precalculus

[modest oasis]

acos kx + kd is what i took it as

k being pi/2

[summer ruin]

this doesn't adress the issue I pointed out though

[modest oasis]

this is what it seems to be

[summer ruin]

you can't know whether d = 0 or not in this case because it is written ambiguously

[modest oasis]

oh

do u mean its not obvouis whether d is -0.5 or c is -0.5

[summer ruin]

yes

[modest oasis]

well this is my practice test from my school

idk why they made it like this

[modest oasis]

how do i make ai write it normally instead of all the brackets and other stuff i dont really understand what it is saying

[willow bear]

!nogpt

[tender quest]

Please do not trust ChatGPT or similar AI tools for mathematical tasks, as they often generate output which "sounds correct" but has numerous factual or logical errors. Use of these AI tools to answer other people's help questions is strictly against server rules (see #rules).

[modest oasis]

I don't use gpt but I use other software and I only use it to check over not generate answers

[willow bear]

it's no good at checking either.

it'll just as happily talk your ear off with bullshit.

anyway, what you've shown is written in a markup language called LaTeX

#latex-help, #latex-testing, #bots are our channels for that

you can paste the code, surrounded by dollar signs on either side, into a discord message and our bot @obsidian monolith will render it for you, like this:

$\csc(x) + \frac{2}{\sqrt{3}} = 0$

[obsidian monolith]

Ann

[willow bear]

granted, this particular example is not hard to read by eye

\frac stands for "fraction" and \sqrt for "square root", and everything else is almost as-is.

[crisp bluff]

I used chatgpt the other day to help with a math problem, not only did it give me a wrong answer, but I had to point out like 3 "dummy mistakes" it made along the way for it to finally arrive at the correct answer. It does weird stuff like accidentally change a + to a - and stuff like that...

#discussion message @modest oasis it's pretty funny actually

But it did help me with figuring out how to go about solving the problem, but you can't trust its math

[winter comet]

I would assume that that its y = 0.75 * cos(pi*x/2) - 0.5, in case the phase shift would be 0

just because if you are multiplying by x it would most likely go in front

it is a stupid problem tho

[modest oasis]

thx the answer was that cos does not affect -0.5 therefore -0.5 is c and not d

[winter comet]

wait the answer was c?

they're asking for the phase shift not the vertical shift...

im getting confused XD

i thought the answer would be a

ohhhh

wait you meant c and d as in the equation formula 💀

mb

[winter comet]

yeah

that's what it looks like

[modest oasis]

the answer was a

i am talking about the formula

[tranquil inlet]

If we have let’s say quartic x^4 + 5, how would adding a x^2 or x^3 or x variable affect the graph?

[winter comet]

graph it

algebraically you'd have to plug some numbers in and visualize it. i don't really know if there's an actual algebraically way to identify how the graph changes, besides comparing it to parent graphs which are probably not necessary to memorize for equations such as x^4 + x^3 +5 or stuff liek that.

actually x^4 + x^2 + 5 may not so bad because its factorable

but x^4 + x^3 + 5 and x^4 + x + 5 seem to have a different, slightly offset vertex 💀

[winter comet]

i just graphed it

it looks ugly lol

[jolly dew]

Hey there! I need a bit of help on this
I know that 3pi/4=(pi/2+pi/4)
sin(pi/2) cos(pi/4)+cos(pi/2) sin(pi/4)
(1)((square root of 2)/2) + (0)((square root of 2)/2)
So my answer I got isn't on here

[obsidian monolith]

Toasted Bread

Toasted Bread

[trim coyote]

wait so this wants you to use half angle identities?

nvm

you use difference

yeah the answer is root(6)-root(2)/4

D

[willow bear]

why'd you hop channels again, did you mean to post this in #calculus ?

[tender crest]

My mistake sorry

[willow bear]

@void vector so what do you not get exactly

[void vector]

[willow bear]

...

[void vector]

So

Lemme take a pic

[willow bear]

oh good, an actual question

[void vector]

Let’s start with a very basic question

[willow bear]

ok that's a bit of a bait and switch...

[void vector]

Ok this question I fully know how to do

Here it gets confusing a bit

[willow bear]

back in discussy you made it sound like you were having issues with shit like "here's a formula, find the largest subset of R on which it defines a function"

[void vector]

Oh that will be soon maybe not subset of R

[willow bear]

bruh just get to the point

[void vector]

Ok fine

I’ll take a pic

Of the question

lol

[willow bear]

ok so i presume this is a status 5 thing

[void vector]

I do not understand the orange

[willow bear]

do you know what the graph of sin(x) looks like

[void vector]

yes

perfectly

[willow bear]

do you know what happens at x = ±pi/2 on that graph

[void vector]

±1

so the x, (domain?) of f(x) is -1 < x < 1 ?

[willow bear]

notation

as t varies between -pi/2 and pi/2, x varies between -1 and 1

bc sin is an increasing function on that interval

[void vector]

oh ok

How would I find the y values for t

[willow bear]

wym the y values

the problem doesn't seem to ask for the range

but you could see y = sin(t + pi/4) and imagine the same graph again

(but shifted)

[void vector]

ok so you would do

-pi/2 < t < pi/2

and then

x 1 and + pi/4 on both sides

so -PI/4 < t< 3PI/4

and then sin ( LHS) , then sin (RHS)

[willow bear]

not blindly, no

[void vector]

oh ok

[willow bear]

you would visualize the graph of y= sin(t) for -pi/4 < t < 3pi/4, and see what values of y are covered

they will NOT just be (-sqrt(2)/2, +sqrt(2)/2)

[void vector]

ohh

Ok i think I understand

Im not supposed to blindly do eveyrthing

last question if I may short and sweet

Part B

[willow bear]

same shit visualize the graph

[void vector]

and you cannot blindly do

Oh ok

if it was cos 3t

you would have to visualise

0< t < Pi

correct ?

and thats basically it :3

[willow bear]

... i guess so

[void vector]

good enough for me

I found out i cant blindly do it

so that probably solved it

ty

!!!

