precalculus

[tranquil haven]

Thanks!

I cannot see what I and J is...

Am I missing something

[patent beacon]

@tranquil haven
i is the unit vector (1,0)
j is the unit vector (0,1)

These are common notations

So b1 can also be expressed as (100, 10)

[drowsy trellis]

How to do this?

[willow bear]

you're missing parentheses, it should be cos(A) = (b^2 + c^2 - a^2)/(2bc), etc

also those three formulas are all redundant, and assume the triangle is called ABC with its sides labeled a, b and c

which is not the case in your picture anyway

in any case: when finding an angle using the law of cosines, you care about which sides are incident to your angle (there will be two) and which side is opposite.

• in the numerator, you add the squares of the incident sides and subtract the square of the opposite.
• in the denominator, you multiply the incident sides.

@drowsy trellis

[drowsy trellis]

Hey! I finally got to meet you! @willow bear

Thanks! But I was wondering how do you determine which one u use to find the angle? @willow bear

[willow bear]

you don't

these are literally all the same formula

just with letters shuffled around

i literally just told you how to determine which side goes where

[willow bear]

does this make sense to you or not?

[drowsy trellis]

What is an incident angle? @willow bear

[willow bear]

i never said the words "incident angle"

i said

... which sides are incident to your angle ...

please read what i say carefully

also, you do not need to ping me every time you say something

👻

[viscid thistle]

https://gyazo.com/49bc4d13d20dc202919e501762a14c9b

Anyone know how to do this?

[willow bear]

have you made any progress so far?

[viscid thistle]

I figured it out

sorry

I didn't let you know sooner

[merry musk]

Any ideas?

[patent beacon]

@merry musk
It's easier to count how many teams DON'T contain both a boy and a girl

[merry musk]

oh

So I was thinking its 16c6, 9c6, and 7c6

?

[patent beacon]

Which is?

[merry musk]

idk what to do with them

multiply them?

[patent beacon]

I don't know what those numbers are, haha

[merry musk]

oh

its combinations

[patent beacon]

• So in general, you can make 16C6 teams.
• You can make 9C6 teams that only have boys.
• You can make 7C6 teams that only have girls.

[merry musk]

thats what i was thinking yeah

[patent beacon]

That means, of the 16C6 teams, 9C6 "don't work" and 7C6 "don't work"

[merry musk]

Wait

that rings a bell

ill subtract them

[sage lake]

`Find the indicated roots. Express answers in trignometric form.

1. The square roots of 4(cos90+isin90)`

Help por favor

[patent beacon]

@sage lake
Still looking for it?

[sage lake]

yeah

[patent beacon]

One answer is 2(cos(45) + isin(45))

Note that √4 = 2

And by Demoivre's theorem, you can put a 1/2 into the sin and cos, rather than take the √

The other answer comes from doing the same thing to 4(sin(450) + isin(450))

450 being the same angle as 90 on the unit circle

[ocean garden]

hi i wanted to ask

if this is true or false

its so weird i cant put my finger on how to solve this

[willow bear]

write this as a riemann sum honestly

[ocean garden]

ngl i dont know how

if it was a reimun sum i could have applied one of the test but i cant figure out which function is the real one

n/n^2+x^2 ?

its n/2n^2 aint it

why am i so stupid

[patent beacon]

There's a few pieces of info you want to find out:

• For a given n, how many rectangles are there? That is, how many terms?

• What are the endpoints?

• How wide are the rectangles?

• What is the function we're putting rectangles under?

[willow bear]

parentheses!!!

\verb|n/n^2+x^2| reads as $\frac{n}{n^2} + x^2$, not as $\frac{n}{n^2 + x^2}$

[obsidian monolith]

Ann

[willow bear]

anyway

what you have is $\sum_{k=1}^n \frac{n}{n^2 + k^2}$

[obsidian monolith]

Ann

[willow bear]

you can write this as $\sum_{k=1}^n \frac1n \cdot \frac{1}{1 + (k/n)^2}$ with some algebra

[obsidian monolith]

Ann

[willow bear]

@ocean garden

[ocean garden]

yah i solved it once i got my head around it

lol

[storm mango]

this all is precalc?

yikes

looks nothing like what I do in precalc

[hollow solstice]

,w d/dx cos(sin2x)

[obsidian monolith]

Results provided by WolframAlpha

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

Requested by mist#7100

[hollow solstice]

okay wait

,w d/dx cos

[obsidian monolith]

Results provided by WolframAlpha

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

Requested by mist#7100

[hollow solstice]

OH

The angle of the function is sin2x

okok

[mild swan]

oh, is it a test?

@gritty cloak

[distant sierra]

hi can someone check a few problems here for me? Its a canvas "quiz" but its just the way our teachers are doing homework since we STILL haven't gone back in person 😫

[stuck lark]

@mild swan ping mods for future reference

[mild swan]

Yeah, I was going to but I never got around to doing it since I had other stuff to do

I was trying to see if I could squeak that out of him and I did 😉

[vagrant sedge]

does anyone here know how to graph an ellipses

[knotty oak]

can anyone help me ?

[arctic trail]

No

[knotty oak]

please i really don't know the answer

[arctic trail]

public class Answer{
    public static void main(String[] args){
        public static int int1 = 1;
        public static int int2 = 1;
        System.out.println(int1-int2);
    }
}

Put this in a java compiler

Tell me what it does

c;

[mild swan]

doesn't it print 0.0000000000000000000003 or something

[merry chasm]

Refreshing some math fundamentals since it's been a while, and I had 2 questions regarding the quadratic formula:

1. Regarding the radicand, are you multiplying b^2 by -4ac or are you subtracting 4ac from b^2?

2. To graph quadratics, it helps to find the line of symmetry, which is expressed by -b/2a, which I'm guessing is from the QF. How does the radicand part of the formula simplify to zero?

