help-0

[glass lichen]

$z=\frac{1}{2}\left(\frac{\sqrt{3}}{2}-\frac{1}{2}i\right)$

[ocean seal]

Mosh

[glass lichen]

thing in the bracket has modulus of 1

[chrome monolith]

So just do this ?

[glass lichen]

yes

that works too

[chrome monolith]

U remove the sqrt and put the half to the outside ?

[sullen nova]

Yo ho ho

If a family has 9 boys. What’s the probability of the next child being a boy?

[minor crypt]

still ~1/2

@sullen nova

[sullen nova]

Why

[minor crypt]

Because the question is not what's the probability of getting 10 boys in a row.

That 10th boy is indepent, in the sense that it doesn't matter how many boys/girls were born before him.

[glass lichen]

the birth of the 10th child does not matter on the previous 9

each birth is an independent event

[glass lichen]

you'd just go through by applying definition of modulus if you feel to do it that way

$\abs{z}=\sqrt{\left(\frac{\sqrt{3}}{4}\right)^2+\left(\frac{-1}{2}\right)^2}$

[ocean seal]

Mosh

[minor crypt]

I still dont know what modulus is.

why they dont teach that stuff in highschool

[agile compass]

Its the distance from the origin

[minor crypt]

oh really?

[glass lichen]

modulus is distance z is from another point

|z-0|

[minor crypt]

oh bruh

[glass lichen]

distance between z and 0

[minor crypt]

I saw modulus being used in another context

like with clocks:
it's 22 o'clock, you take mod(12)->it's 10 o'clock

[agile compass]

That's called modular arithmetic. Not modulus

[glass lichen]

that's modular arithmatic..

[minor crypt]

ooh mb

screenshot please

it's 2021

[shut bough]

$2-1

$\abs{z}=\sqrt{\left(\frac{\sqrt{3}}{4}\right)^2+\left(\frac{-1}{2}\right)^2}$

[ocean seal]

Draglom

[shut bough]

$\abs

[pliant estuary]

<@&268886789983436800> “test” in left corner

[tame falcon]

Thanks.

[fading citrus]

👍

[spiral solar]

i have a doubt in trigonometry

if sinx + siny = 2sin(x+y/2)cos(x-y/2)
then can we write sin^2 x + sin^2 y = 2sin^2 (x+y/2)cos^2 (x-y/2)

[glass lichen]

no

cause freshman's dream still isnt true, despite magic trig being present

[spiral solar]

😞

thanks tho

[vapid swift]

just multiply them you'll get a quadratic equation and then solve it

[fringe yoke]

The limit exists

[halcyon nova]

Ya ik

[fringe yoke]

What do you need help with exactly?

[halcyon nova]

How I get the value

[glass lichen]

have you evaluated a limit before..?

[halcyon nova]

Ya

With graphs

[warped phoenix]

Hey everyone

[halcyon nova]

Not piecewise functions

[fringe yoke]

It may be new for you to do it with piecewise functions

[glass lichen]

so you've done no algebra in the course for limits?

[halcyon nova]

No

[fringe yoke]

When x=1, the function is defined by: f(x) = x^3 + 5

when x<1, the function is defined by f(x) = x^2 + 5

To make sure there that there is a smooth transition, evaluate the limit at x=1 for both of these

[glass lichen]

it's not asking about continuity.. it just wants the values/existance of the limits

[halcyon nova]

Wait so how do I find the x value for these

[fringe yoke]

Then, you will see that the limit coming from the left (f(x) = x^2 + 5 at x=1) is the same as the limit from the right (f(x) = x^3 + 5 at x=1)

If the limit exists from both sides, then it is continuous and the lim x -> 1^- is the same as lim x-> 1^+ , so just evaluate one of these and you cacn solve a)

[glass lichen]

$\lim_{x\to 1^-} f(x)$ means the limit of f(x) to the left of x=1, so the function is defined by $x^2+5$ on $x<1$

[ocean seal]

Mosh

[halcyon nova]

It’s not letting me use that as an answer

[fringe yoke]

But if there isn't a smooth transition, then the limit doesn't exist altogether

[halcyon nova]

I think I have to plug in the x value

[fringe yoke]

No

[glass lichen]

yeah... you have to evaluate the limit...

[fringe yoke]

Just find the value of the function at that input

[halcyon nova]

I got 1

[fringe yoke]

???

[halcyon nova]

As the limit

[fringe yoke]

plug in x=1 to f(x) = x^2 + 5 or plug in x=1 to f(x) = x^3 + 5

[glass lichen]

what expression did you evaluate to get 1...?

[halcyon nova]

a.

[glass lichen]

not what I asked.

I asked what expression you evaluated that gave $\lim_{x\to 1^-}f(x)=1$

[ocean seal]

Mosh

[halcyon nova]

I plug 1 in for x

[glass lichen]

ok.. so how does (1)^2+5=1?

[fringe yoke]

$\lim_{x\to 1} x^3 + 5 = (1)^3 +5$

[ocean seal]

Tim O'Brien

[halcyon nova]

Not for that part

[glass lichen]

then what part are you talking about??

[halcyon nova]

For choosing which function to use

[glass lichen]

yeah...

