help-0

[near falcon]

the central angle is 180?

[coral pagoda]

We know that 360 degrees is how many angles it takes to go around a full circle (not very exciting)

And 180 is the angle of our sector for this picture.

[near falcon]

ok

[coral pagoda]

Right?

[near falcon]

right

[coral pagoda]

Well.... Here, 360 is the full revolution, and 90 is the angle of our sector.

[near falcon]

ok

[coral pagoda]

Agreed?

[near falcon]

agreed

[coral pagoda]

Okay, so already with a couple of examples, we see the number of sectors it takes to fill up the circle is 360/theta

[near falcon]

theta is the arc length of the sector?

[nocturne radish]

It is the angle

[near falcon]

ohh ok

[nocturne radish]

Of the sector taken in consideration

[coral pagoda]

A_s stands for area of the sector

[near falcon]

ok

[coral pagoda]

Well, now we can just do some nice algebra

[nocturne radish]

Theta itself is a Greek letter

Like alpha beta etc

[near falcon]

what abt A_c

[coral pagoda]

A_c is area of the circle

Usually if I don't say what my subscripts are, they are exactly what youd expect them to be :p

[near falcon]

time to note down stuff

[coral pagoda]

And bingo!

[paper bloom]

Nice handwriting

[olive trail]

which channel do i go to ask about something relating to statistics

[paper bloom]

i am doing area of circle luture in class

[nocturne radish]

This is a more simple explanation without going into depths

[paper bloom]

anyone want to join

[nocturne radish]

Lol, is that sarcasm

[coral pagoda]

Gonna go with #probability-statistics

[paper bloom]

no i am not lying

[near falcon]

lemme note it down first

[paper bloom]

i promise

no joke

[olive trail]

somehow missed that when i was looking through channel names

[nocturne radish]

Thanks then

[coral pagoda]

So we come to our conclusion. The area of the sector is the area of the circle times theta/360

[nocturne radish]

Don't note anything first, try to understand

If you still haven't understood I can try to explain in dms

[paper bloom]

can somone explain once more

pls

[coral pagoda]

Same question?

[paper bloom]

no mabye a diffrent one

[nocturne radish]

But the question itself isn't clear

[coral pagoda]

No, it was. What is the area of a sector.

[nocturne radish]

Are asking what is the formula, or why the formula, or an in depth dive into it

You*

[coral pagoda]

Probably the first, but I am not just gonna give a formula. That is not very helpful.

[near falcon]

area of the sector = A_c x Central Angle/360?

[nocturne radish]

It is not

[coral pagoda]

Correct

Where A_c is the area of the circle

[near falcon]

Yay I understand now ty

[paper bloom]

please come the the voice chat it will be super easy for me to under stand

[coral pagoda]

Fantastic :D

[nocturne radish]

But sometimes working backwards from the formula to why it works might help some people understand

[paper bloom]

pls

[near falcon]

Circle stuff is very confusing

[coral pagoda]

I'm here

[coral pagoda]

Everything has the potential to be very confusing at first. It gets easier the more you work with it.

[nocturne radish]

How about a more simple explanation

[near falcon]

Pi is very confusing for younger people

[nocturne radish]

A sector is basically a fraction of the circle

[coral pagoda]

Pi is just a number

But it is a very specific number that shows up all the time when dealing with circles (and other things)

[near falcon]

still confusing

[nocturne radish]

So the area of the circle is pi r²

But a sector is a fraction right?

[near falcon]

yes i think

[nocturne radish]

It is a fraction of the circle

So 1/4 of a circle will have 1/4 of the area right?

[sick scaffold]

is ther anything wrong with my work? (using change of base formula)

[nocturne radish]

Lol how old are you?

[near falcon]

sector = pir^2 Central Angle/360

[near falcon]

must i say

[coral pagoda]

No, you do not have to say

[nocturne radish]

You dont

[near falcon]

ok

[coral pagoda]

I also encourage you not to

[near falcon]

i wont

[nocturne radish]

It was not even a question in the first plave

Moving on

[near falcon]

ok

[nocturne radish]

So like in dackids example

Sometimes, the sectors have angles of 90 degrees right?

[near falcon]

yes

[nocturne radish]

Those sectors are 1/4 of the circle

[near falcon]

not all sectors are 90/360

[nocturne radish]

Sector angles with angles 180 degrees are 1/2

Yes I am approaching the point

But like you said, not all angles are 90 or 180

So how do you figure out how much of a part the sector is?

What if the angle is 30°?

Just divide the angle ( which is also called theta) by 360

[paper bloom]

true

[nocturne radish]

I am assuming you are 14-15 because that's also around my age

[paper bloom]

no i am 13

[near falcon]

then it would be pi r2 x 30/360

[nocturne radish]

And that's also around when they thought me about sectors in school

Yes

[paper bloom]

is that good

[near falcon]

I'll just say 1 thing

[paper bloom]

or what

[near falcon]

im not 15

[nocturne radish]

Neither am i

I studied sectors when I was 9

[near falcon]

ok

[nocturne radish]

So don't let age discourage you

[paper bloom]

where did bob ros go

[coral pagoda]

I'm here

[near falcon]

lol

[paper bloom]

yay

[nocturne radish]

Continuing with the explanation

[paper bloom]

yes

pls do

[nocturne radish]

For finding area of any sector

[paper bloom]

na let continue

pls

sdakf

s

[nocturne radish]

All you have to do is take the angle of the sector, divide by 360

[paper bloom]

okay

[nocturne radish]

That gives what fraction of the circle the sector is

[paper bloom]

ok

[nocturne radish]

The multiply with the area of the circle

Then*

[paper bloom]

and then you find the angle

[nocturne radish]

Done

[paper bloom]

okay

know i want to learn cos

where do i ask that

[coral pagoda]

Cosine?

