ill come back to it in some time ig

[raw hill]

[native snow]

ok the paper seems like a nice challenge i could attempt after my igcses but i simply dont know enough calculus to solve those questions

[knotty wadi]

Why is ts in precalculus? 😭

[past hatch]

Sobs

[hearty grove]

can a 3 dimensional frequecy table be used to display more complex data sets ?

[grave vault]

Is ap pre calc hard guys I have an 87 in geometry rn 💔

[undone pumice]

not rlly

[shut galleon]

i had the same question!

[undone pumice]

i have a 107 in this class and im in 9th grade… its boring icl

[shut galleon]

I'm taking algebra 2 right now and i'm going to be taking it next year

[undone pumice]

builds on a lot of algebra and geometry foundations

[shut galleon]

i'm feeling nervous for it

[undone pumice]

nuu you got this

only units 1-3 are even tested in the exm

[grave vault]

Yea me tooooo

[shut galleon]

except i won't be taking the ap pre calc, just normal pre calc because i won't be in high school yet

[undone pumice]

oo nice

[grave vault]

Oh rlly?

[undone pumice]

ya

unit 4 is like taught but not tested

[grave vault]

I thought the ap exam was the entire year’s content

[shut galleon]

i'm just scared for it because i think algebra 2 is hard and i dont know if i will be able to keep up with the class

[grave vault]

Yea me too I’m taking both next year

[undone pumice]

dwdw you'll be okay

i went from integrated 3 (kinda alg2 stuff) to this class and im fine

[undone pumice]

nah entire year is 4 units

[grave vault]

WHATTT

[undone pumice]

idk why its designed like that but igs less stuff to study on the exam

[undone pumice]

but like long units

unit 1 took us throuhg october

unit 2 we only did half of up to winter break

[grave vault]

Yea

[undone pumice]

unit 2 we finished after winter break until february, my class just started unit 3, about halfway in

[grave vault]

oh that’s not too bad

[undone pumice]

gonna finish unit 3 this month and thru april learn unit 4 and then may is the ap exam 🥀

[grave vault]

Gl solider

[shut galleon]

what comes after calc?

[undone pumice]

tyty its my first ap exam

[undone pumice]

hmm maybe linear alg

[shut galleon]

i'm in 7th grade right now and im taking algebra 2 right now so next year i will take pre calc

[undone pumice]

or you could do analysis

[shut galleon]

and calc in 9th

[undone pumice]

oo nice

[grave vault]

DANG

[undone pumice]

im only in precalc in 9th

[grave vault]

dawg u guys r smart

[undone pumice]

ill finish calc in 11th with bc but i hgihk might js take a free period in 12th man

[grave vault]

We r only allowed to take algebra 1 in 7th grade

[shut galleon]

i go to a private school and it k-12

[undone pumice]

we have accel math 7 but then after that i skipped int math 1

[shut galleon]

so they let me take any math as long as i test high enough

[undone pumice]

to take int math 2 and 3 in one year, so then this year i can take precal

[grave vault]

ahhh I see

[shut galleon]

i didnt really take pre algebra or algebra 1 in school

i just tested past it

and i took geometry last year

[undone pumice]

lucky i was really bored in 7th grade...

i go to a public school sigh

[grave vault]

do u guys remember ambiguous case enough to explain it

[undone pumice]

ummm i kinda do

its like based on, the SSA, the info you're given

how many triangles you could construct

theres 0 (impossible to construct any), 1, or 2

[shut galleon]

oh i hated that stuff

[grave vault]

How do yk how many are possible

[undone pumice]

so yk the law of sines?

[grave vault]

yes

[shut galleon]

i deleted it from my brain as soon as i passed that unit

[undone pumice]

me too icl i got too scared to approach my teacher so i js pretended i knew it

fake it till you make it type shi

[undone pumice]

so in the triangle the angle you're given, lets say theta, if its less than 90 thats the 0,1,or 2 case

if you have sides, a, b, c, and height h

if a<b then use the law of sines to figure out sinB

if sinB>1, 0 triangles, else sinB<1, two triangles (quadrant 1, 2)

and then you have the one triangle case

[shut galleon]

guys my school has this math competition thing for private school i forgot what its called

should i try and join?