[willow bear]

1: you are subtracting 4ac from b^2

2: it doesn't "simplify to zero"; the QF itself gives you the x-intercepts, if any. the line of symmetry is halfway between those.

[merry chasm]

I guess what I don't understand (and maybe it's obvious but I'm not recognizing it cause it's super late) is why is it just -b/2a and not the entire formula?

[willow bear]

are you ok with the fact that the line of symmetry is halfway between the two roots?

[merry chasm]

I think so, assuming that there are two x intercepts

[willow bear]

i mean

ok wait

the assumption isnt necessary

but establishing the line of symmetry without it will take a different route

are you familiar with completing the square?

[merry chasm]

Is that the thing where you find what multiplies to get C and adds to get B?

[willow bear]

no

[merry chasm]

Ah, I think I know what you're talking about

[willow bear]

it's when, for example, you write x^2 + 4x - 10 as (x+2)^2 - 14

for equations of parabolas this is also called vertex form

[merry chasm]

Yea, I remember it vaguely

[willow bear]

because if so, i could tell you that y = ax^2 + bx + c can be written as y = a(x + b/(2a))^2 + (4ac-b^2)/(4a)

and working this out is just a matter of going through the motions for completing the square

[merry chasm]

Ok, I understand where you're coming from. I need to refresh myself on completing the square though.

Thx for the explanation :)

[winter sail]

Ok so, I have to find the intersection point between a cubic equation and a sinusoidal.
So I decided to set them equal to each other right
2x^3-10x+3=-5sin(2x/3)+2
But no matter what I did, I couldn't get rid of the x^3 term...
How do you solve this without using a graphing calculator?

It was a classwork problem and it was the only problem on the classwork review for the final that I just couldn't get (without the use of a graphing calculator but that was kind of cheating). So I just got it wrong :P

[willow bear]

i don't think this is possible without a graphing calculator unfortunately

[winter sail]

A friend of mine told me that you can use the Taylor series to do it but seeing as that's a Calculus topic not an Algebra 2 one...yeah no I feel like my teacher just lied to me.

Ah well...

If anybody has a solution, ping me and please explain. Would be greatly appreciated ❤️

Genuinely curious how you solve it

[tranquil haven]

Hey why is an ellipse equation always equal to 1 ?

[drowsy totem]

You need to read the derivation of equation of an ellipse for that

https://courses.lumenlearning.com/ivytech-collegealgebra/chapter/deriving-the-equation-of-an-ellipse-centered-at-the-origin/

[limpid rampart]

is there a general approach to eliminating the parameter

for a parametric equations

[rough carbon]

Hmmm sometimes you do have to play around with them, esp if you can’t get t(or whatever else the parameter is) =

If there’s trig it’s often good to square both sides

Use a cos^2 t + sin^2 t =1 somewhere

Sometimes adding the x and y can help

Eg x= 2t + 2/t
y =2t -2/t

Add x and y and multiply by x-y

The t’s cancel

[west blade]

Does anyone know how to calculate revenue using an exponential function?

Im trying to find maximum profit

using this function

P(x) =15000((x-5)^2 )(e^(x-5))+1

[sage lake]

Sketch the graph of each polar equation
r=2θ for θ in radians

The book says the graph on desmos is wrong

[willow bear]

can you show exactly what the book says

[sage lake]

It just says "Sketch the graph of each polar equation

[willow bear]

The book says the graph on desmos is wrong

i mean this part

the graph you're showing here looks correct to me.

but you claim the book denounces it as incorrect.

[sage lake]

47

[willow bear]

ah

[sage lake]

Confuse

[willow bear]

they simply draw it over a bigger range of values for theta.

something like -4pi to 4pi.

somehow they chose not to specify that range tho

[sage lake]

I have it up to 12 pi

Still don't know how the book has it shaped like that

Hope this doesn't show up on the final tmr

[sage lake]

oh it went negative

prof only had us going 0 up so I'm not doing neg

[empty bronze]

i need help wit this

[willow bear]

@empty bronze do you still need help with any of these? if so, which one(s)?

[hollow solstice]

basically yeah

extrema refers to a local max or min

[cerulean cedar]

Wait . . . Desmos has dark theme?

This changes everything

[gritty rampart]

What happens to the slope if you take the reciprocal of a function?

[patent beacon]

Are you asking in terms of derivatives?

[willow bear]

$\sqb{\frac{1}{f(x)}}' = -\frac{f'(x)}{f(x)^2}$

[obsidian monolith]

Ann

[willow bear]

this might be what you're looking for.

@gritty rampart

[gritty rampart]

Yup @willow bear I got my question answered. Thanks anyways!

[copper vigil]

whew

[placid cairn]

also whats desmos

[willow bear]

http://desmos.com

[copper vigil]

-1 -4 DNE -1

[viscid thistle]

thx

[runic locust]

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

[obsidian monolith]

xion

[slow quartz]

I know you arent supposed to pay for tests, but its not worth anything and its just a pretest

[echo wagon]

@slow quartz what's a pretest lol?

[slow quartz]

Its a teat you take in the beginning of the year

And then you take a test at the end of the year

[slow quartz]

Test*

I really cant spell

[slow quartz]

@echo wagon

[echo wagon]

<@&268886789983436800>

[stuck lark]

is a pretest meant to be diagnostic

[echo wagon]

Oh rokabe here

Anyway, don't offer to pay

[stuck lark]

@slow quartz

[slow quartz]

No

But he knows literally nothing, and if he doesnt get a certain % on it he has to go for another month

[willow bear]

"he"?

