precalculus

[undone pumice]

and they told me they couldn't apply the formula because the function name wasn't f(x)

and i side eyed them before just going back to speedrunning my worksheet so i could read ao3

[fair garden]

ye ye, that's what I didn't get

[orchid urchin]

the formal definition?

[fair garden]

i red into that definition 25 times in a row

[orchid urchin]

well your not supposed to get it at first, I would read a few proofs and stuff before reading that one

[undone pumice]

ye it took me a bit to realize

[orchid urchin]

I read how to prove it by daniel j velleman (name drop) so I had no troubles

[astral apex]

it's a big step up in complexity from anything in high school math up to that point

[undone pumice]

ofcs the informal def is easier to understand with less symbols and weird letters

[orchid urchin]

the concept is easy but the way its written the formalized version and the proof necessity is what makes it hard

so not even really the actual math

[undone pumice]

i js learned it in a randmo calc textbook..

[fair garden]

particularly the part when it says |f(x) -L|< E

[undone pumice]

never learned the proof tho

[orchid urchin]

read how to prove it by daniel j velleman

[undone pumice]

oh

[orchid urchin]

or the book of proofs

[undone pumice]

is the proof of the formal def of a limit mportant?

[fair garden]

k

[orchid urchin]

its a book about how to prove anything in math

[astral apex]

proof of what?

[orchid urchin]

its free online

a pdf

super useful

[undone pumice]

oh

[orchid urchin]

especially for proving things in la and calc

[undone pumice]

i will look into it

[orchid urchin]

and the smooth transition from calc to real analysis

or functional analysis

[undone pumice]

icl i have trauma with proofs after taking a course with some geo in it

butttt igs its probably important

[orchid urchin]

those aren't real proofs

[undone pumice]

ik...

[orchid urchin]

learning to prove things and actually doing it is way different

[astral apex]

I mean, they are. They're just taught to be organized in an artificially clunky way

[orchid urchin]

and honestly it is harder but the payoff is extremely high

[undone pumice]

interesting..

[fair garden]

So it is a book of proofs of Daniel Velleman?

[orchid urchin]

and highly necessary for higher maths, because as you go up in math the more you gotta prove and the more difficult it will get if you don't know how to prove things.

[orchid urchin]

https://users.metu.edu.tr/serge/courses/111-2011/textbook-math111.pdf

[undone pumice]

oh... i see

[orchid urchin]

you can also search "book of proofs" which is a different book if you don't like the one I gave.

[orchid urchin]

it also helps you get used to the language of more abstract things in math

[fair garden]

thx

[orchid urchin]

the first 2-3 chapters in this book are really hard but after that it gets a lot easier, the reason for that is because chapters 2-3 is basically like learning a brand new language

but then you will lowk be able to flex on ppl

[undone pumice]

lmao

i will see how much i can understand

[orchid urchin]

use ai if you can't find an answer or the internet

[astral apex]

do you know that the expression |a - b| < c can be interpreted as "the distance between a and b is less than c"?

[orchid urchin]

because it will explain step by step

[fair garden]

yep

[undone pumice]

i remember my textbook that i learned about the proof in had pictures like this which helped me to understand it

[orchid urchin]

yeah this describes the relationship -E < f(x) - L < E

[astral apex]

or in other words, the number a is less than c distance away from the number b?

[undone pumice]

ye

[orchid urchin]

which is just |f(x) - L| < E

[orchid urchin]

there are good videos icl that helped a lot

[undone pumice]

ic... ive mostly just been learning calc thru khan academy and textbooks tbh

[orchid urchin]

self study?

[undone pumice]

ye

precal at school

[orchid urchin]

Makes sense, try pauls online math notes

goated resource

and professor leonard's youtube playlist (highly recommended to skim a lot)

that and textbook and a khan academy to guide you as a checklist sort of is elite

[undone pumice]

ah ic

ive not been taking it tooooo seriously tbh, been on integration for a while

cus ik im only gonna be in ab next year anyway

[orchid urchin]

oml calculus made easy is a goated book too for calculus it shows the infinitesimal change method which is a highly intuitive way to look at derivatives

and partial differentiation

literally explains where the rules come from

[undone pumice]

whats a partial derivative btw? i heard abt it but not learned what they are yet

[orchid urchin]

imagine you have three variablex y = x^2 + z^2, a partial derivative is taking the derivative of y with respect to either x or z, if you take the derivative of x then you treat z as the constant and vice versa, the total differention is when you combine the partial differentials

[undone pumice]

ohh

so the partial derivative could be 2x or 2z?

[orchid urchin]

here

its ez

[undone pumice]

ah icic alr got it thx

[orchid urchin]

now with respect to x it looks like this and the dz/dx comes from the chain rule

if you learn about implicit differentiation it will make more sense why that happens

if it was with respect to z then you would have dy/dz = 2x dx/dz + 2z

[undone pumice]

ik implicit

got it that makes sense

[orchid urchin]

since z is implict to x it can be written as z(x) although that is rarely written in practice

same with y

if its respect to x

hence you use chain rule

[orchid urchin]

legit I got so many resources for calc that work so well

for comprehensiveness khan academy is best ofc, but if you want to progress fast you can treat khan academy like your check list and learn through pauls online math notes and professor leonard playlist, and then fill in any gaps according to the checklist

and literally any textbook

calc made easy is my fav tho

[undone pumice]

mm yea im working thru khan integrations stuffs atm

not tried pauls online math notes yet

working thru... i belive the textbook is called stewarts?

or... made by someone called that? i dont remember

[orchid urchin]

pauls online math notes covers calc 1-3 with good practice problems although it is not as comprehensive as khan or professor leonards playlist but it gives real practical applications

[undone pumice]

oh interesting

[orchid urchin]

yeah that ones okay

[undone pumice]

idk one of my discord friends recommended it to me so

[orchid urchin]

if you tried to learn with only pauls online math notes I will say you would not get far in terms of true understanding, however thats why you use more than one resource to be fair, pauls online math notes helps for speedy progression, I got through calc 1 in its entirety in like 2 weeks.

but I also study long sessions and like math quite a bit

[undone pumice]

ah icic

[weary flower]

I believe pauls online maths notes can be used for recalling certain topics more than learning from it.