[nocturne radish]

Trigonometry?

[paper bloom]

yea

[coral pagoda]

The basic definition is pretty easy. One sec

[nocturne radish]

Dackid, was there any loopholes in my explanation?

[paper bloom]

i have to go eat

i will come back after

[near falcon]

1 more question

is Area and A_c the same thing

[coral pagoda]

Super quick. Let theta be our angle. Then cos(theta) is the length of the side next to the angle divided by the hypotenuse.

[\cos(\theta)=\frac{adjacent}{hypotenuse}.]

[ocean seal]

dackid

[coral pagoda]

In this case, the side next to our angle has length a, so the adjacent=a. Note, adjacent literally means next to.
The hypotenuse is the longest side of the triangle, which is c.

So using our lovely formula here, cos(theta)=a/c

Note, this formula is a definition. There is nothing to derive.

[coral pagoda]

No. A_c just denotes the area of the circle. Moreover, I gave it that notation. That's just what I chose to call it. It's just a convenient name.

A_c DOES NOT universally mean the area of the circle. I just wanted A_c to represent that for this scenario. That is all

[gusty ice]

Hi, I had a question on radical expressions in algebra, is there a simpler way to simplify large index numbers and large radicand

[coral pagoda]

What is the question?

And...it depends

[gusty ice]

uh lets say

4 index radical 405

[coral pagoda]

Oh sure. Well, we need to factor 405.

405=20*21=4x5x7x3

Since there are no repeating factors, this is as simplified as it gets

Oh wait, hold up

4=2×2

[arctic laurel]

How did they get the term a to become 6?

[sick scaffold]

this is correct right? change of base formula

[coral pagoda]

Yes, but it isn't very useful.

[gusty ice]

I think I understand, thank you

[coral pagoda]

In fact, that is just the same thing.

Log(10) is one, so nothing interesting has been said there

[coral pagoda]

Hold on, I made a small error.

[sick scaffold]

i'm being asked to proof this. not too sure about where to start

[coral pagoda]

[\sqrt{405}=\sqrt{4}\sqrt{357}=2\sqrt{105}]

Oh, I am dumb

[gusty ice]

if you must, please take your time

[coral pagoda]

[\sqrt{405}=\sqrt{5*81}=\sqrt{81}\sqrt{5}=9\sqrt{5}]

[ocean seal]

dackid

[coral pagoda]

That's better.

[coral pagoda]

Well, what is ln(e)?

[gusty ice]

is it possible to simplify 9 radical 5 further, specifically 9?

[coral pagoda]

Well, 9 isnt even in a square root. Cant do much to that

And sqrt(5) is an irrational number. That is as simplified as it gets

[near falcon]

Area of the sector = r^2piCentral Angle/360?

[coral pagoda]

I don't think geometry changed its rules in the past 30 minutes :p

[gusty ice]

Oh, because I thought you could go beyond and go 3 and 3

[arctic laurel]

How did they get the term a to become 6?

[coral pagoda]

Well, that would be if it was still in a square root. But it is not anymore

[gusty ice]

Oh yes right

Thank you

[coral pagoda]

You betcha

[coral pagoda]

After you expand it out, the coefficients for each power have to match

For x^2, you'll end up with 3 being the coefficient for x^2 on the left and -3+a being the coefficient for x^2 on the right.

Set them equal to each other. 3=-3+a, so a=6

[arctic laurel]

how is it -3+a?

[coral pagoda]

Expand the right side out and see for yourself

[arctic laurel]

x^3+ax^2+8x-3x^2-3ax-24

[coral pagoda]

Yep. You have ax^2-3x^2. By combining like terms, this is just (a-3)x^2

[paper bloom]

bon ros

i mean bob ros

[coral pagoda]

Closer

[paper bloom]

can you please explain me what is Log

[near falcon]

log is a tree

[paper bloom]

no in math

[coral pagoda]

Well, part of a tree

[near falcon]

oh ok

[paper bloom]

k

[coral pagoda]

Hmm, do you know what exponents are?

[paper bloom]

what do you mean by that

[near falcon]

what is the average age for a human being to learn bout circle stuff

[paper bloom]

13

i am pretty sure

[near falcon]

ok

[paper bloom]

i think it depend what country you are in too and school

like for me i go to James Ruse

[coral pagoda]

Well, you are learning some pretty basic things rn. In 10th grade, you learn a LOT more about circles.

