precalculus

[winter comet]

but its relatively easy to understand

of course the later stuff is probably much harder 💀

[chrome ether]

it’s smooth sailing until you hit line/surface integrals which is not until late calc3

[winter comet]

really?

i thought calc 2 was harder than calc 3, and calc 4 was the hardest

sorry uhh

differential equations? is what im calling calc 4 idk 💀

thats what my brother said as difficulty for him

but it could depend idk

[chrome ether]

it’s very dependent on how strong your algebra skills are

bc late calc3 gets pretty computationally intensive

[willow skiff]

Many colleges don't call it calc 4

Like once you get to Green's and Stokes' in multivar calc that's the end of the calculus sequence

[winter comet]

yeah thats why i clarified lol

[willow skiff]

I don't think differential equations should be part of the calculus sequence

It's a subject in its own right

Like you branch out into ODEs and PDEs

[winter comet]

really?

[willow skiff]

Not everything involving calculus should be a part of the calculus sequence

Like real analysis has calculus

But it wouldn't make sense to include it there

[winter comet]

i see your point ig...

like

it uses calculus

but its a lot more...?

[willow skiff]

Also apparently some unis only have Green's and Stokes in calc 4

I take online courses at Indiana University East. The description of Calc 4 from their catalog is "Differential calculus of vector-valued functions, transformation of coordinates, change of variables in multiple integrals. Vector integral calculus: line integrals, Green’s theorem, surface integrals, Stokes’s theorem. Applications."

[winter comet]

i don't know much about calc 2,3,'4' lol

[willow skiff]

As in they split calc 3 into two

Weird

[winter comet]

are those all calc 3? or wut

[willow skiff]

Depends on uni

[winter comet]

hmm

i mean

from a dummy standpoint

[willow skiff]

Yeah it's confusing when different unis call the same thing different names

[winter comet]

multivariable calc sounds like implicit differentiation 🤣 and differential calculus seems like differentials (like dy = f'(x)dx)

but i know its gotta be much more complicated than that lol

[winter comet]

i mean is green's theorem calc 3 or wut

OHH u mean calc 3 is different

i mean uhh

multivariable calculus

[willow skiff]

Yes, you're working with all of those concepts in more than 1 dimension

So like implicit differentiation involves functions of both x and y, f(x, y) = constant

But you could also have f(x, y, z) = constant, of course

[winter comet]

hmm

[willow skiff]

And yeah a lot of the reasoning behind integration in higher dimensions is based on differentials, applied to different dimensions

[winter comet]

you mean you work on a three dimensional x,y,z plane, idk what "constant of course means"

[willow skiff]

Like the area element is now dx dy, and the volume element is dx dy dz

[winter comet]

oh

[viscid thistle]

The channel says 'pre-calculus', but I assume normal calculus is allowed here, yes?

[willow bear]

#calculus is a thing

[remote sable]

How do we do modelling with differentiation

Is this why we say dy/dx = 0

[sudden musk]

Yes

dy/dx represents slope, so dy/dx = 0 then the slope is 0

dy/dx represents the slope of a plotted function*

[remote sable]

Ahh that makes more sense now

[sudden musk]

wdym by modelling of differentiation?

[remote sable]

Like when they give you questions like a cylinder

I’ll show you when I get home

[sudden musk]

ah ok

[hexed apex]

You are walking away from a 4.2m tall lamp post, and you are 1.4m tall. Your shadow is increasing in length at a rate of 2km/hr. At what speed are you walking? Give your answer in km/hr

is my work correct, if not please help

[winter comet]

you wrote 1.2x instead of 1.4x once, but you fixed it after and i'm pretty sure the rest is correct

[fiery creek]

@vernal swift here

[opaque drift]

I‘d say it’s B tell me if I’m wrong

[vernal swift]

how do you come to the conclusion tho I just do not know the steps

wait soning can i dm you?

[opaque drift]

Sure

[vernal swift]

alright

[opaque drift]

@fiery creek is d correct?

[fiery creek]

do you know what transformations are

like vertical stretches, compressions,

translations

reflections

[vernal swift]

Not really I’m not too familiar yet sorry 😞

[opaque drift]

Im sure he knows

[winter comet]

you take the parent graph of 2sqrtx, translate it down 1 and left 3, so d is correct.

[static cliff]

I was trying out fourier transforms and was having trouble, so I just winged it can got to this point

https://www.desmos.com/calculator/3efxqk8kxs

It is pretty close but it is extremely overcomplicated

It also overshoots by a lot

[winter comet]

that's insane 💀

ngl i don't know why you had them there but just to make it look even closer you should remove the floors, max the r and zoom out and it looks perfect :D

XD

just keep zooming out...

XD

[vernal swift]

hey i did my work could you check my answers please 😓

[fiery creek]

@vernal swift oh sorry

i got distracted

so what transformations are acting upon this function

[vernal swift]

no problem 😅

[fiery creek]

ok first of all

I can't read your writing that well

secondly

i want you to follow a systematic process when you solve this problem

let's starts with 2sqrt(x+3)-1

what transformations are acting on this function

look at A and C

[vernal swift]

1 i got d

[fiery creek]

those two graphs probably aren't the right answer

why? because they're reflected

[fiery creek]

ok good yeah

the answer is d

[vernal swift]

2 acd

3 c

4 d

5 d

[fiery creek]

ok it seems like you don't need my help

[vernal swift]

is 6 d?

i know its b or d

[fiery creek]

you can verify these answers on desmos

https://www.desmos.com/calculator

[vernal swift]

desmoos does not work for me unfortunately 😓

[fiery creek]

why not

[opaque drift]

Geogebra is a good alternative

[tranquil jetty]

do u know about trigonometry

[fiery creek]

[fiery creek]

who are you talking to

[tranquil jetty]

anyone

[fiery creek]

yeah I can help with trig

go to #geometry-and-trigonometry and ask

[tranquil jetty]

i did

[opaque drift]

Well, in terms of geometry or series?

