help-23

[whole hill]

Therefore, you must specify direction of travel

Btw, did you see the vid I sent you?

[crude vale]

my butt has a curve

-x^2

[worldly lantern]

huh, no

[whole hill]

But it’s in 3 dimensions. It’s a surface

Not a curve

[crude vale]

oh

[whole hill]

Unless we’re only looking at a specific plane

[worldly lantern]

mine has e^{-z^2}

[crude vale]

well in 2d its a curve

[whole hill]

It is in 2D if you specify the plane we’re in.

XY, XZ, YZ

[whole hill]

Sent it to you because of the “bot enthusiast” role

[worldly lantern]

lmao, the bot enthusiast refers to bots in discord

[whole hill]

Well shit…

[worldly lantern]

its cool tho

[safe radish]

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[white dragon]

i need help with ts vietnamese math c) and d)

[safe radish]

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[gaunt belfry]

Translation not accurate

[vague phoenix]

Vẽ ra

[gaunt belfry]

It would be better if you can post the problem here using the tex bot, unless someone here knows Vietnamese

[white dragon]

🥀

[vague phoenix]

Ko vẽ ko giúp

[white dragon]

p c) lm dc r

con d) th

[vague phoenix]

C/m H trực tâm thử xem

[white dragon]

de bai cho san r

[vague phoenix]

Xét 3 đường tròn c0 đk BC , c1 đk AH và c2 ngoại tiếp abc thì xem trục đẳng phương?

[white dragon]

em ms lop 9 😭

[vague phoenix]

Adu

<@&268886789983436800> nsfw

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[smoky sandal]

.for c you can try proving points AMN and lets say altitude drawn fromA to ** **BC is at G so AMNG are concyclic

[mint jewel]

Just a small and a dumb question. How should I mark inverse cos, sin or tan on my paper. Just wondering because my books dont include it.

[wild cape]

the two most popular ways to write inverse sin are $\sin\inv$ and $\arcsin$

[flat frigate]

ロケット・ジャンプ

[rich gazelle]

Sine: $\sin^{-1}(x)$Cosine: $\cos^{-1}(x)$Tangent: $\tan^{-1}(x)$

[flat frigate]

Ga³¹Br³⁵I⁵³9000✞

[rich gazelle]

Or arc. Like it Sine: $\arcsin(x)$Cosine: $\arccos(x)$Tangent: $\arctan(x)$

[flat frigate]

Ga³¹Br³⁵I⁵³9000✞

[mint jewel]

ight

thanks

[wild cape]

np

[rich gazelle]

Do you have more questions.

[mint jewel]

no more

[rich gazelle]

You are welcome!

[rich gazelle]

Have a nice day! You can close typing .close.

[mint jewel]

.close

[oak pumice]

If you're going with $sin^{-1}$ make sure you don't write $sin(x)^{-1}$

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[flat frigate]

darky

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[strong nexus]

Given $2r_{k - 1} = z_kp + r_k$ with $r_0 = 1$ and $0 \leq r_k < p$, I want to prove that $r_n = r_0 = 1$. Any ideas? $p$ is a prime $> 2$ and so $p \mid 2^n - 1$ for some $n$, and $z_i \in {0, 1}$.

[flat frigate]

ILikeMathematics

[safe radish]

@strong nexus Has your question been resolved?

[slate current]

Write it all mod p

[safe radish]

@strong nexus Has your question been resolved?

[strong nexus]

Whydoes that help?

[slate current]

Well r_k is in [0,p-1] so if you determine it mod p you can determine it completely

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@strong nexus Has your question been resolved?

[hidden depot]

is ts true

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[late bobcat]

I am stuck i need to find the domain of this function

[quiet plume]

Well now you have two restrictions.
I take it you’re having difficulty more specifically expressing t^2<3 as an interval?

[late bobcat]

Yeah

[late bobcat]

I don’t know what to do next

@quiet plume

[quiet plume]

Well the quick way to do it is $t^2<3 \iff \abs{t}< \sqrt{3}$

[flat frigate]

Azyrashacorki

[quiet plume]

But if you want a more complete approach you may want to consider $t^2-3<0$ and see it as a parabola, from which you write a sign table using the roots.

[flat frigate]

Azyrashacorki

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@late bobcat Has your question been resolved?

[open wedge]

also there's a mistake here

$9 > t^2$ does not lead to $t^2 < 3$

[flat frigate]

1 divided by 0 equals Infinity

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[faint glade]

Where am I going wrong here?

[primal gazelle]

2 * 34 is not equal to 64

[faint glade]

ugh, I'm rushing

thank you

.close

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[deft gust]

i need someone to explain how you do this

[lethal shoal]

first u should use $$\tan(\pi+x)=\tan(x)$$

try using that and see what u end up with

[flat frigate]

notyalc

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[thin glade]

I am confused as to why the x restrictions are 0 to 1.5 as the question states that the width must fit into a 1m wide space, which would be x<1 ?

[quick crater]

looks correct, but im gonna guess that x<=1.5 is only based on the fact that h=3-2x

[thin glade]

yes

my question is though

how is that possible if it says that the window can only fit into a space 1m wicd?

