precalculus

[wraith sequoia]

🙂

[viscid thistle]

u might if ur dad is rich

[slow coral]

it's good to aspire

[viscid thistle]

or u are super talented

[wraith sequoia]

Idk about that, people who are 13 or less don't know differentiation ideally

[slow coral]

chain rule i'd imagine

[wraith sequoia]

idts

[slow coral]

idk i didnt read the full question

dy/dx = du/dx * dy/du

[viscid thistle]

hat I am get a double digit rank in jee advanced to even get accepted in mit

plus u need to bring in olympic medals

[grave swallow]

i think it is

[wraith sequoia]

You got a double digit rank in jee advanced?

[slow coral]

you use chain rule when you're differentiating composite functions

[wraith sequoia]

I have more than double my age

medals

[slow coral]

if you're trying to differentiate gf(x) then you'd set u to f(x) and y to g(u)

[wraith sequoia]

oh

I hope I become a single digit ranker

how much does one need for iit bombay computer science?

double digit

Because I'm a tech nerd, math nerd, science nerd, so, I love Computer Science

yeah

[grave swallow]

do u listen deftones?

ur bio

[wraith sequoia]

student loan maybe

idk much about that

My dream is to get in NASA

[wraith sequoia]

I don't even believe I'm getting in MIT

if I ever even going to

Nope, accredited institutions only

[slow coral]

ya

[wraith sequoia]

you need US citizenship well

[slow coral]

probably one of my favourite bands ngl

[wraith sequoia]

you know why

[grave swallow]

listened few of them before

[forest fern]

can someone give me a precalc prob, im going to ap precalc next yr and i wanna see what its like

[marble leaf]

Why not just search up problems?

[forest fern]

i did but i dont know which is beginning and which is harder

ok ty

is that rsm

lmao

13c3

so 13211

13x2x11

286

is it 286

@viscid thistle

hmm

is it a permutation..?

its um

286*6

so

1716

i think idk

lol ty

ty

ruh roh

is that ap?

damn it

im about to be a freshman

ty lol

alr gimme all the rsm

teamwork makes the dreamwork fr

idk

send me some

yes

like 5-10 problems

ill help u

mhm

ill try to do them

in dms

fr

[viscid thistle]

anyone know types of cardinals?

[forest fern]

as in the birds??

[viscid thistle]

inaccesible cardinal

mahlo cardinal

a true infinity

[forest fern]

what is that 😭

okay

[viscid thistle]

a true infinity that cannot be reached

[forest fern]

alright

[viscid thistle]

its useful for power scaling

[forest fern]

yes dawg ill do like 5 problems 😭

[viscid thistle]

also do you guys know what set theory is?

[forest fern]

kinda

[viscid thistle]

Cool i joined this server to understand such things as that, i want to scale goku's cosmology using mathematics

yk who goku is right

yes

yessir

The living world in db countains all sets of mathematics, including set theory and cardinals

[slow coral]

sdbh zamasu 🤮

[viscid thistle]

he goated

in dbs

he got nerfed in dbh tho

[terse thicket]

Is tangent the length of the hypotenuse on a triangle in a unit circle

[flint bloom]

it’s the ratio of the height of the triangle to the length of the triangle

[granite goblet]

frfr

[old isle]

think of its derivative

whats the derivative of e^x?

and for e^(x/2), we generally apply u-sub to x/2 and it follows from there

[grave swallow]

i think he means substitution rule

like

chain rule

but

vice versa

[spice yoke]

can somebody help me solve this partial derivative?

[shy vine]

this is just a regular derivative

to see this $z' = 2\sin(x+2) = 2\sin(z+2)$ or $\pdv{z'}{z} = \pdv{z'}{x}$

[obsidian monolith]

ForJoke

[grave swallow]

derivative of a function is e^x. if we define the unknown function as c^x we can conclude that (c^x) * ln(c) = e^x. (ln(e) = 1) hence the unknown function is e^x it self.

[spice yoke]

right, wait a sec

[spice yoke]

ok what about now

can somebody help me solve this partial derivative?

[shy vine]

technically this is 0

because 2sin(6) is a constant

and the derivative with respect to a number doesn't really make sense

unless you are saying that 2 is a symbol and not a number

[spice yoke]

ah, who cares about technicallity, how would I solve this algebreically, also 2* 4 is 8

[shy vine]

Are you trying to find the derivative at 4?

[spice yoke]

no that would be zero you brought up a good point tho

[shy vine]

derivative at 4 is not 0

[slow coral]

that would be reverse chain rule

integration by substitution is like doing the chain rule but worse in every way

because you have to restate the integral in terms of u

and its sometimes extremely vague how you should do that

[spice yoke]

thats not what I meant but its whatever

[shy vine]

sorry Im confused of what your question is

[spice yoke]

no its allright I have also formulated it wrong and mixed things up, but I finally understood my problem and managed to get a better grip on it

[forest fern]

yo who got some beginner precalc

they dont understad

we can work together

[olive tapir]

hey, how can I get help for precalculus?

[willow bear]

by posting the question(s) you need help with

[spice yoke]

Yo is this correct what I have done here?

[glad jetty]

looks good

[spice yoke]

nice

[spice yoke]

idk, but I would have loved to study in sweden they appereantly have great education system

[marble leaf]

The math SAT is not too difficult. It is a standardized test that is designed to be balanced regarding the general population, so don't mistake it for the hardest math problems. That said, I do feel like the average US math curriculum for grades 1 to 12 is mediocre compared to math systems in certain other countries, although colleges are a different story.

There are many top colleges in the US, so completing a graduate course in the US is a decent option.

It depends what college tho

[forest fern]

math SAT is hella easy

trust

[marble leaf]

Yes, but I didn't want to say that because it doesn't hold for everyone. That's why I said "not too difficult".

[forest fern]

fair

its j alg 1

[marble leaf]

Algebra 1 is sort of the introduction into higher-level math, so it isn't supposed to be very hard. I would say the difficulty begins with integration, but it's different for everyone.

[forest fern]

difficulty is trig imo

[marble leaf]

I haven't taken integration yet but I've heard that a lot of people struggle with it.

[marble leaf]

I didn't struggle with trig but math is a strong subject for me.

So I can see how it could be difficult to wrap your head around.

[forest fern]

should i take multivariable?

[marble leaf]

Idk, what grade are you in and what's the highest level of math you've taken so far?

[forest fern]

im boutta be a freshman going into ap precalc

wbu

[marble leaf]

Then you could take mv calc in 11th grade if things go well for you

Or even 10th

[forest fern]

that would be too hard for me imo

[marble leaf]

Ya you decide ig

[forest fern]

ye

which grade u in

dang u typing an essay

[marble leaf]

I'm about to finish 8th grade and I've completed everything up to alg 2. I haven't taken precalc yet but I have experience with limits, derivatives, and other calc topics so I think I'll be fine.

