precalculus

[tired cedar]

wait nvm x is pi/3 lmao

idk maybe try just npi +/- pi/3

[quartz garnet]

Uhm

You did it right but

pi/3 + n pi, and

-pi/3 + n pi

you forgot the plus sign lmao

😂

[hasty wadi]

WHAT

FUCK

WHAT

BRUHHHHHHHHHHHHHH

[quartz garnet]

HAHA

[hasty wadi]

omlllllllllllllllll

omfg

god, please give me strength

omfg

FUCK WEBASSIGN

I HATE THIS BULLSHIT

[quartz garnet]

👍🏼

[final sigil]

Typical webassign.

[tight mango]

hi

can i get help here

hm

[viscid thistle]

[fringe stream]

$$\cos(A)\cos(B) + \sin(A)\sin(B) = \cos(A - B)$$

[flat vine]

i got it a while ago thanks

[fringe stream]

👍

[thick raptor]

kek

[viscid thistle]

Hey I’m really struggling in pre cal and I have an exam on Thursday but I’m pretty confused. Would someone be willing to get on voice chat with me later tonight (like maybe in 3 hrs or so) and help me with the study guide?

[fringe stream]

@viscid thistle sure! let me know when you want to vc. i'll try my best.

[viscid thistle]

@fringe stream hey thanks. I’m really having a bad day. This course is really stressing me out. I really appreciate it!

[fringe stream]

no worries. hope i can be of help.

[viscid thistle]

How much time would you have about? I don’t need too much

[fringe stream]

i'm pretty much free for the rest of the day today.

[viscid thistle]

Oh ok cool!

[brisk zealot]

?

[hasty wadi]

sorry

it's cot is less than 0

not csc

COS*

sorry

fml

[brisk zealot]

my bad what you need helpwith exactly?

[hasty wadi]

check if the 6 trig identities are right pls

[brisk zealot]

k

so

am i the dumb one

[fringe stream]

sec(x) would be negative.

[brisk zealot]

you put this into a calculator

[fringe stream]

csc(x) would be positive.

[brisk zealot]

oh he means the signing

[fringe stream]

look at your cot(x).

it's negative.

so it's either quadrant II or IV.

but you also said cos(x) < 0.

so it has to be quadrant II.

[hasty wadi]

i made the triangle in quadrant 2

[fringe stream]

in the second quadrant, sine/cosecant are positive.

cosine/secant are negative.

[hasty wadi]

sorry

[fringe stream]

and tangent/cotangent are negative.

[hasty wadi]

i think i fucked up the negatives

[fringe stream]

evaluate your answers accordingly.

[hasty wadi]

brb, lemme update it

cot is already negative in the given answer

that's why there isn't any red negative

but this should be right no?

[fringe stream]

it is correct now.

[hasty wadi]

yay 😄

[fringe stream]

just look at which quadrant x would lie in.

[hasty wadi]

x?

the central angle?

[fringe stream]

yeah, your angle.

[hasty wadi]

ah

that's what i usually do

[fringe stream]

like, if everything is positive, then it would be quadrant I.

you know the ASTC.

[hasty wadi]

before i start evaluating i usually check which quadrant i draw my triangle

yeah i know CAST

but thanks for the help 😃

[fringe stream]

😄

[calm whale]

CAST

ALL STUDENTS TAKE COCAINE = ASTC

[hasty wadi]

lmao

[fringe stream]

🔨

[calm whale]

THERE IS NOTHING WRONG WITH DOING COCAINE, also the acronym is great as it helps you remember it :^)

[hasty wadi]

is my work right here?

im trying to simplify

[tropic current]

isn't cot just cos/sin though

no need to do all of that

[hasty wadi]

i did it by identities

im stupid lmao

i didn't notice that

but thanks for the input

but is the work right over all?

@tropic current

[tropic current]

parentheses sorta ambiguous but...yes

checks out.

@hasty wadi

[hasty wadi]

lol thanks dude 😄

[hasty wadi]

is my work correct here?

[delicate fractal]

=pup csc(x)^2 - 1

[granite stirrup]

Query made by @delicate fractal
Data sourced from Wolfram|Alpha: http://www.wolframalpha.com/input/?i=csc(x)^2+-+1
Do more with Wolfram|Alpha Pro: http://www.wolframalpha.com/pro/

[delicate fractal]

oh it doesn't simplify

[hasty wadi]

its a pythagorean identity i think

[granite stirrup]

Query made by @pine kindle
Data sourced from Wolfram|Alpha: http://www.wolframalpha.com/input/?i=simplify+1%2F(csc(x)+%2B+1)+-+1+%2F+(csc(x)+-+1)
Do more with Wolfram|Alpha Pro: http://www.wolframalpha.com/pro/

[hasty wadi]

-2tan^2x ?

wtf

i posted a pic of my work

[delicate fractal]

yeah csc^2 - 1 is cot^2

not tan^2

[hasty wadi]

idk what i did wrong? 🤔

[delicate fractal]

let me show you

[hasty wadi]

ohhhhhhhhh

i did the wrong identity

[delicate fractal]

$$csc^2 - 1 = \frac{1}{sin^2} - \frac{sin^2}{sin^2} = \frac{1-sin^2}{sin^2} = \frac{cos^2}{sin^2} = cot^2 $$

[hasty wadi]

ahhhhh

[delicate fractal]

I'd suggest you not to memorize the identities blindly, but try to work in terms of sin and cos

so then you don't make that kind of mistake

[hasty wadi]

i got a quiz tomorrow so im trying to memorize it

but it sucks

lmao

[delicate fractal]

yeah it all comes down to sin^2 + cos^2 = 1

[hasty wadi]

can you explain what you mean by "divide thru by"

wait wait wait

lemme do this on paper

lol

[hasty wadi]

ohhhhhhhhhhhhh

fuck dude

that's crazy

[hasty wadi]

LOL I DIDN'T EVEN KNOW THAT, OMFG THAT'S AMAZING

bruh, im gonna have to get a hold of this new method

this is blowing my mind

yeah but we never really went in depth with them

it's something we have gone over tho

yes

lmao, you already blew my mind once

[hasty wadi]

bruhhhhhhhhhhhh wait what?

how does that even work?

fmllll oml

[delicate fractal]

lmao that's too much

[hasty wadi]

tbh, im like so confused as to how y'all use the mathbot so quickly

how do y'all input all that shit into it so fast?