1m wide*

[left gyro]

maybe look later on for it saying that x has to be < 1

for now, it could be doing 0 < x < 1.5 just because h must be positive

"x < 1.5 because h > 0"
then later on
"also x < 1 because the problem requires it"

[thin glade]

Oh i think i get what your saying because in the key it says,

but I dont get where it got the x and h value from?

[left gyro]

thats no good

I think it completely forgot about the x < 1 requirement

Im gonna go check this

can you show the entire key

[thin glade]

I just dont understand how it occurs when x =0.96 when the Area occurs when x is 1.04

as shown beforehand

[left gyro]

maybe youre better off not reading the bottom half

itd only make sense if you change out the 1.04 for 0.96, then remove the x < 1 requirement

Let A'(x) = 0 => x is about 0.96
A(0) = 0
A(max x) is about 1.44
A(1) is about 1.43
then max area is about 1.44 cm^2 when x is about 0.96 cm and h is about 1.09 cm

I used 3 decimal places here since A(max x) and A(1) would both round to 1.43

nvm

[thin bridge]

values they have are all off

[thin glade]

would we also ignore the 0<x<1.5 restriction?

[thin glade]

Nelson moment am i right

[left gyro]

its still required, the solution doesnt ignore that, you shouldnt either

Im saying they ignored the x < 1 requirement and wrote 1.04 instead of 0.96

[thin glade]

so is the 0<x<1.5 a physical constraint and the x<= 1 a like contextual constraint?

[left gyro]

Id say they solved it wrong still

they are both required constraints, leaving out one of them would trip you up in most cases

[thin glade]

bruh

so the solution is just messed up

[left gyro]

yea

[thin glade]

ugh

alright well thank you guys

[left gyro]

np

[thin glade]

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[cyan hazel]

Ik its easy but if the chances are 16/33

[cyan hazel]

Whats the porcentage

[formal grail]

you can do that with a calculator

[vague phoenix]

mult 100 if find percentage

[cyan hazel]

Ik but i cant use it rn

[formal grail]

you can use discord so why not a calculator

anyway it's probably like 47. something since it's just under half of 33

[cyan hazel]

Ty

[formal grail]

48.48 repeating %

[vague phoenix]

fact

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[cyan hazel]

.close

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[clever meteor]

for calc for u substitution

how would i get du from this

apparently its this but i dont get it..

[frosty oar]

differentiate tan theta to get sec²theta

differentiate sec theta to get tantheta×sectheta

take the sec theta common outside

[clever meteor]

oh thanks

.close

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[livid salmon]

For this video https://www.youtube.com/watch?v=7gigNsz4Oe8 ((1:47:36) Integration Using Trig Substitution),
It only gave me one example from Wolfram Alpha, without giving additional.

In Calc 2, are we expected to understand how to use these methods or is it something that she just wanted us to know of? Since I followed her Calc 1 video and everything important was quite comprehensive, and something as difficult as this would definintely have more definitions and examples

[rich gazelle]

Yes, you are supposed to use it. Do you have specific question about Calculus 2? Or a example that you want to do with help?

[livid salmon]

Well I find it quite weird that it just suddenly jumped to that topic without additional examples, so I could use some extra examples

[median vigil]

well you could search youtube for dedicated videos on the topic

or check your textbook, paul's online math notes, etc

[rich gazelle]

Yes, in youtube you can see good explanation and examples.

[median vigil]

i would not expect to fully grasp any given topic from calculus from a video that attempts to cover all of it

[livid salmon]

Umm I'm just a grade 9 student who is interested in Calculus and I currently do not have a textbook for this topic. Would you say Stewart's Calculus would be the best textbook that covers all of Calculus?

[median vigil]

it's a fairly standard book, i think it would work fine for that

[livid salmon]

Alright thanks

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[rich gazelle]

It’s good for you.

[rich gazelle]

You are welcome, have a nice day!

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[twin prawn]

can we press y as y(x) as well?

or do we have to apply implicit differentiation

wait fuck

.close

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[rich gazelle]

Yes, you can.

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[twin prawn]

what would be the labeling of this if i type in the final answer?

cm^2 per... ??

[rich gazelle]

Right!

[twin prawn]

per what tho

wait now that i think about it

[rich gazelle]

Think.

[twin prawn]

yeah its in cm only

the average rate of change is ... cm

[rich gazelle]

They don't flip since you're not measuring a length, you're measuring how much area you gain per unit of side.

[twin prawn]

so cm^2 per cm side

[rich gazelle]

Right!

[twin prawn]

right as in im correct or wrong LOL 😭

[rich gazelle]

Correct.

🙂

[twin prawn]

okii thanks

[rich gazelle]

Have a nice day!

!done

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[twin prawn]

.close

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[desert pasture]

I want to periform lagrange interpolation here

[desert pasture]

Unsure of how it'd work for degree 1

for degree 2 I'll select points 2,3.5,4

[rugged bluff]

least sq

[desert pasture]

Mhm, but I think I need to use lagrange here

[rugged bluff]

sorry i just saw "interpolating"
i would pick 2, 3.5

[desert pasture]

hmm, but lagrange would give a quadratic

Lemme see

[rugged bluff]

2 points shld give you a degree 1 polynomial...