[marble leaf]

No I just was about to say something and then changed my mind lol

[forest fern]

dang same

lowkey thought you were a junior or something

lol

[marble leaf]

Lol ya I talk like that

[forest fern]

lmao

what are u takin next year

[marble leaf]

I think precalc will be quick for me so I might be able to unofficially take mv calc in 11th or 12th

[marble leaf]

At school precalc

[forest fern]

precal next yr?

[forest fern]

ap or normal

[marble leaf]

Ap obvi

Lol

[forest fern]

W

same

[marble leaf]

I might go for a math degree in college along with a cs degree or something

[stuck python]

I did it

a few kids in my school did it too, calculus in general is actually easier than algebra in many respects

at least calculus 1, assuming conceptual parts of math are not something you struggle with

Plus the added advantage of taking calculus as an AP course in highschool is you get a whole year to digest the concepts and be able to work with them, rather than in university where you are only given half a year (or less depending on how semesters go) so in a lot of respects you will actually learn it better

that is, assuming you are being taught just as well in both cases

highly recommend you do it if you aren't struggling right now in mathematics, if anything use this discord. I certainly wish I had something like this going through school

[oblique root]

Wdym unofficially

[forest fern]

i think he means hes not sure

[forest fern]

multivariable in tenth grade??

[forest fern]

ye im taking 2 ap calcs

[marble leaf]

I meant that it's not counted by the school system when I skip levels after taking them outside of school, so in the school system I'm restricted to taking precalc next year.

Basically since the highest level of math I've taken in school is alg 2, I can't take calculus for example next year, I'm restricted to precalculus. Likewise, because I take one math course each year in school, even if I get to mv calculus early I still have to do the school prerequisites, which will take me 2 more years after precalc.

[marble leaf]

That's not what I meant.

[forest fern]

hes not sure as in youre not sure if youre allowed to take it

whos the owner of this server

[stuck python]

no no no haha calc 1

but multivariable is very similar to calc 1

the generalizations are very natural

except maybe stoke's and green's theorem

[marble leaf]

Ya calc 1 is totally doable in 10th, ik someone taking calc 1 in 8th.

[marble leaf]

What about calc 2? Is that also similar?

[forest fern]

same

[forest fern]

i take that junior

[marble leaf]

I take it junior as well, at the current rate

[verbal garnet]

It's the first half of calculus 2

[golden arrow]

Can someone explain to me why if we take annual compount intrest with imaginary intrest rates the capital raises significantly after 8 years ie. We get spiral but if we have same intrest rate but we compound the intrest continiously (instead of annually) we get to a circle and dont make any profit in the end

[marble leaf]

Ya tbh idk if it's actually difficult or not but people have told me it is

[verbal garnet]

Euler's method (for approximating solutions to differential equations) gets increasingly accurate as you decrease the unit step

[slow coral]

<@&268886789983436800>

[verbal garnet]

Mods are asleep I guess

[slow coral]

[verbal garnet]

They were

[marble leaf]

I mean they're still human, right?

[verbal garnet]

Of course.
I don't blame them for anything

[hushed sphinx]

Sheesh, 3 minutes response time. Off with our heads!

[verbal garnet]

More like 20 to me

[warped ridge]

Actually moderation is great here compared to some other servers I'm in. Let's appreciate it

[verbal garnet]

Yeah overall it's great

[warped ridge]

I mean, I'm in a server with like, what, 50k members? And moderation is zero tbh.

[hushed sphinx]

The modping shows at :43 for me, logs clock the ban and cleanup at :46.

[warped ridge]

Well uh mods have a life too.

They aren't living just to moderate the server

So pretty much understandable even if it takes more than that.

[slow coral]

they should be grown in vats to moderate

[warped ridge]

strongly disagree.

[slow coral]

you'd be able to bioengineer them to be the perfect moderator

[elder marten]

equation of circle: (x-a)^2 + (y-b)^2 = r^2
where the centre is (a,b) and the radius is r

[marble leaf]

Haha that might actually work!

[verbal garnet]

This was regarding my ping 20 min earlier in #competition-math btw

[gloomy tide]

is it always necessary to check the solution of radical equation ?

[summer ruin]

it is when you make non-equivalent transformations, yes

[gloomy tide]

@summer ruin what do u mean by non-equivalent transformation?

[summer ruin]

applying functions which are not monotone

ln(x) > ln(y) if and only if x > y, provided x and y are positive numbers, meaning given the inequality x > y it is equivalent to stating ln(x) > ln(y), so it stating ln(x) > ln(y) implies that x > y

x > -5 and x^2 > 25 are not equivalent

same thing work for equations, the equation ln(x^2) = 1 and 2 * ln(x) = 1 are not equivalent because ln(x^2) is defined for all non-zero x, while 2 * ln(x) is defined only for positive x

the equation sqrt(x) = 5 - x is not equivalent to x = (5-x)^2

[lunar copper]

hi

i finished 10th rn

and i wanted to revise precal in summer

is there a certain way in which i should approach the topics under it

for example matrices first, and then idk

[viscid thistle]

have you studies functions?

[lunar copper]

yes

[viscid thistle]

ITF?

inverse trig

[lunar copper]

sin inverse?

tan and cos --

yeah

[viscid thistle]

full?

if yes

[lunar copper]

what does full include

[viscid thistle]

then you may study matrices but it doesn't come under pre calc

[viscid thistle]

well there's a lot

till where have u studies?

basic graphs and all?

[lunar copper]

quadratic equations represented on graphs

finding roots

vertex form

and all that stuff

[viscid thistle]

i mean

in inverse trig

[lunar copper]

not sin, cos and tan graphs

though

our school didnt teach us trig function graphs

[viscid thistle]

study trigo graphs and inverse trigo functions

properly

it's imp

[lunar copper]

inverse trigo is

sin^-1

right

[viscid thistle]

yeah

[lunar copper]

isnt that easy though

[viscid thistle]

but there's more than that

[lunar copper]

oh

[viscid thistle]

there are many properties

[lunar copper]

do you know where i can learn it

in detail

[viscid thistle]

youtube or books

whatever you're comf. with

[lunar copper]

i see

i'll check youtube

[viscid thistle]

what channel would u go for?

just asking

[lunar copper]

organic chemistry maybe

[viscid thistle]

i meant

the youtube channel

[lunar copper]

yeah

thats a channel

the organic chemistry tutor

[viscid thistle]

which one are you gonna refer for itf

oh

oh yes i've read abt it somewhere

[forest fern]

yo

who got some precalc

[cursive cairn]

<@&268886789983436800>

[near flume]

Does anyone know where I can find a better explanation of the tangent and cotangents of sums section here? https://en.m.wikipedia.org/wiki/List_of_trigonometric_identities#Tangents_and_cotangents_of_sums

I'm looking for a source that gives a proof

[soft cedar]

umm...

i think you shoukd try ck12.org

i think youll find good info there under the precalc section and analytic trig

hope this helps

[hollow garnet]

i gotta find the convergence of this

how

nvm i managed to do it

[near flume]

<@&286206848099549185>

[serene dock]

black pen red pen

[near flume]

Do they have a section on angle sum identities when the sum is arbitrary and potentially infinite?

