precalculus

[tawdry canopy]

well yea

[winter comet]

desmos doesn't explicitly tell you about open holes

[tawdry canopy]

it is

[winter comet]

if you hover over tan(x) cos(x) it doesn't do that

weird

i guess it doesn't recognize there are open holes there 💀

[willow skiff]

it depends a lot

[winter comet]

i know desmos is wacky about open holes but i guess i dont know exactly what it trips up about 😔

[tawdry canopy]

cos(pi/2) = 0
tan(pi/2) = undefined

[winter comet]

yup

[tawdry canopy]

why multiplying it equates to 1

[winter comet]

it doesn't, but if you take the limit approaching pi/2 it does

basically, it approaches 1 but doesn't equal 1

[tawdry canopy]

tan x = opp/adj
cos x = adj/hyp

(opp/adj)(adj/hyp)
opp/hyp
sin x

[willow skiff]

what happens if adj = 0?

[tawdry canopy]

tried a bit of algebraic manipulation

[tawdry canopy]

undefined at that value

[willow skiff]

exactly

[tawdry canopy]

well, idk

[willow skiff]

so your tan x would be undefined

as you said, tan(pi/2) is undefined

[tawdry canopy]

maybe

[willow skiff]

you can't work with tan(pi/2) then

but you can take the limit as Vicious Viper said

[tawdry canopy]

0 x 1/0
0/0
0^0

idk

[winter comet]

in the context of just straight up functions, 0/0 is undefined

[willow skiff]

as in $\lim_{x \to \pi/2} \cos(x) \tan(x) = \lim_{x \to \pi/2} \sin(x) = \sin(\pi/2) = 1$

[willow skiff]

these are all indeterminate forms

[obsidian monolith]

southlander!

[tawdry canopy]

use of manipulation

[winter comet]

outside of limit context, 0^0 i think is defined to be 1 💀

[tawdry canopy]

i understand now

[tawdry canopy]

idk

if 0^0 is 1 or undefined

[willow skiff]

the concept is

[winter comet]

actually nvm wiki says it depends on context

[willow skiff]

you should:

1. take the limit
2. simplify the expression inside the limit
3. now you should be able to sub in an x-value directly, if you did the right thing for 2)

[tawdry canopy]

yeah

[willow skiff]

to find the limiting value of something that is undefined

[tawdry canopy]

try limit of x^x as x approaches 0

because desmos recognizes 0^0 as 1

[willow skiff]

you could also try 0^x as x approaches 0

but yeah

there's a very good reason why a lot of mathematicians define 0^0 = 1

binomial theorem for instance

and stuff to do with empty products

[grand shard]

everything outside of calculus says its 1 lol

[tawdry canopy]

jump discontinuity

it equates on two values, 1 and 0

[willow skiff]

interesting

[tawdry canopy]

does limit of x^x as x approaches 0 exist?

i dont understand anything

like x/x = x^0, why x/x is undefined and x^0 is 1

[winter comet]

x^0 is more of a convention thing

[river drift]

x/x = x^0 for x ≠ 0

[jagged patrol]

0/0=1 0^0=1
division property and exponent property i dont understand the problem

[river drift]

0/0 = 1??

[jagged patrol]

a/a=1

[willow skiff]

......

[jagged patrol]

0=a

[river drift]

that's a rule which holds for a ≠ 0

[jagged patrol]

therefore 0/0=1

dividing 0 elements into 0 sets means there is 1 element in each set

well actually there could be 0 as well

because 0 times 0 is also 0

or 5

because 0 times 5 is also 0

maybe 0/0 should be considered undefined or indeterminate because any number satisfies 0/0=x because 0/0 (0)=x (0) 0=0x 0=0

[willow skiff]

yeah this is the reason why

like dividing an empty set is by definition undefined

there's just nothing to divide

as you probably know 0 is not the same thing as the empty set

[jagged patrol]

so 0/1=x
0=1x
0=x

i divided nothing and got nothing

[willow skiff]

you didn't divide by 0 tho

[jagged patrol]

but i got nothing not everythnig

[willow skiff]

also I'm talking about partitions of an empty set

that's not the same as dividing 0 by something

[jagged patrol]

ahh

[viscid thistle]

I think it does

It's like one

(It's one)

[shadow summit]

limits are #calculus , and the limit is 1.

[winter comet]

we were the ones who brought up the limit stuff

also they sometimes introduce limits in precalc

[granite temple]

any specific one

[mighty thistle]

trig is screwing me

got my unit exam tmrw, i got a good understanding of the graphing aspect (70-80% ish) but i got a 40% on my unit circle quiz

I got like 90 min to study, what would u recommend i study?

[willow skiff]

the unit circle cause it's super important

if you're not confident with the unit circle I'm pretty sure you're not confident with solving trig equations

namely, that if sin(x) = k, then sin(pi - x) = k also, or that pi - x is the 2nd solution in a period

similarly, cos(x) = k implies cos(2pi - x) = k, so 2pi - x is the 2nd solution

tan(x) = k is the easy one as there's only one solution per period

https://www.youtube.com/watch?v=x36tRrVGtX0

this might be useful

if you understand the unit circle, the sin reflection identity is across the y-axis
sin theta = y = height remains unchanged

the cos reflection identity is across the x-axis
cos theta = x = width remains unchanged

so don't memorise all these identities

understand them by thinking about x and y on the unit circle, where things are the same

[jagged patrol]

My precalc teacher taught it like first week

[jagged hedge]

I'm cooked

[potent salmon]

hii

cab someone help me slove this with induction

[ocean owl]

hello can someone help with complex analysis

I need to calculate this by hand using residue theorem

[jolly pebble]

Probably go to #real-complex-analysis

[ocean owl]

ok thank you

[undone shoal]

hey sorry guys, I cant get an answer in math-help, so posting here. Are the maximal elements {3,5} and the upper bounds as well? I dont really get it :/

[formal bronze]

Did we divide the 6 by three?

[undone shoal]

seems like you just did 4-6?

[formal bronze]

That isn’t me btw it’s from a video of someone teaching functions

I assume the 4’s went bc of compensation but idk if it makes sense here

Wait correct me if I’m wrong
But the 4 went with the 6, then he substracted the 4 with the 3= 1

[tender cove]

Whats up sd director

[cloud steeple]

Hey

How do i identify a graph that varied from sine or cosine

Idk if this is sine or cosine

[tidal horizon]

It can be either since cosine is just a shifted sine graph

[cloud steeple]

Yeah, i wanna know how to identify

[tidal horizon]

Cosine starts at the peak of the wave while sine starts at zero. You can recreate that graph as either sine or cosine if you wanted to

Just by shifting it horizontally

[cloud steeple]

Oh ok thanks

[grave quartz]

I have a question. Can I manipulate both sides of an equation to prove a trig identity? Or would I have to make the more complicated side look like the less complicated side without changing the less complicated side?

