precalculus

[modern valve]

I don't think it matters if you read it in this book or in Stewart's

It'll probably be mostly the same

[unborn brook]

I'll still set a future reminder to get back to that title when I'm done with the rest of the material with Stewart's. Just out of curiosity.

[viscid thistle]

blud died cuz of maths

[terse aspen]

How do i write 1/2|x-8|-5 as a piece wise function

[modern wedge]

the absolute value function is 2 straigjt lines

how do you find tjose straight lines

[terse aspen]

Idk

[modern wedge]

its the positive and negative of the absolute value

[sturdy hound]

i suggest u watch this video
https://youtu.be/71SfBO-B4dE?si=vk_o_RxzwTKxqN1p
if you have anymore questions then ask me

[compact orchid]

I have a question with a polar eq,

R = 40sin(θ)cos^2θ

Can anyone identify the type of graph this is and how I would begin to solve? just a slight question

[winter comet]

wdym how you would begin to "solve"

[compact orchid]

As in graphing it, than converting to rectangular form. idk if Im breaking the rules of this server so I made a help channel if u wanna talk there

[willow skiff]

well note that you need to convert $r \cos \theta = x$ and $r \sin \theta = y$

so $r^4 = 40 (r \sin \theta)(r \cos \theta)^2$

[obsidian monolith]

south

[willow skiff]

or $(x^2 + y^2)^2 = 40yx^2$

[compact orchid]

ah okay

[willow skiff]

it's very very hard to identify the type of graph

well plotting this graph is not that bad by hand

use the polar form and sub in theta = 0, pi/6, pi/4, pi/3, pi/2 and so on

[compact orchid]

ahhh

okay yea i see wym

[willow skiff]

your graph is odd, in other words $r(-\theta) = -r(\theta)$

[obsidian monolith]

south

south

[willow skiff]

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

[meager pilot]

oh okay

lets first go deep in algebra

[tawdry canopy]

is calc 1 allowed here or this is just for precalc?

[elfin cargo]

Calc 1 go in #calculus

[terse aspen]

Thank you so mucu I will look over it and ask a question tomorrow if I have one

[tawdry canopy]

idk this even exists but ty

[bronze ravine]

Hello!

Does anyone have the Aops pre-calc pdf? I’m unable to afford a purchase but I want to rigorously study it

[raven tundra]

I have one from 2009

[grave solstice]

helloo. does anyone have well described venn diagrams notes

[sturdy hound]

sounds good

[meager pilot]

i really want this

[viscid thistle]

Idk if this sounds dumb but between a & b how do i know if the answer is postive or negative 4x?

[summer ruin]

at x = 0 the derivative is equal to -4

[jagged patrol]

(0,-4) means that -4 is be term

[viscid thistle]

Oh so u just grab a point?

[jovial sluice]

No. the point -4 is on the y axis. For a point to be on the y-axis the value of x must be zero

[muted turret]

How do I determine the equation of the tables

[molten rivet]

f(-2)=0
f(0)=1
f(3)=4
f(7)=6
g(-1)=3
g(1)=2
Like this

[crisp vortex]

Can someone explain this? I get sine and cosine but not the rest

<@&286206848099549185>

[muted turret]

#geometry-and-trigonometry probably will be better

[muted turret]

No like (f•g)((-1) for example. Do I like do something with f(g) first?

[molten rivet]

Ohhh nope
(f.g)(-1)=f(-1).g(-1)

[willow skiff]

no, that's not what that means

it's $(f \circ g) (4)$ not $(f \cdot g) (4)$ for instance

[obsidian monolith]

south

[willow skiff]

yes, that means $f(g(-1))$

[obsidian monolith]

south

[willow skiff]

find g(-1) then sub that into f(x) as your new x-value

[molten rivet]

Wait isn't that f multiple g?
I thought the . Was for multiplying
And (fog)=f(g(x))

My bad my bad

[willow skiff]

yes, that is correct, so just look at the original problem sheet

[warm cove]

Got a exam today but the unit 2A notes I don't have

[viscid thistle]

Does anyone know why the answer is 0? I was told that its not continous bc RHL does not equal to LHL but isnt it the same for -1 too? And 1? Like when i try to input it in the functions they all get different answers

This is the answer i got but arent all the options not continous?

[uncut mulch]

how are you doing the work for 1 and -1

[viscid thistle]

I dont really understand this topic so when i saw this question i just gave up

My teacher didnt really explain it before properly he only explained for 1 question so i only knew how to solve that one

[uncut mulch]

it helps if you draw it first,

use a graphing calc if you feel the need

have you worked with piecewise defined functions before?

(its usually done before calculus)

[fading monolith]

Have you consider my msg?

[uncut mulch]

you don't even need derivatives here

[viscid thistle]

Yes also we r not allowed to use a graphing calculator

If thats what its called??

[uncut mulch]

do you first understand the (limit) definition of continuity

[fading monolith]

Ok then, just was my guess

[uncut mulch]

when you are first introduced to this, it really helps to draw it out first to see what's going on,
and what your calculations represent

[viscid thistle]

Yes

[uncut mulch]

how would you calcluate the the left and right side limits for x=1

[frosty folio]

Hey is anyone on rn?

suck on a problem

stuck*

[tawdry canopy]

bros

what do you think abt this

i just made this as my reviewer for precalculus

but i don't think i could use it anymore

https://www.desmos.com/geometry/1hntxvpume

[viscid thistle]

I and my classmates suck at limits, so our teacher isn't moving to introduction to derivatives(it's been a month)

I'm getting better at those rationalising questions but heavily vomit sucking at limits of trigonometric functions😭
(I still can't solve my basic trigonometric fn chapter)

[fading monolith]

Do you have a example where you struggle?

[cursive ocean]

You’re Filo?
I was reading through it and saw something in Tagalog 😆

[tawdry canopy]

ye

[tawdry canopy]

btw, was this good?

[cursive ocean]

I’m also Filo 😭

[willow skiff]

BIBINGKA

(not Pinoy btw)

[tawdry canopy]

haven't completed this yet

because im focusing on caculus 1

[cursive ocean]

I miss eating Bibingka
It’s one of my favorite desserts

[tawdry canopy]

i dont even seen a bibingka once

[viscid thistle]

Mostly in ques like 17, 18, 19

[fading monolith]

Have you seen special limits as sin(x)/x is 1 as x approaches 0 and similar?

For 19 you must remember trig identities as 1-cos(2x)=2sin^2(x)

[viscid thistle]

You can use lim x ->0 (1-cosx)/x^2 =1/2 as well to speed it up

Just multiply and divide with 4 to get the (2x)^2 term in the denominator for q17

[stiff sluice]

\textbf{3.-} Find all $z \in \mathbb{C}$ such that $z^2 - z + 2 = \frac{1}{16} (1 + i)^{11}$.

[obsidian monolith]

938c2cc0dcc05f2b68c4287040cfcf71

[stiff sluice]

can i

get some help

[fading monolith]

Its a quadratic polynomial so you can apply the formula

[stiff sluice]

which formula btw

[fading monolith]

But I recommend you to rewrite (1+i)^11 as re^iθ

[stiff sluice]

why do you say is quadratic polynomial btw?

u sure?