[delicate fractal]

it's in a language called "latex" which mathematicians use a lot

people are used to it

[hasty wadi]

ahhhh

lmao

that's pretty wild

[hasty wadi]

omfl

just from that one tiny formula

smh

teacher: "how the fuck did you get that formula, where's the proof?"
me: "uuhhhhhhh, no u"

proofs are garbagio dab

[calm thicket]

I know how to do this easily with Law of Sines, but this unit is on trig and I think they want me to use some shortcut with the reciprocal functions, anyone aware of such?

[delicate fractal]

well 30 degrees is a well known angle

[calm thicket]

oh wait sorry if I'm interrupting a convo

:p

@delicate fractal this is tru-

oh wait

divide by sqrt(3) to get y

[delicate fractal]

yeah

[calm thicket]

multiply y by 2 to get r

ez

[delicate fractal]

sometimes things are much easier than they seem

[calm thicket]

Yea

:p

== 105/3

[granite stirrup]

35

[hasty wadi]

@pine kindle hey bruh

i got a question

concerning the trick you showed me

about the pythagorean identities

so when you divide "1+cot^2x = csc^2x" by "cos^2x", how do you get "tan^2(x) + 1 = sec^2(x)"?

ohhhh

so there's no sequence or anything

?

ahhhhhhh gotcha gotcha gotcha

thanks 😃

omfg this trick is legit godly dude

holy fuck

thanks a lot dude

[viscid thistle]

Any suggestions on how to set this up?

The
10(1.00083)^12t btw

[prisma epoch]

I have found a very simple function

$$\varepsilon(x)=x+\frac1x$$

[prisma epoch]

But it has AWESOME properties

Such as

[grizzled hull]

On what set? This on $$\mathbb{R}$$?

[prisma epoch]

$$x\in\mathbb R$$

[prisma epoch]

=tex \epsilon(\frac1x)=\epsilon(x)\ \epsilon(-x)=-\epsilon(x)\ \epsilon(x+y)=\epsilon(x)+\epsilon(y)\ and more

[grizzled hull]

You can use \text{ and more} to get that cleaner.

[prisma epoch]

Indeed

[grizzled hull]

Also, \begin{array}{rcl} \end{array} with & on either side of the = on every line, and a \\ finishing the first two.

[prisma epoch]

Wait ill prove it

[grim yarrow]

$$\epsilon(x) \epsilon(y) = \epsilon(xy) + \epsilon \left( \frac{x}{y} \right) $$

[prisma epoch]

Too

[grim yarrow]

There's a math competition problem hidden somewhere

[prisma epoch]

@grim yarrow

Wait for me to get there

So

[prisma epoch]

Hhaaaha

But

The inverse of epsilon() is epsilon()

So

=tex \epsilon(x)=x+1/x\to\frac 1{\epsilon}=1/x+x

[prisma epoch]

It is

?

[prisma epoch]

That’s not what i mean

Wait brb

[grizzled hull]

o.o....

[prisma epoch]

Ima write a coherent proof brb

[grizzled hull]

Are you using non-standard definitions?

[prisma epoch]

Yeah you just saw it @pine kindle ?

@grizzled hull wdym

[grizzled hull]

The inverse of a function is not the reciprocal of that function.

[prisma epoch]

Wait ill prove it if i can type the latex

[grizzled hull]

usually.

We'll be here when you do.

[prisma epoch]

Sure

[prisma epoch]

=tex \epsilon(x+y)=x+y+\frac{1}{x+y}
\ \frac{1}{\epsilon(x+y)}=\frac1x+\frac1y+x+y=\epsilon(x)+\epsilon(y)
\\text{Using the AWESOME property proved above, stating that epsilon is its own inverse... }\\epsilon(x+y)=\epsilon(x)+\epsilon(y)

[dense zealot]

omg x + 1/x manipulation!

[prisma epoch]

YES

[dense zealot]

Such a waste of time!

[prisma epoch]

No

[dense zealot]

Absolute waste of time

Like every competition has an x + 1/x problem

so boring at this point :/

[true vigil]

you're so boring at this point ;/

[prisma epoch]

:€

[dense zealot]

I am

[prisma epoch]

Yes?

[dense zealot]

My family thinks so too

U can't split a denominator

[true vigil]

why do you say that mate

[dense zealot]

Don't even try to

K thx

[true vigil]

that's just mean

[dense zealot]

How?

[prisma epoch]

Could you elaborate @pine kindle ?