[desert pasture]

right, I messed up the formula

oops

[desert pasture]

thanks

[desert pasture]

I read that as 2,3.5, 5 sorry

😭

[rugged bluff]

😭

[desert pasture]

tq

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[lavish magnet]

I have a request, can someone open this video https://www.youtube.com/watch?v=vMyKYhi6XDk skip to 10:44 and explain to me why he wrote 46cm as 0.46 please.

[brave wolf]

he used meters as his units instead of centimeters

meters are the standard unit for distance in physics, so before doing any calculations, its a good practice to convert to them

in this specific case, it wouldnt really matter, if you put everything in centimeters (so both the 46cm and 14cm). But generally, it's better to convert to the standard units

if you subbed it in cm, you'd just get
(50 * 46) / 14 instead of (50 * 0.46) / 0.14

and thats the same thing, because the extra factor of 100 cancels out

[lavish magnet]

You're right I get the same answer for both

Thank you so much for that explanation it covered all the doubts I had.

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[barren timber]

Why is the angle at Y 90-alpha 🙏🏻😭

[barren timber]

The lines are parallel - AX and the line from Y

[quiet plume]

Since they're parallel alpha is there as well

[silent peak]

yea

[rich gazelle]

It's because they are parallel, do you understand it better now?

[barren timber]

No 😭

I just cant see the parallel line angle rules coming into play

[silent peak]

construct a line parallel to XC

[barren timber]

Okay

[silent peak]

then that angle (90-a) will be an angle and a will be an angle

bcz it will be 90 as they are parallel , hence the Y will be 90-a

i might've said it in a confusing way

[granite gulch]

Hi guyz

New here

[silent peak]

me 2 bro

[granite gulch]

Plz tell me which question u discussing

[barren timber]

Why cant i understand this , ts too simple to be confsue ab sorry💀

[silent peak]

? you got it?

[rich gazelle]

#help-23 message

[granite gulch]

Whats the question. ?

[rich gazelle]

Don't worry.

[vague phoenix]

Check the pins

[barren timber]

No, do u mind referring to the angles with letters like angle at Y or smth , im finding it difficult to deduce which angles ur referring to

[silent peak]

oh ok

yk coresspondence?

[barren timber]

Yea

[spare tundra]

Hello

Why is a^2+b^2 = a+b

[silent peak]

the angle Y at the construction will be 90degree by that coresspondence

[barren timber]

U need to go into the unoccupied/ available area to ask a new q

[rich gazelle]

!occupied

[safe radish]

Someone else is already using this help channel. If you need help with a question, please open your own help channel/thread (see #❓how-to-get-help for instructions).

[vague phoenix]

Wrong btw

[silent peak]

not really , it works for a nd b =1

doesnt it??

[barren timber]

Yea but how does that lead to 90-alpha

[silent peak]

ok now you see that line bisecting Y

you consider the left portion to be a

so the right one will be 90-a

[barren timber]

Why do u consider it to be a

OHH NBM

I SEE ITT

[silent peak]

idk bcz you said 90-a

you can take any vairable

[barren timber]

Thanks guys 😁

[silent peak]

DW

[vague phoenix]

@barren timber

[silent peak]

i am new here btw so i felt happy helping

what did bro do here?

[vague phoenix]

Therefore the angle is 90-alpha

[silent peak]

umm bro is my approach incorrect?

[barren timber]

YEAA thanks! Idk why it took me so long to make that link

[vague phoenix]

No worries

[barren timber]

It’s just alternate angles 😭

Thanks!!

[vague phoenix]

Yw

[silent peak]

@vague phoenix is my approach incorrect btw?

[vague phoenix]

!done btw

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[barren timber]

.close

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[vague phoenix]

I dont understand your approach but maybe

[silent peak]

idk constructin a line parallel and then considerin a portion to be a the rest will be 90-a therefore

bruh no reply

[vague phoenix]

Thats correct

[silent peak]

ohk THANKS

[vague phoenix]

Np bro

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[spare tundra]

how to delete wolfram from my computer and download maple

[stoic torrent]

#discussion #math-discussion

[rich gazelle]

!redir

[safe radish]

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

[primal bone]

https://klipy.com/gifs/google-23

-# Like, this is searchable

-# Reminds me of "old people facebook" posts where.. well, old people just post "Google" as a Facebook post because they don't know how to search for something

[plucky elk]

Can you stop shit posting in help channels

[safe radish]

@spare tundra Has your question been resolved?

[safe radish]

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[slim lion]

why are you only evaluating theta

instead of -100cos(theta)

unless im misinterpreting the question, the growth should be the difference

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[bitter monolith]

anyone with experience in manifold theory or mechanistic interpretability who can help me read some pca graphs of neuron activations?

[bitter monolith]

ex something like this

i kind of understand how GeLU is shaping the embedding space but im having trouble visualizing it for the addition task this model was trained on

[plucky elk]

Try uhh #probability-statistics or #advanced-stats

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[kind basin]

Someone help 🥲

[rich gazelle]

What have you tried?

[kind basin]

Uh....I got stuck at trying g but my answer for f is -15.

Which I don't think is correct

[rich gazelle]

Ok, you need to do the same in g.

With -3.

[kind basin]

Ok I'll try first

[rich gazelle]

[thin bridge]

how are you getting -15

[rich gazelle]

Can you show your steps to get -15?