[fading monolith]

The well-known one, -b±sqrt(b^2-4ac)/2a

[fading monolith]

Its a polynomial of degree 2

[stiff sluice]

but like

can I ask something specific that has been bothering me

gimme a second

like my reader introduces this changed quadratic formula

[stiff sluice]

yeah mb, I confused the i with a z

its quadratic

[stiff sluice]

but is a little different but at the same time similar to the regular quadratic formula

why would they do a distinction when using the quadratic formula for complex vs the regular quadratic formula?

[fading monolith]

Its the same just denoting w^2 by b^2-4ac instead

[stiff sluice]

why dont they do $\pm \sqrt{b^2 - 4ac}$ like my reader at the starts shows the regular quadratic formula but when talking about complex numbers, it introduces this one? is it because a specific reason? seems quite arbirtrary

[obsidian monolith]

938c2cc0dcc05f2b68c4287040cfcf71

[fading monolith]

No particular reason I think that is just personal notation just because

I would say that is related to sqrt on complex plane but I dont think its the purpouse of denoting w^2 by b^2-4ac

[stiff sluice]

is strange because the formula is with w: z = (-b + w)/(2a) but then w is a complex number that satisfies w² = b² - 4ac, like it wants me to take the sqrt(w²)?

[fading monolith]

Not neccesary just telling you what w satisfies

[stiff sluice]

but it doesnt say how w is defined

[fading monolith]

I would just apply the formula like always

w is defined by a complex number satisfying that equality

[stiff sluice]

well for this case, how to apply it?

[fading monolith]

Well, first of all compute (1+i)^11 by taking polar form of 1+i and then raise it to 11

[stiff sluice]

trigonometric form?

[fading monolith]

I meant re^iθ

[stiff sluice]

is it possible with demoivre?

idk if trigonometric form is the same as polar form

this is what I mean

[quasi oxide]

Help plz

I have 3 semicircle on each side of a triangle and it wants me to find how the area of the semicircle are related

[fading monolith]

Recall e^iθ=cosθ+i*sinθ

[stiff sluice]

ohh

[quasi oxide]

But it has to do with the triangle in the middle

[stiff sluice]

okay

but

[stiff sluice]

#geometry-and-trigonometry maybe is better suited

[fading monolith]

Yes?

[stiff sluice]

e^{i times argument}

okay

\textbf{3.-} Find all $z \in \mathbb{C}$ such that $z^2 - z + 2 = \frac{1}{16} (1 + i)^{11}$.

[obsidian monolith]

938c2cc0dcc05f2b68c4287040cfcf71

[stiff sluice]

whats the argument of (1 + i)^11

I believe the ^11 is not important for the argument

right?

maybe I'm tripping

[fading monolith]

I told you to start from 1+i first

Then raise it to 11

Applying Moivre ofc

[stiff sluice]

like there is a property for the argument

arg(z^n) = n x arg(z) + 2kpi

maybe is relevant here?

[stiff sluice]

oh okay

[fading monolith]

No, just want you sent. Compute arctan(1)

[stiff sluice]

,w arctan(1/1)

[fading monolith]

I mean yes this is correct but you just need one value not a collection of them indexed by k

[stiff sluice]

pi/4 but the solutions are restrained to the first quadrant

[fading monolith]

Yes, you can check it geometrically by ploting the complex number

[stiff sluice]

hmm

z = (i + 1)^11

Re(z) = 1
Im(z) = 1

?

like this?

[fading monolith]

No

[fading monolith]

You have that 1+i=sqrt(2)[cos(π/4)+i*sin(π/4))

[stiff sluice]

ohh you applied demoivre

[stiff sluice]

but arent we loosing solutions if argument is pi/4?

[fading monolith]

And by Moivre (1+i)^1=sqrt(2)^11[cos(11π/4)+i*sin(11π/4))

[fading monolith]

Not yet on that expresion just trig form

[stiff sluice]

ok

[fading monolith]

We are not solving the equation yet just computing (1+i)^11

[stiff sluice]

the arctan step always trip me, getting the argument

[stiff sluice]

ok and now you used the property arg(z^11) = 11 arg(z)

[fading monolith]

The +2kπ term is correct since you are doing a loop and returning to the same point but we are just taking the principal value if want to call it like this

[stiff sluice]

hmm

[fading monolith]

I used there Moivre

[stiff sluice]

yeah my bad

[stiff sluice]

wait but this is trigonometric form no?

looks similar

[stiff sluice]

wdym principal value, like I thought we needed all solutions idk

And by Moivre (1+i)^1=sqrt(2)^11[cos(11π/4)+i*sin(11π/4))

What should I do after this?

Put it in the calculator and simplify

, w (sqrt(2))^11 * (cos(11pi/4) + isin(11pi/4))

[fading monolith]

Your polynomial only have 2 solutions, not less or more

[fading monolith]

Yes

[obsidian monolith]

Results provided by WolframAlpha

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

Requested by 938c2cc0dcc05f2b68c4287040cfcf71

[stiff sluice]

Hmm okey

[fading monolith]

To put it simple, 1 and e^(i2π) are the same since both are 1 but not same argument, 1 have arg 0 and the other 2π, a loop

[stiff sluice]

\textbf{3.-} Find all $z \in \mathbb{C}$ such that $z^2 - z + 2 = \frac{1}{16} (1 + i)^{11} \ z^2 -z + 2 - \frac{1}{16} \left( -32 +32i\right) = 0$.

[obsidian monolith]

938c2cc0dcc05f2b68c4287040cfcf71

[fading monolith]

By principal value I mean to restric your argument values on [0,2π)

[stiff sluice]

That's first two quadrants

Right?

[stiff sluice]

Okey

[fading monolith]

Not neccesary

[stiff sluice]

Wdym?

[fading monolith]

Now you just apply the formula

[fading monolith]

Just by looking the expression you cant say where the solutions are going to be

[stiff sluice]

This?

[fading monolith]

Yes

[stiff sluice]

Hmm

What is w

[fading monolith]

First compute b^2-4ac

[stiff sluice]

Like this

[fading monolith]

Yeah

[stiff sluice]

Now what?

[fading monolith]

Mmmm try to express -15+8i as re^iθ again, trig form

[stiff sluice]

Hmm

Ok

r = sqrt((-15)^2 + 64)

,w sqrt((-15)^2 + 64)

[obsidian monolith]

Results provided by WolframAlpha

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

Requested by 938c2cc0dcc05f2b68c4287040cfcf71

[stiff sluice]

r = 17

Theta = arctan(-8/15)

,w arctan(-8/15)

[obsidian monolith]

Results provided by WolframAlpha

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

Requested by 938c2cc0dcc05f2b68c4287040cfcf71

[stiff sluice]

..?

[fading monolith]

Such a ugly number

[stiff sluice]

Argument is impossible to get

This never happened to me before

Is an irrational number?

Did i messed something up when finding the argument?

