precalculus

[fast tinsel]

Using quadratic equation I also end up with x = (-3/4y) ± 5y

Which isnt even close

[trail badge]

I don't know how to calculate the roots with that

But I have an idea for factor out

Write 3xy as a difference

@fast tinsel

[fast tinsel]

I'm trying but don't quite see it

How would you write it?

[trail badge]

Like a even number

[uncut mulch]

how were you applying your quadratic formula?

[trail badge]

4, in this case 4-1

[fast tinsel]

x = (-3y/4) ±sqrt(9y²+16y²) @uncut mulch

[uncut mulch]

that's not quite how the QF works

[undone pawn]

the /4 comes for the whole thing

[fast tinsel]

0h no I see

Yeah of course

[uncut mulch]

$x \neq \frac{-b}{2a} \pm \sqrt{b^2 - 4ac}$

[obsidian monolith]

ramonov:

[fast tinsel]

Exactly

[trail badge]

Missing the 2a denominator

[undone pawn]

^

[fast tinsel]

Gotcha, thanks a bunch to all

[trail badge]

That equation is not a quadratic function

So you cannot use it

[fast tinsel]

Honest mistake haha

[uncut mulch]

wdym you cannot use it?

[trail badge]

Np ;)

What? @uncut mulch

[uncut mulch]

That equation is not a quadratic function
So you cannot use it

[trail badge]

Yeah

I'm not right?

[uncut mulch]

are you referring to the: 2x^2 +3xy - 2y^2 = 0?

[trail badge]

Yes

[uncut mulch]

you can treat it as a quadratic in x or y,
there's nothing stopping you from using the QF

[trail badge]

How/

You need a quadratic form ax²+bx+c

Or

a(x-b)²+c

[uncut mulch]

which it is.

[trail badge]

You have x² and y²

So, an ellipse

(I think)

[uncut mulch]

2x^2 +3xy - 2y^2 = 0 is a quadratic in x where:
a = 2
b = 3y
c = -2y^2

[trail badge]

Hum

But the graph is not a parabola

Let me see ahaha

,w graph 2x²-3xy-2y²

[obsidian monolith]

Display results online and refine query

Requested by ❄Digicat195❄#1491

[trail badge]

WHAT

[uncut mulch]

noone's saying the graph is a parabola

[trail badge]

But a quadratic equation is a parabola

95% of times

[uncut mulch]

generally if its the function of 1 variable yes.

[trail badge]

Ok

[uncut mulch]

but that doesn't stop you from applying the QF here

[trail badge]

I didn't know it

And do you get the roots with quadratic solver?

[uncut mulch]

doing if properly would get you
x = y/2 , -2y
which are the the solutions to 2x^2 +3xy - 2y^2 = 0

[trail badge]

Ohh

So y would be real numbers

[obsidian monolith]

❄Digicat195❄:

[trail badge]

Or something like that

[uncut mulch]

wdym by missing terms?
(also i messed up a few signs earlier)

[trail badge]

A, b and c

[uncut mulch]

2x^2 +3xy - 2y^2 = 0 is a quadratic in x where:
a = 2
b = 3y
c = -2y^2

[trail badge]

Oh ok

Nvm

[rare zephyr]

Just a question

is functional trigonometry calculus or precalculus

[willow bear]

tf is functional trigonometry

[echo plaza]

[fluid shore]

functional analysis.......for trigonometry?

[willow bear]

no

[fluid shore]

[odd helm]

I used sin to solve this but got +71 degrees. Why wouldn’t it work with sin?

[viscid thistle]

uhh, it should

[fluid shore]

Okay what are you even doing?

[viscid thistle]

maybe you forgot a sign

[fluid shore]

Your working is messy

Write it down on a piece of paper and things will become clearer

[odd helm]

That’s the key sorry

[warm crescent]

Using PMI

[willow bear]

induction, you mean.

[fluid shore]

What have you tried

[willow bear]

also maybe move

idk

[fluid shore]

Principle of Mathematical Induction

[warm crescent]

Yes

[fluid shore]

But yea Raftaar, go to a questions channel

[odd helm]

Basically it is saying the vector components for m+n is -4.4i + 13.35j

[fluid shore]

Tenemos is using this one

[warm crescent]

I am stuck on that inductive step

[viscid thistle]

@warm crescent If you don't know binomials, can you think of a way of writing 7 which is related to the number 3?

as dumb as that might sound

[odd helm]

And it wants the magnitude and direction

The magnitude is 14.07

[fluid shore]

I SAID MOVE TO A QUESTIONS CHANNEL

[odd helm]

Uh

[fluid shore]

Not you tenemos

[odd helm]

Ok

So to get the angle what I did was arcsin(13.3/14.07)

And got +71

But the answer key does arctan(13.3/-4.4)

Which gives -71

So are we only allowed to use tan when finding the direction of a vector using its components?