[undone pumice]

hmm idk i mean

you seem pretty good at math

id go for it

[round geyser]

I am doing sin(theta)=cos(90-theta), cos(theta)=sin(90-theta) and what else

[undone pumice]

elaborate on what else...?

[round geyser]

That’s co functions

There is some identities

[undone pumice]

oh...

idk then i never learned that, gl

[round geyser]

like cot(theta)=tan(90-theta) and tan(theta)=cot(90-theta)

[undone pumice]

which would be either: a>=b (if opposite side is more than adjacent, the side can only fit one way) or a=bsinA (right triangle)

[grave vault]

I’m gonna go to sleep and hope for the best 😭

Ty for ur help 🫰

[lost helm]

Can someone check my answers plsss

[distant olive]

where is the question you are looking for help on?

[rough leaf]

that’s like it

there’s also

sin(-x)=-sin(x)

and cos(-x)=cos(x)

[round geyser]

Also tan(theta)=cot(90-theta), and cot(theta)=tan(90-theta)

csc(theta)=sec(90-theta) and sec(theta)=csc(90-theta)

[fossil kindle]

alg 2 in 7th grade is insane

am only taking algebra 1 in 8th

prolly cause my school doesnt offer the opportunities

[undone pumice]

thats still good... my high school has like integated 1 in 9th which uh im pretty sure is like alg1 (never took it so idk) pretty much super easy

[fossil kindle]

oh

well like the top school in my district requires that i take algebra 1 in 8th grade

and i want to attend so ig it works out

what are all the ways to write out complex numbers

i remember theres a + bi but there was another one i forgot

[valid topaz]

i'm taking alg ii over the summer

so i can go to precalc in 8th

[sullen tree]

Y'all use WordMat and is this the right place to ask about defining a discontinuous function?

[undone pumice]

ummm demoivre maybe? i forgot too

[shut galleon]

twins!

[valid topaz]

there's rectangular, polar, and exponential

[undone pumice]

oh polar... right..

[shut galleon]

I'm taking a quiz tomorrow about conic sections and im having trouble memorizing all the formulas

bruuuu

[valid topaz]

hmmm

[undone pumice]

||trust js learn calculus overnight and derive them|| nunu you got thisss which type formulas is it?

[valid topaz]

wait what's the quiz testing

conic formulas are derivable

most of them atleast

[shut galleon]

the ones about parabolas and hyperbolas

and circles and ellipses

[undone pumice]

oh hyperbolas and ellipses, that stuff

got it, so to be fair, hyperbolas and ellipses are very similar in terms of, like, terminology, so that can be helpful

[shut galleon]

my little brain is gonna explode

[undone pumice]

for circles, remember the center (h,k) and dont be like me and forget its radius squared (🥀 my final was..)

uhhh parabolas, i dont think are the trickiest. is it just factoring, finding zeroes, type stuff?

[shut galleon]

im okay with circles

[valid topaz]

and focus/directrix

[shut galleon]

im just having trouble with the parabolas

yes that stuff

i dont like completing the square

okay i gotta lock in

[undone pumice]

ah i see

[undone pumice]

icl its been a while since i did that

[valid topaz]

alr i found this in my notes: "The focus of a horizontal parabola with equation x-h=(1/4p)(y-k)2 with vertex (h,k) is (h+p,k) and the equation of the directrix is x=h-p."

[uneven charm]

What math course did you take in 6th?

[valid topaz]

likely geo

[uneven charm]

Yeah. Some schools just jump straight to alg II I think.

[valid topaz]

ye

[broken idol]

💀

geometry in 6th grade is crazy

i wonder what he will do in senior year

[valid topaz]

bro i was almost forced to take geo twice

[undone pumice]

rlly why

[uneven charm]

I think it's common to do stuff like that in private schools

[valid topaz]

cuz i switched counties

[undone pumice]

ohh

[valid topaz]

and they had some test that you could only take in 5th

[broken idol]

oh

[undone pumice]

damn, howd you get urself out of retaking geo

[broken idol]

the private schools near me do integrated 1 or algebra 1 in 8th grade

[undone pumice]

is that like an advanced option or they force the students into im1

[uneven charm]

That's normal. Only some private schools push like that for math.