Holy complex mother of god

[fading monolith]

Nah you good

Maybe is not the proper way to procced

Maybe that result that says product of roots its c and the sum is b

[stiff sluice]

Which result? Btw

[fading monolith]

If you have x^2+bx+c=0 then the roots r1 r2 satisfies r1+r2=b and r1r2=c

[stiff sluice]

Hmm

But i don't know the roots

[fading monolith]

I know this method is guess

Since compute w is not so useful due the argument

[stiff sluice]

Hmm what would you do?

Yeah trig form of -15 +8i is fked

Dunno why the argument is like an irrational number

[fading monolith]

Complete the square will guide you to the same -15+8i so its not a way

[fading monolith]

Sometimes it is

[stiff sluice]

The exercise is made like that maybe

Idk

This exercises are always a pain in the butt

[fading monolith]

Another method could it be z=z1+i*z2, rewrite the expresion and solve for real and imaginary part. Wont be easy too but its another method

[stiff sluice]

Is that binomial form?

z = a + bi?

Hmm but i need to solve for w

And we have w^2

Wdym?

Idk why is this so painful

[twilit eagle]

more on this,
given w^2=-15+8i, we can set our unknown w=a+bi
then, after expanding, the equation can be split into an equation for the real part and another equation for the imaginary part
those two equations are then solved simultaneously for two pairs of values a and b

[stiff sluice]

(a+bi)^2 = 15 + 8i

Like this?

But we have two variables and one equation how are we solving this?

I must have understood wrong then

a^2 + 2ab + b^2

a^2 + 2abi -b = 15 + 8i

What do I do now?

[fading monolith]

Yes

[fading monolith]

I was saying for z^2-z+4-2i=0 equation

[stiff sluice]

Okay

So no quadratic formula then

[stiff sluice]

But he refers to w^2

[stiff sluice]

(a+bi)^2-(a+bi)+4-2i=0

After expanding we get

a^2 +2abi -b^2 -a -bi + 4 -2i = 0

[stiff sluice]

Now what?

[fading monolith]

Separate real and imaginary part

Both must be 0

[stiff sluice]

Okey

[fading monolith]

But equations are non linear

[stiff sluice]

[fading monolith]

This sucks tbh

[stiff sluice]

Is in my exam

My life sucks

[fading monolith]

For exams I assume they put polynomial such that w is easy to get

[stiff sluice]

they always do this kind of bullshit, idk how i managed to pass intro to calculus

I barely did it

Is just everything painful as hell

I had to retake the course a second time and I am retaking lintro to inear algebra aswell

[fading monolith]

Important thing is understand the process, the w may be or not more or less easy to calculate

On a exam I dont think they are gonna put smth that student is gonna struggle because the value of this or that is not doable

[stiff sluice]

This is from an past exam from 2023

they dont want me to pass i swear

Idk really, I would try other exercises aswell, the same strategy I did for intro to calculus, just secure points with what you can

There are some people who get 10/10 in these exams tho, idk they are superhuman or something, diff breed

[terse aspen]

Hey how do you do lim x->0 (1+x)^1/x

[fading monolith]

Do a change of variables x=1/t

[fading monolith]

Unless they can let you put the result as (-1±sqrt(-15+8i))/2

[terse aspen]

Wdym

😭

[fading monolith]

On the limit do a change of variables x=1/t so if x goes 0 then t goes inf

And then its a well-known limit

[terse aspen]

Ok

Can you help me with another

Lik x-> (x^2 cos2x)/(1-cosx)

[fading monolith]

x going to 0?

Have you seen limit (1-cos(x))/x^2 as x goes 0?

[terse aspen]

Yes

[terse aspen]

I have seen it over x becuase that equals 0

[fading monolith]

Well in my case that is equal to 1/2 so in your limit you can substitute by 2 since its x^2/(1-cosx) letting with limit 2cos(2x) which is 2 as x goes 0

[terse aspen]

How do you know thats 2?

Becuas I have to show my work for my test

[terse aspen]

Hey can someone help me in dms with limits?

[sturdy hound]

i prob can

if it has to do with cos tan sin thing im bad at that tho rn

[fading monolith]

Via Taylor series

Or L'hopital

Or they can just define the limit to be that without proof if you havent seen those I mentioned

[viscid thistle]

I remember those but while trying to convert into the identity, I create a whole another mess

[viscid thistle]

I firstly suck at trigonometric functions chapter itself, I just know the identities but still suck somehow, ig I should've revised my notes 5 months earlier itself

[viscid thistle]

Actually I didn't try these ques but rather searched for these kinda ques as Alex asked for my weak point

[uneven nexus]

What does r^2=sin2theta look like?

[fading monolith]

,w plot r^2=sin(2theta)

[obsidian monolith]

Results provided by WolframAlpha

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

Requested by yui_na99

[severe pond]

I’m taking my precalc final in 4 hours

[terse aspen]

Mines in 1

[molten rivet]

Good luck you both

[bitter vault]

can someone help me with rectilinear motion? (physics)

[uneven nexus]

Why cos x cos 2x =(cosx+ cos 3x) ?

[daring tapir]

Well you wrote it wrong its 2 cosx cos2x = cosx+cos3x

[nimble blaze]

Is here allowed to be a noob in math? 😔

[winter comet]

😔 sure

[wary crystal]

anybody here also started learning calc 1 this year.

[willow skiff]

I forbid you

[willow skiff]

#calculus

[wary crystal]

thanks

[tawdry canopy]

me started learning calc 1

[wary crystal]

nice me too

[tawdry canopy]

nc nc

[tawdry canopy]

I think, it is ok to be noob at math here

if you're dedicated to learn math, you could learn from here

[wary crystal]

are you willing to trade your life?

[tawdry canopy]

for what?

[eager wigeon]

¿Solo ingles aquí?

[wary crystal]

no

[eager wigeon]

Buenas noches*

[wary crystal]

maybe

can only read spanish, not write it

[eager wigeon]

OK ok, good night. This could be an english practice as well

[wary crystal]

am white wash

[eager wigeon]

In english how do you said Derivada?

[wary crystal]

derivative

??

[eager wigeon]

OK, I have a problem with derivatives (?)

[wary crystal]

ooh

[eager wigeon]

And I'm not sure if this is the right channel to ask for

ask for help*

[wary crystal]

go to "?how to get help"

[eager wigeon]

❤️ u

bye

[whole oak]

🤨

[tawdry canopy]

wdym by that?🤨

[eager wigeon]

I mean love u thanks for the right on the point help

[obtuse current]

(Anything in square brackets are subscript)

After careful thought, when given a recursive formula written as, t[n] = xrt[n-x] + xd, I found that I can write it in terms of n using the following equation:
tn = ar^(n-1) + (n-1)d

I want to confirm whether this is correct and when it will not work.