[woeful blaze]

I wanna learn calculus plz

[raw hill]

#calculus

[uneven valley]

why is this chat always full of calc stuff lol

[undone pumice]

We get so off track that people assume this is the calc chat- I have both chats lol but I think some people click pre uni and just dump in here

[limber junco]

U should go thru spivak

[scarlet cedar]

Spivak is for calculus

If you are doing integration in precalculus then no need that one

[keen delta]

total derivatives?!?!?
fake
dz=f sub x dx +f sub y dy or something for z=z(x, y)=f(x, y) or something

[limber junco]

This person is going thru calc

Just looking at message context

You don’t do 3d calc in precalc generally

[scarlet cedar]

That's what I said

Those things doesn't need books like Spivak one

I think you are the one who is not understand these

Because Spivak do not cover partial differentiation or implicit like what evelyn asked

[weary flower]

why are we doing calculus on pre-calc? 🥀

[latent narwhal]

guys what do i do after i combine the logs?

do i change it to exponential?

[weary flower]

yes

[latent narwhal]

and then do i solve for x individually from there?

also for the extraneous solutions is it like x must be bigger than 6 and 4 or smaller

[scarlet cedar]

Take power of 8 both side

[latent narwhal]

okay i get it now i had to factor it first

[velvet dust]

hellow ppl , im cannonball, im here to learn high skl math, altho i have finished my high skl, i still joine here cuz i dint focus in my high skl and got lost, so im gonna take a drop year to fix all these an get into a god univ nxt year hope yall can help :))

[orchid urchin]

id combine them first

[undone pumice]

nice! is there any specific weak points or topics you'd like to focus on?

[round geyser]

Hint use
log (ab)=log a + log b

[gentle lantern]

multiply the terms in the parentheses since both bases are the same

The roll the value to make it into exponential form

[keen delta]

substitute all of the choices to do it in 6 seconds tops

[limber junco]

Exercise; prove this law

[astral apex]

a very good exercise

[fossil kindle]

Hold on

ok

||using ln for this. ln(ab) = (ln a + ln b). raise both by e to get e^ln(ab) = e^(ln a + ln b). e^ln cancels out so ab = e^(ln a + ln b). using product rule of exponents to get ab = e^ln(a) × e^ln(b). e^ln cancels out so ab = a × b||

might have missed a step

[limber junco]

,rotate

[zenith zephyr]

Did u get it?

[astral apex]

I’m afraid this begins by assuming what you’re meant to prove, so it’s not valid

[fossil kindle]

oh wait

wait

[latent narwhal]

hi guys for a question like this, whats the fastest way to look for constants a b and c on desmos?

because ive basically been doing like substitution method on desmos but it takes literally forever and im wondering if theres another way?

[fossil kindle]

well if it gives you the output when x = 0 then you already have the c value

[latent narwhal]

and for a and b? should i just use normal substitution using my c value?

[uncut mulch]

make a table with the given values
use quadratic regression

[latent narwhal]

ohhhhh

okayy i see

[echo apex]

Hello guyts. Uhh I have some questions that I think aren't really related to calculus, but I need them for my derivatives

Cause my exam doesn't just want us to solve the derivatives, but they tell us to manipulate it into a specific form, and I find that harder to do than the derivation itself

[uncut mulch]

claim a help channel and ask directly

post the question, follow the instructions inthe summary

[echo apex]

Well tbh it's not one question, it's more like a whole subject I think

[uncut mulch]

try to be as specific as possible
otherwise people won't know how to help you

[echo apex]

Oki :3

[raw hill]

<@&268886789983436800>

[round geyser]

First think
a^m * a^n = a^(m+n)

And take log of each

Actually specifically

[round geyser]

Set them as x
a^m * a^n = x
x=a^(m+n)
Take log

m*n=log_a x
m+n = log_a x

set them back mn=m+n then add log
log (mn)= log m + log n

[round geyser]

Kate

Check my work please

[limber junco]

there is no log base a
there is only one log and that is log base e

[round geyser]

That’s just a place over

When I set it equal

[limber junco]

why would u need a place holder

log = log

thwere is no other log

one log

[round geyser]

Ok

How would u prove it then

[round geyser]

If I set y=acos(bx) and y=asin(bx)
acos(bx)=asin(bx)
cos=sin

[limber junco]

if gauss used one log why shouldnt we

proof by respecting ur elders

[bronze geyser]

https://klipy.com/gifs/really-really-bruh--k01KQSRXXXR54YTK30WT5J0NQTA

[round geyser]

I agree

Can u tell me how do Guass proofed this

[limber junco]

there is no proof

[bronze geyser]

search it yourself

[limber junco]

log base e is the only good log to work with

they didnt have calculators back then after all

[bronze geyser]

TS LIKE TELLING HER TO ASK GAUSS

Or him

[round geyser]

I only know log product rule is inverses of exponents log rule

[bronze geyser]

I forgot how to check pronouns

[round geyser]

a^m * a^n = a^(m+n) (-) log m + log n = log (mn)

[limber junco]

ok now like

[round geyser]

Idk what to derive

[round geyser]

Make them e^m?

The take on

ln*

[tacit jetty]

So this is the future of the world huh?

What a joke

[bronze geyser]

This person is incredibly stupid

They are limiting their view to one specific area and deciding everything else is the same

[tacit jetty]

Chat I'm kidding

Obviously no one would ever say that

[bronze geyser]

Hilarious

[tacit jetty]

I love jokes dude

Sorry if I went to far though

Too*

[round geyser]

lol

[round geyser]

I thought ur calling me

[tacit jetty]

What grade u guys in?

[bronze geyser]

Freshie

[tacit jetty]

Oooh we got a young one

P diidd ... I mean hey birdli
Why do you like maths

[bronze geyser]

Im assuming you are older then me

Unc

[round geyser]

Senior

[round geyser]

In HS

[bronze geyser]

Keep it sfw

[round geyser]

What’s x

[tacit jetty]

Yes

[bronze geyser]

Mods are not chill

[round geyser]

I’m second oldest

[bronze geyser]

Why do i like maths?