[fringe yoke]

You can choose either one because the limit exists

The limit from both sides is the same

[glass lichen]

We're talking about a.. not c

[halcyon nova]

Ok I think I’m confused

[glass lichen]

$\lim_{x\to 1^-} f(x)$ means the limit of f(x) to the left of $x=1$

[ocean seal]

Mosh

[fringe yoke]

If the function is continuous, then $\lim_{x\to 1^-}f(x) = \lim_{x\to 1^+}f(x)$

[ocean seal]

Tim O'Brien

[halcyon nova]

Ohh

[glass lichen]

That is not what we are talking about

please stop distracting

[halcyon nova]

So I would use the first function

[glass lichen]

you'd look at what f(x) is defined as to the left of x=1

[halcyon nova]

x^2+5

[glass lichen]

so x<1 means f(x) =x^2+5

so $\lim_{x\to 1^-}f(x)=\lim_{x\to 1^-}x^2+5$

[ocean seal]

Mosh

[halcyon nova]

Now what would I need to plug in for x to get a value

[glass lichen]

x=1...

since polynomials have domain R, you can just plug in 1 without worrying about the sided-ness

[halcyon nova]

So it would be 6 as the answer

[glass lichen]

yes

[halcyon nova]

Ok nice it’s right

[glass lichen]

so then do b, 1^+ means to the right of 1

[halcyon nova]

Now for b.

So I would use the second function

[fringe yoke]

Since there is a smooth transition, the limit from both sides is equal

You can use either function it doesn't matter

[glass lichen]

Tim.

stop distracting.

Nowhere does the question talk about continuity / smooth transitions

[fringe yoke]

I am saying that the limit at x=1 is the same for both functions

[halcyon nova]

Is it would be 6 again as the answer

[fringe yoke]

whatever

[glass lichen]

yes, (1)^3+5=6

[halcyon nova]

Ok now for c. I would use the second function right?

[glass lichen]

so the 1 in the limit doesnt have a -/+ so it's the double sided limit

which is defined if the left and right handed limits agree to one value, per what Tim was saying previously

[halcyon nova]

Oh ya got it

[glass lichen]

$\lim_{x\to a}f(x)=L \iff \lim_{x\to a^-}f(x)=\lim_{x\to a^+}f(x)=L$

[ocean seal]

Mosh

[glass lichen]

so since the one sided limits exist and are equal, the double sided also exists

[halcyon nova]

Would f(4)= 22

[minor crypt]

yes

[halcyon nova]

Ok thx

[minor crypt]

so f(4) does exist

[halcyon nova]

And then I plug 22 into the equation

[minor crypt]

no

now you calculate the limit

[halcyon nova]

Oh ok

[terse merlin]

oh my bad

[halcyon nova]

X=4?

[minor crypt]

lim. f(x)=4 yes

[halcyon nova]

But I put 4 in that box and it said it was wrong

[tropic axle]

The limit is 4?

No x approaches 4

So f(x) approaches 22, no?

[halcyon nova]

f(4) is at 22 on the graph

[tropic axle]

Yeah, the limit should also = 22

[halcyon nova]

Oh

So I put 22 in both boxes?

[minor crypt]

no?

[tropic axle]

No, how?

[minor crypt]

16/4=4

[tropic axle]

Where'd the 16 come from

[minor crypt]

x^2

[tropic axle]

Where'd the +6 go

[minor crypt]

insignificant when ta-

oh wait

it's not limit where x->infinity

hehe mb

[tropic axle]

All good

It's 22 for both, fish

[minor crypt]

@halcyon nova so yes, both 22

[halcyon nova]

Ok

Ya that’s right

I am stuck on this one

[glass lichen]

how do you find slope of tangents..?

[halcyon nova]

I’m not sure

[glass lichen]

look at your notes then

[halcyon nova]

I don’t have any

[glass lichen]

well you should have some

[vague coral]

imagine taking math class without having any notes ;-;

[halcyon nova]

This is the last problem for this hw

Ok I got it

[slender girder]

do math students need latex?

[glass lichen]

nope

[spring hazel]

why?

[slender girder]

do you, ti-83?

[glass lichen]

cause they dont need it

[spring hazel]

but why?

[alpine sable]

Channel open or not

[glass lichen]

cause it's not a necessity...

this is just reading comprehension

[vague coral]

If you need to write a thesis, why not, but its not a necessity

[glass lichen]

The extent of my LaTeX is just to help people on here

[alpine sable]

$$\sum_{n=0}^\infty \frac1{2^{(2^n)}}$$

[slender girder]

oh so you do know

[alpine sable]

fk

[ocean seal]

macoro

[vague coral]

geometric series

[alpine sable]

its not

1/2 + 1/2^2 + 1/2^4 + 1/2^8 + 1/2^16 + ...

any help for this

is there an exact answer

[vague coral]

$\frac{1}{2^{2^n}} = (\frac{1}{2})^{2^n}$

[ocean seal]

Herels

[vague coral]

🤔

[minor crypt]

@slender girder can we like not share this many servers holyy

and u got a hxh pfp?

[slender girder]

hmm the chemistry is surreal

[glass lichen]

#chill if you want to have a discussion (or dms)

[halcyon nova]

I got 3 hw assignments left

[alpine sable]

<@&286206848099549185>

$$\sum_{n=0}^\infty \frac1{2^{(2^n)}}$$

[ocean seal]

macoro

[alpine sable]

any exact answer for this?

[quasi scarab]

theres no exact answer i think

[wraith cairn]

https://math.stackexchange.com/questions/583472/sum-of-infinite-series-1-1-2-1-4-1-16-cdots

[heady tusk]

what is h?

[charred flint]

SUPERPRO

WHAT'S A 30-60-90 TRIANGLE?

[heady tusk]

listen

could you do that without having the 30 degree angle

or do you need that

to get the answer

[charred flint]

YOU NEED IT

[vale wigeon]

depends on whether or not you know trig

[heady tusk]

oh ok I'm stupid

the rest ik

tysm

[vale wigeon]

PLUR WHY ARE YOU YELLING

[charred flint]

HE ASKED IN VOICECHAT FOR HELP

[heady tusk]

yeh ik

I'm so sorry

but I'm so tired

but I have to finish

Ik it's wrong

I'm so sorry!!

[warped phoenix]

can someone explain why there are +'s inside the parenthesis of the perfect trinomial?