[outer glacier]

Hi just double checking for pre calc

For law of sin law of co sin what are the cases

Is this correct

[daring tapir]

Am i tripping or would sine rule work for ASS too

[outer glacier]

I think it would

You start with Sin

Then finish with Co sine

[daring tapir]

Why is it ambiguous then

[outer glacier]

To find the second case

Because there's two cases to solve for

[daring tapir]

What even

[outer glacier]

Thus ambiguous

[daring tapir]

What are the cases

[outer glacier]

um

Ass

Sad

SAS

ASA

things like that

[daring tapir]

No shit i was talking for ass specifically

Oh

[outer glacier]

boy

[daring tapir]

Got it nvm

Ignore me lmao

[outer glacier]

https://tenor.com/view/joke-bear-run-away-cute-bye-gif-16047713

[winter comet]

ssa doesn't work

backwards ass :>

[daring tapir]

😭 i will get arrested if i say the joke i wanna so ill just shutup

[winter comet]

💀

[jagged patrol]

ass

[viscid thistle]

n the night

i hear them talk

the coldest story ever know

somewhere far along this road

he lost his soul

[uneven dove]

Nobody in the help forum is helping me is anyone good at trig and willing to help?

[granite temple]

send the problem, don’t ask to ask

[uneven dove]

h(t)=-6.8cos(pi/30(t))+8.3
h(t)=-6.8cos(pi/30(t-12))+8.3
h(t)=-6.8cos(pi/30(t-24))+8.3
h(t)=-6.8cos(pi/30(t-36))+8.3
h(t)=-6.8cos(pi/30(t-48))+8.3.
Each one of these five graphs represents a blade on a windmill. within 120 seconds (two periods) how do I find all the intervals in which all graphs are simultaneously greater than 1.86 meters
the context of the question is you are stuck in a windmill and within two periods which is 120 seconds in this case, you must find all the intervals when somebody who is 1.86 meters tall would be able to walk out

[granite temple]

desmos graph is probably easiest

seems tedious

[uneven dove]

i dont think we are supposed to use desmos thats why im wondering if theres an algebraic way to do it or if i have to manually find each interval

[granite temple]

i just like

huh

why would u need all 5 up

that’s not how a windmill works

[uneven dove]

or i suppose because its preiodic i only need to find two intervals, take the differnce and then continuously add it until i hit 120

h(t)=-6.8cos(pi/30(t))+8.3

this blade starts at the min and is the one the graph is based off of. and the rest are identiccal to this but seperated by a phase shift of -12 because thats how far away they are from one another

i think i figured out what i was supposed to do though

[granite temple]

okay

i honestly cannot picture this

[uneven dove]

h(t)=-6.8cos(pi/30(t))+8.3 This is the graph of one single blade doing a full 360. Which would be enough if I was just looking for when that singular blade is above 1.86 meters, but im looking for when somebody would be able to walk out without getting blocked by a blade and if that blade is at the top that means there may still be one at the bottom blocking you. so you have to graph each blade individually, and find out when all five are simultaneously above 1.86 meters

[stiff sluice]

what is the difference between demoivre and trigonometric form

[winter comet]

i think de mouirve's theorem deals with turning complex numbers to a power into trigonometric form?

[stiff sluice]

so it's the same thing

[stiff sluice]

the argument already has this property

idk how demoivre is giving any more new info

[winter comet]

idk i guess its the same thing

im not really sure ig 💀

[stiff sluice]

same

yet the mods are saying demoivre is under precalc topics

can you believe a 9 year old talking about demoivre

[winter comet]

yeah

[winter comet]

yes i can ._.

💀

[stiff sluice]

idk

[winter comet]

isn't it from your linear algebra class tho?

[stiff sluice]

is not even algebra

idk why they put in there

[winter comet]

it doesn't belong anywhere

[stiff sluice]

😂

[winter comet]

this is the place for lost souls

lost souls get redirected here

[stiff sluice]

ye

[viscid thistle]

[livid harbor]

anybody remember explicit and general formula

[winter comet]

what?

[graceful thunder]

hey guys

im new and i need help with something

i gto a test tmrw on linear functions for grade 10 pre cal

And its confusing me a lil

[winter comet]

do u got a question or anything

[graceful thunder]

I have a unit review that im kinda confsued one

on

i can send some pics

[winter comet]

ok

[winter comet]

do you know what the x-intercept is intuitively

[fallen oar]

is anyone able to tutor me?

i got the test tom

[graceful thunder]

Kinda. Dawg i got back from surgery not long ago and we started this unit

i do not get it lol

[viscid thistle]

Yes

1. y=14×5^(x/5)

[uneven nexus]

Is there any way to compare arcsinx^2 and x^2 quickly

[warm cove]

Most likely failed my precalc exam because didn't know this and it was 80% of this topic 😭

[willow skiff]

because $\sin x \le x$ for $x \ge 0$, $\arcsin x \ge x$ in this domain

[obsidian monolith]

south

[willow skiff]

and the sign flips for x <= 0

the way I think of this is, reflect the graph of y = sin x across y = x

[willow skiff]

btw

pls don't post in multilpe channels

[coral frost]

sorry

[willow skiff]

post once only in #competition-math

[coral frost]

😦

[sinful zinc]

hi guys, do ya know basic calculus?

[willow skiff]

yes but #calculus

[final hornet]

i have a project thats due tonight at 11:59 and the teach wont take any late works can someone help with graphing polar equations i need to use desmos to draw something using polar equations

can someone help?

ive had all week ive searched up videos i dont know how to do it someone please help its a major and if i dont do it ill fail the semester

[winter comet]

that looks more like an art project than math 😐

[winter comet]

just go to desmos and type in the equations and follow the rubric they gave you

"interesting design" is vague

i hate that its objective

like are they gonna grade you down if they dont like it even if you followed all the instructions? smh

(some of my teachers did this 😭)

in similar projects

[winter comet]

you mean you don't know how to graph polar equations in desmos, or that ur just struggling to do it...

[final hornet]

yes idk how to

[winter comet]

first you wanna go to desmos https://www.desmos.com/calculator

[final hornet]

ive tried but nothing works here i tried making a owl

owl face

[winter comet]

😭

[final hornet]

ive been working on it the whole week

[winter comet]

das crazy

i wouldnt know how to make it look like an owl

[final hornet]

he gave us examples but its just too impossible

[winter comet]

that looks nothing like an owl

are you tryna recreate that tho?

XD

[final hornet]

yes 😭

[winter comet]

well you have your cardioid already right

looks like the last one

if you make the entire thing negative it gives you the same cardioid relfected across the y-axis

or is it a limacon

i guess its a limacon 💀

but anyway

[final hornet]

today ive been working on this since 2pm without eating anything my stomach is making sounds bruh

[winter comet]

bruh you should eat something

[stiff sluice]

how do you find prime factorization of a number

this is a sub question from how to find greatest common divisor (gcd) in which I need to know the prime factorization of both numbers

[winter comet]

divide as many multiples of every prime number up to the number that you can...

[stiff sluice]

for example for 69

is divisible by 3

[wide lichen]

u get 23

[stiff sluice]

and by 23

[stiff sluice]

2 x 35

right?

,w prime factorization 69

[winter comet]

u mean 3 x 23?