[uncut mulch]

most teachers frown on mixing sides

you could get around that by doing stuff like

given the goal is prove
a/b = c/d
starting with the left,
a/b =a/b * d/c * c/d
and simplify the bolded part to 1

= rhs

[grave quartz]

Ah, I see. Thank you so much!

[jagged patrol]

+4 and -6 combine like terms

-2

[cloud escarp]

Hi,
Im a high school student. Our school is conducting a maths club in which everyone has to submit a working model (it can be related to any topic in maths) so im a little confused about the working model so can anyone give me some suggestions for my project that would be really helpful i want to present my best at my max potential for this project.
Thanks

[tall fractal]

∫ (cosh^3(x) * sinh^2(x)) dx

[willow skiff]

,w integrate cosh^3 (x) * sinh^2 (x)

[obsidian monolith]

Results provided by WolframAlpha

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

Requested by sooouth.

[willow skiff]

https://ibmathsresources.com/maths-ia-maths-exploration-topics/
here are some topic ideas

[viscid thistle]

he asked it in a helpchannel

[willow skiff]

yeah it's by parts knew it

[willow skiff]

oh you mean the sinh guy

okay

[cloud escarp]

Thankyou 🤝

[willow skiff]

no worries!

[formal bronze]

Can someone explain how the domain went past -2?

[cloud steeple]

Guys

I need help with periodic functions

Like
Sin
Cos
Tg
Csc
Sec
Cot

[cloud steeple]

It dosen't

[placid lotus]

I think the domain is the red line which goes from -2 to +infinity with a discontinuity at 3.

[tame pike]

I’d like to receive support for this question

[willow skiff]

for any function, the inverse function is just going to be a reflection of f(x) across the line y = x

also you can Google what the equation will be

"inverse of exponential function"

[tame pike]

Thanks

I suppose I use log

[willow skiff]

absolutely

log of the same base also

[willow skiff]

so like maybe it would be worth plotting individual points on y = 3^x

then reflecting them and joining the dots

rather than trying to calculate log3 (x) for a bunch of different x values

just saying

[tame pike]

y=x

Thank u for ur support

[willow skiff]

no worries, happy to help

[formal bronze]

Tysm

[willow skiff]

Ah you don't have the graph of 3^x ooops

Anyways if you have it

[jovial hare]

Os this actually a precslculus question

[magic meteor]

It's D

[silent prism]

What is this abomination

[silent prism]

A super roided up one

[river drift]

completely random conclusion unrelated to anything else presented

[fading monolith]

Not how complex log works on complex but ok. Its completely wrong anyway

[viscid thistle]

you cant have this

[jolly pebble]

Kid named complex logarithm:

[viscid thistle]

?

i have no idea what complex logarithm is 😔

[jolly pebble]

You can have it if you're brave enough

But there are multiple possible values of it

Because of periodicity with e^{ix}

[river drift]

,, \ln z = \ln(r e^{i\theta}) = \ln r + i\theta

[obsidian monolith]

cloud

[viscid thistle]

i forgot we were in the complex plane 💀

[fading monolith]

Makes sense on complex but its a whole set and not a single value

[placid lotus]

Sub in the values from the table

[willow skiff]

also why did you delete the image

I was going to say that the amplitude = (max - min)/2

one of the variables gives you the amplitude directly

[tame pike]

Srry about that

I just resent it

[obsidian mortar]

@rigid canopy

See that area

In orange

[rigid canopy]

yeah

[obsidian mortar]

Yea it can be calculated through $\int^2_0 x^2 dx$

[obsidian monolith]

Luh Roub

[obsidian mortar]

Also if youre familiar with derivatives

Integrals are the opposite

[rigid canopy]

so it calculates the orange part

[dark thorn]

This is a fun equation because it looks stupidly complex but all it is is algebra used in pre calc

[viscid vine]

fun problem

can i solve it for you guys orrr

do i wait

[sharp nova]

Here's one: e^5 = sqrt 2x

Would i just solve for e^5, then square them to get rid of the sqrt on 2x, then divide by 2?
making sure my math is mathing

[winter comet]

idk what u mean by "solve for e^5" but yes

[sharp nova]

Goes in the same realm as logarithms and such
I don't really know what it means but anything that is e with an exponent is solvable basically

[winter comet]

i think you're thinking of if there is a variable in the exponent

[winter comet]

(e^5)^2 = e^10

[sharp nova]

Well, i know you can do stuff like this

[sharp nova]

I figured solve for e^5 which is a definite number, then i should be able to give both sides an exponent of 2 to get rid of the sqrt on the right side

ln sqrt 2x = 5 is the original equation, sorry

[winter comet]

yes. your goal is to solve for x, not to solve for 5 tho

[sharp nova]

Which i should be able to do by writing in expoential form?

[winter comet]

yup, just putting it into a calculator will give you a few digits of the irrational form rather than the closed form

[winter comet]

yeah

[sharp nova]

What is e^number used for in the world, anyhow? I don't even know what it is other than the. . . inverse of a natural logarithm, which is the . . . inverse of an exponential function?

I think i have that right

[winter comet]

you know what pi is right?

[sharp nova]

roughly equivalent to 3.14, and is used in cirlces to determine area and diameter?

That Pi?

[winter comet]

yup

e is roughly equivalent to 2.71

and uhh

hmm

[sharp nova]

what was the eponential parent function again?

[winter comet]

you mean e^x?

[sharp nova]

I remember something about all expoentials sharing a coordinate

[sharp nova]

That doesn;t sound right

gimme a sec

[winter comet]

huh?

[sharp nova]

lemme find my notes on it

[winter comet]

ok

[sharp nova]

I think the parent exponential function is f(x) = a^x?
And all exponential functions pass through (0,1) because a^0 is always 1
a is apparently the indicator for whether or not the function slopes upward or not

[winter comet]

yeah

ah i see what u meant by sharing coordinate lol

[jagged patrol]

5=5

[sharp nova]

The hell is a natural logaritm anyway?!?

[winter comet]

log_e(x) = ln(x)

[jagged patrol]

Continuous growth formula

[winter comet]

see i would say e is useful for exponential growth but you dont necesarily need e you just need exponent lol

but its better to work with 💀

if you differentiate e^x you get e^x

[jagged patrol]

Very useful

[winter comet]

indeed

[sharp nova]

I'm not sure i'll ever understand what difference it makes
because if e^x = ln(x), which is another form of logarithms, and logarithms are inverse of f(x) = a^x, then wouldn't e^x be the same as f(x) = a^x?

