precalculus

[round geyser]

So it’s pi

Ik it’s Q1: theta, Q2: pi- theta, Q3: pi + theta, and Q4: 2pi-theta

Theta is in angles

[undone pumice]

Wdym its pi

[round geyser]

pi radians= 180 degrees

[undone pumice]

Oh thats what u mean

[round geyser]

And also this case they used degrees

[round geyser]

Aka 180 - theta

Like Unit 8

[round geyser]

Okay so

My friend is now confused with “but like where is pie coming from”

[undone pumice]

Oh

uh

[round geyser]

I told her “pi radians = 180 degrees “

[undone pumice]

maybe u can js work out each problem only in degrees or smn

or maybe go back to basics with converting degrees amd radians

[round geyser]

I told her that

The ans contains 3 on the denominator, their reference angle is 60 degrees, 4 on the denominator, reference angle will be 45 degrees and then 6 on the denominator, reference angle will be 30 degrees

I also highlighted that

[undone pumice]

right…

Or you could just not use reference angles if thats confusing for her and just have her think abt the unit circle

[round geyser]

I agree but my teacher never gave us a unit circle chart

[undone pumice]

oh

tell her to google it

or draw a picture

[round geyser]

Okay

[round geyser]

Also my teacher used that method to taught us

To convert radians to degrees quicker

[undone pumice]

Ic

[round geyser]

If we don’t see like these

Multiply by pi/180 or 180/ pi

To get to degrees or radians

[undone pumice]

mm

for me i lwk just see what the denominator is like if its pi/6 then its 180/6=$0

*30

[round geyser]

Looks like this

My handwriting isn’t too good

[round geyser]

Now she said “but how do i know the angle”

[coral agate]

Hi, why is the answer for 7h 3/2, where 7h is the vertical asymptopes from the graph?

[raw hill]

Recall that the vertical asymptotes of $y=\tan x$ are at $x=\frac{\pi}{2}+\pi k$, where $k$ is an integer. So, the vertical asymptotes of $y=\tan \left(\frac{\pi}{4}-\frac{\pi x}{6} \right)-2$ occur when
$$\frac{\pi}{4}-\frac{\pi x}{6}=\frac{\pi}{2}+\pi k, \quad \text{ where } k \text{ is an integer}.$$

[obsidian monolith]

Civil Service Pigeon

[raw hill]

,w solve for x if pi/4 - pi/6 * x = pi/2 + pi * k

[obsidian monolith]

Results provided by WolframAlpha

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

Requested by civil_service_pigeon

[raw hill]

Take $k=0$ and you get a vertical asymptote at $x=-\frac{3}{2}$. I'm assuming you made a typo in your original question.

[obsidian monolith]

Civil Service Pigeon

[raw hill]

Hi, why is the answer for 7h 3/2, where 7h is the vertical asymptopes from the graph?

specifically here

[ornate fiber]

can anybody teach me long division (i forgot)

[brazen sedge]

Do you guys know any procedures/techniques when doing establishing trig identities CAUSE THERES so many formulas you need to know + I get lost if I should substitue (e.g cos^2x with its pyhta idenity) factor, do the conjucate, etc

[round geyser]

Sure

do you know what’s division includes

There is 3

[ornate fiber]

nevermind thanks

I got it cleared

[round geyser]

Okay

[lilac moat]

Yoo @round geyser

[round geyser]

Yes

[valid topaz]

uhh

hmm

[lilac moat]

@round geyser just checking if u forgot me

[round geyser]

No

I won’t forgot u

[lilac moat]

Lol

What ya doing ?

[bronze geyser]

i wont forgot you either

[round geyser]

Good

[bronze geyser]

Bad

[lilac moat]

Lol

[deft swift]

W

What r u gonna do with it?

[round geyser]

What will happen if you complete the square

[uncut mulch]

you'll eventually end up at the same point as other methods

[viscid thistle]

ohh it will be (pi+2npi)/2 where n is a constant

[round geyser]

Two cases are

cos x = 0 and cos x =1/2

X=0 which is pi/2 and 3pi/2

[viscid thistle]

there are infinitely many solutions to cosx=0

[round geyser]

0<=x<2pi

[viscid thistle]

oh my bad

[round geyser]

Yea

[hushed sphinx]

But the question you showed says "all values of theta", not just between 0 and 2pi.

[lilac moat]

@round geyser jack always here 🫡

[round geyser]

Yea

[round geyser]

What’s the form will look like

[round geyser]

We have this

[lilac moat]

You stuck on smthing shoud i help ?

[uncut mulch]

not "constant"

just being some constant doesn't work

[undone pumice]

*integer

You could write it like this, how my teacher showed

[round geyser]

Guys I’m doing Bearing in trig what are some advices that you guys can give

And I’m not using laws of cos/sin

[uncut mulch]

draw diagrams

know your parallel line theorems

know the definition of bearing where to measure it from

[undone pumice]

Icl idk what bearing is so I can’t help sorry

[round geyser]

Btw day 1 I’m doing DMS, solve missing angles

It’s like sin/cos/tan(degrees+(mins/60),(seconds/3600))

[uncut mulch]

so whats your issue with that

[round geyser]

What should I be careful of when I’m solving bearing problems

[uncut mulch]

everything i mentioned above

[foggy forum]

you just measure it from north clockwise right? and yeah like the sum of the co interior angles = 180

[steep nymph]

Im currently taking AP pre calculus and im going to take AP calculus BC next semester. Is there a good way I can learn Calculus BC over the summer so I dont struggle when I get back?