[near flume]

For the identities tan(sum_i=1^n)=(e1-e3+e5...)/(e0-e2+e4...)

?

A lot of the resources I find on this are aimed at just basic trig identities - I'm looking for something that covers the more the more complicated formulas I've referenced which use more advanced math

I can't really ask in the advanced channels since they don't have a channel for trig

[serene dock]

advanced identities?

[near flume]

In the general angle sum section

There's a formula for sin angle sum involving infinite products

The ones for tangent and cotangent use elementary symmetric polynomials, etc.

But I didn't find any source explaining it online other than wikipedia

[hollow garnet]

how do i do the volume of a curve around an axis out of the curve?

[minor lodge]

Hi!

Can someone please assist me with 2. ?

[stiff tapir]

Depends on shape dawg. That could mean anything. Look into Paul’s notes. It’ll tell u how to do it and the difference between volumes of revolution (methods of disks, etc) as well as volumes described by multiple integrals

[hollow garnet]

I'll see into it thanks

[pale marlin]

Why does lim x->infinity n choose x = k for some constant k plot an ellipse on the complex plane?

[hushed sphinx]

The phrasings "lim x -> infinity" and "for some constant x" don't look like they belong in the same thought.

[stiff tapir]

Lmao

[lunar copper]

i should be familiar with radian conversions before starting inverse trigonometry right

[pale marlin]

Sorry

Fixed

[gloomy tide]

are there any study group here

[summer ruin]

ideally switch to radians completely

[lunar copper]

ah

so just practice radian conversions then

do you have any conversion practice worksheets

[summer ruin]

there's nothing to practice though, π = 180°, rest of the angles can be obtained by division

[lunar copper]

what about 1 degree = pi/180 radians

and the other way around

[summer ruin]

if the question involves angles which are not part of the standard trig table then the question isn't supposed to be solved analytically in the first place

and calculator doesn't really care which angle you use - in radians or degrees, as long as you use it correctly

so only the angles pi/6, pi/4, pi/2, pi and so on matter

[summer crag]

Why is a invertible function and it's inverse always symmetric about the line y = x , also can we make a reflection of a function about the generalized y = mx+c line , and does it have like some general condition to exist (just like how the inverse of a function exist iff fof⁻¹ = I and f⁻¹of = I (this condtition is for reflection about the line y=x )) ?

[stiff tapir]

you cant really solve any problem if you dont know how either radians or degrees converts to coordinates

[lunar copper]

standard trig table?

ive never heard of that 😢

[lunar copper]

what the...

i really need a baseline from where i should start learning

someone told me to do inverse trig before doing differentiation and i needed radians before inverse trig

now im dying

[wanton vector]

It is symmetric on the line y=x because the property of an inverse function is that for any output y it gives back the original value x wich is basically like swapping y and x axes. About the second question im not sure

[wanton vector]

Depending on how much time you have (i.e. are you writing a test in a week or do you learn it just for fun and have years). If you dont have much time just start with differentiation and when you encounter some problems look them up and learn those. If you have alot of time or find yourself lost/missing alot of basics check if you can comfortably do the following:

1. linear and quadratic functions, solving equations, Pythagorean Theorem, Quadratic Formula, polynomials in general etc.
2. Trigonometric functions like cos(x),sin(x),tan(x) as well as exponentional functions etc.
3. you might as well do the inverse functions too like log(x), arccos(x) etc.
   You dont necessarily need radians for those but it makes everything easier.
4. Limits. Limits are commonly used to define differentiation and are thus useful if you want to understand whats going on.

[lunar copper]

i just finished 10th and im in vacations

for like 2 months

[wanton vector]

From the four point i mentioned, at what point are you currently?

[wanton vector]

@lunar copper

[lunar copper]

i would say

im done with the second one

but i have to strengthen them

and also

i havent done any polynomials

only problems with a degree of 2

[wanton vector]

degree of 2 are also polynomials, polynomial is just the general term

[lunar copper]

i see

[wanton vector]

But if you study them a bit you will soon realise that if you understand linear and quadratic functions you will also soon understand any polynomial (the only thing that really changes alot is how hard it is to find the zeros of the function)

[lunar copper]

quadatics is easy

you can just

complete the middle term

or use formula

i saw one of those fun polynomial videos where factorizing increases with difficulty based on the degree

and from 2 to 3looked like a huge jump

ive done logs but i havent really completely done exponential problems

ive only learnt substituting x values to find y values for exponential functions

[wanton vector]

For quadratics you have the quadratic formula, wich is pretty simple. For degree 3 and 4 there also exists a formula, although never taught/used in school because it is too long. Any polynomial above degree 4 doesnt have a general solution only using addition, subtraction, multiplication, division and roots

[wanton vector]

@lunar copper you should probably either do exponentials, polynomials or, if you want to, start with limits and the concept of differentiation and seing whats missing like that. Introductory Videos about limits etc. often stick to simple functions that you already know so you should be able to follow those. Also that approach is more fun in my oppinion.

[lunar copper]

sorry i fell asleep

ok i'll just revise exponential and polynomials

also should i learn factorizing a cubic equation

[wanton vector]

No. In case you need to do that just find one zero of the function through trial and error and factor it out to get a quadratic.

[rigid flax]

i hate factorising cubics

you have to try one by one

But idk how those scientist calculate cubic when the answer is disgusting

[hollow summit]

They use advance methods like newton rampson etc

[slow coral]

i wouldnt call newton-raphson advanced by any means

and even then it wont get you the exact algebraic factorised form

[gritty dirge]

insert cubic formula

[forest fern]

STOP

my ptsd

unit circle

RAAAAAAAAAH

[rigid flax]

will we learn that in high school

or os it simple

can i learn it on youtube

[slow coral]

yes easily

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

oh you might've meant cubic formula

then maybe not

not because its particularly advanced just because it's very lengthy and a bit messy

and it's generally easier to just factorise at hs level

[hollow elbow]

how to synthetic division when dividing by polynomial degree greater than 1

[oblique root]

like dividing by a quadratic for ex

[gray magnet]

can't you just do the same thing

wait i don't think that works

what if you factorise it then divide by it's factors

also why have i never heard of synthetic division

[sleek dome]

Pls help I don't understand stand integration

[hollow elbow]

yeah thats what I tried but In not sure where to go from when I end up with some extra remainer part (1/x-7 for example)

[stiff tapir]

Area under curve

[stark quest]

why is an inverse function its reflection about y=x?