[true vigil]

like "haha you're dumb" "I guess my family thinks so too" it's just super disproportionate lol I was just kidding

[true vigil]

unless you're kidding too in which case I'm getting old

[dense zealot]

What no I was saying that cuz everyone thinks I'm boring

Fr

[true vigil]

I have no idea if you're boring I was just repeating what you said

[prisma epoch]

$$x+y+\frac{1}{x+y}\to x^{-1}+y^{-1}+(\frac{1}{x+y})^{-1}$$

[prisma epoch]

That’s what i did

@true vigil @pine kindle

[true vigil]

hermitian

[somber trellis]

1/epsilon(x) is definitely not epsilon(x)

then 1 = epsilon(x)^2 and epsilon would be constant

[prisma epoch]

Well think about it

[grim yarrow]

What you wanted to say was

[prisma epoch]

$$\epsilon(x)=x+1/x\to\epsilon^{-1}(x)=x^{-1}+(\frac{1}{x})^{-1}$$

[grim yarrow]

$$\epsilon(x^{-1}) = \epsilon (x)$$

[grim yarrow]

That's true

Not the other one

[somber trellis]

that's false

I mean

yeah

1/(x+1/x) is not 1/x + 1/(1/x)

[prisma epoch]

It is

[severe verge]

wats the question

[prisma epoch]

I think

[grim yarrow]

hold on pulling my everytime pic

[true vigil]

=pup 1/(x + 1/x) - (1/x + x)

[severe verge]

get common denominator

[somber trellis]

1/(a+b) is not 1/a+1/b

[granite stirrup]

Query made by @true vigil
Data sourced from Wolfram|Alpha: http://www.wolframalpha.com/input/?i=1%2F(x+%2B+1%2Fx)+-+(1%2Fx+%2B+x)
Do more with Wolfram|Alpha Pro: http://www.wolframalpha.com/pro/

[prisma epoch]

@severe verge find propertis of epsilon(x)=x+x^{-1}

[somber trellis]

1/(1+1) = 1/2

1/1 + 1/1 = 2

[prisma epoch]

Yeah you get 2 results

[severe verge]

oh okay

[prisma epoch]

No!

You don’t understand

If you lemme talk you’ll understand what i meant

[severe verge]

hold on just let them talk :l

[prisma epoch]

Thank you

So

$$\epsilon(x)=x+x^{-1}$$ right?

[severe verge]

ya

you can also write it as $$\frac{x^2+1}{x}$$

[grizzled hull]

@grim yarrow I will need those posters in a few years.

[prisma epoch]

So $$\epsilon(x^{-1})=\frac{1}{x+\frac{1}{x}}$$ right?

[severe verge]

nope!

[prisma epoch]

I meant (epsilon(x))^(-1)

[severe verge]

oh, then ya

[prisma epoch]

Ok

[true vigil]

shhhh im listening

[grim yarrow]

~

[severe verge]

chill

[prisma epoch]

And $$a/(\frac{b}{c})=ac/b$$ right?

[true vigil]

sure

[severe verge]

whats a,b and c

[prisma epoch]

Real numbers i guess

[severe verge]

ya

[prisma epoch]

So

$$\epsilon(x)=x+1/x\to\epsilon(x)=x+x^{-1}\to\epsilon(x)-$$ OOOOOOH I SEE WHERE I WAS WRONG

[severe verge]

ok!!

nice

[true vigil]

ban

[severe verge]

why?

[prisma epoch]

Dude why?

[true vigil]

no mercy

[severe verge]

mercy

[prisma epoch]

What rule did i break?

[severe verge]

none

[true vigil]

yeah im messing with you

for telling everyone they're wrong lol

[prisma epoch]

Tho in my observations i have this: $$\epsilon(1/x)=(1/x)+(1/(1/x))=1/x+x=\epsilon(x)$$

[true vigil]

yeah

[prisma epoch]

Is that true?

@true vigil ?

[true vigil]

yeah

[prisma epoch]

Well

Then...

[severe verge]

ya

[prisma epoch]

I should be able to re-write all my theorems to make them true, then

Also it means $$\not\exists\epsilon(0)$$, no?

[severe verge]

ya, doesn't exist

can't divide by 0

[prisma epoch]

Mmhf

Bbbbbut

Ah

No nvm

[severe verge]

ok

[prisma epoch]

Mmmmmmhf

[severe verge]

nyaa

we're busy

[hasty wadi]

sorry

[grizzled hull]

#help-2 @hasty wadi

[prisma epoch]

#help-2

$$\epsilon(x)=1$$

[prisma epoch]

=wolf solve x+1/x=1

[granite stirrup]

Query made by @prisma epoch
Data sourced from Wolfram|Alpha: http://www.wolframalpha.com/input/?i=solve+x%2B1%2Fx%3D1
Do more with Wolfram|Alpha Pro: http://www.wolframalpha.com/pro/
🐺 Try out the new =pup command! It's much more concise.

[prisma epoch]

WTF

IS THAT

=wolf solve x+1/x=2.5

[granite stirrup]

Query made by @prisma epoch
Data sourced from Wolfram|Alpha: http://www.wolframalpha.com/input/?i=solve+x%2B1%2Fx%3D2.5
Do more with Wolfram|Alpha Pro: http://www.wolframalpha.com/pro/
🐺 Try out the new =pup command! It's much more concise.

[prisma epoch]

Should be 2 and 1/2

=wolf solve x+1/x=2

[granite stirrup]

Query made by @prisma epoch
Data sourced from Wolfram|Alpha: http://www.wolframalpha.com/input/?i=solve+x%2B1%2Fx%3D2
Do more with Wolfram|Alpha Pro: http://www.wolframalpha.com/pro/
🐺 Try out the new =pup command! It's much more concise.

[prisma epoch]

Indeed

Ok

=wolf solve x+1/x=(1+(5)^(1/2))/2

[granite stirrup]

Query made by @prisma epoch
Data sourced from Wolfram|Alpha: http://www.wolframalpha.com/input/?i=solve+x%2B1%2Fx%3D(1%2B(5)^(1%2F2))%2F2
Do more with Wolfram|Alpha Pro: http://www.wolframalpha.com/pro/
🐺 Try out the new =pup command! It's much more concise.