[undone pumice]

honestly just skim over AB material. BC is basically AB with extra units, just faster. make sure you have good trig, algebra, foundations and maybe learn basic derivatives and integration

my school makes us take AB before BC so idrk but

you got this

[steep nymph]

Thanks 😊

[undone pumice]

[steep nymph]

I was actually thinking of taking the AP Calculus BC course on Khan Academy. Do you think thats angood idea?

[undone pumice]

Hmm. You could try that. Remember that Khan Academy doesn't reallllly go into full depth

[steep nymph]

oh really?

[undone pumice]

I recommend it as a source to get a very basic understanding and as a tool for practice, but not as a one-stop-shop

[undone pumice]

Yeah. You can only cram so much into like, a 10 minute video on derivatives and such

I like the Calc AB course they have along with YT videos and a textbook I pirate- I mean, found online.

[steep nymph]

That sounds good. I aint really into textbooks though.

[undone pumice]

Yeahh I understand reading isn't for everyone.

When I get bored I just watch youtube vids

On whatever topic it is I don't get

[steep nymph]

I do love reading. I just dont belive math and reading go together.

[undone pumice]

Mm. *reading math

[steep nymph]

i do that sometimes

[steep nymph]

ive read a few ,a

math books but they’re pretty boring

[undone pumice]

Yeahh

i get that xd

[quasi meadow]

Idk what calculus bc is, but when I was learning calculus, I used this website called “Paul’s online math notes” and it was very good at helping me learn the fundamentals of calculus, again though, I don’t know if this is what you will be doing in calculus bc. Here is a link: https://tutorial.math.lamar.edu/

[runic shard]

hello

is there anyone who can help me in mastering calculus?

[low yoke]

what do you need

[runic shard]

i need to understand basics calculus

[low yoke]

be more specific, what are you struggling with?

[runic shard]

okay, i am struggling to understand the relation and functions

[low yoke]

what relation?

And what is the problem with functions?

Imagine the function like a box, in where you introduce some input, the box make some math calculations and in the other side you get another number

Imagine it like this

I don't know your math level nor your age, so this may be too basic for you, let me know

[runic shard]

" like a function which has either R or one of its subsets as it range is called a real valued function. Further, if its domain is also either R or a subset of R, it is called a real function. "

I was trying to understand this line given from my maths book, i really couldnt understand the difference between a real valued and real function

[runic shard]

ohh alright i get it now

[low yoke]

You can imagine a non-real valued function like the box that does some mathematical operations that transforms your real input into a non real output

Like for example, imaginary numbers

or to integers

[runic shard]

hmm

so box containing non-real valued function having some mathematical operations

[low yoke]

You can imagine the box as having real input but non real output

for example, giving out rationals

So for example:

[runic shard]

okayy i get it now

thanks

[low yoke]

obviously x != 0

[steep nymph]

Calc bc is Calc 1 and Calc 2 in a single course.

[lilac moat]

@round geyser where did u go

[round geyser]

？

[modern cypress]

can someone help me in #prealg-and-algebra

[lilac moat]

Nice to see u

[round geyser]

Thanks though

[lilac moat]

Just wanna see u alive or not

[lilac moat]

I didn't see your msg anywhere i tho u 😭

[quasi meadow]

Lol idk what calc 1 of calc 2 are, is it an American thing?

[steep nymph]

I guess so 😭

[quasi meadow]

Well we haven’t started calc or pre calc in school yet, I’m in year 10, or 9th grade according to google

[steep nymph]

Oh lol

So youre just learning this for fun

On your own

[quasi meadow]

Yea

I always loved maths and physics so I like to do some indépendant learning from time to time

[steep nymph]

Thats cool.

[quasi meadow]

Yea it’s useful as well, it is also good what you are doing trying to get ahead, it makes all school work easier

Even when if is not related to the topic bc of the inherent understanding you get

[steep nymph]

Im trying to get ahead too and the main reason i actually want to learn it solely is because Calc bc is considered one of the hardest AP classes

And if I understand it before I take the class it would help me

[quasi meadow]

Yea, well keep at it and if I have some advice for you, the theory is incredibly important, but make sure to spend a good amount of time on a variety of practice problems because otherwise you might as well be where you started as soon as you go back to school

[steep nymph]

Do the practice problems keep you from forgetting the material or is it so you understand the material better?

[quasi meadow]

It’s about putting into a practical situation, it’s all well and good knowing what a derivative or a limit is, but if you can’t actually use it to solve problems, then if is essentially pointless, practice problems just help with that aspect of it

[steep nymph]

Oh okay. Is there a specific website you recommend to get good quality practice problems?

[quasi meadow]

Yea, Paul’s online meth notes, and the organic chemistry tutor on YouTube, that is what I used

[steep nymph]

Ok. Thanks 😊

[quasi meadow]

Good luck!

[steep nymph]

You too!

[undone pumice]

Calc 1 and 2 are yeah I think US names for a calculus course

Each represents one semester of said course

calc 1 is semester 1 and calc 2 would be semester 2 (so harder). We also have calc3 which would be after calc2 and calc 3 is I believe multi variable calc

[undone pumice]

Oo glgl! I’m in 9th grade too. Taking ap calc ab next year

[undone pumice]

Mm glgl r u takin ab first or just doing bc? honestly if ur doing ab first like me Icl its not really that bad to bc

[quasi meadow]

Good luck to you as well!