.

[summer ruin]

you have 2x-1 on the left and square root on the right

square root is never equal to negative number, negative of that - the negative root is never equal to a positive number

therefore 2x-1 must be <= 0

x <= 1/2

[green sun]

During an in-class demonstration of momentum change and impulse, Mr. H asks Jerome (95.0 kg) and Michael (91.0 kg) to sit on a large 14.1-kg skate cart. Mr. H asks Suzie (44.3 kg) to sit on a second 14.1-kg skate cart. The two carts are placed on low friction boards in the hallway. Jerome pushes off of Suzie's cart. Measurements are made to determine that Suzie's cart acquired a post-impulse speed of 12.0 m/s. Determine the expected recoil speed of Jerome and Michael's cart.

anybody know how i would solve?

[dense eagle]

m1v1=m2v2
where m1 is combined mass of Jerome, Michael and 14.1 cart, v1 is their post-impulse speed, and m2 is combined speed of Suzie and 14.1kg cart, with v2 being her post-impulse speed

[deft turret]

yall i need help

i was recommended for ap calc

but i need to learn the stuff for the placement test

and its TOMORROW

im in im2

and i need to learn im2 and im1 and some 8th grade math asap

what should i do

or else im cooked

do yall hafve a study guide

[stray bane]

ur cooked

ur actually so finished

[trim coyote]

💀

YOU ARE DONE

YOU CAN'T LEARN OF ALL CALCULUS IN 1 DAY

IT TOOK ME LIKE 3 MONTHS OR SOMETHING

AND I AM STILL CONFUSED ABOUT SOME TOPICS 💀

[deft turret]

idk im still practicing

[trim coyote]

🫡 GL BRO

[deft turret]

thanks ill need it

[young sandal]

if u pull this off............

u will see places

[shrewd patio]

3 months?!

[leaden wind]

@deft turret what happened now?

[viscid thistle]

if you remember your rules then u gucci

[spring tiger]

Bro is done

Good luck brother

[viscid thistle]

nah we got to believe

[leaden wind]

hes most definitely cooked

just like me

im gonna be cooked and violated today

[viscid thistle]

💀

[young sandal]

VIOLATED!??!?!

[young sandal]

everyone in this server must believe in him

[viscid thistle]

fax

Through the power of positivity

[young sandal]

we gotta show hes not alone

all of us are in this with him

but its prolly over by now

so

[viscid thistle]

@deft turret results?

[deft turret]

I’m gonna take the test today

But do y’all remember all the rules

[viscid thistle]

depends

what is it that you dont understand

[autumn barn]

Can someone help me solve these?

[primal girder]

hey! im doing pre-cal (logs) rn and im trying to find a solution, which came down to -((x-3)(x+1)), i forgot how to find the solution here :') because of the factored -1

anyone can give me a refresher 😅 ?

[fading monolith]

Polar form of a complex number z=x+iy is re^iθ yeah but be careful, r=sqrt(x^2+y^2) and θ=arctan(y/x)

But again be careful with the angle, because its gonna depend on what quadrant you are

For converting a eq to a polar eq is just remember that x=rcosθ and y=rsinθ

For rectangular form is just apply that re^iθ=r(cos(θ)+isin(θ))

[fading monolith]

You want to solve -((x-3)(x+1))=0?

[primal girder]

yeah!

i want to find my x's

from factored form

like normally you would x=3 & x-1 but idk what to do about the -1 infront of the equation

i forgot

[fading monolith]

Multiply both sides by -1

[primal girder]

so it would be -x+3=0 & -x-1=0 right?

making my x's= 3 & -1 ?

(zero product rule)

@fading monolith

[fading monolith]

I meant, from -((x-3)(x+1))=0 multiply both sides by -1 and get (x-3)(x+1)=0

[primal girder]

huhhhh but then they're the same

it's as if -1 is irrelevent

[primal girder]

Went off from this and entered the x:3 on a logarithm answer and it was correct, ty :) im good now!

[fading monolith]

Nice ^-^

[primal girder]

lmao i see now. -x+3 is 3 but so is x-3 (its also 3) :')

would it have been the same if it was another number than 1, i.e. 3?

like i dont ever need to worry about factored out numbers

[willow bear]

indeed, you don't need to worry about constant factors

those dont affect the roots

[primal girder]

nice!!

[willow bear]

they might create more places for you to trip up tho esp with signs

[primal girder]

thank you so much ^-^

yeah..

i just forgot about this stuff even tho i reviewed it not long ago

[teal moon]

Any1 know how to solve number 3

[chrome ether]

factor theorem

[deft turret]

Y’all

She didn’t even let me take the test

😭

[trim coyote]

I mean

I used Khan Academy 💀

[deft turret]

It’s cause

This was the most competitive year with high scores from honors students

And I’m not in honors

So she said hi it’s getting priority I wouldn’t even be able to get my chance for the test

@viscid thistle but tomorrow ima ask her something to see if I can still take it and if I score higher than other she might put me in ap calc

Cause ap calc can only receive 10 students form im2

So hopefully she’ll let me take the test to give me a chance

Only god will write the rest of my story now

[raven cloud]

hello someone please help

im supposed to rotate conics

(5(x^2))-2xy+(5(y^2))-12=0

this is the equation and i need to find the new equation in terms of x prime and y prime

[winter comet]

you mean derivatives?

wait i'm stupid

you just mean the new function

lol

[leaden wind]

@deft turret any news?