But even then it still begs the question of practical usage

[winter comet]

do you know what a derivative is

💀

[sharp nova]

Doesn't sound familiar

[winter comet]

i really can't think something that specifically uses e without calculus

something that practically uses e and has to use e (like can't really bypass it)

like exponential growth sure but you can just use f(x) = a^x

💀

doesn't have to be a=e

[winter comet]

btw uh
f(x) = a^x
is just a general parent exponential function
f(x) = e^x
is like very commonly used exponential function, usually what people/I think of when they/I hear "exponential function"

f(x) = a^x
since a = e^ln(a)
f(x) = e^[ln(a)x]
if you replace ln(a) with c, because both are arbitrary constants, u get
f(x) = e^(cx)
so really a^x = e^(cx), they are related

[sharp nova]

AH

https://tenor.com/view/eye-gif-21462193

[winter comet]

💀

[white stump]

e comes from compound interest, but it has really nice properties in calculus which is what makes it so important

[sharp nova]

huh
thanks

[winged pawn]

How would I solve these problems

[willow skiff]

are you familiar with the problem where you just have a rectangular grid?

if so, extend the figure in part a to a rectangular grid

count the number of ways which pass through the top right corner and the point below it
multiply by 2
then do total ways - previous answer

seems like you might need generating functions for the other two

the other two are pretty insane

or you know just count how many ways there are to get to each intersection point

[cloud steeple]

Help

$\frac{sec(x)+csc(x)}{1+tan(x)}$

[obsidian monolith]

Callisto(Moon)

[cloud steeple]

How do i put this in terms of sin(x)

[daring tapir]

lets try to see if turning everything in terms of sin and cos work

[cloud steeple]

Ok let me try

I got

$\frac{cos(x)}{cos(x)(sen(x)+cos(x))}+\frac{cos(x)}{sen(x)(sen(x)+cos(x))}$

[obsidian monolith]

Callisto(Moon)

[daring tapir]

take the lcm

and see if stuff cancels out

[cloud steeple]

Om thanks

[fiery mountain]

What does he want?

[unborn brook]

Am I supposed to be punished for this

[quiet pine]

it looks like a magnetic field lol.

[winter comet]

pretty sure its just the unit circle 💀

[quiet pine]

nuhnuh, i see those vectors going from one point to the next

[winter comet]

theres no arrow so u dont know which direction the vectors are going in

plus thats a dotted line not vectors

[quiet pine]

Nuhnauh nauhnuh nuh

👀

[vernal path]

that reminds me of the graph on my mic's packing

decibels/angle or sth

[unborn brook]

It's the polar coordinate system

At least it was intended to be so

The graph of the equation was actually a perfect circle

[winter comet]

same thing just without unit

[cold nexus]

Could someone explain to me why its -14 and not -13 because I'm pretty sure -34+21 is -13

[terse pebble]

,calc (5.81)(1.67)

[obsidian monolith]

Result:

9.7027

[terse pebble]

9.7027 > 6.626 hence when you divide 6.626/9.7027 it’ll be < 1

[cold nexus]

Well it says the correct answer is 6.83 its just saying I got it wrong because I had 10^-13 instead of 10^-14

[terse pebble]

i just explained it to you

literally

[terse pebble]

^

,calc (6.626)/((1.67)(5.81))

[obsidian monolith]

Result:

0.68290269718738

[terse pebble]

what we have is

0.683 x 10^(-13)

but in scientific notation

6.83 x 10^(-14)

[cold nexus]

Ohhh

I didn't even notice that

Thx

[hushed veldt]

bruhh

this class some bs

[shadow estuary]

hi

[jovial hare]

Hi

[winged pawn]

isn't there a way to do that question using combinations?

[willow skiff]

for b and c you've got to be kidding me

for a it is possible and that is what I have suggested

[winged pawn]

I see

im cooked for this lmao

they also said you can use binomial theorem for it

which I have no clue how

but i'll get it

[willow skiff]

but actually just do this

it's not worth doing something super convoluted

[winged pawn]

got it, thx

[rain flower]

hey guys how i calculate this function f(x) = -x² + 7x + 12 ? Cause the square root of delta is not exact

my delta is = 97

[willow skiff]

,calc 7^2 - 4(-1)(12)

[obsidian monolith]

Result:

97

[willow skiff]

it is exact!

the solution is just to leave the sqrt(97) as a square root

don't try and write it as a decimal or it won't be exact

[rain flower]

okay

but

what now?

x = -7 sqrt(97) / -2

[rain flower]

how did you call this?

[willow skiff]

discriminant

[willow skiff]

$x = \frac{-7 \pm \sqrt{97}}{-2}$

[obsidian monolith]

south

[willow skiff]

you were missing the plusminus

[rain flower]

i mean the bot but okay lol

[willow skiff]

oh LaTeX

[rain flower]

ah okkkk

[willow skiff]

https://en.wikibooks.org/wiki/LaTeX/Mathematics here

[rain flower]

yeah i was trying to type it

now how i calculate this thing?

just stay there?

[willow skiff]

oh you are going to have to round your answer

but we can still calculate those roots

[rain flower]

ok

[willow skiff]

,calc (-7 + sqrt(97))/-2

[obsidian monolith]

Result:

-1.4244289008981

[willow skiff]

,calc (-7 - sqrt(97))/-2

[obsidian monolith]

Result:

8.4244289008981

[willow skiff]

there

[rain flower]

wow

i think i made something wrong

[willow skiff]

,w -x^2 + 7x + 12 = 0

[obsidian monolith]

Results provided by WolframAlpha

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

Requested by sooouth.

[rain flower]

cause my book is tell me the answer is 3 or 4

[willow skiff]

are you sure it's not x^2 + 7x + 12 = 0

[rain flower]

'-'

[willow skiff]

yeah you wrote the question wrong

[willow skiff]

this factorises as (x + 3)(x + 4) = 0, so x = -3, -4

[rain flower]

yeah yeah

sorry about that

nvm

[willow skiff]

it's okay

at least you know the quadratic formula

[rain flower]

-x² + 7x - 12

now is correct

[willow skiff]

ahhhhhhhhhhhh

okay yes x^2 - 7x + 12 = (x - 3)(x - 4)

ahh I see

[willow skiff]

multiply both sides of -x^2 + 7x - 12 = 0 by -1

[rain flower]

hm okay

yeah it worked

is just because of 12

i accidentaly changed the sinal

signal

idk

[rain flower]

thanks man

it worked

[willow skiff]

the sign

no problemo!