[prisma epoch]

=wolf solve 1/x+x=0

[granite stirrup]

Query made by @prisma epoch
Data sourced from Wolfram|Alpha: http://www.wolframalpha.com/input/?i=solve+1%2Fx%2Bx%3D0
Do more with Wolfram|Alpha Pro: http://www.wolframalpha.com/pro/
🐺 Try out the new =pup command! It's much more concise.

[prisma epoch]

Hi? Wolf?

WHAT

IS HAPPENING

K ima stop here and ink my observations

See ya guys

[viscid thistle]

Any suggestions on how to set this up?
The
10(1.00083)^12t
btw

[true vigil]

just operate

[fringe stream]

nope.

$$(a \pm b)^2 = a^2 \pm 2ab + b^2$$

[fringe stream]

😄

[dense zealot]

Binomial expansion is the better term to use

[prisma epoch]

To the 9

$$(a^3)^3=a^{3*3}=a^9$$

[dense zealot]

6th

@prisma epoch I'm dissapointed

no!

[prisma epoch]

Omfg

Learn your axioms @dense zealot

[dense zealot]

$$(a)^b^c = (a)^bc$$

[granite stirrup]

Rendering failed. Check your code. You can edit your existing message if needed.

[dense zealot]

:/

Oh wait I literally just said the reason why

-_-

Kill me

I don't know how to multiply ok don't judge me ;-;

[prisma epoch]

It’s not about multiplication

It’s about exponentiation

[dense zealot]

No!

It's multiplication uwu

[viscid thistle]

Exponent to exponent is exponent x exponent, forever right?

[dense zealot]

ya

[viscid thistle]

so you could say e^ipi

is really e^i^pi /

?

[dense zealot]

yes

[viscid thistle]

🤔

[prisma epoch]

Yeah

[viscid thistle]

learning some stuff tonight

[dense zealot]

Imaginary nums r weird tho

Don't go messing with them

[viscid thistle]

Yeah I got a problem with understand why math people just say "Ahhh just forget them they don't make sense". Maybe the numbers we using are wrong ? How does one simply ignore part of the math

[dense zealot]

imaginary numbers raised to powers have multiple branches

They get weird

[prisma epoch]

$$(a^2)^3=a^2a^2a^2=aaaaaa=a^6$$

[dense zealot]

like the principal root of an imaginary number doesn't exist

[viscid thistle]

thats it right there

[dense zealot]

Sqrt(4i) = -2i and 2i

[viscid thistle]

(a^2)^3 = 3 occurrences of a^2. so you aren't even multiplying yuo're just adding the exponents in the total equation

I got a big test on limits tomorrow

[solemn sluice]

@ReEquip#9036 u still need help on that?

@ReEquip#9036

Oh wioos

K

U can't cancel out

The sin

[viscid thistle]

If you use the identity that cot = cos / sin, your RIGHT part of the equation would be sin theta / 1 - cos theta.

You wrote sin theta - cos theta not sure how you did that

[solemn sluice]

Change

[viscid thistle]

ReEquip i got the solution for your other bit still ned it?

[solemn sluice]

One of them

Oh

[viscid thistle]

Ok here goes so ignore the left side

We know cot = cos/sin right?

[solemn sluice]

sin^2theta - 1 + sin^2theta i presume

[viscid thistle]

So you get, 1 OVER 1- cos/sin

That sin is below 2 denominators, complex fraction

So how to get rid of that? Multiply each term by the least comment denominator

Since we know below the fraction we got 1- cos/sin

LCD is Sin

so multipl top by sin (which is 1 x sin theta)

then in the denominator 1 times sin theta again, = sin

minus cos X sin / sin

So you get sin theta / sin theta - cos theta = itself

Just un do what we did

So we got a sin in the top

we can throw it under everything in the denominator

sin / sin = 1

• cos / sin = cot

ez pz

It's hard to think about it that way but in calculus it's a good idea to keep in mind throwing stuff over denominator bar

Ok, ReEquip think about how we got rid of the sin in our complex fraction. We had 1 / 1 - cos/sin

We multiply by sin. Since that's our LCD, we can multiply all terms by it

[fringe stream]

$$\frac{\sin(\theta)}{\sin(\theta) - \cos(\theta)} = \frac{\frac{\sin(\theta)}{\sin(\theta)}}{\frac{\sin(\theta)}{\sin(\theta)} - \frac{\cos(\theta)}{\sin(\theta)}} = \frac{1}{1 - \cot(\theta)}$$

whoops.

there. that should help you visualize better.

[viscid thistle]

ReEqupi im writing it down for you ill send a picture in a sec

[viscid thistle]

I got you, one sec

[fringe stream]

...

did you look at what i posted?

i simplified the left side to get to the right side.

you divide both the numerator and the denominator by sin(theta).

because you want cot(theta) in your denominator, right?

you choose what you divide by based on what you need.

[viscid thistle]

@fathom creek

You divide everything by the numerator so that way the top = 1. Why do we choose 1? Well, we're set equal to one on the other side. Be careful not to complicate the whole identity thing by thinking that way though. Manipulate what you can

[tawny osprey]

need some help here

[viscid thistle]

Sup

Will help if I can

[tawny osprey]

Forgot how to use the tex bot xD

[viscid thistle]

I don't know anything about it :3

[tawny osprey]

Basically i'm doing (2/x-3) + (x+5/3-x)

[viscid thistle]

Combining?

[viscid thistle]

Common denominators first.

[tawny osprey]

I always end up with the wrong answer in the end

[viscid thistle]

What's your least common denominator?