[kind basin]

I can't 🥲 I throw the page away cuz I was frustrated

[rich gazelle]

Ok, you only need to substitute the x value with the -2 and then evaluate.

[kind basin]

Thank you, I'll try.

Like this?

[safe radish]

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[pale bone]

how would i find this

[worldly lantern]

can you use inverse trig

[dull sequoia]

Draw a picture

[pale bone]

guys like in generally

idk how to do this

🙂

[dull sequoia]

Draw a picture

Sine is what over what

[pale bone]

opposite over adjacent

[dull sequoia]

Nuh uh

[worldly lantern]

you have to atleast know values of tan for that to work

youve gotta remember common values of sine in the 1st quadrant and then you extend that to a general solution...

i cant explain much here because idk how to tbh

[pale bone]

wat

[open wedge]

SOH CAH TOA

🥀

anyways you need to understand basic trig and the unit circle

[pale bone]

i doo

[open wedge]

yk what a unit circle is?

[pale bone]

yess

[open wedge]

yep, $x$ coordinate is $\cos \theta$ and $y$ coordinate is $\sin \theta$

[flat frigate]

1 divided by 0 equals Infinity

[open wedge]

i think you know that right?

[pale bone]

yes

(cos theta, sintheta)

[open wedge]

so try 1)

you see $\sin \theta$ is positive

[flat frigate]

1 divided by 0 equals Infinity

[open wedge]

that means that your $y$ is positive

[flat frigate]

1 divided by 0 equals Infinity

[pale bone]

yes

[open wedge]

so look at this diagram, it can only in the 2 top quadrants

correct?

[pale bone]

yes

[open wedge]

so the top-right quadrant

it's just some right triangle identities

and the top left quadrant

i'd love to think of it as how geometry works

[pale bone]

Ye but how does that realte

to sine

1/2

.close

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[crisp breach]

x^2+y^2=18...max value of x-y

[crisp breach]

I asked the same question yesterday but x+y

[quick crater]

mm is there any topic here?

like calculus? competition? ect

[crisp breach]

No

How do i start?

[quick crater]

mmm for calculus i think it was like lagrangian multipliers or aomething? i dont know either

but anothwr way would be to square x-y

[crisp breach]

No no

x^2+y^2-2xy

[quick crater]

yeah, it would be equivalent to maximizing this

[crisp breach]

Thanks

.close

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[daring sonnet]

For c I tried applying chain rule

But I suppose rate of change of gradient just mean d^2y/dx^2?

[main mural]

c as in part c or mx+c?

cus you only sent parts a) and b)

[daring sonnet]

Part c

[main mural]

send it

[daring sonnet]

Ohh

No part b

[main mural]

yup

no t is involved here

[stoic torrent]

The question simply means to ask you the rate of change of gradient, aka of the first derivative right?

Well now that you think about it, to calculate rate of change of some quantity, which operation do we use??

[daring sonnet]

Differentiation!

[stoic torrent]

Good!

Now what do you see what we have to do here?

We simply need to differentiate dy/dx (gradient) wrt x to get rate of change of gradient right?

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@daring sonnet Has your question been resolved?

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[lost jewel]

<@&268886789983436800>

[safe radish]

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[vague phoenix]

This guy name is weird also

[open wedge]

frfr

[open wedge]

you wanna code smth on java?

[vague phoenix]

Next semester gang

[open wedge]

im coding tiến lên miền nam in cpp

[vague phoenix]

I am making drawing tools on haskell

Vip

[open wedge]

oh you can make THAT?

especially in haskell?

that's goated

[vague phoenix]

Yeah

Dm i show

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[open wedge]

<@&268886789983436800>

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[agile umbra]

Can someone help with the b question?

[agile umbra]

What to do when theres 3 curves

[brave wolf]

draw it

[agile umbra]

I put it on my calculator but it wont let me put just x without the f(x)

[brave wolf]

x = -pi is just a vertical line (at x = -pi)

[agile umbra]

Yeah

[agile umbra]

How do i do the integration for the area calculation?

When theres 3

Do i just minus them all

[brave wolf]

nope

[brave wolf]

this is really just an area between two curves

with certain bounds on x

[agile umbra]

Yeah

Wait let me count the limits

Guys

How to put just x on the calculator

🥹

[brave wolf]

the x = -pi?

[agile umbra]

Yeah

It wont let me put it without y

[brave wolf]

why do you need to put it to your calculator

[agile umbra]

To get intersection points

WAIT

I got it

[brave wolf]

it's just x = -pi

[agile umbra]

Just one sec

The limits are 1.571 and -3.142

[brave wolf]

or just -pi and pi/2

[agile umbra]

Aa

So how do i calculate

[brave wolf]

well now you need to set up your integral

[brave wolf]

this region is just region between 2 curves (with certain x bounds you just computed)

what are the 2 curves

[agile umbra]

The cosx and x-π/2

So do i only minus them?

[brave wolf]

yep

[agile umbra]

Do i need to do anything with the -π?

Or does it just funvtion as a limit

[brave wolf]

the x = -pi really only serves as an x bound

[brave wolf]

yeah

it does just that

[agile umbra]

Oh oke

Thank you!!!