[covert galleon]

hey lads just asking, i've been trying to find a book of excercises for Non-linear system of equations (i think thats what its called translated, the ones with more than two equations which equals a certain variable) (the ones that you learn in algebra), and for the life of me i cannot find them, anyone have a suggestion?

most books i've checked only has linear equations

[summer ruin]

there isn't such a book

just search for algebra books instead

[shadow hinge]

Can u ask for help here?

[willow skiff]

yes

[shadow hinge]

Alr then. Imma post my query

How would you solve:

[willow skiff]

the 1st question should have a white circle at (1, -2)

sorry at x = 1 there is a removable discontinuity

with the 2nd function, continuous at x = 0

[shadow hinge]

How would you prove that using continuity tests tho…

[willow skiff]

you need to check that the left hand and right hand limits are equal to each other

but also that the the limit equals the actual value of the function at the point

[shadow hinge]

So f(1) =-2

[willow skiff]

the question is broken

I assume they mean f(1) = 0

even though the limit exists and equals -2

[formal bronze]

Can someone help me understand how the 2 became negative in this?

The original question is h(x)=2x-x²

[jolly pebble]

2*(-x)=(-2)*x=-2x

[formal bronze]

Ohhh so you just removed the functions and timed them together.. makes sense tysm

[quick pagoda]

is there any seperate # for calculus like differentiation or integration etc for jee mains or advanced level

[jolly pebble]

#calculus

[river drift]

this server does not have channels dedicated to any particular examination

[viscid ore]

is anyone able to help me with this problem been struggling with it

[covert galleon]

I mean even after looking at algebra books, they still only have Linear System of equations, not Nonlinear

[winter comet]

"the ones with more than two equations which equals a certain variable"
are you thinking of linear systems of equations with 3 unknowns and 3 equations? or do you actually mean a nonlinear system

[covert galleon]

In thai it's translated as Nonlinear, maybe I wrote my explanation wrong
It's more of like
2equations with 2 unknowns

With 2 variables

[winter comet]

like
5x+4y = 6
4x + 3y = 2
this?

[covert galleon]

Yes

[winter comet]

that just a regular system of equations

linear

uhh

[winter comet]

that is a linear system of equations, did you look through the book content or only at the titles?

[covert galleon]

I've looked at the book contents as well

[winter comet]

strange

[covert galleon]

I've went from JEE exercises to God knows what

[winter comet]

i feel like the majority if not all algebra books should have it...

[covert galleon]

I've accidentally stumbled upon PDEs on my search

And ODEs

Fun topic

[winter comet]

why are you doing regular linear algebraic systems of equations?

💀

[covert galleon]

No I'm doing it because my teacher has asked me to find him a book with exercises so he can teach the kids a little better

[winter comet]

oh

[covert galleon]

I mean we have them in thai, but it only contains like 60ish questions

Actually I have the PDF why don't I just send it bruh

Here something like this

[split hound]

can someone help me please?

[viscid thistle]

No calculus channel available to me so I'll put it here

The function p represents the profit per item sold, where x is price sold for, a is the production cost, and y is the profit per item
p(x)=x-a
The function c is used to model the amount of customers and how the amount of customers decays as the price increases, where x is price the item is sold for, b is the total market, and m is the percent decay per dollar of price increased, and y is the amount of customers.
c(x)= bm^x
Given these variables, when, in terms of the given variables, will the total profit be maximized

[obsidian pewter]

-> cos wave amplitude is now 1/2
-> Period is now pi

Start from 0, 0.5 and sketch key points

The next key point is pi/4, 0

[lusty phoenix]

I have a question, after we find possible zeros of a polynomial function with [p/q] , do we have a choice of using synthetic or long division to find the rest of the real zeros or only one can work?

[obsidian pewter]

Wdym

Use synthetic division for all your zeroes and check - if one works, use the quotient to do synthetic division

[lusty phoenix]

like this for example

do we have a choice of using long division if we dont wanna do synthetic?

[obsidian pewter]

Yes

But synthetic is faster

IMO

[lusty phoenix]

I see

thank you

[viscid thistle]

Frrr

Lowk long division my opp

[obsidian pewter]

Same

[viscid thistle]

Takes up half the paper, and is weird

[left cave]

guys can someone tell how to cover parabola, ellipse and hyperbola in the least possible time 😭?

[viscid thistle]

Ask the chat gpt bot that is good at teaching

[left cave]

bruh watt😥

[fading monolith]

!nogpt

[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).

[rain flower]

hey guys

i need help with this

Find the values of m for which the function f(x) = mx² + (m + 1)x + (m + 1) has a double real root.

my last answer was delta = -3m +1 -4m² 💀

i'm not expert in math but i think was is not right

nvm guys

i find the answer lol

[jagged patrol]

If you want to cover it in the least possible time then dont learn much

[viscid thistle]

Does anyone know where x went? I know it took x as a common factor but in the beginning it had x^2, shouldnt x^1 remain?

[willow skiff]

oh wait

yeah that's clearly a misprint

,w (d/dx (cos 2x)/x^2) - (-2x sin(2x) - 2 cos(2x))/x^3

[obsidian monolith]

Results provided by WolframAlpha

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

Requested by sooouth.

[willow skiff]

other than the misprint it's correct

[viscid thistle]

Thank you!!!

[daring tapir]

That just means discriminant = 0

Sub the valuea

[rugged flame]

how do i start out with calculus. Like i know limits and stuff. Trigonometry is done, im good with algebra and graphs

[willow skiff]

https://tutorial.math.lamar.edu/Classes/CalcI/CalcI.aspx - these are really good

yes then you should start by learning the rules for differentiation

sum rule and constant multiple rule

then product rule, quotient rule, and chain rule

[rugged flame]

i know some of these rules

[willow skiff]

https://www.khanacademy.org/math/calculus-1

[rugged flame]

THANKS! I NEEDED THAT

[willow skiff]

no worries!

[rugged flame]

where you from btw?

Australia ig

ur name is south and ur profile pic....

[tame pike]

How do I graph these log functions?

[tame pike]

Thank u

[unborn brook]

Why do we constrain k as such?

Is it to avoid repetition?

