help-0

[ocean seal]

Stallion

[strong carbon]

@alpine sable

[native temple]

oh distributive property

How did I miss that

I need to study matha gain

again

lol

[strong carbon]

Let's move to an unoccupied channel.

[alpine sable]

Ok

[bronze spade]

Ok, I'm back

[junior rock]

Yeah I think it is

For 5 degree polynomial if they flipped

It means 5 vertical asemptopes

[bronze spade]

I'm assuming you're working in R. In R a polynomial can have a maximum of 5 roots. Then if you take the inverse function of your polynomial, you'll have 5 points where the inverse is not defined, with 5 asymptotes

but 5 is a maximum, it could also be 1, 2, 3, or 4 depending on the number of roots your polynomial actually has

you got it ?

[junior rock]

Wait let me show you the question

@bronze spade he said this

[bronze spade]

Are you talking about the invserse of reciprocal function ?

damn, sorry

[junior rock]

Yeah

[bronze spade]

Let's say you have a polynomial P

are you talking about

$P^{-1}$

[ocean seal]

allevmelc

[bronze spade]

or

$\frac{1}{P}$

[ocean seal]

allevmelc

[junior rock]

Y= 1/x

[bronze spade]

It does not make sense to me. What were the answers for linear and quadratic polynomials ?

If they were respectively 1 and 2, then was matters is the number of roots your polynomial has

Which can be a maximum of 5 in R for a 5th degree polynomial

when I say R, I'm referring to

$\mathbb{R}$

[ocean seal]

allevmelc

[junior rock]

Shut up

[tame shell]

yeet'd

[deft copper]

is $\exists ! x \in X : P(x)$ equivalent to $\exists x_i \in X : \forall x_j \ X \setminus {x_i} : x_i \neq x_j \land P(x_i)$?

[ocean seal]

jabra

[quasi pulsar]

i went wrong somewhere towards the end according to the marking scheme

maybe i’m just retarded but i can’t find what i did wrong, probably a simple mistake

dark blue is step 1
light blue is step 2
pink was my answer

i went wrong between steps 2 and 3

[deft copper]

-3 * 3.5 is -10.5

not 10.5

hence C is 18.5

[quasi pulsar]

@deft copper ❤️ ty

always the easiest bit that’s catches u out !

[deft copper]

yep

[onyx flower]

how the fuck do you integrate xf(x)

[ionic jewel]

integration by parts

wait

no

not sure that actually ends up working

[onyx flower]

im in ab i haven't learned how to do that yet

the only "parts" i know is if its addtion or subtraction

[ionic jewel]

u = x
du = dx

v = F(x)
dv = f(x)

xF(x) - integral of F(x) dx
xF(x) - second integral of f(x)

think thats right

where F(x) is the integral of f(x)

[onyx flower]

nvm i get it

its too easy

[molten rose]

i found the three roots of z

but i dont know how to do part b

it does not happen to involve vieta's formulae by any chance does it

[magic tiger]

all the people here do such complicated math while im in high school doing mostly basic things that i pick up easily

bruh moment

[onyx flower]

the only thing hard is knowing the names

[magic tiger]

true

[molten rose]

well if youre talking about me by any chance, this is schoolwork

[magic tiger]

yes i know you're probably in college doing extremely complicated stuff while I'm just sitting here having no idea what u doing

[onyx flower]

there is nothing abstract about math you can conceptualize things pretty easily by getting shown how to do it unless your doing some super specialize shit

[mental prairie]

part b should be preeettyyy fine

I think

[magic tiger]

[mental prairie]

just treat z^(3k) as (z^3)^k

makes sense?

[molten rose]

de moivre right?

[mental prairie]

and you know what z^3 is for each z_1 z_2 z_3

[molten rose]

yes

[mental prairie]

yeah so you know what w is in a+bi format

where you know what a and b is

then can you try expressing that back in Re^ai form?

oh wait

the power k thing is a bit of problem

[molten rose]

so it's just 3z^(3k) ?

[mental prairie]

yeah

3(z^3)^k

where z^3 becomes -1 -i

[molten rose]

that was pretty simple, how did i even get stuck on this lmao

[mental prairie]

it looks intimidating

[molten rose]

deceptively so

[mental prairie]

from like 30 cm away

you lean in and squint

and it goes away

[molten rose]

well that and

ive been awake for 13 hours

my brain isnt really functioning

[mental prairie]

13 is fine righhht

its just close to sleep time

[molten rose]

but i have to do some practice problems

[mental prairie]

like 16 is usual time

[molten rose]

unless i want to fail the test i have in 9 hours

[mental prairie]

oh god

good luck

tbh sleeping is probs much more important

is it only complex stuff in your test?

[molten rose]

not at all

it's my final Further maths exam

I didn't take a single further maths class this entire year

i literally started four days ago

and now im suffering

[mental prairie]

oh dang!

why do you have the exam?

[molten rose]

Hm?

[mental prairie]

like you didn't take the class

[molten rose]

well yes, but i couldnt drop the subject either

by then it was too late

Well I'm going to post another question

I know about the integral tests for convergence

but uhh, i don't see how to find the summation here

[muted raft]

probably riemann sum

[molten rose]

is it just the harmonic series?

[mental prairie]

whats the height of the rectangle between (x-1)/n and (x)/n

[molten rose]

the height < x^2 right?

[mental prairie]

maybe but here it looks like they've used bigger rectangles

so I did (x-1)/n and (x)/n

[molten rose]

1/n^2 ?