Who said I liked math

[tacit jetty]

Why you here then

[tacit jetty]

I'm also a senior

[bronze geyser]

To do interesting math problems

[tacit jetty]

So you like it

Admit it

[bronze geyser]

No

https://klipy.com/gifs/l-death-note-3--k01KQSRXXXR54YTK30WT5J0NQTA

[round geyser]

I do

I enjoyed it

[tacit jetty]

You want solution

?

[round geyser]

Sure

[bronze geyser]

Ts is not interesting to me as i have not learned logarithms

[round geyser]

x=?

[round geyser]

Can u use exponents properties

x^-1=(1/x)

[bronze geyser]

K ill give it a try

uhi got it

But my answer doesnt have formal proofs

@round geyser x=1/3 right?

[round geyser]

I’ll check it for u

[round geyser]

I got -1/3 =1/3

[bronze geyser]

-1/3 does not equal 1/3

[limber junco]

this is a true statement

[bronze geyser]

.

[round geyser]

True ?

[bronze geyser]

No it is not

[round geyser]

I plugged in x=1/3

[bronze geyser]

I am correct

[round geyser]

Ok

[bronze geyser]

tfym okay gng

verify it

[round geyser]

I’m wrong ur correct

[tacit jetty]

Plugging in values is one thing but how to prove it

[bronze geyser]

@tacit jetty i got to this step

and then just noticed 1/3 works

[tacit jetty]

Yeah but there's got to be a way to get 1/3 is the only solution or there are others

[round geyser]

This one I got x=1/2

[bronze geyser]

Try it out yourself super senior

[round geyser]

I get it bc

-x can be 1/(1/x)

[tacit jetty]

Got it bro

By comparison

[tacit jetty]

Stay fresh lil bro

[cerulean locust]

what even goes on in pre-calc

[bronze geyser]

https://cdn.discordapp.com/attachments/1489750875726414007/1500915309735968829/IMG_1886.gif

[cerulean locust]

wait that would be fire

math class where all yall do is just

disscuss math

[bronze geyser]

wanna propose that idea to the mods

i cant do it tho because i dont think i am supposed to be in this server

[cerulean locust]

how would the discord mods make a new math class all together?

do you mean like my school board

[limber junco]

that should be every maths class

[cerulean locust]

ok i mean more like

[bronze geyser]

?

[cerulean locust]

casually

[limber junco]

yea those exist

its called reading groups

[bronze geyser]

u shud make a server

I can help if u want

[cerulean locust]

nono

[limber junco]

im in a reading group i discuss maths with friends

[cerulean locust]

i mean like

[limber junco]

there are classes that are just discussion too

if u continue maths

[cerulean locust]

a real math class at school thats just casual discussion

[cerulean locust]

i mean

[limber junco]

yea

those exist

[cerulean locust]

i plan to prolly minor in math in collage

[limber junco]

depends on which school

[limber junco]

why not major

[cerulean locust]

i want to go to MIT, but uh

[limber junco]

it is the best subject after all

[cerulean locust]

wanna major in computer science and or software enginering

[limber junco]

ew

cs

[cerulean locust]

what am i supposed to go to MIT and not major in a technology class???

[limber junco]

uh

the physical sciences exist

[cerulean locust]

right but

technology really interests me

[limber junco]

the "technology" part in any institute of technology shouldnt be taken literally btw

[cerulean locust]

like for my classes next year, i put video game development high priority and computer science essentials and APCS as medium priority

(i put drawing and painting I for my low priority if ur curious but thats not math)

[limber junco]

also

nvm

[swift sphinx]

you have to start building a strong profile then, MIT is insanely competitive along with Harvard, Yale, Princeton, etc. That means people who have perfect grades and extracurriculars get rejected every year because they usually lack emotion in their essays or they didn't do anything meaningful outside of school.

[bronze geyser]

Yup

[viral ibex]

anyone know half time word problems

[round geyser]

Yea

[round geyser]

Let me see

[viral ibex]

igu gimmie a se

[round geyser]

Show me

[viral ibex]

The half-life of radium-226 is 1590 years. Suppose a sample originally contained 18 mg of radium-226.
Determine an exponential model of the form
to model the amount of radium-226 remaining in the sample after t years. Round k to 5 decimal places.
How long will it take for 90% of the radium-226 in the sample to decay? Round to the nearest year.

[round geyser]

Yea then I do

Do you do A=Pe^kt

[viral ibex]

no i do this 1
2

⁢𝐴0=𝐴𝑜⁢𝑒^𝑘⁢𝑡

[round geyser]

?

That’s similar

[viral ibex]

ya

[round geyser]

A0 is the finial, Ao is the initial

If it’s decay, k=1/2 or 0.5

[viral ibex]

ah okay

[round geyser]

U will need two equation

First for solving k

Second one is solving t

[viral ibex]

wait but what do i do if i get and answer like this 4.334554e

is there a simplified version of that

[round geyser]

No I don’t think so

Unless u multiply by e

[viral ibex]

ahhh

okay

[round geyser]

First one A=18e^(-0.00044t)

[viral ibex]

ouuuuuu okay

[round geyser]

Because it’s a decay so P=1 and A=1/2

So then it’s 1/2 P = Pe^(1590k)
ln(1/2 )=ln(e^(1590k))

[viral ibex]

mmmm

[round geyser]

k=(ln(1/2)/1590)

[wispy spoke]

@drowsy verge

[undone pumice]

<@&268886789983436800>

[wind salmon]

guys how can i study for the ap precal test on tues

[gloomy vector]

Btw if you want you can ask in #study-discussion too

[undone pumice]

umm do u have ap classroom

mcq isn't too bad

i would def practice frq and wording

u should be good idk i haven't studied

beyond what we did at school

lwk js wanna get the test over with and glad i get to miss some of my fourth period that day

[winter osprey]

wait since when is there AP Pre-Calc?

wth

[fast igloo]

does anyone have a precalculus topic list

[undone pumice]

idk a few years ago?

its new i heard

its not the first year for sure cus ik kids that were in it last year and we did mock frq's from like 2024s test or something