[glass lichen]

it's not a perfect trinomial, and that's just the factorization

[minor crypt]

• • • = -

[warped phoenix]

@glass lichen ok basically just remember that a difference of cube is factored like that

because im prob thinking too hard into this

[glass lichen]

$a^n-b^n=(a-b)\sum_{i=0}^n a^ib^{n-i}$ in general

[ocean seal]

Mosh

[warped phoenix]

what does i stand for

also what is the weird big symbol

and what does n stand for

[charred flint]

do you know what a for loop is?

[warped phoenix]

no...?

[glass lichen]

dont worry about if you dont know it

[warped phoenix]

oh ok

[glass lichen]

I was just giving you the general difference of powers factorization

[alpine sable]

thx

fishraider

[celest hatch]

can anyone explain the nth roots of unity ?

👀 or gimme some notes

[charred flint]

so you wanna solve z^n=1 right?

and multiplication in complex numbers means you multiply the magnitude and add the angle

the magnitude bit means that z has to have length one

the angle bit means that n*angle equals 0 or 360 or 720 etc, whatever rotates back to (1,0)

so like for n=5, 1/5 of a turn works, 2/5 works, etc

and you get this pretty picture for what the roots look like

[dull onyx]

can someone explain Sigma to me:(

[celest hatch]

@charred flint i was talking about this 👀

[charred flint]

sigma means from (variable=bottom) to (top), add up the (inside at each variable)

@celest hatch yea I just avoided all that language, same thing

[celest hatch]

👀 oh..i got it bruh..thanks

[dull onyx]

hmm i think i get it

[celest hatch]

in simple words it is a kind of summation... you just need to put the values in the given function from lower limit to upper limit {as per given in the question} and add them all

[dull onyx]

ooo

thank u!’

[queen wigeon]

for example, $\sum_{i=1}^{10} i = 1+2+3+4+5+6+7+8+9+10 = 55$

[ocean seal]

mchen10

[dull onyx]

oh wow

can it square the numbers

[queen wigeon]

what do you mean?

[dull onyx]

like

get the square of each number

1^2

wait

[queen wigeon]

like this: $\sum_{i=1}^{10} i^{2} = 1+4+9+16+25+36+49+64+81+100$

[ocean seal]

mchen10

[dull onyx]

yes

kay thank u ive seen sigma around but never knew what it meant

[queen wigeon]

np

[frosty goblet]

Heya, can someone pleaes help me with this? I still don't really understand how I can get to the asnwer

ohh

[queen wigeon]

what do you get when you simplify the right side?

[frosty goblet]

So if you expand it gets to sina - sinb/sinasinb

[queen wigeon]

no

[frosty goblet]

oh lol

can you split it

[queen wigeon]

$\sin (a-b) = \sin a \cos b - \cos a \sin b$

[ocean seal]

mchen10

[queen wigeon]

here's the formula

[celest hatch]

Convert the cot function in the form of Sin and cos..

Cot = cos/sin

My bad

[frosty goblet]

kk thanks guys

[celest hatch]

[warped phoenix]

my book is saying that what's inside the parenthesis is a perfect square trinomial....i dont see it

[minor crypt]

(2x+1)²

[warped phoenix]

?

how did the 4x term magically disappear

[minor crypt]

mood

you get it now?

[warped phoenix]

😦

no

where did the 4x term in the middle go

when you did (2x+1)^2

[minor crypt]

let's write the two seperately:
(2x+1)(2x+1)

do this on a sheet of paper

[warped phoenix]

ok

[minor crypt]

use the disributive property

[warped phoenix]

so it becomes $(4x^2 + 4x + 1$

[ocean seal]

TheMane3

[minor crypt]

so where did the 4x go?

nowhere, it's right there

[warped phoenix]

ohhhhhhhhhhhhhhhhhh

🤭

i see

[minor crypt]

remembering these 3 will go a long way

[warped phoenix]

the first two are examples of perfect square trinomials, and the third one is a difference of 2 squares right?

[minor crypt]

correct

[warped phoenix]

yayyyyyyyyyyyyyy

[sleek elbow]

Im confused about trig, what happens to go from 6sin(50°) = AC to 4,60 = AC. Like, what does the calculator do to the 50° to get to 4,6?

Basically like, if I wanted to go from 6sin(50°) = AC to 4,60 = AC without using a calculator, what would I do

[placid zinc]

That looks like a typo

,w 6sin(50 degrees)

[ocean seal]

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[placid zinc]

Oh the , is a decimal place hah I'm so English

[sleek elbow]

😄

its like, what does a calculator do to an angle to get the missing side

[placid zinc]

Okay yeah on your calc do sin(50) then multiply that by 6

[sleek elbow]

what does the sin function do

I want to understand what the calculator is doing to understand trig fundamentals you know?

So its not that magic thing the calculator does

[minor crypt]

have you learnt about radians yet?

[placid zinc]

So the sin function takes advantage of a triangle property: that if you know the ratio of two sides, you also know the angle of the triangle.

[warped flower]

sin fxn is basically an odd fxn that varies between -1 and 1 kinda

u use it in mathematics and waves

[placid zinc]

sin is the function that converts between those. Know the angle, get the ratio.

[sleek elbow]

waves 👀

[warped flower]

which are basically sin or cosine fxns

even in AC

Alternating current

[minor crypt]

yes, the sin fucntion is a wave actually

[sleek elbow]

so if I wanted to do it on paper, lets say, sin(5/7), what would I do

[minor crypt]

,w graph sin(x)

[ocean seal]

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[sleek elbow]

oh oops

wait

[minor crypt]

wave

[placid zinc]

Haha that's for a higher class. It's important you know what sin is, but actually calculating it isn't possible for you right now

[minor crypt]

can't

[sleek elbow]

thats frustrating

[minor crypt]

wait there's a way?

to calculate a random sin I mean

[warped flower]

sin 5/7 is basically the value of height of a triangle and hypotenuse

where 5/7 is the angle bw hypotenuse and base

[sleek elbow]

Like if I want to calculate sin(30°) on paper, I couldnt?