[near falcon]

hmm

10th grade is still a long time away

[coral pagoda]

But I will admit, I forgot almost everything we learned on that stuff

[paper bloom]

i mean it depened on your school

[coral pagoda]

Geometry is not something I've put a lot of focus on

[paper bloom]

why

[gusty ice]

Sorry, I have a bit more questions on radical functions, how exactly does division with radicals work

[near falcon]

I almost forgot whats 2+3

I always say 6 but its 5

[paper bloom]

LOL

LOL

[near falcon]

bc im too used to multiplication

[coral pagoda]

Other math topics hold my interest. Moreover, they are also the classes I am in right now. Geometry took a bit of a back seat

[paper bloom]

any topic a 13 old should do

i really like maths

[coral pagoda]

cyretsu, do you know what exponents are?

[near falcon]

same

[coral pagoda]

I imagine so

Whatever you want.

[gusty ice]

Yes

[paper bloom]

so can i do calculus

[coral pagoda]

Okay, let me let you in on a little secret. [\sqrt{x}=\left(x\right)^{\frac{1}{2}}.]

[ocean seal]

dackid

[coral pagoda]

So if you know how exponents behave, you know how radicals behave

[coral pagoda]

Sure! It's likely you don't have the fundamentals yet, so learn them if you want to do calculus early!

[paper bloom]

i will not understand it

i need to improve algebra

[coral pagoda]

Not yet. But you certainly habe the ability to understand it

[paper bloom]

give me a algebra question

pls

[coral pagoda]

Algebra is incredibly fundamental to working with more advanced mathematics.

[paper bloom]

YEA

what class are you in

[coral pagoda]

I'm in college. I am taking topology and abstract algebra rn.

[paper bloom]

what college

[coral pagoda]

I am not going to disclose that info.

[paper bloom]

i am sorry

for asking that

are collage and university the smae

[coral pagoda]

You're fine. Location/age are things that probably should not be discussed in a server with over 20,000 people in it

[coral pagoda]

There's probably a difference, but I sure as heck dont notice it :p

[tired drum]

How many 3 digit even numbers can be made with 0,1,2,3,4 and 5, without repetitions of numbers? Can someone help me with this

[silk sapphire]

Universities offer post-undergrad studies, while colleges just offer 4 year programs

[coral pagoda]

Ah, good to know. I am at a university then

[paper bloom]

52

[paper bloom]

52

[coral pagoda]

Is a number. I can agree

[tired drum]

How’d you do it?

[paper bloom]

okay give me a minute to write it in discord

[tired drum]

Kk

[coral pagoda]

Question, is 012 a possibility here?

Or is that considered a two digit number?

[tired drum]

Yeah that’s 2 digits lol

[coral pagoda]

It does make a big difference

Okay. I got a feeling their approach didnt take this into consideration.

[paper bloom]

no sorry i think it is 60

i did something wrong

[coral pagoda]

Getting mixed signals here :p

[near falcon]

lol

[paper bloom]

i am trying

[tired drum]

Ight send working when u got it

[paper bloom]

k

[coral pagoda]

Do you know what nCk means?

It'll make writing it down easier

[near falcon]

whats a nCk

[paper bloom]

nCk

neverheard of that

[near falcon]

same

[coral pagoda]

n choose k. How many combinations of k items can you make from n items

[tired drum]

It’s combinations

[near falcon]

x

[tired drum]

Yeah

[coral pagoda]

Yep, precisely what you need

[near falcon]

all i do is, start from 1 number by 1 number

[coral pagoda]

Okay here is the deal. There are 3 possible digits the last digit could be, 0,2, or 4

[tired drum]

Ye

[paper bloom]

okay

[coral pagoda]

Great. Now the middle digit can be any of the 5 remaining digits

[paper bloom]

okay

but then can you just write that in the answer

we need working out right

[near falcon]

Im already confused

[coral pagoda]

Okay cool. Now, there are two possibilities: either 0 has been used or it hasn't

[tired drum]

So wouldn’t it be 5! x 4! times 3?

[coral pagoda]

If 0 hasn't been used, then the choice of the last digit is free, so any of the four remaining works

[coral pagoda]

No

[tired drum]

Wait nvm

[paper bloom]

it would be 5 time 2 time 4

tell i can remember in my working out

[coral pagoda]

However, if 0 has not been chosen, then you have exactly 3 digits left to choose from (you can't choose 0)

[paper bloom]

k

[sudden patio]

Hey

content://com.android.chrome.FileProvider/images/screenshot/1634621873389963715025094858063.jpg

[paper bloom]

what is this

a question

[sudden patio]

.

[coral pagoda]

Something you probably shouldnt click

That is better

[paper bloom]

yea

that is why i aske

d

[sudden patio]

How do I solve these 2 questions?

[tired drum]

@coral pagoda got an answer for my question yet?

[paper bloom]

ohh yea

We have, digits 0,1,2,3,4 and 5
Even numbers-
(i) when 0 is at unit place, then
There are 5 ways to fill 10's place and 4 ways to fill 100's place
So, no. of ways =4×5=20

(ii) when 0 is not at unit place, then
There are 2 ways to fill unit's place, 5 ways to fill 10's place and 4 ways to fill 100's place
So, no. of ways =2×5×4=40
2 or 4
∴ total number of even numbers 40+20=60

the answer

[sudden patio]

Pls help me too

[paper bloom]

dackid helped me

i will

[coral pagoda]

Okay cool. If 0 is chosen first, you have 5*4 ways of arranging it.