[undone pumice]

i can give u the 4 units in my class

first one is like, holes and finding zeroes and concavity and stuff

second unit is like, sequences, exponentials, logs, modeling

third unit is typical trig stuff, working with sin cos tan graphs and their reciprocals, identities, plus some polar

fourth unit is stuff like unit vectors, parametric equations, determinant of matrix, etc

[winter osprey]

yeah its def new bc when i took precalc in 2020-21 year that did not exist

but thats good that it does now

[undone pumice]

ah

ik its not really any college credit, i js want it to bump up my gpa

[winter osprey]

bingo that would make ense

yeah no mine was also just a GPA booster, since they made it a dual-enrollment class through a local community college

[undone pumice]

ah icic

i dont think we offer precal DE, only in school AP, honors, or regular

[winter osprey]

yeah no my school was pretty small (like 900 ppl total, my graduating class was like ~220)

we didnt have as many weighted courses as other schools

[undone pumice]

ah

uhh

i think theres like 900 kids in my graduating class

heres my class rank

[winter osprey]

ik my friend from Texas was tellin me the schools over there are huge

[undone pumice]

im in cali and i go to a public school so ye its big

about 1200 kids in my graduating class actually

[winter osprey]

yeah mine was in cali too

gah damn

[undone pumice]

our city only has one high school soooo ye

[winter osprey]

but rank 4 is very impressive outta that many ppl

i think i was like rank 2 or 3 outta like 224

[undone pumice]

igs

im only taking 2 aps

[winter osprey]

rank 1 guy was like a triple varsity athlete with a 4.6+

[undone pumice]

our school weights honors as like a 5

so i have 4 honors

*honors/ap

and two regular (pe and chinese, which i need to take for graduation requirements)

[winter osprey]

yeah ours too

yeah no definitely keep takin those honors/weighted classes

[fast igloo]

thank you a ton 🫠

[undone pumice]

you're welcome, good luck!

[dry verge]

So I understand that a controls the width and d controls the height, but what do b and c do?

[valid topaz]

they control the horizontal and vertical "slants" for lack of a better term

basically tilting the coordinate axes

[round geyser]

What’s this mean

[scarlet cedar]

Move to the right 2 units and shift down 2 units

[mint sequoia]

GPA is over 4?

[mint sequoia]

[undone pumice]

weighted gpa

APs and Honors = 5s for As

Unweighted is just 4.0

[mint sequoia]

Oh is it just a highschool marking scheme?

[undone pumice]

ye

[mint sequoia]

In university they must have used 4.0 then.

That guy's GPA is 4 but first of the class, interesting.

The 2nd one is 4.6, though.

[undone pumice]

each of the class rank is based on weighted or unweighted

so the max unweighted GPA is 4.0, so everyone wiht a 4.0 is 1st in class for unweighted

valedictorian and others is based on weighted. so 4.6 puts (me) at 4th in my graduating class of 29

[mint sequoia]

Ah.

Still 2nd

[undone pumice]

ack need to lock in during sophmore and junior to drag my gpa up only taking like 2 aps next year so i think thats like a 4.6 but i can take more in 11th :c

[mint sequoia]

Yay.

[dry verge]

Ah no, I forgot what to do with the point at (1, 0).

(-1, 5) doesn't feel right.

[mint sequoia]

Looks like it's being stretched on the y-axis, then a point got translated.

[dry verge]

Stretched along the y-axis? Does this mean that the point at (1, 0) should be at (0, 1)?

[mint sequoia]

Well you can see the start point is an unit square.

It's dilated by 2 units.

I haven't came back to matrix transformation for too long, but recall the y-axis dilation matrix?

[dry verge]

Oh yeah!

[mint sequoia]

I forgot the formula for a transformation vector, but seems like you need to add in vector [1,2] too.

[dry verge]

I'm confused because [1, 2] is already on the graph.

Both vectors have been graphed. I just need to find the coordinates of the last point.

[mint sequoia]

You are moving a specific point to the left 2 units and up for 1 unit?

then -2, 1..? I forgot mostly about this but there must be something for a specific point translation.

[dry verge]

Like this?

This is (-2, 1).

Let me try this.

Nope, that doesn't seem to be the point.

Ah well, I'll do a different lesson.

[round geyser]

It’s their inverses

[spring jungle]

https://www.youtube.com/watch?v=w_JYhUEPX54

this is for all of you

[dusk bone]

geez gng is calculus hard

[orchid urchin]

7/10

[winter osprey]

i would say its not that bad when you first encounter it

[undone pumice]

Not really though it may take some time to grasp the intuition behind concepts

[winter osprey]

idk how other schools do their courses but at mine, pre-calc wasn't really needed before calc, its just ramped-up algebra 2, only the last unit on difference quotients and intro to limits is only really the "pre-calc" part of the course

[orchid urchin]

being good at algebra is the most important thing

[winter osprey]

true, otherwise u spend more time on the algebra than the calculus

[undone pumice]

My school requires it though I agree it’s mostly unnecessary

[winter osprey]

they used to allow u to skip it, but it wasnt an option during my high-school time

[undone pumice]

We have these pathway laid out for us and all include precal

[winter osprey]

oh boy do i remember when you had to meet with your counselor and build your academic plan/pathway

[undone pumice]

Oh ye we had counselor visits to pick classes. These are the “standard” pathways 🥀

[winter osprey]

what is integrated math

[undone pumice]

It says u can skip ab but I heard the counselors aren’t really accepting of that and my counselor kinda annoying so

[undone pumice]

Algebra plus geometry plus statistics

Split up into three years of math with bits of each just getting more advanced

[winter osprey]

oh ok i see

[undone pumice]

So integrated 1-3 come before precalc

[winter osprey]

i took alg 1 in 8th, so when i got to high school my pathway was Accelerated Geometry --> Alg 2 --> Pre-Calc & AP Stats --> AP Calc AB

[undone pumice]

Oh stats with precal lucky

I’m taking ab next year

[winter osprey]

and by your profile youre a 9th grader?

if so thats pretty good i think the youngest we had in my class were juniors so 11th

[undone pumice]

Ye

[haughty crown]

Damn that’s tragic

My best friend decided he didn’t need precalc so he self studied, tested out, and took bc calc sophomore year