Because sin gave me a different answer than tan

[rigid sun]

,w arcsin(13.3/14.07)

[obsidian monolith]

Display results online and refine query

Requested by maleb1964#6739

[rigid sun]

,w arcsin(13.3/-4.4)

[obsidian monolith]

Display results online and refine query

Requested by maleb1964#6739

[rigid sun]

definetly not the same thing

@odd helm

doesn't even make sense because sin is odd

idk check all your work and make sure you're in degrees

[fluid shore]

What have I told you about working with math problems? Work in SYMBOLS, not numbers.

Get a general formula for whatever it is that you're calculating. It's simpler that way

Also, your diagram is way too small

Draw a bigger one

[rigid sun]

,w 1.238 radians to degrees

[obsidian monolith]

Display results online and refine query

Requested by maleb1964#6739

[rigid sun]

you sped

you literally got the same thing they did

@odd helm

I heard somewhere that finishing the math problem, then claiming you got a different answer than the answer key is much more productive than stopping halfway thorugh

probably from ann

but ann is crazy

[fluid shore]

No she isn't.

[undone pawn]

she's crazy smart

[rigid sun]

bro thats not the point

tenemos your answer is right

you just need to finish the problem

[willow bear]

[rigid sun]

[willow bear]

whomst out here calling me crazy

i agree with your quoted statement tho.

[echo plaza]

you agree that you're crazy?

am I missing something?

[odd helm]

Hold on you still got +70 when you did that though

When the answer key got -70 degrees

Afk

[willow bear]

no

i agree that finishing a problem and arriving at a different answer is generally more productive than giving up halfway through

[odd helm]

Wait when you say I didn’t finish the problem what was I supposed to do to complete it?

Or is this convo unrelated to me?

[rigid sun]

the answer key did not get -70 degrees

tHe AnsWer KeY gOt --70 DegReEs

[odd helm]

Well I mean if you look above it says -70 and they just added 180 so that it would be in the 2nd Quadrant since we have a negative x value and positive y for the vector components

Hm actually

The answer might be the same

It is nvm

I see what you mean now lol

[rigid sun]

thats what i said

lol

[odd helm]

Thank you

[harsh cipher]

hi all I got a question.

I have a question

when asked to find one coterminal angle between 0 and 2pi

can I add or subtract 2pi?

[stuck lark]

yes, add/subtract integer multiples of 2pi to your original angle

[patent beacon]

For example, 3π and π are "coterminal", which is that they have the same position on the unit circle

[harsh cipher]

but in my question it's pretty basic. So I need to be able to answer "n" being 1.

I'm at the beginning of this unit. "Radian measure" Angles in standard form

[stuck lark]

So I need to be able to answer "n" being 1.
context?

[harsh cipher]

addiing 360

[patent beacon]

u waht

You can post a picture if you'd like

[harsh cipher]

theta+ n (360). when theta is in degrees

360 degrees

why can't I subtract 2pi for question B

[stuck lark]

bc that doesn't change the original angle to smth between 0 & 2pi

[jaunty mason]

The cubic equation $x^3 - x + 3 = 0$ has roots $\alpha$, $\beta$ and $\gamma$, determine the value of $\alpha^3(\beta + \gamma) + \beta^3(\alpha + \gamma) + \gamma^3(\alpha + \beta)$

[obsidian monolith]

Tāhā:

[jaunty mason]

Don't know where to begin on this one ^

[valid violet]

I wonder if you use alpha+beta+gamma=0 and alpha.beta.gamma=-3

Maybe if you distribute it will simplify

,w expand a^3(b+c)+b^3(a+c)+c^3(a+b)

[obsidian monolith]

Display results online and refine query

Requested by gfauxpas#9497

[valid violet]

Yes @jaunty mason do you know vietas formulas

That's how you do it

[jaunty mason]

i do

i tried expanding it too but couldn't figure out where to substitute the values i obtained from vieta's formulas

@valid violet

[valid violet]

Well for each of (b+c),(a+b),(a+c)

You can use a+b+c=0

[jaunty mason]

what

[valid violet]

b+c=-a for example

[jaunty mason]

ah

wow i get it

big brain

[rare zephyr]

Help with no.6

[willow bear]

@rare zephyr what is giving you trouble in 6?

[rugged nimbus]

Nvm

[fluid shore]

Fluffy, still need help?

Yeet yourself over to one of the questions channels and ping me

[rugged nimbus]

Okay

[willow bear]

welp, flexman is offline

[fluid shore]

Don't worry, he'll come over soon

Either that or he'll leave the server, angry that you weren't there to give him a solution to his homework problem.

🙂

[rare zephyr]

@fluid shore i was just trying to find some details that I might have missed

@willow bear pretty sure it aint supposed to go this way

[willow bear]

are you seriously using the sum formula on TWO TERMS???