[paper bloom]

but ask dackid he is the smartest

[sudden patio]

Hey

Pls help

[sudden patio]

In solving these questions

[tired drum]

Bro wait your turn lol

[coral pagoda]

If 0 is chosen 2nd, you have 412 ways of choosing it

If 0 is not chosen at all, you have 3x5x2 ways of expressing them.

[paper bloom]

do you think my ans is correct

[coral pagoda]

Add these all together and you should get your answer

20+8+30=58

[paper bloom]

ohh

and i got 60

[sudden patio]

Sir

[tired drum]

Oh

[sudden patio]

My turn?

[tired drum]

Alright yeah your turn

[paper bloom]

i am so sorry i did not know that

i tried

[near falcon]

TeXit Is So Useful

[paper bloom]

😦

sad

i guess i am not good at maths

[near falcon]

you are

just in a different way

[coral pagoda]

Wait, I mathed wrong. You may be in luck

[sudden patio]

@coral pagoda

Help

[paper bloom]

wait

which one is correct then

[coral pagoda]

My mind keeps forgetting there are 6 digits instead of 5

[paper bloom]

what do you think

[coral pagoda]

Everything but the first part was right. This should give you the correct result now

[paper bloom]

ohh then how did i get 60

in that question

ohh i understand know

[coral pagoda]

You cannot have 0 to be in the hundreds place

[paper bloom]

yea

and that is why i got it wrong

[sudden patio]

BRUH

@coral pagoda

Will you help me pls

[paper bloom]

what is your question

lets do it

[coral pagoda]

I am going to go to bed. Please ask in an unoccupied channel

[sudden patio]

.

[paper bloom]

ohh yea

its my bed time to

[coral pagoda]

I hate to be a buzzkill, but they cant help you with this one.

[sudden patio]

Bruh

[coral pagoda]

Not yet anyways

[sudden patio]

Ok

Ill do it myself then

Thanks.

[paper bloom]

mabye ask other chats

[coral pagoda]

There are 9 other channels to ask in

[paper bloom]

yea man

[sudden patio]

All are dead right now

[paper bloom]

ask other server

[coral pagoda]

That's a good thing

[paper bloom]

then

yea

because its not in use

so use that

anyways bye dackid

[coral pagoda]

Adios

[paper bloom]

Adios

you spaninsh

bye

[tired drum]

Wair @coral pagoda

Wouldn’t the answer be 40

[pseudo hearth]

hi

i like u

@tired drum

[sudden patio]

Bruh

[near falcon]

what da

[vapid yew]

hi

long division method

[alpine sable]

how do i use implicit differntiatiation to do 3xy^2+y^3=8

[civic jungle]

Isn't this literally the same type of problem as the first most basic implicit differentiation example you learn?

[opaque totem]

yea

[civic jungle]

That pink has troubles starting it (I presume) raises some questions

[alpine sable]

?

[alpine sable]

help me then

[opaque totem]

move the 8

than differintiate it

[alpine sable]

bro why am i moving the 8

[eternal osprey]

can someone help me create a general equation for nth derivative of this equation

[alpine sable]

it turns into 0

bc im finding derivative

[opaque totem]

yea ik

but just to make it ncie

step by step

Then u differintiate it

like 3*2xy^2-1

@alpine sable

[eternal osprey]

moriaty at first glance would you know the formula for the nth derivative in the picture shown above?

[alpine sable]

what

[civic jungle]

@eternal osprey If your other browser tabs are for this problem, can I just say, watch your parentheses

[opaque totem]

@eternal osprey use quotient rule

[alpine sable]

do i not use product rule

[opaque totem]

why product rule?

[eternal osprey]

I know how to derive it... but finding nth derivative is different. So far I have concluded that the top term must be -n-3

[alpine sable]

for 3xy^2

[opaque totem]

use additionand substraction rule

like 3y^2 is count as one

for using product rule uneed like 2 term

for example

(3x+2)*sqrt4x-1

ehh do u get it @alpine sable ?

[alpine sable]

ican do 3x and y^2 for product rule

[opaque totem]

ohhh sure just try it but

if u wanna crosscheck with my answer

my answer is

-y/2x+y

[alpine sable]

Guys I've been doing this for a some time now can any 1 help?

[compact lynx]

and you're trying to find... which values of x satisfy the equation?

[opaque totem]

i got x=-7 and x=1

[compact lynx]

what I would do is split the equation into two parts

[opaque totem]

do u need step by step?

[alpine sable]

Photo math says that but doesn't makes sence

[compact lynx]

think about it this way

ah shoot

[opaque totem]

what

[alpine sable]

This is an example

[opaque totem]

Ohhh

[alpine sable]

Of the question

[opaque totem]

for me like

[alpine sable]

The different is in that question the "C" is already 0

[opaque totem]

there is 2 possible thing right

either x-5=2(|x+1|) or x-5=-2 blabla bal right

[civic jungle]

Geometric solution :)

[opaque totem]

ahahahaha yeaa

[alpine sable]

Alright I see the photo math back again it makes sence

thanks guys

[opaque totem]

yepp anytime!

[queen drum]

hi i'm not sure on how to tackle this problem

i tried taking the derivative of the original equation and setting it equal to the tangent line equation

but i don't think that's what i'm supposed to do, right?

[alpine sable]

@opaque totem wtf am I doing wrong

[opaque totem]

yepp

[alpine sable]

?