[winter osprey]

Damn wth

[round geyser]

Tips for solving this

[raw hill]

$\tan$ and $\arcsin$ are both odd, so
$$\tan \left(\sin^{-1} \left(-\frac{8}{17} \right) \right)=-\underbrace{\tan \left(\sin^{-1} \left(\frac{8}{17} \right) \right)}_{\text{standard right triangle fare}}.$$

[obsidian monolith]

Civil Service Pigeon

[round geyser]

I get -15/17

[raw hill]

should be negative

and also that denominator looks wrong

actually the numerator is also wrong now that I did it

[round geyser]

Ohhh

15/-8

[raw hill]

did you do adjacent/opposite instead of opposite/adjacent

[round geyser]

Yea

It’s -8/15

[raw hill]

good

[round geyser]

I notice that equation it’s just switching 17 to 15

[raw hill]

yeah pythagorean theorem

8-15-17 triple

[round geyser]

I see

[round geyser]

Also the trick to remember triple is
“odds is just square then and write continuously” like 3 squared them is 9 then 4+5 adds up to 9 so it’s
3-4-5

“Evens is take half and squared them then add one and minus one”
Like 8 take half is 4 and squared them is 16 then add one is 17 and minus one is 15 so
8-15-17

[raw hill]

Seems like you’re just describing a special case of a general parameterisation of Pythagorean triples?

[round geyser]

Is it good to remember

[raw hill]

You might as well remember the more general version

[round geyser]

What is it

[raw hill]

$m^2-n^2$, $2mn$, $m^2+n^2$

[obsidian monolith]

Civil Service Pigeon

[round geyser]

Ohhh

a=m^2-n^2, b=2mm, c=m^2+n^2

[raw hill]

mhm

[misty hedge]

wat would that mean

[round geyser]

U want 4 to have a triple

[hushed sphinx]

Pick arbitary positive integers for m and n, with m>n, and you get a Pythagorean triple.

[round geyser]

Also whether u double them, triple them it will still be a triple

Like 6-8-10, 9-12-15

[hushed sphinx]

(You also get a solution if you pick non-integers as m and n, of course, but then the side lengths won't necessarily be integer).

[round geyser]

Yep

[round geyser]

I like to study algebra but I wanted to take accounting

So next year I’m majoring in accounting

[hushed sphinx]

This is at least the umpteenth weird x^x equation you've posted over the last weeks. Just type it into Wolfram Alpha already!

[round geyser]

I heard u have to use lambert w function

Which I never learned

Okay

[round geyser]

It’s 2

[raw hill]

me when they ask for an inverse and I say this

[round geyser]

Really

Do u know that the f^-1(x)=(1/x) is 1/x?

[raw hill]

This is a standard example of an involution.

Namely the example
$$f(x)=\frac{b}{x-a}+a$$
for $a=0$ and $b=1$.

[obsidian monolith]

Civil Service Pigeon

[obsidian geyser]

Why is it called a secant line

[raw hill]

Did you try looking it up?

[dry verge]

I finally got how to do matrix transformations.

... at least for the unit square. So I'm getting somewhere now!

It's just an extension of mapping vectors.

[high fulcrum]

Quick question: do all precalc classes show the unit circle or do only a few do that?

[keen delta]

I would assume some don't really

cuz the unit circle is a horrible way to learn it

well not horrible in a sense

[bronze geyser]

This is merely a subjective opinion

[keen delta]

duh

the way I see it is that it's used for just values which u just use 2 triangles for, even then it's virtually inapplicable aside from that

what does the unit circle even do(aside from help with the graphs ig)

[bronze geyser]

Its useful in engineering too

[undone pumice]

i think it depends, mine does but tbh i learned it before precal so ykw if some places teach it before they might not go over it again

[winter osprey]

I actually first learned it in algebra 2 so right before precalc

But we definitely used/learned it again in precalc

[undone pumice]

ye same in the course right before precal

[winter osprey]

Fuck I don't even remember what we did in precalc

Cuz it was just ramped up alg2

[undone pumice]

pretty much

i think the only things i learned in precalc were in the first two weeks of school, where i learned diff quotient and concavity. and thats about it for stuff i didnt know 🥀

[winter osprey]

yeah see the rest is just a review/more ramped up algebra 2

i do remember doing matrix operations tho

[undone pumice]

oh ye

[winter osprey]

for like solving systems of linear eqs

[undone pumice]

thats ap precalc unit 4 but we never learned that

[undone pumice]

but igs i know these too even if my teacher never taught those

[winter osprey]

yea

[undone pumice]

just like, set it up and try to get one side to uhhh like the id..entity? or something? like 100, 010, 001 pattern

by fixing certain points as anchors by manipulating them to be 1 andd then adding or subtracting that row/column to change the other operations and match whatever u do on that side to the augmented matrix or something of that nature i lwk dgaf when i learned that

[winter osprey]

yeah yeah gauss-jordan elimination with the augmented matrix

lowkey doing that right now in preparation for my algebra qualifying exams for my masters program

[undone pumice]

nice

i haven't done them in like 10 months lol

[winter osprey]

yeah me too it had been a while, even though i was in a linear algebra class this semester, it was an upper-divison more abstract one so it was more proving than computing

but still needed to know how to compute things even back from precalc

[undone pumice]

mm i see

[eternal moss]

how much matrixs do you need to know for precalc

[winter osprey]

really just the basics of matrix operations

adding a multiple of a row to another, swapping rows

you might need to know how to find the determinant, which is typically just the 2x2 or 3x3 case

i dont think they teach the concept of rank and kernel and such in pre-calc so not really many conceptual things

[still brook]

hey guys how do i do this verification

[raw hill]

Recall that
$$\tan^2 x+1=\sec^2 x \implies \sec^2 x-1=\tan^2 x.$$

[obsidian monolith]

Civil Service Pigeon

[still brook]

i recall

[copper ledge]

(cosx/sinx) is cot x

[still brook]

OMG UR RIGHT

[copper ledge]

[still brook]

now what

[copper ledge]

you should have continued from here to make it simpler
cos x/sin x is cot x and then you are left with a 1/sinx which is cosec x

[copper ledge]

but also from here you can compute cotx/cos x

[still brook]

dude u lit said to use cot x

[copper ledge]

yeah

[copper ledge]

-# I meant cot x as in here

[still brook]

omg i got it!

ty

how do i solve this?