[rough leaf]

why not bc

[undone pumice]

bcs my school is a bihhh

and my counselor said noooo

[rough leaf]

im taking 3 maths rn so i can do calc bc bext year

[undone pumice]

it doesn't rlly matter

i can do bc in 11th

and have a free period in 12th anyway

so idrc

[rough leaf]

we ahve enough ppl taking bc bext year

to have a multivariable class in junior

[undone pumice]

lucky

my school wont let me do multivar

i asked

[rough leaf]

then in 12th i can go to community college or sum for diff eq

[undone pumice]

unfortunately

my school is full of bums

most of them will be taking bc senior

[rough leaf]

yeah

[undone pumice]

well actually kind of all of them

based on the pathway

[valid topaz]

diff eq is fun

[rough leaf]

my school has most taking precalc senior

[rough leaf]

bro pdes look scary asf

[undone pumice]

yeah thats the regular pathway at my school as well, theres a bunch of stup- academically challenged seniors in my class

[valid topaz]

but they're fun

most of the time

[round geyser]

Hey I was busy

[bronze geyser]

everyone learns at their own pace maam

[undone pumice]

ikik...

but its like...

[bronze geyser]

Being gifted does not give you the right to diss ppl

in fact you should be even more humble

[undone pumice]

they're not even trying...

like...

[bronze geyser]

O

[undone pumice]

they dont do their homework...

[bronze geyser]

like they vape off all day

always the internationals who vape all day

[undone pumice]

they told my teacher, to her face, "i already got accepted into college this class doesn't matter"

[bronze geyser]

crazy

Nvm valid

[viscid thistle]

how do you find the equation of a dented polar graph?

[steep nymph]

My schools actually lets us go straight to bc

[undone pumice]

aghhh lucky

i see

[steep nymph]

Its to save time, but its probably gonna kill me

If I dont prepare

[undone pumice]

lol

icic

[steep nymph]

Lol

So youre in Ab rn?

[undone pumice]

nop unfortuantely

im in precal rn

taking ab next year in 10th, bc in 11th

[steep nymph]

So we're pretty much equal

[undone pumice]

oh

r u in 10th rn?

[steep nymph]

Nah 9th

[undone pumice]

oh

[steep nymph]

And im doing precalx

Calc*

[undone pumice]

ic

[steep nymph]

Maybe ask your counselor or something. He/she could probably give you the opportunity to take bc

[undone pumice]

i asked 🥀

[steep nymph]

That sucks 😕

[swift shuttle]

I reckon ur already acquainted with precalc

[undone pumice]

apparentely "you're alr ahead of most kids bla bla no bla bla"

[steep nymph]

I mean you could always get "more ahead"

[steep nymph]

Ig so

[undone pumice]

sigh

if only

[swift shuttle]

Might be a good idea to start learning in your own if you've got time

[undone pumice]

its alr at least i dont have to worry about struggling in AB or sumn

yeah i do

[steep nymph]

It is

[undone pumice]

been studying calc on my own

[swift shuttle]

Wonderful

[undone pumice]

struggling in integration and such

but

[steep nymph]

Thats great.

[undone pumice]

working on ittttt

[steep nymph]

If youre already at integrals youre basically done with most of calc ab

[undone pumice]

ikik

thats why ive been studying

that way its chill in ab next year

[steep nymph]

Ye

[steep nymph]

Are you going to keep going after bc?

[undone pumice]

nop

i asked about multivar

im sure you can guess my counselors response

given what i just told you about what she said about skipping ab

.....

i asked about dual too

[steep nymph]

Does your school atleast offer it?

[undone pumice]

no

we dont have a multivar class

[steep nymph]

Dang that sucks

[undone pumice]

since the pathway ends at bc

i go to public school and a lot of ppl here dont like math

so our program kinda underfunded

[steep nymph]

My old school was like that buy I transfered

[undone pumice]

oh...

[steep nymph]

But*

I hate typing on phone

[valid topaz]

i don't think most high schools offer multivariable calc courses

[steep nymph]

Yk, you could do dual online

[steep nymph]

Mine does

[valid topaz]

there isn't even an alg ii teacher at my school so we have to go to a hs to do alg ii

[undone pumice]

guess what my counselor said to that...

i mean i could do it on my own but likeee

[steep nymph]

Uhhh.. no?

[undone pumice]

Woah, how'd you guess.... Yeah.... er

I'm planning to use dual to just get rid of some of my gen ed stuff to graduate HS like my art and stuff instead of rigorous work

[swift shuttle]

You could try finding partners/classmates if studying alone feels, well, lonely

[steep nymph]

Well if the career you're looking for needs more math then its probably worth it

[undone pumice]

my sister is also on the same pathway as me but likeee

[valid topaz]

hmmmmm

[undone pumice]

i dont think she wants to take multivar

and highk my precal grade is higher than hers soooo (ahem)

[steep nymph]

What grade do you have?

[steep nymph]

My school has courses up to linear alg

[undone pumice]

like

100

[steep nymph]

You're smart 🔥

Ive got like a 96

[valid topaz]

what kind of hs do u go to

[steep nymph]

Public

[undone pumice]

nice

my teacher curved some of the tests so thats why

like one of our tests was out of 36 but all our tests end up curved

[steep nymph]

Oh my teacher would never do that

[undone pumice]

so the first test went down to like... 33? i think

[undone pumice]

🥀 depends on the overall class avg

if the class avg is like 14-15/18 then she'll curve

if the class avg is 15-16/18 then no curve

my class struggles with trig a lot it seems, been curving a lot of those quizzes

[steep nymph]

Yeah. I believe the class average for the first test we took this quarter was like a 22/28 and I got like a 26/28

[undone pumice]

ouh i see

theres two ap precal teachers and the other one is lwk more chill and usually manages to convince my teacher to do a curve lmao

so i used to have like 107 but now its 100 on the dot

[steep nymph]

Our school only has like one AP pre calc teacher, the rest are dc

[undone pumice]

oh

We have two, so like 11 periods total

And we have like regular precal teachers too

Before i switched into AP i was in regular, idk how many regular teachers there are but like... pprolly more. def 2 ccus me and my sis had diff teachers

[undone pumice]

whats dc by the way?