[opaque totem]

minus the 2

by 1

wait wut

holdon

lemme pc u

damnn i cant

[alpine sable]

What

[opaque totem]

pc= private chat

what what?

[alpine sable]

Oh

Try now

[near falcon]

How do i find the arc length of the sector?

[gray isle]

apply the formula for arc length

[near falcon]

erm whats the formuka

[gray isle]

and/or consider the fraction of the arc and a full circle

[summer cairn]

$\sqrt{xi}=\frac{x}{2}(1+i)$

waht

...

is this right

[near falcon]

am stupid to know man

[opaque totem]

i feel like its wrong but idk

[devout summit]

Are you asking for all x in general?

[summer cairn]

yes

[devout summit]

Nope. That isn't correct

[summer cairn]

but why

let me check my paper

aha found it

$\sqrt{xi}=\sqrt{\frac{x}{2}}(1+i)$

[ocean seal]

wd4q5dy

[devout summit]

And also, square root is not that well defined in complex numbers. So you get two forms

[summer cairn]

$\sqrt{x^2}=|x|$

oh wait

[ocean seal]

wd4q5dy

[summer cairn]

what

[devout summit]

Like, you could say $\sqrt{i}=\pm\frac{i+1}{\sqrt{2}}$

[ocean seal]

Euclid31415

[summer cairn]

okok

$\sqrt{xi}=±(\sqrt{\frac{x}{2}}+\sqrt{\frac{x}{2}}i)$

if you want it to be more clear

[ocean seal]

wd4q5dy

[devout summit]

Or you could consider a "principal" square root

[devout summit]

This does look ok

[summer cairn]

oh

wait

what if x=i

[devout summit]

I thought you assumed x some positive real

[summer cairn]

i didnt assume anything

i just wrote it on paper

maybe it only works for positive reals

let me verify

[devout summit]

If x=i then you have to consider square roots of i again in this format

[alpine sable]

d

[opaque totem]

find the m which is the derivative, so like x^2/81 become 2x/81

[alpine sable]

look

[opaque totem]

look?

[alpine sable]

Is the m wron

Wrong

[opaque totem]

lemme calculate yaa give me 2 minute

yepp

i get

2x/5y

[alpine sable]

What

[opaque totem]

check ur answer again maybe miscal or u forget smtg

[alpine sable]

Ok

[opaque totem]

use quotient rule

for me

[rich basin]

I can't seem to reason how the associativity law works in matrix multiplication

in which A(BC) = (AB)C

[opaque totem]

ahahahah borutoeyepower

jogan

[alpine sable]

4. Determine the quotient

a. 2x2 – x – 10 by 2x – 5

b. 4x2 + 16x + 15 by (2x + 5)

5. Determine the result of the power of the algebraic form:

a. (3x + 2y)3 =

b. (3y2 – 2y)4 =

pls help

[opaque totem]

pink have u get it?

or u still stuck 😆

[sharp barn]

if the channel is free quick question how do we find for (c)

[alpine sable]

no

[opaque totem]

rip

[sharp barn]

@opaque totem sorry for ping but u know how to solve (c)?

[opaque totem]

sorry broo idk

[keen mulch]

@sharp barn didn’t I help you with this?

[sharp barn]

u help q6

[keen mulch]

Yeah we already did it?

[sharp barn]

wait fuck wrong question

question c

[keen mulch]

v=u+at

[sharp barn]

huh?

sorry for caps

[keen mulch]

Do you know that formula?

[sharp barn]

i know a= v-u/t

[keen mulch]

Same thing

Just rearranged

You need to rearrange to find t

[sharp barn]

what we finding is t right?

[keen mulch]

Yes

Rearrange the formula I gave or you said to find t

[sharp barn]

so the acceleration is 2.5

[keen mulch]

You’ll use the acceleration from part b

[sharp barn]

v is after? u is initial?

[keen mulch]

Which is f/m

Yes

[sharp barn]

so its 14 s?

[keen mulch]

Yes

[sharp barn]

then for d how does the graph look like?

like this?

but it say sketch right?

and there is nothing to plot

[keen mulch]

You can plot 35,14

[sharp barn]

oh

then how do we explain for f

[keen mulch]

There can be a change in direction which means there is acceleration

[sharp barn]

thats the answer for f?

@keen mulch sorry for ping but how do we explain for (d)?

it has 3 marks

[upper bone]

Informatics

[vale wigeon]

you will have to translate for those of us who don't speak Romanian.

[strange raven]

Hi

I know how to do A-B

In a set

But how to do |A-B|?

Which is inside mod

Is it just the numbers of elements in the set?

[strong furnace]

yes

cardinality is the term

[craggy basin]

what is polynomial function’s formula??

[alpine sable]

A polynomial function is a function that involves only non-negative integer powers or only positive integer exponents of a variable in an equation like the quadratic equation, cubic equation, etc. For example, 2x+5 is a polynomial that has exponent equal to 1.

[jade birch]

$p(x)=a_{n}x^{n}+a_{n-1}x^{n-1}+...+a_{2}x^2+a_{1}x+a_{0}, n\in \mathbb{N}_0$

[ocean seal]

.itsjustnai

[barren sinew]

channel busy?