[mental prairie]

almost

[molten rose]

okay im just blurting out random guesses

let me think

[mental prairie]

like the height of this rectangle

or this one

[molten rose]

(2/n)^2 right?

[mental prairie]

maybe

feels almost right

look at the curve

at 2/n the curve is at a height of ?

[molten rose]

i messed up the parentheses

[molten rose]

4/n^2

man this really looks like i dont know how to read a graph right?

[mental prairie]

nah

you knew, just had to ask yourself the right question

which is just a lot of squinting and leaning in

besides you're tired now and will be fresher at the exam

branes run faster in exam halls xD

okay so you know the height and can find the area of any one rectangle

try seeing if you can add up the areas of all the rectangles, it looks like it'll be greater

[molten rose]

so the series should look like = 1/n^2, 4/n^2, 9/n^2, ..., 1 ?

[mental prairie]

9/n^2

yeah those are the heights alone

[molten rose]

the widths are just 1/n

i'm sorry, what is the summation supposed to represent

the heights or the areas?

[mental prairie]

well lets look at the question again

[muted raft]

You are trying to approximate the area under the curve using oversized rectangles.

[mental prairie]

that integral down there is the area under the curve

you want to compare that to smth

and it looks like the areas of the pieces are more

you've figured out the heights of the pieces

[molten rose]

tbh the reason this is harder for me than it should be is because the only thing i learned for this topic was this

[muted raft]

Shouldn't you be learning riemann sum before beginning integrals

[mental prairie]

he's in school

not uni

[muted raft]

I mean that is literally how integral started

from riemann sum

[mental prairie]

yeah

but schools aren't like that XD

[muted raft]

so it usually makes sense to teach how stuff starts right?

[mental prairie]

it does

but schools aren't like that XD

[muted raft]

F

[molten rose]

we were taught the integration rules and then we were off to the races

[muted raft]

typical highschool I guess

[mental prairie]

have you not been through school ? 0-0?

[muted raft]

Forgot about it I guess

[mental prairie]

ahhhh

[ionic jewel]

i learned Reimann sums before integrals

well

i didn't really but i did in school

[muted raft]

It makes more sense to learn riemann sums before doing any integrals yeah

[mental prairie]

I'm not sure what that is

[muted raft]

channel busy

[molten rose]

lower and upperbounds for an infinite sum

can be used to determine if the sum converges or diverges

[mental prairie]

okay that makes sense

but you don't need that for the question you have here

here you need to know that the integral represents the area under the curve

[molten rose]

right so where were we

[mental prairie]

and as per

you have to find the sum of the areas of those rectangles

[molten rose]

the area of the rectangles was represented by $\sum^{n}_{i=1}\frac{1}{i^3}$

[mental prairie]

almost

veeerry close

[molten rose]

and the area under the curve provides the lower bound for that area

[mental prairie]

remember the series looks like this

[mental prairie]

exactly

[ocean seal]

AdorableDeplorable

[mental prairie]

umm

[muted raft]

no

[mental prairie]

not exactly

take a breather

the height times base is area

[molten rose]

im sorry but wasnt the area of each rectangle = (1/n)^2 * 1/n

[mental prairie]

well isn't (1/n) constant?

all the rectangles have the same height?

[molten rose]

no

[molten rose]

yes

$\frac{1}{n}\sum^n_{i=1}\frac{1}{i^2}$ then

[ocean seal]

AdorableDeplorable

[molten rose]

thats probably wrong too actually

[muted raft]

yes it is wrong

[mental prairie]

yeah the height gets smaller and smaller

as i increases

because you are dividing by a bigger number

the height of the rectangle at 2/n was?

[molten rose]

4/n^2

[mental prairie]

and for 3/n?

[molten rose]

9/n^2

[mental prairie]

4/n?

[molten rose]

16/n^2

[mental prairie]

mhm

5/n, 6/n, 7/n etc

you know the heights at each point

and you know the width

can you fix this now?

the area of the rectangles is......?

[molten rose]

(i/n)^2

[mental prairie]

very close

one more factor...the width

[molten rose]

but that's a constant right?

we moved it out of the summation?

[mental prairie]

aha yeah

you can move it out

that's correct

so like

1/n ( sum of { ( i/n)^2 } )

I can't latex 😢....yet*

[molten rose]

n^2 is a constant term too actually

[mental prairie]

jaa

you can pull that out too

now you can do the rest

[muted raft]

[\frac{1}{n} \cdot \sum_{i=1}^{n} \qty(\frac{i}{n})^2]

[ocean seal]

zslya

[mental prairie]

Sanks

okay so now you're on your own to complete the question

[muted raft]

You can simplify the series even more

[molten rose]

yep, i got it

I'm unable to do basic arithmetic in my current state of mind, I swear I'm not as clueless as I seem right now, I'm off to bed

thanks for putting up with me though

[muted raft]

you just need to take out 1/n^2 out and sum i^2 only

[mental prairie]

yeah there's a reason for picking FM

[mental prairie]

he mentioned doing that

but sleep is what you need now

Ciao man

sleep tite

[ocean patio]

i have no idea on how to do this

[glass lichen]

if they're the same shape then they're just translations of each other

[ocean patio]

so its still x^4?

[glass lichen]

yes

[alpine sable]

Hey could someone help out

[craggy dirge]

how do you do c?

