precalculus

[viscid thistle]

Guys I'm confused on how u would use l hospitals rule to evaluate the limit

[mental steeple]

Can anyone help me with this I’m not sure what to do next

[tight compass]

What are trying to show?

Trying to show what you have is equal to something?

[mental steeple]

Simplifying the tanx+cotx /csc^2

@tight compass

[tight compass]

simply to what?

Hmm try to get sin^2x + cos^2x in there.

@mental steeple

[mental steeple]

Just simplify

Simplifying simple trig expressions

[tight compass]

Try what I suggested.

You need end up with something nice.

[mental steeple]

okay

[mental steeple]

Not sure how I do that

[tight compass]

Observe you have sinx/cosx + cosx/sinx.

[mental steeple]

Yes

[tight compass]

What should you do to get sin^2x + cos^2x?

[mental steeple]

Multiply?

[tight compass]

Yes.

Try to get a common denominator cos(x)sin(x).

[mental steeple]

Do I do

Sin^2x + cos^2x / sinxcosx

[tight compass]

Yes.

[mental steeple]

And divide all that by 1/sin^2x

[tight compass]

Yes. Also what does sin^2x + cos^2x equal to?

[mental steeple]

2sin^2xcos^2x

Nvm I’m not sure

[tight compass]

Huh? That is not right.

[mental steeple]

how would I add that

[tight compass]

Try to recall pythagorean theorem.

[mental steeple]

Oh it equals

1

😂

[tight compass]

Yes.

After that you should get something simple.

[mental steeple]

Then divide?

[tight compass]

Yep.

[mental steeple]

This is what I got

[tight compass]

So what are you left with?

[mental steeple]

sin x cosx

[tight compass]

Not quite.

Try again.

[mental steeple]

Did I divide wrong

[tight compass]

Yes sort of.

[mental steeple]

what did I do wrong

[tight compass]

You have sin^2x/(cosxsinx).

What do you think should happen?

[mental steeple]

Where do I have that

Oh did u cancel the 1s out

?

[tight compass]

1 * a = a.

a/1 = a.

Do you know how to multiply fractions.

[mental steeple]

Idk not sure

Give me an example

I’ll multiply it

[tight compass]

a/b * c/ d = ac/bd.

[mental steeple]

Oh yea

[tight compass]

That is how I got that up top.

[mental steeple]

Btw for this it would be sinx * sinx / cosx *sin x

Right

[tight compass]

Yes.

[mental steeple]

Tanx?

[tight compass]

So what is the final answer?

Yes.

[mental steeple]

huh but my teacher got 1 as the answer

Want to see his work

[tight compass]

Not sure how your teacher got 1, unless they evaluate tan(x) at x = pi/4.

[tight compass]

Hmm 🤔.

[mental steeple]

right I’m confused to

I’ll ask him

[tight compass]

Ok I don’t see anything wrong with his solution.

I can’t seem to find anything wrong with ours.

[mental steeple]

okay

So both are right?

[tight compass]

Checking again.

[mental steeple]

👍🏼

[tight compass]

@mental steeple I found his error. In the last line tanx from previous line is not equal to sin^2x/cos^2x.

[mental steeple]

Yea I saw that to

Not sure where he got the cos2x from

And sun

sin

So we are right correct?

[tight compass]

Yes we are.

[mental steeple]

Nice I’ll tell my teacher about it rn

[mental steeple]

The 2 confuses me for this one

[tight compass]

Expand what each trig function means.

[mental steeple]

?

[tight compass]

Like express it in terms of cos and sin.

[mental steeple]

Ik that cot^2 = cos^2x/sin^2x

[tight compass]

Yes.

[mental steeple]

But idk what to do after

For csc

[tight compass]

What about csc^2(x)?

[mental steeple]

1/sin^2x

[tight compass]

Ok what do you do think we should do now?

[mental steeple]

Divide?

[tight compass]

Yes.

[mental steeple]

2Cos^2x

[tight compass]

Close.

[mental steeple]

Bruh I just got that wrong on my test smh

oh

[tight compass]

It should be cos^2(x)/2.

[mental steeple]

Oh

dam I got that wrong lol

It was that easy

[tight compass]

Next time be patient and work it out first before asking for help.

[mental steeple]

Just the 2 threw me off

Otherwise it’s easy

Also quick question if something was 1/cos^2x + sin^2x / cos^2x would that equal 1+sin^2x / cos^ 2x = cos^2x /cos^2x = 1

[tight compass]

Yes you can add it since the denominator are equal. Generally a/d + b/d = (a+b)/d. But 1 + sin^2x is not equal to cos^2x. It’s 1-sin^2x = cos^2x.

It follows from sin^2x + cos^2x = 1.

[mental steeple]

Okay ty

[spiral crescent]

you guys got a good math problem?

[sterile steppe]

I need some help evaluating a problem(top of the page)
When I can evaluate it jn 2 different ways(right and left side) I just don’t which one is correct

Btw I just graphed the angles at the bottom of each one

This is the correct picture

My bad

[hushed sphinx]

Note that tanx=1 happens for x=kpi+pi/4, and those x also give sinx=±sqrt(1/2).

However on the left-hand side you also get some spurious solutions caused by the squaring early on -- that is, x=kpi-pi/4 also gives you sinx=±sqrt(1/2) but don't satisfy the original equation.

[sterile steppe]

wait the x values also give it as +-?

I thought it was just positive

oh wait nvm forget that

ohhh ok this makes sense now

thank you

[umbral willow]

uh how does one find the intersect of 2 exponential functions

google wont help me

[hushed sphinx]

Set f(x)/g(x)=1.

Or find the intersection of their logarithms.

[umbral willow]

let me try that

[umbral willow]

thanks it worked

[velvet star]

question, how many point(s) does a tangent line intersects a curve of a function?

[steel tulip]

Depends on the function

Zero times to infinitely many times

[hushed sphinx]

You need to figure out exactly what "intersect" means to you first. Of particular relevance: Does the point of tangency automatically count as an "intersection"?

[sharp mist]

What does p represent in the way of graphing conics in polar equations represent?

ep/1-ecos(theta)

[ancient bloom]

Does anyone mind helping with a hw problem?

\

this is the math problem

when I factor it I get 131^2 k^2 t^2 -168t+48

17161+k^2 t^2-168t+48

my professor said I need to use the quadratic formula for this problem

But I'm still very confused

[viscid thistle]

Use the quadratic formula

a=17161*k^2

b=-168t

c=48

[brittle ice]

I need help with 63

[willow bear]

@brittle ice do you still need help with this

[brittle ice]

yeah

[willow bear]

if $z$ is such that $p(z) = 0$ then what is $p(\bar{z})$?