[fluid shore]

No okay look

[rare zephyr]

what

[fluid shore]

What are you doing there?

Your working seems to be all over the place

You have to be systematic

[willow bear]

i mean, there is nothing wrong with it from a mathematical standpoint, but TWO TERMS? come on

why not just

[rare zephyr]

I mean this aint supposed to be homework

[willow bear]

write those two terms

and a plus sign

inbetween

[rare zephyr]

a + ar = 5

?

[willow bear]

ar^2 = 16
a + ar = 5

yes

just like that. without any overcomplications

[rare zephyr]

ahhh got it

I got the answer now

[willow bear]

see all you had to do was use your think pan for a moment instead of plunging forward with formulas whose purpose you understand only hazily

[sacred osprey]

Is there a way to find the inverse of the function
\
$\vfunc{f}{(-1, 1)}{\bR}{x}{\frac{x}{1-x^2}}$?

[willow bear]

by defn? lmao

[obsidian monolith]

Karteufel:

[valid violet]

Set y=f(x) and solve for x=f-¹(y)?

If it is indeed invertible

[sacred osprey]

No offense, but that's not very helpful. It's like saying "just take the inverse! Unless you can't." I understand the basic idea of how to find an inverse. However, I'm stuck on this particular function. I believe it's bijective on the given domain, but it isn't for all reals

[valid violet]

Are you trying to find its inverse or prove it has one?

[sacred osprey]

Find it

[valid violet]

Bijectivity is a statement about the domain and codomain

Idk what you mean by bijective but not on all reals

Anyway, if you're convinced it has an inverse

Write down

y=x/(1-x²)

And solve for x using algebra

[sacred osprey]

I mean function with the domain $(-1, 1)$ (the given domain) is bijective, but the same function with the domain $\bR$ is not bijective

[obsidian monolith]

Karteufel:

[valid violet]

That need not concern us

That would be a different function

[sacred osprey]

The algebra is where i'm having the trouble

[valid violet]

If you have an equality a=b/c

How do you write the same eqn without fractions

Algebra i

4=5/t solve for t

[sacred osprey]

I know how to do basic algebra. It's getting it to the form $x = g(y)$ where $g$ is a function that i'm having trouble with. Essentially, separating the variables appropriately. The polynomial equation i'm dealing with is $x^2y+x-y=0$

[obsidian monolith]

Karteufel:

[valid violet]

That's just a quadratic in x

Factor it

[sacred osprey]

I think that's the insight i was missing! I'll give it a shot. Thank you!!

[valid violet]

Good luck

Idk how easy it will be

[sacred osprey]

I didn't bother factoring. Used the good old quadratic formula and it worked like a charm. I feel so dumb not having seen the quadratic equation staring me in the face 😅

Thanks a billion

[valid violet]

I meant quadratic formula when i said factoring

You just need to figure out whether + or - gives you the right solution

Np

[rugged nimbus]

Hey i wanna ask

Is this correct?

Or shud i put all the fraction in front?like:

1/2.4/5 (sinh2x-cosh2x)
??

[fluid shore]

Do you think that's correct

Like, okay, consider what you just said about removing the fractions. Is your expression, as written above, correct?

[rugged nimbus]

Ya?

I can put the fraction in front or not?

I dont think i can continue

[fluid shore]

What the fuck are you doing

[rugged nimbus]

-_-

[fluid shore]

lmao okay, you are not wrong when you want to put them over a common denominator

[rugged nimbus]

Me always wrong

[fluid shore]

However, check your arithmetic

For example:

$\frac{4\cosh(2x)}{5} = \frac{4e^{2x} + 4e^{-2x}}{10} = \frac{8e^{2x} + 8e^{-2x}}{20}$

[obsidian monolith]

Abhijeet Vats:

[rugged nimbus]

Lol

I jusy realize

[fluid shore]

You made a mistkae going from your 2nd line to your third line

Yea

So, fix it and place paratheses at the appropriate locations

[rugged nimbus]

Okayy

[fluid shore]

Keep track of your negative signs

That's what i meant by arithmetic

Lmao

[rugged nimbus]

Nice thanks hahaha

So i cant put the fraction in front isnt it? @fluid shore

[fluid shore]

Not in the way that you did

But i don't see the point, putting it over a common denominator is simple enough

[rugged nimbus]

[fluid shore]

❤️

Good luck on the problem

[rugged nimbus]

Can i ask again

[rugged nimbus]

Help

[summer monolith]

How do I go about solving this equasion? Wolfram gives no steps for it.

[willow bear]

the left hand side is a product of several things

and the right hand side is zero

you should know how to deal with equations of this kind

[summer monolith]

I think I've figured it out.

[willow bear]

you did.