[tranquil jetty]

i have no idea

whats the difference

[fiery creek]

wdym desmos isn't telling you

what is the function

[warped cipher]

@vernal swift do you still need help?

[vestal bison]

i think u can think of it in the logical way

see as x increase y also increases right? so we eliminate A and C where the outcome decreases

for the other 2, id say try the x values by logging them into the equation

since ur not familiar with transformation

[viscid thistle]

i changed a and r to 1,000,000,000,000 now my computer is making noises i didnt know computers could make

[runic turret]

so i'm in exponential equations and inequalities

and the rule is to make the bases equal first

but then the teacher gave an optional assignment to figure out how to solve ones where the bases aren't directly powers of a common number

how in the world would you go about doing that

what kind of power can turn 2 into like 3 or something

[summer ruin]

do you have a specific example

[runic turret]

$2^{4x+1}=3^{x+2}$

[white stump]

Put both to the power of e^ln(

[runic turret]

howd that help

doesnt e^lnx just =x

[white stump]

So you can get a common base of e, the ln has special properties where the linear function part will come out if the power and just multiply the 2 or the 3

[runic turret]

shit wait a minute let me try

so $e^{\ln{2^{4x+1}}}=e^{\ln{3^{x+2}}}$

[white stump]

Yes

But ln(a^b) = bln(a)

Then you can take the ln( on both sides to get rid of e then solve

[runic turret]

$(4x+1)\ln{2}=(x+2)\ln{3}$ ?

[white stump]

Yes

I would expand that

[runic turret]

4x ln2 - x ln3 = 2 ln3 - ln2

x(4ln2-ln3) = 2ln3-ln2

[white stump]

Yup

Unpleasant numbers but thats it

[runic turret]

x=(2ln3-ln2)/(4ln2-ln3)

dont the ln3-ln2 and ln2-ln3 cancel

?

theyre inverses

ln3-ln2=-(ln2-ln3)

[white stump]

?

Oh

[runic turret]

a-b = -(b-a)

[white stump]

On the top there's a 2 and on the bottom a 4

They're different numbers, your result is fine imo

[runic turret]

right

if it was 2(ln3-ln2) / 4(ln2-ln3)

i could've

but still

thanks

[white stump]

Np

[runic turret]

wouldve been just -1/2

damn that wouldve been so neat

[white stump]

Math isn't always neat 🤷‍♂️

But when it is its cool

[ashen hull]

How it solves

[runic turret]

expand then like any other equation

shove everything that isn't x to the right

[ashen hull]

Expand what

[runic turret]

the parenthesis

multiply it out

[ashen hull]

But there is Ln out there

[white stump]

But not of x

[runic turret]

(4x-1)ln2=(x+2)ln3

4xln2-ln2=xln3-2ln3

[ashen hull]

Oh

[runic turret]

4xln2-xln3=ln2-2ln3

[solar olive]

u can make it nice i guess

[runic turret]

x(4ln2-ln3)=ln2-2ln3

[solar olive]

by writing it as x = ln(9/2)/ln(16/3)

i think thats more neat

[runic turret]

whar?

[white stump]

If its the same value imo it doesnt matter how disgusting it looks

[ashen hull]

Ln2(4x)+Ln2=Ln3(x)+2Ln3

[white stump]

Honestly that answer instead bad

[runic turret]

how did u get x inside of the ln

nvm i'm stupid

[ashen hull]

?then?

[white stump]

?

Isn't that bad*

[ashen hull]

Ln2(4x)-Ln3(x)=2Ln3-Ln2
x(4Ln2-Ln3)=2Ln3-Ln2

[white stump]

Yes

[ashen hull]

Then what we should do

[white stump]

Divide

[ashen hull]

Ok
After that

[summer ruin]

you don't have either of these two present in this fraction

[runic turret]

yep i noticed

[viscid thistle]

Logarithms should be appreciated more by the masses.

[static cliff]

I tried out adjusting the shifting of the function to see if it could match better and got here

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

I still need to fix the curves at 1 and 0

[static cliff]

So I found this method on stack overflow I somehow it works

I adjusted it and now when the sliders are set to max it matches the step function, it just does not work for negative values of x
But that can be fixed by just putting some negatives and adding it to the the below one

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

The original one that I found was this

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

Also, the adjusted version lags wayyy less than the other one I made

I am pretty sure it works because the exponents make it sharper on the curves as the values get larger

The only downside is that it goes crazy at small values of lowercase n and that it does not look as cool

Also, this method is a little bit cheaty because it uses floor functions

But it gives me an idea to include exponential function to my original desmos to get rid of the curve near 1 and 0

Hopefully that method works

This is the link to the stack overflow where I found the desmos

https://stackoverflow.com/questions/22070187/making-a-sine-wave-steeper

[static cliff]

I adjusted it a little bit more and got the negative values of x also working

https://www.desmos.com/calculator/jmeo70ltlc

I just made another function for the negative values of x and multiplied the two together

[static cliff]

Okay

After a lot of trial and error I was able to straighten the lines near y=0

I did not use exponents the the stack overflow method

Because it kept getting out of hand

So I used absolute values

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

I believe I can repeat the process for the curves near y=1

Because the idea was that it essentially cancelled eachother out

[static cliff]

I believe I have gotten close enough

Finally

After even more trial and error I was able to remove the curves by even more

https://www.desmos.com/calculator/9xqmntcnz4

The only weird thing is that now the bottom is slightly more curved

But this is wayyyy better than what I had this morning

This is exciting

[static cliff]

Now I don't have to zoom out @winter comet

Hehehehe

At least not as much

[ebon ridge]

Hello everyone, I think my algebra skills are kind of lacking. Can someone show me or explain to me the step by step process of how the top expression simplifies to the bottom expression?