[warped flower]

yea

u can

[minor crypt]

we just memorize that one

[warped flower]

it is 1/2

[minor crypt]

[placid zinc]

You can actually calculate sin(30) with pythag haha

[sleek elbow]

you know what I mean

any angle in there

[placid zinc]

But that's one of the very few

[warped flower]

just memorize sin 0, 30,45,60,90

[minor crypt]

we memorize 0, 30, 45, 60, 90

[warped flower]

every other trig value

can be derived frm these sine values

[sleek elbow]

sin(64°) there we go, is there a way for me to calculate that?

[minor crypt]

nope

[placid zinc]

The rest are not something that can be exactly calculated, the calculator uses approximation methods

[minor crypt]

not that I know of

[sleek elbow]

THATS SO FRUSTRATING

[warped flower]

sin (60+4)

u can use that

[minor crypt]

no lol

whats sin(4)

[warped flower]

and technically sin 64 will be pretty close to sin 60

[sleek elbow]

I feel like it is in the way of me understanding it completely

that I cant do it on paper

or even just know what the calculator is actually doing

[warped flower]

no shit sherlock but it will still give u a better case than sin 64

[minor crypt]

the only problems you'll get, you will be able to do on paper

[sleek elbow]

got an example?

[minor crypt]

you'll get stuff like sin(15°) where you use the half formula and stuff

[sleek elbow]

oh

[placid zinc]

Sorry haha. I felt that way too. Ultimately you'll get used to the idea that the sin function is too good for paper

[glass lichen]

0,30,45,60,90 are called exact value angles

[sleek elbow]

too good for paper 😕

[minor crypt]

more like too good for human

[glass lichen]

so you could compute sin(75) exactly for example

[sleek elbow]

But isnt it known how the function works? Someone had to invent in, no?

[glass lichen]

yeah, you compute fractions to however many decimal places you'd need

[warped flower]

ur going too deep into it dawg just memorise 5 values and chill

that’s all

[sleek elbow]

I wanna understand

[glass lichen]

No, it's important to ask why stuff is true / how it works

[minor crypt]

when you see radians, it will make a bit more sense

[glass lichen]

Yeah unfortunately you cant really understand trig / what the functions mean/do to an angle until you hit the unit circle

right angle trig just says "this function means this ratio"

[sleek elbow]

jesus what is this

[warped flower]

na obv it is but u cant find sin 67 in any way possible maybe simplify it a bit into another angle but calculating the exact value without a calc is retarded

[minor crypt]

el unit circle

[glass lichen]

No need for the r-word.

[warped flower]

bruh what 😭😭😭

[minor crypt]

it may seem hard, but there's a lot of tricks to easily memorize them

[warped flower]

tf is the r word now

[glass lichen]

refer to the last word.

[sleek elbow]

My mind wants to know so badly how the calc goes from

sin(50°)

to

0,766

[warped flower]

y’all are ❄️ it’s just a word chill out

[minor crypt]

fun fact: being "en retard" means you're late in French

[glass lichen]

yeah, retarding device is a brake

[warped flower]

exactly

[minor crypt]

again, when you get to the unit circle, it will make a lot more sense

[warped flower]

so retard just means little slow than the regular bunch

[glass lichen]

calling someone a r-word however is never ok.

anyway

[warped flower]

never did

[glass lichen]

cool

[glass lichen]

there are ways to compute it if you work in radians (a different angle measuring system)

re: Taylor Series

[sleek elbow]

ye :/ So there is no real sin function, like I would Imagine a function like this for example

f(x) = 2x + 4

So now I want to know if there is

sin(angle) = [something here]

[sleek elbow]

👀

[minor crypt]

It's really nice that you're asking yourself all these question, but don't try to rush the answers too fast. You'll get there eventually.

[minor crypt]

there is, I just grapghed it earlier

,w graph sin(x)

[ocean seal]

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[minor crypt]

this is what the sin function looks like

[sleek elbow]

what is it written down?

[glass lichen]

y=sin(x)

[minor crypt]

f(x)=sin(x)

[sleek elbow]

wait

but like

f(x) = sin(x) thats fine

but

sin(x) = [what goes here]

[minor crypt]

something in radians

oh no wait

sin(something in radians)=a value between -1 and 1

[glass lichen]

$\sin(x)=\sum_{n=0}^\infty (-1)^n\frac{1}{(2n-1)!}x^n$

from memory?

[sleek elbow]

but at least that satisfied me

[ocean seal]

Mosh

[minor crypt]

wtf is that

[glass lichen]

maclauren series

[minor crypt]

that scares me

[alpine sable]

what is that O_O

[sleek elbow]

so if I plug in the angle for all x's on the right side I will get opposite side divided by hypothenuse?

[minor crypt]

not quite

[sleek elbow]

🤔

[minor crypt]

The sin you learn with triangles doesn't directly translate to sin in the unit circle. Don't get me wrong, it's still the same sin, just applied differently.

[sleek elbow]

Okay but this describes what is being done to the angle to get the opposite divided by hypothenuse?

[minor crypt]

I have no idea what that describes

[vague coral]

its just an approximation of sinx

[glass lichen]

$\sin(x)=\sum_{n=0}^\infty (-1)^n\frac{1}{(1+2n)!}x^{(1+2n)}$

is the correct one

[sleek elbow]

okay but thats what is being done to x?