[jade birch]

nope

[barren sinew]

whats wrong with my math here

[keen mulch]

Crumple zones add time to a crash by absorbing energy, seatbelts exert a force back to the person which prevents the momentum from sending the person flying into the steering wheel, etc. Something along those lines should suffice @sharp barn

[clever hare]

hello there i need help on how to do this question

[novel loom]

how is the answer 81 and not something else?

[vale wigeon]

@clever hare @novel loom one of you will have to move to another channel.

[clever hare]

oh alright

i guess i'll go then

[alpine sable]

I don't think the answer is 81

[alpine sable]

You have to determine the condition of existence. Once you have calculated that, use the properties of powers and bring the term with the unknown to the left side. Add the left terms, divide both terms, and set the base equal to 0, check the solution and there you have the answer : )

[vale wigeon]

this.....looks and sounds unnecessarily confusing, nerno

[alpine sable]

How does it look confusing ?

I just gave him all the steps to calculate it

[vale wigeon]

"condition of existence" for a problem that involves nothing more than simple application of exponent laws? please

there is no left or right side either

[alpine sable]

There is tho

Wait

I'm about to grab a piece of paper, one sec

[vale wigeon]

wait are you french

[alpine sable]

No I'm not french

[strange raven]

Hi

How to prove the above is true?

2.16

We have to just write truth tables for all abcd and e?

[vale wigeon]

no...

you first determine whether P is true, then determine whether Q is true, then find the truth value of each statement from a to e

[strange raven]

Yes after I determined

I know

I know P is false and Q is true

[alpine sable]

@vale wigeon almost done btw

[strange raven]

@alpine sable please help. I'm crying

[vale wigeon]

so you know the values of P and Q... do you know how to evaluate P or Q?

[strange raven]

No, all I know is p is false and q is true

[vale wigeon]

so you don't know how to do Boolean algebra?

[strange raven]

Wait, I'm looking at it

[sullen imp]

Thx, I came to the conclusion that the sequence is convergent

[vale wigeon]

\begin{tabular}{c|cc}
or & T & F \
\hline
T & T & T \
F & T & F
\end{tabular}

[strange raven]

@vale wigeon the truth tables right?

[ocean seal]

Ann

[strange raven]

I know

[vale wigeon]

please tell me this isn't foreign to you

[strange raven]

Yes I know

No

It's not foreign

I solved a lot

[vale wigeon]

so why can't you apply these tables here?

[alpine sable]

@vale wigeon ^

[vale wigeon]

nerno you definitely misunderstood the problem

[strange raven]

so @vale wigeon you are telling to apply all those to the tables right?

Okay

Thnx

[alpine sable]

What have I misunderstood? So wait, r you trying to say I did all this for nothing

[craggy basin]

tysm can you sight me atleast 1 geometric sequence example

[tight birch]

do i have to add +C? this is a physics problem btw

in our previous modules, they do not add +C so im confused :/

help pls

ohhh i seeeee. that helped thanks

[formal fossil]

hi, i need help . determine f′(4) if
f(x)=x√x

[alpine sable]

I prefer to solve it by assuming p = √x.

f(p) = p²p = p³.

dErIvAtIvE of this should be easier.

[alpine sable]

Other ways include x√x = x(x^(1/2)) = x^(3/2) and then apply power rule.

Or, use product rule.

[dense portal]

why is this the answer

this is my work

im getting a diff answer

can anyone identify wat im doing wrong

[alpine sable]

What does
P: A ç B
Q: |A-B| = 6
mean?

[alpine sable]

Step 3 looks sus.

Why 4/u?

[dense portal]

because 3/3 is = 1

and 2/3 + 3/3 = 5/3

for the exponents

[alpine sable]

Wait a sec.

Yeah, my bad.

[alpine sable]

Then the last step is definitely sus.

[dense portal]

yeah thats what i was thinking

idk how else to combine them tho

[sturdy walrus]

What do they mean by "sup" here?

[vale wigeon]

supremum

[dense portal]

ohh

thanks

[final wave]

hi everyone im 11 and when i need help i can ask here right?

[tight birch]

yap

[final wave]

thank you i appreciate it!

[steep lion]

I've asked this previously, made some progress, but I still need help because I don't think I fully understand this question. How do I prove that f is differentiable in 0?

I tried using this, but it only tells me that f diverges and is not differentiable? Did I write it wrongly?

[coral steeple]

i could be wrong, but i think you just need to demonstrate that the limit of the x != 0 case is -1/2

[steep lion]

That might work, how do I prove it though? I thought you had to do something with the first expression (ln(cosx)/x^2)

[coral steeple]

at x = 0, the x != 0 case is 0/0, so i assume you'd apply l'Hopital's rule

[rigid smelt]

i dont think you should use this to prove it exists, because it becomes much more rigorous. You just have to prove that f'(x) is continuous at x=0

usually you use first principle to prove the continuity because its faster, you dont have to find the derivative and then do the limits to check the continuity at some random points

also, you applied the first principle wrong

you are proving that it exists at 0, so your x should also be approaching 0 from both sides

which means you use the other branch of the function and not the upper branch (ln(cos(...))/x^2) thing)

channel might be busy, you should move, unless madmobius doesnt have any other questions

[alpine sable]

Im going to rip out my hair

this quesiton is unholy

[rain trout]

use vectors?

wow they want us to use cross product?

[high scaffold]

What is locus ?