.close

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[naive wyvern]

Can I ask about smth I don’t understand

[naive wyvern]

What is this thing genuinely what

[rich gazelle]

Ofc, state your questions and what ideas you have.

[dull sequoia]

That looks like f is a rational function

[naive wyvern]

I don’t understand anything

[still charm]

This is called a Pade approximant

[dull sequoia]

A quotient between two polynomials

[frank widget]

man everyday this server gives me new names bruh 😭

[still charm]

It's like a taylor series but with a rational function instead of a polynomial

[dull sequoia]

Looks like this requires b₀ = 1?

[naive wyvern]

But what this this function look like or isn’t there a specific look

[still charm]

Whoops mb you're right

[dull sequoia]

I mean it’s just a thing you can write down, unless you give some more context on where you found it there isn’t much to it

[naive wyvern]

I have like homework but I’m trying to understand what this thing is
I can send a question

[dull sequoia]

Yeah giving context usually helps

[naive wyvern]

Wait it’s just polynomial divided by a polynomial I don’t understand

[dull sequoia]

Yes it is

[frank widget]

yo send a question so we get the context in which u asking

[dull sequoia]

It’s like you’ve sent a polynomial and said I don’t get it

There’s nothing to get

[naive wyvern]

Yeah cuz I don’t understood what that function is

Understand

[frank widget]

f(x) is ratio of 2 polynomial what doubt u got in that?

[dull sequoia]

Well it’s called a rational function

But beyond that not much can really be said

[naive wyvern]

$f(x) = \frac{x^2 + 3x - 4}{x^2 - 5x}$

[flat frigate]

ℳ

[naive wyvern]

What’s the domain

But don’t say the answer please can u explain what to do

[frank widget]

look

domain is all value of x such that function is defined/finite

now at what x is function not satisfying that criteria?

[naive wyvern]

Can’t be 0 right? Can’t divide by 0

[frank widget]

yes and?

[naive wyvern]

I have no idea

[frank widget]

so 0 and 5 is where f(x) is not finite

[naive wyvern]

But why 5

[frank widget]

so domain is all real value except 0 and 5

x(x-5) is denominator

[naive wyvern]

Wait that’s how I’m supposed to do it?

[frank widget]

at both 0 and 5 , denominator is 0, making function undefined

yeah

[naive wyvern]

Put it in likw ()

Ohhh I got it tysm

[frank widget]

there is just one problem

wait

[naive wyvern]

What

[frank widget]

see, if numerator and denominator both become 0, then u have to use limits

[naive wyvern]

Why

[frank widget]

see, 0/0 is any number, so u have to verify by limits whether both sides give same answer or not, if not that point isnt in domain, and if it does it is in domain

[dull sequoia]

It’s still not in the domain regardless

[naive wyvern]

So can u do Quadratic Formula?

[dull sequoia]

You only care about this if you want to find the limit to that point

[frank widget]

wait rly?

[dull sequoia]

Of course, you can’t divide by 0

The rational function (x-5)/(x-5) is equal to 1 everywhere but isn’t defined at x = 5

[frank widget]

dang i thought for 0/0 case u have to use limits to verify domain

[dull sequoia]

No you still can’t divide by 0

[frank widget]

ig u are right

[dull sequoia]

Yes

If the denominator is a quadratic then the quadratic formula will give you its roots

[naive wyvern]

Oh wait so it’s alr
I can do the () thing or Quadratic Formula? No other way to find it?

[dull sequoia]

Any method you like for finding roots of quadratic will work

We just care about finding the roots

[naive wyvern]

Ohh and one of the roots is always a zero?

What if it’s like x+1

Oh wait

[dull sequoia]

Where did anyone say it’s always zero

[naive wyvern]

Yeah I’m asking

That’s the point of the question mark

[dull sequoia]

The roots is when the denominator is 0, not when x is zero

There’s a zero root if b₀ = 0, can you see why?

[naive wyvern]

Wait what u confused me

[dull sequoia]

A “root” of a polynomial p(x) is a number “a” where p(a) = 0

[naive wyvern]

Oh yeah

[dull sequoia]

It is not always p(0)

[naive wyvern]

When do u know it is for sure

[dull sequoia]

But 0 can be a root of p, this happens when p has no constant (b₀ = 0), can you see why this is the case?

[naive wyvern]

Nope

That’s the first question btw 🫩
I’m cooked on this

[dull sequoia]

What is a polynomial with constant term 0? Write it out

[naive wyvern]

Zero?

[dull sequoia]

What is a polynomial

[naive wyvern]

I don’t know

No like I know but I don’t know how to explain that

[dull sequoia]

Try your best to explain it

[naive wyvern]

It’s like

Idk

There’s X

a

And n

[dull sequoia]

I’ll say that’s a pretty poor explanation

[naive wyvern]

Yes I know

[dull sequoia]

You should revise what a polynomial is

[naive wyvern]

I know what it is I don’t know how to explain in English

[dull sequoia]

Come back to this question after you figure out what a polynomial is

Ah I see

You should still be able to write out the general form of a polynomial

[naive wyvern]

I’m worse in English than in math so uh not really

[dull sequoia]

You seem to be able to recognise a polynomial

[naive wyvern]

Yes cuz I know what it is

[dull sequoia]

So as I said, if on the bottom, b₀ = 0

What does that mean for the roots for the bottom?