[minor crypt]

+or- 1/(odd number)factorial times angle to the nth power

[ocean seal]

Mosh

[minor crypt]

and now its even more complicated

[vague coral]

???
its just a formula to calculate sin of something

[sleek elbow]

So this is exactly what sin() is doing to the angle to get the opposite divided by hypothenuse?

[minor crypt]

so positive or negative, 1 divided by an odd number factorial, multiplied by the angle to that odd number

[sleek elbow]

not sure if im tripping somewhere

[vague coral]

Its a different topic

Maclaurin series is used to find an approximate value of sin(x)

It has nothing to do with hypotenuse

[minor crypt]

is used? you sure about that

I'm betting 100$ no more than 3 people have used it this month

[vague coral]

What grade are you?

[sleek elbow]

9

[minor crypt]

me?

[glass lichen]

Newton used the concept to compute pi accurately, much faster than previous attempts

[vague coral]

yes you

[glass lichen]

though iirc he used tan's

[minor crypt]

graduatin hs tommorow

[sleek elbow]

Sin(x) = opposite side divided by hypothenuse

so then

opposite side divided by hypothenuse is equal to the stuff from the picture right?

[minor crypt]

hmm

[glass lichen]

if x is acute and in radians, yes

[sleek elbow]

what does acute mean?

[glass lichen]

0<x<90

[sleek elbow]

oh okay

THANKS

FINALLY

[glass lichen]

0<x<pi/2 but I digress

[minor crypt]

oh yay finally

[vague coral]

but why are u explaining maclaurin series to a 9th grade

[sleek elbow]

there is a function that does all this thats very complicated

thats all I needed to know

[glass lichen]

They wanted to know what sin(x)=

so I told them

[minor crypt]

lmaooo

[vague coral]

[minor crypt]

you mightve traumatized the dude

[glass lichen]

and I didnt explain anything, I just posted it

[sleek elbow]

its all good

no need for explanation I didnt understand a thing about that formula

I didnt want to either

just wanted to know that there is one

and see it

[minor crypt]

it's gonna take you a semester to understand trig (not that formula though)

so u shouldnt rlly expect to quickly understand all of it by asking in a disc server

[sleek elbow]

of ofc not

[vague coral]

I started to understand trig after 1 year tho

[sleek elbow]

just wanted to see the formula

that it

[vague coral]

The formula Mosh gaves you is just an approximation.

[minor crypt]

what grade are u in Herels?

[sleek elbow]

oh thats fine

Now im comfortable just using a calculator

[vague coral]

I'm doing studies to enter an engineer school

[minor crypt]

school or college?

[vague coral]

Its complicated

[minor crypt]

[vague coral]

Search in google : Classe préparatoire

[minor crypt]

ah you're french

[vague coral]

No, but I speak french

[minor crypt]

wait one of the first results was Casablanca

are you moroccan?

[vague coral]

No

[minor crypt]

:(

[vague coral]

Look at my profile

[minor crypt]

ooh cote d'ivoire

so you get your 'bac' this year, right?

[vague coral]

Last year

[minor crypt]

oh nice

you only need one more year of this preparation thing?

and then you can go to college?

[vague coral]

Yup

[minor crypt]

good luck man

[vague coral]

thank you, its going to be hard as fck

[minor crypt]

it wouldnt be fun if it was easy

[vague coral]

I need to sacrifice this year to succeed

Goodbye video games, goodbye internet

[cosmic granite]

hi! I'm dealing with a complex problem i've never seen before. I'm trying to find a common ratio for 2 values. The problem is: Let's imagine there is a box. There is a chance you find this box empty if you open it and there is also a chance you find something in it. The chance of finding something should be calculated this way:
1- Day starts at 12 AM and ends at 12 AM. Total of 24 hours. Each hour passes, the chance of finding something in this box gets higher. until the 24th hour, the chance of finding something inside reaches it's maximum. You can open the box unlimited times per day to check if there is something inside.
2- Everytime something is found in this box, the chance of finding something again gets lower. When nothing is found, the chance of finding something inside this box becomes maximum. The chance gets lower everytime you open the box and find something inside. Until you successfully found something 100 times inside the box, chance gets 0.
3- I should find a way to calculate the chance of finding something inside this box based on 2 variables. 1st: What hour is it (from 1 to 24), and how many things found (from 0 to 100)

[minor crypt]

$P(finding something in the box)=\frac{H}{24} \times \frac{100-N}{100}

where H=hour of the day and N=amount of things found in the box$

@cosmic granite

wait that's wrong

[cosmic granite]

uhm

[placid zinc]

This seems like a very soft explanation for something that you likely want hard numbers for.

[minor crypt]

still wrong

[placid zinc]

how does the odds increase every hour? How do the odds decrease upon finding an object?

[minor crypt]

I think it's safe to assume it's a linear increase.

[placid zinc]

It seems a bit like opening as many times as possible will just always get you max items?

[cosmic granite]

there is no specific odds given. except for if items found = 100, chance becomes 0 no matter what time is it

[ocean seal]

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

[minor crypt]

I think that's it

[cosmic granite]

yes, if you open as many boxes as possible in a day, it will only give you 100

i'll try that ashfraf!

[minor crypt]

$P(finding something in the box)=\frac{H}{24} \times \frac{100-N}{100}

where H=hour of the day and N=amount of things found in the box$

[ocean seal]

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

[placid zinc]

Is it possible to find 100 items in hour 1?

[cosmic granite]

everything is possible if you got unlimited tries

[minor crypt]

does that matter

[placid zinc]

You have to know more about this system you're describing

[cosmic granite]

but you shouldn't have the time to try unlimited tries in 1 hour for a human

[placid zinc]

This ain't enough info

[cosmic granite]

sadly this is the info i was given xd

[halcyon nova]

Is this channel in use?

[minor crypt]

Kaynex, he only has to give the ratio. Not find the chance for an exact situation.

