help-0

[ornate peak]

yeah i used that thanks

Nah i was solving some sample papers

[empty vigil]

Hello

I was trying to write my question by I realized that I dont understand what I want. LOL. Nevermind for now 🙂

[dull wedge]

I've solved the recurrence formula for the fibonnaci sequence, but I don't quite see how that helps me here

[ancient saddle]

Hello, what did you get after solving the recurrence formula?

[dull wedge]

1/sqrt(5) * ((1 + sqrt(5) / 2)^n - (1 - sqrt(5) / 2)^n)

[oak chasm]

Are you missing parentheses?

[dull wedge]

oh yeah oops

trivially the F(n+1) grows faster

but uh

solving that mathematically

[placid zinc]

Consider that |(1 - √5)/2| < 1

As that exponent gets large, that term goes to 0

@dull wedge

[dull wedge]

that is true

[placid zinc]

Should be very easy to get that limit, with that simplification

[wise zealot]

I don't necessarily have a question about math but has anyone ever read "The Landlady" Its the story where the guy needs a hotel and the lady kills him

[fiery berry]

Hi does anyone have gcse additional extended math quadratic sample questions

[oak chasm]

@dull wedge On the last line, the things to the power -n go to zero as n goes to infinity.

[vale wigeon]

@round delta no

we do not solve things for you here

[round delta]

oh sorry

[vale wigeon]

@reef atlas are you sure you want the first digit of 2^(2^2021) + 1, and not the last?

knowing the first digit of 2^(2^2021) + 1 would seem to require knowing the value of log_10(2) to some seven hundred decimal places

[oak chasm]

,w N[Log[10, 2], 700]

[ocean seal]

Results provided by WolframAlpha

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

Requested by Chai T. Rex#7323

[livid cypress]

need help

too hard

[oak chasm]

@livid cypress How do you find the slope of the tangent at a point on a curve?

[livid cypress]

differentiate it

u get rx^r-1

[oak chasm]

OK, so what is the slope at x = 1?

[livid cypress]

r^r-1

[oak chasm]

Sorry?

[livid cypress]

what

[oak chasm]

Why not fill in 1 for x in what you said the derivative was?

[livid cypress]

r(1)=r?

[oak chasm]

OK, so use point-slope form of a line.

(y - 1) = r(x - 1).

[livid cypress]

y=rx

wait

no

[oak chasm]

No, it's y intercept isn't zero.

[livid cypress]

y=rx -r + 1

[oak chasm]

Use point-slope form.

Don't use slope-intercept form.

You don't know the y intercept.

You know a point on the line.

You know the slope.

Use point-slope form.

[livid cypress]

what the heck is point slope form

[oak chasm]

(y - the y coordinate of the point) = m(x - the x coordinate of the point)

(y - 1) = r(x - 1)

[livid cypress]

right

[oak chasm]

The x intercept is when y = 0.

Fill in 0 for y. Solve for x.

[livid cypress]

(-1 + r)/r?

r-1/r

OHHHH

ur crazy

[oak chasm]

Point slope form is very useful.

[livid cypress]

thats insane jarvis

your right

its because i simplified it a little too early init

[oak chasm]

You were using slope-intercept form, but you didn't know the y intercept.

[livid cypress]

i see

thanks papi

[oak chasm]

You're welcome.

[dull wedge]

#help-0 message

[livid cypress]

how do you do ii

@oak chasm

if you integrate x^r is it (x^r+1)/r+1

im close to getting it

[oak chasm]

Well, the area is the definite integral, right?

[livid cypress]

im integrating from 0-1 and subtracting the triangle from the point to 1

[oak chasm]

OK, that'll work.

Another way is to get the definite integral of the function from 0 to (r - 1)/r.

Then get the definite integral of the function minus the function of the line from (r - 1)/r to 1.

[livid cypress]

but then you wouldnt get whats on the right?

oh

[oak chasm]

Then you add those definite integrals.

[livid cypress]

let me try that

no

too hard

not getting it

wait i did it wrong

let me retry

[lusty ibex]

thats wring

[livid cypress]

no i still cant do it

[lusty ibex]

you cant

[livid cypress]

mr T. Rex

i need ur massive brain

@oak chasm

[oak chasm]

OK, so solve the line equation for y.

[livid cypress]

y=rx-r+1 ?

[oak chasm]

(y - 1) = r(x - 1)
y - 1 = rx - r
y = rx - r + 1

Right.

[livid cypress]

yep

why is x^r in the second integral

[ocean seal]

Chai T. Rex

[oak chasm]

That gives you the height of the vertical cross section of the area.

The height between the curve and the line.

Then the integral adds all the heights together to give you the area.