[tawny osprey]

Yeah I see now

[tawny osprey]

I just need to learn how to use the LCD

[fathom creek]

yikes..

[tawny osprey]

I'm horrible at factoring XD

But thanks guys

LOL

[final sigil]

By the definitions above, we've all commited the crime.

[tawny osprey]

those signs lol

[grim yarrow]

Yep don't kill puppies

[fringe stream]

$$(0 + 1)^2 = 1^2 = 0^2 + 1^2$$

[fringe stream]

@pine kindle got'em.

[tawny osprey]

All the trial and error

[grim yarrow]

Don't kill animals

[final sigil]

^

[tawny osprey]

Yeah my goal is to just learn calculus to the fullest

I love math tbh

[final sigil]

I do too.

[tawny osprey]

Just working on patching up the holes in my foundation

[fringe stream]

everyone loves math!

[tawny osprey]

Need to be a god in algebra before I decide to tackle calc in uni

[final sigil]

^

[tawny osprey]

I know, but if you suck at algebra then it's terror

[final sigil]

TBH it can be.

[tawny osprey]

I just want to be good for computer engineering

and EE

I understand the derivative so far

just integration is a bit hard lol.

[quartz garnet]

https://cdn.discordapp.com/attachments/370640905436397578/391473602408480769/latex.png

[fringe stream]

lol

[quartz garnet]

[viscid thistle]

Yeah I don't want to sound like a jerk Gaussian but I think yuo might have over complicated the problem by showing the "invisible" factors. The skill exercise was LCD, not shortcuts. I think thats a disservice :/

[quartz garnet]

Cross multiplying on that one is a very unwise thing to do

very

[viscid thistle]

That -1

[quartz garnet]

very unwise

Yeah that's not a shortcut as well

Recall how you add fractions

[viscid thistle]

a -b b-a yea I get it

[quartz garnet]

=tex \frac{3}{4}+\frac{5}{8} = \frac{3\cdot 2}{4\cdot 2}+\frac{5}{8}=\frac{11}{8}

[viscid thistle]

No that wasn't the problem

[quartz garnet]

I know, it's about adding two fractions with silly x's in them

https://cdn.discordapp.com/attachments/363224154469826562/411007169731887104/latex.png

[viscid thistle]

Im almost 100% certain the goal and skill of it was LCD and multiplying out.

[quartz garnet]

Try and cross multiply \
$$\frac{5x^8+4x^5-7x+7}{x^2-x-7}+\frac{4x^{10}-5x^2+46}{-x^2+x+7}$$

[quartz garnet]

x'D

Also yea babowwz, the LCM of a and b is not necessarily ab

[viscid thistle]

(x-3)(3-x)

[quartz garnet]

For example the LCM of 4 and 6 is 12, not 24

Thinking about it it's not Least Common Divisor it's Least Common Multiple

😂

GCD, LCM

is always 1, thinking in positives

But least common divisor in terms of whole integers

[viscid thistle]

(x-3)(3-x)

[quartz garnet]

The least common multiple of (x-3) and (3-x) is (x-3)

Cause they don't know what to say

[viscid thistle]

🤦

Why aren't you multiplying the denominators and factor / cancel ? That's the skill

That's what you LEARN in precalculus!

[quartz garnet]

Would you calculate $$\frac{7}{3}+\frac{2}{-3}$$ as \
$$\frac{7\cdot(-3)+3\cdot 2}{3\cdot(-3)}=\frac{-15}{-9}=\frac{5}{3}$$ \
or $$\frac{7}{3}+\frac{-2}{3}=\frac{5}{3}$$

[quartz garnet]

^^

[viscid thistle]

k

[quartz garnet]

"It is best not to talk when you don't know about it well enough." - Some teacher of mine

[viscid thistle]

Wow some quote and a bunch of totally unrelated math problems as examples which didn't really teach the person who was asking for help how to find a common denominator

So now what, when he/she has another one that's not x-2 2-x ?

You're crazy

Teach the skills not the tricks

Foundation first

[quartz garnet]

Wow some person that tries to find the faults in everything and not teaching the practicality

^

Also, that's not a trick, y'know

that's a basic algebraic manipulation

basic.

also

who was asking for help how to find a common denominator

the common denominator is (x-3)

[severe verge]

wot happened

[quartz garnet]

Something stupid

Don't worry about it

[severe verge]

Ok

[viscid thistle]

Halp with 3?

How would I even set that up?

[grizzled hull]

In this class, were you given the forumla for half life?

I didn't blink and miss a bunch of messages popping in and out, did I?

[tight mango]

can someone help me "verify" :
(secx-tanx)(cscx+1)=cotx

like make the left side equal to cotx

plz asap

[fringe stream]

change everything to sine and cosine.

[tight mango]

ok then what

i got 1/cosxsinx + 1/cosx - 1/cosx - sinx/cosx

):

[tawny osprey]

@quartz garnet thanks for mentioning LCM, I remember now.

[viscid thistle]

A series has four terms, starts with 5, and has a sum of 200. What are the terms if the series is geometric?

[hexed ermine]

Use the sum formula of a geometric series; S_n=a(1-r^n)/1-r

Where a is the first term, r is the ratio and n is the number of terms

So 200=5(1-r^4)/1-r

Solve for r to get the ratio and mulitply the ratio by each consecutive term starting at 5 to get the terms

[viscid thistle]

@tight mango sec = 1/cos , tan = sin/cos , csc = 1/sin, cot= cos/sin

[viscid thistle]

That's a really tough one by the way. Type it into Symbolab Identity Solver. They'll give very specific steps on completing it.

[viscid thistle]

@grizzled hull no, no formula, its math not science but this math teacher is super unhelpful

[viscid thistle]

how so?