[obsidian monolith]

Results provided by WolframAlpha

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

Requested by 938c2cc0dcc05f2b68c4287040cfcf71

[winter comet]

wait

3 * 23 💀

[stiff sluice]

ye

[winter comet]

is 3 but yea

[stiff sluice]

typo

[wide lichen]

ready

[winter comet]

same 💀

[stiff sluice]

what about gcd between 69 and 420

gcd(69,420)

[stiff sluice]

3 x 23

[wide lichen]

3

[stiff sluice]

it was a typo

[winter comet]

gcd is greatest common divisor yeh?

[stiff sluice]

ye

[winter comet]

usually i see it as greatest common denominator 💀

but THERE AINT NO DENOMINATOR

😲

[stiff sluice]

,calc 2^5

,calc 64 * 7

[obsidian monolith]

Result:

448

Result:

32

[stiff sluice]

,calc 2^453

[obsidian monolith]

Result:

240

[stiff sluice]

how do I find the prime factorization of 420

[winter comet]

just go down the list of prime numbers and take as many multiples of them out if you dont know what to divide it with
divide by 1 -> 420 * 1
divide by 2 -> 420 = 210 * 2
divide by 2 -> 420 = 105 * 2^2
can't divide by 2 again
divide by 3 -> 420 = 35 * 3 * 2^2
can't divide by 3 again
divide by 5 -> 420 = 7 * 5 * 3 * 2^2
all those numbers are prime so boom

[muted turret]

Synthetic division is literal sudoku puzzles

[stiff sluice]

elaborate

[stiff sluice]

perfect, what about gcd(69,420)

like look at this

, w gcd (69,420)

[obsidian monolith]

Results provided by WolframAlpha

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

Requested by 938c2cc0dcc05f2b68c4287040cfcf71

[stiff sluice]

why is it 3

[winter comet]

3 is the most amount of factors the two numbers share

[stiff sluice]

,w gcd(14,420)

[obsidian monolith]

Results provided by WolframAlpha

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

Requested by 938c2cc0dcc05f2b68c4287040cfcf71

[stiff sluice]

ok thanks

[muted turret]

Oh yeah chat is the inverse function of f(x)=2^x = f^-1(x)= log2x?

Wanna confirm 100% cause I have some graphing to do

[winter comet]

log_2(x) yes

[muted turret]

If you use the base rule it’s an inverse?

[winter comet]

what base rule?

[muted turret]

Like 2^x becomes log(2)x

[winter comet]

if y = 2^x, x = log_2 (y)
so f(x) = 2^x has inverse f^(-1)(x) = log_2(x)
u just mean definition of logarithm when u say "base rule" ig?

[muted turret]

By base rule I meant logaB=C to a^C=B

[winter comet]

ok yeah

[warped saddle]

okay who can help me..

[mild swan]

!status

[tender quest]

What step are you on?
1. I don't know where to begin.
2. I have begun but got stuck midway.
3. I got an answer but I was told that it's wrong.
4. I got an answer and would like my work checked.
5. I have a question about someone else's work/solution.
6. I have completed the problem and don't need help anymore. Thank you.
7. None of the above

[warped saddle]

1

[mild swan]

Start with question 1

Do you know what f(g(4)) means?

[warped saddle]

itink its 2

[mild swan]

You are correct! Why is it 2?

[warped saddle]

g(4)=3

and f(3)=2

[mild swan]

Very good!

See if you can apply similar logic with the others 🙂

[warped saddle]

these are my answers

[spring cape]

aight question

how will i correlate limits with scatterplot chart?

like literally this then correlate with limits and continuity

[summer ruin]

what do you mean by "correlate with limits and continuity"

this plot has nothing to do with neither limits nor continuity

that's the same thing

[wide lichen]

really just concluding

that is, if the answer you got is not explicitly shown in the options, check what the options are and in this case you realize that one of them is your answer but written in a different way.

[unborn brook]

why aren't we accounting for the fact that, for example, (1,1) can be obtained in two distinct ways?

[uncut mulch]

how are you getting the two distinct ways

there's only one way to get that,
if each die shows 1,
as outlined in the sample space

[unborn brook]

Doesn't the order matter? First die: z; second die: t

Then (1_z, 1_t)

& (1_t, 1_z) are distinct events

[lethal quest]

Why does it say “each die”

[daring tapir]

Its not that apparent in here, so lets just assume the die were coloured

Red die and blue die, now it should be more clear that there is in fact only one way

[summer ruin]

the question doesn't say that the dice are colored, if you want to considere them as ordered pairs - you can and then indeed you can get (1, 1) in two ways, but the question doesn't consider that

it just asks for two equal dice what's the probability of getting a sum of 8

it would matter if you asked a question like what's the probability that the sum is 4 and red dice rolled at least 3, because then the pair (1_red, 3_blue) can't be counted unlike (3_red, 1_blue)

[vernal summit]

anyone know good website to self teach precalc

[winter comet]

precalctendo

[winter comet]

uh idk, khan academy or smthn?

[fiery crest]

So I start a precalc class in a few weeks and I didn't do much of any math. What's vital to know and where should I start. I tried with Khan academy but there's wayyyy too much and it feels really disjointed

[willow skiff]

of course, you can't learn every single thing in precalc, would take months or longer

it really depends on if you've properly practised and understood the content from before precalc

you should know how to use the distributive law (FOIL)

you should be very comfortable with factoring quadratics, just to name a few topics

[inner topaz]

what do you struggle at

[vague basalt]

i just finished pre calc this semester and they went over the prerequisites in the beginning of the semester which helped. don’t know if your class will do that though.

[unborn brook]

Should I be fluent with the binomial theorem to prove this?

FYI,I know that I can just use mathematical induction

The thing is I'm told that the property holds true for any integer (?)

[unborn brook]

Maybe I should've asked this in #calculus ?

[fiery crest]

Pretty much all of algebra 2 and anything related to graphing an geometry

[whole void]

no

[whole void]

it’s just using the fact on the left

[whole void]

that’s a lot

[inner topaz]

most important stuff imo are knowing how to factorise, knowing how the important graphs look like in general (trig functions, exp, log graphs), and some trig identities

[whole void]

do u have something u need help with in particular?

[inner topaz]

you are going to go through them again so dont worry too much

[inner topaz]

but these are extremely important even going onwsrds after precalc

[fiery crest]

No I'm not www

By missed I mean like didn't do ever

[inner topaz]

oh

[fiery crest]

Yeah like idk what trig functions or identities are

[inner topaz]

its not very hard theyre quite intuitive so if you got the book or go through yt for those topics

[formal bronze]

Does anyone have a good video on how to count 1 over 2 plus 3 over 5? Stuff like that, I have issues and lose marks because of it 😭

[jovial sluice]

There are many different identities. But it's pretty straightforward when you catch it. Qutoient identies are a good place to start. You already know tangent is the oppsoite side of a right triangle divided by the adjacent side of a right triangle (sin/cos). An important thing to remember if you're doing proofs is to find how you can convert to sin and cosine

always looking to see where you can find sin and cosine in an expression will almost always help you simplify

[fiery crest]

Oh I don't know tan,sin or cos

[jovial sluice]

If you don't know tan, sin or cos then you will never understand trig identities. I would start there

[willow skiff]

It follows really easily from z* = re^(-i theta)

[stiff sluice]

Factor 215 − 1 = 32,767 into a product of two smaller positive integers

[chrome ether]

it's a large power minus 1, what factorizations do we know that can be useful here

[winter comet]

215 - 1 != 32767
i have no idea what thats tryna say

[willow skiff]

2^15 - 1

[winter comet]

o

[whole void]

u can use difference of cubes

[neon parcel]

can anyone tell me how do I start with precalc like what are the topics I should do

[terse pebble]

are you preparing for a course?