[minor crypt]

[halcyon nova]

Wat

[minor crypt]

no

go ahead

[halcyon nova]

Ok cool

[minor crypt]

still no screenshots

[halcyon nova]

Do u see it

[minor crypt]

yeah its find

fine*

[glass lichen]

double angle then get sin(t), cos(t) and tan(t)

[halcyon nova]

Umm could u explain that a little more

[glass lichen]

well do you know double angle formulas...?

[minor crypt]

bruh I read that as 20

[halcyon nova]

Oh I did too

[minor crypt]

lol

[cosmic granite]

@minor crypt the solution you gave me seems to work. i'll run more simulation tests and let you know

[halcyon nova]

So I just need it multiply it by 2?

[minor crypt]

you making a game?

[glass lichen]

so that's a no..

$\sin(2x)=2\sin(x)\cos(x)$ for example

[ocean seal]

Mosh

[cosmic granite]

yes

[minor crypt]

wtf u type that fast?

or were u expecting the question

[glass lichen]

?

[halcyon nova]

So what equation do I need to use to for a.

[glass lichen]

I.. just posted it?

[halcyon nova]

Oh

[minor crypt]

it took you less than a second to type that formula

[glass lichen]

I just posted double angle for sine.. and a is sin(2t)

[halcyon nova]

Ok I’ll be back in a min

[glass lichen]

Ok..

[minor crypt]

I wanna have that typing speed

I type about 70wpm (letters only)

let's not talk about symbols and number

literally can get as bad as 8wpm if I don't know where to find that symbol

[halcyon nova]

Ok I finished for a.

Now what’s the equation for b.

[pallid sail]

u should use the identity sin^2(x)+cos^2(x)=1

but keep in mind that cos is negative in the second quadrant

[halcyon nova]

Wait how do I put the squared when I plug in the value for sine

Cus I have the value of sin(x)

[pallid sail]

sin^2(theta)=9/64

u just raise it to the power of 2

[halcyon nova]

Ohh

Got it

[pallid sail]

ok so i've got a rather simple problem from analytical geometry that is stumping me

i've got a circle with its center at 4 and -3

and it touches the line y = -6

i've tried finding the diameter by replacing the x and y coords with 0 and -6 respectively in the circles equation

but for whatever reason it gives me the wrong diameter?

it should be r^2 = 9

[alpine sable]

could you show the original question as stated? or preferribly, show a pic of it

[pallid sail]

they havent given us its equation, we only know that its concentric to that circle

we were also told that it touches the x axis

[alpine sable]

wait what? where's the "center at 4 and -3" portion indicated? can you please post a pic of the question?

[minor crypt]

y=-6 does not have only 0 as an x-coordinate

[pallid sail]

Its concentric to the circle whose equation is above us

doesnt that mean that their center coordinate is the same?

[minor crypt]

it touches the lines y=-6, but their intersect is not necessarily (0;-6)

[alpine sable]

yes it does, but you aren't answering my question

[pallid sail]

yeah idk why i wrote those k and n values

i replaced the coordinates (0,-6) in the equation

[minor crypt]

that's where you went wrong

[pallid sail]

i got the coordinates from this formula

[minor crypt]

their intersect is not (0;-6)

[alpine sable]

that isn't either my question.

[minor crypt]

,w graph x^2+y^2-8x+6y

[pallid sail]

I already told you, there is no equation. "The equation of the circle that is concentric to the circle x^2+y^2-8x+6y=0 and touches the x axis and the line y=-6 is:"

[minor crypt]

the issue has been found already

[alpine sable]

i wasn't asking for the equation but for the question, but yeah you've been told your issue.

[minor crypt]

you replaced x with zero, that's where you went wrong

[pallid sail]

yeah thanks im dumb

i got confused because i was using this equation x^2+y^2-8x+6y=0 in geogebra to check where they intersect

[alpine sable]

whenever you are asking something here, be sure you include your question as stated instead of throwing info vaguely because it will likely cause more confusion.

[minor crypt]

we can see it fish

[halcyon nova]

Ik

[minor crypt]

again, there should be a formula somewhere in your textbook

[halcyon nova]

I tried using this

It didn’t work

[minor crypt]

the "trick" is to write it as: (sin²x)²

[pallid sail]

by the way, could u help me on how to actually solve my problem?

do i just use the touch equation or something

r^2 * (k^2 + 1) = (kp - q + n)^2

[minor crypt]

what is the problem again

[pallid sail]

i just need to find the diameter

"The equation of the circle that is concentric to the circle x^2+y^2-8x+6y=0 and touches the x axis and the line y=-6 is:"

[minor crypt]

just continue, you're on the right track

[pallid sail]

yep it gave me the right answer

[minor crypt]

1. find the intersect of y=-6 and the circle
2. use the r²=.. like you tried before

[pallid sail]

however i havent used the fact that it touches the x axis at all

so thats making me doubt the way i solved it and think that i just got the right answer by sheer luck

[minor crypt]

solved=solved

if anything, give yourself a pat on the back for finding a simpler way to solve the problem

[pallid sail]

using the x axis gives the same result so i think that its the correct way

sorry for bothering u with such a simple problem and thank you very much for guiding me

[halcyon nova]

It says I didn’t simplify enough

But the answer is right

[minor crypt]

hmm

[pallid sail]

(1-cos2x/2)^2

is sin^2(x/2), not sure if that will help you though

[halcyon nova]

So what should I change?

[minor crypt]

I was thinking maybe get rid of the denominator '2'

put it outside the brackets

[halcyon nova]

I only have one check left

[minor crypt]

oh no

[halcyon nova]

Next try has to be right

Maybe the cos4x/2 should be cos2x?

[minor crypt]

no

absolutely not

[halcyon nova]

Aghhh

Should we get another perspective?