[stark quest]

I think Grant Sanderson goes through it on the way to the quintic : https://www.youtube.com/watch?v=aaW30_f2on0&t=5135s&ab_channel=TimothyNguyen i also prefer his approach of merging completing the square and s&p over the quadratic formula

[stiff tapir]

Given a function y=f(x). x associates an x vaule with an corresponding y vaule which is determined by the rule of the function. An inverse function of y=f(x) “undoes” this rule. Such that f^-1(f(x)) =x. The reason it reflects across the x=y access is because you are essentially changing the dependent into the independent

[dense verge]

Any tips for linear algebra? specifically proving a basis of R³

[hushed sphinx]

You'll probably want the #linear-algebra channel. (But be a bit more specific about what you need to do when you ask there).

[gray magnet]

It’s derivatives

[gray magnet]

Synthetic long division is weird

Just use long division

[gray magnet]

It’s parts of calculus so I think you should ask somewhere else

https://youtu.be/9vKqVkMQHKk

This is a good video though

[unique sundial]

Guys Im in 8th and I just started learning calculus. Any tips or video guides to help me?

[gray magnet]

https://www.youtube.com/playlist?list=PLZHQObOWTQDMsr9K-rj53DwVRMYO3t5Yr

i like dis

dis a good

[unique sundial]

is it for beginners

[gray magnet]

the derivative a the fuction

[gray magnet]

yeee

[unique sundial]

thanks!!!

[gray magnet]

or like the gradient of the line that is tangent at that point if that makes sense

[coarse slate]

Hello?

[dreamy escarp]

hello, does anyone know any precalculus concepts that are much easier or faster if they were to be done with calculus

[hollow elbow]

even if i would never use it, I'm curious how?

[gray magnet]

i don't even know how it works

[pastel fossil]

Can anyone explain why my book says that the function f(x)=3(-1/2(x-1))^2+2 has a horizontal stretch of 2?

if K=-1/2 wouldn't it just be the value of k?

There is no explanation, it just is a 2 for some reason and I am not sure why.

[gray magnet]

well the whole point of precalculus is to get ready for calculus so i don't think there is any

[shy vine]

triangle inequality

since PF1F2 is a triangle, the sum of any two sides must be less than the 3rd side

[slow coral]

isnt this the precalc channel

what is this advanced mathematical sorcery

[shy vine]

This does look like precalc to me

this is just fancy geometry

[slow coral]

i meant the notation

tf is d(P, F1)

[shy vine]

distance between P and F1

this notation is more often used for a "metric"

although metrics are analogous to distances

the "standard" metric is the distance we are all familiar with

[barren tulip]

read LADR

in short, to prove a basis of R^3, you must prove it spans R^3, and that it is linearly independnt

Bascially: Prove some $x \in \mathbb{R}^3$ is in the span of the potential basis, and vice versa, and also that it is linearly independent, or that there is only one linear combination of the potential basi that equals the 0 vector.

[obsidian monolith]

amukh1

[barren tulip]

:D ah wrong channel shoot sorry

[shy vine]

nah friedburg better as an intro

[barren tulip]

I wouldn’t know, I only have ladr

[viscid thistle]

anyone know a good alg2 midterm practice final

I currently have an 89.2% in the class and I need to ace this last test to end with an A

[shy vine]

2c is the third side

d(F1, F2) = c + c = 2c

[lime oasis]

anyone know any videos or books that explain calculus to someone whos never done it before

[shy vine]

what part are you looking for?

[elfin girder]

quick q does sinx-cosx have a specific value or..

[dull current]

Hi how would you solve this?

[burnt hare]

is anyone interested in checking my work for my midterm prep packet? it’s 9 pages lol just as much as you would want to do

[summer ruin]

<@&268886789983436800>

[summer ruin]

<@&268886789983436800>

back to back

[burnt hare]

sure yea hollup i’ll dm u

[burnt hare]

sorry i forgot😭😭

gimme literally one second

Yea so as much as your willing to check

and i have several days till i need to hand the thing in too so whatevs

[burnt hare]

oh it’s all good homie thanks for trying

anyone else that wants to look at my work feel free to tell me the numbers i got wrong

[patent prism]

[formal fox]

third page!!

check your qudratic equation

i think it should be 9+16 under the radical

[formal fox]

fourth page top a) check the range. it’s a parabola so it won’t be what you put

[formal fox]

fifth image -> check your solution to the top right problem. specifically the orignal function’s domain and range

[formal fox]

fifth image again at the very bottom. make sure you remember the formula is:
f(x)=a(x-h)^2 +k

you seem to have made the 7 into a -7 by using the logic for inside the parenthesis. remember -> this one follows the “true” sign, not the opposite sign
also - you switched you domain and range here.

alright i’m stopping at the seventh page. hope this helped

[burnt hare]

thanks homie

[red prism]

What does this mean can anybody explain in a simpler language

[hushed sphinx]

,rccw

[summer ruin]

absolute maximum/minimum value is unique, but points at which it is achieved are not unique

[hushed sphinx]

"Essential" in the last sentence is a rather strange word choice.

And it seems confusing that is speaks about "maximum and minimum values" in the first sentence and "absolute maximum or absolute minimum values" in the second -- but I can't imagine any distinction it's trying to make between those two phrasings.

[shy vine]

I guess they mean local max/min vs global max/min

[hushed sphinx]

Yeah, but that can't be it because local max/min are definitely not unique.

[shy vine]

Yeah idk what the difference is then

[summer ruin]

<@&268886789983436800>

[hushed sphinx]

(Wonderful, autodelete is glitching again).

[stiff tapir]

Why is this the channel where moderators are always pinned

[uncut mulch]

observer bias

[grave forge]

[viscid thistle]

Guys change the first letter of "Sigma" to L what you get?

[uncut mulch]

a <@&268886789983436800> ping

[viscid thistle]

?

[smoky delta]

This isn't the channel for that snexky

[viscid thistle]

Ok sorry apologies

[warm patio]

might be a little dumb but im doing logarithims and since they are inverses of an exponential function im thinking

a^x = y
set a = 3
x = 2
y = 9

3^2 = 9
since logarithims are inverses we flip x and y but then we get 3^9 = 2??

and even if we solve for y i still end up getting

y = loga(x) or 9 = log3(2)

[brazen scaffold]

so 3^2 = 9 yeah

logarithm is the inverse of exponential

[warm patio]

since 2 is x and 9 is y we flip them when finding inverse right

[brazen scaffold]

logarithm is just like saying
base to the what equals this number inside

so log 3(9) would be saying

3 to the what equals 9

so what is the answer?

[warm patio]

2

[brazen scaffold]

there you go

so log 3(9) = 2

log base (number) = exponent

[warm patio]

wouldnt the format be x = loga(y) then?

[brazen scaffold]

does that make sense yeah?

[brazen scaffold]

what is x, a and y?

[warm patio]

x = 2

a = 3

y = 9

[brazen scaffold]

yep!

x is your power

a is your "base"

y is your number inside

[warm patio]

im on stewarts precalc textbook and its giving me

y = loga(x) which is where my confusion is stemming from

[brazen scaffold]

ah maybe you misread the things?