[winter comet]

sure. A = delta = triangle thing
(2x*Ax + (Ax)^2 )/Ax

just expanding (Ax)^2...
(2x * Ax + Ax * Ax)/Ax

factor out Ax
Ax(2x + Ax)/Ax

cancel out Ax on numerator and denominator
2x + Ax

[ebon ridge]

Oh snap, I can't believe I didn't notice that

Thanks for helping 😁

[winter comet]

https://tenor.com/view/its-blank-kung-fu-panda-gif-25603607

wait nvm

im just blind

wait actually yeah that ones blank, not the ones before tho

[winter comet]

bro i can barely see any bends anymore

[vast quartz]

ive still never learned exactly what "factor out" means. how did you just make one of those Ax's vanish from the 2nd to third step?

wait omg

i see it 😭

i didnt notice the part where 2x was being added to Ax rather than multiplied

[static cliff]

If you go to the bottom and click on the r slider and click enter

Then close the new box

I think it should fix itself

[winter comet]

yeah like

ab + cb = b(a+c)

a = 2x, c = Ax, b = Ax

[winter comet]

it didn't work...

:<

[static cliff]

Hmmmm

That is weird

https://www.desmos.com/calculator/yauhzggov6

Try this link

[vast wind]

just take Delx common on both numerator and denominator and then they cancel each other

[unique salmon]

Guys, isn't integration just the function expanding its domain😃

(JJK reference)

[winter comet]

that is the dumbest thing i've ever seen someone say today 💀💀

integration just a function's domain expansion 😎 100%

💀💀

yk what nvm its actually funny 💀

[winter comet]

thats better 👍

[random zephyr]

is there a simple to understand guide for calculus

cause i am LOST

what does f mean?

[random zephyr]

function

[winter comet]

join the club 💀

nah jk

[winter comet]

ngl most guides make it confusing for me

i dont blame ppl getting confuseed

its not actually that hard, i think

[random zephyr]

more confusing?

[winter comet]

i mean like

textbooks and stuff

[random zephyr]

yeah too cluttered

[winter comet]

yeah

they use random variables for random things and it just doesn't give me a good idea of what the subject is about

heck i was getting confused reading a section on stuff i already know lol

[random zephyr]

one of the most confusing subjects has to be calculus

my brain cant comprehend text

i need to reverse engineer

can i reverse engineer calculus?

[unique salmon]

Guys calculus makes no sense to me

But I understand how to do it

Like I know how to differentiate equations, implicit differentiation, integration yadayadyada but I don't get what's it's for

How it's derived etc.

[winter comet]

i'm not going to lie. i don't think its confusing, i think ppl confuse with it

idk

like if they dont have a working way to learn it, its much harder to learn

like i can read textbooks sure, but its very slow because it makes me overcomplicate things

actually talking about it with people (or with myself) makes me understand it more

teachers are sometimes helpful, videos are sometimes helpful

sometimes not tho

depends on how good the teachers/videos are :l

everything depends lol

i think its hard to learn, but not hard to understand

of course i haven't completed it so i can't talk but at the same time i think i get the idea so maybe i can 🫠

just my pov

[ebon ridge]

I agree. Trying out different resources will help a lot. I also ask the question, "why?" A lot when I am studying. I always question my own assumptions, "why did I make that assumption?" "Why does this matter? How did this concept come about?" Etc, etc. Critical thinking comes from a lot of experimentation and curiousity. By understanding what a concept is, you can understand the components to this concept better

Relating equations to the very essence of a concept is very powerful

[winter comet]

yeah

[lyric meadow]

sure i have a few things to say about it

i’ll say them maybe later or maybe tomorrow

i’m tired rn

[stuck valley]

really, everything that has to do with differentiation is the same, although I have yet to understand integrals so I cannot say that for integration.

[random zephyr]

4÷2(3)

The correct answer is 4/6?

[vapid plaza]

The correct response is to ask for clarification because this notation is ambiguous

[willow bear]

the correct answer is use fraction notation, instead of DELIBERATELY being ambiguous for no reason at all other than to be a dick.

[split pelican]

How would fraction notation help exactly? 4/2(3) is still fairly ambiguous imo

[willow bear]

i mean proper typeset fractions

[split pelican]

Ah

[willow bear]

$\frac{4}{2 \times 3}$ vs. $\frac{4}{2} \times 3$

[obsidian monolith]

Ann

[willow bear]

and in plaintext you should also write 4/(2 * 3) vs. (4/2) * 3 ideally, though 4/2 * 3 i personally would read as the latter

[split pelican]

Yeah

[random zephyr]

I absolutely agree

But some dude on tiktok live gave an example like that

He dick fr

[willow bear]

tiktok
math

[random zephyr]

Calm down

I was curious

[dense eagle]

btw, is this kind of notation also ambiguous? like is it clear that its not (sin(\omega) )* t

[hallow tide]

not ambiguous

nobody ever writes that to mean sin(omega) * t

[spring kettle]

Are matrices precalc

[hallow tide]

they're covered in some pre-calculus courses yeah

[spring kettle]

😢

[willow bear]

i mean it's not that ambiguous

but you should write $y = A \sin(\omega t)$ anyway

[obsidian monolith]

Ann

[willow bear]

if only because that stops people tripping up

[sudden musk]

Why is it ambiguous, clearly no one writes it for sin(omega)*t

or they will write y = A * t * sin(omega)

to avoid confusion

[zenith river]

proving lagrange remainder ( taylor polynomial ) , i dont understand how he got F'(si ) = to that thing

[sudden musk]

we have a channel called #calculus

[zenith river]

ok

[simple urchin]

I need to write a proof to show that a linear function guarantees an output for ever even number.

Like y=mx+b is true for all even numbers. Can anyone help me with writing such a proof?

[willow bear]

"a linear function guarantees an output for every even number" sounds a bit strange

@simple urchin can you post the original problem exactly as it was stated?