[undone pumice]

i would uh

square

[still brook]

no

its wrong

[undone pumice]

it is?

[ionic temple]

well
u cant split the fractions like that

[still brook]

i cant split denom. like that

yea

[undone pumice]

^^ as I said i would recommend squaring (as step 1)

hmm

lemme think actually

[copper ledge]

squaring as in? are you saying multiplying and dividing by (1-cos x)

[undone pumice]

(nvm i change my answer actually i think itd be easiier to manipulate the RHS)

[still brook]

whats rhs

[ionic temple]

to me
on LHS
it would be very nice if u get a difference on squares on the bottom

[undone pumice]

rhs = right hand side

LHS is left hand side

[still brook]

oh ok

[ionic temple]

and this
there is a way to make the RHS into one

[undone pumice]

ye with conjugate right? trying that rn

[ionic temple]

yep

now work the LHS

[ionic temple]

idk what conjugate means here ngl

[undone pumice]

uhh

after getting (1-cosx)/sinx on the RHS

i multiplied by (1+cosx)/(1+cosx)

to get (1-cos^2x)/sinx(1+cosx)

[undone pumice]

and then simplify the top to sin squared then divide the one in the denom out

[still brook]

STOP IT EVELYJ

[ionic temple]

mhm that works

i did the conjugate on the other side tho

so like (1-cosx) on the LHS for top and bottom

[undone pumice]

errr not like that

[ionic temple]

then do the same thing where u cancel

[still brook]

oh ok

[undone pumice]

u can simplify the top to sin^2x

[still brook]

STOP IT

[ionic temple]

lmao

[undone pumice]

mm i see interesting

[ionic temple]

mhm

both lead to both sides being equal so it shouldnt matter lol

[undone pumice]

ye

[still brook]

okg i got it

evelyn look

wait i lied

im stumped

[copper ledge]

start from here, what is (1-cos x)(1+cos x)?

[still brook]

1 - cos2x

[copper ledge]

did you mean to say 1-cos ^2 x

[still brook]

i cant find the up arrow button

yes

[copper ledge]

okay and whats that in terms of sin x

[still brook]

boi

cot^2 x

wait wym sinx

[copper ledge]

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

now tell

[still brook]

WAIT IM WRONG

CAESER YOU LIAR

[copper ledge]

what?

[still brook]

omg holy freak im dumb

WAIT NO

[still brook]

is this right

[copper ledge]

look man, if you arent following my steps then we can't communicate properly. Maybe someone else can help you then

[still brook]

im lost

[copper ledge]

whats this?

in terms of sin x

[still brook]

sin^2x

[copper ledge]

put that here

[copper ledge]

common out sinx from the denominator

and cancel it with one from numerator

[still brook]

omg i got it

ty

[copper ledge]

alright

[still brook]

how do i solve this?

[restive totem]

You want one answer or many ??

[still brook]

from 0 to 2pi

[restive totem]

Ok

3x + pi/4 = pi/2 + pi/4

So x = pi/6

@still brook

[still brook]

yes one sec

wait i thought ur sposed to find vals where costheta = -sqrt2/2?

[restive totem]

I was not supposed to find x ??

I guess there are 2 place where costheta become -root2/2

First is on top left and second is bottom left

So 3x + pi/4 = pi + pi/4

So second value of x = pi/3

Ye now we are good 👍

So final x = pi/3 or pi / 6

@still brook

[round geyser]

I love this

[round geyser]

When I see this what should I do

[compact bay]

ask for help in #precalculus

[gentle lantern]

Can you combine like terms on the left side?

[compact bay]

which u are doing lol

[gentle lantern]

son

[round geyser]

I’m solving for x

Btw

The domain is already restricted

Bc of pi/4

[round geyser]

Is there a formula for that

[compact bay]

maybe theres an identity

[gentle lantern]

I may be wrong. That was a genuine question lol

What subject of math is this?

Trig identities?

[round geyser]

I’ll say trig

Also that’s under my pre-calc class in HS

[gentle lantern]

i didnt learn that yet

[compact bay]

ya i just found a property online 1 min

[round geyser]

Do u know the SOHCAHTOA

[gentle lantern]

Yes

[round geyser]

Good

[gentle lantern]

However i fail to see how that can help in that equation

[round geyser]

I agree

[compact bay]

i guess u have to use this

[round geyser]

So it’s

[gentle lantern]

Holy shit there is an identity for it

[round geyser]

2x+3x/1-(2x)(3x)?

[gentle lantern]

I would most def say that this is trig identities but this is more complex than what we are currently doing in my precalc class

[round geyser]

Is this how u plug

[compact bay]

the right hand side is pi/4 so its arctan(1)

[round geyser]

I haven’t learned how to solve it

[compact bay]

so u have that thing=1

[round geyser]

But ik the unit circle

[compact bay]

i think u can solve as a quadratic

[round geyser]

tan(pi/4)=1

[compact bay]

ya so arctan(1)= pi/4

[round geyser]

Draw a right triangle

[gentle lantern]

Find out if its a special right triangle

[round geyser]

I assuming I get 2x+3x/1-(2x)(3x)=1

[gentle lantern]

:p

[compact bay]

ya i think thats it

[round geyser]

5x=1-6x^2

[compact bay]

yep

[round geyser]

Add these to both side

6x^2+5x-1=0

[compact bay]

u know how to solve a quadratic?

[round geyser]

Yes

I’ll do ac method

[compact bay]

ok then thats it

[round geyser]

x^2+5x-6=0
(x+6)(x-1)=0
Divide by 6 to get
(x+1)(6x-1)=0
x=-1 or 1/6

Since tan has no negative value, x=-1 is discarded so x=1/6

[compact bay]

yes but theres a domain involbed

[compact bay]

ya

[round geyser]

I’m learning how to graph sine and cosine

Btw

[compact bay]

oh that part was so hard for me

[round geyser]

Here’s my notes

I don’t take good notes so ask me if you don’t know which part

And I’ll explain it

[compact bay]

ok

ya i kind of remember now

thanks

[round geyser]

Yw

Also that’s my fav class

[compact bay]

ok

[round geyser]

Good to remember?