[eager pebble]

I tried plugging in pi/4 but I just got 0/0 at the end

[late tundra]

use lHospital's rule

[late tundra]

or use the identity
cos(2x)=(cosx)^2-(sinx)^2

[eager pebble]

wait of course

thanks lol

[tranquil pilot]

hi everyone i got a question, someone can help me with a signal analysis with Fourier series?
its goes like this:
if f(x) = 4x, -1<x<3. Find:
the first 5 harmonics

u guys know a book where i can find some info about how to find harmonics in those cases

o the formula that is used to find that

[mossy reef]

So let's say I have a wheel and theres a 1% chance of winning after winning this 1% chance they spin another wheel and the outher wheel you have a 5% chance of winning 100,000$ what are the odds of winning the 100,000

[late tundra]

5%

[wary stream]

No need to type in caps

[lusty plaza]

google's first result explains it

[quartz plinth]

Hey guys

I need help in Maths

g(x)= 2/[2x+6] – 3

This is the given x^

[haughty dirge]

How do i find the length

[minor dagger]

<@&286206848099549185> can someone please help. me with these two

[wary stream]

Don't ping the helpers right away

[minor dagger]

you guys are aarguing ToT

[minor dagger]

my bad

[lusty plaza]

I would have such a hard time not banning people from this server if I was an admin

[minor dagger]

I read the info. and rules ToT

[lusty plaza]

yikes

[round socket]

OMG

LMFAO WHAT THE HECK

[lusty plaza]

hopefully he catches a ban

[alpine sable]

<@&268886789983436800>

[round socket]

I JUST CAME HERE TO DO HW AND YALL BE HOMOPHOBIC?

[alpine sable]

musty is being racist, caught in 4k

[sly mantle]

👢

[round socket]

did he get banned

[sly mantle]

yes

[round socket]

anyone wanna help me with my hw doe

[alpine sable]

nice boots

[glass lichen]

you never posted a question

[round socket]

am i allowed to @ helpers for help

i know

i was just asking

[glass lichen]

after 15 mins like the rules say. . .

[round socket]

oh i dont read rules

ok

good idea

brb!

[glass lichen]

then go do that

[round socket]

taking a ss RIGHT now

BABY ITS THE BLACK BUISNESS

ITS THE BLACK BUISNESS

[minor dagger]

what

[round socket]

WHEN YOU SEE US OUT HERE GETTIN GETTIN ITTT

JUST SUPPORT!

[minor dagger]

ToT

[round socket]

WOOO

SUPPORT

ok nvm i need help

[minor dagger]

same

this math is. due. really soon and. im so confused.

[haughty dirge]

the hell is going on

[minor dagger]

i. need help

[round socket]

I NEED HELP IS WHATS GOIN ON

[minor dagger]

with math

[round socket]

NAH ME FIRST

[minor dagger]

ive been waiting. before. you

[proud burrow]

@haughty dirge just subistute value of time in the given equation

[minor dagger]

patient

[round socket]

ASRAR HELP ME!

@proud burrow !

HELP!

[wary stream]

Please calm down

[round socket]

sorey

[proud burrow]

@round socket sorry but I am not good in geometry let me try

[round socket]

ok

[alpine sable]

Is it urgent?

[proud burrow]

@minor dagger you can send your question

[round socket]

um yes

yes but no but yes

if you know what i mean

like

yes but like

not really no

[alpine sable]

Is it a test??

[round socket]

but like yes

no

its old hw

that was due MONTHS ago!

best to do it asap!

amiright????

...

.....

....

[minor dagger]

yes

[round socket]

NO ME FIRST

[round socket]

has it been 15 minutes yet

should i spam them

[wary stream]

Dude calm down

[round socket]

oh its only beeen 5 minutes

[proud burrow]

@round socket yeah just be patience

[round socket]

nvm

[minor dagger]

so 3(5+h)^2 is 3h^2+30h+7h buut how would i plug that in the slope equation to find the rate of change?

[wary stream]

And also spaghetti was here first, before you

[late tundra]

115

[round socket]

ugh everyone wanan help spaghetti but not me

like helo

OMG

ty

i did it myself

[minor dagger]

...

[round socket]

i THOUGHT it was 115

but i felt like

it dindt make sense

wait imma move to question-8 CHANNEL

SOREY SPAGHETTI HAVE FUN!

[late tundra]

that's the only option that makes sense

[minor dagger]

thanks

[alpine sable]

Ok so first join the centre of the circle T to P, R and Q. Now it's given that angle PTQ =130°.
Now look at the triangles PTR andd triangle RTQ.
PT=QT(Radio if the same circle)
TR=TR (common line segment)
PR=QR (common chord)
So angle PTR = Angle RTQ [CPCT]
Now take angle PTR as x. Here you go

[quartz plinth]

g(x)= 2/[2x+6] – 3 < given x

[proud burrow]

@minor dagger what's the question I am unable to understand can you explain me

[minor dagger]

so

i'll send it again

@proud burrow can we go to a. different channel?