[sick steppe]

the plot thickens

[stuck lark]

@slow quartz seeking outside help on such a test defeats its purpose and is academic dishonesty. while you may ask for help on reviewing topics, please don't ask for help on this test, and don't offer cash in return for help on this server

[slow quartz]

Again, its not worth anything

It has 0 academic value

I asked in #discussion and everyone said it should be fine to ask that question

Because its just a pretest

@stuck lark

[echo wagon]

This seems to suggest it has value. And it also seems like you just want someone to do it for you.

[slow quartz]

Its literally just to determine how long you stay

:p

If I cant ask for help on the pretest then I'll delete the question

[stuck lark]

it'd be unreasonable to ask for help on a test whose purpose is to measure how well you've learned the material to decide how much more time you need to learn it

[slow quartz]

It isnt tk measure what we've learned

Its called a pre test

As in

Before you do anything

[uncut mulch]

regardless the purpose is to measure how much you know
go through the entire thing yourself first

and given the context, you'll learn what's needed through the course

[slow quartz]

No, its summer school

Its just reviewing what we elarned during the school year

[sick steppe]

yeah... so do it yourself

[stuck lark]

then i can't distinguish this from any other final

seeking help on it is academic dishonesty. don't seek help on it and in general don't offer cash for help

[uncut mulch]

It isnt tk measure what we've learned
Its just reviewing what we elarned during the school year
...

[hushed onyx]

Question

I'm on the algebra part of trig and i'm wondering if I should understand why each formula works, or memorize each formula (such as 2pi/b) and understand how they fit in in different dircumstances / problems

[plucky gulch]

its better to understand, cuz its hard to memorize everything

[hushed onyx]

Understand each formula?

[plucky gulch]

yes

if you know where they come from, thats good

[hushed onyx]

What do you mean by "where they come from"?

[plucky gulch]

how did we get them

[hushed onyx]

Oh

Algebraic Derivation?

[plucky gulch]

?

[hushed onyx]

Like, can you give an example of a formula, and what "understanding" it would mean?

[plucky gulch]

hmmm what about
$sin^2 (x) + cos^2 (x) = 1$

[obsidian monolith]

Herels

[hushed onyx]

well for me

[plucky gulch]

did you know that we can prove it by using Pythagore theorem ?

[hushed onyx]

yeah

but i think of it in slightly different way

[plucky gulch]

Thats the spirit

[hushed onyx]

sin is y and cos is x, and x^2 + y^2 is radius, and unit circle radius is 1, so yeah

[plucky gulch]

well, everyone doesnt think of something in the same way

we think of the easiest way we can understand

sorry if my english is bad

[plucky gulch]

that works too

[hushed onyx]

But how do you understand that the asymptotes of a tangent function are pi/2b + (pi)n/b

[plucky gulch]

what is n and what is b ?

[hushed onyx]

b is what the function is being stretched / compressed by

n is an integer

[plucky gulch]

,wolf graph tan x

[obsidian monolith]

Results provided by WolframAlpha

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

Requested by Herels#2593

[plucky gulch]

hmm I dont get it

[hushed onyx]

y = tan(2x) for example

b is 2

compressed by a factor of 1/2

[plucky gulch]

oh

well you get the asymptotes by looking at the limits

if lim tan(bx) when x goes to pi/2b is infinity, they x=pi/2b is an asymptote

[hushed onyx]

I didn't cover limits yet

[plucky gulch]

you just cant start talking about asymptote without learning about limits

that's bullshit

[hushed onyx]

?

Like i know what it is

[plucky gulch]

you need to learn about limits before asymptote

[hushed onyx]

When are limits usually taught

[earnest jackal]

i learned asymptotes in algebra 1

[west blade]

hey guys Im having trouble calculating this derivative could someone help

y=ln^4(1-3x)^3

[zealous rampart]

does anybody know how to do this

[hushed onyx]

yeah i think you learn asymptotes before limits

[plucky gulch]

nah

I don't know where you are from but limits are necessary to understand asymptotes

[hushed onyx]

nah

i get the concept of an asymptote

maybe it adds another dimension

but i think in the us curriculumn they teach asymptotes first

[polar pasture]

me🔫

[charred rock]

hey guys! sorry if this doesnt constitute as precal? but its in my precal module and just wanted some really quick help (in voice chat if possible) with long division

i get most of it, im just stuck on one small part

[hushed onyx]

post the problem

[wet oar]

What is the best way to review the course?

Khan academy?

[charred rock]

i actually figured it out Mug thanks though

[visual brook]

I think everyone is taught asymptotes before limits everywhere

[hushed onyx]

yeah

[slender copper]

do you need help with that

[viscid thistle]

ye

[slender copper]

k

there's a limit when x approches 3

and when there's a limit, you know that the limit when x approaches 3 from the left and right is the same

so when we look, the limit when x approaches 3 is -5, if i am looking correctly

so that means the answer for the first 3 blanks is -5

and since at x=3, there is an open circle, it means that the function isn't defined for f(3) meaning that the answer to the last blank is "undefined"

[viscid thistle]

how do u see that tho

[slender copper]

hmm

[sick steppe]

the graph clearly approaches y=-5 as x approaches 3... it's just something you look at and recognize

[slender copper]

^

[viscid thistle]

oh alr

what about this

[slender copper]

yeah i don't know that, i've only just started learning this kind of stuff

if i'm correct tho, I think that you have to find the derivative of that function, and then plug in x=pi/3

don't take my word for it tho

[viscid thistle]

oh ok

would this be like -1 then

[timber pawn]

That's the value of f(3)

But the question is asking for f(3-)

So the answer should be the value the left side of 3 approaches to

[faint nest]

how do i do this

[slender copper]

think about it this way, when you're narrowing in on 3, don't take you pencil off the paper

[viscid thistle]

wat would it be then

[slender copper]

bro, just approach x=3 without taking your pencil off the paper, it should be pretty simple

if you can't solve this, then may be you're going to need a refresher on the basics of limits

[viscid thistle]

-4?