[obsidian monolith]

Ann

[regal harness]

hello, Im confused on this question. Is there an identity to use or something?

[drowsy elm]

Use properties of conjugates and the definition of a polynomial to show that $p(\overline{z}) = \overline{p(z)}$

[obsidian monolith]

Eevee Trainer

[willow bear]

i was addressing this question to jef

[drowsy elm]

Just figure out the θ that makes the first equation true, in the fourth quadrant. Then find sine & cosine of that angle

[drowsy elm]

Oh sorry

[drowsy elm]

In particular perhaps consider using inverse tangent

[gentle bolt]

is this all the topics that should be covered in pre-calc?

[gentle bolt]

deciding on if I should use these lessons or this one https://www.youtube.com/watch?v=FkUEsP9efFg&list=PLDesaqWTN6ESsmwELdrzhcGiRhk5DjwLP&index=2

[gentle bolt]

this one seems like the better course to watch right

[ionic sparrow]

Hii can anyone confirm if this is correct

[vapid plaza]

I think you want to check (i) again

[ionic sparrow]

Oh

The second one I think it might be is 2 because it matches based on the y-axis Bht it’s also similar the choice answer #1

[vapid plaza]

?

[ionic sparrow]

Like it could be choice two but idk the difference between choice 1 and 2

[vapid plaza]

You need to know the difference between (i) and (ii).
In (i) x approaches -4 from the left
In (ii) x approaches -4 from the right

[tight compass]

Usually system of equation, partial fraction decomposition, trig is covered in precalc. At least where I am from.

[quick harbor]

Need some help, I can send an image of the work

Domain and range of relations and functions

[vestal rock]

Lemme see if I can help, is it ok if you send the image regarding the problem?

[flat falcon]

Hello, I wanted to know what I should know to start deriving functions?

[crisp palm]

@flat falcon https://www.youtube.com/playlist?list=PLZHQObOWTQDMsr9K-rj53DwVRMYO3t5Yr

great series to watch to help understand calculus

[full pagoda]

differentiate

[crisp palm]

oh

derive differentiate

[vestal rock]

I'm pretty sure what he asked isn't in precalc at all

[crisp palm]

i am an idiot

🗿

i READ IT WRONG

[full pagoda]

no i'm pretty sure you interpreted it correctly lol

i'm like 98% sure they meant differentiating

but everyone always says deriving

[obsidian hinge]

^^^

[vestal rock]

pretty sure that's how its called when I started learning calculus.

[full pagoda]

deriving does not mean differentiating lmao

if you know calculus you should definitely know that

[vestal rock]

ik

[vestal rock]

no i did not know the difference by the time I finished calculus AB

[crisp palm]

but yeah

did they mean derive or differentiate

[vestal rock]

pretty sure the former if in #precalculus

[rare canyon]

Hello, I'm in need of help for a differentiation proving question I'm stuck at, I can send the question and what my working is so far, hoping someone could help me with where I went wrong/where I'm stuck at?

At the side it says k is a constant

[uncut mulch]

where's

coming from

[rare canyon]

is that how I'm supposed to differentiate x²k?

[uncut mulch]

no

how exactly are you getting that for the derivative of x^2*k

[rare canyon]

Product rule

[uncut mulch]

show in full detail

i don't want to keep asking how you did...
every time

[rare canyon]

Ack... That's all I wrote man, I'm not even sure what I'm doing so...

[uncut mulch]

how exactly did you apply the product rule?

it looks like you skipped stuff and./or didn't apply it properly

and also applying product rule to this is a bit overkill

[rare canyon]

like the whole equation, I'm supposed to use quotient rule to differentiate it, right? So I took the denominator multiplied by the first derivative of numerator,

but am I not supposed to use product rule to differentiate x²k?

[uncut mulch]

well to differentiate you fraction you could apply the quotient rule
but the issue with what you did is that you didn't differentiate x^2*k properly

you "can" apply the product rule if you want, but you'd need to apply it properly

[rare canyon]

oh wait

k is a constant

so it's essentially kx² right?

damn I didn't need to use the product rule

nvm I get it now, thanks for the help!!

[viscid thistle]

hi

i need help

[hushed sphinx]

That's not PREcalculus

[viscid thistle]

ok

sorry

[pallid summit]

Although it's differential stuff, I am happy to help. Why don't you try to differentiate it partially,if you know. Otherwise, I can give you a solution. I think the answer is a set of points which satisfy the condition above.

[viscid thistle]

i already did it now

its -2,2, 2,-2

[pallid summit]

Good to know

[viscid thistle]

thanks

[pallid summit]

No problem:)

[short saddle]

$P(X)$ is a real polynomial such that $P(X+1)-P(X)=X^{2022}$. Prove that $P(2/3) \geq P(0)$.

[obsidian monolith]

erictheeonicpizhao

[vale escarp]

how do i do this?

<@&286206848099549185>

do i find the magnetitude of each vector?

[steel aurora]

What is it asking for

[vale escarp]

it diodnt specify

[uncut mulch]

these look like nested combinations/binomial coefficients

just evaluate

[blissful stone]

is this about finding the discriminant?

[rare canyon]

nah

was asking about proving

it's resolved now so

[blissful stone]

alr

I should begin doing some precalculus in the nearest future

[short saddle]

To locate a whale, two microphones are placed 6000 feet apart in the ocean. One microphone picks up a whale's sound 0.5 second after the other microphone picks up the same sound. The speed of sound in water is about 5000 feet per second.

a. Find the equation of the hyperbola that describes the possible locations of the whale
b. What is the shortest distance that the whale could be to either microphone?

ig draw a diagram but i can't visualise

[fair cave]

still need help?

[short saddle]

yes

[fair cave]

ok could ya get the diagram?

[short saddle]

i'm literally going to sleep

[cursive estuary]

ok so 😂 how tf do u do this 😭 maybe im just not getting it but why is the f(x)= equation so huge ??

this is an example I got from trying to solve a hoemwork questions but I don't understand the instructions

[hybrid pewter]

f(x) in the explanation is a general rational function, a polynomial over another polynomial
the goal is to find the horizontal asymptote, if it exists, or to say one doesnt exist
to do this they are splitting the general rational function into 3 cases depending on the degrees of the two polynomials that compose it

so 18/(4x^2 + 5) is case (1) where the degree of the numerator is less than the degree of the denominator

[chrome haven]

A spherical zorb with a radius of 1.5m is being filled with water at a rate at 100π cm^3/s. At what rate is the height of the water increasing when the water is 20cm high??