[warm patio]

even on professor leonard

y = loga(x)

[brazen scaffold]

aight lets thing carefully yeah

y = a^x

so a to the x = y

[warm patio]

yep

[brazen scaffold]

to find x you need to do log a on both sides

log a (a^x) = log a (y)

log a (a^x) = x

x = log a (y)

nani???

what is going on here?

[warm patio]

Yeah im like

[brazen scaffold]

maybe it is i making the mistake somewhere?

[warm patio]

It looks correct

[brazen scaffold]

yeah it does

the log rule i used as well should be corect

[warm patio]

ill just stick with x = log a (y)

really confused as to why they have it reversed though

[brazen scaffold]

wait hold on

x = log a (y)
so log a (y) means that a to the what = y
to the what is x
so a^x = y

we already said that tho

yeah no they seem slightly off

[warm patio]

Any ideas?

[brazen scaffold]

?

[warm patio]

like any ideas on how they got it or do i stick with this^

[brazen scaffold]

aight let me write it down real quick

[brazen scaffold]

they got this wrong then

[viscid thistle]

Guys can someone explain complex numbers on my dms

Pls

[fiery dirge]

i can

[stiff tapir]

It’s too complex 🫤

[viscid thistle]

Even if it's too complex I like complex situations in maps

Maths

[topaz wraith]

the inverse of a^x is loga(x) because loga(a^x) = x
(definition of inverse fuctions) if that's your question

but the original function and the inverse "swap" their domain and range, so if inverse of f is g: Df = Rg and Rf = Dg

[obsidian monolith]

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

Nevemlaci

[topaz wraith]

@warm patio

[viscid thistle]

Give me the integral general rule

[stiff tapir]

I was doing a play on words

[viscid thistle]

Lol your tricky

@Mode

<@&268886789983436800>

Finnaly he got banned

[indigo halo]

Does anyone know a good pre-calc (e)book?

[west rune]

How do I set up the equation for alk?

[misty plover]

for alk i guess u have to use 24000=8000*(1.17)^x

then x*12 to get the number of years when the city of Alk's population get triples

which also means that city of Bems population doubles in every (x*12) years

[lunar copper]

hi i just started learning about derivatives and came across this function in the "essence of calculus" series

the video said that he gave this function to the computer to look at many times between 0 and 10, and compute the distance function given "s(t)+dt", minus the value of this function t"

i didn't necessarily understand what he meant in this phase of the video

https://www.youtube.com/watch?v=9vKqVkMQHKk&list=PLZHQObOWTQDMsr9K-rj53DwVRMYO3t5Yr&index=3

this was the video at 6:30 if anyone is curious

[summer ruin]

he said compute s(t+dt) - s(t) for every point t and fixed dt

[lunar copper]

s(t+dt) - s(t) is the function for the distance time graph?

[summer ruin]

he later adds he divided the difference by dt

[lunar copper]

all the possible values you can input into a function to get a real number output

[lunar copper]

so s(t+dt) - s(t) /dt is the function for the distance time graph in the video?

[summer ruin]

sure, but it's a function of dt

[lunar copper]

wha..

dt is an infinitely small change in time right

how can it have a function

im sorry if i sound dumb i dont really like functions

[summer ruin]

because the set of all values of t is already predetermined, its' some segment [a;b]

[summer ruin]

.

if you change dt the graph that you see will change

[summer ruin]

it's finitely small, he says he chose dt to be 0.01

[stiff nebula]

Does anyone know if this working out is correct for this question?

If not, can you please write a step by step working so I can better understand?

[dark scarab]

@stiff nebula There are somethings that are not clear, for example when you take the u substitution (correct step), the t^2 dt is transformed into du so you don't need the t^2. Also recall that coefficients can be moved outside of the integral sign

[dire aspen]

Is this really precalculus

[oak path]

In Precalc, never seen that

[rose rover]

LOL this is spesh level

[oak path]

?

[rose rover]

specialist math is a math subject for the australian curriculum

[oak path]

Oh

[rose rover]

i have this formula on my formula sheet

[dire aspen]

Because it’s not precalc lol

It’s calc 2

Dk why they’re asking in precalc channel tho

[summer ruin]

all you have to do is compute product AB and solve a couple of equations

that's the point

why not just write general B

b_11, b_12, ...

maybe you should be open minded and actually try my suggestion

a matrix B with entries b_11, b_12 and so on

[hushed sphinx]

With letters.

So you get 8 unknowns and a bunch of equations that relate them.

[summer ruin]

the rest is just solving 4 equations for entries of B

[hushed sphinx]

(This belongs in #linear-algebra, by the way).

[gray magnet]

it would be the derivative of the distance time graph

[gray magnet]

YOOOOOO FELLOW AUSSIE

[rose rover]

heh

[short saddle]

Given x^2>=4/m^2, find the minimum value of x

[gray magnet]

Where is the calc channel

[dire aspen]

#calculus

[gray magnet]

Thx

[autumn wadi]

Is there any name for this "theorem"? I also don't rlly understand what it's saying

[zinc fulcrum]

this theorem has an analogue in differential equations and when sources “use it” they sometimes say they “used the method of undetermined coefficients” although i’ve never heard it named as a theorem in differential equations or difference equations

[languid schooner]

Not sure if there is a name for your theorem.

You may think about it like this; Someone long time ago have done different problems in same shape tons of time and they already know what the solution looks like. Then they will propose that that form of solution they have come up is a "general solution".

When it comes to proving what they have is THE general solution, mathematicians often like to apply some existence-and-uniqueness-theorem to justify themselves, but that’s another story.

Applying method of undetermined coefficients means, you have the table of "general solution to common particular problems" in your mind already, what you need is just the accompanied coefficients to complete your solution.

One more classical example is partial fraction. You know how the decomposition will go already. The only thing left is solving for the unknown constants A,B,C,…

[autumn wadi]

Damn

Thanks, the two of ya

[dapper estuary]

Is that correct because my calculator gives me another answer

Or am I solving it wrong

[uncut mulch]

they made a typo, they wrote cos but they used to correct ratio in their calculations

you shouldn't have followed what they've written

[dapper estuary]

what's correct ratio?

[uncut mulch]

consider the position of x and the 100m side relative to your angle

relative to the given angle,
is x the opposite, adjacent or hypotenuse

[dapper estuary]

opposite

[uncut mulch]

relative to the given angle,
is the 100m side the opposite, adjacent or hypotenuse

[dapper estuary]

adjacent

[uncut mulch]

yes,

[dapper estuary]

oh

[uncut mulch]

hence what's the trig function that relates those three things,
sin, cos or tan

[dapper estuary]

it's tan

thank u so much ily

[kindred sluice]

Can someone confirm if I did this correctly?

[desert socket]

final answer 7pi derived r = 14

[hushed sphinx]

Right, there doesn't immediately seem to be anything that indicates the scale of the diagram.