[fading monolith]

Yes

Consider the case k=n and see what happen

[pseudo turret]

anyone have any good recommendations for a good precalc textbook

[willow skiff]

Axler's Algebra and Trigonometry

or Axler's Precalculus

[willow skiff]

they both cover the same material but this is more detailed

[viscid thistle]

soygpt

[pseudo turret]

ok thanks

[obsidian pewter]

Axler is the goat

But like the front of the AP Calc BC book is where I learned most of my precalc (the review portion)

[hushed harness]

pretty much brand new to logarithms right now and im lowkey lost at this part. I got up to here but dont know where to go next.

got cut out in the picture but the packet says to use the natural log

i have no idea if im even doing it right rn

[tidal horizon]

You applied the right rules but there is a step where you could have isolated x

And then if you wanted to, the denominator simplifies to ln(0.6) as well

[willow skiff]

alternatively, $5^{(\log_5 3)x} = 5^{x + 2}$

$(\log_5 3) x - x = 2 \implies x = \frac{2}{\log_5 3 - 1}$

[obsidian monolith]

south

[willow skiff]

same thing by change of base rule

[narrow basin]

Could someone provide a correction? I'm unsure about my answer because my teacher said it was wrong.

[river drift]

it's correct. so it may be that your teacher wants you to justify it in some different way, in which case you would have to ask your teacher directly

[narrow basin]

I really appreciate it!

[jagged patrol]

Plug in some values you think would make whole numbers by matching the argument to powers of the base

[willow skiff]

that's not what the change of base rule says

order of operations is super important

[willow skiff]

say you wouldn't think $\log_{16} 32 = \log \frac{32}{16} = \log 2$

when it's really $\frac{\log 32}{\log 16} = \frac{5 \log 2}{4 \log 2} = \frac{5}{4}$

[obsidian monolith]

south

[willow skiff]

the biggest difference is that the first one is still a logarithm

when 16 and 32 are related by powers of 2 so you should have a fraction

[buoyant shell]

which answer choice would it be

[willow skiff]

it's not A

choose another answer choice and I'll tell you if it's right

[buoyant shell]

d

[willow skiff]

yeah it's D

[buoyant shell]

thanks

[willow skiff]

explanation for why above ^

nw!

[buoyant shell]

👍

[formal bronze]

Y’all how is this not one to one?
I understand from the graph of it bc of the horizontal line test, but still I can’t figure out how in the equation way

[willow skiff]

oh it's cause $(x_1)^2 = (x_2)^2$ does not imply just $x_1 = x_2$

[obsidian monolith]

south

[willow skiff]

you could also have $x_1 = -x_2$

[obsidian monolith]

south

[willow skiff]

that's what they mean

[formal bronze]

@willow skiff Tysm

Apparently this is with x square’s I get it now, Ty again !

[ocean leaf]

can i get it for free online?

[obsidian pewter]

lol I was joking

But like yeah most resources are free

The university of Waterloo also has most of its pre calculus courses online

https://cemc.uwaterloo.ca

[ocean leaf]

i'll check it out, thanks anyway

[obsidian pewter]

Np

[muted turret]

Is this some high school or precalc channel or university precalc channel?

I am just wondering cause I may need help with sketching a trigonmetric wave

[river drift]

there isn't enough of a distinction between "high school precalc" and "university precalc" to have separate channels, so this covers both

[muted turret]

Ahh ic

[obsidian pewter]

Where we live, Uni precalc doesn’t exist

Most precalc is taught in high school

[mint pulsar]

see , you can also solve it in 2 variables

[radiant grove]

I have given this sinus function: in the form f(x)=a*sin(bx+c)+d

I have to determine all the parameters:

a=1
c=0
d=0

I am stuck with b . I cant figure out. how long the funtion takes for one cycle. anyone got an idea?

[lapis gull]

for sin to be 2 pi whats x?

after you get that value you get the answer

here sin is one at pi/4 so its reaching its peak at half the x expected so b would be 2

[hybrid crow]

without b cycle cant be identified

[balmy pebble]

someone help me with

piecewise function

i dont get it

@cinder veldt

[cloud pivot]

hi

how would i do this without having a unit circle handy

or memorized

can i plug sin 1/2 into my calc to get these or what

[winter comet]

if sin(x) = 1/2, you know that one value of x = arcsin(1/2). Similarly, sin(x) passes 1/2 two times per period. not sure how you would do this part without the circle, but the other value per period is pi - arcsin(1/2). Anyway, then since sine has a period of 2pi, you know that the two solutions are x = arcsin(1/2) + 2pi n and x=pi-arcssin(1/2) + 2pi n for every value of n. But now I just realized most calculators will calculate arcsin(1/2) as an approximate answer instead of an exact answer in terms of pi.
honestly i would just try to know the unit circle bre 😔

[cursive ocean]

I think it’s best to memorize the unit circle tbh

Although scientific calculators have an inverse sin function, which can be used for finding x in that equation (for that question, calculator mode MUST be in Radians mode and not Degrees mode because the value in the given equation is not written in degrees ), the calculator is going to give an exact value in degrees for x, which is: 30. However, it will not give the other correct value , which is 150.

Which is why I think it’s best to know or memorize the unit circle because 30 is not the only answer for that question

[cloud pivot]

ahhhh im cooked i got a test tmrw 💔

[cursive ocean]

I saw this on TikTok
this is for the sine and cosine values of these 5 angles: 0, 30, 45, 60, and 90

I still think memorizing the unit circle is easier tho ‘cause that’s what I did when I was in high school 🫠

[cloud pivot]

ahhh tyvm

i heard it was a good dea to memorize it

but i never took it seriously LOL i see why i should have now

[olive phoenix]

YO

can someone help me with my study guide and walk me throug hit

a call would be nice i also made a forum in the #1021175428326633542 #1315516203128590497 it has my study guide on there if someone can come help me much appreciated

[unborn brook]

Is the only way to prove this identity is to assume it is true and then combine the two to see if they undo each other?

Plus what is that kind of proof called?

[river drift]

define $f \circ g \circ \ell = h$ then by definition $h^{-1}$ is the function such that $(h \circ h^{-1})(x) = (h^{-1} \circ h)(x) = x$

[obsidian monolith]

cloud

[river drift]

so to prove that h^{-1} is given by a certain formula you just need to show the formula follows that definition

[atomic agate]

Calculator says what

[feral bear]

help me please number 7

[chilly fern]

Imma be taking this class during my winter semester, what do you guys think i should have do to prepare myself for the class?

[lunar kraken]

hey'

could anyone help me with continuous fourier series and transforms?

i kind off have my test

[modern valve]

you should probably ask in #odes-and-pdes instead, and post a specific question so people know what you want help on

[lunar kraken]

thank u

[lapis dove]

Do half of the course online somewhere like khan academy

then you wont struggle with bad grades if thats what your worried abut

[chilly fern]

Yeah thats my main concern

I dont want anything lower than a B

[lapis dove]

What grade are you in

Won’t matter if it’s senior, although you being here means most likely your not a senior

[winter comet]

why

[viscid thistle]

That's actually genius ngl

[lapis dove]

Won’t go towards college apps

[tawdry canopy]

actually, you can do it with just one hand

[sharp nova]

I don't remember how to solve this, but i remember it being very simple

seems like it was something like . . . I(20) = x?