[neon parcel]

I want to understand few topics and it requires calculus, not enrolled in any course

[terse pebble]

well it depends on what you know already

but khan academy is a good start

[neon parcel]

just logarithms and functions a little

[winter comet]

what do you want to know

[neon parcel]

topics of pre calc

[winter comet]

you said you want to understand a few topics and it requires calculus...

but you wanna just learn all the topics of precalc first?

[neon parcel]

yeah

[winter comet]

ok

[winter comet]

khan academy has a list of the topics

[neon parcel]

got it ,thanks

[tulip marlin]

is there a law for taking the logarithm of a logarithm that simplifies it? ex log(log(log(x)))

[warm vector]

Lookup standard curriculum for ap precalc, it’ll set you in the right direction @neon parcel

[warm vector]

So logarithms are the inverse of exponential functions. So in essence you are just asking 10^y= x Then taking the y to do it again, 10^w = y, then again 10^z = w. So there really isn’t a law for nested logarithms, just having to solve it 3 times

[tulip marlin]

thanks!

[coral wagon]

Hi, could someone help me understand Taylor’s theorem, especially the Taylor polynomial, please?

[winter comet]

#calculus , what u tryna understand?

[coral wagon]

Actually, I have an exercise that says, knowing that 2<e<3 , estimate the value of e to within 0.001 using the Taylor polynomial of a suitable order n , centered at the origin, for the function f(x)=e^x. But honestly, I don’t understand how to use these approximations with the Taylor polynomial. And I also don’t understand how the limits come into play. In fact, I don’t understand anything about the Taylor polynomial. 😭

[coral wagon]

No one?😭

[frail grove]

hi, can someone please help me with complex numbers?

[whole void]

with what in particular

[frail grove]

i have a wuestion wich i m stuck in

Given the points in the complex plane: A(2; −3) et B(1; 1) et C(1; 2) determine the barycenter of {(A, 2); (B, -1); (C, 3)}

i m not sure how to solve it as i m still learning the complex

[fading monolith]

What do you mean by (A,2)?

[bitter vault]

when integrating, do i divide the whole equation by the highest power ? or do i divide each variable by it's respective power?

[winter comet]

respective

[bitter vault]

oh okay thanks

[buoyant trout]

Im stuck at (a)

can anyone help

[placid lotus]

What this question is pretty much asking in simpler terms is: When that function is flipped / rotate along y = x, under which y-values (since we are interchanging the x and y variables) would there be a function (passes vertical line test)

An easy way (which works most the case) would be the stationary point. So, at what x-value does the stationary point occur and this should be a

[inner topaz]

yep

you can switch the y and x on the graph and see if it still a function

and see how u can split it for it to be a function

[placid skiff]

khan academy is good

[sonic kayak]

Could I use trig sub on this?

[inner topaz]

def

sec should work

[winter comet]

how?

[remote furnace]

Is there any tips yall have I’m struggling with pre cal currently and it’s holding down my gpa a lot I currently have 2 more test to bring my grade up from a d- to maybe a c-

[hollow widget]

Do problems

Understand

[unkempt helm]

what year are you in

[remote furnace]

Wdym

[remote furnace]

Should I try to redo problems that were given in school n practice them?

[winter comet]

yeah

[sonic kayak]

Biggest thing about math is practicing. Think of it like a muscle, the more you use it the stronger it gets. Doing a bunch of practice problems will definitely help you in the long run. Just make sure you understand the problem too because thatll help you tackle future problems. Try not to look at your notes much unless necessary

[unkempt helm]

class? year? grade?

[daring tapir]

,w int sqrt(pi^(2x)-4)/pi^x

[obsidian monolith]

Results provided by WolframAlpha

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

Requested by enderdoesntmind

[daring tapir]

looks like 2/pi^x = sint should work

[sturdy hound]

Try going to your teacher for help right after class for more specific questions

[remote furnace]

11th grade

[unkempt helm]

you're doing precalc in 11th?

[remote furnace]

Thanks its just math gets confusing at times and I don’t try to understand it

[remote furnace]

Yeah why? Am I dumb or smth 😭

[unkempt helm]

nono

precalc usually starts in 9th grade here

[remote furnace]

Damnnn

[unkempt helm]

try doing tons of past papers

if you don't know the concept well

go over your subject syllabus/book

[remote furnace]

I moved states so I feel like I haven’t really gotten used to doing math the new way here

[unkempt helm]

what i mostly like to do is upload the chapter pdf to chatgpt and ask me to teach the concepts

[remote furnace]

I haven’t tried that yet

[unkempt helm]

and then i'll ask it to give me a series of questions that increase in difficulty

which helps you apply what you've learnt better

if you do hard questions directly you won't solve any

if you do simple questions only you can't do hard ones

use the 4o model chatgpt has

the other one is incorrect at times

should be fine for precalc though

that's all i have to say

[unkempt helm]

nws

america is weird

[remote furnace]

Yeah

Thx tho bro

[remote furnace]

@unkempt helm sorry for the ping man but should I start studying like next week since I wanna enjoy my break this week I still have break next weeks it’s just I wanna relax without any studying for these 3 days and lock in next week yk

[inner topaz]

yeah it is have done a year abroad in us

[formal bronze]

Can someone explain to me how we got 6 and 12?

It used the formula of (A + B) to the power of 3

But isn’t 3 to the power of 2 9? Or did we multiply it?

[winter comet]

(x+2)^3 = (x+2)(x+2)(x+2)
= (x+2)(x^2 + 2x + 2x + 4)
= (x+2)(x^2+4x+4)
= (x^3 + 4x^2 + 4x + 2x^2 + 8x + 8)
= (x^3 + 6x^2 + 12x + 8)

[winter comet]

2^0 for the first term, 2^1 for the second term, 2^2 for the third term, 2^3 for the fourth term

[winter comet]

if you're using binomial expansion

[formal bronze]

Isn’t it more simple than this ? It seems more complicated 😭

[winter comet]

thats just distribution...

[whole void]

what does "the new way" mean? and what r u doing currently in pre calc

[whole void]

i dont think thats recommended

[formal bronze]

It usually was just as quick as this without doing all that

[formal bronze]

Thank you

[whole void]

look up the binomial theorem if u r curious

[formal bronze]

.

[winter comet]

thats the wrong one but yea...