[noble vessel]

How do I solve this?

[vestal bison]

i tried but couldn't solve it either can you also tag me when you get the solution because i am also interested in this question as well

[deft turret]

yall
my friend Erik
he is in 10th grade
and he likes a 9th GRADER
what yall think about it

[cunning schooner]

i liked a 10th grade girl as a 11th grader

its just a single year

[chrome ether]

!redir

[tender quest]

This channel is only for on-topic discussion. Please take casual conversation to #discussion or #chill.

[chrome ether]

🤓

[cunning schooner]

https://tenor.com/view/doomer-doomer-sad-depressed-gif-15543940

this is me rn

fucking 4 am

[winter comet]

cheers mate

[winter comet]

good for him ._.

[fading arch]

you need to use (a+b)/2>=√ab

[fading arch]

use (a+b)/2>=√ab

[noble vessel]

$16^{x^2 + y} + 16^{x + y^2} \geq 2\sqrt{16^{x^2 + y^2 + x + y}}$

[obsidian monolith]

Normed

[noble vessel]

How does this help?

I think we want equality here?

[fading arch]

at the end you'll end up with an equality

i already tried this problem and struggled, and the solution was to use a+b/2>=√ab

at the end you find -1/2 for both

[fading arch]

it help because it makes a side of the inequation "1/2" because of the original equation

[noble vessel]

Can you tell me what's the next step here?

[fading arch]

sorry it's backward

but you end up with this and then have to use a trick to make the 1/4 into a 1

[noble vessel]

What's the trick?

[fading arch]

you add 1/4+1/4-1/2 on the exponent

and 16^(-1/2)=1/4

then you simplify both side by multiplying by 4

do you just want the all answer ?

i can just send it it's easyer

[noble vessel]

Yeah sure that will be very helpful

[fading arch]

sorry its a little bit messy

[noble vessel]

thanks!

[tawdry anchor]

Hello can anyone help me with this. I can only get the apparent power but i dont how to get the true power when only the voltage and current are given in a waveform. The apparent power is 2080 by multiplying the voltage and current by .707 to get the effective value but i dont know how to get the true power from.there. please help.

[winter comet]

i know this is random, but does anyone have any tips for drawing graphs with only a pencil

cuz

i absolutely suck

my intervals are not consistent, my lines aren't straight, ect. lol

seems like a drawing skill issue ngl

[willow bear]

are you using grid paper?

[winter comet]

no

[random yoke]

are you using a ruler

[winter comet]

no

i mean like i can

it just seems like i should be able to make one in some way without pulling out a ruler

accurate enough so that i dont make mistakes

guess not tho ;-;

[willow bear]

i mean, grid paper's whole purpose is to help you draw graphs neatly.

so maybe start using it.

[plush terrace]

i need help with homework

[chrome ether]

!da2a

[tender quest]

No need to ask “Can I ask…?” or “Does anyone know about…?”—it’s faster for everyone if you just ask your question! See https://dontasktoask.com/

[tawdry anchor]

Does anyone know how to solve inductive reactance. I need your help

[chrome ether]

you'd be better off asking this in a physics server, check #old-network for the link

[reef grove]

Coil up bro

[clever elk]

Hey, I have a super simple question regarding derivatives.
Doing a derivative of b^x with respect to x, can also be written as ln(b^(b^x)), rather than (b^x) * ln(b). I've been told that it's not correct to do this, which is weird, given that i've just used the power rule of logarithms to rewrite it.
Why is ln(b^(b^x)) not correct?

[summer ruin]

because it's equal to ln(b) * b^x which is not equal to b^x

unless b = e

[clever elk]

ln(b^a) = a*ln(b)?

[summer ruin]

yes

[clever elk]

I'm arguing for ln(b^(b^x)) being more true than (b^x) * ln(b), given that b = 0 is allowed in ln(b^(b^x)) but not in (b^x) * ln(b).

d/dx (0^x) is

[summer ruin]

you're already trying to say something about an ill-defined concept and asking why stuff you do is incorrect?

[clever elk]

I've been told that im incorrect

But not why i'm incorrect

so I've come here to ask why I'm incorrect

[summer ruin]

yes because b^x cannot be rewritten as ln(b^(b^x))

[summer ruin]

the equality simply doesn't hold

[clever elk]

What do you mean? I'm not following you?

[summer ruin]

,w plot 2^x and ln(2^(2^x)) from 0 to 1

[obsidian monolith]

Results provided by WolframAlpha

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

Requested by transparent_elemental

[clever elk]

Huh? 2^x can not be rewritten as log(2^(2^x)), but d/dx (2^x) can

[summer ruin]

of course, since they're different functions

[clever elk]

Yeah, so what are you proving here?

[summer ruin]

it seemed like you were talking about b^x being the same as ln(b^(b^x))

[clever elk]

Where did I write that? can you please quote it?

[summer ruin]

in your very first comment

[clever elk]

Ah, do you mean:

[compact spade]

Need help on these two problems

87 & 114. 88 not necessary

[willow bear]

@compact spade have you made any progress on #87?

[compact spade]

Nope

Don't even know how to start

[willow bear]

ok, let's see...

do you notice anything special about your points?

specifically, the first and the third points -- (0, 0) and (4, 0)?

[compact spade]

Yep, reflected evenly across x = 2

[willow bear]

not what im looking for.

[compact spade]

Ah

[willow bear]

the points themselves.

[compact spade]

X intercepts

[willow bear]

yes, they are the x-intercepts.

[compact spade]

Ahh ok

Oh shit ok I think I got it

[willow bear]

does this enable you to continue?

[compact spade]

Ty

[willow bear]

ok great

on to 114?

[compact spade]

Yes please :)

[willow bear]

any progress with that one?

[compact spade]

No, none yet

[willow bear]

do you know what partial fraction decomposition means?

[compact spade]

Kind of?