[fickle latch]

It's long division

[crisp kernel]

I known

[fickle latch]

but with letters instead of numbers

[crisp kernel]

know*

[crisp kernel]

MAN

[fickle latch]

It's a shitty implementation of polynomial division

It's basically an extension of numeric long division

A better way of dividing polynomials is synthetic division

Which is way way faster and requires less brain cells

[toxic sleet]

21x^2 + 25x - 4

factorise the quadratic...

[alpine sable]

The sum of the area of ​​two squares is 26cm² , which also has the difference of their sides 14cm , calculate the area of ​​the values ​​of these squares approximately

[fickle latch]

have you two... tried anything?

[alpine sable]

x²+y²= 26²
x-y=14

right?

[fickle latch]

pretty much

ah wait no

doesn't need 26 squared

just 26

[alpine sable]

ok

[fickle latch]

Well?

What are you confused by?

[alpine sable]

how i make it a equation

[fickle latch]

Well there's the method of elimination for starters

google it if you don't know what that means

[opal mesa]

(7x-1)(3x+4)

[fickle latch]

there's also substituting variables

@opal mesa can you not just give out answers

[opal mesa]

this was another question

[fickle latch]

Yes I know

Point still stands

[opal mesa]

ok i am sorry sir

[fickle latch]

Thank you

[opal mesa]

😂 👍

[next pulsar]

Is there some obvious solution to this which I am missing?

[fickle latch]

you can google second order linear diff. eq for starters

Is it linear?

I have no clue

[next pulsar]

Yes it is linear but that’s not the point of the question

This is not solvable using any techniques I learned so far, I don’t need the general solution, just one specific solution, there is meant to be something obvious which satisfies this but I have no idea how to find it

[jagged imp]

z=x?

[fickle latch]

lmfao

[next pulsar]

🤯

[fickle latch]

yeah that works

[next pulsar]

Well thanks bro

[fickle latch]

z=kx works actually

huh

[near falcon]

erm, how do i find the area of the sector

[fickle latch]

define sector

have you tried googling

[near falcon]

erm no

[fickle latch]

then do that jesus

[near falcon]

ok

[edgy cipher]

can someone check this

[near falcon]

still dont understand

[fickle latch]

@edgy cipher 1. that's not a question 2. why would we do that

@near falcon what kind of sector do you mean

[edgy cipher]

im not sure if i did this right

[fickle latch]

Looks like a quiz site eh

Have you tried pressing the check answers button

[near falcon]

area of a sector, like a circle

[edgy cipher]

this isnt a quiz bro ive done this many times this is a practice quiz that i take and i see how i did than i take the real test

[fickle latch]

ah ok

Don't care, press the check answers button to see if you did it right

[edgy cipher]

ok

[sage violet]

besides its not graded

[edgy cipher]

im going to see all the answers tho

[fickle latch]

@near falcon so basically, a sector is like a slice of pizza right?

[near falcon]

ye

[lofty raptor]

Can someone explain me this/solve it with me in DM?

Function y= f(x) is given down.

Calculate f'(2) and f''(2)

[fickle latch]

How do you know how much pizza you're getting when you slice it?

[near falcon]

erm by finding the central angle?

central angle/360

[fickle latch]

yeah that's it basically

[near falcon]

ok

[lofty raptor]

Erm if someone can i can pay you for it too.

[fickle latch]

whoe

crigne

<@&268886789983436800>

[fading zephyr]

is this an exam

[lofty raptor]

Such a dumbass tagging mods i can pay for private math lectures

[lofty raptor]

Regular thing in school

[flint badger]

??

[fickle latch]

we got a cheater here don't we

[flint badger]

You're not gonna pay someone to do work for you here

[near falcon]

yeah we do

[lofty raptor]

To teach me how to do it*

[near falcon]

he's paying someone to teach

[flint badger]

Ok

Then why did you ping mods lol

[fading zephyr]

there is no need to offer money for that in this server, and in fact, offering money is against the rules

so please don't do that here

[sage violet]

in a way all of us are willing to teach as long as it abides with all the rules

[lofty raptor]

Alright im just beeing generous

[fickle latch]

Either way

discrete functions don't have derivatives

[sage violet]

yep

[fading zephyr]

they mean the finite differences approximation

this is common in numeric methods

anyway, good luck

[tight locust]

haha

[barren river]

The total area of this triangle is 39

How do i solve this

Its asking for the value of X

[autumn dock]

Hi

[alpine sable]

0.5 x (x-3) x (x+4) = 39

[autumn dock]

Good day

[alpine sable]

Simplify and solve for x

[quartz oxide]

Just plug triangle area formula

[glass lichen]

dont give answers

does nothing to actually help

[autumn dock]

a question, do you know the formula for triangle area?

[quartz oxide]

Probably

[alpine sable]

Oh sorry, I'm not much active here

[barren river]

The height/bottom x2

If i recall correctly

[quartz oxide]

You sure?

Triangle area is 1/2 bh

[autumn dock]

No, 1/2 x height x bottom

[quartz oxide]

“Base”

[flint badger]

bottom?