[compact bay]

ya thats nice lol

[round geyser]

What would sin/cos/tan^-1 would look like

[compact bay]

uhh

thats tanx/arctan x right?

sin x/ cos x=tan x

[still brook]

ok ty

[round geyser]

What are some where’s to solve this

ways*

[mint sequoia]

Well, let x^3 = A.

[round geyser]

I’ll call it y

[mint sequoia]

It will return you $8A^2 -9A +1=0$

Oh sure, same context by the way.

[round geyser]

I’ll do ac method

Will u do another method

[obsidian monolith]

Mercury (ヤフォダ)

[mint sequoia]

What method?

[round geyser]

Slide and divide

y=x^6
8y^2-9y+1=0
y^2-9y+8=0
(y-8)(y-1)=0
divide by 8
(y-1)(8y-1)=0
y=1 and 1/8
x^3=1 and x^3=1/8

[round geyser]

Mercury check

[mint sequoia]

Yup.

Now just solve for x.

Wait hang on.

x^3 = 1 or x^3 = 1/8, not x^6.

[round geyser]

Okay

[round geyser]

Difference of cubes
x^3-1=0
(x-1)(x^2+x+1)=0
x=1

[scarlet cedar]

You can just take cube root for 1 though

[round geyser]

I want to see 3 roots

[scarlet cedar]

But a number cube up = 1 is just 1

[round geyser]

Yes

[round geyser]

Also 8x^3-1=0
(2x-1)(2x^2+2x+1)=0

[mint sequoia]

I agree with Minh, it is just tedious.

[round geyser]

X=1/2

[mint sequoia]

Wait what, aren't 1/8 = x^3? Then you take cube root of 1/8?

[scarlet cedar]

Why is 8x^3-1

[round geyser]

Bc I crossed multiply

[deep brook]

you can solve that but its not really useful

[bleak kestrel]

equal to sin^2(x)

[deep brook]

what about cube-rooting?

[round geyser]

It’s still the same

But u get x=1/2

[hallow tendon]

Guys when there’s limit notations, am I supposed to write the notation for the left of the graph first, and then the right side below it?

[raw hill]

I suppose there's no strict rule that requires you to write the left-hand limit first

but it's common convention to do so since we (usually) read graphs from left to right

[hallow tendon]

Right thought so because I was watching a YouTube and he first did it from left to right then switched up so I just wanted clarification hehe

[raw hill]

[round geyser]

Correct this persons mistake

[round geyser]

^

[fossil kindle]

they forgot to divide by 8 since they multiplied by 8 when moving a value to c value

so x = {1, 1/2}

[round geyser]

Yep

On number 8 is

+-1,2,i,2i

8 solutions

[maiden birch]

how hard is ap precalc

[stone badge]

is there a guide for the desmos tips and tricks?

[mint sequoia]

Why is x=2? I thought x= 1/2?

[round geyser]

Stated

[round geyser]

Regression I can help

Make a table mark them x1, y1

then y1~mx1+b or y1~ax1^2+bx1+c

[undone pumice]

you dont have to do that custom regression thing for just linear or quadratic, theres alr setting for that

that'd only be, say, on my last practice ap exam

when i did a regression for

ln(t-1)

[stone badge]

thank u so much

[round geyser]

And today when I had to make equations for sin/cos x

[undone pumice]

by hand?

[round geyser]

I get to use y1=~ sin/cos (bx1) +c

[undone pumice]

oh

uh

[round geyser]

Delta math

[undone pumice]

before

i just like

foundd the midline

and like the amplitide

and perio

[round geyser]

Yes

They had that on there

For period

Find the point that has “2pi/ b”

That’s ur period

If it’s amplitude

[undone pumice]

its

2pi/b

[round geyser]

Count midline to the graph

If it’s two units then amplitude is 2

[undone pumice]

ye

keep in mind reflections

idk if u guys learned reflections or shifts yet

[round geyser]

Negative a

[undone pumice]

ye

[round geyser]

Here’s my notes

Find reflections

[undone pumice]

ah

[round geyser]

We did

Horizontal shifts and vertical shifts

[undone pumice]

ah

nice

[restive nest]

can anyone explain this pls

[raw hill]

Reposted here: #help-7｜zen1thxyz message

[round geyser]

sinsin-1(x)=x

[raw hill]

wrong order

[north bane]

Hello

[round geyser]

They’re inverses

[undone pumice]

lwk the ap exam was rlly boring i sat there for so long in the middle after the non calc mcq trying not to fall asleep for like 50 mins

[exotic barn]

It doesn't hold for all x, because arcsin(x) is restricted to [0,pi] so sin(y) will plot values between -1 and 1

[round geyser]

I wonder what happened if it’s like x=-2 or 2

[undone pumice]

ye with restricted domain

[exotic barn]

well arsin(x) isn't defined there

[round geyser]

It won’t work?

[undone pumice]

it won't work

cus its outside the specific domain that arcsin can be in

[round geyser]

It does?

[undone pumice]

welllll acctually x=2 is less then pi and more than 0. but x=-2 wont work. i thinkkk

[round geyser]

Ok

[round geyser]

What should I sub in

[nimble wolf]

you can js substitute values for this one

[round geyser]

x=? or y=?

[nimble wolf]

I can think one easily.

[round geyser]

x=log_3(23+2^y)

I get x=3 and y=2

[nimble wolf]

yep

[round geyser]

I just plug in x=1, y=2 (1,2), x=2, y=3,(2,3), then I thought of what if I flip my solutions so then it’s x=3, y=2 or (3,2)

[plucky ginkgo]

@sage crescent

[haughty crown]

Yeah precalc blows ass

[violet furnace]

Hi

l have a question

[haughty crown]

So

I don’t think that’s precalc

I could be wrong tho

[violet furnace]

I have the solution. Do you want it?