[naive wyvern]

They’re zero?

[dull sequoia]

One of the roots will be 0

Because every term has an x so you can factorise an x out

[naive wyvern]

Ohhh righttt

[dull sequoia]

They won’t all be zero, only one of the roots is zero

[dull sequoia]

Hence this comment

[naive wyvern]

Oh I think I understand that part

Not the function thing tho

[dull sequoia]

Is the question about the domain of f?

Because initially you just wrote f and there wasn’t a question

[naive wyvern]

Wdym

I’m asking about the domain

[dull sequoia]

The domain of f is everywhere except when the denominator is 0

Do you agree?

[naive wyvern]

If b0=0 so when you put x = 0 the whole expression becomes 0 which means x = 0 is a root?

[naive wyvern]

Yes

[dull sequoia]

For the denominator yes

[naive wyvern]

Ohhh I get it

[dull sequoia]

So the only “missing points” from the domain will be the roots of the polynomial in the denominator

Does that make sense

[naive wyvern]

Now for the domain
Is there a specific way/s to find it

[naive wyvern]

Yess

For example this

[dull sequoia]

No, solving for the roots of polynomials is a hard task

In general there are no fast ways to do it

[naive wyvern]

$f(x) = \frac{x^4 - 5x^3 + 6x^2 + 4x - 8}{(x-1)(x+2)(x-3)(x+4)(x-5)(x+6)(x-7)(x+8)}
$

$f(x) = \frac{x^4 - 5x^3 + 6x^2 + 4x - 8}{(x-1)(x+2)(x-3)(x+4)(x-5)(x+6)(x-7)(x+8)}$

[flat frigate]

ℳ

[dull sequoia]

Can you inspect what the roots of the polynomial in the denominator are?

[naive wyvern]

I mean domain for the function if you understand what I mean

[naive wyvern]

No

[dull sequoia]

Yes, solving for the domain is the same as solving for the roots of the denominator

Which, in general is impossible to do

[naive wyvern]

Ohh mb

[dull sequoia]

You can’t tell me what are the roots of the denominator?

[naive wyvern]

U can find the domain of the function? So why do I need to do that in my hw 💔💔

[naive wyvern]

Not really

[dull sequoia]

What are the roots of the quadratic (x-3)(x+2)

[naive wyvern]

3 and -2? I don’t know

Wait that’s right?

[ocean wadi]

Do you know what a root is?

[ocean wadi]

Ya

[dull sequoia]

How did you find that

[naive wyvern]

Damn I didn’t even use calc for this

I remember my teacher showed smth like that

It needs to be a zero right

So if u multiply smth and it equals to a zero so one of them has to be a zero so it’s either-2+2 or 3-3? I think

[dull sequoia]

If you look at (x-3)

When will this be 0

[naive wyvern]

If x = 3

[dull sequoia]

Why

[naive wyvern]

Isn’t 3-3 =0? Or -3

[dull sequoia]

You should be more certain

You’re right

If you put -3 you’d get -3-3 = -6 that is not 0

[naive wyvern]

No I meant 3-3 is -3

[ocean wadi]

Is it?

[naive wyvern]

I don’t know

[dull sequoia]

This is basic arithmetic

3-3?

[naive wyvern]

So 0

[dull sequoia]

Then why did you say it’s -3

[naive wyvern]

I forgot basic I can’t do 2*1 w/o calc I’m not even joking

[ocean wadi]

[naive wyvern]

Actually I can do that that’s 2

Wait now fr so 3-3 is 0

[dull sequoia]

You should practice your arithmetic

[naive wyvern]

And -2+2 is 0

[dull sequoia]

Yes

[naive wyvern]

Yeah I should

[dull sequoia]

So that’s why those are the roots

[naive wyvern]

Okay so I got that

Now what

[dull sequoia]

Now, if I had (x-3)(x+2), and x = 3 (the root of the first bracket)

Then the first bracket is 0 yeah?

[naive wyvern]

Yes

[dull sequoia]

So I have 0 * something

Which is just zero

[naive wyvern]

Wait I see what you did here

So only one root is 0

[dull sequoia]

So whenever I have a product of brackets, if one of the brackets is zero, the entire thing is 0

[dull sequoia]

No!!

[naive wyvern]

OHHHHHHHHH

[naive wyvern]

WAIT WHY

You said ittt

[dull sequoia]

The root is these numbers

[ocean wadi]

They are explaining why it's a root

[dull sequoia]

The roots make it zero, the roots aren’t themselves zero

[naive wyvern]

I’m so confused

What are you explaining here

[dull sequoia]

You’re saying look at x = 0 for (x-3)(x+2)

[ocean wadi]

The root occurs when y = 0 or f(x) = 0 if it helps you visualise

[dull sequoia]

You’re saying that x = 0 is a root here

It is not

[dull sequoia]

That’s what you said here

[naive wyvern]

No and I hate this function I failed that exam w 52

You’re making me more confused

[ocean wadi]

Sorry

[naive wyvern]

Oh so what

What am I supposed to do

[dull sequoia]

YOU said one of the roots is 0

[naive wyvern]

Oh yes me

[dull sequoia]

Right here, you said this

This is WRONG

the roots is not 0

The roots MAKE it 0

[naive wyvern]

Yes so they’re 2 and 3

[dull sequoia]

(It being the brackets)

[naive wyvern]

Then what

[ocean wadi]

|| say y=(x-3)(x+2) What numbers make it so that y=0, in other words (x-3)(x+2)=0 ||

[dull sequoia]

-2 and 3

[naive wyvern]

Oh ok ok

[dull sequoia]

So you found what makes the entire thing 0, by looking at the roots of each bracket

[dull sequoia]

It works because of this

[ocean wadi]

Yes

[naive wyvern]

Ohh okay

[ocean wadi]

What is 100 times zero

[dull sequoia]

Now look at this problem and figure out what makes the bottom zero?