[livid cypress]

okay

[oak chasm]

You can also do this:

[ocean seal]

Chai T. Rex

[livid cypress]

ohhh i see

because you were adding it

if i did the integral subtracting the triangle

i got (3r+1)/2r(r+1)

instead of r-1 at the top

what am i supposed to get if i integrate x^r from 0 to 1

[ocean seal]

Chai T. Rex

[oak chasm]

That's also the subtracted integral here.

[livid cypress]

i had 1/2r

[oak chasm]

Oh, right.

Yeah, you're right.

[livid cypress]

so i did the integral wrong

i had 1/r+1

[ocean seal]

Chai T. Rex

[livid cypress]

1/r+1

[ocean seal]

Chai T. Rex

[livid cypress]

(x^r+1)/r+1

[oak chasm]

OK, so 1 filled into that is 1/(r + 1). 0 filled into that is 0.

So, yes.

1/(r + 1) - 1/(2r)

[livid cypress]

ohhh i added them instead of subtracting

i see

sorry i just wasted so much time

[oak chasm]

No, that's fine.

[livid cypress]

thank you very much

[oak chasm]

Mistakes happen a lot.

[livid cypress]

appreciate it

[oak chasm]

You're welcome.

[vale wigeon]

dx! dx!!! dx!!!!!!!!

[oak chasm]

Ahh, yes.

[alpine sable]

How do I find the angle of two vectors through cross product?

[remote iron]

How do I write this in complex terms?

[jagged imp]

as in the angle between them? ||a cross b||=||a||||b||sin(theta) where theta is the angle between them

[oak chasm]

@remote iron Sorry, channel is busy.

[alpine sable]

Thanks.

[remote iron]

@jagged imp Can you help me out, quickly please?

[jagged imp]

no

i will not

[remote iron]

Okay.

[covert agate]

how can we prove that if m | k and n | k then lcm(m, n) | k

[oak chasm]

Use the definition of divides.

[sage summit]

rather the definition of lcm

[vale wigeon]

rather both

[wispy olive]

Can Anyone explain this proof for Pythagorean theorem?

[oak chasm]

On the right, the white area is the hypotenuse squared.

On the left, the white areas are the legs squared.

[undone dock]

The negative space is a^2 + b^2 in the first diagram and on the second it's c^2

[oak chasm]

And there are four copies of the triangle added.

[undone dock]

But they're equal

[wispy olive]

Uh what? What space?

[oak chasm]

So, c² + 4t = a² + b² + 4t.

[undone dock]

The white space

[wispy olive]

Let me try to comprehend.

[wispy olive]

I see.

Woah.

But your way @undone dock, something feels weird.

Oh wait.

@oak chasm so you are saying that.

In the left.

[wispy olive]

The bigger white space is the length of the grey one multiplied by the width of the black one, and the smaller square is width of grey one * length of dark one.

I see I see.

[oak chasm]

You have four copies of the triangle plus a square with one leg, a, as the four sides (area a²) and another square with the other leg, b, as the four sides (area b²). So, the area of the enclosing square is a² + b² + 4t.

[wispy olive]

Mhm.

Let me think.

WOAH this is crazy!

Mind is blown.

Woah!

Logic was so high even about 2200 years ago.

Thanks @oak chasm and @undone dock .

[oak chasm]

You're welcome.

[wispy olive]

Amazing!

I will read more Pythagorean Theorem proofs.

@oak chasm can you tell me how you understand these so fast and so easily?

They look pretty un-related and weird and hard to comprehend at first.

[oak chasm]

Well, the side of the white square is a - b, so its area is (a - b)².

As you can see on the left, the enclosing square has side length of the hypotenuse, so it's c².

The area of the triangle is 1/2 ab.

So, by the left diagram:
c² = 4(1/2 ab) + (a - b)²

[wispy olive]

How do you know it is a - b? Proof?

[oak chasm]

See on the right?

[wispy olive]

Oh I thought that was for the left one.

Wait.

[oak chasm]

The height of the light grey is one leg, a. The height of the dark grey is the other leg, b.

[wispy olive]

What is the a and what is the b?

And what is the c?

[oak chasm]

The height of the white square is a - b.

[wispy olive]

How?

[oak chasm]

c is the hypotenuse.

[wispy olive]

Why?

[oak chasm]

Why what?

[wispy olive]

What are the proofs of these?

[oak chasm]

Proofs of what?

[wispy olive]

That the height of it is a - b?

[oak chasm]

a is one of the legs.

[wispy olive]

And what is a and what is b?

[wispy olive]

Which leg?

[oak chasm]

b is the other leg.

Take a look at the right diagram.

[wispy olive]

Okay.

[oak chasm]

Do you see how the height of the white square is the height of the dark rectangle minus the height of the light rectangle?

Do you see how the height of the dark rectangle is one of the legs?

Do you see how the height of the light rectangle is the other leg?