[sick steppe]

told you this already... just plug the stuff into first principles

[viscid thistle]

so would it be 0

[slender copper]

yes

bingo

[viscid thistle]

for which

[slender copper]

huh?

[slender copper]

this one

[viscid thistle]

ohk

[viscid thistle]

d/dx(5sec(pi/3)) right?

is pre-calculus hard

[sick steppe]

no

[viscid thistle]

calculus*

[sick steppe]

you dont want to differentiate a constant. . .

you also didn't even read what I wrote, given I said first principles

[slender copper]

it's hard until you start learning it

it's alright

like it looks really confusing

[viscid thistle]

istg im so streesed on what to pick for next year

[slender copper]

but once you start learning it's not

hmm

[faint nest]

wait i figured it out but i cant figure out the asymptotes

[viscid thistle]

we have statistics, algebra III/trigonomentory, and Pre-calculus

[slender copper]

the equation for the asymtotes were also on the pictire i sent you

[viscid thistle]

for next year, idk what to choose

[slender copper]

hmm

[outer inlet]

I have to utilize that h is approaching 0, anyone know what to do?

[sick steppe]

so via first principles..?

[outer inlet]

I guess

yeah

[faint nest]

is it y=-36/64? @slender copper

[viscid thistle]

can someone help me for some time on what to pick for next year

[slender copper]

statistics is really boring, pre calc you can learn by yourself, I would go with alg III

[sick steppe]

it's a yes or no.

[outer inlet]

yes

f^1(x)= those

[viscid thistle]

wdym learning by yourself?

[sick steppe]

f^1(x)??

[outer inlet]

I don't even know

we just started precalc

and I am confused

[sick steppe]

you just differentiate w/ first principles

idk why you're doing redundant things like raising a function to the 1st power

[outer inlet]

oh ok

so like how is this supposed to be set up?

is it lim (x+h)/h

[sick steppe]

no

[outer inlet]

hmm

[sick steppe]

it's first principles

[outer inlet]

so the first is 2x

[sick steppe]

$f'(x)=\lim_{h\to 0}\frac{f(x+h)-f(x)}{h}$

[obsidian monolith]

Mosh

[outer inlet]

so its that

[sick steppe]

that's first principles.... yes

[outer inlet]

ok thanks

so lets say for this one

[slender copper]

khan academy

[outer inlet]

how would you do that one

[slender copper]

like literally, just study by yourself

it's easy enough

[outer inlet]

x^2 gets plugged in the x+h

[viscid thistle]

ok but i mean in school lol

[slender copper]

yeah, statistics imo is boring, pre calc you'll learn on your own time, alg III you'll learn at school

[viscid thistle]

so pre calc u wont learn in school?

did you master calculus or no?

[slender copper]

nope

i'm learning it rn

[viscid thistle]

oh

what are the things or the formulas you usually take a lot in that course

[slender copper]

which one

[viscid thistle]

pre calc

[outer inlet]

I don't know where to put this h

[slender copper]

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

[viscid thistle]

oh so these things are in order right?

[slender copper]

yeah pretty much, khan academy does the work of organizing the material

[viscid thistle]

like you gotta go first with complex numbers and then polynomials and so on?

[slender copper]

yes

i mean

yeah

[viscid thistle]

oh alr

[slender copper]

i guess that's recommended

and also

even tho khan is great

you should also consult other sources

[slender copper]

HOLD ON

you do what you want to do

[viscid thistle]

i need some advices mate

i need some time to think about it

i mean im taking algebra II atm and my average is alright

[slender copper]

ok here's the thing

[viscid thistle]

like in the 80%

[slender copper]

i don't know what alg III is all about

i'm just basing my opinion off of a quick search online

[viscid thistle]

its like algebra II but a bit more detailed ig?

[slender copper]

you should talk to your teacher about it

[viscid thistle]

eeggggh

what do you study now

which lesson

in pre calc

[slender copper]

oh, i'm pretty much done with it

i'm doing the calc AB course rn

i just started

[viscid thistle]

you mean AP calc?

[slender copper]

yeh

https://www.khanacademy.org/math/ap-calculus-ab/ab-limits-new

i'm doing that rn

[viscid thistle]

aaaaaaa

but like you need pre calc to do ap calc right?

[slender copper]

ok but going back to course selection, a 9th grader who's never taken those courses officialy won't be able to help you much

[slender copper]

it's helpful to learn pre calc

[viscid thistle]

what grade are you?

[slender copper]

9th

[viscid thistle]

bruh moment

bruh moment

[wet oar]

Dang 9 grade

[slender copper]

LOL

[wet oar]

How long did it take for you to learn pre calc bro

[viscid thistle]

like a grade 9 studying ap can destroy a grade 11

but in our school AP classes are for grade 12 only

[wet oar]

What it usually is for 11th grade too

[viscid thistle]

kinda

[slender copper]

i knew most of pre calc, stuff like conics and matricies was new

[viscid thistle]

why my name is blank

[wet oar]

Oh

[slender copper]

ok i got class now

gtg

[viscid thistle]

alr cya

[wet oar]

See ya

[viscid thistle]

why tf my name is blank

[wet oar]

I think it’s your nickname for this server

You can change it

Go to the three dots when looking at channels then you should see it

[viscid thistle]

lmao i dont have perms

no lol some moderator changed my nickname cuz i dont have a name

if you press on my pfp

i dont have a name

[wet oar]

Oh lmao

[wet oar]

Nice

[viscid thistle]

what grade are you?

[wet oar]

Going into 11

[viscid thistle]

oh

same here

what courses do you take?