[wary stream]

Channel is occupied

[minor dagger]

oh thanks

nvmd

[quartz plinth]

Aiii I’ll wait

[proud burrow]

@minor dagger what does net change means here I don't get that

[minor dagger]

i have. to find the net. change

so thats

[wary stream]

#help-6 is open

[minor dagger]

i sibstitute the numbers into the equation then subtract it

but how would i find the average. rate. of change like that

[proud burrow]

@minor dagger see change means you have to different you just can't subistute the number and subtract

[minor dagger]

i had to distrubite

but for b

the average. rate of change means i. use. the slope. formula

how. can i do that if there is an h

[proud burrow]

@minor dagger like how you used slope formula

[minor dagger]

I'll try to see if it accepts the answer

wait

which would be y1 and. y2

would y2 be the 5+h or the 3h^2+30h+75

[proud burrow]

wait you have understood wrong about net change and average rate of Change

[minor dagger]

oh..

[proud burrow]

Since f(z) = 3 - 4z^2

f(-2) = 3 - 4(-2)^2

= 3 -  4(4)

= 3 - 16

=-13

f(0) = 3 - 4(0)^2

= 3 - 4(0)

= 3 - 0

= 3

The net change is simply the difference f(0) - f(-2) = 3 - (-13) = 3 + 13 = 16

[minor dagger]

im only confused with. this one. because there is. letters

[proud burrow]

See this example you will understand what's the net change

[minor dagger]

yes, i know how. to solve it like thata

but. i. dont know how. to. do it. withaletter. like

5+h

[proud burrow]

So you got here confused

[minor dagger]

yes

[proud burrow]

@minor dagger wait let me try if I can find it out

[minor dagger]

okay, thank you

[maiden carbon]

Oh wait is this still in use?

[proud burrow]

@minor dagger I think we can't eliminate h

[minor dagger]

so how can the average. rate of change be found

[proud burrow]

Because we don't know what is h or what's the function of h or anything about h

@minor dagger I Thik you told before like using slope before you told

[minor dagger]

i. was able to. figure it out

for slope

3(h+10)

but i cant for net. change @proud burrow

can you help me with. that one?

[proud burrow]

@minor dagger sorry but the question you have asked is actually a new concept for me and confusing to me sorry to say but I can't help you

[minor dagger]

its okay, thank you. though!

[haughty dirge]

you mean the 20?

[proud burrow]

Yes out t= 20 in your given equation and then solve for length

*put

[acoustic reef]

This chat being used?

[late tundra]

nope

[acoustic reef]

Does that look right?

Verifying Identity’s

[late tundra]

yes they r all correct

[acoustic reef]

🙂

Thanks!

[ivory zodiac]

guys this question is physically impossible, right?

cause Fa would have to be greater than 245 N

[ionic jewel]

that doesnt sound right

[ivory zodiac]

but if it's the minimum, which is 245 N, the acceleration is 5.3 or smt like that

and anything less than that, the system will move the other direction

[ionic jewel]

no

theres no reason you couldnt accelerate it at 0.3 m/ss

[ivory zodiac]

how would that work??

because the friction on the table is 45 N

and the m2 weight is 200 N

so to make it move in the direction of M1, you need to overcome 245 N

[proud burrow]

You should also add the foce due to hanging block with friction because they are in same direction

[ivory zodiac]

the hanging block doesn't have friction tho

[proud burrow]

I am not telling to add friction I am telling to add forces

[ivory zodiac]

yes

200N + 45 N

[pure hill]

I don't see anything impossible, yeah its true that the force should be greater than 245N

[ivory zodiac]

right, but anything greater than 245 ends up giving a number larger than 0.3m/ss

[pure hill]

but acc to me the answer should be 252.5N

[ivory zodiac]

i think i got taht answer too

but when i verified it

A ended up being 5.3 smt

(m1+m2)a = Fnet

[ionic jewel]

the verification is wrong

[pure hill]

ohh yeah right I totally missed that

[ivory zodiac]

pls do tell

[ionic jewel]

you didnt account for friction then

[pure hill]

just a sec let me do a bit more calculation

[ivory zodiac]

Fnet counts the friction in

shoudl it not

cuz

[ionic jewel]

this doesnt include it

[ivory zodiac]

hold on a sec

[ionic jewel]

but again i havent done physics in a while but its definitely possible to do

[pure hill]

can you please tell what the answer is because i am getting 258.5N

[proud burrow]

@pure hill how did you find fnet

[pure hill]

see first I found the force due to the hanging block and due to the friction on the block that is placed on the table that was fnet

and then to find the force

[pure hill]

I simply used that

but in place of fnet

I put F

[pure hill]

and then I added F and fnet

[ivory zodiac]

even if u account for the friction

(which i don't rlly think u should cuz it should be included but i could be totally wrong)

u get 4.6111

i think its cuz

u need a certain acceleration to even overcome the weight and the friction

and 0.3 m/ss is simply not big enough

[pure hill]

I just am asking that do you know the correct answer?

[ivory zodiac]

nope

this was a quiz given my a physics teacher who makes tons of mistakes and my class and i r losing our minds

so our concensus is he just made a mistake

but i dropped by here just to make sure

[pure hill]

you don't need that acceleration you want a particular force that is going to overcome all the opposing forces and then provide extra 0.3 m/ss acceleration

[ivory zodiac]

yes

but all the answers we get

we r tryna verifyu

[pure hill]

so its totally possible

[ivory zodiac]

to see if we get the correct acceleration

and its just not working

[pure hill]

see verification in this type of questions is a bit tricky

[ivory zodiac]

ah wells its fine thank yall for the help i must go sleep i am spent

[pure hill]

when you do verify you need not just put (m1+m2)a = fnet where you are takng fnet = 245N no thats totally wrong

[ivory zodiac]

ur help was very much appreciated bunny and asrar and darklord

but it cannot be anyyyy less than 245 n

so if i were to put 245 n, i expect an answer less than or equal to 0.3 m/ss

but its fine im tired

[pure hill]

you are not getting it you don't have to verify

[pure hill]

well its okay then

[proud burrow]

There's no conditions given so it may be more or less than 245

[ivory zodiac]

yee tyvm

[ocean seal]

xHardcorexism

xHardcorexism

[calm kiln]

This free?