[wispy olive]

Oh yes!

[oak chasm]

So, the height of the white square is (a - b)².

[wispy olive]

So next.

[wispy olive]

I see.

Yes it is.

[oak chasm]

OK, so the area of each triangle is 1/2 ab.

There are four of them.

So, the areas of the triangles on the left diagram is 4(1/2 ab) = 2ab.

The area of the white square is (a - b)².

[wispy olive]

How how?

[oak chasm]

1/2 base times height.

The base is one leg.

[wispy olive]

Oh yes.

[oak chasm]

The height is the other leg.

[wispy olive]

It is.

[oak chasm]

So, the enclosing square has the side as the hypotenuse of the triangle.

So, c² = 4(1/2 ab) + (a - b)².

[wispy olive]

Why so?

Why is 4/that?

[oak chasm]

Well, the area of one triangle is 1/2 ab.

There are four copies of the triangle.

So, the area is 4 times one of the triangles.

[wispy olive]

I see.

[oak chasm]

So, the area is 4(1/2 ab).

[wispy olive]

I see.

[oak chasm]

So, c² = 4(1/2 ab) + (a - b)².

[wispy olive]

But....

All of these are equal.
Right?

[oak chasm]

Yes.

[wispy olive]

Okay.

So.

[wispy olive]

Area of what?

[oak chasm]

The area of the four triangles in the left diagram.

[wispy olive]

Yes.

Altogether.

Right?

[oak chasm]

So, the area of the left diagram is 4(1/2 ab) + (a - b)².

[wispy olive]

I see.

WOAH!

Then what do we do?

[oak chasm]

It's also c².

[wispy olive]

What?

[oak chasm]

Since the side length of the enclosing square is the hypotenuse.

So, the area is the hypotenuse squared or c².

[wispy olive]

Can you please tell this in simpler words?

[oak chasm]

Simpler words?

[wispy olive]

Yes.

[oak chasm]

Side is simple.

Length is simple.

[wispy olive]

Yes.

Yes.

What is the enclosing square?

[oak chasm]

The largest square on the left.

[wispy olive]

The one which has all the triangles in it?

And the white square too.

[oak chasm]

Yes.

[wispy olive]

Okay.

I see.

[oak chasm]

It has the hypotenuse of the triangle as a side length.

So, the area is the hypotenuse squared or c².

[wispy olive]

Yes.

[oak chasm]

So, c² = 4(1/2 ab) + (a - b)².

c² = 2ab + a² - 2ab + b²

c² = a² + b².

[wispy olive]

This rough line is the hypotenuse?

[oak chasm]

No, that's a diagonal of the square.

[wispy olive]

Okay.

[oak chasm]

Do you see the enclosing square?

[wispy olive]

Then what is the hypotenuse?

[oak chasm]

Do you know what the hypotenuse of a right triangle is?

[wispy olive]

Can you draw or mark it?

[wispy olive]

Yes.

[oak chasm]

Do you see the four right triangles?

[wispy olive]

Yes.

[oak chasm]

Do you see the hypotenuses of them?

[wispy olive]

Wait.

No.

Wait wait.

[wispy olive]

Yeah I do.

See this.

[wispy olive]

Yes.

I do.

Next?

[oak chasm]

Do you see how they're the sides of the enclosing square?

[wispy olive]

YESS!!!!

Next what do we do?

[oak chasm]

I already did it.

The area is 4(1/2 ab) + (a - b)².

The area is also c².

[wispy olive]

I see.

[oak chasm]

So, c² = 4(1/2 ab) + (a - b)².

So, c² = 2ab + a² - 2ab + b²

So, c² = a² + b².

[wispy olive]

WOAH!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

SO AWESome and FascinATING!!!!!!!!!

Thank you very very much @oak chasm .

[oak chasm]

You're welcome.

[wispy olive]

@oak chasm pleaseee?

[oak chasm]

I look at what side of the triangle is the side of each square.

So, the largest square has the side as the hypotenuse in the last one.

[wispy olive]

Can you answer this for like all types of problems?

[oak chasm]

What do you mean?

[wispy olive]

Or is it different for Algebra and Geometry and stuff.
Or is it different for topics even under these!

[wispy olive]

I mean, when you look at a problem like this, which looks hard and un-relatable to me, how do you understand it is so well so fast?

[oak chasm]

I figure out what the side of the square is in terms of the triangle sides.

[wispy olive]

So here you are just talking for Basic Geometry?

[oak chasm]

Like the side of the largest square on the last one is the hypotenuse of the right triangle.

[wispy olive]

This applies to all areas and kinds of math(or at least all till Calculus if they are different).

[oak chasm]

Not really, since you're not dealing with squares and right triangles in all areas of math.

[wispy olive]

I see.

So how do you understand problems so fast and so well for all of math?