[winter comet]

they can still decline you even if you get accepted if they dont like your grades for last sem

[lapis dove]

Really? My whole school, no county ig I could say just don’t care about their last year grades

I don’t really know however so I can’t be sure

[sharp nova]

I feel like this is just asking for the inverse.
Am i wrong?

[winter comet]

yes, its asking you to graph the inverse

[regal tulip]

does anyone know this answer

is quite easy

very easy

[winter comet]

what about it?

[fallow oak]

i forgot integrals

so no

[regal tulip]

40
_

3

[winter comet]

40/3 yea

[hallow imp]

I think it's how much money 20 comes will cost

Since it's the inverse

[willow skiff]

if you want to do it the function way then let $a = I^{-1} (20)$

hence $I(a) = I(I^{-1} (20)) = 20$

in fact $I(I^{-1} (x)) = x$ for all $x$

[obsidian monolith]

south

[willow skiff]

since I(x) is the number of ice cream cones, number of ice cream cones = 20

yeah this is confusing

easier would be to note that I(x) has:
input = number of dollars, output = number of cones

hence I^(-1) (x) has:
input = number of cones, output = number of dollars

number of dollars for 20 cones

[jagged patrol]

I^-1 mean I inverse
I^-1(20) outputs a number for the input of I when the output of I is 20

Oh yeah south explained it better

[jagged patrol]

Also @sharp nova important note f^-1 or f inverse ≠ (f)^-6

So if you have the function f(x)=x f(6) would equal 6

But f^-1(6) wouldn't be 6^-1 or 1/6

[dim acorn]

I have a question and I'm getting contradicting answers, idk if this is where I ask. However my dilemma is when performing the transformation g(x) = f(2(x+1)) would you shift to the left one or compress it first

[sharp nova]

HUH?
I didn't realize that this worked on logarithms as well

i thought it was just exponents with the same bases

[jolly pebble]

No one except yourself knows what the "this" you're referring to is

[sharp nova]

sorry, using the one-to-one property to solve for x in logarithmic equations

apparently if you just have two logarithms you can just. . . discount them from the rest of the equation?

and solve using just the arguments inside?

[jolly pebble]

Yes

[sharp nova]

I know you can do the same with exponents, an example being
3^2x-5 = 3^7+4
and rewrite as
2x-5 = 7+4

[jolly pebble]

This is because the logarithm is an injective function

I.e. it has an inverse

You can see it as raising the base of the logarithm to the power of either of the sides

[jagged patrol]

Do it in the order listed

In the question

[river drift]

well exponents of the same bases and logarithms are inverse functions, so the fact that one is invertible implies the other

[jagged patrol]

Logarithms are invertible by definition as well

[shy folio]

i need help understanding how f^-1(x) works on a graph

so i have a question which is "give the domain of g^-1(x)" and the graph that it gives me is g(x)=2arcsin(x)

is the domain [-pi,pi]

[river drift]

the domain of the inverse function is the range of the original function

[terse aspen]

Can someone help me with this the simpliest way possible number 35

[viscid thistle]

multiply and divide with $1- sin \theta$

[terse aspen]

🤯

The conjugate okay thanks

[terse aspen]

Can you walk me throgu number 63

[viscid thistle]

Busy rn sorry

[terse aspen]

Oh pk all good

[south wave]

How would I do 3c? How would I expand it ( the rhs) or...

[willow skiff]

LHS = (cos x cos y)^2 - (sin x sin y)^2

Then try to factorise or something

[sturdy hound]

can someone help me, when im creating a piecewise function from an abs value function, how do i find the domains of the piecewise function

this is an example of what im talking about the yellow highlight part, how do i determine that part

because ive tried setting the piecewise in the same format greater than equal to/greater than/ lessthan equal to/less than to 0 but it doesnt work

[willow skiff]

that's just the definition of $y = |x|$

[obsidian monolith]

south

[willow skiff]

$x$ if $x \ge 0$ and $-x$ if $x < 0$

now replace $x \mapsto x - 3$, everywhere that $x$ appears

[obsidian monolith]

south

[sturdy hound]

thank you

[willow skiff]

the other definition is $|x| := \sqrt{x^2}$

[obsidian monolith]

south

[willow skiff]

that may be even more unintuitive

try choosing a positive x and a negative x to see how it works

np!

[zinc matrix]

help.

[south wave]

<@&286206848099549185>

[shut hazel]

The question asks for 10 terms. Start with 2, 3 terms and see if you can find a pattern.

[tropic hemlock]

could anyone please help me with simple induction? i dont understand the last step in proving the IH and IG and where to sub them into the formula

[willow skiff]

!help

[tender quest]

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

[viscid thistle]

Just substitute ri8

[south wave]

Thx so much Natalie

[viscid thistle]

yw 😊

[onyx nacelle]

hi, i need help with this math problem

i need to find the values of x in which that is correct

this is the answer btw

[fading monolith]

For the base you have that x-3>0 and cant be 1 so x=/=4. For the inside the log it must be x^2-4x+3>0

[onyx nacelle]

why > 0?

[fading monolith]

Which one?

[onyx nacelle]

for the quadratic one

oh wait yea

[fading monolith]

Definition

[onyx nacelle]

it cant be zero

[fading monolith]

Yep

[onyx nacelle]

and the same for the base aswell

it must be > 0, thank you

and can you help with number 9? We must find the smallest whole number for which that is true

i dont know what to do with the 2x - 3 in the log

[solid shuttle]

simplify that 3^(2log...) instead

[warped shuttle]

Write a function named f which fofof(x) = x
f should be a reciprocal function [(ax+b)/(cx+d)]

anyone have an idea ?

[onyx nacelle]

no, i did that, but then what? I got to the point where its 2log(2x-3) <= 8

and dont know what to do from there

[solid shuttle]

divide by 2 first

[onyx nacelle]

yea?

[solid shuttle]

and then 4=log_2(16)

[onyx nacelle]

ohhh

so 2x-3 = 2

[solid shuttle]

2x-3<=16

by the way

mind that 2x-3>0

[onyx nacelle]

hmm something is wrong

im getting this as an answer

and we are trying to find the smallest whole number that is an answer to it

in this case its 5, but in the answers its 2

[solid shuttle]

just solve 2x-3>0

[onyx nacelle]

oh my god when i flipped the 3 to the other side i wrote it as a nine 🤦‍♂️🤦‍♂️🤦‍♂️

im really sleepy, sorry

and is it possible that there are more than one logs with variables in them?