[wet oar]

This year I took pre calc, pre-ap chem, statistics, world history, sports, and Spanish

[viscid thistle]

oh no pre ap chem is my nightmare

[wet oar]

I’m scared for AP chem next year yeah

[viscid thistle]

there we go

look at this

one sec

[wet oar]

Ok

[wet oar]

Those are good options

[viscid thistle]

ig

[wet oar]

Like Good amount of aps and honors

[viscid thistle]

how do you study pre calc?

online or in school?

[wet oar]

I went in school most of the year

Some days we did zoom meeting in like November and December

[viscid thistle]

what did you have like previous math classes?

algebra II?

[wet oar]

Yeah

And algebra 1/geometry in 8th grade

[viscid thistle]

and when you went for pre calc, did you think it was hard?

[wet oar]

Not really you just have to know the concepts and practice a lot

The kids who struggled did not study or know the formulas

[viscid thistle]

how many hours do you study for it?

per day

[wet oar]

Like 1 hour every school day after class

[viscid thistle]

oh

ok here's a question

im taking algebra II rn and about to finish school in like 2 weeks, do you think i should go with trigo or pre calc?

[wet oar]

Pre calc

[viscid thistle]

hmm

[wet oar]

My class covered both

So depends

[viscid thistle]

do you take any type of geometry lessons in pre calc?

[outer inlet]

@sick steppe I got these using the method of skipping them but idk

are these using the second principle and should I redo them

[sick steppe]

what's the 2nd principle?

[outer inlet]

idk

but is this right

[sick steppe]

no clue, I'm not checking a bunch of questions you can check yourself

[outer inlet]

rip

I'm just gonna hand it in

[wet oar]

Most of it is just building on the concepts in geometry with more trig stuff

[viscid thistle]

ah

okay

[median ivy]

do we also count the x intercepts as solutions?

[patent beacon]

@median ivy
A solution of the system happens when the blue and green intersect

There's visibly 4 intersections, but there's infinitely many solutions to the system; whenever cos(2θ) = 1.

[copper vigil]

0<=theta<2pi

presumably

we make a cut along the positive x axis

just because

it's like taking the input theta modulo 2pi

@patent beacon

it's like a clock for instance. after 12 o clock comes 1 o clock

instead of 13

but clocks are weird since we start at 1 instead of 0

it should really be 0 to 11

and not 1 to 12

0:30 pm

[barren hatch]

Hey could I get some help?

[copper vigil]

k

[barren hatch]

I’m stuck on this problem. I’m supposed to find the exact cube roots of the complex number, no decimals, and I’m supposed to use radians and leave my answer in polar form -4sqrr(2)(1-i) I’m horrible at these and don’t know where to start

[copper vigil]

consider a circle.

are you listening?

[barren hatch]

Yes

[copper vigil]

consider a circle.

now divide it into 3 equal parts.

at what angles, 0<=x<360, will the trisections of the circle occur?

[barren hatch]

3pi/4, 17pi/12, 25pi/12

[copper vigil]

are you sure?

the first section is made at 0

i should have clarified that

0, 120, 240

convert those into radians

[barren hatch]

Oh ok I was way overthinking it

[copper vigil]

please.

hurry up

[barren hatch]

0,2pi/3,4pi/3

[copper vigil]

yep

now just multiply your original number by e^(i*theta)

where theta must be each of those values

so you will have 3 solutions

gg

[barren hatch]

Ok thanks

[copper vigil]

wait no i'm sorry

[copper vigil]

multiply the cube root of your original number by e^(i*theta)

for each theta

[barren hatch]

Ok sounds good thank you

[copper vigil]

haha secx

sex

lol!

[viscid thistle]

lmao

[copper vigil]

how many times will i give you the same answer

((f(c+h)-f(c))/h)

[viscid thistle]

ya it was wrong last time

i got it right the 2nd time after

[copper vigil]

$

$\frac{f(c+h)-f(c)}{h}$

[obsidian monolith]

EndTimes

[copper vigil]

where f(x) = 5secx

and c = pi/3

this is called a difference quotient

"RISE OVER RUN"

maybe you have heard that phrase before

it's just asking what the slope is over a very small interval

very small in this case meaning infinitesimally small

[viscid thistle]

is it still over h

[copper vigil]

ok let's review some notation conventions

if i tell you that f(x) = x^2

and i ask you for f(5)

what is that?

[viscid thistle]

10

[copper vigil]

5^2 = 10?

[viscid thistle]

o thats squared nvm

i thought it was *

25

[copper vigil]

right

and how did you get 25?

[viscid thistle]

plugged in 5 for x

[copper vigil]

yes

so do you see your error now

i gave you the general formula for any f(x)

but the question is telling you that f(x) = 5sec(x)

[viscid thistle]

oh ok

[copper vigil]

so try that again

[viscid thistle]

idk actually

[copper vigil]

ok let's make this really simple

$\frac{f(c+h)-f(c)}{h}$

[obsidian monolith]

EndTimes

[copper vigil]

what is f(x)?

[viscid thistle]

5secx

[copper vigil]

now we are given that c = pi/3

what is f(c+h)?

[viscid thistle]

f(pi/3 +h) idk

[copper vigil]

almost

what did we say that f(x) was?

think

[viscid thistle]

5 secx = pi/3 + h

idk

[copper vigil]

if you have f(x) and want f(c+h)

then you have to let x = c+h

5sec(pi/3+h)

[viscid thistle]

o ok

[mellow tapir]

endtimes

what is he asking

[copper vigil]

difference quotient

scroll up

[mellow tapir]

wouldnt the limit just be like

(5sec(pi/3 + h) - 10)/h?

[copper vigil]

yes

because 10 = 5sec(pi/3)

,w 5sec(pi/3)

[mellow tapir]

yeah

[obsidian monolith]

Results provided by WolframAlpha

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

Requested by EndTimes#8053

[mellow tapir]

cuz cos(pi/3) = 1/2

1/1/2 = 2

*5

=10

[copper vigil]

good job.