[steep nymph]

dual credit

[undone pumice]

ohh

[nimble wadi]

How can i cancel the sin from $\sin\left(y\right)=\sqrt{\left(\frac{x}{e}\right)}$

[obsidian monolith]

Quinn

[echo sinew]

By applying arcsin to both sides

[nimble wadi]

arcsin(sin x) != x right?

only sin(arcsin x) = x

[echo sinew]

Only for -π/2 ≤ x ≤ π/2

[nimble wadi]

alr

[nimble wadi]

but then for values outside that range it's true?

[echo sinew]

Yes, for -1 ≤ x ≤ 1

[echo sinew]

Nope

[nimble wadi]

oh

[echo sinew]

Take x = 3π/2 for example

[nimble wadi]

so you meant only in that range its true

[echo sinew]

Yes exactly

[nimble wadi]

k

thats prob the inverse

ignore piss filter

i generated this graph with ai trust

[echo sinew]

Indeed, at least for the restriction they chose

[velvet wyvern]

lie

[fossil kindle]

scary

[lilac moat]

@round geyser yo gang u there

[round geyser]

What’s the graph of sin^-1

[lilac moat]

1/sin

[lilac moat]

I have to draw ?

[round geyser]

If you want

[hushed sphinx]

sin^-1 usually stands for arcsin, not cosec.

[lilac moat]

Mb

It's simple

[lilac moat]

You need O.o

[round geyser]

?

[lilac moat]

Yooo gang @round geyser @velvet wyvern

[round geyser]

What

[vale hill]

anyone got good resources for ap precalc?

[raw hill]

Have you tried looking through past messages? For example, [here](#math-discussion message).

[undone pumice]

why not just use ap classroom

oh and i like this one youtube channel where they explain each lesson in under 3 minutes

and google frq styles online and do practice frqs

[steep nymph]

It has good resources, but it has too much bloat

[jaunty lake]

my dual credit class precalc just started trig

is it harder than alg 2 trig or should it be like the same?

[undone pumice]

oh fair fair

[undone pumice]

starts off similar, idk if you've learned unit circle before, then you'l probably learn inverse trig (arcsin, arctan, arccos) and then reciprocal trig (1/sin = csc, 1/cos=sec, 1/tan=cot) and then i think polar functions a bit

[jaunty lake]

went through unit circle / trig the first semester of alg 2

but kind of forgot mostly everytihng about it since then

[steep nymph]

Def harder

[undone pumice]

ah

then it'll kind of be re-learning and review before new stuffs i dont think you'll have learned before

[jaunty lake]

yea but my teacher not letting us use calculators at all so i think its kind of over

[undone pumice]

rip

on all of our tests we have 6 non calc and 6 calc questions

so we learn how to work algebraically and then do work with calculator + by hand

[steep nymph]

Pre calc is like 99% no calc lol

Im guessing its only when you reach calc that calculators are actually allowed

[vital dune]

Yes

[steep nymph]

because "Calc"ulus and "Calc"ulators

[undone pumice]

really? thats stupid

we're supposed to use our calcs a lot to prep for the ap exam n stuff

according to my teacher

like

[steep nymph]

For me, a calculator is only used for regressions, solving for trig values that aren't on the unit circle, and finding points on graphs that are near impossible to find by hand. Otherwise, you should be expected to do it without a calculator.

[undone pumice]

i see

[jaunty lake]

I think id been doing fine with no calculator but it feels weird

[steep nymph]

Tbh yeah, but you can do stuff in precalc so much faster and easier if youre allowed to use a calculator.

[swift shuttle]

It's just a time save overall

But nothing crucial

Unless you're doing something like calculating integrals or plugging different values for derivatives or so

But that takes time

You can do something like solving quadratics I guess?

[fossil kindle]

for me it was like 6th grade

and i think thats the case for us schools in general?

[steep nymph]

Same for me, but you dont get to "really" use a calculator for like most of the questions until you reach calculus

[nimble wadi]

they let us use a calc in grade 7

[lilac moat]

@round geyser yo good evening man

[granite hamlet]

never used a calc for much of anything ngl

[round geyser]

Graph this then I’ll respond

[worldly scarab]

v_\text{cart} = \text{speed of the axle}, \quad \omega = \frac{v_\text{cart}}{R}

whats the bot that transalte this

[undone pumice]

Do you need help with this or

[round geyser]

Yes

[undone pumice]

So change the fraction to multiplication

so flip the numerator and denominator

Then think how to simplify the numerator on the left

[swift shuttle]

Yeah that one's kinda obvious if you get rid of that (÷)

Just be aware of your domain if you're gonna graph this

[compact timber]

The graph is a straight line passing through the origin with a slope of 2, but with two specific "holes"

[undone pumice]

what does the d:r and r:r mean

[round geyser]

All real numbers

[undone pumice]

but

the domain and range aren't all reals

the domain is undefined where there are holes

the range is undefined where there are holes, as it skips over that value

[undone pumice]

also, you can't just write r, it has to look like

[round geyser]

I meant to write that

[undone pumice]

ah

[round geyser]

But as the time passed by

I merged it accidentally

[undone pumice]

oh

so does it make sense how the domain and range dont include all real numbers?