[summer monolith]

kewl

[fluid shore]

When someone else asks a question, do not just interrupt with your question.

[summer monolith]

sry

[fluid shore]

@rugged nimbus what is your question?

[rugged nimbus]

Is that correct?? I mean the formula and all.. I know some number i wrote it wrong

Confuse how to let
y = 2 arcsin x

[fluid shore]

2(A+B) is not pi/2

Not as you have defined A and B

[rugged nimbus]

But Pi/2 is given in question

[fluid shore]

Yes but it’s actually 2A + B = pi/2

Not 2(A+B)

[rugged nimbus]

So i multiplied both sides with cos right?

[fluid shore]

Also, cos(2A+B) = cos(2A)cos(B) -sin(2A)sin(B)

[rugged nimbus]

Ohh okay

[fluid shore]

You wrote sin(A)

Try it again and make your working less messy

Leave a line between each statement

Then you’ll be able to spot mistakes easily. It’ll also be clear to you

[rugged nimbus]

I will.. i was very confused i wrote eveything n come up with that result still wrong haha

Thanks btw

[fluid shore]

Of course you’ll be wrong

[rugged nimbus]

Almost had a bad day

[fluid shore]

With that kind of presentation, it’s no wonder you’re not getting questions right.

[rugged nimbus]

Im sooo clueless tbh

[fluid shore]

I’m being very serious here; good handwriting is half the battle won.

[rugged nimbus]

Got it

[fluid shore]

,rotate

[fluid shore]

Okay what do you want to do?

[candid lake]

Find the sum

[fluid shore]

Okay how are you gonna do it?

[candid lake]

?

[fluid shore]

Don't question mark me

What's your approach

What are you confused about

Etc etc

[candid lake]

I already subbed the formula for k^2 n k

[fluid shore]

Okay

And?

[candid lake]

I'm not sure what to do with the 2

[fluid shore]

Well, think of it this way

For each term in the sum

You have a 2 that's added in

Like there's no change to it or anything

You just have 2 added in n times

So what happens to that?

[candid lake]

Remains 2?

[fluid shore]

,rotate -90

FUCK

[fluid shore]

Okay so now you have that summation right

And for every possible integer k from 1 to n

You have 2 for each term

How many 2s are there?

[candid lake]

2n

[fluid shore]

There are 2n 2s?

[candid lake]

You have 2 for each term, last integer is n

[fluid shore]

So the sum is 2n?

[candid lake]

Yea

[fluid shore]

Good, now start simplifying

[candid lake]

Something like this?

[winged blaze]

"Don't question mark me" lmao why you gotta be an ass

[hard hornet]

?

[winged blaze]

just quotting Abhijeet above, that's how he responded to someone

[fluid shore]

I’m not an ass

I’m a nice guy

@candid lake that certainly looks correct

[winged blaze]

I don't doubt you are great at your craft, and we appreciate you helping people out here in this room, but here's some advice -- nice people don't talk like this

[fluid shore]

🙂

[gentle vigil]

I don't see anything wrong with it tbh

[serene heath]

really making a mountain out of a molehill here

[fluid shore]

mountain out of a molehill, lemon

Lel

[candid lake]

Thanks for the help

[serene heath]

u saw nothing

[candid lake]

I'm pretty used to that so I don't pay much attention to it

[winged blaze]

lol

[fluid shore]

No worries

[harsh cipher]

hi guys

how do you find point p without cos, sin

[valid violet]

why dont you want to use cosine and sine

[harsh cipher]

In the video. The instructor seems to have gotten those numbers without them.

by going to "x coordinate" and "y coordinate".

I got confused how he got those numbers without using cos and sin

-_-

[valid violet]

the usual way to do this is to find the equivalent angle in quadrant I where you know sine and cosine and then adjust according to sign in quadrant III

[harsh cipher]

well this is what he did...and I did not get that...

[uncut mulch]

x-coord = cos(220°)

it is very likely that they used trig

seeing as how the title is "sine - cosine functions"

[candid lake]

The answer was correct
I just had to simplify it
U guys r wizards

[rugged nimbus]

Anyone know how they multiply it then came out with that result

[willow bear]

$\frac{1 - 4t^{-2}}{2 + t^{-2}}$

[obsidian monolith]

Ann:

[willow bear]

are you able to simplify this so that there are no more negative powers

this is just algebra

[rugged nimbus]

I change negative powers become fractions?

[willow bear]

what do you mean "change negative powers"

[rugged nimbus]

Like t^-2 become 1/t^2

[willow bear]

okay, sure, you CAN do that. this will leave you with $\frac{1 - \frac{4}{t^2}}{2 + \frac{1}{t^2}}$

[obsidian monolith]

Ann:

[languid crane]

how is this precalculus

[rugged nimbus]

Okay thanks

Wait ill try

[willow bear]

you seem to be under the impression that there is always one and only one thing you "have to" do when seeing a given algebraic relation

[rugged nimbus]

Kinda confuse, yes

[willow bear]

and as such you ask, "[do] i [have to] do such and such?"