[naive wyvern]

Hum

[dull sequoia]

Or in other words, what are the roots of the polynomial in the denominator?

[naive wyvern]

It’s like zero a hundred times right

So zero

[dull sequoia]

The other guy really isn’t helping here ngl

[naive wyvern]

Zero

[dull sequoia]

No that’s what the roots do

[naive wyvern]

Nothing can help me btw

[dull sequoia]

But what are the numbers

What are the roots

[naive wyvern]

-2

3

[dull sequoia]

For your problem not for the one I made up

[naive wyvern]

But -2+3 is no zero

[naive wyvern]

Ohhh

But there’s a lot of numbers

[dull sequoia]

Then there’s a lot of roots

[naive wyvern]

There’s only 2 roots no?

[dull sequoia]

Nothing wrong with that

[dull sequoia]

Nope

[naive wyvern]

Oh it’s possible? I thought only 2

Okay wait I will tell you all the roots

1

[dull sequoia]

Only 2 for quadratic

[naive wyvern]

-2

3

4

5

What

Ohhh

-4

-6

7

-8?

Wait so if I have like (x-5) so the x is just the 5 but with the opposite thing like if it’s -5 x is +5?

[dull sequoia]

yes

that's exactly right

[naive wyvern]

Wait I got it now omg

[dull sequoia]

so the domain of f is all real numbers

EXCEPT

everything you just listed

[naive wyvern]

OHH

[dull sequoia]

so R \ {1, -2, 3, -4, 5, -6, 7, -8}

[naive wyvern]

So they’re trying to trick me because it’s a lot of numbers

[dull sequoia]

i guess so yeah

[naive wyvern]

I get it nowww

[dull sequoia]

they're not realy trying to trick you

they want to show you it doesn't matter how many are on the bottom

[naive wyvern]

Omg

[dull sequoia]

you just take them all out

[naive wyvern]

Yes but why so many

[dull sequoia]

if there's 2 or if there's 300 of them

[naive wyvern]

How is this even gonna help me in the future

[dull sequoia]

to get rid of your misconception that there can only be 2 roots

[dull sequoia]

it teaches you to think critically and be precise

the point isn't to learn all this maths

[naive wyvern]

Ohh I see but without you I couldn’t understand it

[dull sequoia]

the point is to build and train your style of thinking to be one of problem solving and breaking problems down into smaller digestable bits

[naive wyvern]

[dull sequoia]

do you see how we had to break it down into the brackets thing

[naive wyvern]

Yess

[dull sequoia]

and we could understand how that worked for quadratics

and then we can extend that thinking into many brackets

this is the style of thinking they want to teach you

[naive wyvern]

If I’m gonna pass my exam I won’t forget you

[dull sequoia]

they are just doing it through maths

[naive wyvern]

Nice but they’re kinda hurting my brain

[dull sequoia]

yeah maths is hard, very unnatural for humans to do

[naive wyvern]

I will write frosst on my exam

[dull sequoia]

omg im honoured

well i hope you pass!

[naive wyvern]

I need 55 at least

[naive wyvern]

Thank you but don’t be so hopefull

[vast sequoia]

is this uk

[naive wyvern]

What

[vast sequoia]

is it a uk exam

or usa

[naive wyvern]

Ohh no

[vast sequoia]

where from

[naive wyvern]

if I’ll say

You will laugh

[plucky elk]

!redir

[safe radish]

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

[plucky elk]

!done

[safe radish]

If you are done with this channel, please mark your problem as solved by typing .close

[naive wyvern]

Yeah

[ocean wadi]

type .close

[naive wyvern]

Wait but

One more

Question

§f(x) = \frac{x^4 - 2x^3 - 7x^2 + 8x + 12}{(x^2 - 1)(x^2 - 4)(x^2 - 9)}§

$f(x) = \frac{x^4 - 2x^3 - 7x^2 + 8x + 12}{(x^2 - 1)(x^2 - 4)(x^2 - 9)}$

[flat frigate]

ℳ

[naive wyvern]

What’s here

[ocean wadi]

Do you know what the difference of two squares means?

[naive wyvern]

No

[ocean wadi]

Okay, please expand (x-a)(x+a) for me and let me know what you get

[naive wyvern]

I don’t know

[ocean wadi]

Do you know how to expand double brackets?

[naive wyvern]

OHH

it’s smth like a^2-b^2??

[ocean wadi]

Yes but please in terms of x and a

[naive wyvern]

I don’t know

Because a is first now x is first

[ocean wadi]

okay sorry

[naive wyvern]

On that algebra exam I got 46

[maiden parcel]

how did u got that result , or do u remember seeing this somewhere ?