[round geyser]

I was keep writing that since Unit 1 of Pre-Calc

[round geyser]

Yes

[undone pumice]

oh

[round geyser]

Now I’m on trig

Unit 10

[undone pumice]

mm yeah i usually js do interval notation

[undone pumice]

yeah us too

[round geyser]

Yep

[round geyser]

Are u going to do bearings

[undone pumice]

idk

lemme see if theres anything on that in our curicullum of trig

[round geyser]

Looks familiar

?

[undone pumice]

uhh

idk what that means

looking at ap classroom rn

[mint knoll]

What's that, arithmetic progression or what?

[undone pumice]

we only have this stuff left

[undone pumice]

uhhh ap classroom is a resource for ap classes (advanced placement), mainly an US thing

[round geyser]

A= Angle A

[mint knoll]

Ok

[round geyser]

It’s using pythagorean theorem

[undone pumice]

whats the little a mean?

[round geyser]

And SOHCAHTOA

[round geyser]

Side a

[undone pumice]

im confused like

i get the angle part

but whats the number after

like 40'

[round geyser]

40 mins

[undone pumice]

whats 40 and what does the ' mean

oh

uh

i dont think we're learningthat

[round geyser]

‘ = mins

[mint knoll]

Angle sub divisions

[round geyser]

‘’ = seconds

How about (degrees+(mins/60) + (seconds/3600))

[valid topaz]

hmm

[round geyser]

Oh btw I’m using Desmos scientific

[valid topaz]

desmos is great

[round geyser]

Yep

[round geyser]

That’s the one I have to type in

If I see reciprocals

Take 1/ that

[mint knoll]

How are you supposed to solve that without a calculator, that expanded form of Pythagorean with cosA and finding cosA using expansion?

[round geyser]

It’s with

[mint knoll]

🥀

[round geyser]

What does it look like

On the rt triangle form

Btw

C is 90

[mint knoll]

I lowkey ignore c

And solve like vectors

[valid topaz]

vectors mentioned rah

[round geyser]

I need angle B, side a and b

A is 36.333 degrees

[lilac moat]

@round geyser ye Jake alive yeee

[sonic wave]

I know this isn’t really the place to ask, however I thought this would fall more into the “general” kind of question, so I’ll keep it brief.
I’m a biology undergraduate and I seek to get better at mathematics and statistics (emphasis on the latter), however my maths education throughout academia has been sloppy, and the issue is that I don’t know what I don’t know. Like until a few weeks ago, I had never seen partial fraction decomposition…
what’s the best approach in you people’s opinions?
I need very solid bases, preferably sooner than later, but I don’t mind taking longer amounts of time

[uncut mulch]

try Khan academy

to get you started

[undone pumice]

Yes, I'd also recommend Khan Academy. You can take placement tests on there and see what you know of each course and build on any gaps

[uncut mulch]

Pick what you need, skip past stuff you're already confident on
seek other resources for more depth into certain topics

[sonic wave]

Sounds like a plan, thank you peeps

[undone pumice]

good luck!

[low yoke]

I'd totally recommend you to go through the James Stewart Precalculus book

it cover all the basic stuff

It does not cover basic statistics, but basic math

[sonic wave]

statistics can come at a later date, for now I want to consolidate my bases and see from there. Thank you for your suggestion!

[low yoke]

You can find it online in PDF format

[steep nymph]

How much of mathematics have you studied till now?

[hollow condor]

Can someone help me find the phase shift?

Never mind, I believe I got it.

[round geyser]

@lilac moat how can u solve this

[waxen marlin]

wt fis this beginner math

why is this here

[round geyser]

While waiting do u know why

[waxen marlin]

uh

no'

[waxen marlin]

x^2 + 12x + 35= 899 bro

x^2 + 12x= 864

[undone pumice]

ummm im assuming its like

[waxen marlin]

quadratic

done

[undone pumice]

how mathematicians like

assign values to like

divergent series

[waxen marlin]

24

[undone pumice]

using like

regularization or something

[round geyser]

Btw

When I do this

I did is find the median

Substitute

[undone pumice]

median?

[round geyser]

y=x+6

[waxen marlin]

wtf do u mean median man

[undone pumice]

uh

[round geyser]

The middle

[waxen marlin]

ok whats the medina

[undone pumice]

thats not how it works bro

[round geyser]

(y+1)(y-1)=899

[waxen marlin]

no offense but what r u saying

[undone pumice]

if you're going to substitue

[waxen marlin]

ts ragebait bro

[undone pumice]

don't use y...

use u bro

[round geyser]

I like to use that

[waxen marlin]

weirdo lol

jk

[undone pumice]

um

well

i mean

its kinda confusing

with y also being an output

[round geyser]

I meant to do t

Like t=x+6

[undone pumice]

oh

i usually do u since thats what my math teacher taught

[round geyser]

(t-1)(t+1)=899

[undone pumice]

but igs if its not y then thats better

[round geyser]

Foil them

[waxen marlin]

ew foil

i hate that

[round geyser]

t^2-1=899

Add one

[undone pumice]

difference of squares...

[round geyser]

t^2=900

Sqrt them

t=+-30

[undone pumice]

agh this feels like a lot of work

[waxen marlin]

dude jake what are we doing

this is not it

this is so long

[undone pumice]

so uh

that was like

[waxen marlin]

just foil original and quadratic

[undone pumice]

15 lines of work

[waxen marlin]

americans xd

[round geyser]

Here

[undone pumice]

guys i live in america believe me we dont do 20 lines of work

[round geyser]

That’s my work

[waxen marlin]

yeah we just

no?

can we just not

[round geyser]

I haven’t have time to change it to t

[waxen marlin]

we can just not do that

and save us some time

[round geyser]

My opinion

Foiling that and subtract takes time

[waxen marlin]

bruh

[undone pumice]

this takes like 1 min gng...

if i tried substituting my teacher would probably give me a +0 on an algebraic frq lmao

[round geyser]

Who’s way was that

[waxen marlin]

four fucking lines

jesus

we dont need that much

[undone pumice]

lol in my working i js skipped doing the foil in one line cus like ts can be done in ones head 🥀

[waxen marlin]

fr

jake what are we on

[round geyser]

Would u substitute this one

[waxen marlin]

yeah

for sure

just not for all of them like that one.