...

is English not your native language?

[rugged nimbus]

Not

Why

[willow bear]

what is your native language, if you don't mind sharing

it looks like there's a language barrier here

[rugged nimbus]

Yah haha

Somewhere in asia

I just not yet familiar with some words

Wow i found it thanks @willow bear

@languid crane i hate math but tried my best >:00

[languid crane]

its good

dw

[zinc haven]

can anyone help me wrap my head around this? i've tried to log both sides but it didn't really get me anywhere

xlog(a)=ylog(b) and wlog(a)=zlog(b)

[rigid beacon]

is it A?

@zinc haven

[zinc haven]

no, the correct answer is E

[rigid beacon]

damn

not sure how they got that rip

[serene heath]

what happened after u took logs?

[zinc haven]

this is the solution but I don't get it

i just have those two equations but I don't know what to do from there

[serene heath]

can you isolate lna/lnb?

[zinc haven]

that's actually a good idea i'll try it

it works! thank you!

[viscid thistle]

wdym by isolate?

[pale bison]

Solve for lna/lnb

[plain lake]

combinatorics is just systematic counting

basically

so a asks you to count how many unique combinations of prime factors are there, and b,c ask which do and do not contain 2

you've done choose before right

so if there were no repeats, like say we had 2,3,5,7 as prime factors no repeats

then our factors would be the total number of ways to write these numbers, or the total number of ways to choose combinations of these numbers of length 1-4

or for example, 4C1 of length 1, 4C2 of length 2 etc

[fleet granite]

48

Add 1 to the exponent of each prime

Then multiply

[plain lake]

i mean yes but also the questions says with combinatorics

also if you're gonna use that you probably want to prove it or have proven it

i mean it's not long but like

it's basically just a streamlined version of the combinatorially argument that doesn't need to use choose i guess

yes

so

you agree that each divisor of 5880's prime factorization must only contain prime taken out of it's prime factorization, and for each prime it can't appear in the divisors factorization more times than it appears in 5880's prime factorization

so our question can be reframed from how many divisors are there of 5880, to how many unique ways can we choose 1,2,3,4,5,6, or 7 numbers from {2,2,2,3,5,7,7}

uh

not really sure what that means

so like 3 * 5 * 7 would be an example of like a divisor with 3 prime factors

a way to count these with 3 prime factors is to say we're choose 3 numbers out of that list above to multiply

so for length 3 it'll be 7C3-repeats

if we had all distinct prime factors, which we do not

you subtract off how many of those triplets are going to be repeats

so like for example 7 * 3 *2 will appear 6 times

uh no also wait

i just realized this is gonna be hyper messy without multiset

i mean there is another way that's much nicer that pan pan eluded to earlier

i mean yes this is correct

i thought you had to use choose tho

i mean yeah that's the smart way to do it

that's kinda combinatorics ish

[fleet granite]

Basic Olympiad math

Lol no

[plain lake]

why'd you go down in level

[fleet granite]

Idk it’s Olympiad

Sort of

[plain lake]

olympiad is like hs but not really

as far as a level you could learn it reasonably early

but it's not really taught in school at all

[fleet granite]

No

Yep

[odd helm]

Shouldn’t the domain be (-4, infinity)?

Idk why it is -4/3

[fluid shore]

Okay when is the square root of something not defined

[odd helm]

When it is a negative inside

But it wants me to graph

[fluid shore]

Okay so for what values of x is it the case that 7x+4<0

[odd helm]

-4/7

[stuck lark]

values not single value

[odd helm]

Oh yeah it’s x<-4/7

[fluid shore]

Okay so we can agree that when x>= -4/7, the square root is actually defined?

[odd helm]

Yeah

[fluid shore]

So what can you conclude from that?

[odd helm]

That the domain is [-4/7, infinity)

[fluid shore]

Cool

[odd helm]

But the domain in the key said -4/3

[fluid shore]

Do you think that's correct?

Suppose I plugged in -4/3 for x, right? So, i will get:

$\sqrt{7 \cdot \frac{-4}{3} + 4} = \sqrt{\frac{-28}{3} + 4} = \sqrt{\frac{-16}{3}}$

[obsidian monolith]

Abhijeet Vats:

[odd helm]

Yeah that doesn’t work

[fluid shore]

Mmh

[odd helm]

Alright thank you

I knew that the key was probably wrong just wanted to make sure

[viscid thistle]

one of these days someone should try [x,infinity]

see what happens

[fluid shore]

No u

[summer monolith]

Why this sinθ*cosθ stands without brackets? It's supposed to be 2(ab). Not 2ab. Isn't it?

sinθcosθ+sinθcosθ

[willow bear]

what's wrong with $2ab$

[obsidian monolith]

Ann:

[willow bear]

what's wrong with writing a product of three things of which the first happens to be the number two

[summer monolith]

I thought 2(ab) is not equal 2ab

[willow bear]

then what did you think the difference between those was?