[candid minnow]

how do you find the relative displacement given 2 points in a 2d coordinate system

[torpid narwhal]

hi i'm trying to get the sum of all even numbers from 0 to 2n, for any positive integer n

so i have

Sigma (i=0 to n) 2i = 0 + 2 + 4 + ... + 2n
= 2n + Sigma(i=0 to n-1)
= 2n + 2(n-1) + Sigma...

[vagrant cobalt]

n(n-1)

Its a known formula

[torpid narwhal]

= 2n + 2(n-1) + 2(n-2) + ... + 2 + 0

[vagrant cobalt]

Maybe n(n+1) for your case

[torpid narwhal]

= 2n + 2n - 2 + 2n -4 +... + 4 + 2+ 0

and if you cancel the constants out

dont you get 2n

?

[vagrant cobalt]

Take 2 common

[torpid narwhal]

hm?

[vagrant cobalt]

2 common from each term

You end up with 2 times

Sum of integers from 1 to n

[torpid narwhal]

oh wait so

i get to
(2n - 0) + (2n - 2 ) + (2n - 4) + ... + 4 + 2 + 0

[little wadi]

my bad

[glossy tendon]

Sum of Integers from 1 to n is $S_n = \frac{n(n+1)}{2} = 1+2+3+...+n$
Multiply it by two $2S_n = 2\frac{n(n+1)}{2} = 2(1+2+3+...+n) = 2+4+6+...+2n$

[ocean seal]

robin

[torpid narwhal]

that's not helpful

[arctic dirge]

Please help me in this question

[alpine sable]

Is $x^{1}-x^{-1}=/frac{x^{2}-1}{x}$?

,w x^{1}-x^{-1}=x^{2}-1

,w x^{1}-x^{-1}

[arctic dirge]

thanks

[lofty compass]

Algebraic vectors

[alpine sable]

3+(-2)+(-1)=0

[alpine sable]

I really don't know. I don't think it's something to do with that.

[nocturne flint]

x²- x⁴

[lofty compass]

Don’t know how to do the first part

[alpine sable]

So if we use this, $\frac{(3+(-2))^{2}}{3(-2)}+\frac{((-2)+(-1))^{2}}{(-2)(-1)}+\frac{((-1)+3)^{2}}{(-1)(3)}$?

[ocean seal]

Ranok Hui

[alpine sable]

Andrea is opening a gourmet donut shop. The fixed monthly costs (rent, insurance, electricity, etc.) will be $18,000. It costs $0.25 to produce each donut.

Write a function c(x) to represent the cost of business based on x number of donuts product

can i do

c(x) = 18,000(1.25*x)

I interpreted 3 -2 -1 in, and got 3

oh ok

nice

[oak matrix]

No bc 18000 is a constant so it would be added

[alpine sable]

oh yea

c(x) = 18,000+1.25*x

like tha

right

[oak matrix]

0.25 x

c(x)=18000+0.25x

[alpine sable]

ok

thx

love ya

<3

love ya a lot

@oak matrix

[oak matrix]

Btw can anyone help with one

[alpine sable]

<34333

[oak matrix]

Yw :))

[oak matrix]

Please It’s 1 am

[alpine sable]

I guess?

I'll try some other numbers

[tranquil tulip]

damn i feel so bad ur helping everyone but no one is helping u 😭 if i knew how i would help

[alpine sable]

x=2
y=-1.5
z=-0.5

[oak matrix]

Haha thanks I’m literally gonna fail😭😭

[nocturne flint]

Check that p(X) is a multiple of g (X) or not p(x)=X³ - 5X² + 4X - 3 g(x)= -7

can someone help

[alpine sable]

I got 3 again?

[alpine sable]

I found my ncr and npr worksheet

Idk negative factorials...

I can't help

,w \frac{4!}{(4-15)!15!)}

0

[ocean seal]

Results provided by WolframAlpha

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

Requested by Ranok Hui#1943

[remote shard]

can someone help me real quick

[alpine sable]

Sure

[remote shard]

I need the formula of a revolution around a certain x axis

how do I tweak the formula

so the integration formula and then i need to find the volume around line x=4

how do i change that

[alpine sable]

Oh no, I don't know integrals

[alpine sable]

How do I find tan, csc, or sec in unit circle

[shrewd sable]

All of those can be derived from sin and cos

[oak chasm]

@alpine sable They switched the numbers by accident.

Should have been 15C4.

[alpine sable]

Yeah but like how

Is sec reciprocal or cos ?

[oak chasm]

It is.

csc is reciprocal of sin

tan is sin/cos

cot is cos/sin

So, just get sin and cos from the unit circle, then use those.

[alpine sable]

Oh damn I completely forgot that’s how it works

[ocean seal]

Chai T. Rex

[alpine sable]

So if sec is -2 would it be -1/2 cos In unit circle ?

[oak chasm]

Right.

sec = 1/cos, so yes.

[alpine sable]

And what abt -1?

[oak chasm]

For the secant?