[desert socket]

yea figures. I was stuck and the prior examples provided at least 2 pieces of info.

ty

[hushed sphinx]

www.parliament.uk says:

The clock dials, framed in cast iron and glazed with 312 separate pieces of opal glass, are 7m in diameter

[desert socket]

4.2m long
The minute hands are made of copper sheet 4.2m long. They weigh 100kg, including counterweights, and travel a distance equalling 190 kilometres (120 miles) a year.

the 4.2 translates to about 13.75 feet which i guess i shouldve then rounded to 14

but thats not specified.

the rounding at least

[hushed sphinx]

Yes, but I think those 4.2 m must include the counterweight part sticking out behind the rotation axis.

[desert socket]

gotcha.

The clock's gun metal hour hands and copper minute hands are 8.75 feet (2.7 m) and 14 feet (4.3 m) long respectively.

googling feet provides exact length

shouldve just googled it first time since they used a real world example

thanks

[hushed sphinx]

The numbers are internally consistent between 7m and 190 km:

$ calc 190000/365.2425/24/4
    ~5.41877428466475469494
$ calc 7*3.1415/4
    5.497625
$ 

[dusky lark]

if i am solving for a missing quantity such as the angle sector given theta and the radius, should i convert the the theta value to radians if they gave it to me in degrees?

[granite stream]

I am having a block regarding a question in my homework, here is the equation: e^(2x) - e^x - 132 = 0. I am quite confused as I have tried a few different ways of solving but its just not coming to me, any help would be appreciated. Does anyone have any suggestions on how to go about solving this?

Oh wait this may be the wrong channel, my bad

[mellow kindle]

Take x = e^x
So your equation of
e^2x - e^x - 132 becomes
x^2 - x - 132 = 0
Solve the quadratic
x1 = 12, x2 = -11
e^x = 12
ln(12) = x = 2.485
We ignore x2 because you can't have a negative result to a logarithmic question

[granite stream]

Thank you so much for the response. I was able to figure it out on my own but thank you again!

[mellow kindle]

Oh nice good job

[dusky lark]

how do I find the exact value of the expression sin45 + cos30

[mellow kindle]

Or use your calculator if your school allows you

[dusky lark]

how do I find cot (-pi/6) using reference angles

[gray magnet]

I am assuming it it in radians

[solar olive]

cot(-pi/6) = cos(-pi/6)/sin(-pi/6) = -cos(pi/6)/sin(pi/6) = (-sqrt(3)/2)/(1/2)= -sqrt(3)

cos(-x) = cos(x) and sin(-x) = -sin(x)

because cos is an even function

and sin is an odd function

[tame flame]

Hey! This may be the wrong chat but I don't know where to ask, I just got a new calculator and when trying it out I found that it says √2 = √2. How do I fix it?

[solar olive]

what kind of calculator? maybe u could send a pic

just press other number?

[tame flame]

Fixed it

[solar olive]

yeah u prob accidentally put sqrt(2) and pressed ok

🤷

my casio calc doesnt look like that tho so idk

[tame flame]

Yeah, unfortunately we didn't get to keep the school ones over summer

[autumn wadi]

so, how do I rigorously prove that:

1. if I substitute a limit's value into the function I'm taking a limit of, if the numerator of the function is nonzero and the denominator is 0, then the limit doesn't exist
2. If I did the same, but now both numerator and denominators are 0, then the limit may be exist
   ?

[summer ruin]

it seems like you want to prove something else than what you're saying there

"if i substitute a limit value... ...then the limit doesn't exist", but first part already assumes it exists?

[autumn wadi]

Ah right.

Hm...

How do I show that the limit won't exist unless I can factorise the numerator with a common multiple (which will show that it is a "removable discontinuity") tho? am I speaking sense here?

[vapid plaza]

Are you talking about rational expressions only?

Because you cant just “factor out” a zero from an arbitrary function

[autumn wadi]

Ah, true...

yes, I am

[graceful heart]

Hello, I want to learn Calculus Can anyone help me?

[tender quest]

Please read #❓how-to-get-help

[warped cipher]

Like resources?

[mellow kindle]

Pre calc or calc

[pure pelican]

Pls explain L'Hospital's rule with example .

[lime bison]

Ok guys so my friend is doing this double angle problem and I wanna know how the third solution isn't 7pi/6 (could possibly be 11pi/6) but why would quad 3 not be included?

[graceful heart]

pre

[graceful heart]

no just generally like formulas

[viscid thistle]

are the solutions given by sin(theta) = 1/2 or sin(theta)= -1?

[warped cipher]

Check pins

In this channel

[lime bison]

Yep I figured it out, I tried to do it the precalc way which I got stuck on but I used u-substitution and got -1 as a given solution hence I got 3pi/2 for my third measurement

[untold spindle]

<@&268886789983436800>

[lime oasis]

anyone know any precal video for beginners??

[lime oasis]

?

[turbid oxide]

I am confused on part b. Here is my work and the solution from the back of the book

hm actually they say to express the real part

and jcos3t isnt real so my answer is correct

[rich elbow]

When given sin2(x-pi)

what is the horizontal shift of the function

is it pi to the right? or 2pi to the right

[old kindle]

how hard is precalc?

[willow bear]

depends on how adept you are w/ algebra, by a long shot

[royal gust]

Im so tired of mathematicians putting calculus in everything

Wait

This is pre calculus channel

What have I been doing if not calculus

[gritty dirge]

well, sorry to break it to you bud, a lot of math is calculus based. Even basic stuff like area of a circle to the value of pi came from calculus.

motion formulae are in that list

[royal gust]

I dislike calculus

[gritty dirge]

but please dont hate calculus. its a wonderfully useful tool with many real applications

[royal gust]

I always get integration and differentiation mixed up

[gritty dirge]

think of integration as just adding up a bunch of area of rectangles under the curve, with each rectangle being of infinitesimal(infinitely small) width, so you're "integrating" area together. differenciation is just the opposite

[royal gust]

Eh

I was talking about equations

Im only in year 1 of maths

[gritty dirge]

year 1 as in?

are you in grade 11?

[gritty dirge]

ok...

[royal gust]

No

As in year 1 of a level mathematics

I dont know how grades work

[gritty dirge]

a level

ok that is year 11

in total

a levels are a high school program of 2 years

[royal gust]

Year 12

Yeah

[gritty dirge]

then how are you a year 1 math student

im confused

[royal gust]

Year 1 of a level maths?

[gritty dirge]

anyways, calculus is a huge component of math in the a levels

[royal gust]

Oh

I thought it was only 2 modules

[gritty dirge]

you're gonna need to get comfortable with it

[gritty dirge]

yea but they're big modules

[royal gust]

skip

[gritty dirge]

and you also have differential equations

[lapis bramble]

just leaned logarithms!!!!! calculus here I come

[wanton matrix]

yay

[autumn wadi]

whaddabout your trig

[stiff nebula]

What do you guys learn in precalculus?

[uncut mulch]

algebra, functions, polynomials
exponents, logs

[shadow summit]

Can someone help me with this problem? I know that A^2 creates an identity matrix but I can't figure out the second part, "find another matrix (not I) with the same property."