[mellow tapir]

lol

[mellow tapir]

so what is this quesion asking for

[copper vigil]

but it was given that you did not have to simplify

literally to just write the limit

[mellow tapir]

so its just

(5sec(pi/3+h)-5sec(pi/3))/h?

[copper vigil]

yes

[mellow tapir]

i c

[viscid thistle]

isnt it 5sec(pi/3)*tan(pi/3) cuz the derivative of 5 sec(x) is 5 sec(x)*tan(x)

[mellow tapir]

yeah but u don't have to worry about the derivative

cuz ur using the limit definition of the derivative

it says, "You do NOT have to simplify this answer."

so it wants you to just plug in x/3 for c

$\frac{f(c+h)-f(c)}{h}$

into this

[obsidian monolith]

rohan!

[mellow tapir]

so

$\frac{f(\pi/3+h)-f(\pi/3)}{h}$

[viscid thistle]

oh ok

so its just this

[obsidian monolith]

rohan!

[mellow tapir]

yeah

just like that

[mellow tapir]

same thing

$\frac{4(x+h)^4+2(x+h)^5-4x^4-2x^5}{h}$

i might've done it wrong b/c i tried to do it kinda fast

but it should be something like that

[viscid thistle]

wouldnt u use the definiton of derivative for it

[mellow tapir]

that's what i did

oh crap

[obsidian monolith]

rohan!

[mellow tapir]

its more like this lmao

f(x+h)-f(x)/h

[viscid thistle]

o ye

[mellow tapir]

yeah just like tha

[viscid thistle]

is the answer written as that then?

[mellow tapir]

yeah

i think either of them work

but urs is prob more right

b/c it says not to simplify

[viscid thistle]

ye

[barren hatch]

I just wanna check if two of my answers are right

I know they’re should be three

Could you help?

1. 8(cos 135+isin135)

2.8(cos(-45+isin(-45))

[polar wharf]

Guys I'm having a hard time understanding calculus

Would anyone care to explain

[willow bear]

calculus is a big subject with a lot of things that one might have a hard time understanding

youre gonna have to be a little more specific

and we might actually want to move to #calculus for obvious reasons

@polar wharf

[polar wharf]

Differentiation and intergration

[polar wharf]

What are we doing when we're integrating...

[willow bear]

ok so it's a conceptual thing youre stuck on

in some sense, $\int f(x) \dd{x}$ could be viewed as the answer to the question ``The derivative of what function is $f(x)$?''

[obsidian monolith]

Ann

[willow bear]

in this sense, integration is to differentiation what square roots are to squaring

there are, of course, more geometric/visual meanings you could ascribe to integration

i don't know if those were what you were looking for

[patent beacon]

@barren hatch
You also have to take the cube root of the 8. The question asks for radians. I'll use the common cis(t) for cos(t) + isin(t).

8cis(3π/4) gives 2cis(π/4)
8cis(11π/4) gives 2cis(11π/12)
8cis(19π/4) gives 2cis(19π/12)
Those are the three cube roots

[autumn solar]

how would you solve this? I tried getting the derivative abut im not sure where to go from there

i think i may have done derrivative wrong as well bc i got 2x+3+h but im unsure

I think the slope is 5 but idk how to go from there to find the rest of the equation

[trim hemlock]

is (1,3) the tangent point?

seems like (1,3) lies on f(x)

welp supposed its the tangent point, you found the slope, and then plug in the tangent coordinates back into the point-slope form to find the tangent line

[autumn solar]

Ohhh wait

[trim hemlock]

btw the derivative of f(x) isnt 2x+3+h

dont know how you got the slope correct

[autumn solar]

Is it h+5?

[autumn solar]

Oh I was looking at the answer key on the worksheet

But I didn’t know what to do after the derivative

[trim hemlock]

the slope is indeed 5

but the derivative is not 2x+3+h

check your derivative rule again

[autumn solar]

I think I just forgot to plug in 1 for x

[trim hemlock]

no

again its not 2x+3+h

the "h" is where you messed up

i dont know where you got that h from

[trim hemlock]

h is supposed to be appraoching 0

and that looks extremely wrong

write it out carefully and as a limit

dont try to shortcut it

your simplification was all correct, only one thing is thats not how you differentiate

[autumn solar]

I was talking to a friend earlier and he got this

Would it be correct (if you plug in 0 for h)

At the end

[trim hemlock]

yes

again tho

badly written out

[autumn solar]

How so?

[trim hemlock]

there is supposed to be a limit notation after the = sign each line

to represent that this is a limit

and not some random simplification

[autumn solar]

ah ok

tysm

[lyric stratus]

@trim hemlock

[trim hemlock]

Can you please stop trying to ping me and get my attention

Its late and i need to rest

If you just have some kidn of questions just leave it here and ask someone else

[sick steppe]

dont ping random users, especially when you havent asked a question in almost a month

[lyric stratus]

soryy

[sick steppe]

is it a test?

[lyric stratus]

worksheet

since i dont got a printer

[sick steppe]

ok..... what have you tried then?

[lyric stratus]

wait

im all done

can someone just make sure they are correct?

just say I and I will dm u

[chilly belfry]

https://youtu.be/mxMoR37zEeY

[viscid thistle]

would this be correct

[mild swan]

This looks good to me

[viscid thistle]

ye it was thx

[mild swan]

👍

[vapid mica]

A raffle drawing contains all the 15 Edison baseball players including 1 captain and 1 vice captain. If three names are drawn one after the other without replacement, what is the probability that neither captains will be selected?

would this be 13/15 * 12/14 * 11/13?

[main cedar]

This is not precalculus

But yes, that is right

[wooden rock]

what does expanding it mean

[vital girder]

does anyone know where to start for this precalc question

[storm crane]

what do you mean by where to start? question a? do you know what domain is?