[alpine sable]

Yeah

[oak chasm]

So, take the reciprocal of -1 to get the cosine.

[alpine sable]

Ima says -1/2?

[oak chasm]

That's not the reciprocal of -1.

[ocean seal]

Chai T. Rex

[oak chasm]

What does that become?

[alpine sable]

Stays -1

[oak chasm]

Right.

So, if secant is -1, cosine is also -1.

[alpine sable]

So for reciprocal it will always have 1 on top and the we use under it ?

[oak chasm]

Yep.

Or flip a fraction if you have one of those.

So, if the secant is 2/3, the cosine is 3/2.

If the secant is -4/5, the cosine is -5/4

But for nonfractions, yes, 1 over the number.

[alpine sable]

Can you help me solve this one

Idk what to do after getting 2.11

[oak chasm]

What is the question asking?

[oak chasm]

Oh, OK.

,w acos(-0.51)

[ocean seal]

Results provided by WolframAlpha

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

Requested by Chai T. Rex#7323

[oak chasm]

@subtle oasis Sorry, channel is busy.

@alpine sable Cosine is the x value, right?

[alpine sable]

Yeah

[oak chasm]

OK, draw a unit circle.

[alpine sable]

Yeah I got one on my screen rn

[oak chasm]

Then, draw the line where x = -0.51.

It'll be a vertical line that touches the circle at two points, right?

[alpine sable]

Yeah since it’s cos

[oak chasm]

OK, so you have two angles that touch the circle at those points, right?

You have one angle. How do you get the other?

[alpine sable]

It’s across from it but hold on I’m kinda having trouble getting to -.51 on the unit circle

[azure yew]

9 + 10 =

[oak chasm]

@azure yew Sorry, channel is busy.

[alpine sable]

It would be at around like 2pi/3 right ?

[oak chasm]

That's one angle.

How do you get the other?

[alpine sable]

4pi/3

[oak chasm]

No.

That's a number, not a "how".

[alpine sable]

Drawing a straight vertical line down

To line up with the other fraction

[oak chasm]

No, here's how you do it.

Start at angle pi.

Go clockwise to get the first angle, right?

[alpine sable]

5pi/6 is the next one right

[oak chasm]

No.

Start at angle pi.

You can go clockwise to get the first angle, right?

[alpine sable]

By angle pi you mean (-1,0) right

[oak chasm]

Yes.

That's where angle pi hits the circle.

And you can go clockwise to get to the first angle, right?

[alpine sable]

Pi/2?

[oak chasm]

Stop with the numbers please.

Please answer the questions.

[alpine sable]

Yh i see the next angle

While going clock wise one angle

[oak chasm]

Do you see that it's clockwise from pi?

OK.

How far clockwise from pi?

[alpine sable]

30 degrees

[oak chasm]

No.

How do you find how far clockwise an angle is from pi?

[alpine sable]

By checking the degrees ?

[oak chasm]

No.

We're working with radians.

Stop working with degrees, please.

[alpine sable]

Oh the pi fractions

[oak chasm]

No.

No fractions.

[alpine sable]

Then I’m not too sure

[oak chasm]

Did you get a fraction of pi for the first angle?

[alpine sable]

Ok so ima clarify something you wanted me to start at pi right ? After that go clock wise one angle right ?

[oak chasm]

What angle did you get?

[alpine sable]

This one

[oak chasm]

No!

What angle did you get?

[alpine sable]

I don’t know how to do this well that’s why I’m terrible at it

[oak chasm]

You got 2.11, right?

[alpine sable]

Yeah

[oak chasm]

You didn't get a fraction of pi, you got 2.11.

Please stop with the fractions of pi, since we're not dealing with those.

So, how many radians is that clockwise from pi?

[alpine sable]

1.03

[oak chasm]

Right!

Now the other angle is that counterclockwise from pi.

What angle is 1.03 radians counterclockwise from pi?

[alpine sable]

<@&286206848099549185>

[oak chasm]

@alpine sable Sorry, channel is now busy.

[alpine sable]

Give me like 2-4 min because I’m still struggling a lot on this

[oak chasm]

@alpine sable The angle increases as you go counterclockwise, right?

[alpine sable]

Yeah

[oak chasm]

So, what's pi + 1.03?

[alpine sable]

4.17

[oak chasm]

Right.

Which answer has 2.11 and 4.17 or nearby?

[alpine sable]

Answer D

[oak chasm]

Right.

Do you want to do another problem?

[alpine sable]

Yeah I have one for tan

[oak chasm]

OK.

[oak chasm]

@alpine sable One second. Last problem, we had this:

The top angle is just as far from pi as the bottom angle.

Does that make sense?

[alpine sable]

Yeah

[oak chasm]

OK, so you find out how far the first angle is from pi.

pi - 2.11.

That's 1.03.

Then the second angle is that far from pi.

pi + 1.03.

4.17

Does that make sense?

[alpine sable]

Oh yeah that makes it seem a lot simpler than I originally imagined

[oak chasm]

Yeah, you got confused into thinking it was a fraction of pi because I said to look at the unit circle, I think.

[alpine sable]

It’s because I didn’t know we could describe angles in radians

[oak chasm]

Oh, OK.

[alpine sable]

I’ve never done that I always used degrees, and fractions but now I got it

[oak chasm]

OK, let's do your tangent problem:
https://cdn.discordapp.com/attachments/490557019623915520/846997524832190494/image0.jpg

[alpine sable]

Alright

[oak chasm]

Now, here's a trick with tangent.