[willow bear]

there's no kind of, you either do or you don't

regardless of whether you know how to find one

im asking if you know what a pfd is

[compact spade]

I'm gonna go with no

[willow bear]

https://www.youtube.com/watch?v=QKkdYW77xNI

give this a watch

then come back to that problem

[compact spade]

Got it, will do

Thank you so much for your help btw, really really appreciate it

[unique salmon]

Yall ever just do a math question and think about why you need it

[clever elk]

yeah

I never really understood why I would need to know geometry-constraint questions until I worked with CAD

..or calculus and linear algebra questions until I worked with machine-learning

and I suck at it. But just having some base understanding of how one can interprete equations in natural language is super useful

[tender mist]

Nope. I just like doing math. It's like solving puzzles, and I like doing that, lol

[unique salmon]

Anyone know what kinda math you need for computer science?

[unique salmon]

I love maths as well, I just do it for fun too, but sometimes I fail to understand its practical use

[unique salmon]

Except for discrete maths

[unique salmon]

Wrong server bro

This is physics

Recommended the physics and engineering server

[tender mist]

Join the server called "1 server is unavailable due to a temporary outage"

That should help with your physics problem

[willow bear]

if someone said something in violation of the rules, take that to @tall sequoia's DMs

or ping moderators with a link to the offending message

...

i mean, i saw that

[zealous mango]

can someone pls help me 😢

[crisp timber]

Interesting. Its a bit tedious to me since I don't take trig class, but let me see.

[jolly wind]

pretty easy stuff

[vestal bison]

i dont understand this question and solution at all. you see at the end it says real coefficients and complex coefficients in two questions? both of them got the same coefficients which is 1

and like whats linear factors

[summer ruin]

factors of the form (x-a) where a is a root

[summer ruin]

2i is also a coefficient

it says coefficients of linear factors, not coefficients of P

[vestal bison]

does it matter a is real or imaginary?

[summer ruin]

depends on the field you're considering

[vestal bison]

but how? isnt coefficent the number in front of the unknown

[vestal bison]

so is (x- √2) a linear factor?

or (x-3)?

[summer ruin]

yes

[vestal bison]

so anything is a linear factor basically?

[summer ruin]

coefficients of a polynomial ax^2 + bx + c are a,b,c

[summer ruin]

no

x^2 + 4 is not a linear factor

[nocturne wigeon]

Anyone here help me with a quick trig questions littery 10 seconds

[vestal bison]

because it has power of 2?

or any powers in general?

[summer ruin]

it's not a linear polynomial

[vestal bison]

there's a geometry and trigonometry channel

[vestal bison]

what is a linear polynomial

[summer ruin]

a polynomial of the form ax+b

[nocturne wigeon]

Yeah I’m asking if anyone of yous can help me over there

[vestal bison]

so anything in this form is linear factor?

like as i said x-√2 etc

[summer ruin]

yes

[vestal bison]

i got the linear part but i still dont get how 2i can be a coefficient

all the x values i see got 1

[summer ruin]

👆

[vestal bison]

and i is not an unknown

[vestal bison]

oh x^0

okay

[summer ruin]

x-2i is a linear polynomial with complex coefficients

1 and -2i

[vestal bison]

like 3x^2 + 5x -5

but 5 has unseen x^0 right

so basically its a coefficient as well

[vestal bison]

okayy i got this part

what about the irreducible quadratic factors?

[summer ruin]

they cannot be factored into linear terms over field R

but it is possible over complex numbers

as seen in the solution

[vestal bison]

here it says that thing in a but

also √2 is not a real coefficient?

[summer ruin]

it is real

[willow skiff]

The idea behind this is that there are some polynomials which only have complex roots

Even if all the coefficients of the original polynomial are real

[vestal bison]

huh but √2 doesnt come out

i lost all my knowledge in math tbh i guess need to start w numbers

[summer ruin]

it does? the polynomial has both (x-sqrt(2)) and (x+sqrt(2)) factors

[willow skiff]

I guess you just need a bit more time yeah, luckily it's just reviewing definitions which is the 'easier' part of maths

Knowing the different types of numbers

[vestal bison]

oh okay okay nah i know these

i misunderstood the thing with complex and yk

[willow skiff]

Yeah so just refresh your memory so that you can apply this knowledge to other situations

[vestal bison]

complex is just the imaginary ones

[willow skiff]

True, transparent was using terminology from abstract algebra

Which is beyond your level

[willow skiff]

Yeah basically

A lot of people tend to mix up 'complex' and 'imaginary': it's no big deal actually

imaginary technically means like 2i, 3i, -sqrt(2)i, pi * i

And not a + bi

And there's more than one definition ofc

[vestal bison]

so here (x^2+4) is the irreducible quadratic factor right ?

[vestal bison]

oh okay

[willow skiff]

Yes

It has roots x = 2i and x = -2i

[vestal bison]

we didnt use i because it asks for real ones

right

[vestal bison]

yeah but it asks real coefficients so thats why we did not factorize that am i right

[willow skiff]

Mhm

That's it

[vestal bison]

alright thank you

[willow skiff]

No worries

[vestal bison]

i got one more question, so is the statement "every polynomial has at least one real zero" is incorrect right?

also uhm i got this polynomil i tried rrt but it didnt work so i guess this doesnt have any real zeros and how do i factorize this and find the complex zeros?

$$x^4+2x^2+1$$

[obsidian monolith]

ghiolimer

[vestal bison]

i usually use desmos but i dont wanna use it 24/7 bc i need to learn this thing

[summer ruin]

depends on which field you consider

ah nvm I interpreted the question differently

but yeah it is incorrect

[vestal bison]

okay

how do i find zeros the polynomial above

oh okay

i got it

okay nvm

[summer ruin]

it is quadratic in x^2

[vestal bison]

i did it

lol yea

still, thanks

[vestal bison]

i have another question regarding this. you see a polynomial with a degree 3 has 3 roots whether real or imaginary. but u see sometimes these roots have multiplicity. do they also count as roots again? or n=3 means the polynomial has 3 different roots

for example i got a polynomial here i factored it and got

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

[obsidian monolith]

ghiolimer

[vestal bison]

it has -2, -2, and 2

so i guess -2 counts twice right?

otherwise we would have -2 and 2 and we would have one left and imaginary roots come as couples

am i right

[primal tusk]

Ohhh precal

[primal tusk]

If i recal it becomes
2x+4 times x-2 or sumthim

If thats the case then it becomes x=2

[compact spade]

I could solve this normally, but not with the method it wants me to use

[summer ruin]

what do you consider to be "normal" method?