[minor crypt]

I still think getting 1/2 out of the brackets is the solution

so you write is as 17/8

times...

[halcyon nova]

Hm

I’m gonna be very sad if I get this wrong

[minor crypt]

u should ne

be*

this is exactly why I hate online tests/hw

does your teacher check the answers him/herself?

[halcyon nova]

It auto grades

[minor crypt]

:(

what if you just multiply 17/4 with everything

[halcyon nova]

I don’t think it would work

Cus it wouldn’t say my answer was right if I was that far off

[minor crypt]

-17/8 (-3 + 4 cos(2 x) - cos(4 x))

[minor crypt]

it's not far off though

this is my final guess

75% chance it's correct

(based on nothing)

[halcyon nova]

Should we try to get someone else?

[minor crypt]

not sure what they could do

but if you wanna wait it out, sure

[alpine sable]

what's the issue?

[halcyon nova]

This

It says my answer is right but not in the right form

[minor crypt]

no one knows what your teacher typed as the correct answer

[halcyon nova]

So we are trying to find another way to write it

[minor crypt]

trust me and try this

[halcyon nova]

Will u help me redo the problem if it’s wrong?

[minor crypt]

redo the problem?

wdym

[halcyon nova]

I get another similar problem if I get it wrong

But I don’t wanna do all this over again

It took me like 30min for this

[minor crypt]

understandable

[alpine sable]

the issue comes with the word "simplified", there is no strict defn of "most simplified" version, so yeah your teacher should have kind of a different and better way of grading

that doesn't rely on hoping to post the same answer as them

[halcyon nova]

This kinda makes sense

[minor crypt]

it's one of the two

do you have a textboox @halcyon nova

[halcyon nova]

This is an example

[alpine sable]

then yeah, write it in the expanded form

[minor crypt]

this one then

[lime harness]

How do I solve for r? A/2Pi = r^2 + rh

ik i can factor but then i still have r in there

[halcyon nova]

Ey

[lime harness]

A/2Pi = r(r + h)

[halcyon nova]

I write this?

[minor crypt]

yes

actually wait

[alpine sable]

@lime harness please read #❓how-to-get-help , this channel is occupied.

[minor crypt]

begin with 51/8

then cos (2x)

and finally cos(4x)

share a screenshot before you send it

[minor crypt]

that's right

[halcyon nova]

Ok moment of truth

[minor crypt]

now say "bismillah" and send it

[halcyon nova]

YESSS

IT WORKED

[minor crypt]

the power of Islam

[halcyon nova]

Finallyyyyy

[halcyon nova]

JAK bro

[alpine sable]

so your teacher has a concept of "most simplified" as the expanded form rather than the factored form, remember this for the next problems.

[halcyon nova]

I have 5 questions left of my hw

Then I’m done and it’s summer break

[minor crypt]

I have summer break and I'm helping with homework

what's wrong with me

[halcyon nova]

Ur earning favors🤷‍♂️

[minor crypt]

true

I like maths and I like helping people That's why I'm here I guess

[halcyon nova]

Nice

frikin heck

Right answer wrong format

[minor crypt]

not again

[halcyon nova]

😭

[minor crypt]

this one is probably: sqrt(2)/4 + sqrt(6)/4

[halcyon nova]

Not that either

I’m gonna die

[minor crypt]

[strong citrus]

Every even integer greater than 2 is
the sum of two primes.

Is this correct?

[minor crypt]

yes

[strong citrus]

How?

[minor crypt]

I found a way but it seems really unnecessary

you can write the denominator as sqrt(2)^4

[halcyon nova]

But it says to rationalize the denominator

[minor crypt]

hmm true

[halcyon nova]

Maybe I need to simply one of the squares

Sqrt(6) maybe

[minor crypt]

maybe just 1/4*(sqrt(2)+sqrt(6))

[halcyon nova]

🤔

[minor crypt]

it's the only "rationalized" option left

this is what I was thinking at first

[halcyon nova]

Ya but there can’t be a radical in the denominator

[minor crypt]

yup

[minor crypt]

so that's why I'd go with this one, only option left

[wraith cairn]

lol this is the most useless formula I've ever seen.

[halcyon nova]

We finished that

[halcyon nova]

Do u have any ideas for this^

[minor crypt]

how many tries do u still have?

[halcyon nova]

Last one

[minor crypt]

[halcyon nova]

I only get 3 tries

[minor crypt]

I found another way, but unnecessary again:
$\frac{\sqrt(2)*(1+\sqrt(3))}{4}$

[ocean seal]

Axhraf

[wraith cairn]

that is right, just check it with a calculator.

[minor crypt]

I'd go with this one tbh

fishraider talking to fish

[halcyon nova]

What about this?

[wraith cairn]

no

why would you use that

[minor crypt]

lmao

sqrt of sqrt

that's the sketchiest thing

[vague coral]

sin(30+45)=sin30cos45 + sin45cos30

[minor crypt]

we know

he solved it already

[halcyon nova]

I’m gonna try it

[minor crypt]

nooo

[halcyon nova]

It worked.

[minor crypt]

ur kidding

[halcyon nova]

😂

[minor crypt]

nah

nonono

bullshit that worked

[minor crypt]

wtf

ur teacher is quirky af

who'd write it like that lmaooo

[halcyon nova]

Last assignment of this cancer class

[wraith cairn]

are you sure the program that looks at your answers isn't just looking at the value of your answers.

I'm pretty sure sqrt6 + sqrt2 over 4 would've worked.

[halcyon nova]

I tried that

[wraith cairn]

you tried sqrt 6 + sqrt 2 over 4? @halcyon nova

[halcyon nova]

Yep

[halcyon nova]

^

[wraith cairn]

wut...

that is incredibly stupid then.