Need HELP!

[rocky wind]

you may wanna try any one of the math help channels

[chrome haven]

cheers

[median oasis]

still need help?

i believe the area of the circle in at 20cm is .56pi m^2

or 56 pi cm^2

and (100pi cm^3/s)/(56pi cm^2) = 25/14 cm per second

[median oasis]

if ur wondering how i did this i used Pythagorean theorem

[viscid thistle]

woah

[median oasis]

?

[viscid thistle]

your handwriting is terrible

[median oasis]

i cannot zoom

it's hard

[viscid thistle]

from what i gather the radius is 1.5

[median oasis]

i was writing on notes on my phone 😆

i am talking about radius of the circle cross section

at the waterline

[viscid thistle]

the length of the chord?

[median oasis]

idk damn know

[viscid thistle]

ok

sure

use pythagorean theorem

and then double your answer

[median oasis]

🤨🤨

[haughty robin]

can someone help explain this?

idk which quadrant im supposed to go to

[stable yacht]

Besides that being a very recognizable ratio, the interval of [0, 2π) is nothing special.

[haughty robin]

ik your supposed to find the inverse

but how do i know which quadrant to go to

[stable yacht]

What do you mean by which quadrant? You mean to physically draw the triangle?

[haughty robin]

no, after you get the inverse you are supposed to figure out what quadrant it came from

cos^-1(4/5) = 0.64

then you need to find the reference angle

but idk what quadrant equation for reference angle im supposed to use

[chrome haven]

answer in the book iis 1/56cm per second

[median oasis]

idk how that's possible

ru sure

it should be 100/56 cm

or 1/56 m

[median oasis]

it says the interval 0-2pi so it's all 4 quadrants

[thin raft]

Why does partial fractions fail sometimes?

E.g. $\frac{1}{(x^2+4)^2}$

[obsidian monolith]

AstroRP

[thin raft]

How do I partition this?

[willow bear]

you can't, unless you're willing to go into complex number shit

this is already an elementary partial fraction though

[thin raft]

and how would that look like

because wolframalpha doesn't show anything (real or complex)

[willow bear]

$\frac{1}{(x-2i)^2(x+2i)^2}$

[obsidian monolith]

Ann

[willow bear]

,w partial fractions 1/((x-2i)^2(x+2i)^2)

[obsidian monolith]

Results provided by WolframAlpha

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

Requested by Ann#0413

[willow bear]

it gets something done

i guess you'll end up with complex logarithms which are going to be hell to work with

but it gets something done

[thin raft]

ah nice ty

[mellow tapir]

Friend was doing sequences, find explicit formula

$\frac{-6}{5}, \frac{7}{15}, \frac{-8}{45}, \frac{1}{15}, \frac{-2}{81}, \dots$

[obsidian monolith]

! Brontochad (RYC4blushysully)

[willow bear]

...19, 19, 19, 19, 19, ...

[mellow tapir]

Turns out if you write the bottom as a geometric sequence it works super nicely

1/15 = 9/135 so it continues the arithmetic sequence on top

[vagrant crown]

hello

i am new

i was bored today so i made piecewise functions with a single equation

https://www.desmos.com/calculator/gnobhw2wmy

it doesn't support >=, <=, =, or != in the domains though

[median oasis]

one time i made a penis on desmos

and i also made a person

👍

[willow bear]

you know desmos can already do that, right? :P

{condition1: formula1, condition2: formula2, ...}

[steel fern]

So I'm solving the problem 9x^2-6x+7=0

The actual answer is 1/3 ± √6i/3

[willow bear]

some of the issue appears to be in your handwriting, which messes up the equation(s) you're working with

also plugging things in incorrectly in some places

just in the first line alone:

1. why does the -b term appear not to be part of the fraction? the fraction bar should extend clearly to cover it.
2. the stuff under the root is b^2 - 4ac, which in your case should be 6^2 + (-4)(9)(7), not 9^2 + (-4)(9)(7) as you wrote.

it all went downhill from there

[steel fern]

lol
ok

[steel fern]

Where am I going wrong @willow bear

[willow bear]

you have literally not fixed the very things i just mentioned to you

[steel fern]

Hold on

[willow bear]

.

read this again

[steel fern]

I didn't see it lol

[willow bear]

[steel fern]

Oh so I'm just an idiot who's doing math at 4 am

Ok

Lol

Sorry

[willow bear]

why are you doing math at 4 in the morning

[willow bear]

quiz?

we won't do your homework for you.

ok then posting this here is pointless

everyone here has their own problems to deal with

nobody gives a shit about yours

[median oasis]

after b^2 it should be - not +

[supple owl]

war was here

[willow bear]

"a discord trans"

[grizzled orchid]

b&

[willow bear]

thank you

[supple owl]

guys can you reminde me by the binomial theorem ?

[willow bear]

$(x+y)^n = \sum_{k=0}^n \binom{n}{k} x^{n-k}y^k$

[obsidian monolith]

Ann

[supple owl]

$what do \binom{n}{k} mean$

[obsidian monolith]

MRme001

[willow bear]

binomial coefficient, a.k.a. "n choose k"

$\binom{n}{k}$ is defined as $\frac{n!}{k! (n-k)!}$

[obsidian monolith]

Ann

[supple owl]

thanks

[pale solstice]

in the function 4/(x^2+x) why is there a graph under the x axsis?

i understand that x goes to ifinity when x approches -1 from the left and 0 from the right

i think it is because x is defined between -1 and 0, should i take the derivitive and look for when the derivitive is 0 to determent when x is defined between -1 and 0 ?

[willow bear]

it's part of the same graph, the function is just negative there

[pale solstice]

should i take the derivative and the look for max point to determine when that part of the graph starts?, in this case its -16

[willow bear]

do you mean the highest point of that part?

if so then yes

...your phrasing is hard to parse

[pale solstice]

yes

yea im not the best with either math terms and explaining math in english, but thanks for the help!

[final saddle]

drawing 1/4*(x^2+x) might help u visualise that graph

that's a reciprocal of parabola

[pale solstice]

ill try thanks for the tip

[final saddle]

zeros of this graph will be a vert asym of the reciprocal graph

and loc min will become loc max

hence the "max point" of that particular part

[final saddle]

cuz u can't divide by 0 so it will be undef so asym

[final saddle]

cuz as y becomes larger, the reciprocal becomes smaller

[pale solstice]

thanks for the help, ill keep that in mind

[willow bear]

missing parentheses

[final saddle]

💀 mb

fixed

[silk fjord]

⬇️

[valid parrot]

I don’t know how to prove this, can someone help ?