[vital girder]

i know what it is but im not sure how to find any of this info on a graph

i usually solve it through equations

[storm crane]

domain just means the range of all possible x values

[vital girder]

right so is it 5,-5 then for the graph

[storm crane]

• 5 < x < 5 yeah

all the numbers between -5 and 5 are part of the graph

[vital girder]

ah okay ty

is there a specific formula for c

[storm crane]

zeros is a way of saying x-intercepts

'cause usually to find them you set the equation equal to zero, like
y = x ^ 2
0 = x ^ 2

[vital girder]

oh okay and the once u get the x intercepts are u able to formulate an equation to sub in f(x)

for d and 3

e

[storm crane]

this is not a continuous function, you're doing trying to find the equation

you just need to look at the graph and see where the function crosses the x axis

similar with d, you just need to look at the graph at x = 2 and find the y value

[vital girder]

oh okay

thank you

[wispy cedar]

y - 0 = d/dx(cos(2x)) (x-pi/4)

[gleaming pier]

Hey can anyone help me out with this? I got cosx=-4/41 but the answer has a radical of 41 on the numerator. Why is that? I’m doing 4c.

[storm crane]

did the answer you got have a radical on the bottom instead?

[gleaming pier]

No the answer I got was just 41 at the bottom

[storm crane]

i'm thinking you did pythagorean theorem wrong and forgot to square roote

[gleaming pier]

Okay so I’m supposed to square root the 41

[storm crane]

yes but do you understand?

[sick steppe]

more linear algebra, but with laplace expansion you can evaluate determinants along any row or column and get the same value

[gleaming pier]

Sorry I’m still a bit confused

[storm crane]

how did you calculate the hypotenuse? where did you get the 41 from?

[gleaming pier]

I did x^2 +y^2=r^2 then I plugged in the numbers giving me 41 however I didn’t square root it because it would have given me a decimal

[storm crane]

yeah you don't need to calculate the exact number, you just leave it as squareroot(41)

[gleaming pier]

So then what steps would I have to take to insert 41 on the numerator as well being seen as a radical

[storm crane]

it's called rationalizing, you just multiply the top and the bottom of the fraction by squarroote(41)

[plucky rampart]

Excuse me, what was the formula to get theta with a point on the Cartesian plane?

Nvm

[mellow tapir]

arctan(x/y)?

[viscid thistle]

maybe this is a better place to ask? #help-2 message

[viscid thistle]

hey

i have a question about exponential regression

if anyone can help

[viscid thistle]

It's funny how this is the quietest Channel on this server

[wet jackal]

I swear I hate half angle identities

[storm crane]

yup

did this become a socials channel? lol

[unborn blade]

can someone explain why this is negative? pls ping me

[storm crane]

when i factor out -16(x^2-4), i get:
x^2-4 + (4x^2),
which simplifies to x^2 - 4 + 4x^2
so yeah it should be a plus

[unborn blade]

damn

so this is from the answer key to a practice test

and theres like 4 of these kinds of mistakes in there

:/

[ivory pendant]

hey can anyone here help me?

I am very confused on this

[fleet yew]

-m(cost, sint)

(-kmcos^2t)+(-kmsin^2t) = -km(cos^2t+sin^2t) = -km

@ivory pendant

qed

[opal estuary]

got our tests back and i stil dont understand njumber 4

[uncut mulch]

what don't you understand about it?

[opal estuary]

lmao how to expand (2+h)^3 :/

xD

[willow bear]

did you mean #3 and not #4 then?

[opal estuary]

uhm number 3 and 4

please

[willow bear]

anyway, there are many ways to arrive at the expansion of (2+h)^3

[opal estuary]

what formula can you follow for it?

[willow bear]

one is to apply the formula (a+b)^3 = a^3 + 3a^2b + 3ab^2 + b^3

but if you do not remember that, treat it as (2+h)*(2+h)^2

you know how to expand a square, right?

[opal estuary]

i dont understand how she got 2^3 + 3(2^2)h+3(2)h^2+h^3

ye i do know for multiplying binomials

[uncut mulch]

one is to apply the formula (a+b)^3 = a^3 + 3a^2b + 3ab^2 + b^3
binomial theorem

or go the long way

[quaint citrus]

Can someone help mee

Please

[toxic flame]

[quaint citrus]

Can I send it to u?

[toxic flame]

just ask in here

[quaint citrus]

Could someone help with this please

[toxic flame]

like, all of it?

[quaint citrus]

if u told me how to do it generally I could maybe figure it out👉👈

Parametric equations

I’ll take what I can get

[toxic flame]

@quaint citrus ok. so for the first problem, you want to write these two functions as one by trying to get rid of the t.

so multiply the second equation by 2 and add it to the first

see what happens to the t

[quaint citrus]

Y=-4?

[quaint citrus]

It gets canceled out

[toxic flame]

right

[quaint citrus]

To both?

[toxic flame]

did you end up with 2y+x=-4?

[quaint citrus]

Yea

[toxic flame]

awesome

your final answer should be y=(x-4)/2

[quaint citrus]

Y wouldn’t x be negative

[toxic flame]

because i messed up. nice catch

for the third question, you can substitute $\pm\sqrt(x)=t$ into the equation with $y$.

[obsidian monolith]

coycoy

[quaint citrus]

So y=2 +_ sqrt(x)-1

[quaint citrus]

Y=(-x-4)/2 correct?

[toxic flame]

yes

[quaint citrus]

To both?

[toxic flame]

no just to the first one.

that is the answer to question number 1

[quaint citrus]

Gotcha

[toxic flame]

cool

[quaint citrus]

For number 3 I have y=2 +_ sqrt(x)-1

[toxic flame]

right. depending on your instructor, they may or may not accept that as an answer

it is technically not a function unless you choose a sign. i would list both and say that it could be one or the other

[quaint citrus]

Okk I see

[frigid sonnet]

i need help with "Find the zeros of the function algebraically" i need someone to break down this for me.