[halcyon nova]

Yep

Anybody there?

[warped flower]

what’s good

use double angle formula for this one

[halcyon nova]

Nvm I got it

[alpine sable]

Could anyone help me?

I am clueless

[upper pebble]

use the formula in the top right corner

[halcyon nova]

https://cdn.discordapp.com/attachments/858855159726473226/858855176332378142/image0.jpg

My answer is right but it needs to be simplified

[alpine sable]

💔

[alpine sable]

So simplify it

👁

[halcyon nova]

I’m not sure how

[warped flower]

fac

[alpine sable]

I’m not sure how to either

😭

[warped flower]

bruh

why tf do u have raise to the power 4 and 2

[upper pebble]

can you find the area of the base Moazan

[warped flower]

it’s simple addition of sins or cos

[alpine sable]

I can’t with just the width

[halcyon nova]

@warped flower let’s go to channel 2

[upper pebble]

the object is a square pyramid, meaning the base is a square, so all of the square's sides are equal length

[alpine sable]

So we have the width of 17.2 cm

Oh so 17.2 x 17.2

is the base

[upper pebble]

correct

[alpine sable]

And the perpendicular height is 24.4?

[upper pebble]

yes

[alpine sable]

Alright tysm!

[upper pebble]

np

[halcyon nova]

https://cdn.discordapp.com/attachments/858855159726473226/858855176332378142/image0.jpg

I need help simplifying this

Answer is right but it needs to be different form

[warped flower]

u hundos doing a test or sum rn 😂

u desperate

[halcyon nova]

I have 2 questions left of my hw

It’s my last assignment and I’m done

[warped flower]

ok so look up addition formulas for coz and sin

and see which one gives u an answer in the form of cos x cos y

and follow the steps

[halcyon nova]

Do u know which one I should use?

[glass lichen]

use the one for cos(x)cos(y).. since that's what you have..

$\cos(a)\cos(b)=\frac{1}{2}(\cos(a+b)+\cos(a-b))$

[ocean seal]

Mosh

[warped phoenix]

6x^2 - 7x - 20

[halcyon nova]

Does this mean I have to restart the question?

[halcyon nova]

What’s the equation for sin?

[glass lichen]

what do you mean...?

[halcyon nova]

sin8x-sin4x

[glass lichen]

cba to tex it

[urban mural]

Hey guys can someone dm me real quick ive a maths question regarding time and money

[alpine sable]

wait till some mod give you consent

[vague coral]

[alpine sable]

<@&268886789983436800>

[atomic trellis]

bruh what is wrong with you

[sly mantle]

ty

[atomic trellis]

he got banned

[warped flower]

bruh

[alpine sable]

ty rojo

[warped flower]

i really thought someone needed help

[atomic trellis]

this guy is on something

[warped phoenix]

lmao wtf

did i see that right?

[atomic trellis]

the guy who got banned that is

[warped flower]

on cock

[vague coral]

[warped flower]

i mean coke

[warped phoenix]

yeah i saw it for like half a sec wtf

[warped flower]

🤭

[atomic trellis]

bruh

[vague coral]

its the same dude

[warped flower]

bro

[alpine sable]

[atomic trellis]

just ask

omg

its this guy again

[vague coral]

...

[sly mantle]

b&

[alpine sable]

谢谢

[atomic trellis]

why is this guy trying to get banned from a math server

[warped flower]

ahlie 😭😭😭

fax

[vague coral]

well

[warped flower]

he really mathematically gay

[alpine sable]

idgi blocked

[golden birch]

1+1=?

[warped flower]

ur mum

[vague coral]

10 in binary

[sly mantle]

@golden birch don’t troll

[atomic trellis]

(e^pi*i)+2^2-1

ez

[golden birch]

I thought this is a help channel 😓

[vague coral]

You are boring

[atomic trellis]

it is but please be serious

[sly mantle]

it’s not a troll channel

[warped flower]

bro’s in 1st grade

[atomic trellis]

i figured the answer

(e^(pi*i))+2^(2)-1

[warped flower]

u really went that far huh

[atomic trellis]

(e^(pi*i)) is equal to -1, 2^2 is 4, so -1+4-1=2

[atomic trellis]

yes, yes i did

[quiet crown]

pog

[alpine sable]

ln(e) and let's move onto #chill

[warped flower]

sex

[sly mantle]

everyone else please don’t shitpost

@warped flower knock it off

[atomic trellis]

natural log of e?

[alpine sable]

yes

[atomic trellis]

ok

[golden birch]

(ln e)^6+(ln 1 *30595)+ln e

[warped flower]

i saw vex and thought sex

[quiet crown]

Nice one.

[sly mantle]

next shitposter gets muted

[golden birch]

Shit got serious, I'm really sorry for that.

Anyways this channel is available for anybody just post your question underneath me

[velvet citrus]

Compute the indicated product.
−1 3
4 0
7
3

well that didnt paste well

i have a matrix and its asking me to compute the indicated product how do i do that

-1 3 7

4 0 3

[placid zinc]

Product of what and what?

[visual kernel]

how to model with trig sine or cosine wave

the cat clock movement

<@&286206848099549185>

[stable crag]

i suggest drawing the problem out

and labelling the different points of what its asking for

[visual kernel]

I tried but its confusing

[stable crag]

take each eye individually first

and work out when they both reach the top

[visual kernel]

how do u work out

[jagged hemlock]

oh man

ant eyes

I cant read that

[stable crag]

open original and zoom in homie

[jagged hemlock]

yup

I can see it...

I cant see it at all

[stable crag]

use your computrer

[jagged hemlock]

??

woah

way clearer

[stable crag]

same image

...

[jagged hemlock]

I zoomed too.

[stable crag]

anyway

one eye takes 14 minutes to close and open

one eye takes 21 minutes to close and open