[oak chasm]

I don't do so well in all areas of math.

[wispy olive]

Does it come by experience(I do not like that but it is what it is)? Are there tricks? Are there methods?

Still, I could learn a lot from you.

[oak chasm]

Yes, experience and understanding.

[wispy olive]

The way you answered this question.

I was fascinated how it can be so nice!

[wispy olive]

Ah I see.

[oak chasm]

Well, the people who came up with the proof made it nice.

[wispy olive]

Can I get tricks or methods or stuff for it? Or all from experience?

[oak chasm]

Just what I told you.

[wispy olive]

I think you did not study it earlier still you could so easily answer it so fast!

[oak chasm]

Find out how the side of the square matches something on the right triangle.

[wispy olive]

Ah, so all experience?

[oak chasm]

Like the first proof.

The two squares on the left diagram.

One of the squares matches up with one leg of the right triangle.

One of the squares matches up with the other leg.

The square on the right diagram matches up with the hypotenuse.

[wispy olive]

I see.

[oak chasm]

And then the rest of the area of both diagrams is taken up by 4 triangles.

So, a² + b² + 4t = c² + 4t

a² + b² = c².

[wispy olive]

Oh.

[oak chasm]

And in the second proof, the side of the largest square matches the hypotenuse. The side of the white square matches the difference of the legs.

[wispy olive]

Woah, you also include capital letters at the beginning of a sentence and full stops at the end, like me. I like to keep grammatical accuracy too.

[alpine sable]

W(5, -2) and Z(-1, -5)

it says to find the distance between these points

I got root 45

but in the answer sheet it says

[daring roost]

It would be the hypotenuse if you cut it in half diagonally.

[alpine sable]

can someone help me please?

[daring roost]

That is sqrt of 45

[alpine sable]

how?

root of 45 is 6.7

[daring roost]

Because 3 is the same as square root of 9

[alpine sable]

that is cubed root of 5

right?

[daring roost]

No.

That’s a very big mistake

[alpine sable]

??

[daring roost]

The cube root is like a smaller number.

At the top of the square root

Essentially 3 is the same as square root of 9

[alpine sable]

can you explain what the 3 means

I thought it meant cubed root

[daring roost]

It’s part of the number

It’s 3 X square root 5

[alpine sable]

ohh

[ocean seal]

Chai T. Rex

[alpine sable]

can you tell me how you would simplify root fo 45 to 3 times root of 5

[daring roost]

Because 3 is the square root of 9

[oak chasm]

Factor 45.

[daring roost]

Square root of 9 Times Square root of 45 is square root of 45

[oak chasm]

45 is 3 times 3 times 5.

45 is 3² times 5.

So, you can take the square root of 3² and the square root of 5.

[alpine sable]

so am I supposed to just know 45 is 3 times 3 times 5.

?

[maiden holly]

Prime factorization?

[kindred herald]

If not, you're supposed to know how to do prime factorization of any number

[ocean seal]

Chai T. Rex

[oak chasm]

@maiden holly Yes.

[alpine sable]

ahhh

ok

thanks for your help everyone

[kindred herald]

Also 45 is a result of the multiplication table, which uhm... 2nd graders (?) learn

[alpine sable]

u don't have to be pretentious about it

[oak chasm]

Do you know the prime numbers?

Like 2, 3, 5, 7, 11, etc?

[kindred herald]

Sorry, didn't mean to

[oak chasm]

You have 45.

Is it divisible by the first prime, 2?

Nope.

Is it divisible by the next prime, 3?

Yes, so factor that out: 3 times 15.

Is 15 divisible by 3?

Yes, so factor that out: 3 times 3 times 5.

[alpine sable]

yeah I forgot how to do this

[oak chasm]

Is 5 divisible by 3?

Nope.

Try the next prime.

Is 5 divisible by 5?

Yes.

It is 5.

So, 3 times 3 times 5.

You can also stop early if the prime you're trying squared is higher than the number.

So, we had 3 times 3 times 5 and we were checking whether 5 was divisible by 3.

Well, 3 squared is 9, which is higher than 5.

So, 5 is a prime and you must be done.

[alpine sable]

https://www.youtube.com/watch?v=ja-8g_-ELlU

is this what you're doin rn?

[oak chasm]

That's so you don't have to check so many primes.

Yes, this is one way to do that.

[alpine sable]

ok thanks

[oak chasm]

You're welcome.

[twilit dune]

Every natural greater than one can be expressed as a sequence of prime numbers multiplied together

[ocean seal]

Bkas

[agile ruin]

How to differentiate above fraction? I tried using the double angle formula.