[toxic flame]

is there a specific function you want to find the zeros of?

[frigid sonnet]

@toxic flame you dont have to do this exact problem but this one is mine i just need to learn how to do this

i know i need to make f(x) = 0 but i dont know the formula for this

[river mortar]

Maybe it'll help

[storm crane]

'rotate

,rotate

[frigid sonnet]

@river mortar thanks checking now

[jolly fern]

How do I simplify (sinx - cosx)^2

[hallow thunder]

i would expand it out first and see if any trig identities appear

[jolly fern]

yea, sin^2 + cos^2 and sin2x appear

so I tried 1-sin2x and it said that answer and it said it was wrong

[hallow thunder]

strange

thats definitely a valid way of writing it

[jolly fern]

thats what I thought too

[uncut mulch]

did you use appropriate parentheses?

[jolly fern]

yes

[uncut mulch]

did you try not applying the double angle identity too?

[unborn pawn]

yeah try applying double angle

[uncut mulch]

NOT applying

[nocturne jacinth]

The top also could have been factored instead of using quad formula. (X-3)(X-7)

[indigo delta]

whatever is harder

[uncut mulch]

what's integerated math 3

"integrated math" is vague

is there a course description

[indigo delta]

personally, i think pre calc is pretty useless

if integrated is algebra 2 and pre calc in one, do pre calculus and do algebra 2 over the summer

pre calc is just trig functions

which are hard but can be self taught

[uncut mulch]

different places structure their math courses differently

so i don't have any idea what you're actually being taught atm

[indigo delta]

just do whatever is harder

if int 3 doesnt have precalc in it then yes

[uncut mulch]

pre-calc is mostly functions, graphing, intro to logs and exponentials,

which may also be part of an intermediate algebra course

its a fine line between the two

[chilly belfry]

https://youtu.be/sFX-wrcZH1M

[viscid thistle]

pls help

[plucky gulch]

You can take the derivative of f

[willow bear]

no you can't

it's not given as differentiable

you don't need to either

[plucky gulch]

true

[willow bear]

you are given that f(kx) = f(x) for all k >= 1 and x in R

from here it is not hard to show f is constant on (0, +infty) and on (-infty, 0)

[viscid thistle]

ohh ok
arigato gozaimas

[tranquil haven]

Hey when something approaches one but is undefined at one, would it be good to describe it as 1 - 1/infinity

[willow bear]

??

probably not

[tranquil haven]

How would I describe it?

[willow bear]

idk, your current description is too vague

[viscid thistle]

are you referring to asymptotes

[ancient rampart]

How do i do 8?

[plucky gulch]

,rotate

[uncut mulch]

what have you tried?

are you familiar with basic function notation?

[ancient rampart]

i dont know how to start

is it ((x+h)^4 - x^4)/h

[uncut mulch]

yes, that's how you'd start

then expand the (x+h)^4 using binomial theorem or otherwise

[ancient rampart]

ok

thanks

[unborn blade]

Hi, can someone explain this

im confused on the second step

how is xy' all of a sudden negative

(btw this is from a practice test answer key, this isn't a real test...)

nvm im gonna assume it's a typo

[uncut mulch]

there is no typo

distributive property

[unborn blade]

ah

i didnt see the outer pair of brackets

ty

[wooden rock]

Hay yall

I need a challenging properties of logarithms problem

[willow bear]

how about this: let $a, b, x$ be positive real numbers not equal to 1, and assume also that $ab \neq 1$. find an expression for $\log_{ab}(x)$ in terms of $\log_a(x)$ and $\log_b(x)$.

[obsidian monolith]

Ann

[willow bear]

@wooden rock

[wooden rock]

o cool uh

ig ill do that for fun

i needed one for a final math project lol

[small tree]

i want to study precalc can u plz recomd me resources and a good textbook that i can follow

[fluid acorn]

I would recommend use either Khan or the website Art of Problem Solving, they have some pretty cool e-books

[viscid thistle]

This site is great: https://tutorial.math.lamar.edu/

[dusk edge]

For textbook I would recommend Stewart’s calculus

Idk what precalc is but this is real calculus

It’s got a lot of exercises so it’s suitable for self study

Also pretty easy to follow

[sick steppe]

precalc is the course before calc..

[worn crest]

Would anyone here be able to hop on a call and help me study for a test I have in a few hours? There's some practice problems I want to run through and would greatly appreciate it if someone could

[dusk edge]

So what topics does it include then?

Like trig and stuff?

[sick steppe]

likely logs, trig, the stuff to prep for calc

[dusk edge]

Ohhhh

So basically high school level?

[sick steppe]

https://www.youtube.com/watch?v=9OOrhA2iKak&list=PLDesaqWTN6ESsmwELdrzhcGiRhk5DjwLP

[restive bridge]

Reviewing summations as I prepare for Calculus.

On Chegg, it gave one of these answers to the booklet questions:

https://i.imgur.com/XuGyU28.png

Wouldn't the answer actually:

1 + 3 + 5 + . . . +[2(n-1)+1]

Which would become 2n-1

No?

Nevermind that's wrong

No wait, I think I'm right.

Would love to hear a second opinion

[sick steppe]

yes it should be 2(n-1)+1

[restive bridge]

Woot.

Gonna report this answer as incorrect on Chegg.

Ty brother

[sick steppe]

or just.. dont use Chegg in the first place

[restive bridge]

Chegg got all of the answers for even numbers.

[sick steppe]

so?

[restive bridge]

I use the even numbers to reinforce my knowledge.

How else am I to double check the answers for even numbers?

[sick steppe]

wolfram

desmos

both are free

[restive bridge]

Oh dope, I'll check those out.