[leaden wind]

Goodluck bro

[chrome ether]

https://math.libretexts.org/Bookshelves/Algebra/Algebra_and_Trigonometry_1e_(OpenStax)/12%3A_Analytic_Geometry/12.04%3A_Rotation_of_Axes

[viscid thistle]

💪

[versed mesa]

Can anyone explain number 4 for me please?

2**

Highlighted pls

[willow bear]

,rccw

[exotic barn]

You wanna determine the tangent line at x = π/4. So you need the derivative to find out the slope at x = π/4 first..

[versed mesa]

Ahh ok

[exotic barn]

If you did that you can use this tangent line formula

[versed mesa]

Also I moved into 3 and I don’t understand 3)a) either

Derivative of the equation I just made?

[obsidian monolith]

adonhs

[versed mesa]

Ln(1/root2)

[exotic barn]

wait we moved to 3 now?

[versed mesa]

I still don’t know 2

Just was going to move on until someone answered 😭

[exotic barn]

then why did you go to 3 lol

chill

[versed mesa]

Mbmb

Sooo derive my ln?

[exotic barn]

so the only struggle is to determine the derivative

you need chain rule for ln(sin(x))

[versed mesa]

Ahh okok

[exotic barn]

any idea how to do it

[versed mesa]

Working through it

I’m more familiar with product and wuotient

[exotic barn]

well we can analyze when you are done

[versed mesa]

Yeyey

Alr wait

Gotten to there in chain rule and I’m lost

After that

[exotic barn]

,rotate

[exotic barn]

so you wrote dg/dx = 1/sin(x) • x ?

[versed mesa]

That’s my y

Dy/dx

🥲

And I just have multiply sign

Not sure what’s other side

Is du/dx

[versed mesa]

Oh so isn’t that du/dx just cos(x)

[exotic barn]

oh it's multiply sign?

[versed mesa]

Yes mb

When I get really confused

I go to basics

[exotic barn]

oh then you're missing one final part

[versed mesa]

Cos(x)?

[exotic barn]

ya

[obsidian monolith]

adonhs

[exotic barn]

That's your derivative, it's basically g' = cot(x) too

[versed mesa]

Okok

Then I sub in x to find slope? Then find c by rearranging right

[exotic barn]

then you plug π/4

[versed mesa]

Ya tyyyy

[exotic barn]

so what's g'(π/4)

[versed mesa]

ALR I’ll work on that. And the last thing I wanna do tonight is question 3

[exotic barn]

so you wanna talk 3 rq?

[versed mesa]

Yes pls

[exotic barn]

3a) or 3b)?

[versed mesa]

Uhh just a

I understand b

[exotic barn]

May I ask how did you solve b)

[versed mesa]

I solved b

Because ln is natural log, therefore loge

[exotic barn]

yeah i wanna know how you did it

[versed mesa]

So loge(7x-4)=0

[exotic barn]

yea continue

[versed mesa]

Then I puttttt

Ok now I forgot that, like where I put the log, because I did this weeks ago

Tryna refresh

Hm

Ok you u got me

[exotic barn]

did you do e^(...) on both sides?

[versed mesa]

Honestly idek

[exotic barn]

ok i tried to show you something but nvm

[versed mesa]

💀

[exotic barn]

so to solve log equations generally you can do this:

[versed mesa]

Actually cuz you seem to know what to do, do you mind helping me with a complex unfamiliar question?

[obsidian monolith]

adonhs

[versed mesa]

So that’s why there’s an e on that side

[exotic barn]

yea it cancels out with the log_e or basically ln

[versed mesa]

I see

[exotic barn]

similiarly what would you do on 3a)?

[versed mesa]

Yes

I was wondering why a 2 would go there

I tried using like the ab=c thingy

Idk

Are you up for a more complicated one too?

[exotic barn]

using this what would you do in 3a)?

[versed mesa]

In 3-

3a

[exotic barn]

ye

[versed mesa]

I would get rid of log2 from the left, and put just 2 on the right. This leaves with (5x+12)=2^6

Then algebra from there

[exotic barn]

ok perfect that'S what i wanted to hear

now i am open for your complex question 😄

[versed mesa]

Yayaya

ALR, so I wrote down some basic notes from what I remember teacher saying. The left side I briefly understand. Otherwise the rest is confusing

[exotic barn]

,rotate

[exotic barn]

So we got a cylinder with surface area 120π cm²

Based on this information we want to maximize its volume, interesting

[versed mesa]

Hard eh?

[exotic barn]

We can start off with the surface area formula first

[versed mesa]

Yes

[exotic barn]

120π = 2πr(r+h)

[versed mesa]

My teacher had a diff formula for SA

[exotic barn]

2nd thing to do is set up the volume formula of a cylinder

I forgot an r, thanks

[versed mesa]

All g

[exotic barn]

your teachers is basically multiplied out 😄

[versed mesa]

Wondered where it fit in

Yeye

[exotic barn]

120π = 2πr² + 2πrh ... 1st equation
V = πr²h ... 2nd equation

So basically we want to make a volume function first and then maximize it

[versed mesa]

Ok

[versed mesa]

Is that formula still the same?