[rigid smelt]

theres no need to use an identity here

[gray isle]

should be able to throw quotient rule at it

[rigid smelt]

or just chain rule the hell out of it

[agile ruin]

Ok thanks

[fresh bolt]

hello

can someone explain to me this

why n/2 lg (n/2) become n(lgn - lg2)

[spare fern]

The 2 outside is multiplied by n/2

And log laws

[fresh bolt]

ohh

so it becomes n lg(n/2) which is n(lgn - lg2)?

[spare fern]

Yeah

[fresh bolt]

ok thanks

[keen salmon]

Guys how do we find

[shell widget]

You can try taking the log of that limit

since it's of the form 0^0

[barren helm]

hi

[keen salmon]

that's worked, thanks

[barren helm]

um hi

[iron loom]

hello! can anybody help me with my assignment? still dont understand it even tho ive been looking at it for an hour already

[split oriole]

Any perticular question

[iron loom]

how do you solve number 1,3 and 4? ;-; i got the 2nd question but no hope for the other 3

our prof didnt rlly teach it clearly

[split oriole]

Okk equation of line when slope and point is given is $\frac{y-y_1}{x-x_1}=slope$

[ocean seal]

Algebra

[split oriole]

When angle is given slope is tan(angle)

[iron loom]

is this for no.1 a?

[split oriole]

For all part of 1

Like for a part (-2,1) is point and angle is 45 so noe

$\frac{y-1}{x+2}=\tan(45^{o})$

[ocean seal]

Algebra

[iron loom]

oh ok ok thank you!

how about 3 and 4 ;-;

[split oriole]

Slope when two points are given (x1,y1),(x2,y2)

Is

$\frac{y_2-y_1}{x_2-x_1}$

[ocean seal]

Algebra

[rich basin]

<@&286206848099549185>

[iron loom]

mhm

[loud sentinel]

Hey does anyone know how to solve 24.c) … the answer is 151200

[iron loom]

thank you @split oriole !!

[weak oasis]

does anyone know how to tell whether a negative number to a power is -(3)^2 or (-3)^2 when there are no parenthesis present?

[light sparrow]

if you have something written like 3^4 - 2^4

that would mean (3^4) - (2^4)

if they mean (-3)^2 they would write brackets, otherwise it means -(3)^2

[weak oasis]

ok thanks @light sparrow

that’s always been something that has confused me

<@&268886789983436800> thanks

[ember ravine]

im reviewing math and btw im grade 6 lol

[cinder finch]

Oh that’s alright

[weak oasis]

why was i always taught to assume the negative was inside the parenthesis ?

[pliant oracle]

why would you need to assume the negative's inside the parenthesis, would you not just see it written with or without?

[thorn kindle]

you can actually replace every negative sign with -1 *

[pliant oracle]

I feel like, given the wording of the original question, it's more likely they meant that 'to raise a negative number, say -2, to a power, we write it as (-2)^4 etc'

[strange raven]

Hi

I have a question of abstract algebra

[gaunt sky]

@strange raven instead of saying you have a question, actually ask it next time :p

go ahed

[alpine sable]

I have a very easy question

If a number is divisible both by 12 and 5, by which other number will they also be divisible?

[weak oasis]

when there isn’t a parenthesis present and it just says -7^2 is what i mean

[alpine sable]

<@&286206848099549185> sorry for disturbing but I will stay quiet after I get my question cleared

Uh

Will we be playing hide and seek?

[ocean seal]

Renegade

[ionic jewel]

any number divisible by 5 and 12 is also divisible by 1,2,3,5,6,12,60 at least

[alpine sable]

Oh thank you very much :)

[ionic jewel]

the answer is $\frac{\pi^2}6$, you can look up one of many proofs for it

[ionic jewel]

@alpine sable

[glass lichen]

Evaluate or see if it converges?

I mean... p series QED

For convergence

Yes

[ionic jewel]

yeah they all converge for exponents greater then 2 (maybe 1, don't remember) but evaluating it is much harder

[glass lichen]

1/n diverges

It's harmonic

[ionic jewel]

yeah i means n > 1

not n >=1

but i don't know if it's n > 1 or n >= 2

[glass lichen]

They diverge too, in regular summation at least

Boundary is 1

Re zeta(-1)=-1/12

[ionic jewel]

yeah well zeta(-1) is a trap

alright thanks

[celest bluff]

Hey, I'm trying to make a 3d rendering engine from scratch and am now tackling refraction.
In a 2d plane refraction is like this

apologies for my horrible illustration

So I know v1, N, i, and r. I need to find v2.