[viscid thistle]

ShoutOut to @pine kindle for showing me that f( bunch of garbage) -f(x) /garbage I could just do the power rule on f(x) and not write all that stuff out. Just finished my test think I got 49/50

I did the write out too but such wow that was huge observation/discovery

[patent beacon]

... Did they teach you the power rule?

They might have expected you to use the definiton of the derivative

[thick raptor]

:l

[viscid thistle]

We just had to simplify it out and factor delta x and cancel

Not definition just the limit as it go to 0

[thick raptor]

they teach limits in precalc?

[viscid thistle]

Same answer to powi meant calc channel my bad

It was huge discovery that it was really about recognizing it was -f(x]

[thick raptor]

:l

[viscid thistle]

What?

[thick raptor]

nothin'

[viscid thistle]

C'mon out with it

[thick raptor]

nothin' really

I'm just "meh" about it all

And bored

[viscid thistle]

Lim delta x to zero for (x +delta x) squared- 3x squared / delta x

[true vigil]

@pine kindle

[viscid thistle]

Ignore it all and see f(x) = 2x squared power rule 6x :D

[thick raptor]

Ew, @pine kindle uses developer mode.

[viscid thistle]

3x squared not 2x

[thick raptor]

@pine kindle if you weren't in developer mode, it'd look like that

[thick raptor]

Oh yeah, it's called compact

[viscid thistle]

yea it was with the 3 in front yup

I multiplied it out and did it to make sure but I didn't realize it was like that

that I didn't have to care bout that whole mess

We know f(x) so we can just do power rule super quick and forget the ugliness

Yea we just learned some more rules, got about 8 so far and sin x = cos X derived

and I think cos is -sin x?

Not that yet

We're doing s(t) for velocity and one dimensional motion (kinematics)

-16t^2 + 4t +t^2

or maybe it was -4t

gotta check my papers

[marsh sage]

hi guys! 😄 I kinda need help with exponential function

[clever inlet]

?

[marsh sage]

When is the base not allowed to be equal to one? Why is it not allowed to be one?

[clever inlet]

what do you mean?

[robust osprey]

Wow

[marsh sage]

that's my problem u.u I don't know what to answer

[robust osprey]

WOW

[clever inlet]

it is allowed to be equal to 1

it's just not a very useful function

[marsh sage]

Thank you so much! 😊

[robust osprey]

Omg

[clever inlet]

f(x) = 1^x is basically the same as f(x) = 1

[neat falcon]

what's the limit of (x^2+1)/(x-1) as x->+1

[severe verge]

doesn't exist

[neat falcon]

thanks

[viscid thistle]

@neat falcon what you do is first plug your number in for x in the whole equation. If you wind up with 0/0 there is a limit. If you get any number other than zero over zero it doesn't exist. But interestingly, that non zero over a zero is a vertical asymptote too.

[neat falcon]

thanks

[viscid thistle]

Hello

anyone avail ?

[quartz garnet]

but to no avail

[calm thicket]

Was able to do it using law of sines and finding the longer length, wondering if there's a faster/cleverer method.

https://www.desmos.com/calculator/0ardpzmvhs <- my inefficient solution

[hasty wadi]

can i please get assistance on this quesition?

[fringe stream]

tan(x) can also be 0.

[hasty wadi]

that's what i got

[hasty wadi]

?

[hasty wadi]

where did you get 1/3

?

wait, lemme show you my work. im confused on what i did

[fringe stream]

uh, wtf?

[hasty wadi]

is that correct?

[fringe stream]

one step is not.

[severe verge]

u seem to have deleted a tan(x) from 2nd line to 3rd

ahh

3rd line, tan(x) should not be on the right

but other than that looks good

[fringe stream]

also, when you simply cancel out tan(x) from both sides, you neglect one solution.

[hasty wadi]

this is my work

what did i do wrong?

[fringe stream]

how did that become 0 in the second step?

you're dividing by tan(x) on both sides.

the left one is tan^2(x), which is right.

what about the right one?

[hasty wadi]

yes

the negative square root

but im like confused on how there can me a differernt answer for negative 0

OHHHHHH IM SO STUPID

fuckk

hold up i think i got this

@pine kindle wait dude

i got somewhere

but my answer is still wrong

i got here

[severe verge]

what about 0

[hasty wadi]

0?

[hasty wadi]

where does the tan (x) = 0 come from ?

so i basically have the right answers for +- 1/sqrt(3)

[severe verge]

tan(0)=0

[hasty wadi]

but why does tan (x) = 0 come into play?

[severe verge]

if tan(x)=0 then both sides are 0

[hasty wadi]

but tan x doesn't equal zero here

[severe verge]

right

so ur missing solutions

[hasty wadi]

?

how do i find the other solutions 🤔

[hasty wadi]

this is what i did

tmw ur still confused af to what u did wrong

[severe verge]

do u see that tan(x)=0 is a solution

[hasty wadi]

where in the equation solving process does tan(x) = 0 ?

[severe verge]

let y = tan(x)

then the original equation becomes
9y^3=3y

[hasty wadi]

yes

[severe verge]

then u can subtract 3y from both sides

9y^3 -3y=0

factor the left hand side

[hasty wadi]

9y(y^2-1/3) = 0

[severe verge]

not quite

yea

so y = 1/sqrt(3) is a solution

y=-1/sqrt(3) is a solution

y=0 is also a solution

[hasty wadi]

and so is 0 ahhhhhhhhhhhhhhh

wait wait wait

i get it when you do substitution

but

how do you get tan (x) = 0 from the method i did?