[exotic barn]

I believe we can either solve for r or h from 1st equation and then plug it into the 2nd equation

[versed mesa]

Like cuz there’s r^2+r

In the multiplied out version

[exotic barn]

yes i already mentioned that

[versed mesa]

I’m confused about it

[exotic barn]

then lemme change it

[versed mesa]

Sorryyyy

[exotic barn]

120π = 2πr² + 2πrh I think it's easier to solve this for h

[versed mesa]

Yes

[exotic barn]

120π - 2πr² = 2πrh

[versed mesa]

When she went to isolate h, I got very confused

[exotic barn]

Now we can divide by 2πr

and we get

[versed mesa]

120/r. -r=h?

[obsidian monolith]

adonhs

[versed mesa]

Oh I didn’t do 120/2

[exotic barn]

Now we can plug this into our 2nd equation

[obsidian monolith]

adonhs

[versed mesa]

Got it

Then do we find r?

[exotic barn]

Yea

We find it by maximizing our function V(r)

We wanna find the greated volume

[versed mesa]

How to maximise?

[exotic barn]

this means in terms of calculus extreme values

[exotic barn]

we differentiate

first

Can you do it?

[versed mesa]

Will try tn

Rn*

[exotic barn]

can you type

[versed mesa]

I got

[exotic barn]

it

[versed mesa]

Sorry working out

60pi-3pi^2

[exotic barn]

almost

[versed mesa]

Oh

[exotic barn]

it was r³ right

where did r suddenly disappear?

[versed mesa]

Is it miussed?

Cuz r^3

Becomes

[exotic barn]

we differentiate with respect to r

[versed mesa]

3r^2…?

[exotic barn]

yea yoou're missing that

[exotic barn]

you only wrote pi

[versed mesa]

Oooo Shi

[exotic barn]

instead of 3pir^2

[versed mesa]

I promise I wrote

Omg

[exotic barn]

ok dw

[versed mesa]

I remember I saw the r

[exotic barn]

So we get

[versed mesa]

And was like stupid mf typo

💀

Yes

[obsidian monolith]

adonhs

[versed mesa]

Correct

[exotic barn]

The very first thing when it comes to extreme values is to set the first derivative to 0 and solve

[versed mesa]

If we wanted minimum, would we antidiff?

[obsidian monolith]

adonhs

[exotic barn]

haha nice outside the box thinking but no, definitely no

[versed mesa]

😭

[exotic barn]

doesnt have to do anything

[versed mesa]

O

[exotic barn]

notice

[versed mesa]

We just leave it as is?

[exotic barn]

extreme values such as maximum or minimum are special

because if you noticed

their slope is 0

it's a horizontal tangent

if you think about

and since the first derivative tells us the slope

we want to find when the slope gets 0 because this means either max or min

just for understanding

[versed mesa]

So derivative is a slope even if it’s a cylinder

[exotic barn]

The derivative tells us the slope of the function

at any moment

[versed mesa]

Alright

[exotic barn]

cylinder is not a "function" it's a solid

we just made a function that describes the relation between radius and volume, that's it

and we want to maximize it

meaning find out the max of that function

[exotic barn]

So can you solve this equation?

[versed mesa]

So solve equation when it =0

[exotic barn]

If we wanna find extreme values we solve first derivative = 0

Now solve this and tell me the solutions

[obsidian monolith]

adonhs

[versed mesa]

Well

When I do it, I keep diving everything and I get 0

Wait

[exotic barn]

slow down

haha

[versed mesa]

I should plus 3pir^2

[exotic barn]

yes

[obsidian monolith]

adonhs

[exotic barn]

continue

[versed mesa]

Alr

Divide by 3 both sides

[exotic barn]

what about pi?

[versed mesa]

Pir2 =20pi

Divide by pi

[exotic barn]

divide by 3pi 😄

[versed mesa]

Got r^2=20

[exotic barn]

saves you one line

[versed mesa]

😭

Then root 20

[obsidian monolith]

adonhs

[versed mesa]

How to do root 20 is 2root5

[exotic barn]

lemme show

[versed mesa]

Is it surfs

Surda

[obsidian monolith]

adonhs

[versed mesa]

I see

[exotic barn]

SO

since r > 0

we are only interested in the positive solution

[versed mesa]

Yes

[exotic barn]

for the sake of education

I will show how to confirm that it is a maximum

[versed mesa]

ALR

[exotic barn]

We cann basically differentiate again

[versed mesa]

Ahhhhhh

[exotic barn]

So what is V''(r)?

[versed mesa]

It would be

6pir

[exotic barn]

Given V' = 60π - 3πr²

yes

So V''(r) = -6πr

Now check this

[obsidian monolith]

adonhs

[exotic barn]

So we basically plug in our solutions into the 2nd derivative

and check if it is negative

do you follow?

[versed mesa]

If negative, it is min?

[exotic barn]

nno

[versed mesa]

Oh

[exotic barn]

if 2nd derivative negative it is max

[exotic barn]

I wrote it out nicely

take notes

[versed mesa]

I did

[exotic barn]

ok

So let's try

[versed mesa]

Crocodile les than and greater than kills me

[exotic barn]

nah

[versed mesa]

Well tell ya what. I have: 6pi(2root5)

[obsidian monolith]

adonhs

[exotic barn]

right

[versed mesa]

Why negative pi

[exotic barn]

-3πr² differentiated is -6πr

[versed mesa]

I had positive 3pir2

Oh

[exotic barn]

yea wrong lol

[versed mesa]

Oh

Oh

[exotic barn]

forogot the minus

[versed mesa]

In the

V(r)

Wait no

[exotic barn]

huh

[versed mesa]

V’(r)

I was looking at deriv when =0

[exotic barn]

here.