If I was dealing with 2d space I'd probably google this and figure it out in a bit.. but I'm dealing with this same problem in 3d space.

v1, v2 and N are 3d vectors. I know both i and r, v1 and N. I need to find v2 (all 3 components, magnitude is 1), but I am really really confused how

I saw something called Rodrigues' rotation formula but I am pretty new to vector maths so I don't know how to apply it to this problem.. if someone could tell me that'd be really great

Just the mathematical expression is fine and I'll adapt it to shader code

So basically,
v1 is a known 3D vector with magnitude 1
N is a known 3D vector with magnitude 1
v2 is an unknown 3D vector with magnitude 1
i is the angle between v1 and N, it is known
r is the angle between v2 and N, it is known

and I'd like to find v2.

[plain osprey]

How do i check if they r equal?

Could u send that in a different channel please?

I still haven’t gotten help

[celest bluff]

lol you posted ur q before i got help

but its k my question is super niche i doubt itll be solved today

[plain osprey]

Mb it’s been a long time

I thought it’s fine

[celest bluff]

its fine dont worry about it

ill repost if i dont get an ans by tmrw, most people probably cant help with this niche type of q

also please translate the q before sending it in another channel

[glass lichen]

By definition of span

[tight locust]

how many terms are in the expansion of (a+b)^n

1, 2, 4, ... ?

<@&286206848099549185>

[vale wigeon]

n+1

[tight locust]

wow i'm dumb

thanks

[thorn kindle]

have you heard of pascal's triangle?

[tight locust]

right my bad it's 3 not 4 for n=2

the triangle explains that

[buoyant hearth]

Do you guys have any tips for 12 grade?

[ionic jewel]

what math are you doing in 12th?

[buoyant hearth]

I think we will start with calculus and idk about the rest😅

[ionic jewel]

alright calculus isnt too dependent on previous math, mostly new concepts so the same thing applies: stay on top of things and you should be fine

[fervent gust]

do more maths

[tight locust]

yeah intro calc is very basic don't worry about it

[buoyant hearth]

Ty everyone!

[celest bluff]

Hey, I'm trying to make a 3d rendering engine from scratch and am now tackling refraction.
In a 2d plane refraction is like this

So I know v1, N, i, and r. I need to find v2.
If I was dealing with 2d space I'd probably google this and figure it out in a bit.. but I'm dealing with this same problem in 3d space.
v1, v2 and N are 3d vectors. I know both i and r, v1 and N. I need to find v2 (all 3 components, magnitude is 1), but I am really really confused how
I saw something called Rodrigues' rotation formula but I am pretty new to vector maths so I don't know how to apply it to this problem.. if someone could tell me that'd be really great
Just the mathematical expression is fine and I'll adapt it to shader code
So basically,
v1 is a known 3D vector with magnitude 1
N is a known 3D vector with magnitude 1
v2 is an unknown 3D vector with magnitude 1
i is the angle between v1 and N, it is known
r is the angle between v2 and N, it is known
and I'd like to find v2.

Sorry my q got buried so Im just reposting

[fervent gust]

looks more like a physic question than a maths question imo

[celest bluff]

Its vector math tho

Ignore the physics part

Im not asking in the sense of what is v2 because of the law of refraction

Rather just, if I have these values what is v2

[dawn galleon]

i was muted for calling someone a sweetie

ight

[celest bluff]

great

I think i may have gotten the formula correctly

ok nevermind I dont think I did

So Im still not so sure about the formula

[simple elm]

okay so x^(m/2)/x^(m/3)= x^(m/2-m/3) and then i am lost

im supposed to make it simpler

[oak chasm]

Simplify the fraction.

@simple elm What's m/2 - m/3 as one fraction?

[simple elm]

that is what i dont know

all i see is that m/2 is 0,5m and m/3 is 0,3m

which doesnt help me at all

maybe it does hold on x^0,2

[tidal grail]

How do you find this (4)^3/2

[simple elm]

ir doesnt

[ocean seal]

Chai T. Rex

[simple elm]

yea i dont know

[ocean seal]

Chai T. Rex

[oak chasm]

OK, so you multiply the denominators together.

See how I did that?

Then you multiply the top of one by the denominator of the other.

[simple elm]

wait i dont even have this formula available on my sheet

[oak chasm]

a times d

Top of one is a

Bottom of the other is d.

b times c

Top of one is c

Bottom of the other is b.

See how I did that?

Let's try that with real fractions.

[simple elm]

thats really weird, how was i supposed to know this answer if the formula sheet for my class doesnt have this formula :/

[ocean seal]

Chai T. Rex

[oak chasm]

See how the bottom of the result is where you multiply the bottoms together.

And then the top of one is 2. The bottom of the other is 3.

So 2 times 3 is in the top.

The top of one is 1. The bottom of the other is 7.

So 1 times 7 is in the top.

Does that make sense?

[simple elm]

that doesnt help :/ why cant it just be solved with the formula that i actually have..

m/2 is 0,5 and m/3 is 0,3 makes sense right? 0,5-0,3 is 0,2 therefore x must be x^0,2 but i dont understand why that wouldnt work when the formula says so

[oak chasm]

No, 1/3 is not 0.3.