[lost helm]

Yall can someone help me with this short problem

[waxen marlin]

sure

[undone pumice]

sure whats the prob

[waxen marlin]

dibs.

lol

[waxen marlin]

B

[undone pumice]

Yeah cus B is where the derivative is positive

[waxen marlin]

im so frigging smart

[undone pumice]

aka the original function has positive slope, meaning its increasing

[lost helm]

Aight yo appreciate it chat😎

[undone pumice]

in the future that'd prolly belong in #calculus btw

[waxen marlin]

np

[waxen marlin]

it should?

seems rly simple for calc idk

[undone pumice]

it is rly simple

but like

ppl in precal like

dk what a derivative is

[waxen marlin]

oh

wait

what are u learning in math rn

like

[undone pumice]

trig

[waxen marlin]

r u pre calc

or math 3

or what

[undone pumice]

precalc

[waxen marlin]

oh

[undone pumice]

like

unit circle stuff

[waxen marlin]

is that after algebra 2?

[undone pumice]

i think

my district does like integrated 1-3 so idk

but after integrated 3 its precalc

then after precalc is calc

[waxen marlin]

wait so ur in math 3?

[undone pumice]

no its after math 3

[waxen marlin]

holy

[undone pumice]

math 1,2,3 --> precalc --> calc

[waxen marlin]

no math 3=precalc

[undone pumice]

no like

math 3 is like

easier

ish

[waxen marlin]

oh

slightly ig

bro

im so not locked

[undone pumice]

idk

icl

[waxen marlin]

frehsman year math 1

😭

[undone pumice]

math 3 was a bunch of review and precal is more review on math 3 😭

[undone pumice]

oop

thats the regular track at my school too dw

[waxen marlin]

i genuinely dk how its so bad]

[waxen marlin]

REGULAR IS BAD

regular is white people bad

no offense

[undone pumice]

oop

rip

[waxen marlin]

actually its different phases

[undone pumice]

the "advancedd track" is supposed to be

[waxen marlin]

but still

[undone pumice]

math 2 freshie --> precal soph --> calc junior

math 2 is also easy tho so like

i took ts alr

[waxen marlin]

isnt math 2 just geo

[undone pumice]

pm

a lot of geo

with like

some algebra

[waxen marlin]

ew

[undone pumice]

basic trig, like unit circle but not like reciprocal trig

[waxen marlin]

wait so i should be in math 3 this year???????

wtf

[undone pumice]

(i hated the geo in it oh my lord-)

[waxen marlin]

cuz i did geo laste year

[undone pumice]

idk

[waxen marlin]

fuck bro

[undone pumice]

different districts do diff pathways

[waxen marlin]

oh

[undone pumice]

i mean ur in calc right? thats good

[waxen marlin]

no

bro

[undone pumice]

oh

nvm

[waxen marlin]

im in fucking math 1

but i should math 3

if math 2 is just geo

[undone pumice]

wait

[waxen marlin]

with a lil alg

[undone pumice]

oh

uh

wait

so you're in 9th in math 1..?

[waxen marlin]

yes bro

sadly

[undone pumice]

then why did u have that calc question 🥀 im confused

[waxen marlin]

bro it was so easy

[undone pumice]

ik but like

[waxen marlin]

i just learned it

at home

cuz asian parents

[undone pumice]

nice

lmao same

[waxen marlin]

oh twin

[undone pumice]

i have to do calc next year

[waxen marlin]

lucky

[undone pumice]

so igs its more reasonable for me

[waxen marlin]

i have to do geo next year

😭

[undone pumice]

oof..

and i can't skip AB cus my counselor a bihhh

[waxen marlin]

but ap calc ab is tough according to my sophomore friends

u got that

tho

[undone pumice]

at your school they get to take it in soph?

[waxen marlin]

yes

if u get math 3

and get reccomended

[undone pumice]

we have precal so we have a barrier in between math 3 sigh

[waxen marlin]

oh sad

[undone pumice]

i took math 3 in 8th so like

if there was no precal id be in calc alr

but im stuck in this bum ahh easy course

[waxen marlin]

oh dang

lwk genius alert?

[undone pumice]

no like i swear

i do not study one bit for ts

and i still have 100

my classmates r kinda bums tho icl

[waxen marlin]

holy genius

[undone pumice]

idt they study either

[waxen marlin]

dang

i gotta step up lwk

anyways i gtg now

thanks for giving me a reality check ig lol

[undone pumice]

loll

nah its nun

seeya

[sonic wave]

I’ve gotten to a crisp taylor series, however I find myself struggling as you can imagine

[sonic wave]

well, I as the university program

[viscid thistle]

Me doing anything but starting analytic geo☹️

Litteraly can I just skip to calc

[stable pendant]

A drug follows first-order elimination with a plasma concentration function C(t)=10e^-0.5t mg/L Calculate the total area under the curve (AUC) from t=0 to t=∞

how to do

[copper ledge]

$\text {To calculate the area, you can integrate the given function within the given bounds i.e,} \int_{0}^{\infty} 10e^{-0.5t} , dt$

[obsidian monolith]

| caesar |

[blissful night]

20

[lost helm]

Also

Can someone help me with these two other problema

[tender quest]

Asking the actual question right away is more likely to get responses.