[broken idol]

btw how do you not have a display name?

[valid topaz]

by begging the tag coordinator to take the geo exam right there

[undone pumice]

oh

damn xd

[broken idol]

force

they have to

[undone pumice]

oop

[uneven charm]

I did alg 1 in 8th too and alg 2 in 9th with geo.

[broken idol]

some private highschools only let you in if you have done im1 or im2 in middle school or else they force you to take summer courses

[undone pumice]

at my school its like an option but most of the kids in there were rlly stupid lmao

[broken idol]

my school has a wierd system where our clases our 1 semester long

[valid topaz]

me?

i do

[uneven charm]

So what happens after the first semester? Do you just switch classes?

[valid topaz]

᲼

[broken idol]

oh

its not loading for me for some reason

[valid topaz]

hmm

[undone pumice]

icl i couldn't focus on my integrated 3 work cus my classmates would always be doing some stupid shi like throiwng pencils at each other

[uneven charm]

My goal is MV calc in 12th

[broken idol]

yeah, one or two credit courses such as math ap or ela are one semester long and hald credit courses are 1 quater long

[valid topaz]

mv calc is boring tbh

but it was fun for a bit

[undone pumice]

oh thats weird

[uneven charm]

either that or lin alg

[undone pumice]

how do you do ap exams then, do you just do them at the end of the year

[valid topaz]

i'd advise u to maybe take that before mv calc

[broken idol]

yeah, i had spanish and human geo in semster one

[undone pumice]

oh i see...

dman

*damn

[uneven charm]

Is alg 2 in 9th good?

[broken idol]

so when semester two started i had math after 8 months and it was confusing cause i forgot stuff

[broken idol]

yeah

[undone pumice]

think so, ahead of "regular" pathway at my school

[undone pumice]

oop i see...

[shut galleon]

i took geometry in 6th grade

[broken idol]

but parents protested so they are changing it back next year

[uneven charm]

wow

[broken idol]

damn, I am taking that this year 😭

cant compete with these sweats

[undone pumice]

oh peak uh at least theres that

[shut galleon]

i actually hate math

[undone pumice]

oop rlly

[valid topaz]

why

[undone pumice]

honestly real icl

[broken idol]

atleast math is better then english

i hate ela

[undone pumice]

i like getting good grades and having a high gpa but i dont like having to actually study for my class now that its challenging is that what its like 4 u 🥀

[broken idol]

i dont want to read of mice and men again

[shut galleon]

all i wanna do is play golf

[undone pumice]

real, frick romeo and juliet

[undone pumice]

ahhh we had to read that too in august

[undone pumice]

who cares about some random poor bums in the country like-

[shut galleon]

actually i am in 9th grade english right now

[undone pumice]

oh cool

[broken idol]

its my second time reading it

😭

[undone pumice]

😭 oop

sounds even worse

[broken idol]

girls in my middle school actually cried when we watched the movie and they killed lenny

[shut galleon]

i my school does the martian chronicles instead

[broken idol]

oh we do 4 books per year

[undone pumice]

bro you wanna know what my teacher said

he said

"guys the movie has a different ending they actually go to a village and live a peaceful life"

[shut galleon]

so this year my school did the martian chronicles and the importance of being ernest

[broken idol]

😭

[undone pumice]

and then 5 seconds later lenny died and my teacher went

"just kidding guys!"