[compact spade]

Add row 1 to row 2, get value of x. Add row 2 to row 3, plug in value of x to solve equation for y. Then plug in both values to any of the three equations to solve for z.

[summer ruin]

this is gauss-jordan elimination

[compact spade]

Oh lmao alright

Thank you

[half pollen]

omg elemental

can you help me with verifying something 😭 please

Question:

1/a + 1/b = 3/2018```

Somebody mentioned:

1/a + 1/b = 3/2018
2018 can be prime factorized as 2 * 1009
Hence you rewrite as: 2 × 1009 ( a + b) = 3ab 

Now, at least one out of a and b must be divisible by 1009, so it's either:
1) Both
2) One( a) 
3) One (b)
Each will give you 2 ordered pairs 
So 6 possible pairs

But this is wrong reasoning right? ab can't both be divisible by 1009

unless he assumes that gcd(3, 2(a+b)) = 1?

[summer ruin]

I know zero number theory

[half pollen]

awww

i know 0 number theory too

😭

okay thanks np

[compact spade]

Ok last one

I mean, for today

There will certainly be more

[summer ruin]

if the parabola passes through points (x,y), then these points must satisfy the equation of parabola

[half pollen]

bruh

[compact spade]

Yes

I understand that part

[half pollen]

you can have three equations right for the three unknowns?

[summer ruin]

well write it down then

[half pollen]

Lol

[limpid wasp]

That means we substitute
(x, y) = a point that is on the parabola
to y = ax² + bx + c

[half pollen]

yes they've been told that twice

[compact spade]

Wait no I think I get it

Ok ty

[half pollen]

you'll have three equations in three unknowns

they you use gaussian elimination to get the unique values of a,b, and c

[elfin anvil]

If z = r cis θ, and -π < θ < -π/2, is it right or wrong that √z = √r cis (θ/2)?

(sorry I don't know how to type cis in latex, or to format fractions in parentheses)

[winter comet]

you mean when finding the roots of z?

this is more accurate

i think ^

oh wait yeah thats what you said 💀

[proven void]

how to get better at math

[winter comet]

1. learn a concept to the point where you can repeat it back to yourself so that you REALLY know it
2. practice it

very broad

two step process

💀

[proven void]

I need help with math, can someone help

[willow bear]

we can't help you until you post the problem(s) you need help with

and "i need help with math" is like

the vaguest possible request

[proven void]

its something related to symmetrical points I dont understand

[willow bear]

https://www.google.com/search?cq=point+symmetry+and+line+symmetry

otherwise clarify what you don't understand here

• symmetry wrt a line means mirror reflection across that line
• symmetry wrt a point means a rotation by 180 degrees around that point

[proven void]

what would be line symmetry of (1;3) wrt y-axis/line

what is this?

[willow bear]

a formula that

• computes a point symmetry, not a line symmetry
• is way over-caliber for your problem

[willow bear]

draw yourself a grid with axes

here is the point (1, 3)

mark on this picture where the point (1, 3) will go when mirrored across the y (vertical) axis.

[proven void]

(-1;3)

[willow bear]

it is like a miracle that you are now able to answer your own question.

[proven void]

what about x axus

[willow bear]

mark on this picture where the point (1, 3) will go when mirrored across the x (horizontal) axis.

or somehow end up telling me its coordinates.

[proven void]

(1;-3)

[willow bear]

so (1, 3) will stay in place?

that's more like it...

[proven void]

haha sorryy

im new

what about wrt origin

[willow bear]

well,

mark on the picture where the point (1, 3) will go when rotated 180° (half of a full revolution) around the origin.

[proven void]

(-1; -3)

ty!

[willow bear]

i did precisely nothing

except stick your nose in the problem, and some key words, a bunch of times

all of this you were surely able to do on your own

[proven void]

sorry.

[willow bear]

i am neither demanding nor expecting an apology

[proven void]

why so serious today ann

alright.

[willow bear]

??

[proven void]

how to tackle

[willow bear]

do you know what an increasing function looks like, graphically?

[proven void]

with a positive slope

[willow bear]

ok

do you know what a maximum or minimum value looks like graphically?

[proven void]

I dont get it.

[willow bear]

you know the graphical meaning of supremum but not of maximum?

[proven void]

how to tackle

[willow bear]

i literally tried taking you step by step through the things you needed to take note of

your response was to completely defenestrate all that and (implicitly) call for somebody else

[proven void]

I dont know how min max works

[willow bear]

https://www.google.com/search?q=minimum+and+maximum+on+a+graph

defenestrate means to throw out the window

[proven void]

tl; dr?

[willow bear]

❌

[proven void]

what about it ?

[willow bear]

you should do your own research on this topic. read your notes, read your textbook, watch khanacademy or ochem tutor

theres so much out there

put some effort in, lmao

[proven void]

I just started this class today ngl I might have already gone too far ahead of myself

I think this is going to be seen next week

[willow bear]

what class is this

[proven void]

pre university real anal

[runic turret]

how would i use the base change formula here

"solve $2^{\log_3 5} * 5^{\log_3 31,5} * 7^{\log_3 0,6}$"

[fiery fable]

hi can someone please explain where he got x-4 from?

this is adding rational expressions

[willow bear]

,rccw

[willow bear]

what was the original problem?