[summer ruin]

just use a number analogy

if (a)^2 = 1, then what else could be squared to output 1?

[austere zodiac]

A and A^-1 its the same

[shadow summit]

yeah i figured that out already, but i cant seem to form a general rule to create another matrix with the same property.

[summer ruin]

the exercise doesn't ask for that

[shadow summit]

how else am i supposed to find another matrix with the same property then?

[austere zodiac]

A^-1=(Aadj)t/|A|
try this property

[summer ruin]

I suggested you one path

if you can't think of anything then trial and error is another completely valid way

and it doesn't even have to be of the same dimension, the question just asks for a matrix with property A^2 = I

[shadow summit]

i think thats just the question being worded poorly, my teacher doesnt find this textbook very good but its the one mandated by the school

[summer ruin]

no I think you're just overthinking it

[shadow summit]

what does the "Adj(A^t)" mean?

[summer ruin]

a lot of basic LA exercises are really just trial and error and that's normal, it tests how well you understand the basic relationships and how well you can construct the desired result if needed

[summer ruin]

like if you just consider this equation for some variable "a" that outputs 1 when squared, then you can fairly easily guess what other variable will square to 1

(not necessarily -1 or 1, this is an abstract equation)

[austere zodiac]

A=A^-1=This

[shadow summit]

when i was trying to find a general rule for the problem i was able to get it nearly correct but the diagonal numbers weren't 1

[austere zodiac]

This will be the property

[summer ruin]

general rule for matrices with this property is certainly not going to involve actual computation of A^2, it's deeper than that

and it's very likely to be far more than what's being asked

[shadow summit]

ok

[austere zodiac]

sorry if i dont helped you

[shadow summit]

its fine

[austere zodiac]

its hard to explain especially if I am not talking native language

[shadow summit]

whats your native language?

[austere zodiac]

Spanish

[shadow summit]

thought so, your username gave off spanish vibes

[austere zodiac]

its from a song

[short saddle]

show me again

[lucid trench]

the adjugate of transposed matrix A

[plucky oak]

im struggling with precalc tests even though i can do the practice and hw, any advice

[uncut mulch]

take a few past papers under test conditions to try identify the cause

[winter shuttle]

how do i find real solutions to (4^x+2)(2-x)-6=0? (0,0.5 and 1 are easy to guess and they are the only solutions from the graph of it)

[forest canopy]

It's easier to guess them and then prove that they are the only ones, rather than trying to solve directly

f(x) = (4^x+2)(2-x)-6 is continuous, so you know when f(x) = 0 by checking where the sign changes (intermediate value theorem)

You already know that 0, 0.5 and 1 are such number, so you only need to know that it doesn't change sign before 0, between 0 and 0.5, between 0.5 and 1 and after 1

[winter shuttle]

yeah i was trying to do exactly that, to show there are no more solutions..but trying to show, say, that it is always negative between 0 and 0.5 seems difficult

[forest canopy]

You can look at the derivative of the function to know when the function is increasing or decreasing, it would then be easy to check what it's inferior to on some intervals

[lament oyster]

need help?

anyone

i am here

[opal tree]

If you really wanna suffer, you can learn about Newton's method or Lambert W

[white widget]

Does anyone have a summary of infinite and trigonometric limits?

[dusky lark]

how do i find the coordinates i should use when graphing y=6sin(2/3x) -3

[white widget]

first you need to know which interval you want to represent

[dusky lark]

the period value?

and the amplitude/ vertical shift for the y axis?

[white widget]

having the sine function written, just quote values ​​to build a graph the way you want, as long as the maximum value of y is 1 or -1

[leaden ocean]

Can someone help me, how will I know. How much each point on the x-axis is when graphing transformations of sinusoid functions

[stiff tapir]

Likely break under pressure

[stiff tapir]

If two ticks is pi/3 then 1 tick must be pi/6

[forest nacelle]

can i please get help w log functions

we have to try and create a graph from locator points n the equation

is there a certain equation we use to do this

[storm schooner]

y=log(x)

[dense mango]

ok and

[vital cairn]

Study for 10 mins or so an hour before the test

[ripe meteor]

Hello I need help with part b. I thought the answer was 19 but I got it wrong. Could someone look at my work for part b and tell me what I did wrong?

This is pre-calc compound interest formula. Nevermind I got the answer I just needed to add 19 to year 1995.

[untold spindle]

<@&268886789983436800>

[gusty fulcrum]

hallo

I need help with precalc

[gusty fulcrum]

how would I solve this?

[willow bear]

evaluate f(2) first

[gusty fulcrum]

how?

[viscid thistle]

💀

[gusty fulcrum]

someone actually help me please

would I start from that bottom point???

[rigid flax]

are there enough info?

[gusty fulcrum]

nvm I got it

i asked someone else, thx anyway

[solar olive]

evalute f(2)

from the graph, f(2) = -2

now do g(f(2))
= g(-2)
ffrom the graph, its 1

[tardy glen]

hello guys

i am trying to solve this

and i just discovered the u substitution

but i still can t figure it out

[summer ruin]

u substitution isn't going to help you here

[tardy glen]

oh

i am thinking to set up u=cos x

then i just have u^4

no ?

[summer ruin]

no

[tardy glen]

ok i think i have it

should i integrate by part since i have 0 in exponent ?

[vapid plaza]

The standard approach for even powers of sine or cosine is to keep using trig identities to reduce the exponent

Maybe consider using
2cos^2(x) = 1 + cos 2x

[solar olive]

cos(x)^4 = 3/8 + 1/2 cos(2x) + 1/8 cos(4x)

[autumn wadi]

Ah yes

Calculus in precalculus

[solar olive]

dont be too pedantic smh 🙄

[autumn wadi]

Either u use reduction formulae or product to sum

[solar olive]

alternatively, turn it into taylor series, integrate per term and leaev it as that

/s

[shy vine]

or just do the physicist approach by and say cosx = 1

(turns out its not a bad approximation)

[tardy glen]

ok guys the job is done thanks you

[tardy glen]

this helped a lot

( i am maybe in the wrong channel sry i am new and i don t have acces to the calculus channel )

[shy vine]

I think you need the undergrad tag, idk specifically tho

[tardy glen]

this work well too

[shy vine]

(actually i dont even have )

[autumn wadi]

Nah

I got pre uni

[shy vine]

I only have 1 role lmao

[autumn wadi]

active

[shy vine]

I didn’t even choose that

It just gave it to me

[polar tulip]

does anyone know how to find the inverse?

[solemn lantern]

first u would do y=sqrt (x^2-1) then you would do x = sqrt (y^2-1) and then you would solve for y and that is ur inverse function

[ripe meteor]

When you do the inverse write y as f^-1(x) =

[solemn lantern]

yup at the end make sure you do that

[ripe meteor]

At the end

[polar tulip]

ok thank you!

what about the x>= 1

do we do anything with that?