Asking "Can I ask...?" or "Does anyone know about...?" doesn't give people enough information to decide whether they can help, and answering can feel like a promise to help with the actual question, which they might find themselves unable to.

[gaunt swallow]

Which questions???

[fossil kindle]

bro my school only offers precalc in like 10th grade

[shut ridge]

can anyoone be a tutor for Applied Calculus I?

is someone a tutor here😭

[fossil kindle]

prolly not

[heavy dagger]

Yes

[undone pumice]

Mines too

That’s the like enhanced accelerated track at my school or smn precal 10th

[drowsy sundial]

Ik it’s silly, however, for the fourth step, why did we not keep it the same and just say (shift one unit right) ?

As in “y=-√(-x+1)” instead of “y=-√(-(x-1))” ?

[valid topaz]

because -x+1=-(x-1), which is a shift 1 unit to the left, not right

[drowsy sundial]

yeah no I understand that but like, why don’t I just keep it as the function? √(1-x) instead of √(-(x-1))

[swift shuttle]

Well it's just a greater demonstration, you can use the other just fine

[valid topaz]

i mean -(x-1)=1-x, so they're the same

it's purely choice

[drowsy sundial]

but the graphing are different

[swift shuttle]

Because our original function was √-(x)
So it's clearer to see the shift as √-(x-1)

[drowsy sundial]

because the shifting is to x so if x is negative then the shifting changed as well, right?

[swift shuttle]

Not at all tho

[drowsy sundial]

rly? So when doing the steps I could just use y=-√(-x+1) and say (shift 1 unit left) ?

[swift shuttle]

Shifting 1 to the right just means that we're changing the x value to (x-1)

Hence why they replaced x by x-1

So -√-(x) to -√-(x-1)
Which simplifies to -√-x+1 or -√1-x

They're just the same

[swift shuttle]

What do you mean by that?

Like from which step to which

[drowsy sundial]

I’m trying to understand ur explanation one second 😅

Honestly I still don’t understand

I’m sorry

[swift shuttle]

It's okay

[drowsy sundial]

If the function says √(1-x)

It means shifting one unit left, no?

[drowsy sundial]

Why did we change it at the fourth step and say shift one unit right

[swift shuttle]

It means rotating by the y axis and shifting to the right

Remember that we're starting off of √x

[drowsy sundial]

so the 1 isn’t for the x but to y?

[swift shuttle]

And √1-x has a negative value of x

Since x is negative, that has the effect of rotating by the y axis

[drowsy sundial]

yes! That I understand

now the unit 1 movement I don’t understand

the positive is at 1, hence moving left

[swift shuttle]

If you take 3 on the number line and rotate it by the center u get -3
So that's for starters

Now we know that shifting to the right is (x-1)

Because that gives us that each value of x is one less than it should be

[drowsy sundial]

wait

wait

but now why is it negative?

Rather than positive 1

wait wait

since we finished with the reflection about x axis

now we focus on the shifting

[swift shuttle]

You subtract 1 to move right, and add 1 to move left

[drowsy sundial]

so we talk about x and say that the shifting goes to the right

due to the negative on x being used and now we’re talking about shifting

am I correct? Or did I just fuck it up lolll

[swift shuttle]

Remember that we're doing each step individually before simplifying

[drowsy sundial]

yeah ik that

[swift shuttle]

So we think of √x for starters
Then we rotate by y axis to get √-x
Then we shift to the right by one by replacing x with (x-1)

When you plug that (x-1) to your √-x, you get √-(x-1)

And then we simplify

√1-x

I assume you're trying to say that we can just say that (1-x) is a shift to the left instead of doing the rotation and shifting to the right?

[drowsy sundial]

yes

but now I understand

I’m just trying to write it down and get it in my mind

thank you so much

[swift shuttle]

But then you'd be excluding the rotation itself

Because if you say it's a shift to the left, that's just (x+1)

So we have to include the rotation

<@&268886789983436800> help!

[drowsy sundial]

I’m so sorry, thanks for helping me, but honestly I still don’t understand why you said shifting to right when the function shows the 1 as positive and the rule is if 1 is positive then shifting to the left

I feel so silly, sorry and thank you again

[swift shuttle]

The thing is, you don't just subtract 1 from, you subtract it from x

It's not √-x(+1)
It's √-(x-1)

[drowsy sundial]

ohhh

now everything clicks

[swift shuttle]

The whole x changes

[drowsy sundial]

mhm

I got u

thanks again!

[raw hill]

<@&268886789983436800>

[steep nymph]

Tbh just do what the people above have recommend. Using Khan Academy is a great way to figure out your math level and expand upon it.

[surreal anvil]

hi

[lone temple]

hi

[subtle glade]

M SO GLAD FOR WHOEVER MADE THIS CHANNEL

thanks

😭

[umbral jacinth]

why no uni matematics channel

[echo sinew]

There are, maybe Discord isn't showing you them? 🤔

[umbral jacinth]

not falling for this

[wheat lily]

#get-advanced-access

[echo sinew]

Wdym?

[round geyser]

Hey

I need help on this

[undone pumice]

Flip the fraction and simplify numerator and denominator of the left side

[round geyser]

I’m trying to sketch this

[round geyser]

We can’t cancel 1+x with x+1

[undone pumice]

…..?

[undone pumice]

yes simplify it so it is simpler to graph

And just add holes and asmyototoes

asymptotes

[round geyser]

So we do have HA

[undone pumice]

uhhh ill work it out

[round geyser]

I get y=-1

[undone pumice]

what did you simplify it to?