[fickle latch]

the word you're looking for is base

[flint badger]

you could also use (base * height)/2

[autumn dock]

thanks, im just telling the words that he/she understand it better

if he/she used the bottom word

so he'll understand better

[barren river]

well idrk the terminology in mathematics

[autumn dock]

he is foreign person i think

[quartz oxide]

Bruh

[flint badger]

you should know it

they'll appear in the questions

and you may not know what theyre talking about

[barren river]

They do appear but not in english

[quartz oxide]

||In Chinese is 底|| , base is not necessarily bottom bruh

What if they mistake something for base just bc it’s at the bottom

[flint badger]

@barren river where are you from?

[autumn dock]

no problem, can i disturb you in dm please

[barren river]

Very apparently im a chinese

[flint badger]

ok.

[barren river]

Nah as long as u guys can understand what i mean its fine

[autumn dock]

Oh!!! , I love china

[barren river]

anyways how do i solve that

[flint badger]

Well what is the base and what is the height

[barren river]

X+4 is the base

[flint badger]

Looking at the diagram

Yes

[barren river]

X-3 is the height

[flint badger]

ok

plug them into the formula

[barren river]

X+4(x-3)/2

[glass lichen]

[autumn dock]

Oh OK, there's no force. i just wanted to speak with you a bit and give you some proposal

[flint badger]

make sure u write it like ((x+4)(x+3))/2

theyre all being divided by 2

u could also just do

[autumn dock]

have you learned how to solve equations?

[flint badger]

1/2(x+4)(x-3) @barren river

[barren river]

yes

[flint badger]

this is better

[barren river]

but that just confused me earlier

[flint badger]

if u write it like this, its less confusing

[autumn dock]

OK, so you can solve it now using it

[flint badger]

because its 1/2bh

[barren river]

so do i just

[quartz oxide]

Expand

[barren river]

X(x-3)+4(x-3)

[quartz oxide]

Put everything to the left

And factor

[barren river]

what

[quartz oxide]

Expand first

[barren river]

The a^2-b^2 one?

[glass lichen]

there's no difference of squares, just expand the binomials then solve the quadratic

[barren river]

im having some confusion

[flint badger]

Whats the formula

@barren river

First of all

[barren river]

the uh

height and base x2

[flint badger]

no

Its height times base times 1/2

[barren river]

Fuck i meant height x base /2

[flint badger]

sorry I wish I could write in chinese

ok that is fine, but make sure u multiply height and base first

yea so look

[barren river]

wdym multiply

[flint badger]

if u plug them in it looks like this

multiply is the x

times

[barren river]

oh

[flint badger]

idk how else to say it

not "x" like variable but like 3 * 3 = 9

[barren river]

yea i got it

[flint badger]

ok

so what is the base

[barren river]

x+4

[flint badger]

right so b = x+4

what's the height

[barren river]

X-3

[flint badger]

h = x-3

that makes sense right

?

[barren river]

yes

[flint badger]

ok, now just put them in their spot

so if it is base x height / 2

how will u write this

so that u can solve it

[barren river]

(x+4)(x-3)

/2

[flint badger]

yea

what is that equal to

[barren river]

uh

[flint badger]

remember u know area is 39 right?

[barren river]

yea

[flint badger]

so its ((x+4)(x-3))/2 = 39

so what should we do first to solve this

[barren river]

perhaps make the 39 to the left side or something

[flint badger]

Remember if u have a fraction like this

U want to get rid of it first

How can u get rid of the fraction

[barren river]

times it

[flint badger]

$\frac{(x-4)(x-3)}{2}$

so it makes more sense

$\frac{(x-4)(x-3)}{2} = 39$

[ocean seal]

eggdog

[flint badger]

there

[flint badger]

ok so multiply by what though

instead of times u can say multiply, they are the same thing

[barren river]

uh

Idk lmao

[flint badger]

Ur right

Multiplying will get rid of the fraction

But what should you multiply by

[barren river]

2

[flint badger]

Right so

$\frac{(x-4)(x-3)}{2}\cdot \frac{2}{1}= 39$

ok u dont have to write it out like this, i think u know

but u want to multiply it by 2 on both sides

what will it look like after u do that

[barren river]

x+4)(x-3) equal 78

[flint badger]

exactly

can u figure out what to do next

[barren river]

like

uh

[flint badger]

@barren river ok do you not know? its ok

if u dont

[barren river]

maybe u can get the 78 to the left side and replace the original with 0 but idk

[flint badger]

u have to do something called foil

[barren river]

so like

X(x-3)

[flint badger]

except its not x+9 and x+1 right

[barren river]

And +4 (x-3)

[flint badger]

no not like that

try to look at the diagram

or the picture I sent

how can u apply it to (x+4)(x-3)

unless they taught u different way idk

[barren river]

X(x) + 9(x) + x(1) + 9(1)?

[flint badger]

yeah thats right but now multiply everything

[barren river]

right so like

[flint badger]

because right now u have things in parantheses that can be multiplied lol

parantheses is this ()

[barren river]

X(x) +4 (x) +x(-3) + 4(-3)

[flint badger]

uhh no

[flint badger]

go back to this

this was right

so now what's x(x)

[barren river]

X^2

bruh

[flint badger]

yea, now do that for everything wlse

and then tell me the whole thing xD

[barren river]

X2 +9x+x+9

[flint badger]

yea, x^2

but i think u kno

[barren river]

yes

[flint badger]

can u combine anything?

make sure it is simple

[barren river]

x2+10x+9

[flint badger]

right

now remember u kept saying