[median oasis]

i don't think that's precalc

[dusky bramble]

are you sure this is correct ?

If you multiple the square root by M
the M^2 is canceled out, leaving you with

$\sqrt{P^2+4\cdot{pi^2}\cdot{n^2}\cdot{M^2}}$

and as M approached infinity, this entire expression does the same

[obsidian monolith]

Deus_Vult

[steel fern]

Ok

[onyx gorge]

i guess it applies to any math, but i’m in precalc rn.

does undefined = undefined? or does it not equal anything bc it’s… undefined

[astral apex]

technically the word 'undefined' has no business showing up in a proper equation

but people do it all the time in math classes and it's understood what they mean

like there will be a function, say f(x) = 1/x

and people will write "f(0) = 1/0 = undefined"

what they really mean is f(0) is undefined

[vapid plaza]

1/0 “is” undefined, but not that 1/0 “is equal to” undefined

[astral apex]

right

[onyx gorge]

i’m solving trig equations and such and i’m checking my solutions. and i had to find out the cot of pi

so it popped up in that context

[astral apex]

cot(pi) is undefined

sometimes people may write cot(pi) = undefined, which is sloppy, but it's generally understood

[onyx gorge]

wait let me write out what i remember

cos^2(pi) * cot(pi) = cot(pi)

would those two expressions equal each other?

[astral apex]

I see

I mean, both sides are undefined

I see the point is you can erase cos^2(pi), since it's 1

but you could even just say "cos^2(pi) * cot(pi) is undefined" and stop there without using an equation

[onyx gorge]

would they equal each other though

that’s all i’m worried about because my math core was on that

same exact problem

[astral apex]

I assume they mean for you to say yes

[onyx gorge]

OH THANK FUCK

[astral apex]

kind of a sketchy problem though

[onyx gorge]

yea i may have solved it wrong but i checked it over twice

unlikely but very much possible

[opaque berry]

is precalc hard learning it for the first time? I'm in algebra 2 right now and I hear it's like a whole new concept in math so I wanteed to hear other people's opinions on it

[obsidian hinge]

nah it's not bad

precalc is pretty easy

calc is the first bit of real actual math you get to see

[opaque berry]

algebra 2 or precalc which one do you think is harder learning for the first time

[astral apex]

I mean

if you ask me, it's all the same shit

[obsidian hinge]

equal tbh

precalc builds off algebra 2 just like algebra 2 builds off algebra 1

again, calc is where you first see math

[opaque berry]

alr cool thx

[astral apex]

precalc has the unit circle and common trig values, it can be a lot to take in

[obsidian hinge]

trig makes sense as an extension

he'll be fine

it's not bad

as long as you understand em

and why it works the way it does

[astral apex]

agreed

but that's easy to say when you do understand it 🙂

[obsidian hinge]

hm fair

[opaque berry]

i don't remember anything from trig because it was during quarantine and I was playing valorant during all the zoom classes...

damn

[astral apex]

some students find all the factoring degree 4 polynomials and crap from algebra 2 harder than anything in precalc

really depends on what you're stronger in

[obsidian hinge]

gods i forgot we had to do that lmfao

[opaque berry]

im good with the polynomial stuff i think

can someone help with #help-25 pleaseeee

[onyx gorge]

same concepts, different lingo

learning sines, cosines, csc, and all that jazz is like learning a new language but once you get the hang of it, it’s super easy

[opaque berry]

👍

[astral apex]

it's a chore

you have to guess a root by the rational roots theorem

[onyx gorge]

is fifth degree polynomials in precalc?

[astral apex]

not really, but algebra 2

[onyx gorge]

i do not remember learning that in alg 2

oh wait, p’s and q’s and synthetic division?

[astral apex]

they even do descartes' rule of signs

[opaque berry]

i wish i'm that one kid in the back of class that pays no attention in class and is always watching youtube videos in class but still somehow knows all the math and is a genius

[astral apex]

it's done because you have to guess a root, and you might get unlucky and not try the right one until the last possible one

[onyx gorge]

used to be me until this year

[opaque berry]

lucky

what are you learning rn

[onyx gorge]

precalc

calc ab junior year and bc senior year

assuming i pass the classes

[opaque berry]

same for me

[astral apex]

possible but would take some trial and error

[opaque berry]

i dont even know anything about calc but i already hate it

[onyx gorge]

my friend’s taking it rn and she said just know the unit circle by heart

[rose basin]

Basically this question asks me to find the vertical intercept and I'm wondering if I solved it properly using this equation that I did here.

Answer is b = 8,000

[hushed sphinx]

Is the second of your images part of the problem or your answer?

[rose basin]

Part of the answer

It's just what I did to find my answer

[hushed sphinx]

Can you state a concrete formula for profit as a function of items sold?

Plug 2000 and 3000 into that and verify that you get 24000 and 32000 out.

[rose basin]

Yeah it works

I was able to solve the problem

Thanks

[viscid thistle]

It's better to learn how to derive or recall it again and agaon

Learn quadrant one, there are three values, 1/2, sqrt 2 /2 and sqrt 3 / 2

the pi values in quadrant 1 are more obvious on inspection. Add pi to move half a unit circle to quadrant 3, add pi/2 to move a quarter a unit circle to quadrant 2

[onyx gorge]

true true

[karmic zephyr]

brooo

its 1am

and i just got to vectors

and this shit is tripping

like, why i gotta find out how to represent it in how many one unit movements it made

[willow bear]

you don't "gotta" do shit if you're so repulsed by it

but this is the decomposition of a vector in the standard basis

and especially in linear algebra one is often interested in looking at vectors through a different basis than the standard one

to say it in a highly abridged manner that skips over most of the details

[karmic zephyr]

not repulsed, just dazed and confused xD

[fringe raft]

because think of the cartesian coordinates as an incomplete quantity and you want something to tell you about the direction of functions and curves

[hollow elk]

what are all the topics i have to learn before studying precalulus?

[hollow elk]

i learned trig

what about exponentials

are polynomials used in precalc?

how

ok

how advanced should my polynomial skills be?

what does 3rd degree include eg. algabraic geometry

simplifying dividing and multiplying then i can move on to precalculus?

ok thanks i might be able to do that in a couple of days

no prior knowledge tho

possibly

thanks

ik what to study now

[tired pilot]

I have this complex analysis problem but I'm pretty sure it's just a geometry/precalc problem about hyperbolas. I have $z\in\mathbb{C}$ where $z-1=r_{1}e^{i\theta_1}$ and $z+1=r_{2}e^{i\theta_2}$. I need to show the region described by the conditions $r_1 > 0, 0 < \theta_1 + \theta_2 \leq \frac{\pi}{2}$ is the region between the unit hyperbola $x^2 - y^2 =1$ and the x axis in the first quadrant. I'm stuck showing how z satisfying the constraints involving $r_1$ and $\theta_1 , \theta_2$ imply z is in the region described above, I think I see how to show the opposite inclusion.