[versed mesa]

Hence I had positive 3

[exotic barn]

no that has nothing to do anymore

when we differentiate we differentiate the function not the = 0... equation

or any arbitrary equation

ok?

dont give up

[versed mesa]

Got it

That was just for r

No need to use it anymore, just r

[exotic barn]

So finally we found the radius, yes

[versed mesa]

Yes

[exotic barn]

so we can calculate the volume and done

[versed mesa]

Okkkk

[obsidian monolith]

adonhs

[exotic barn]

How can we find the volume now?

[versed mesa]

Write it out

So

[exotic barn]

you mean what exaclty

[versed mesa]

60pi(2root5)-pi(2root5)^3

[exotic barn]

yesssssssssss

we plug it in

[versed mesa]

Then how to simplify

Like how to

60pi brackets yk

How did you get 8pi onwards?

[exotic barn]

due to the ³

2³ = 8

ah no mistake with the pi

[versed mesa]

And root5?

Ikik

Ikik*

Ong

Okok*

Okkk make more sense

[obsidian monolith]

adonhs

[versed mesa]

And that’s it?

[exotic barn]

Now we can simplify more

[versed mesa]

O

[obsidian monolith]

adonhs

[versed mesa]

Ah ok

To confirm

[exotic barn]

That's the maximum volume

[versed mesa]

Is that root(5^3)

[exotic barn]

yes

root(5)³ = root(5) * root(5) * root(5) = root(5)² * root(5)

[versed mesa]

Okk

[exotic barn]

you also got 2sqrt(5) on your paper sheet

[versed mesa]

Yes

Cuz I heard my teacher say it

💀

[exotic barn]

😎

[versed mesa]

Thank you so much 😭

[exotic barn]

are you indian btw?

because of the

.
. .

[versed mesa]

Nope

White

[exotic barn]

ohok

[versed mesa]

Also do you have any websites or math things that create problems related to differentiation, integrals and logs?

[exotic barn]

you reminded me of @bold oxide

[versed mesa]

Was he dumb

[exotic barn]

no she is smart

[exotic barn]

uhm not really :/

if you want problems go through the help channels here lmaoo

[versed mesa]

Okok

And what about finding sample questions?

[exotic barn]

ask your teacher or dont you have a book?

with problems

[versed mesa]

Good point

💀

[exotic barn]

maybe this is for you

https://discord.com/channels/268882317391429632/716264872018706443

go ask there for book recommendations or some

[versed mesa]

Okkk thank you

[viscid thistle]

Anybody know how to preform linear and exponential regression without a calculator

[tender crest]

If a=\0 line 2bx+3cy+4d=0 passes through intersecting point of y^2=4ax and x^2 =4ay
Then

d^2+(2b+3c)^2=0
d^2+(3b+2c)^2=0
d^2+(2b-3c)^2=0
d^2+(3b-2c)^2=0

[willow bear]

what is capital D?

[tender crest]

I don't know

[willow bear]

then we can't help you

[tender crest]

We?

[willow bear]

if you don't know the meaning of a symbol in your own question and it isn't already defined, then nobody here can help you

[tender crest]

D is written in line equation

[willow bear]

no, the line equation has lowercase d

it doesn't have uppercase D

[tender crest]

I hope it is good now

[tender crest]

It was by a starting message so they took capital D but both are same D=d

[tender crest]

I guess you are still not capable to solve?@willow bear

[willow bear]

bold assumption

[tender crest]

Because your behaviour was not appropriate

No problem

You are not going any direction even question is fully correct now

[rancid holly]

i think it's more about the fact you just posted a problem and didn't say what you need help with, now you're shit talking but still not giving the problem any thoughts, you surely should have tried something

[willow bear]

and if you haven't tried anything, it's your responsibility to say honestly and openly "i have no idea how to start this problem and need pointers"

[paper tartan]

What have you done?

we need to see your work, or at least your thoughts on the problem

[tender crest]

I don't know how to start the problem

[paper tartan]

we’re not going to do the problem for you

[tender crest]

I can only kmow intersection poimts

I found poimts by two parabola equations

[willow bear]

show us the points

[tender crest]

When a=1 it is (4,4)
a=2 i got (8,8)

[willow bear]

did you only do it for a=1 and a=2?

yes/no

[tender crest]

Yes

I can do it for a=3,4 and so on

[willow bear]

ok, then do it for general a. repeat all your algebra, but don't substitute a=1 or a=2 or a=whatever else, just keep it as a.

[willow bear]

you will spend 20 years doing the same exact work for different numbers.

so maybe don't.

[tender crest]

(4a,4a)

[willow bear]

ok cool

is that the only intersection point that you found?

yes/no

[tender crest]

Yes

[willow bear]

then there is another intersection point which you missed.

[tender crest]

Let me find it again

(0,0) ?

@willow bear

[willow bear]

yes that's correct

so you have your two points (0,0) and (4a, 4a)

what is the line that goes through them?