[severe verge]

when u divided both sides by tan(x)

u forgot the possibility that tan(x) could equal 0

[hasty wadi]

but how can tan (x) = 0 when dividing it?

[severe verge]

this is why factoring is better :l

[hasty wadi]

that's why im so confused on how to get tan (x) when doing it my way

but we dont know what tan (x) equals to

[dense zealot]

9x^3 = 3x
x^2 = 1/3, x=0
x = plus minus sqrt(1/3), x=0

[severe verge]

for all intensive purposes, tan(x) is just another variable

[hasty wadi]

^ur using substitution tho @dense zealot

[dense zealot]

It still works

...

Gives all the solutions

[severe verge]

u coulda left it as tan(x) and nothing would change

[hasty wadi]

i know substitution works

i never was tought that, they just said "hey divide it and ur set"

smh

[severe verge]

9(tan(x))^3=3(tan(x))
(tan(x))^2=1/3, tan(x)=0
tan(x) = plus minus sqrt(1/3), tan(x)=0

rewrote bleh's solution without substitution

[dense zealot]

x=0 uwu

[hasty wadi]

ahhhhhhhhhhhhhhhh

okay

fml, im just sticking with substitution

lmao

[dense zealot]

Lol

[viscid thistle]

Is there such thing as a dumb question?

Cuzzzz I need help

[patent beacon]

There is absolutely such thing as a dumb question. You're probably not about to ask a dumb question though, trust me.

[hexed ermine]

in b4 quick maths meme

[viscid thistle]

It's 67, I'm just really confused about it. I started off by solving the perimeter in terms of a, being
a=(-3b + 300)/2, then plugged that into the area formula, in this case would be A=a*b. Found the vertex since we're looking for max area. I got 3750. The book says it's 75 feet lmaooooooooooo pls help am special )))):::::::

The chapter is about Polynomial and Rational fun. btw

[patent beacon]

So you found the max area, but you're looking for the dimensions that give you the max area

[viscid thistle]

Here imma try something wild

[patent beacon]

So let x be the length of the bottom and top of the pens
Let y be the length of the left, right, and middle.

2x + 3y = 300
y = 100 - 2/3 x

A = xy
A = x(100 - 2/3 x)
A = 100x - 2/3 x²

A = -2/3 (x² - 150x)
A = -2/3 ((x - 75)² - 75²)
A = -2/3 (x - 75)² + 2/3 (75²)

So, the maximum area is 2/3 (75²), and it happens when x = 75. Using that:
y = 100 - 2/3 x
y = 50

== (2/3)*(75^2)

[granite stirrup]

3750

[patent beacon]

Indeed, you found the correct max area, but that's not what they wanted

[viscid thistle]

Oh alright thank you! I understand it now, sorry I'm a bit slow at this hour ahah

[hasty wadi]

pls need help with this

[severe verge]

let y = csc x

y^2+y=2

y^2 + y - 2 = 0

factor

(y+2)(y-1)=0

y=1 or y=-2

csc x = 1, or csc x = -2

sin x = 1, or sin x = -1/2

sin(2 n pi)=0, so thats not a solution

but basically solve sin x = 1, or sin x = -1/2

[hasty wadi]

@severe verge

can you check my work and see if my answers are right? im on my last submission and i don't wanna fuck up lol

[severe verge]

how many submissions do u get

[hasty wadi]

5

im on 4/5

[severe verge]

how did u use so many of them

[hasty wadi]

i kept redoing problem but it seems like im fucking up

[severe verge]

well idk what ur last step was

seems like u skipped like 3 steps to get there

[true vigil]

last submission means it's graded

😒

[hasty wadi]

it's not graded

@severe verge i took arccsc

[severe verge]

is that a thing?

;o

[true vigil]

are you lyyyiiiinngggg

[hasty wadi]

@severe verge arcsin b/c = arccsc c/b

^i did that

[severe verge]

?

[hasty wadi]

hold up, lemme add steps

[severe verge]

steps are good

im gonna go to sleep =w=

[hasty wadi]

@severe verge thanks for the help dude from earlier, i really appreciate it 😃

i need help still rip, last submission

[severe verge]

go with your heart

[hasty wadi]

fml, this is gonna be the first homework assignment i get a 90% on

smh

i'll do the problem again

and hopefully it's right

[true vigil]

it was graded then

I thought you said it's not graded?

this really makes me think

does it make you think woog

[hasty wadi]

@true vigil lmao, woog is going to slep

@true vigil the assignment is graded when it's turned in. i get 5 submissions for each problem, i still have one last try to get it right. after this submission, the question locks and i can't answer it again. i don't want it to be locked on the wrong answer

im scared

idk if this is gonna be right or not

LETS FUCKING GOOOOOOOOOOOOOOOOOOOOOOOO

FUCK YEAH, FUCK YOU WEBASSIGN YOU DUMB ASS BITCH

[severe verge]

can u chill

[hasty wadi]

sorry

am hyped lmao, this stupid question took me so long

[true vigil]

what do you think should happen to him

[hasty wadi]

?

[true vigil]

your call

we can go a gaussian elimination

what about lying to my face about whether it's graded

huh

[hasty wadi]

hm? what?