[solid shuttle]

everything is possible in this world

[onyx nacelle]

yea but i can only derive that they must be > 0

and i dont think thats enough to solve it(?)

[solid shuttle]

depends on the problem

[onyx nacelle]

ill just hope i dont come across such a thing, thank you so much though

[inland ether]

I could use some help with non right triangles

[atomic linden]

I'm gonna cry. I wanna skip Maths.

But I can't.

[crisp bane]

I've never got this concept but why is sum from k=1 to n of a_n =na_n

[raven tundra]

Why? Math is fun

[jolly pebble]

I doubt the person you're replying to thinks math is as fun as you do.

[raven tundra]

trust, math is fun

Just gotta look in the right places

[dusty palm]

hello im having trouble with this study guide my teacher gave me im not sure what to do from here:

i took the natual log on both sides but an unsure how to simplify it from here

[crisp bane]

ln((125)^x) =xln(125) and ln(1/25) =ln(1)-ln(25)

By logarithmic properties

[sturdy hound]

i ended up finding a solution that is easier for me, doing sign checks yay

[sturdy hound]

i think before u take the natural log of both sides u should make both sides have the same base so i would simplify this to 5^3x = 5^-2

and then try simplifying from there

[sturdy hound]

u can review these properties as well to study

[dark cypress]

ngl i personally would just use same base rules

also are there specific scenarios where you have to use ln?

if so please explain

would the answer to the question change based on me using ln and base log?

[dark cypress]

talking about this

[sturdy hound]

ln is more simple for me imo

[sturdy hound]

and also i gotta think about this question lol

[dark cypress]

why not just take log base 5 of each side?

[dark cypress]

whats the difference between ln and e?

[sturdy hound]

that might take longer

[dark cypress]

wait

no

[sturdy hound]

ln is basically log base e of something

if you take the log base 5 of each side u would still ahve to simplify it anyways

so why not just do it all in one step

[dark cypress]

whats difference between ln and log like when you use them, does it make a difference?

[sturdy hound]

hmm

idk im dumb

i just like ln cuz it doesn tshow the base i guess 😭

[dark cypress]

i personally would just convert each side to apower of 5 and use same base rules

cuz thats sooo much easier

[sturdy hound]

i think thats what i said to do

"i think before u take the natural log of both sides u should make both sides have the same base so i would simplify this to 5^3x = 5^-2 "

thats what i said earlier

[dark cypress]

oh yea

you coulda just replied to it lmao

i have a test on all of this tommorow 😭

im deadass studying what a log is

am i cooked

wait

mods

[sturdy hound]

sorry i thought u were trying to learn

[dark cypress]

im sorry for swearring

mb mb guys

[dark cypress]

i am

i got a 69 percent on my last quiz

[sturdy hound]

i have my math final tomorrow dont worry

[dark cypress]

failed but 1 point 😭

[sturdy hound]

im prettyh sure i was supposed to get 50% on my test but my teacher curved it so much it ended up as an 80%

cuz the teacher changed it from out of 80 to out of 40 points

💀

[dark cypress]

bro on a spanish test i lost 8/10 points and got a 100

[sturdy hound]

dang

[dark cypress]

she doesnt give ec and hates me too

💀

[sturdy hound]

oof

[dark cypress]

but its mb for sleeping in that class

[dark cypress]

💀 lucky

on a physics test i got a 50 percent with extra credit 💀

[sturdy hound]

i heard physics is realy hard

[dark cypress]

it is

especially as a freshman

💀

[sturdy hound]

FRESHMEN?

at my school juniors take physics

[dark cypress]

yea

[sturdy hound]

how are u taking physics as a freshman

[dark cypress]

im taking it as an ap too

[sturdy hound]

ok how

[dark cypress]

its like the program at the school i attend

its mandatory

[sturdy hound]

so does everyoone learn physics early then?

[dark cypress]

yea

[sturdy hound]

oh thats odd

[dark cypress]

theres 48 people and all of us learn ap physics first

[sturdy hound]

i guess biology will be refreshing for u then

that is dumb

[dark cypress]

then ap chem then ap bio

idk bout seniros

[sturdy hound]

why do u learn all the aps first

[dark cypress]

no we take all the science classes

[sturdy hound]

at my school u have to take the honors class first b4 taking the ap class

[dark cypress]

just as aps

its mandatory for me

i dont have a choice

[sturdy hound]

so for example freshman i took honors bio, next year i had ap bio and honors chem

[dark cypress]

what year you in?

[sturdy hound]

that sucks

[dark cypress]

sophmore?

[sturdy hound]

yes

[dark cypress]

damn

[sturdy hound]

what

[dark cypress]

you taking pre-calc?

[sturdy hound]

yeah

im assuming ur taking it too right

[dark cypress]

im tryna take bc and physics c (physics 1 with calc) by junior year (both ap)

[dark cypress]

ehh kinda

[sturdy hound]

next year not sure if i wanna take ap calculus ab or bc

but i have an A- rn so..

[dark cypress]

depends i mean

bc is calc 1 and 2

[sturdy hound]

if i just worked harder i probably could have an A rn

[dark cypress]

but ab is just calc 1

bc is 2 college semesters of work

[sturdy hound]

oh so is bc just faster learning pace then

[dark cypress]

basically

and harder too

if you take bc then you might be able to calc 3 (3d calc) if your school offers it

[muted shore]

bc doesnt cover all of calc 2

you should probably take a dc calc 2 class before doing calc 3 at school assuming no prior experience

[sturdy hound]

i think after ap calculus bc for us its multivariable calculus

[dark cypress]

no

its the same for everybody

[sturdy hound]

its different for us tho

im not sure if we take linear algebra or multivarialbe after bc but its one of those

[dark cypress]

idk bro

its your school

aight gotta lock in

ttyl some day in the future?

yea

for sure

[sturdy hound]

ok same lol

[sturdy hound]

yeah

im going to try to stay off discord for 2 hours challenge

cya

[terse prism]

What would base level precalculus look like?

[digital mango]

Limits derivatives is what im learning rn

[winter comet]

that's moreso in preparation of calculus

[daring tapir]

Its just calc 1 isnt it 💀

Not really preparations

[winter comet]

yes thats why im saying its just in preparation for calc 1 at that point

[daring tapir]

True

[digital mango]

Oh so then precalc would probably be something like trig related?