1/3 is 0.333333333333333333 forever.

[ocean seal]

Chai T. Rex

[oak chasm]

@simple elm

,calc 1/3

[ocean seal]

Result:

0.33333333333333

[oak chasm]

If you're doing exponents in algebra, you should have already learned to do fraction addition and subtraction.

So if you don't know how to do it, it's important to learn it.

@simple elm Here's a video that teaches it: https://www.khanacademy.org/math/cc-fifth-grade-math/imp-fractions-3/imp-adding-and-subtracting-fractions-with-unlike-denominators/v/subtracting-small-fractions-with-unlike-denominators.

[simple elm]

well tbh my teachers would tell me to skip everything i didnt know the answer to when i was in school so missed alot of maths

[oak chasm]

Oh, that's not good.

[simple elm]

yep and now im struggling badly

[oak chasm]

Khan Academy has a lot of nice teaching stuff.

[simple elm]

i basically didnt learn any maths from grade 6 to 1st grade highschool

[oak chasm]

It's free and everything.

Here are their math classes: https://www.khanacademy.org/math.

In each math class, at the very bottom is a test you can take to see if you need to learn anything from it.

Like you can go to the arithmetic class and take the test.

It's OK to get the answers wrong.

If you do, it just tells you what to brush up on.

And then you can look through the arithmetic class and go to that section.

And then they have video lessons and practice problems.

And you can ask for help here if you get stuck.

@simple elm

So, try their arithmetic test at the bottom of the arithmetic class. Go through the sections you need to brush up on.

Then go to algebra 1 and do the same.

[simple elm]

oh i just watched that video

okay now its much easier

how that i know that i can multiply them with the the same number

[oak chasm]

OK, what do you get for m/2 - m/3?

[simple elm]

3m/6-2m/6

which is supposed to be m/6

i think

nope its wrong

i mean i extended the thingy

m/2 with 3 and m/3 with 2

oh i forgot the original equation

my bad

[oak chasm]

You're right.

m/2 - m/3 = 3m/6 - 2m/6 = (3m - 2m)/6 = m/6

,w m/2 - m/3

[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]

@simple elm

It's m/6.

[simple elm]

yes i got that too

i cant believe i had forgotten how to do the fractions with unlike denominators

[next mural]

What is that expression exactly??

[gleaming sandal]

Hey. Can someone please double check that the answer I got is right?

[next mural]

Wny did you multiply x at the end are you sure thats what the question wants?

[daring roost]

Let me work it out.

[gleaming sandal]

I wanted it out of the way, but I see. Let me try not to get it out of the way

[daring roost]

Substitute the F(x) and g of x values

[topaz scaffold]

Should have multiplied by √(x^2 - 1) in the beginning I think

[next mural]

X may be just symbolic as the input of the function

[topaz scaffold]

Instead of +1

[daring roost]

I think it is meant to be timed by X

[dawn galleon]

ho ho

ho ho

[daring roost]

Because what other purpose does X serve

[next mural]

It just divided g and f without an input? I've never seen that b4

[daring roost]

Same.

[gleaming sandal]

I was just as confused haha

I guess it's just the function

[topaz scaffold]

Yea it is

[next mural]

Since yall already here

Whats that expression

[placid zinc]

Very general question to ask haha

[next mural]

Pardon?

[placid zinc]

For any rational p you give me, I can give you a q such that:

• q is also rational
• q² is always between 2 and p², non-inclusive

The expression itself is the way I give you back that q, the form is unimportant though

[next mural]

Ok gotcha

[placid zinc]

Shows that there's no "closest" rational to √2

[next mural]

No no, just where it was plucked out from

[arctic delta]

can someone peak at #help-2

[next mural]

@placid zinc just curious how it was derived do you happen to know?

[placid zinc]

We want it to have the properties that I laid out above. Any function that does that, would work

There's probably infinitely many functions that do this, so Rudin drew from a hat, so to speak

[next mural]

Ok gotcha thanks!

[storm swan]

hi i need some help on this

im confused as to why my answers arent right

[quiet patio]

Graph Theory Question: Must the number of families in Florida with an odd number of children be even?

[gleaming sandal]

Sup. Did I answer the question right? Ty in advance!

[quiet patio]

I don't think quite. Account for the sqrt. So it should be g(sqrt(3)) = sqrt(3) + 1

[gleaming sandal]

Oh I see it. Thanks. Fixed

[grizzled herald]

Because tan theta < 0 it must be in quadrant 2 or 4. Based on the signs of the given cos theta values it must be quadrant 4. Hopefully that will help you adjust your value for the last side value.