[undone pumice]

as the function right?

[round geyser]

Yes

[undone pumice]

thats what i got too

so that z

means instead of va we have holes

Basically a straight line with 3 holes, where do you think the holes are?

[round geyser]

It’s the domains

Of -4, +-1

And then plug with -1

[undone pumice]

yup

[round geyser]

Like this

[round geyser]

Does it look correct

[orchid urchin]

is there anywhere where I can test myself to see if I understand all of precalculus? I am self study

[undone pumice]

khan academy

[rough leaf]

I used khan academy

And found a practice ap exam online

[waxen marlin]

AI ❤️

use claude

tell it to generate you a test

without answers

specify all of pre calc

[undone pumice]

!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).

[subtle yarrow]

I think in this case it’s okay

[undone pumice]

i mean like...

what happens when u ask for the practice exam answers

in my experience ai makes easier questions then u might see on actual pre cal exams

[subtle yarrow]

Could be, but it’s still a source if they are out of luck

[waxen marlin]

D:

wait thats lwk a cool command

!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).

[waxen marlin]

!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).

[waxen marlin]

cool

sry for ping

[undone pumice]

lol

rather unfortunately it is rather used in these channels, many people find chatgpt as their best tutor which is simply not right

[round geyser]

Check it

[winter barn]

That looks right

[round geyser]

Thanks

[winter barn]

My handwriting used to be like that

[round geyser]

Is it neat though

[winter barn]

Neat enough

[round geyser]

Thanks

[violet parcel]

forgot to bring my book home anyone have a pdf of this? need page 735 and 777

[round geyser]

If you want tmr I’ll go to my pre-calc class and take a pic

[round geyser]

That class had that exact text book

[violet parcel]

I need it tn 😭

[round geyser]

Sorry

Then

[violet parcel]

it’s okay Ty for the help

test tmr and test Friday

[round geyser]

Is it this

[violet parcel]

nope I found it on internet archive tho

they let me borrow an account

[round geyser]

Okay

[opaque depot]

i think thats Larson's precalc

[round geyser]

Okay

[opaque depot]

nvm its not im stupid

[violet parcel]

pre calc was lowkey easier than algebra 2

[pine mural]

This is an earlier version of McGraw Hill/Glencoe's Precalculus textbook.

[pine mural]

Larson has produced many Precalculus textbooks.

[opaque depot]

i see, the page # is very similar to larson's textbooks

[pine mural]

I actually have found many of Larson's textbooks online.

I think his Big Ideas Math series is freely available for pdf.

[opaque depot]

https://tenor.com/view/shocked-shocked-cat-silly-cat-cat-kitten-gif-7414586676150300212

[pine mural]

https://bim.easyaccessmaterials.com/

It's an official source.

I've only ever used Larson for Pre-Algebra.

My instructor used the McDougal Littell Pre-Algebra textbook that he authored.

[round geyser]

I made a mistake it should be this

There is Slant asymptote

[winter barn]

Let me try it myself

[round geyser]

Okay

[winter barn]

Oke so

@round geyser

Tbh

I did by putting values

I didn't checked domain and range

Like x ≠ -3

[undone pumice]

oh i din't see this leme work ts out

[warm flame]

im hitting grade 12 and needa study pre calculus, i dont know nun abt ts where do u recommend i should study

dont mind my name yo👀

[viscid thistle]

Strange obscure desmos equation I found

[crude lance]

Drop the equation

[viscid thistle]

Equation :3

[torn cargo]

Tuff ahh equation

[viscid thistle]

Dropped another one

[orchid urchin]

i feel like eulers formula and de moivre's theorem should be taught in standard precalc, because although you can't fully prove it you are able to in calculus when you get to tayler series n stuff

plus there is a very good geometric intepretation that connects it all together

[orchid urchin]

try getting this one:

[orchid urchin]

I think I will use AI, I can probably patch up gaps faster, and gain more fluency and mastery over precalculus, especially speed.

[warm flame]

is khan academy a good web to study pre cal?

if not cn yall tell me where should i study it

[fossil kindle]

thats acc super cool

[rough leaf]

Do they not?

Ik khan teaches all that stuff

[round geyser]

Yes

[robust terrace]

hi

can someone help me with using the binomial theorem

[rough leaf]

I can tey

I don’t have much time I need to catch my bus to school

[robust terrace]

I just need to know how to do something like f(x) = x^4 - 5x^3 + 3x^2 + x +1

[round geyser]

One word summarize

Rational root theorem

[rough leaf]

Bum ahh thm

It’s so much work

[robust terrace]

ill look at it and try, thanks

[round geyser]

Yw

[rough leaf]

In this case it’s js plus minus 1

Rifht

[round geyser]

Or think that as (ax^2+bx+c)(dx^2+fx+g)

[rough leaf]

x-1 is a root i believe

cuz rhe sum of the coeff is 0

[robust terrace]

and then i have to sub it into (f(x+h)-f(x))/h and simplify

[rough leaf]

Nah

Js synthetic division

[round geyser]

Btw

I got two decimal ans

[round geyser]

Try this one

Foil them

And set them equal to the coefficient

[rough leaf]

They could also is do synthetic

Cuz we know x-1 is a factor

[round geyser]

Yep

[robust terrace]

what is a rational zero

[round geyser]

X=1

[round geyser]

,w f(x) = x^4 - 5x^3 + 3x^2 + x +1

[obsidian monolith]

Results provided by WolframAlpha

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

Requested by tofu5477

[wary rover]

I have solved this question and I think option D is correct but the book says option A is the answer so what's wrong with option B and C.