[obsidian monolith]

DootDooter

[tired pilot]

Geometrically we should have something roughly like this:

The last thing I could think to try was to solve for z in terms of $r_1,r_2,\theta_1,\theta_2$ and then try to sub into $x^2-y^2\geq 1$ looking for some nice angle relationship.

[obsidian monolith]

DootDooter

[tired pilot]

That got me here:

Assuming I didn't make some super dumb algebra or trig mistake, which I might have because my brain is currently kinda fried.

But I don't see any nice relationship that is useful from here. If anybody sees any way to proceed ping me.

Wait maybe I see it

$z+1-(z-1)=2$ so $r_2 cos(\theta_2) - r_1 cos(\theta_1) = 2$ also. So, $r_1 r_2 cos(\theta_1+\theta_2)\geq 0$.

[obsidian monolith]

DootDooter

[tired pilot]

Pretty sure picking theta one and two in the interval I need and reversing my steps in that last image will get me the identities that I need.

[misty gulch]

https://dontasktoask.com/

[cedar harness]

ok sorry

[misty gulch]

ask your question, just don't ask to ask

[bronze pendant]

hey guys do you mind helping me with the one i got wrong? (i got my answer for the 1st one by doing <340cos40, 340sin40> )

[willow bear]

the wind is blowing southeast while your vector is pointing east

[spring tendon]

$$ \begin{aligned} &y \geq-2\ &y \geq x+3 \end{aligned} $$

[rose basin]

Anyone here know how to solve this problem? I don't understand how to solve it.

[abstract lodge]

if u take the natural logarithm of e^anynumber, theres a power rule that allows u to cancel the e and move the exponent down

so take ln of both sides

look at the top example

so u can just ln both sides and isolate x

[rose basin]

Alright thanks for the help

[hollow elk]

i am gonna study logarithms

i am a begginer but i do however know the very very basic concept such as what the function does

could someone give me recommendations on what to learn

[abstract lodge]

what grade are you in?

[abstract lodge]

i would suggest getting a strong understanding in normal algebra first

like use khan academy or some other source to learn basic algebra then move on from there

[safe stump]

anyone have other alternative step-by-step solution without prior knowledge of L'Hospital Rule?

I want to know why that limit become natural logarithm, using theorems and such

zoomed in graph can show me the value, but still not satisfied with that one

[tight compass]

This is what they had. We have an indeterminate form of 0/0 when we take the limit as x->0. So taking the derivative wrt x for the top and bottom of (2^x - 1)/x we have it's ln(2)2^x. Now take the limit as x->0 we have it's ln(2).

As for an alternate proof, maybe graphing the function in desmos and zooming in to seem what values it's you think it's converging to and the using the definition of a limit to prove the function converges to that.
I can't think of anything else right now.

[safe stump]

Have done with graphing proof and i saw the irregular shape after zoomed in the graph. However, the algebraic solution that u told me or from the pic above is kinda recursive. I just curious whether there is algebraic way to solve it without prior knowledge of derivative itself. Assume that equation is just an algebraic equation and as a people without calculus knowledge, i want to solve it just using algebra

[viscid thistle]

I need help one those two questions please

[safe stump]

Maximum means something with differential. Open your book

for 9a, use the limit definition of derivatives and the derivative law of trigonometry

[viscid thistle]

Those are the two types?

One with limit deriv and the other one is with trig

[safe stump]

yeahh what else do u think??

[viscid thistle]

Ohh I got it

[safe stump]

if you know what is sec(x) means, then everrything's trivial

[viscid thistle]

I understand now

Thank youu!!!

[safe stump]

ur welcome

[sonic merlin]

let's say I start investing 160 dollars at the start and i don't add anymore money and every week I earn 5% profit, what's the equation for this scenario?

[woven valley]

160(1.05)^w where w is every week after investing that 160

Pic unrelated

Oh wait

Are we reinvesting this money

“Compounding interest”

If we are then the equation above is fine

[hushed sphinx]

If you're offered an investment that will give you 5% profit each week, it's a scam, no ifs or buts. Run.

[sonic merlin]

its a hypothetical question, wasnt offered anything

[woven valley]

Bruh=moment

[sonic merlin]

i was curious

thanks

[sonic merlin]

yeah its compounding interest

[woven valley]

Yeah we’re good then, the standard form for compound interest would be a(b)^t where a is the original investment, b is the increase (this number should always be greater than 1 to represent an increase) and t represents integer unit for measuring time, like 2 weeks or 5 months.

[lucid current]

can i get a quick rundown on why a certain thing is the way it is? I'm in calculus but ive completely forgotten about sin, cos and tan related stuff

i cant remember how to actually reach this result

[astral apex]

apply arctan to both sides

[honest gorge]

Real quick I was wondering if I did this problem right

Trying to find the vertex

[astral apex]

the way you take minus signs out of the parentheses is no good

[honest gorge]

Wait why isn’t a negative leading term

[astral apex]

I mean you go from

$(-x^2 + 4x) - 5$

to

[obsidian monolith]

ManifoldCuriosity

[astral apex]

$-(x^2 + 4x) - 5$

[obsidian monolith]

ManifoldCuriosity

[astral apex]

when you take out a minus sign in situations like this, you have to flip the sign of everything inside the parentheses

[honest gorge]

Oh I did that

[astral apex]

oh I see, you do it in the next step

just so you know, the equation where you didn't do it yet is technically wrong

[honest gorge]

So I should do it early?

[astral apex]

in one step

$(-x^2 + 4x)-5=-(x^2-4x)-5$

[obsidian monolith]

ManifoldCuriosity

[astral apex]

but ok, you do get there

but then you have another problem

[honest gorge]

Oh okay but I dont think I solved it correctly

[astral apex]

you correctly write + 4 inside the parentheses

but then you balance it with -4 outside

which would be right if it weren't for the negative sign in front of the parentheses

[honest gorge]

I did that because -4/2^2=4

[astral apex]

that part's good

it's the (-4) you wrote after the parentheses

[honest gorge]

I thought we do that to both add the -4 to both sides

[astral apex]

that minus sign in front of the parentheses means you're really doing -4 to your expression

so you have to balance that with the opposite, +4

should be:

$-(x^2-4x+4)+4-5$

[obsidian monolith]

ManifoldCuriosity

[astral apex]

now somehow you do end up with -1 below that

which is right

but it doesn't follow from what you wrote

in the end your answer is right

but the work has several mistakes

[honest gorge]

I had double negatives I wrote -(-4)

-5

[astral apex]

ohh

ok I see it

[honest gorge]

So I got the right answer but my steps are confusing?