[formal bronze]

@winter comet I think I get it now thank you again, the lesson is about factoring 4 terms pretty much

[winter comet]

thats just derived from distributing XD

[formal bronze]

I don’t think so? The one my country uses is this exactly and it’s how it’s done

There are different ways different countries use I’m not too sure tho

[winter comet]

you'd use (a+b)^3 = a^3 + 3a^2 b + 3ab^2 + b^3 here

rather than the difference XD

but yea its the same

basically

i guess if you say b=-b then its the same sure

[winter comet]

🔥

[formal bronze]

Yes omg sorry I copied the wrong one I thought this was (a+b)^3 sorry, but thank you so much this helped me 🤍

[heady forum]

Hello every one

Just wanted to ask

I am an international student going to an American university next year if things go as planned

I was wondering. Are there any sources I can use to learn some advanced mathematical concepts given in the first years of college beforehand

And also to learn the translations of the mathematical concepts I already know in my mother language

[steel kernel]

How did he get the 0 exponent in (-2)⁰??

[winter comet]

1 sec

[winter comet]

from the expansion

[steel kernel]

I see

[whole void]

It’s the binomial theorem bruh

[sturdy hound]

Khan academy maybe

[unkempt helm]

why not

[uncut mulch]

chatgpt is unreliable when it comes to math

[waxen inlet]

its gotten a lot better at math tho

its able to solve competition math problems sometimes

but it still makes ocassional mistakes

[chrome trench]

Most of the time*

[waxen inlet]

no not really

ive asked it to solve difficult problems and it doesn't make a mistake 75-80% of the time

[whole void]

it messed up this simple problem

[uncut mulch]

the issue comes when you don't know something, you wouldn't be entirely sure whether its right

it sounds confident and may end up confusing you more

and ultimately you'd need to ask someone to confirm/explain anyway

[waxen inlet]

this is what im getting

[whole void]

i got 12

(from chatgpt)

[waxen inlet]

when did you try this

[whole void]

just a moment ago

[waxen inlet]

Huh

Maybe my ChatGPT is smarter than your ChatGPT

I’m not saying that ChatGPT is right 100% of the time, but it has gotten a lot better than where it was a year ago

[waxen inlet]

Or you can just look at its steps yourself

If you understand what it’s saying, you should be able to verify whether or not it did the calculation correctly

A lot of the times you have problems where you can’t think of the right way to solve it, but ChatGPT can give you a way that you might not have thought of

[waxen inlet]

Yeah true, if you don’t understand what it’s saying you’re outta luck

[whole void]

like this? (for reference phi(n) counts the number of integers from 1 to n relatively prime to n, its interesting)

and this is the best chatgpt does bruh..

[waxen inlet]

For more obscure stuff like the phi function (I didn’t even know what that was until now) it doesn’t do as well, probably because it was trained on less data involving it

[whole void]

no the phi function is actually not at all obscure

[waxen inlet]

Yeah, but it’s not super common like other functions

like log tan etc.

It can do elementary calculus pretty well

[winter comet]

seems pretty obscure to me... 💀

[whole void]

phi? no its not

[winter comet]

a phi function? where is it taught

[waxen inlet]

^the fact that you had to clarify what the function is shows that it’s not that common

[whole void]

i dont know why u care so much about where its taught, but its a kinda common number theory thing. its useful in cryptography, number theory, etc. theres even this random thing about it?

[whole void]

i mean its one of the first results on the wikipedia page for arithmetic functions

[winter comet]

ah ok its just not in an area i have studied 😂

i asked where its taught because if its not commonly taught then its obscure lol

[waxen inlet]

Yeah ChatGPT is unlikely to be well trained with such functions so it also flops more often on those kinds of questions

[whole void]

i think of something obscure as in not used. power towers are obscure in that regard, i think

[winter comet]

no i take back my statement that its obscure, i wouldn't know

it would be obscure to a precalc channel tho

🤣

[whole void]

thats not true. it did do pretty well for other questions about totient function

[whole void]

thats true but this is a separate discussion

[waxen inlet]

It can still get it right, but it’s more likely to get a question like the derivative of a basic trig function right than a question regarding the totient function

Anyways ChatGPT=not always reliable but significantly better than where it started

[whole void]

yeah derivative of a trig function is common knowledge though

[whole void]

what is this?

miserable

[hasty lily]

!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).

[hasty lily]

A bit late but

[whole void]

yeah we were just doing a test. I was pointing out the wrong answer it gave

[unkempt helm]

yes but generative models adapt to your learning style, and books dont

and also you get immediate feedback

not to mention it'll never run out

and unlike a book, it can make new questions that mix topics together

[chilly fern]

i have my winter pre calculus class coming up in a week, is there any way i can prepare myself to line myself up and get an A. Is there any Math i should try and sharpen up on so i dont get stuck

[waxen inlet]

Make sure to know your basic algebra very well (exponents and simplifying exponents, rational exponents and radicals, factoring quadratics and cubics, algebraic properties (distributive, cancelling out with numerator and denominator, etc)). People who master these typically do very well in precalc, while those that don’t struggle

[chilly fern]

Thank you! 🙏

I will sharpen up these

[topaz coral]

guys i want to know precalculus step by step

[stiff sluice]

Khan academy + Paul's online math notes + openstax + Stewart precalculus

[tough lake]

Wait who’s stewart

[willow skiff]

Textbook author

[ashen condor]

Chatgpt genuinely sucks at math

[fossil solstice]

Is skipping calc AB and going straight to BC too crazy or not

Nobody at my school does it

[winter comet]

i think its the best way to go, i dont see the point of AB lol

[tough lake]

Yeah I give it quesrions or ask him to generate questions for me with an integer answer or with an single expression as answer it gives me a question but it doesn’t end in integer or single expression and sometimes it forgets to use the laws of exponents and gaslights me into thinking that chatgpt is right I’m wrong and confused me with my mathematical knowledge

[waxen inlet]

Yeah, the only way to properly use ChatGPT for solving your problems is idea generation

It can give you the idea/method of how to solve the problem, and you take it away from there.

but sometimes it doesn’t even come up with the right idea

[tough lake]

So 2 to power 2/3 I need to times by 3 to make common denominator with other but I how can I get a number that when multiplied on bottom gives me 3 when multiplied on top gives me 2 making 3 2/3

Yup

[patent forum]

$$
\begin{itemize}
\item $a^n \cdot a^m = a^{n+m}$ (same base)
\item $a^n \cdot b^n = (a \cdot b)^n$ (same exponent)
\end{itemize}$$

[obsidian monolith]

harue
Compile Error! Click the reaction for more information.
(You may edit your message to recompile.)

[tough lake]

So 3 to make common denominator I have to find a number that when multiplied on bottom and with top gives me same as 2/3 which doesn’t exist

I’m saying this because I’ve been told the only way I can make common denominator is to find a number that multiplied on bottom and multiplied on top is same as the desired denominator

So I can make 3 1/1 to 3 2/3 without finding a same number that when multiplied on bottom is 3 and on top is two

[patent forum]

Basically a common denominator is two denominators that be divided evenly

[tough lake]

2 2/3 x 3 to make 6

Yes

Ohhhh

Ok got it

[patent forum]

I have an idea

Whenever you have to add fractions just cross multiply

And multiply the denominators together to get your new denominator

that's it

[tough lake]

👍👍

[tough lake]

This is a fast trick for adding fraction

Because instead of multiplying the number that will lead you to a common denominator with numerator and denominator, you multiply only the numerator of LHS with the denominator on RHS giving you the same effect as multiplying RHS denominator eith the LHS denominator and LHS numerator

[viscid thistle]

What’s a laplace transformation ?