[summer monolith]

Haven't thought about it yet

[willow bear]

if you thought $2(ab) \neq 2ab$, then surely you must've had some ideas about their values and concluded that they must have been different

[obsidian monolith]

Ann:

[willow bear]

you're either ignorant of or have forgotten the fact that multiplication is associative, and as such $(2a)b$, $2(ab)$ and $2ab$ all refer to the exact same thing, the parentheses being entirely redundant

[obsidian monolith]

Ann:

[summer monolith]

What I thought is that a 2 needs to be put behind brackets in sinθcosθ+sinθcosθ

[willow bear]

so what you're saying is that you don't know the true purpose of parentheses

[summer monolith]

Whatever. I seem to be a retard. Things escape my head as soon as I learn them.
Pls be patient with me.

[willow bear]

the true purpose of parentheses is to indicate which operations are to be done first

that's it, really

sometimes this indication will line up with what the standard order of operations (encoded by mnemonics such as GEMA, PEMDAS or BODMAS) dictates; in this case, the parentheses may be removed

sometimes it won't, and then the parentheses are necessary

internalizing that simple fact ought to make some things click into place

[viscid thistle]

i think he means

$a = \sin \theta$ and $b= \cos\theta$

[obsidian monolith]

mop:

[viscid thistle]

and he's asking why they didn't write $\sin(\theta)$ and $\cos(\theta)$

[obsidian monolith]

mop:

[viscid thistle]

actually maybe not lmao

[summer monolith]

Found the PEMDAS and BODMAS.
As for the GEMA...

[fluid shore]

Why are you doing calculus if all this isn’t clear to you?

[summer monolith]

Not all
I used to be good at it at colledge
4 out of 5 final mark
Besides it's a precalc section

[uncut mulch]

Grouping
Exponents
Multiplication
Addition

[summer monolith]

thks

[summer monolith]

Why did they put the multiplier X inside of the expression of S instead of the way I did?

[clever inlet]

looks like an error

considering what they did on the next line

[willow bear]

looks like the ] and the x accidentally swapped places

[summer monolith]

Good. At least it wasn't me being this time.

[summer monolith]

Can you confirm that these are misprints as well?

Getting somewhat paranoid about missing something

[fluid shore]

Yea they look like misprints

[summer monolith]

Thks

[trim fable]

how would u do #2?

[languid crane]

What do you think?

[trim fable]

uh

c=1.25x(8/100) ?

@languid crane

[languid crane]

what is l(d) ?

And are you using x for multiplication

If you are, pls stop

[trim fable]

oh ok

L=8.0 (d/100)

[languid crane]

ye

[trim fable]

or should it be L = d(8/100)

[languid crane]

what do you think?

You’re supposed to have a composite function

[trim fable]

tbh im trying to

self teach myself this

before school starts and

ye i have no clue on what this stuff is

sooooooooo

[languid crane]

what’s exactly the problem?

[trim fable]

that im trying to learn this

[languid crane]

yeah?

[trim fable]

lol

oh uh u can teach me?

[languid crane]

i can try, yes

[trim fable]

ok yay

coz we usually copy examples out teacher does and then we do the homework ourselves so

[languid crane]

What are you studying from?

[trim fable]

i was trying to do the lesson on my own

class notes

[languid crane]

I see

[trim fable]

like the thing i sent is the note

[languid crane]

U have a textbook?

[trim fable]

yeah

advanced functions

[languid crane]

Okay so

I’m assuming you know what a composite function means, right?

[trim fable]

no

i dont

lol

[languid crane]

Maybe you should look into that first?

[trim fable]

ok

oh ok so

its a function that depends on another

ok so i use my first equation in number 2?

so would it just be

that equation times 1.25?

[languid crane]

No

[trim fable]

oh

[languid crane]

Oh actually

It would

sorry

[trim fable]

OH

Lol no need to say sorry

[languid crane]

My mistake

[trim fable]

so it would be:
C=1.25 [ 8(d/100)] ?

[languid crane]

c(l(d))

[trim fable]

ye

[languid crane]

yes?

[trim fable]

yes

it would be that

[languid crane]

Do you need anymore help or you’re ok for now?

[trim fable]

hmm

would this be right?

also what is #4 asking

[languid crane]

no?