[astral apex]

yeah

[honest gorge]

Alr I’ll fix it

[astral apex]

you seem to know how to do it, just not written up in a usual way

[honest gorge]

What if I did it by equaling the equation to 0

[astral apex]

you can do it all the same way

[honest gorge]

Ok Alr Ty

[astral apex]

sure thing

[honest gorge]

Is this better?

[astral apex]

fixed some things, but you forgot about x for a few lines

you wrote x^2 - 4 + 4 in the parentheses

instead of x^2 - 4x + 4

also you should have a + before your 4 after the parentheses

[honest gorge]

Can someone explain this to me?

[uncut mulch]

what have you tried?

do you know the intermediate value theorem

[honest gorge]

No

[uncut mulch]

consider looking it up first

[honest gorge]

Okay so I have to substitute both values in the equation?

[uncut mulch]

yes, (separately)

[honest gorge]

This is what I got

Wait but they are both negative so is there no zero?

[viscid thistle]

There is a zero, it goes down, then stop, then goes down

[honest gorge]

Yeah I’m confused now

There’s no number between -3 and -4

[grand vigil]

help

help

<@&286206848099549185>

[viscid thistle]

It like this but going down instead

[uncut mulch]

Wait but they are both negative so is there no zero?
not necessarily, depending on the function, there could be a zero in the given interval
the IVT can't be used to conclude that there no zeros

so in this case since both are negative, IVT cannot be used to determine if there's a zero in that interval

[grand vigil]

help

plshelp

[stable yacht]

It’s an equilateral triangle. You know the angles.

And you have an altitude.

[grand vigil]

hm

[civic sierra]

Have you learnt about derivatives?

[honest gorge]

A little bit

But didn’t go into detail

[grand vigil]

wait i will give a sum it's impossilbe to do

[civic sierra]

So you havent been taught what they represent right? And their use?

[honest gorge]

I have but it’s really confusing to me

[uncut mulch]

if the signs were different, IVT guarantees that there will be at least one zero
otherwise it doesn't do much

the IVT can't be used to conclude that there no zeros
so in this case since both are negative, IVT cannot be used to determine if there's a zero in that interval

[civic sierra]

You'd have to show that there exists/doesn't exist a zero using derivatives, I can't think of another way

[honest gorge]

This is the example that was given

Wait wrong one

This is it

[civic sierra]

This is in accordance to

Do you have an example where the signs are the same?

[honest gorge]

This is the only one that was given

[civic sierra]

I guess since it specifically requires using IVT your answer is that it cannot be determined then

[honest gorge]

Oh okay alright Ty

[viscid thistle]

I need help please

[stable yacht]

“Least productive” should be when P = 0. You should be able to set the equation equal to 0 and solve.

[viscid thistle]

can i have help pls

[agile sable]

Can you be more specific?

[viscid thistle]

all the answers that i entered are incorrect

[stable yacht]

The question is worded really awkwardly, but from how I understand it, most of your answers are correct.

C is incorrect simply because (0, 2) falls on the circumference of a circle with a center at (2, 2) and a radius of 2.

It also looks like D is not asking what it intends to ask. Your answer is correct, but I think there might have been an error with the question.

[agile sable]

Do monsters have width?

[hushed sphinx]

We can use the IVT to prove that there is a zero in (-1000,0), and that there is a zero in (0,3) and that there is a zero in (4,1000). If we then also know that a polynomial of degree 3 can have at most three zeroes, then arguably we have determined that there is no zero in [3,4] "using the intermediate value theorem".

[fast monolith]

Can I borrow some help to get this started please?

[fallow quiver]

The ball in is air for as long as there's vertical motion.

The objective starts from y = h_0 and ends up at y = -h_0 finally again, when that happens it's finally not in air.

Use those facts.

[glacial mirage]

I think it’s asking to find whether a point lies within or on a circle given the origin and radius

[hazy dust]

hey this one has been driving me bonkers, i think i have to use implicit dif/related rates but i’m losing my mind some help would be appreciated

[willow bear]

would you like the slightly cheaty but legit solution, or the solution your teacher likely expects from you?

[hazy dust]

both would be good to be honest

i’d like to learn the proper solution but seeing the cheaty solution could help speed me up on an exam

[willow bear]

cheaty: the radius and height of your cylinder are given by r(t) = 5 + t and h(t) = 8 - 4t, and the volume is V(t) = pi * r(t)^2 * h(t) as you wrote. in all this, t=0 is the moment in time that is of interest to us. your goal is to find V'(0), which you can do by expanding out V(t) and applying little more than the power rule.

'proper': same thing except you differentiate V wrt t symbolically, treating r and h as functions of t (which they are) and ending up with a mess of r, h, dr/dt and dh/dt into which you then plug the numbers. no mention is made of any specific point in time

[hazy dust]

ah thank you

i think my mistake was not interpreting r and h as functions of t

which totally makes sense now but i just got confused since the usual style of questions doesn’t normally give 2 values (ie radius and height) and couldn’t figure out how to apply it

cheers man 🙂

[viscid thistle]

Why do we turn terms into smaller with '

like

x' = (x - 1)

whats wrong with x -1 ?

[agile sable]

X-prime, as its called is a way of saying its different but similar to x

x = (x - 1) isn't valid

[vapid plaza]

It’s all a matter of notation
x’ is just a symbol or letter used in math, similar to a or b

And it meaning in use depends on context:
In calculus it usually means the derivative of x
In other places it probably just means the new value of x after some change

[chrome scarab]

Hey can someone help me with rhis question?

The second pic is my try

[chrome scarab]

<@&286206848099549185>

[shut jewel]

uhm sry but what is the question asking? I dont really comprehend this

[hazy dust]

i’ve been given a relation and am calculating the dy/dx using implicit, but it is asking for it in terms of s only how do i find without y?

find dy/dx in terms of only x

that’s what i got

<@&286206848099549185>

[past meadow]

sorry for the late response, but you can solve the implicit equation for y explicitly since y>0

@hazy dust

Then, you can either take the derivative of that directly, or substitute what you got for y into the implicit derivative you've already found.

[tranquil haven]

How would I differentiate this?