[tender crest]

y=x

2by+3cy+d=0
Y(2b+3c)+d=0

[willow bear]

yes correct

[willow bear]

not good

[tender crest]

Huh

[willow bear]

y = x => x - y = 0

[tender crest]

I relplaced x to y

In the line equation

[willow bear]

you observe that d=0 and 2b and 3c are in the ratio 1 : -1

[tender crest]

(0,0) gave us d=0

[willow bear]

yes

[tender crest]

How you got that ratio?

2bx+3cy=0

[willow bear]

well my reasoning was that the equation of our line is x - y = 0, up to a constant multiplier

but you can also put x=y=a into it and divide by a and get the same result more directly

[tender crest]

Why only a? Not 4a?

[willow bear]

same difference

if you want to be more formal you can put x=y=4a

and then divide out by 4a instead

it doesn't matter at all

[tender crest]

2ba+3ca=0
2b=-3c

What should we do next?

(2b+3c)^2=0

Option A

Thanks ann..sorry for early messages

[willow bear]

it's whatever

[bold oxide]

damn-

[viscid thistle]

i think this comes under precalc

but this would be d right

i mean what i did was i differentiated it

f'(x)=4x(x^2-2)

=4x(x-root2)(x+root2)

then equated this to 0

so the zeroes are root2 and -root2

so then upon putting it on the numberline i got d

not too sure tho

if i went wrong somewhere

[primal girder]

Hii! i have an exam coming up (march 14) and I was wondering if anyone was kind enough to give me some tutoring for just 30 minutes, im struggling w/ logarithms, i can't today cuz of work but i can do it tomorrow! and can be up as early as a bird. And you wouldn't have to feel like you absolutely need to do the meeting if you're too tired :') ~ leaving this here ~ (sorry if this breaks any rules)

[summer ruin]

why if you only found the critical points?

the value of the function doesn't tell you whether it's local maxima or local minima

you also missed 1 critical point

[viscid thistle]

you got the wole serbver here to assist

just ask a question on logs and we shall answer

i hope

[primal girder]

and yeah its been super helpful, i get log but rn im just fkin up on too many practice questions so asking 1 question at a time might just be more of a waste of time :') but i found some help!

[viscid thistle]

as long as you have found help

just remember to make a formula sheet to refer to so you dont get stuck on a question

[viscid thistle]

no as in

uhh how do i explain it

i didnt find the value of the function

i equated its slope to 0

to find out whether the function is rising or lowering at that point

[summer ruin]

by definition neither of these is happening if the slope is zero?

[viscid thistle]

im tyring to figure out how to explain it

basically what we learn is to

differentiate the function

equate it to 0

and then find the values of x at 0

and then i use the wavy curve method

to find the local and maximum minimas

which is this

so if f'(x) = 4x(x+root2)(x-root2)

id plot accordingly

i mean i hope that makes sense

[summer ruin]

and why did you conclude that the answer is d)?

[viscid thistle]

because my final number line looked like this

sorry for the bad drawing

on mouse

[summer ruin]

where are the two local maxima then?

[viscid thistle]

(-root2,0) U (root2,inf)

unless u count this as one maxima

[summer ruin]

that doesn't even make sense

maxima and minima points are points

they're not intervals

[viscid thistle]

wait sorry i just told u where the function is increasing

wouldnt those points be the maximas

or am i getting confused

[summer ruin]

well if that was the case you should've also checked another point on the left as local minimum, but you didn't

the point can't possibly be local maxima/minima if the derivative is not zero at that point

[viscid thistle]

so wait

for the point to be a local minima or maxima

the derivative has to be 0 at that point?

[summer ruin]

that's the necessary condition, yes

all local minima/maxima have derivative equal to 0

[viscid thistle]

ah whats the explanation behind that

[summer ruin]

but not all points where derivative is 0 are local minima/maxima

[viscid thistle]

i always thought the local minimas and maximas were like this

[viscid thistle]

so in the given question

how would we find out, there are 3 cases wehre the derivative is 0 i belive

that is -root2, root2, and 0

[summer ruin]

this drawing is correct and you need it to solve the problem

but you don't quite understand what it means

if the derivative changes sign from + to -, then it's local maxima

and if it changes sign from - to +, then it's local minima

[viscid thistle]

yep the slopes of those curves right

oh so when the derivative i.e the slope is 0

we have to check whether its going from + to - or - to +

if im understanding correctly

and depending on that

it becomes a local minima or local maxima at the point where the slope is 0

which is why u told me the local minima/local maxima can only exist when the derivative is 0

i hope i havent butchered ur explanation too much

[tender crest]

10. B
11. C

[hexed apex]

i got feedback and need help fixing it

[fading monolith]

You have to check the continuity at x=2 and x=5

The rest of points is trivial

[hexed apex]

ah yes i have shown that in my work

sorry this is the feedback i recieved

how do i show that the function is continous at every real value?

[fading monolith]

The limit for the rest of points x0 exist and coincides with f(x0)

Since x<2 on 1/(x-3) you dont have any problem

The polynomial is continous and the exponential too

[hexed apex]

hmmm yes you're right

im pretty sure i thoroughly explain that in my work but im not sure why i am not getting the mark

[uncut mulch]

you shouldn't have used
both 1/(x-3) and x-3 when getting evaluating f(2)

[hollow crypt]

hello

can you guys help me

with a pre calculus problem

about hte pascals triangle

ping me

[hexed apex]

ah ok but isnt x-3 okay to evaluate f(2)? since its x > or = to 2

[crisp wedge]

i need help big time with this. btw you have to solve using cube roots.

pls ping me

[uncut mulch]

yes, but you shouldn't have used 1/(x-3) for f(2)

[hexed apex]

okok thank you

[onyx lotus]

hi i have a quick question, is :
(3x^2+y^2)/(8y-2xy)

the same as:

(3x^2)/2y(4-x) + (y)/2(4-x) ?

so would these be the same?