[naive wyvern]

Yess I saw it

[maiden parcel]

aight try to remember

[naive wyvern]

It was in the algebra exam I failed as I said

[maiden parcel]

u havent studied for it

[naive wyvern]

I DID

[maiden parcel]

whats (a+b)^2

[naive wyvern]

a^2+b^2

[maiden parcel]

close u forgot smth else

[naive wyvern]

Wait I remember

Something with ab right

Oh yes

It’s a^2+ab+b^2

No way that’s wrong

I remember it

[maiden parcel]

u have got closer but no

[naive wyvern]

WHAT

WDYM NO

[maiden parcel]

its a^2 + 2ab + b^2

[naive wyvern]

and what did I say?

[maiden parcel]

its 2 ab

[maiden parcel]

ab

[naive wyvern]

What’s the difference

[maiden parcel]

ab * 2

[naive wyvern]

Oh

So that’s why I failed

[stoic torrent]

i think you need to revise your basics once again @naive wyvern

[naive wyvern]

Help I can’t

I don’t have time my teacher gives 1000 assignments for the same day I’m not even joking

[maiden parcel]

it wont take u that long

and helping u will take even longer

[naive wyvern]

Ok ok I will

WHAT

THATS NOT NICE TO SAY

[maiden parcel]

oh sorry if i said smth wrong

my apologies

[naive wyvern]

No it’s okay dw

But please hel

Help

With the function

[blazing swallow]

if your basics are not strong, those assignments will take you longer, and you will be worrying about the arithmetic rather than learning what you're supposed to be learning

[naive wyvern]

.

[blazing swallow]

it sucks, but going back to basics will make a world of difference

[naive wyvern]

But there’s a calculator

I can use it

I think

[blazing swallow]

but if you can do more calculations in your head, then homework wouldn't take as long, right?

[naive wyvern]

Right right

[maiden parcel]

calculator wont help u most of the time

[blazing swallow]

you can review stuff that isn't arithmetic too, like finding roots of factored expressions (e.g. (x-1)(x-2)(x-3))

[naive wyvern]

1
2
3
Correct?

LESGOOOO

[blazing swallow]

world champion 🏆

[naive wyvern]

Thank you thank you

I deserve it

[blazing swallow]

how about $(x^2-1)(x^2-4)(x^2-9)$?

[flat frigate]

حسیب ♥

[naive wyvern]

WHAT

tf

Okay wait

I’m thinking

1
2
3
Again?

[plucky elk]

partial credit

[plucky elk]

write each term in factored form like this person said here

[naive wyvern]

I don’t know how to do that

[plucky elk]

did you understand this

[naive wyvern]

Yes

[plucky elk]

can you finish:
a^2 - b^2 = (a - b) * ?

[naive wyvern]

^2?

[plucky elk]

no

[naive wyvern]

what why

Ohh it’s not that one wait I know what this is

(A+b)

[plucky elk]

when you say it's something you understand, it confuses helpers

[naive wyvern]

Sorry

[plucky elk]

right

[naive wyvern]

[plucky elk]

did you understand why this is true:
a^2 - b^2 = (a - b) * (a + b)

or is it just something you memorized

[naive wyvern]

Yes

[naive wyvern]

This

Like I said yes about this

[plucky elk]

you should go back and do this then

[naive wyvern]

Okay so x^2 + ax + (-a^2) + ax
So um x^2 + 2ax - a^2?

[plucky elk]

no

[naive wyvern]

Why

[plucky elk]

your firsts and lasts were correct

[naive wyvern]

What wasnttt

Ohh it’s -ax

Then u cancel it

So X^2 - A^2

?

[plucky elk]

right so now you should understand this if you just expand the right side

[naive wyvern]

ohhhh I understand nowww

[plucky elk]

can you factor x^2 - 1 now?

[naive wyvern]

Ummm

[plucky elk]

remember 1 * 1 = 1

[naive wyvern]

I don’t know

I tried thinking

[plucky elk]

what if a = 1

[maiden parcel]

1^2 = 1

mb

[naive wyvern]

What about it

[plucky elk]

what does this equal?

[naive wyvern]

If a is 1?

X^2-1

[plucky elk]

yes

[plucky elk]

can you answer this now

[naive wyvern]

Ohhh so
(X-1)(x+1)

[plucky elk]

right

[naive wyvern]

YESSS

[broken forum]

[naive wyvern]

[plucky elk]

can you find another root in addition to the 3 you already found

[naive wyvern]

Pi day ur helping more than my teacher tbh

[plucky elk]

1 on 1 tutoring usually is more helpful

[naive wyvern]

There’s another root?

[plucky elk]

yes. 3 more exactly

[naive wyvern]

Now I know what u mean

If it’s 3 more so

[plucky elk]

using this, x^2 - 1 = 0 when x = 1 and when x = ?

[naive wyvern]

All the numbers but with. -

[naive wyvern]

-1

[plucky elk]

right

[naive wyvern]

Wait but if you have X^2
And ur x is -2
It’s -2^2
Or (-2)^2
It’s not the same

[plucky elk]

x^2 - a^2 means x^2 - (a)^2

plug in a = -2