I kinda thought that was review of alg 2

it was like linear and angular velocity

[winter comet]

precalc is review of algebra 1, 2, and introductory trig and sometims calc yea

[terse prism]

Oh ok

[sturdy hound]

can someone take a short look at this pdf and give me recommendations for more practice questions?

wait this pdf doesnt work let me get a different one

here are screenshots i would really appreciate it if someone could find any more practice questions i can do liek these questions

[viscid thistle]

Does anyone know if the answer is a or C? Cus on chatgpt it says C but my question bank answer key says its A (but sometimes it puts the wrong answers to trick students on purpose)

[rustic oasis]

A is correct

[viscid thistle]

time to use commands

[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).

[tender quest]

The purpose of this server is to help you learn, not to hand out answers. Do not ask someone to give you the answer directly.

[viscid thistle]

wait i didnt read the question

MB

sorry :P

[rustic oasis]

But he asked whether a or c , so I assumed that he got A and just confirming !

[viscid thistle]

sorry

[rustic oasis]

Ok so can u tell yr process if u are not confirmed with yr answer

[versed mirage]

Hello, i'm working on a demonstration right now, and i needed to use summations(not sure of the term) but i'm not sure on how it works with funtions(i'm using wikipedia and they don't develop much further than just that you can use them in summation)
Does anyone know where i could learn how to use summation with functions?
(Is this the right chat)

[jolly pebble]

I'm not sure what you mean by summation with functions

[versed mirage]

I'll try to take a screen shot of the thing

[jolly pebble]

Something like this: $\sum_{i=3} f(i)$?

[obsidian monolith]

daniel

[versed mirage]

Yeah

Exactly

[jolly pebble]

So what is your issue?

[versed mirage]

I'm just wondering how do i write the rest, like after

[jolly pebble]

As in what it's equal?

[versed mirage]

Yeah

[jolly pebble]

That example I posted is just $f(3) + f(4) + f(5) + \dots$

[obsidian monolith]

daniel

[mystic shell]

Hey uhh I need help understanding system of equations with and without substitution and process of elimination

In word problems

[versed mirage]

And for like the sum of all number in between two other number(such as 2 and 3)

?

[jolly pebble]

Then it's f(2) + f(3)

[versed mirage]

I meant more like in between those number,

[jolly pebble]

If it's from $k$ to $n$ it's $f(k)+f(k+1)+f(k+2)+\dots+f(n-1)+f(n)$

[versed mirage]

With like 2.3

[obsidian monolith]

daniel

[jolly pebble]

You can't use non integers in sums

It's always integers

[versed mirage]

Good to know

I'll need to find another way then, thanks for answering

[warm cove]

I studied so hard for my precalc test and this test I found it so easy it is geninually concerning for me as I don't usually find math a strong point for me

[jolly pebble]

How is it genuinely concerning that you're doing well

That's good

[warm cove]

Because I don't usually feel as confident like I did on that test

[jolly pebble]

That's good

Keep improving 👍

[warm cove]

[main glacier]

you can really only use these two

[muted turret]

Anyone have strategies for graphing these functions?

[atomic linden]

It aint fun when I start learning calculus.

[barren jewel]

Get the estimated values for f and g on the graph then use those values in the other function for example

Let’s say I have a graph the says the f value that equals 1 and g value that equals 2

Let’s take (f+g)(x)

We can add the f and g values together

[meager pilot]

guys i know grade 6 to 8 maths geometry algebra and trigonometry form youtube should i start learning precalculus??

[uncut mulch]

yes

[warm vector]

Why not, but I would also make sure you know deep into algebra very well first

[muted turret]

Not like knowing the y values of each x value BUT knowing an easier way to graph each function’s section

[barren jewel]

In that case idk

[sturdy hound]

look at the behavior of the graphs
for example g(x) has a larger negative value around the left of the graph, while f has a smaller value, and they both grow in size which means if you were to add them together the value would be large negative and then eventually grow to positive

[sturdy hound]

also not sure if this is going to help but these were the notes from my lecture that might be related

[terse aspen]

Hey if a function can algebraically be switched with the x and y and coefficients moved to the x side than is it a inverse thats all thete is to it?

[summer ruin]

inverse on what domain is a question worth considering

[terse aspen]

Hey can you pls walk me through this i must be dumb or smth

Nimber 14

[quiet hornet]

is there a command to rotate the image...

[terse aspen]

🤯

[quiet hornet]

the swimming pool is 8 feet longer than it is wide.
let w represent the width of the pool: the length of the pool is (w+8)

the pool is surrounded by a walkway of width four feet. the combined area of the pool and the walkway is 1280 ft³
if the walkway has a width of 4 feet, then we can find its dimensions including the pool by adding 4*2 to the width and length of the pool, so the area of the walkway and pool combined are (w+8)(w+16).

set this equal to 1280 and solve
(w+8)(w+16) = 1280

wish i could draw...

[terse aspen]

Would you add 4 twice to each measurement since 4 extends all around

[quiet hornet]

oh yeah

www

[terse aspen]

Wait im a dumbadd

Ss

[quiet hornet]

me too lol

[terse aspen]

Its 24 since the positive one and than just add to lengrh for length

Thats ok

[raven tundra]

Actually, calculus is overhyped. But if it's not your thing, I respect that

[sturdy hound]

u need to check after u get y by itself again by plugging either the inverse function into the original or the original into the inverse, if you get x then it is the inverse function,

also you can check using the horizontal line test on the original, if the function touches the horizontal line more than once that means its inverse function is not a function

[jagged patrol]

,rccw

[obsidian monolith]

Couldn't find an attached image in the last 10 messages.

Dec 14, 2024, 8:50 PM

[jagged patrol]

,rccw

[jagged patrol]

,rccw

[jagged patrol]

,rccw

[jagged patrol]

,rccw

[jagged patrol]

perfect

[unborn brook]

Is it wise to leave the conic sections for calculus itself rather than taking it during precalculus?

I've just checked and seen that Stewart's book has a section for conic sections, which doesn't really contain something that the section from the precalculus book doesn't.

[unborn brook]

So it appears like this is indeed an option

[modern valve]

I would just do whatever your class does. Are you self-studying?

[unborn brook]

Yep

[modern valve]

What's in the conic section part of your precalculus book

[modern valve]

I'd say it's probably up to you

it probably won't hurt if you skip it

[unborn brook]

"Rotation of axis" confuses me though. I can't see it in the index of Stewart's

[modern valve]

Don't worry about it

[unborn brook]

So it's covered?

[modern valve]

It won't prevent you from learning calculus