[solemn lantern]

i think that just means the x values have to be equal or greater than 1 cuz if its like 0 which is less than then the square root wouldnt be a real number

[polar tulip]

does making the function inverse do anything to that though?

[solemn lantern]

im not too sure

maybe try graphing the inverse?

[opal tree]

f(x) fails the horizontal line test if the domain was R. The x>= 1 domain restriction makes sure that it suffices the horizontal line test and that f(x) is truly invertible

The range of f(x) will become the domain of f^-1 (x)

[polar tulip]

ohh ok got it thank you!

[polar tulip]

anyone know how this graph would look like? and how to find values of c?

[willow bear]

do you still need help with this?

if yes:
are you able to graph y = x^2, y = 5.6-0.8x, and y=5 individually?

[polar tulip]

yea, i just dont know how to find the limits

[willow bear]

well sketch the graph first

take the portion of y=x^2 that lies left of the line x=2

and the portion of y=5.6-0.8x that lies between 2 and 7

and the portion of y=5 that lies right of x=7

[glossy carbon]

correct.

[hot roost]

https://www.khanacademy.org/math/precalculus

Would just doing this be enough for Calc AB?

[thorn creek]

it should be adequate prep for enrolling in calc AB

[viscid thistle]

Guys

a question

[willow bear]

the question never came

[thorn creek]

it was lost in translation

[summer ruin]

<@&268886789983436800>

[ripe meteor]

If the focus is (0,-2) and the vertex is (0,0) then the equation of the parabola should be x^2 = -4ay, correct? Since the vertex is (0,0) and the focus is (0,-a) I thought it would have been x^2 = 8y because x^2 =-4(-2)y but it's marked incorrect by the program.

Any ideas?

[stark shuttle]

since the foci is below the vertex, then i think it will be:

x^2=-8y

because the parabola is facing downwards

[ripe meteor]

Right!

Thank you!

[stark shuttle]

you're welcome 🙂

[opal vault]

wait why do u guys

multiply out the denominator

just keep it in the lhs

[ruby sapphire]

[opal tree]

Fractions get annoying

[thorny heart]

Recently entered grade 10. i wanna know wether i should start studying this

how do i remove the he him tag? seems kinda cringe

[uncut mulch]

#Channels and roles at the very top

[thorny heart]

thx

[gusty fulcrum]

If u wanna do apcalc by senior year i’d do that but some schools don’t require to go up to the ap calc level. So just study it if ur major relies on it, like for example nursing doesnt need precalc so you’d study stats, but like lets say engineering, you’d def wanna take the calc route

[thorny heart]

thx for the info. any thing else to study for someone who wants to do chemistry?

[gusty fulcrum]

I’m not rly sure at the top of my head, i’d say do research on your own but definitely calculus for chemistry, and probably statistics too.

[thorny heart]

alr

[untold spindle]

<@&268886789983436800>

[timber spindle]

What exactly about geometry do i need to know or would i be fine if i skipped geometry and went straight into algebra 2?

[ripe meteor]

I'm currently taking pre-calculus in college. We are currently going over Conic sections. We already went over piecewise functions, complex zeros, properties of rational functions, polynomial and rational inequalities, exponential and logarithmic equations.

[thorny heart]

i use brilliant and it starts with conic sections

[ripe meteor]

Nice! If you have any recommendations for resources then feel free to share because im self learning.

[opal tree]

That's a thing?

AP precalc 😭

Ain't no way

[thorn creek]

college board, always looking for a way to soak more money out of students

someone is paying college board the fees for when you take an AP class

if it's not you, it's your school district

or whatever other entity funds your school

my kids' high school pays the fees for AP students i think, but i'm not 100% on this tbh

of course

but the universal is that College Board expects to be paid

[solemn lantern]

i also took precalc at a college and this is basically what we also did

for me it was mostly a repeat of algebra 2 but a little bit harder and some more work

shouldnt be too hard

[solemn lantern]

for me i did algebra 2 and then geoemtry and we didnt really need to know much geometry for algebra 2 and i did fine in the class without knowing geometry

[ripe meteor]

That's great! I'm glad you had a good foundation of algebra. I had good teachers in the past but I also had awful teachers that I wouldn't go to ask for help and so I became an autodidact in certain subjects.

Me

[timber spindle]

In your opinion, do you think I should just go over triangles then go on to trigonometry?

[opal vault]

i mean ofc

geometry is triangles

thats like 90 percent of it

[opal tree]

What about them specifically

[astral bronze]

A conic( cone shaped) are two intersecting cones using the formula for volume of a cone in 3 dimensions you can isolate specific slices

It poses an interesting question like when an circle becomes an ellipse becomes a quadratic which is useful in hyperbolic trigonometry, relativity, and many others

[opal vault]

conics

so bad

they are a bunch of memorization ngl atleast for me

with the exception of parabolas and circles ig

[ripe meteor]

I think conics are interesting. Let me talk about the ellipse.

If the foci are near the vertices the ellipse is more of an oval shape however if the foci is closer to the center its more of a circular shape. Some ellipses are more oval than others. Planets orbits are an ellipse shape. The Eccentricity of an ellipse describes the ovalness or the roundness of an ellipse. It measures the ovalness.

The sun is considered a foci

The planet orbit with more eccentricity is mercury.

If eccentricity is near zero then the ellipse is more circular but if its closer to 1 then its more oval.

[ripe meteor]

I don't think it's about memorization. It's more about understanding. Math is the language of the universe.

There are vertical and horizontal ellipses each with their equation that is reversed.

[thorn creek]

the sun isn't just "considered" a focus (foci is the plural, and so "a foci" is agrammatical), it is at one of the foci, that's a basic consequence of orbital mechanics

[ripe meteor]

sorry I meant to say is one of the foci

vertices is plural of vertex I get it

[thorn creek]

actually the sun orbits the center of mass the same as the planet, but because the sun is wildlyl more massive its orbit is very tiny

an eccentricity of 1 describes a parabolic orbit

and greater than 1 a hyperbolic orbit

some comets have orbits with eccentricity 1 or greater

they will make one pass and then depart forever

[ripe meteor]

Google- The eccentricity of an ellipse is always less than one. The closer the eccentricity is to zero, the more circular the ellipse. The closer the eccentricity is to one, the more elongated the ellipse. Eccentricity e= c/a

[thorn creek]

yes, and an eccentricity of one describes a parabola

[ripe meteor]

Oh I didn't know that I learn something new everyday

Im now learning about conics

Current unit

[ripe meteor]

Thank you for the correction! Sun is at one of the foci, not that it is considered a focus. I understand now.

[ripe meteor]

Are saying that some comets orbits hyperbolic meaning you only see it once and passes? That's pretty sad that people only get to see it once. Are there elliptical comets? I google search and it says that comets are highly elliptical. So, is the majority have elliptic orbits?

[opal vault]

bro since

when

did this

translate to keplers laws

[opal vault]

all