I need to get a general formula for displacement based on gravity and it's altitude

$\rho(t)$ needs to be substituted later based on the position then

[obsidian monolith]

sentinel

[stable forge]

Could someone help me with my last few problems, there’s some proving Identitys, a double angle problem, and a few other things

[willow bear]

@stable forge don't ask to ask, just post your problem(s) that you need help with

[rocky wind]

the last term in the denominator is $(\rho(t))^2$ since you're squaring the denominator of the previous fraction.

[obsidian monolith]

vin100

[spiral locust]

What I do

[stable yacht]

What question are you asking? That is just an expression.

[mental steeple]

Can anyone help me I have to verify the identity

[patent beacon]

There's only sin/cos on the left, so convert everything to sin/cos on the right

[mental steeple]

This is what I did ignore the cos/1 in second step

[full pagoda]

why'd you turn sec^2(x) into cos^2(x)

[onyx gorge]

omg i love these hold on

sec^2(x) is equal to 1/cos^2(x)

[mental steeple]

Okay

So 1/cos^2x/sin^2x/cos^2x-1?

@onyx gorge

[onyx gorge]

yes that’s good

now for the denominator, combine the two terms by transforming the 1

[mental steeple]

Wdym

[onyx gorge]

you have this in the denominator right?

[mental steeple]

Yes

[onyx gorge]

you need to somehow combine those two terms

so find a common denominator

[mental steeple]

Cos2x

?

[onyx gorge]

just cos^2(x)?

oh wait

[mental steeple]

I think

[onyx gorge]

yea cos*2(x) is the common denominator

so how would that effect the 1

[mental steeple]

It would be 1/cos2x

[onyx gorge]

does 1/cos^2(x) = 1?

[mental steeple]

no

[onyx gorge]

so how could you change the 1 so that the denominator is cos^2(x) and would still equal 1

[mental steeple]

Can’t you do cos2x/1 then cross multiply which the cos2x cancels out then your left with sin2x-1 which equals -cos2x

[onyx gorge]

you mind writing out the work and taking a picture of that?

[mental steeple]

ok

[onyx gorge]

my mind is dying

[mental steeple]

@onyx gorge

[onyx gorge]

gasp

no

[mental steeple]

:(

[onyx gorge]

would you ever do this?

[mental steeple]

No

[onyx gorge]

same concept, you can only cross out if it’s multiplication

[mental steeple]

So we are subtracting right

[onyx gorge]

yea

no multiplication

[mental steeple]

How do I do it though

idk how to subtract it

[onyx gorge]

lookey

[mental steeple]

Oh I was thinking of that didn’t know I could do that

[onyx gorge]

it’s way harder to figure out sometimes because it’s letters and not numerical

yea, that’s valid

[mental steeple]

So do I subtract scrips

across

[onyx gorge]

yes yes

[mental steeple]

Wouldn’t the top =1

[onyx gorge]

sin^2(x)-cos^(x)/cos^2(x)

nah. that’s sin^2(x)+cos^2(x)

[mental steeple]

That’s what u get?

After subtracting

[onyx gorge]

yep, for the denominator of the entire expression

[mental steeple]

where did you get cosx

Isn’t it cos2x

[onyx gorge]

i may have typed it wrong

let me write

[mental steeple]

Ok

[onyx gorge]

and now it’s just division!

[mental steeple]

-cos^2x / cos^2x = -1?

Sin^2x/cos^2x = tan ^2x

tan^2x -1?

[onyx gorge]

don’t over think

[mental steeple]

what where did you get the 1/cos^2x

[onyx gorge]

the original equation

sec^2(x)

[mental steeple]

ohh

Yes I didn’t see that

Lol

[mental steeple]

Thank you

[onyx gorge]

divide, cross multiply, and you get your answer

don’t be afraid to convert

[mental steeple]

Got it

[ebon barn]

I’m confused on relative maxima and minima

I just started summer precalc btw

[onyx gorge]

what the kronk is that?

[ebon barn]

It’s just saying if the graph is at a relative minimum or maximum

[young peak]

yow just a simple question, is integration the inverse process of differentiation or the reverse process?

dunno if reverse and inverse are the same

[heavy sonnet]

I don't think reverse is a formal description

They're inverse operations

Though they take functions as parameters not singular number.

(although a constant could be thought of as a function that returns the same number independent of the input)

[viscid thistle]

Is it always the case that if g(f(x)) is one to one this implies f(x) is also one to one and it g(f(x)) is onto then this implies g(y) is also onto? Prove whether the statement is true or not

[stuck lark]

@viscid thistle if u agree then prove it, if not give a counterexample

[viscid thistle]

The problem is I don't know whether it's true or not .
I feel like it may be true but I don't know how to prove it

[stuck lark]

u can try getting an idea of whether its true by playing with examples

if ur proving, it helps to unpack definitions (in this case those of 1 to 1 & onto)

[clever gazelle]

Someone can help me with this problem
-3x(2x+3)>-(-3+4x)

[worthy idol]

-6x²-9x > 3-4x
4x-6x²-9x > 3
-6x²-5x-3 > 0
6x²+5x+3 < 0

Solving 6x²+5x+3 = 0:
D = b²-4ac = 25-24×3 = 25-72 = -47 => x∈Ø => there are no solutions for -3x(2x+3) > -(-3+4x).

x∈Ø.

[ebon barn]

Should I factor when simplifying

Just look at the last two lines

The answer key says I don’t need to factor out the h but I feel like I should

I mean, doesn’t that make it…simpler?

[stable yacht]

It depends on what you are doing with it.

If you are finding zeroes, trying to factor saves you time over the quadratic formula.

Especially if one of the zeroes is 0.

[gritty crane]

1. Let "F" be a function of Real variable, defined by f(x)=mx+b /(this bar means such that) 2f(2) + f(4) = 21 and f(-3) -f (1 ) = -16. Find 1/3 f(1)
2. If f(x) = ax^2 +bx +c ; f(-1) +f(1/2)= 15/4 ; f(-1)=0 ; f(1) = 8 . Find f(5)

[ebon barn]

Not doing anything with it. So I guess it doesn’t matter either way.

But yeah I get what you’re saying it would definitely be smart to factor if you are doing pretty much anything with it.

[bitter drift]

Oh we just did that topic

Any questions?

[stoic crater]

Does anyone know why they use the cross product of u and v

Instead of v and u

[stoic crater]

Yeah lol

[bitter drift]

Bcz Matrixes are non commutative

So the order you multiply them matters

[stoic crater]

Oh

But then how would a person know which is the correct order?

[bitter drift]

I think you have learnt This right r.n - a.n

Where r is your general point and n is the normal vector

[stoic crater]

I don't think my precalc class taught that

what is an?

a is a specific point, right?