The costs aren’t right

[trim fable]

oh

[languid crane]

nvm dude

[trim fable]

oh

[languid crane]

They are

[trim fable]

ok

[languid crane]

Sorry for confusion it’s midnight here

And I’m kind of tired

[trim fable]

oooof

aww u should sleep

[languid crane]

Nah

[trim fable]

u should

is it winter break for u?

[languid crane]

Last night stayed up til 2am 🥺

Amd ya

What do you think 4 means

@trim fable

[trim fable]

oh

c=1.25(d(l))

[languid crane]

U mean l(d)

?

[trim fable]

oops

so #5 is

so i just write an equation?

[languid crane]

Uh

What it says

[trim fable]

so like

is that what it wanted?

[languid crane]

Uh...

Not sure, probably not

[trim fable]

oh

why not

[languid crane]

”#4. Write an equation of the Cost C in terms of the distance driven d by using substitution”

[trim fable]

yes

which was

[languid crane]

Do that

[trim fable]

c=1.25[l(d)]

was it not?

[languid crane]

plug into the l(d) eq

?

[trim fable]

c=1.25[8(d/100)]

[languid crane]

simplify it maybe

[trim fable]

oh

10d+1000

[languid crane]

No

[trim fable]

hmm

[languid crane]

Whats 8(d/100)

?

[trim fable]

8d+800

?

8d/800

[languid crane]

Where did you get that from?

[trim fable]

LOL

my brains in winter break mode

lol

idk

[languid crane]

Why would it be 8d/800 ?

Explain it

[trim fable]

coz ur

distributing the 8

to d/100

[languid crane]

What is 8 times d?

[trim fable]

8d

[languid crane]

And what is 8 times d/100?

[trim fable]

8d/100?

[languid crane]

Yes

Now multiply that by the 1.25 in the cost equation

[trim fable]

oh

i see my mistake now 😛

silly me forgot how to multiply thats super sad

[languid crane]

what do u get?

[trim fable]

i got

10d/100

[languid crane]

yeah u can simplify that, right

[trim fable]

d/10

[languid crane]

yeah

Now u can do 5 and 6

[trim fable]

so all i had to do was

use c=d/10

[languid crane]

Ya

[trim fable]

oh

ok

@languid crane

it would just be the same values as

the second column

[languid crane]

yes

[trim fable]

do write the equation or

value?

[languid crane]

More precisely third column

[trim fable]

then what about

the second one?

[languid crane]

?

[trim fable]

what do i put in that one

[languid crane]

Which one

[trim fable]

ok so

value in second but

equation in third?

like this?

example^

[languid crane]

C=50/10 = 5?

[trim fable]

yes

[languid crane]

c(d) i think now

Like C(d) = d/10 is the actual eq

[trim fable]

ye

ima take a break cya

[languid crane]

i’m gonna sleep

Cya

[trim fable]

how would u do this

can anyone help me with that

[clever inlet]

which part

[trim fable]

example 1

a

[clever inlet]

what have you tried

[trim fable]

oh ill show u

im actually trying to self teach myself this

before school starts again

so ye i wasn't taught this yet so im just learning this stuff from here 🙂

[clever inlet]

ok

[trim fable]

idk if thats right

@clever inlet

[clever inlet]

if you are doing part a)

[trim fable]

yeah

[clever inlet]

then the first set should be the domain of g

[trim fable]

oh

ok

so

-3
2
7
5
11

right?

[clever inlet]

yep

second would be the range of g

[trim fable]

ok

1
5
3
-1

[clever inlet]

yes

[trim fable]

now?

[clever inlet]

now

[trim fable]

domain of x in the second one?

[clever inlet]

let's go from set 1 to set 2 to set 3 with one element

[trim fable]

oh

what do u mean

[clever inlet]

let's take element 7 in set 1 (our domain for g)

[trim fable]

ok

[clever inlet]

what element does it map to in set 2 (our range for g)?

[trim fable]

5

[clever inlet]

yep

[trim fable]

so u meant

draw lines

[clever inlet]

and what does 5 map to in set 3?

[trim fable]

right

[clever inlet]

yes

[trim fable]

ok

done

wait i should

organize the numbers from

lease to greatest first right?

[clever inlet]

it doesn't really matter

[trim fable]

ok

[clever inlet]

but it can be nice to do so

[trim fable]

ill keep it

like this

to make

things simpler

ok s

now what

[clever inlet]

from set 1 to 2

you have 7 -> 5 right?

[trim fable]

yes

[clever inlet]

what should 5 in set 2 map to in set 3?

[trim fable]

uh

3?

i dont have any

numbers in

set 3 tho

[clever inlet]

look at f

[trim fable]

oh

1

[clever inlet]

yes

[trim fable]

oh so u write the range of

[clever inlet]

so you have 7 - > 5 -> 1

[trim fable]

x in set 3

[clever inlet]

so we know that

f(g(7)) = 1

[trim fable]

oh

[clever inlet]

and so (7, 1) is an element in f o g

[trim fable]

oh..