[trim coyote]

yeah

cuz you distribute in the denominator

then you multiply the numerator and denominator of the second rational equation by y

then add

[primal girder]

hey

if you bring down an exponent when doing logarithmics

can you cancel that same log with same base exponential?

or is the exponent that was brought down in the way

i.e. say log(2)^x -> xlog(2). Can you simply input 10^x to cancel the log on xlog(2)

[brisk adder]

What was the question

[primal girder]

ok gimmie a sec

10-8(1/2)^x=5

i did ln eventually just to bring down my x

on both sides

and i got the right answer but idk if i can cancel ln while x is infront of it?

[brisk adder]

can you show me what you mean

[primal girder]

okay

look at the bottom part

the part i put in a box

[brisk adder]

but isn't x not in the logarithim so if you cancel it wouldn't be the same?

[primal girder]

so basically

im not allowed to do this

x needs to be times a solved log

right?

[brisk adder]

yeah

[primal girder]

okayokay

another question, could i send x to the other side though, especially if it were an actual number ?

as a division?

[brisk adder]

why not?

[primal girder]

okay!!

[brisk adder]

you're still preserving the equality

[primal girder]

yeah

log just still feels like new water to me

ty :)

[primal tusk]

Uhhh how do you manually do sin and cos

[primal tusk]

Wait limits is a precal topic!?

[willow bear]

wdym by "manually", and of what angles?

[primal tusk]

No angles
Its a special limit

[willow bear]

a limit?

!original

[tender quest]

Please show the original problem, exactly as it was stated to you, with the entire original context. A picture or screenshot is best. If the original problem is not in English, then post it anyway! The additional context might still be helpful. Do your best to provide a translation.

[primal tusk]

Idk if limits fall in precal or bascal

[primal tusk]

Hold on

[willow bear]

just post it here now that you've brought it up...

[willow bear]

right... and what were you going to do with this?

[primal tusk]

Its cos and not sin but still
Idk how to manually solve without using a scientific calc

[willow bear]

well you don't need a calculator to find this limit

[primal tusk]

Dw its not from a test
My math midterms are done
I just guessed this part of tue test since i really didnt know how to solve it

[primal tusk]

How so?

[willow bear]

i'd begin by substituting $t := x+2$ so you get $$\lim_{t\to 0} \frac{1-\cos(t)}{2t}$$

[obsidian monolith]

Ann

[primal tusk]

Hmm

[willow bear]

and then you either recognize the special limit of (1-cos(t))/t or derive it from the other special limit, which is sin(t)/t

which can be done in a number of ways, all of them involving some symbolic trig fuckery

[primal tusk]

Yeah
Actually i flat out gave up on special limits because of trigo lol

Everything except special limits was easy to understand

[tender crest]

is the answer 0?

[pine geyser]

No

[tender crest]

then?

[pine geyser]

Oh wait

Yes I the limit is 0

I did some stupid calculations in ma head

Sorry

[sleek path]

i made a help thread but didnt get any answers so imma post it here

f(f(x))=1+x find f'(1)

any way we can prove it except by saying its obvious f(x) is linear equation?

what i tried was x--->f(x) to get f(1+x)=1+f(x)

and some more rando shit which sadly didnt help

and actually this is where i reach a more awkward state

any function which satisfies

f(1+x)=1+f(x)

doesnt necessarily satisfy

f(f(x))=1+x

which seems mind blowing to me

what sort of manipulation did i do which allowed the possibility of so many new functions to arise? even infinite

what step was wrong?

[fiery creek]

f(f(x)) = 1 + x find f'(1)

why not take the derivative of both sides?

[f(f(x))]' = f'(f(x)) * f'(x)

by chain rule

[sleek path]

then?

[fiery creek]

what is f'(f(x)) * f'(x) equal to

given you differentiated both sides

[sleek path]

1 obv

[fiery creek]

f'(f(x)) * f'(x) = 1

yes

[sleek path]

but that gets me nowhere 😭

[fiery creek]

wait shit

mb

😔

[sleek path]

bro i spent pages worth doing this

like in different ways

it all came back to the same thing 😭

[fiery creek]

hmmm

[sleek path]

also this q has confused me even more

[fiery creek]

given f(f(x)) = 1 + x let f(x) = u

[sleek path]

because of this

[fiery creek]

therefore f(u) = 1 +x

the equation becomess

f'(u) * f'(x) = 1

[sleek path]

which is the same thing dawg

substitution wont change what u are differentiating

[fiery creek]

let me think bro

[sleek path]

mb mb, its just that the q has got me on my nerves

[fiery creek]

f'(u) = 1/f'(x)

wait

why not f(x) = x

doesn't that work?

f'(1) = 1

@sleek path

[sleek path]

bro i know the ans

alr

btw no f(x)=x is wrong

f(x)=x+0.5

[fiery creek]

you should ping helpers

i can't do this

😭

[sleek path]

dw man my whole coaching batch couldnt 😭

[sleek path]

should i ping the whole role?