[winter osprey]

its putnam so goes in #competition-math

[undone pumice]

I lwk took a nap but then I woke up when we started the frq

[keen delta]

0 because 1/n^3 approaches 0 as it approaches infinity

frfr

[low mountain]

Any recommendations for a place where I could learn pre calc and calc ( I also don't really know the distinction so could anyone help me with that ? )
I would love it if the source could go ahead and use natural language logic to explain the intuition behind pre calc and calc while being easy to follow and have practice sets

[uncut mulch]

khan academy

pre-calc is pretty much the pre-requisite knowledge required for calculus

geo,trig, exponents,logs, algebra, functions

[hushed sphinx]

<@&268886789983436800> casino scam (already gone)

[violet furnace]

Wrong

[green crown]

Hi! I need help with the task below. If the plane intersects the axes (x, y and z) 2 units from the origin, does that mean that the plane intersects at (2,0,0), (0,2,0) and (0,0,2)?

The task:
A plane intersects each of the axes 2 units from the origin, on the positive side. Find the equation of the plane and a parametric equation of it.

Thanks in advance!

So the plane passes through these points:
A: (2, 0, 0)
B: (0, 2, 0)
C: (0, 0, 2)

And so to find a parametric equation of the plane, i need a point that the plane passes through (for instance point C?) and two non-parallel vectors that are parallel to the plane?

Since both A and B lie in the plane, can i say that vector AB is parallel to the plane? Would that also mean that AB is the direction vector of the plane?

Vector AB = (-2, 2, 0)

And so the second vector would be (2, 2, 0)?

I am not suree

[hushed sphinx]

(-2,2,0) is one possible vector in the plane, yes.

[neat sundial]

Can anybody explain calculus to me

I wanna learn integration..?

[green crown]

Okai, but so the second can be (2, 2, 0)?

[neat sundial]

Like techniques to solve integrals...

[hushed sphinx]

The vector (2,2,0) does not lie in the plane.

On the other hand, AC is also there, so you could use that.

[green crown]

Oh

[green crown]

But how do you know that?

[hushed sphinx]

Finding two non-parallel vectors within the plane is one valid way to make a parametric equation for it.
Another would be to write down the equation for the plane (first part of the exercise), and then solve that for z as a function of x and y (or another way around) so you have a parametric equation of the form (x, y, ...x...y...) where the third expression is the solution you found for z.

[hushed sphinx]

I cheat a bit and have already figured out that the only vectors that are parallel to the plane are ones where the three components sum to 0.

[green crown]

Ohh okai, i will try to write down the equation first

But then i would need the normal vector, right?

Of the plane

And i can for instance use point A

(2, 0, 0)

Waait, but then (2, 2, 0) would be the normal vector, no?

[hushed sphinx]

In principle you would need a normal vector first, but with numbers as simple as these ones, it might be intended that you can simply wing it and get away with that.
(It's not that difficult to guess a linear combination of the three coordinates that will give the same result for all of your three points).

[hushed sphinx]

No, (2,2,0) is not normal to the plane either.

[green crown]

Oh okei

Hmm maybe i can find the normal vector by finding the cross product between vector AB and AC?

I think i can do that

[hushed sphinx]

That ought to work.

[green crown]

Okii

I will try thaat

[hushed sphinx]

(But there's also one very simple thing that you can immediately say the coordinate sets (2,0,0) and (0,2,0) and (0,0,2) have in common).

((Though if you do the cross-product way, it should immediately hit you when you see the result of that...))

[green crown]

Soo, the equation of the plane is 4x+4y+4z=8

x+y+z=2 would work too

[hushed sphinx]

Exactly!

[green crown]

Yayy, thank youuu

And noww i can find the parametric equation

So i will use point A

(2, 0, 0)

AB = (-2, 2, 0)

AC = (-2, 0, 2)

Since they are not parallel, i can use these two vectors as the "parallel vectors to the plane"?

In order to find the parametric equation

[green crown]

$\alpha: \begin{cases} x=2-2t-2s\y=2t\z=2s\end{cases}$

[obsidian monolith]

dream

[hushed sphinx]

Yes, that looks like a good parametric representation for the plane.

[keen delta]

where's the answer dawg

[keen delta]

find the cross product of the vectors AB and BC

that works me thinks

I might be stupid tho

[bitter forum]

can someone dm me and explain what the heck is calculus just define it even if i dont understand i am curious kid0

[tame shard]

Err

[bitter forum]

lol

[tame shard]

Just read the wikipedia article on calculus

[bitter forum]

man its ezz just i need to learn 9th to 12th grade maths first lol but i'm genius hahha i will learn itt

https://tenor.com/view/i'm-very-curious-marques-brownlee-i'm-really-intrigued-mkbhd-gif-4281814105517995158

me in 8th

[chilly arrow]

why did u post that integral then 💀

[bitter forum]

i generated with gemini LOL

[chilly arrow]

its not really doable

i replied to it

[bitter forum]

what ai says - If they say it's impossible because there’s no simple antiderivative, tell them the answer is exactly (\frac{\pi ^{2}}{12}).

[obsidian monolith]

VJ THE PIRO

[tame shard]

!noai

[tender quest]

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

[bitter forum]

Oh sorry

What's !noai ??

[tame shard]

Its a factoid. You type it and the bot just spits out the content

[neat sundial]

Hi there guys 👋🏻

Can someone explain me integration techniques...?

[ancient inlet]

power rule?

[round geyser]

I wonder what would sec and csc x looks like

[ancient inlet]

IBP
U - sub

[round geyser]

It secant and cosecant

[ancient inlet]

yeah

[round geyser]

I’m wondering

Is it like they have asymptote of -1 and 1

[ancient inlet]

when you integrate, you increase the power by 1 and divide by the new power

[round geyser]

Not on integration

[ancient inlet]

and don't forget to ALWAYS + C as C is a arbitrary constant

[round geyser]

I’m graphing it

[ancient inlet]

im answering to that guy called aaron

[round geyser]

Do they have period and amplitude

[daring osprey]

you can go on any graphing calculator online and graph them

[round geyser]

Like y= asec (bx+c)+d or y= acsc (bx+c)+d

[round geyser]

I’m graphing it manually