[clever inlet]

the entire idea is

starting from elements in the domain of g

[trim fable]

oh ok

[clever inlet]

let's call the element a

[trim fable]

ok

[clever inlet]

find g(a)

and then plug this new number into f

f(g(a))

[trim fable]

oh

so for this

it has 3

uh

f(g(x))'s?

so at

f(g(7))=1

f(g(5))=2

f(g(11))=8

only 3?

@clever inlet right?

[clever inlet]

that looks about right

[trim fable]

oh ok

but im still kinda

confused on

the relationship

between these numbers

[clever inlet]

what do you mean?

[trim fable]

like

what does f(g(7))=1 mean

for example f(6)=1 means that y=1 when x is 6

so for this it means

is it combined?

2 functions

im confused now lol

[clever inlet]

yes

the idea is

[trim fable]

oh

[clever inlet]

you are kind of piping the output of g straight into f

[trim fable]

oh

ohhhh

ok

i get what u mean

ok

but thinking about it

can be confusing coz

idk lol

i guess practice will help

so then

[clever inlet]

yeah

[trim fable]

what would this be for that

[clever inlet]

well from your previous working

[trim fable]

f x g = f(g(x))?

domain is 7,5,11

[clever inlet]

you know that (f o g)(x) = {(7, 1), (5, 2), (11, 8)}

yep

[trim fable]

and range is 8,1 ,2

[clever inlet]

yep

[trim fable]

ohhhhh ok

ohhh okk

makes sense thanks

oh so this was for

fxg

so gxf is different right

[clever inlet]

yep

same process though

[trim fable]

oh ok

[clever inlet]

probably shouldn't use x as the symbol here

[trim fable]

why

so first set according to the diagram is

domain of g would it be

the same as the previous question

-3
2
7
5
11

[clever inlet]

open circle is pretty much the general accepted notation for function composition

[trim fable]

oh

ok

[trim fable]

u mean the

green area?

the circle?

can u work through this with me too?

[clever inlet]

ok

[trim fable]

yay

do u have time tho

[clever inlet]

yeah

[trim fable]

iif ur busy

u dont have to

ohhh ok

[clever inlet]

start with the domain of f

[trim fable]

oh

[clever inlet]

since for g o f

we are first putting some number into f, getting this output, and piping it into g

[trim fable]

oh ok

why does it say

domain of g then?

is that wrong

[clever inlet]

that sample is for f o g

[trim fable]

oh ok

[clever inlet]

if you are doing g o f, then it's different

[trim fable]

wait so

i can still use the same format

[clever inlet]

yes

[trim fable]

like the first diagram?

[clever inlet]

yes

[trim fable]

when do i use

the second one?

[clever inlet]

they're just different representations of the same thing

[trim fable]

oh ok

[clever inlet]

the second one is more detailed

[trim fable]

oh ok

can i try this one

with that format

[clever inlet]

ok

[trim fable]

ok yay

so first set is

domain of f

[clever inlet]

yes

[trim fable]

ok

😛

so it would be

-2
-1
5
6
3

[clever inlet]

yes

[trim fable]

oh ok

so now what

[clever inlet]

find what they map to in set 2

[trim fable]

uh

what do i put into the green

circle?

[clever inlet]

i would probably draw the circle afterwards

[trim fable]

oh

so just do set 1 rn

will it go outside the circle?

[clever inlet]

just try draw the mappings into set 2 first

the green circle would be the element in set 2 that also map to some element in set 3

[trim fable]

huh

im confused :C

[clever inlet]

for part a)

when you did mapping from set 1 to set 2

there were elements in set 2 that didn't map to anything in set 3 right?

[trim fable]

yes

so that would go into

the green circle?

[clever inlet]

if they do not map to set 3

they would belong in the larger oval, but outside the green circle

[trim fable]

i guess ill use the same method as the first

oh ok

ohh ok

thats the only difference ok

i understand

ok i did it

[clever inlet]

nice

[trim fable]

Domain of gxf= 3,6

range = 1,5

right?

@clever inlet

[clever inlet]

looks right

[trim fable]

oh yay

ok

oh ye

i have a question so like

i drew both the functions

but then how would u know what f(g(x)) would be?

[clever inlet]

ok

for any value x

what's the output of g?

[trim fable]

see thats the graph

uh

idk ;-;

its range?

[clever inlet]

g(x) = 3x - 2 right?

so you want to find f(3x - 2)

[trim fable]

yes

@clever inlet

[clever inlet]

how do you find it?

[trim fable]

uh

idk :C

[clever inlet]

well

f(x) = 2x + 1

[trim fable]

hmm

would u

[clever inlet]

how would you evaluate say f(3)?

[trim fable]

make 2x+1=3x-2?

then

oh nvm