[bitter drift]

Yh

[plucky slate]

sin^2 x = sin x^2 ???

[old isle]

that is an identity

not an equation

every real number is a solution to that

oh wait

sin^2x and sinx^2 are the same thing right?

unless you mean sin(x^2)

[stable yacht]

,,sin^2(x) = sin(x)^2

[obsidian monolith]

Lidoh

[stable yacht]

I think that was what was being asked. But it is a bit confusing when you don’t use parenthesis for the argument of sin.

[raw python]

$\frac{a - bx - 16}{\sqrt{3}x(\sqrt{a - bx} + 4)} = \frac{a}{\sqrt{3}x} + \frac{-bx}{(\sqrt{a - bx} + 4)} + \frac{-16}{(\sqrt{a-bx} +4)^{2}}$

[obsidian monolith]

texaspb

[raw python]

is this expansion correct?

[viscid thistle]

no

i dont think so just by looking at it you can add all those and get a common base from those partial fractions

[obsidian monolith]

Preetham

[viscid thistle]

can someone help me w this

[slate reef]

,rotate

oof

[slate reef]

uuh I don't get it
why is there 2 prices of apple pies

[viscid thistle]

no clue:(

[slate reef]

@viscid thistle hmm I think i understand now

so

f(p) has linear relationship therefore it is in the form ax + b

a and b are constants and x is the amount of pies bought

if you substitute those values given you get a system of equations

3000 = 500*a + b
2300 = 325* a + b

and then you solve for a and b

[viscid thistle]

ohhhh

[slate reef]

in this case a will be the price of each unit of pie
and b will be a constant that means something like "the price of starting the production of pies"

[viscid thistle]

omg thank u sm u are a lifesaver

[slate reef]

you are welcome!

[winged spire]

i cannot figure out sum and difference formulas for the life of me

and manipulating sin/cos waves, will post an example soon

If someone knows a trick to look at them differently, but i cannot figure out the proper way to break down cos(x) into a sum and difference formula to solve it

[lone tendon]

Anyone how to find all solutions for the following equation: sin(-3x)=0.5? Only found one solution so far which is: (2*pi/3)n + 7pi/18

[slate reef]

sin(X) = 0.5 only for X = 30 ° (pi/6) or X = 150° (5pi/6)
however that is true only for the first lap in the unit circle so you need to add 2pi*n to your solutions (where n is a natural number that represents the numbers of laps around the unit circle)

[lone tendon]

I did it but there seems to be a second solution taking n into account in the soln as well which I have not been able to find out how to write from the eq above

[slate reef]

yeah so
for examploe : sin(pi/6) = 0.5
so : -3x = pi/6 --> x = -pi/18

but thats only for the first lap around the circle

so your answer in this case should be
x = -pi/18 + 2*n*pi (n is natural)

the other solution is when -3x = 5pi/6

that also contains the + 2 n pi

[lone tendon]

ooh ok

[brave heron]

Who can find the general term for this serie

[viscid thistle]

le haut c trop compliqué pour comprendre

mais en bas je crois que c 48 et après 192

[viscid thistle]

it should be -3x = pi/6 + (2pi)n

[viscid thistle]

cos(165)=cos(120+45)

[past meadow]

For the first one, you'll notice that the numerator is a factor of the denominator

so if you can factorise the denominator, the numerator should cancel and you might be left with something cleaner

something similar is true for each of the rest.

[inner copper]

someone pls help it’s related rates

[plain sable]

Can u send the diagram if they gave it in the question ?

[inner copper]

they didnt attach a diagram unfortunately

[plain sable]

Oh ok

[plain sable]

Try this.

I forgot to substitute r=d/4 in the final result u can do that and check…

[low slate]

How would I solve the top equation, can someone please help with this I’m stuck with what identities I need to use

<@&286206848099549185>

[fast oxide]

,rotate

[fast oxide]

sin(x+y)/cos(x)sin(y)=1+cos(x)tan(y)?

[fast oxide]

.

[viscid thistle]

Question on Set Theory and describing Rational Numbers (it’s in my pre calc text, apologies if this should be asked elsewhere).

[vivid void]

the first one implies that Q has undefined terms

which is incorrect

[viscid thistle]

So thr first line is incorrect and my second line is correct?

[vivid void]

yes

[viscid thistle]

That is disconcerting. The first one is how it’s written in my text. The second is what made more sense to me.

So now I wonder how much else is wrong in thr textbook

[low slate]

Yes

[tawny dirge]

how do i solve this

[low slate]

I’m not sure the identities I need to use @fast oxide

[slate reef]

if you put this imaginary number in polar form you can do it easily

[wooden lily]

I am not sure on how to solve this question. can anyone help me?

[viscid thistle]

f(α+β)=tan(α+β)

Using the figures, tanα = -1/x and tanβ = -3y

Then you can simplify to get the final answer

Oh wait

tanα = 1/sqrt(3) and tanβ = -2sqrt(2) (since x=-sqrt(3) and y=2sqrt(2)/3)

[wooden lily]

Thx Alot i love you. What math does a mf

[viscid thistle]

Help. I'm stuck converting the trig function into exact form.
I've derived the function to -cos(5pi/6)
I have checked the marking guides and it is equal to root/2
What's the process for getting from the function to the esact value/ratio?

[viscid thistle]

So I finally figured that bit out but now I have to put it into the gradient formula y-y1=m(x-x1)

I did similar except instead of using pi/6, I made it 1/2 exact ratio since sin pi/6 exact ratio is 1/2, or am I not supposed to do that and leave it as pi/6 because you can't convert it as it is a point and not part of the sin function?
(Also I'm most farmiliar with slope intercept form over general form so that makes working backwards that little bit harder)

Also I see questions happening in both places. In future is it better to just go straight to a "help" room?

[viscid thistle]

<@&286206848099549185>

[spare cobalt]

wrong channel

[viscid thistle]

Hi

So the question is Given f(x^2)=f(x)+x^2 find f'(1)

I don't want the answer

but a hint

I'm stuck

[tight compass]

Take the derivative of both sides.

[river jasper]

Dont if you put x=1 you get 1=0?

[tight compass]

Using the chain rule and try to express f'(1).

@viscid thistle

[viscid thistle]

yo

Ight cheers

i'll try that

[river jasper]

?

[tight compass]

It's f'(1) not f(1).

[river jasper]

In f(x^2)=f(x)+x^2

[tight compass]

wdym?

[river jasper]

If you put x=1 in that you get f(1)=f(1)+1

[viscid thistle]

i got an answer

one sec

nah nvm im totally wrong