[fiery creek]

yeah that's the point of helpers

[sleek path]

<@&286206848099549185>

pls help 🙏

[sleek path]

i felt like pinging so many people just for my doubt is bad

[fiery creek]

don't give a shit about what people here think lmao

be greedy

[sleek path]

💀

[pure lily]

HmMM

[pure lily]

okay so f(f(1)) is 2 but i can't really use it if i take the derivative of both sides

$(f(g(x)))' = f'(g(x)) . g'(x)$

[obsidian monolith]

Adversary

[pure lily]

$f'(1) = 1/f'(f(1))$

[obsidian monolith]

Adversary

[pure lily]

as I said we know f(f(1)) is 2 but we do not know f(1) let alone f'(f(1))

idk any way to do it aside from calling f(x) = ax+b

[naive sluice]

What do you study in precalc

[pine geyser]

The main topics in the Precalculus course are com- plex numbers, rational functions, trigonometric functions and their inverses, inverse functions, vectors and matrices, and parametric and polar curves

Also it depends on the place you are studying in

In our country we don't study complex numbers and inverse functions of trigonometry

[wind linden]

i just need some guidance

[viscid thistle]

start by drawing a triangle in the fourth quadrant

such that the y component is -5 and positive x component is 12

hypotenuse is 13

so sin alpha gives you -5/13

cos alpha is 12/13

now for beta the triangle should be in first quadrant

cos betas given

sin beta will be 5/13

Now use the double angle formula for sin (a+b) = sin a cos b + cos a sin b

-60/169 + 60/169

Yo

[viscid thistle]

your answer should evaluate to zero

as far as i can say

[wind linden]

ooh okay thats what i did but somehow i got the hyp as 17 for alpha by accident lol ty

[viscid thistle]

Welcome

[primal girder]

small question: when** log(10^1/10^2)**, is the answer 1 or -1? In my mind, log10 = 1, but then 1^-1 is just 1 too. I'm supposed to link a bunch of equations w/ different answers but 1 doesnt come up, just -1. Did i do something wrong?

[willow bear]

log(10^-1) isn't the same as (log(10))^-1

your lack of parentheses is what made you misread your OWN expression like this

log(10^-1) is -1, not +1

[primal girder]

oh so i need to solve any exponents in my parenthesis

before doing log essentially

and i dont feel too good about bringing a minus infront of log. The reason is im scared of it being undefined

so it would be log(1/10)?

which would be -1

!

thank you ann :) 🫶

[primal girder]

lmao okay i guess this would be the same, its -1 times the results of log(10) = (1) -> -1 x 1 is -1 okayyyy

[crude path]

if lim f(x) = y
does that mean lim fprime(x) = the derivative of y

[summer ruin]

no

[willow bear]

no. also, you can just use the apostrophe symbol to write the derivative

f'(x)

[fading monolith]

Since derivative is a limit is not trivial and not always true the interchange of limits

[primal girder]

what the hell is this supposed to me

log(2) divided by 2??

[river drift]

,, 10^{\frac{\log(2)}{2}}

[obsidian monolith]

cloud

[primal girder]

hehe ok ty <3

oh wait can i just bring up the /2 infront of log

such as 2log(2)

and also log(2^2)

and then cancel all logs and just get 2...

[river drift]

you can apply a similar principle in this case

[primal girder]

what do you mean by that?

[river drift]

well in this case, since you are dividing by 2, you can write that as multiplying by a fraction

[primal girder]

ooooooh

1/2?

infront of log

ya?

[shut quarry]

is this too ambigous ?

[river drift]

yes

[dire aspen]

This should go in pre-alg

[shut quarry]

it s real analysis

[dire aspen]

do you know what channel you posted this in

[shut quarry]

yes

[dire aspen]

ok

[obtuse dagger]

Does anyone mind explaining how $\sqrt{x^2-30x+226}+\frac{12}{5}x-36=0$ is equivalent to $x^2-30x+226=\frac{144}{25}x^2-\frac{864}{5}x+1296$?

[obsidian monolith]

Punisher

[obtuse dagger]

^Where did the -864/5x come from?

[fleet pendant]

$\sqrt{x^2-30x+226}=-\frac{12}{5}x+36$ \
$(\sqrt{x^2-30x+226})^2=\qty(-\frac{12}{5}x+36)^2$

[obsidian monolith]

Anonymous

[sleek path]

i found the solution from someone on reddit

they substituted x-->g(x) where g(x) is inverse of f(x)

giving f(x)=1+g(x)

differentiating both sides

f'(x)=g'(x)

which is only true when f'(x)=1 as inverse is just mirror image about x=y

[gleaming halo]

anyone know what the question wants me to do?

[trim burrow]

It looks to me as though they’re asking you to find a and b such that the piece wise function f(x) is still differentiable at x=1 (idk why it’s on a precalc homework but oh well)

[willow bear]

what part of it confuses you?

[signal zinc]

the notation

[willow bear]

if you know how to find g(1) you should have no trouble finding f(g(1))

do you know how functions work, generally?

Y/N

[signal zinc]

yea just never done composite functions before but i answered them all right now

[willow bear]

i mean

ok wait do you need any more help or did you figure it out just now

[signal zinc]

no it should be alright thank you

[tender crest]

Series log(n/(n+1) where n=1 to infinity is divergent?

log1-log2+log2+log3+....-log(n+1)

-log(n+1) which is -infinity so divergent

[tender crest]

But when we see limit n tends to infinity log{n/(n+1)} =0 which is convergent

[fading monolith]

Take y=3x+3/(-3x+2) and change variables x=3y+3/(-3y+2) and try to get y

[willow bear]

missing parentheses around numerator.

[fading monolith]

Are you serious... the exercise is there, cant be any misunderstand

[willow bear]

yes i am serious. you're promulgating bad habits.

[tender crest]

Hello