@fiery fable

[willow bear]

,rccw

[willow bear]

hi can someone please explain where he got x-4 from?

so then x-4 is part of the original problem, isn't it?

[fiery fable]

oh

sorry

thank you

[lofty geyser]

Help with polygons

[willow bear]

ok let's just cut away the black bands that are 2x as tall as the image itself

@lofty geyser progress so far?

[lofty geyser]

what are black bands

oh

Uhh so far I found c d f e are part of a heptagon

Right?

[willow bear]

sure

anything else?

[lofty geyser]

Nope

Still confused on how to do it

[willow bear]

ok, let's start simple

do you know how to find the sum of the angles in a simple (non-self-intersecting) polygon?

[lofty geyser]

The interior angles?

[willow bear]

yes, the interior angles.

[lofty geyser]

is the answer 745.7

[willow bear]

doesn't sound right at all, neither for my leading question nor for your original problem

how did you get this?

[rancid bramble]

hi

is it true i dont need to study for unit 4

for the ap pre calc test

just 1,2 and 3

<@&286206848099549185>

[opaque field]

So I was about to screenshot my math problem, but then i see a notifacation

https://en.wikipedia.org/wiki/User:Severe_Activities_Wiki/sandbox

read it...

[chrome ether]

!redir

[tender quest]

This channel is only for on-topic discussion. Please take casual conversation to #discussion or #chill.

[chrome ether]

what

[opaque field]

I know

[chrome ether]

this does not merit a helper ping

[opaque field]

Im just saying

i was about to screenshot something

but then that came up

...

[chrome ether]

if you're trying to skimp and scrape by with a 5 maybe you can drop unit 4 if you can answer every unit 1-3 question correctly

but that's highly unlikely

so get studying on unit 4

[viscid thistle]

Would any of these chapters help with calculus?

[dusky zenith]

Does anyone have the AP precalc practice tests by college board? I can’t seem to find them and apparently they have released some practice tests

[winter comet]

chapters 5, 6, and 7

7.9 literally says differentiation

💀

[drowsy nova]

drhgfds

[proven void]

how to find roots of 1/x

[chrome ether]

it has none

if by "roots" you mean "zeros"

[split pelican]

What about 1/+-infinity /s

[proven void]

reason/motives

[chrome ether]

literally basic intuition?

if i divide something into lots of tiny pieces i can't ever make the size of any of those pieces zero

[proven void]

whatever

I was expecting something mind blowing but it isnt

[willow bear]

start with the equation 1/x = 0

multiply both sides by x

you get 1 = 0

[proven void]

I thought it was going to be something more involved, thanks.

[jolly stump]

Thats a great way to think about it. Thank you.

[chrome ether]

npnp

[white rapids]

8.1-8.8 and maybe a little bit of trig and alg 1/2

[viscid thistle]

Hello, I am a student in honors pre-calculus and scheduled to go into AP Calculus AB+BC next year. I am struggling with grasping this current level of trigonometry as a whole and wondering if anyone can give me some good ideas of where to start from the bottom-up so I can begin to comprehend it

[white rapids]

Study the unit circle

[wind jungle]

Hi! I have no clue how to solve this problem. I keep getting

-x(-x+40)(x+5)

for factors, but I don’t see how that would work as a solution for volume because of the negative coefficients.
Help much appreciated, thanks!

[willow bear]

-x(-x+40) = x(x-40)

on the other hand this problem is poorly stated bc it doesnt actually say anywhere that the other two dimensions can't be x^2-40x and 1

[wind jungle]

ah, i see. thanks for clarifying

[wind jungle]

when i graph into desmos though, it has negative volume (y) inside the domain {0 < x < 40}

and now the textbook is asking me to get the maximum volume so idk

[tired stone]

ios this correct?

[willow skiff]

Yes

You should do $\log_a x = \frac{\log x}{\log a} \implies$ tho

[obsidian monolith]

south

[willow skiff]

The arrow is used any time you want to connect two statements

But they aren't exactly equal to each other

[hallow linden]

I finally tried understanding euler's formula

Basically tried visualizing it myself using compound interest

[willow skiff]

Nice

[barren jewel]

HELP

I NEED HELP WITH INFINITE INTEGRALS AND LIMITS

[willow bear]

1. WHY ARE YOU SHOUTING?
2. THIS SOUNDS MORE LIKE A #calculus ISSUE!
3. YOU MIGHT WANT TO ACTUALLY POST THE QUESTION(S) YOU NEED HELP WITH!

@barren jewel

[barren jewel]

I don’t see it 😦

[willow bear]

hm

oh this might be bc it's in the early university category

[uncut mulch]

you could also just claim your own personal channel

[barren jewel]

Hmm good idea!

Thx

[winter comet]

yo so actually this precalc channel is MY channel, uh, don't talk here anymore

🤣 jk 💀

[half pollen]

yo so actually this server is MY channel, uh, don't talk here anymore

[winter comet]

nooooooo 😭

oops i talked in his server

twice

[stable gull]

mmm nah i claim this channel

talks tag is wild

i don yap that much do i 😦

😭

[river drift]

the "talks" role says you want to be pinged when a lecture ("talk") is happening on the server. you chose this option in id:customize

[full wing]

lets see if you guys can solve:

pi=2ln(x)/x, solve for x

for anyone who doesn't know, a variable such as x can be any number

[signal vault]

Can someone tell me the difference between evaluate and differentiate with respect to x ? Both means same to me

[willow bear]

it sounds like the function written under "differentiate wrt x" was obtained by taking your thing and then differentiating it a 3rd time

[signal vault]

So thrid deravative . Thanks

[willow bear]

"differentiate" by itself does not mean "take the 3rd derivative"

just for the record

[whole shoal]

Help

[peak token]

how do i convert -7√7 into an entire radical?