[true vigil]

look at my anime girl in the eyes

and look at my gtm

does it look like i'm joking

[hasty wadi]

it's part of homework, of course it's graded in the homework category

[true vigil]

of course it's graded

if you need help with something graded

and someone asks if it's graded

[hasty wadi]

lmao, my teacher just wants us to at least do the homework. i just wanna make sure im understanding it and getting it right

[true vigil]

say yes and try to come up with a lame excuse

for why we should help you

[hasty wadi]

wait wat???

im so confused

i wasn't making any excuse LOL

[true vigil]

you should

[severe verge]

[true vigil]

instead of lying blatantly

[hasty wadi]

omfgggg, im not lying dude

it's not graded individually by question

[hasty wadi]

it's graded by progress of how many questions you've done

bruh you didn't understand what i meant

this is what i mean

[true vigil]

guess I have tRoUbLe UnDeRsTaNdInG EnGlIsH

huh

when someone says something's not graded

I think it's not graded

guess that's my fault huh

[hasty wadi]

it's not graded on whether it's not right or wrong. homework is obviously graded by how you do it

[true vigil]

obviously

[hasty wadi]

why am i warned?

im like so confused LOL

isn't all homework graded tho?

it's homework

im asking help on how to do a problem, im not blatantly asking for the answers

i even showed work dude

to see what im not understanding

i could give two shits about the point, i just wanna understand how to do it

cuz then i wont do good on assessments

and that would be bad

lol

[somber trellis]

how about "can someone explain how to do this so I can get my homework right"

[hasty wadi]

i just come here to learn how to do problems and get help on how to do something if im doing it wrong. people on this server have helped me a lot with doing this stuff, im not here to fucking use you guys.

[somber trellis]

telling someone it's not graded when it's absolutely unarguably graded is shitty too lol

if I were you I'd just take the criticism and move on

[hasty wadi]

im sorry if i made y'all upset fml, i didn't mean to make a scene

i just wanted help lol

it was jsut a question on homework, idk how asking for help wrong. it's not graded individually by problem. it's graded by progress and the teacher seeing if were doing the homework. i got confused on what y'all meant.

i wouldn't use y'all for the "A" grade, i come here to learn and make progress on myself. i get help from many people here and i wanna say thanks, i just got confused on what y'all meant by "graded"

[true vigil]

dude it's done

it's not that big a deal honestly

you were already half-warned because of other bad interactions

so this time you get a full warning

that's it

[hasty wadi]

what other instances was i half warned?

[true vigil]

dunno

[hasty wadi]

🤔

so i can't ask for any more help on my homework (because it's graded)? @true vigil

[true vigil]

you can

as long as you show work and desire to learn

and when someone asks if it's graded, you say so

[hasty wadi]

ok, i just got confused. sorry bout that

[true vigil]

no problem

[severe verge]

wow u have the do not disturb​ role :0

[hasty wadi]

also, yes i come here wanting to learn. that's what i like doing 😃

[true vigil]

yeah do not disturb jacobian

[severe verge]

that means no pinging jacobian#2564

oops

[hasty wadi]

LOL

[true vigil]

lol

yeah I got bugged because you were being a bit pushy with the "it's the last submission" thing

and that's such a red flag

[hasty wadi]

i got annoying with that because i wouldn't be able to submit a answer for it

[severe verge]

no pushy allow

:0

[hasty wadi]

it would've just made me want to quit on the question

i wanna learn how to do it and get it right

[true vigil]

then you're not here to learn really just to get your homework right

you see that right?

[hasty wadi]

the stuff i need to learn is on my homework, that's what my teacher bases his assessments off of

i wanna learn how to do it

to be good at pre cal

and actually see what my mistakes are and learn from them

[true vigil]

you've got some cognitive dissonance going on

[severe verge]

t!wiki cognitive dissonance

[brisk mica]

📖 | ** https://en.wikipedia.org/wiki/Cognitive_dissonance **

[somber trellis]

okay but i'd die for a single unresolved chord

[hasty wadi]

im so confused

[true vigil]

it doesn't really matter

[viscid thistle]

@true vigil wait we can't get help on homework? Or we can't lie about it?

[true vigil]

you cant lie

if you give a lame excuse it will probably work for graded homework

[viscid thistle]

But we would get in trouble if we were asking for answers on an online class quiz or something?

[true vigil]

yeah

probably

[viscid thistle]

Ahhhhh alright, thanks

[hasty wadi]

i need help understanding this concept of finding the solutions. i know how to find the infinite sets but i don't know how to find the solutions that go from [0,2pi) from the infinite sets

i get stuck and im just confused on how to find the solutions from the point where i find the infinite sets

[viscid thistle]

First, you're swapping in and out of theta and x

the problem asks about what you're doing to x, use no theta's then

Identity is right ☑

sec^2 x -1 = sec x -1

you get sec^2(x) -sec (x) =0

You're right to factor and get sec(x) =0, and sec(x)=1

So we know secant is 1/cosine

Your answers are correct

but you made 1 mistake

the interval they're looking for is [ , )

Including that 0

your answers shuld be 0, pi/2, 3pi/2

The interval they ask about includes 0 because there's the [

@hasty wadi

[flint dock]

can someone help me with #5 ahhh

i made a 17 on this quiz :'))

oh i mean #3 ****

i wrote the correct answers down while going over it but i need to redo it so i know how to do the math

[hasty wadi]

@viscid thistle

it's still wrong

[patent beacon]

cos(x) = 1
x = 0

sec(x) can never be zero, so there's no solution there.

The only solution is x = 0

@hasty wadi

[hasty wadi]

?

im confused still

from the infinite sets i got, i plugged in for "n" to get all my solutions that are from 0 to 2pi

why is pi/2 and 3pi/2 wrong?

[patent beacon]

So we're at
sec(x)(sec(x) - 1) = 0

So,
sec(x) = 0, 1

[hasty wadi]

yes

[patent beacon]

sec(x) can never equal zero, no solution there.

sec(x) = 1
cos(x) = 1
x = 0 + 2πn

[hasty wadi]

arcsec (0) = arccos (0)

[patent beacon]

arcsec(0) = arccos(1/0)
Which is nonsense, of course

[hasty wadi]

oh fuck