It gives a slope.

[alpine sable]

Dang

[oak chasm]

So, the tangent gives a slope of 3.3.

So remember that for later.

[alpine sable]

Ok

[oak chasm]

What angle has tangent 3.3?

[alpine sable]

Well wouldn’t we to arctan (3.3) ?

[oak chasm]

,calc atan(3.3)

[ocean seal]

Result:

1.2765617616837

[alpine sable]

And then go on from there

[oak chasm]

Right, so that angle.

[alpine sable]

Oh ok

[oak chasm]

Now let's think about this.

We have a line with a slope.

[alpine sable]

Yeah

[oak chasm]

,w plot 3.3x

[ocean seal]

Results provided by WolframAlpha

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

Requested by Chai T. Rex#7323

[alpine sable]

So it’s going to go diagonal

[oak chasm]

Right, like the graph above.

[alpine sable]

Yeah

[oak chasm]

So, see the upper right section?

That goes up and right from (0, 0)?

[alpine sable]

Yeah first quadrant

[oak chasm]

OK, now what happens if we start at that angle and add half a revolution to it?

[alpine sable]

It will be in quadrant 3 where the other half is

[oak chasm]

Right.

We get exactly the opposite angle going at the same slope the other way, right?

[alpine sable]

Sure

[oak chasm]

OK, so how many radians is half a revolution?

[alpine sable]

You want me to answer with numbers or pi

3.14 right ?

[oak chasm]

Either one.

Right.

So, if you have an angle, that angle plus pi will give the same tangent.

[alpine sable]

Oh ok so there’s 2 pi or 7.28 radians per circle, I didn’t know that

[oak chasm]

Because it makes the same slope.

Does that make sense?

[alpine sable]

Yeah

[oak chasm]

OK, you can also subtract pi.

You can add or subtract as many half revolutions as you want and you'll end up with the same slope.

So, we have:

,calc atan(3.3)

[ocean seal]

Result:

1.2765617616837

[oak chasm]

Add a half revolution.

[alpine sable]

4.41

[oak chasm]

Right, so which answer?

[alpine sable]

Adding pi to 1.27

D

[oak chasm]

Right.

[alpine sable]

Oh ok got it

[maiden carbon]

Ok still having trouble with this https://i.kawaii.sh/q9EZFkm.png
I know that they are congruent but how would i get the angles from the 3 sides

I was thinking to assume RVT was 90 total since it looks like it but it has no marking so im confused

[oak chasm]

No, don't assume.

[maiden carbon]

I need RS to be able to use trig on it

since then ill have all 3 sides

but I dont and thats what im trying to find

so this is a pre-trig problem (maybe?)

[ocean seal]

Chai T. Rex

[maiden carbon]

yes

i still cant use trig since i need 2 sides though

or am i thinking about this wrong

oh lmao wait i can use other triangle

[ocean seal]

Chai T. Rex

[oak chasm]

Top line is for left triangle. Bottom line is for bottom triangle.

[maiden carbon]

I was gonna do cos(6/12)

and get S

then subtract S from 180

and do the a/A = b/B for the rest

[oak chasm]

You don't know that it's a right triangle.

[maiden carbon]

oh right yeah i forgot

this is a review test for the whole year so yeah

[oak chasm]

Law of sines works for any triangle.

So, use it for the left and right, as I did above.

[maiden carbon]

I am confuse

[ocean seal]

Chai T. Rex

[oak chasm]

@quasi pulsar Sorry, channel is busy.

[quasi pulsar]

it’s ok

[maiden carbon]

Yeah i know law of sines i kinda forgot how to use it, it was a few units ago

all i remember is

a/sinA = b/sinB = c/sinC

the issue is that i need more than one side for that to work right?

[oak chasm]

What?

[maiden carbon]

hm?

I only have RV

[oak chasm]

No, you have a/sin(A) = b/sin(B) = c/sin(C).

Right?

[maiden carbon]

Right

[oak chasm]

So, you have everything as variables and it's still true, right?

[maiden carbon]

yeah

im just trying to figure out how that works

[oak chasm]

Read this ^

[maiden carbon]

yes i see the equation, why does it work for this problem though

[oak chasm]

No, read it.

Don't see it.

Read it.

[maiden carbon]

the issue im facing with understanding it is that afaik you need atleast all 3 sides of a triangle, or an angle and the opposite side

[oak chasm]

No.

Do you see how I got the second two equations?

[maiden carbon]

Well i dont know how you got them but i understand that RSV + VST is 180

the issue is that i dont know what they are split apart

I just know the sum

[oak chasm]

Right, you don't need to.

You keep trying to figure out irrelevant things.

Of course you can't find that, so that's obviously not the way to solve this since you can't do that.

When you can't do something, it's generally not the way forward.

[maiden carbon]

i dont know why this is relevant, i dont understand the equasion

or why it works

[oak chasm]

OK, you know law of sines, right?

[maiden carbon]

yes

[peak niche]

a/SinA =b/SinB = c/SinC ^

[maiden carbon]

yeah but as far as i know you need atleast multiple values for that

[peak niche]

Yea you need 2 sides and an angle or 2 angles and a side

[ocean seal]

Chai T. Rex

[oak chasm]

From the left triangle.

[maiden carbon]

yeah

but this wouldnt be solvable unless i had either RVS or RS right?

[oak chasm]

Stop with that.