[tender mist]

I don't think the negative can be put into it, but anything going into a square root (specifically square, not cube or higher), has to be multiplied in by the square of the term going in. So you want to multiply the 7 inside the radical by the square of the outside term (so the square of the 7)

[surreal crescent]

Why is it called precalc if calc introduces completely new topics that are different from anything before it? Why not just call it algebra 3 with a hint of geometry

[river drift]

because it's supposed to have all the topics required to prepare you for a calculus class

since calculus has a fair amount of prerequisite material

[winter comet]

because technically speaking precalc is KIND OF skippable, although you still need to know the stuff in it if your algebra class went over the 'precalc' stuff you're good. also calculus isn't THAT different from anything before it

it certainly uses the skills taught before it

it just has a few abstract concepts

but these concepts are built from facts you learn before so yeah...

for instance, calculus has derivatives. this is just the slope of a tangent line. slope is an algebra 1 concept i think, and if you didn't learn what a tangent line was in algebra 2 then you should have at least learned it in precalc before taking calc

because they kinda just do fancy stuff with tangent lines

thats the entire derivative part of calculus lol

tangent lines of graphs

[near lintel]

how can i do this?

[willow bear]

do you know trig?

[near lintel]

yes

[willow bear]

ok

what can you tell me about theta, given that the slopes of both ramps are 3/5?

[compact spade]

a

help

please

ah

[surreal crescent]

From this moment forward I propose we call Pre-calc: Agebra 2, Pt. 2: Cubic boogaloo

[winter comet]

well

im not going to lie

how about we call precalc algebra 3

and calculus algebra 4 ngl

calc 2 algebra 5

calc 3 algebra 6

THEN we ok

👍

[surreal crescent]

Calc ain’t really algebra

More… Infinite geometry

[winter comet]

...sure

i guess

i mean

its a graph

but i guess if ur taking the integral then yeah its infinite geometry

[compact spade]

This is due tomorrow and I'm completely lost can I get some help on this really quick

[winter comet]

but the derivative is more like a graph

[surreal crescent]

Are these matrix’s?

[winter comet]

the matrices are equal. that means all the elements are proportional, right?

[unkempt cave]

Can you go straight from honors geo to precalc with trig when the recommended middle class is algebra 2

[compact spade]

Uhhh I would assume so?

Wdym by proportional

[winter comet]

i used the wrong word actually

umm

[compact spade]

equivalent?

[winter comet]

when the matrices has the same dimensions

[compact spade]

yes

[winter comet]

and the elements are equivalent yeah

[compact spade]

yes

[winter comet]

so what are you stuck on

[compact spade]

wait i swear to god is that fucking it

is it that easy

[winter comet]

🤣

yes

lol

[compact spade]

i

ok

[winter comet]

xD

[compact spade]

thank you

[winter comet]

👍

[compact spade]

i will be back later 💀

[winter comet]

bro was overcomplicating it

XD ok

[surreal crescent]

Wait now I’m confused, what the hell is z

[winter comet]

in their problem?

in that specific one there is no z

[surreal crescent]

Ye

[winter comet]

but i'm assuming it was referring to a set of problems

and some of them have x,y, and z

some of them have only x and y

ect

yeah it says problems 1-4

LOL

it says find x and y or x and y and z

lol

[compact spade]

ok no i am now actually lost

what the fuck is this shit

[winter comet]

those are 3 by 2 matrices

there is no x and y or z

[compact spade]

i noticed

[winter comet]

so um

are there more instructions?

or more part of the problem or something?

[willow bear]

3 by 2

[winter comet]

oh mb LOL

[willow bear]

@compact spade do you know how to add matrices

it is actually dead simple

[compact spade]

on god?

[winter comet]

XD

yeah

[compact spade]

sorry im tired no shit was absolutely the wrong phrase

i am so sorry

that came off as REALLY mean i can barely think let alone type

[winter comet]

really?

i thought it was funny XD

[willow bear]

there are far meaner things you could have said

by several orders of magnitude

anyway

[compact spade]

hey i know those

[winter comet]

and direction

then you got a vector YAY

💀

[willow bear]

addition, subtraction and scaling of matrices is just entrywise.

ie you add them entry by entry

[compact spade]

ok will get back to you

[willow bear]

like you would with vectors

[compact spade]

thank you

[surreal crescent]

Please, tell me when I’m going to stop dealing with graphs and actually do some fun stuff

[compact spade]

you're in precalc?

[surreal crescent]

Yes

[winter comet]

like

never?

[compact spade]

like 1/3 of the way through

oh

[winter comet]

i mean

calculus is graphs

[compact spade]

i have had a different experience

[winter comet]

linear algebra is graphs

maybe not probability

[compact spade]

you go to triangles at some point though

[surreal crescent]

I’m on combining functions

[compact spade]

yeah you're like halfway out of graphs i think

[winter comet]

you mean like composite?

[compact spade]

for this year

[winter comet]

actually linear algebra is very weird graphs i think

i havent taken so i cant really say fs

but i'm very sure its got graphs 💀

[surreal crescent]

It’s just algebra but with cubics 😭

[winter comet]

wdym cubics

you mean like three dimensions

or multiple dimensions

[surreal crescent]

No, like f(x) =x^3+x^2+x+3
G(x)= (2x^3+5x^2+x+2)/x+1)
Find (3(f/g))(x)

[winter comet]

um

would that be relatively basic linear algebra?

[surreal crescent]

Idfk, my state does stuff wierd, I’m in precalc honors rn

[winter comet]

huh

[surreal crescent]

In the middle of a unit on applications of functions, doing comic sections next

[winter comet]

conic sections?

comical sections xD

[willow bear]

that is not what linalg means

[surreal crescent]

wtf, laws of sin and cos are on my silabuss

[surreal crescent]

Ain’t that calculating infinite dimensions

[winter comet]

what is it then

i didn't know if math subjects have strict definitions lol