[river drift]

the laplace transform of a function $f(t)$ is given by [ \mathcal{L}f(t) = \int_0^\infty e^{-st} f(t) \odif t ]

[obsidian monolith]

cloud

[river drift]

https://tutorial.math.lamar.edu/Classes/DE/LaplaceIntro.aspx

[viscid thistle]

Thanks

[burnt aspen]

I have 12 random points that any 3 of them are not in a line.
Is it possible to draw a circle which 3 points are on the circle, 4 points are in the circle, 5 points are out of the circle?

This is highly skillful problem.

[dusty gale]

l

[indigo solar]

anybody good with igcse maths?

[next vessel]

you still need help?

First of all if any 3 point are not in a line, it means you can draw circle at any 3 point of your choics

[valid mason]

Just ask the question and someone will get to you

[burnt aspen]

of course.

need help.

[noble solstice]

can someone teach me precalc?

or is it jus something to know?

[noble solstice]

someone help me check my answer for this equation i got 474.6667 and i wanna know if im right or not the equation is: 2+3^4 times 6 - 8/3 times 5

someone js check that for me and i cant check it on desmos or a calculator cuz it keeps saying error or like failed wtv

[winter comet]

following the order of operations yes

[noble solstice]

hooray

thank you

[winter comet]

obviously they rounded it btw

like the 6 in reality just keeps repeating

[noble solstice]

i asked my dad and he was like NAH so i js decided it would be better to ask you guys lol

[winter comet]

474 + 2/3

[noble solstice]

and yea same as pie its rational as we can see before it has another decimal expansion

[winter comet]

uh pi isn't rational

but yea

[noble solstice]

people say it is idk why but i js agree with my math teacher lmao

gotta learn somehow

[winter comet]

its not buh if they say that they wrong 😭

ig you gotta appease their wrongness sometimes but just know

just know fr

[winter comet]

i hate teachers like that

😂

[steel kernel]

How in the world can I determine if these 2 is a function

[river drift]

it's a function if each input is mapped to only one output

[steel kernel]

Why??

Owh nvm

[kind glade]

Do you guys have to graph to find out if a function is Removable jump or discontinuous

[winter comet]

not necesarily

[willow skiff]

<@&268886789983436800>

[lyric meadow]

don't do that

[whole void]

https://projecteuclid.org/journalArticle/Download?urlId=bams%2F1183510788

very likely too much for u (as it is for me at this point) but here’s a famous short proof

https://en.m.wikipedia.org/wiki/Proof_that_π_is_irrational

[noble solstice]

too laye bro i alr knew it was irrational

late*

[whole void]

yeah

[noble solstice]

they told me awhile ago

sorry

[whole void]

I mean if it was rational pi would probably fall out of use to some degree

[whole void]

(but that has an explanation)

[noble solstice]

they alr explained it?

idk what u dont get

[whole void]

but it’s transcendental so there’s no way

[whole void]

nah no one explained it before but it doesn’t matter too much

[noble solstice]

ur arguing with urself?

[whole void]

nah I’m just adding a comment on one thing I said

[noble solstice]

everyone told me and someone explained it prolly not texted but ina vc they did

[whole void]

probably not texted? like explained as in a proof? but ok anyway

[noble solstice]

he showed me?

idk what else i can really say

[whole void]

I don’t mean to berate but like what proof of it did he give? just curious
like an outline I’m just wondering

[noble solstice]

uhh why would i give u tha information?

sir are you with the FBI?

[whole void]

??? ok anyway

[noble solstice]

u js asked it weirdly

his name is content moderator in another server lmao

people told me then i went to another server recommended by these people and asked people and then i went to another and got an answer

but lets js leave it at that

[blazing pendant]

i am pretty sure it is impossible to distinguih between i, and -i, but how do i prove that

i mean it is possible to distinguish 1 and -1

because (-1)*(-1) =\= -1, but (1)*(1) = 1

[winter comet]

wdym by "distinguish between"

[blazing pendant]

any property of -i which i doesnt have, or viceversa

[winter comet]

mk

[blazing pendant]

Notice I didn't ask for a way to tell which is which

I am fine if you can give a property which provably, only one has

[winter comet]

maybe i = -i 🤯

💀

[blazing pendant]

That is the joke I hope to make

[urban cosmos]

i is i to the power 1 and adding 3 to it forever, and -i is i to the power 3 and its multiples

[whole void]

i is a root of x^2 + (1 - i)x - i, -i is not

[blazing pendant]

but

-i=(-i)^3

and

-i is a root of x^2 + (1 - (-i))x - (-i)

Also, i know for certain there is no polynomial method to check

as

as if (a+bi)^n = c + di (a,b,c,d are reals, and n is an integer) than (a+b(-i))^n = c + d(-i)

ig in p adic fields you could distinguish between i and -i, by simple taking remainder when divided by p, but my knowledge of p-adic stuff is only from pop math videos, which are probly not that informative

(p=1 mod 4)

is there anyway to do this for normal i ?

[fringe maple]

hey, question for yall -
im like midway semester 1 algebra II and really, really bored as of late. I was wondering if anybody had a list of specific concepts that need to be understood prior to precalculus study? thanks!

[acoustic spade]

I imagine you can find a syllabus for your school/exam board etc online

[urban cosmos]

check out Greene Math's Math Full Courses playlist on youtube

[stiff sluice]

can I get some help

[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/

[stiff sluice]

!dask

[twilit tangle]

what did you want help with?

[stiff sluice]

Rectangle $WXYZ$ is drawn on $\triangle ABC$, such that point $W$ lies on segment $AB$, point $X$ lies on segment $AC$, and points $Y$ and $Z$ lies on segment $BC$, as shown. If $m\angle BWZ=26^{\circ}$ and $m\angle CXY=64^{\circ}$, what is $m\angle BAC$, in degrees?

[obsidian monolith]

938c2cc0dcc05f2b68c4287040cfcf71

[viscid thistle]

@stiff sluice still need help with this?

[stiff sluice]

yeah

[viscid thistle]

What is the value of the blue angle?

[viscid thistle]

It's black so I can't remix on this

[stiff sluice]

180

[viscid thistle]

$\angle{AWB}= \angle{AWX} + \angle{XWZ} + \angle{BWZ}$

[viscid thistle]

We know the values of angle AWB , angle XWZ and angle BWZ

[stiff sluice]

right

AWB is not 180?

BWZ is 26

XWZ = 90

180=awx+90+26

180-90-26=awx

,calc 180-90-26

[obsidian monolith]

Result:

64

[stiff sluice]

awx = 64

[viscid thistle]

It is 180

[viscid thistle]

Yeah

Same process for the other side

Except instead of 26 you have 64

You got the triangle question asked in the help channel?

[stiff sluice]

axc = axw + wxy + cxy

[viscid thistle]

Not xwy

Wxy

[stiff sluice]

180=axw + 90 + 64