You know some methods of solving it.

They aren't working for you, right?

[maiden carbon]

yeah

[oak chasm]

So maybe stop thinking you should use them.

For your methods, you need to have either of those.

For mine, no.

We're not using your methods, so we don't need the requirements of your methods.

[peak niche]

Give the angle an X value and solve by equation?

[maiden carbon]

AH i was confused i thought you wanted me to solve the first equasion

[peak niche]

Just an idea

[maiden carbon]

second equasion is the one thats actually solvable

since it has atleast one variable on each side

[oak chasm]

No, it isn't.

[maiden carbon]

wait it isnt?

[oak chasm]

Neither one is solvable.

We just want the equations for now.

Then, in the bottom two equations, we fill in things that are equivalent.

[maiden carbon]

why is the first equasion on the bottom there

i dont get how TVS/RS is equal to RSV/8

[oak chasm]

Law of sines.

[maiden carbon]

or are you interpreting all the triangles as one

instead of two

[oak chasm]

LAW OF SINES

[peak niche]

Find the other angles in terms of x

[oak chasm]

No.

[maiden carbon]

yes i know law of sines but its a different triangle

[peak niche]

Then make it = 180

[oak chasm]

One equation is for the left triangle.

@peak niche No.

[peak niche]

Awh

Ok

[oak chasm]

One equation is for the right triangle.

[maiden carbon]

https://i.kawaii.sh/Z7KwWAm.png

[oak chasm]

Do you see that one is for the left and one is for the right?

[maiden carbon]

Am confused by this

because its a different triangle for each

[oak chasm]

No!

[maiden carbon]

not the same one

[oak chasm]

Do you see that that's for the left triangle?

Both angles are in the left triangle, right?

Both sides are in the left triangle, right?

[maiden carbon]

oh right

[oak chasm]

Oh, I see.

You see that $\angle TVS$ is in the right triangle.

[ocean seal]

Chai T. Rex

[oak chasm]

Look at the top two equations.

[maiden carbon]

yeah i saw now

[oak chasm]

They're for the left and right trinagles.

[maiden carbon]

the angle is the same for both

[oak chasm]

Right.

I replaced one with the other.

Then I replaced one angle with 180 degrees minus its supplementary angle.

Does it make more sense now?

[maiden carbon]

yeah

on the last equsion why do you do 180-

if you are already solving for half

if you are using RSV

[oak chasm]

See how I get these from the second two equations?

Bah.

[ocean seal]

Chai T. Rex

[oak chasm]

See how I got these two equations?

[maiden carbon]

... no

i remember that you can put something in front of the sin but i forgot what it does

[oak chasm]

The bottom two equations here, multiplied by the denominator on the left.

This is algebra.

This isn't your trigonometry knowledge.

[maiden carbon]

im just a bit confused because why would it be sin(180-RSV) and not just sin(RSV)

[oak chasm]

Read this.

[maiden carbon]

yeah RSV+VST = 180 but if you are doing sin(RSV)/8 it should solve for RSV

[oak chasm]

What are you talking about?

The 180 minus is in the other equation!

[maiden carbon]

what

[oak chasm]

You're talking about something over 8.

[maiden carbon]

https://i.kawaii.sh/KImt2vF.png

im talking about this

[oak chasm]

That's in the TOP equation.

Do you see an 8 in that?

[maiden carbon]

oh wait

ok now im confused

you have 180-RSV in there, but you have it over 12

[oak chasm]

Right.

[maiden carbon]

if you wanted to solve for 12 i would assume you do VRT

[oak chasm]

What does solving for 12 even mean?

12 = 12.

[maiden carbon]

i mean

[oak chasm]

It's already solved.

[maiden carbon]

sin(VRT)/12

[oak chasm]

VRT?

Where do you see that anywhere?

[maiden carbon]

ok so holdup 180-RSV is VST and sin(VST)/12 is essentially the same thing as what you put

[oak chasm]

Right.

[maiden carbon]

but then why put 180-RSV

[oak chasm]

Because it's equal to what was there before.

So we can replace it.

[maiden carbon]

ah

[gilded cipher]

hey

can anyone help me with a question

[oak chasm]

@gilded cipher Sorry, channel is busy.

[maiden carbon]

im guessing i cant solve the last equation yet either

[oak chasm]

No.

[oak chasm]

Do you see how I got these ^

[maiden carbon]

yes, you put the denominator from one side and cross it to the other

[oak chasm]

Right.

[ocean seal]

Chai T. Rex

[oak chasm]

Do you see how I got that?

[maiden carbon]

uhh

where did RS come from it wasnt in the old equation

[oak chasm]

See these?

[maiden carbon]

yes i see them, dont understand them anymore

[oak chasm]

OK.

[maiden carbon]

this keeps getting more confusing because this is no longer what we are going off of

idk where RS came from

[oak chasm]

I was explaining that.

But you can't understand the last step.

If you forget what's happened, it's really hard to make progress.

Since every step is based on previous steps.

[peak niche]

If in doubt guess 9 that's my motto

[oak chasm]

@leaden ferry Sorry, channel is busy.

[maiden carbon]

you combined the last 2 steps and i dont get it

[oak chasm]

Do you get the previous steps?

[leaden ferry]

Ah, of course. I'll just repost it on the other channels that is not active...

[maiden carbon]

yeah i understand the very last step of the other image

[oak chasm]

OK, do you see that both left sides are the same?