[valid topaz]

hmm

[shut galleon]

and were gonna read romeo and julliut and an inspecter calls

[undone pumice]

ooh i see

[shut galleon]

im actually really bad at spelling haha

[undone pumice]

so far weve done, of mice and men, uhhh this book called born a crime, uhhh a poetry unit

[valid topaz]

someone should've told shakespeare to stop using that fancy english

[broken idol]

oh

[undone pumice]

we have this book called no fear romeo and juliet..

so on the right half of the page instead of "the pink flower" it'll be like "romeo wants to pretend like he got some last night to act cool in front of his friends, this is a sexual entrende" or smn

oh and we also did a short story unit

and a unit on this random ahh graphic novel about war

[shut galleon]

my mom wants me to skip a grade because im already taking all 9th grade class

actually i think she wants me to skip two

[undone pumice]

oh thats cool

[undone pumice]

oh.. wow

[shut galleon]

but like

im scared

[undone pumice]

hmm... do you have a counselor you could ask about it

[shut galleon]

yeah

he said it would be easy to do becaues my schedual already looks like one of a 9th grader except for like

electives

[valid topaz]

i want to skip

but my parents don't let me

[undone pumice]

real, mines wouldn't let me do dual math this year

[shut galleon]

watch me become a high school drop out or something

[undone pumice]

lmao nooo you can do ittt

[shut galleon]

i actually know this kid he used to go to my school his name is cj

[valid topaz]

and my counseler frankly doesn't help that much

[undone pumice]

yah my counselor lwk a bi-

[shut galleon]

he was in linear algebra in 10th grade and he got a 1570 on his mock sat

[undone pumice]

wouldn't put me into ap precalc or ah possibly mention that was an option

[shut galleon]

that he took at the start of 10th grade

and he dropped out like a few months ago

[undone pumice]

oh wow

[shut galleon]

he was actually really nice i was friends with him

[undone pumice]

my counselor also wouldn't explain anything about a-g and stuff like that either

(and ghosted me when i emailed asking about how its calculated, cus i wanted to know about the math part of it, rah)

[undone pumice]

oh thats cool... i mean i guess high school isn't for everyone, depending on aspirations and goals and stuff

[valid topaz]

my counseler js replies cryptically

[undone pumice]

lmao

cryptically? im curious haha

[valid topaz]

and doesn't even answer my questions at all

[undone pumice]

mine had this autoreply thing set

like "Most classes are full! Please don't bother me through email!"

"I'll answer your question within a school week! If you come in person!"

[valid topaz]

she just uses the same "template" to write every email, and sends me links to random sites that don't even help

[undone pumice]

oop

yeah a lot of our resources are highk very uh

outdated

eventually my math teacher helped me schedule an appointment tho i got lost like 3 times on the way to her office...

a teacher found me wandering trying to figure out the classroom numbers...

[shut galleon]

guys its so hard....

i think math is not my element

[undone pumice]

nuuu its okayy

you can do ittt

[round geyser]

Wow

This one x can be anything

Btw 0 works

[raw hill]

,w (x sqrt x, x+sqrt x), x=2

[obsidian monolith]

Results provided by WolframAlpha

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Requested by civil_service_pigeon

[round geyser]

And hint: use fractional exponents

[fringe phoenix]

X cant be anything dawg

[surreal spire]

xsqrt(x) = x + sqrt(x)
y = sqrt(x): y³ - y² - y = 0
=> y(y² - y - 1) = 0
=> y = 0 or y = φ or y = 1 - φ [ rejected ]
=> y = 0 or y = φ
=> x = 0 or x = φ + 1

φ = Golden Ratio

[undone pumice]

How would you guys find the max and min from [0,12] this was on the calc section of my wuiz the other day but I couldn’t figure it out

[undone pumice]

(Fah I got a 14/18 on my quiz… oops)

[drowsy herald]

Write your answer

[worldly scarab]

is it like 1348.5? o

(cos(45)*1200)+500

[round geyser]

Remember 45-45-90

[round geyser]

It’s just 1200+500=1,700 m

[round geyser]

It’s x: x : xsqrt(2)

[dusky jacinth]

high schooler here the stuff you guys do is isnane

[dusky jacinth]

pure madness what am i looking at

[valid topaz]

what is this demonic possession

and the min and max can be found on any differentiable function by js taking the derivative and testing critical points

[low slate]

you cannot ask people to just "give you the answers" as this is not the purpose of this server.

[low slate]

this is incorrect.