[alpine sable]

Multiposting

[glass lichen]

Yes I can

[cosmic plover]

Could you pls tell me

[glass lichen]

No

[hushed pasture]

$1) (x,y) \in A-B \implies (x,y) \in A$ and $(x,y) \not\in B \newline \implies x^2 + y^2 \le 4$ and $ x^2 + y^2 < 9 \newline \implies x^2 + y^2 \le 4$

[glass lichen]

Cause we dont give answers out

[ocean seal]

Salah

[cosmic plover]

Yea sry it was urgent

[glass lichen]

why is it urgent...?

[hushed pasture]

so A-B = A

[cosmic plover]

I have test tmrw

[glass lichen]

I mean, you can sufficiently just draw the sets A and B, then note stuff about their differences and intersections

[cosmic plover]

Its ok if you cant help, thanks

[glass lichen]

I just helped, the fuck do you mean

[alpine sable]

You already received help in questions-1, why are you asking again

[glass lichen]

That too

[cosmic plover]

Mind your tongue..... Kindly

[glass lichen]

Yeah, no.

[alpine sable]

[glass lichen]

Read the rules next time

[cosmic plover]

Da heck, I deleted it now.
Ok?

[alpine sable]

???

[cosmic plover]

Sorry for inconvenience

I messed up sorry

[alpine sable]

If you didn't understand the explanation tell the person, don't pretend you got it and ask again

Dick move

[cosmic plover]

Bruh why is everyone using filthy language?

Idk why....

[glass lichen]

I mean, why did you break a rule?

[cosmic plover]

Bruhh i won't do it again......
Sorry for everything

[alpine sable]

Try another channel

[cosmic plover]

I just wanna be friendly😑😶

Sorry @alpine sable and @glass lichen

@glass lichen , just asking may i know which rule i broke, so that i will not do that again......

Sorry for the ping

[glass lichen]

That was said already

[glass lichen]

.

[cosmic plover]

Ohhh

Ok sorry

I will not do that again

Really, why is that not acceptable in the server, i just wanted help for the revision....

So that i can get help early.....

[jolly stone]

suppose that {W} is a random Poisson process of waiting getting help with mean W, and W_help is exponentially distributed time (idk lol)
if you request for N people to help at the same time, the expected time you need to wait is W/N, BUT everyone else has to wait at W_help to receive help

and this is definitely not M/M/infinity queue

[dark granite]

it is because by doing so you are taking up more space than necessary that other members of this server could be using to ask their questions ONLY once.

[cosmic plover]

Umm sorry for everything i caused, and thanks for the info

I'm feeling guilt to post in the server now.....😫
Like i'm getting a feel that i've made a crime....😟

[dark granite]

you're not in any legal trouble lmaooo. You've learned your lesson not to multipost again.

[cosmic plover]

Yeah thanks

But what about ugly language , is that 'ok' in this server?

[dark granite]

First off, why would you ask that? It's best to refrain from such language anyway. Secondly, it depends on what you meant by "ugly". Some language which some may define to be ugly is actually allowed, while other language which some may define to be ugly is very much not allowed.

[cosmic plover]

Bruhh, is it allowed?

[dark granite]

That use of the F word is allowed.

[dark granite]

Again, why would you be asking this question anyway?^

[cosmic plover]

Ahh I'm done with the argument bro, thanks.

[dark granite]

Okay. It's not an argument lol. Just refrain from such language in the first place.

[cosmic plover]

Hmm

[half steppe]

hello. Is the Z here supposed to represent the set of all Integers?

[dark granite]

yes @half steppe

so 12Z is the set {...,-36,-24,-12,0,12,24,36,...}

[half steppe]

so its an infinite set

[dark granite]

yes

[half steppe]

but what does the 12 before it do?

why 12Z and not just Z

oh

[dark granite]

12Z is the set of all integer multiples of 12, so this set must be infinite

[half steppe]

all multiples of 12

right

thanks man

[dark granite]

you're welcome!

[glass lichen]

would a+12Z just be every integer then, cause every integer is remainder + multiple of 12 (something something division algorithm)

[dark granite]

no because a is fixed to be one of those things: 0,1,2,...,11

a can't take on all values at once

a is an arbitrary element of {0,1,2,...,11}, but it is fixed by the time we get to a+12Z

[glass lichen]

im aware of that, but nowhere does it say a is fixed to be only one value

it says it takes on a value from Z_12

[dark granite]

right it takes on one value. We don't know what that value is exactly, but a is fixed. and so a+12Z is not the set of all integers.

so a+12Z is [a] in Z_{12}

which clearly can't be the set of all integers

[half steppe]

and after the intersection with {N_l,...,N_l} the result is ofcourse a finite set

[dark granite]

right because {N_l,...,N_h} is finite

[pastel schooner]

What does the highlighted mean? Like domain of every x?

[alpine sable]

It's the set x is taken from

[dark granite]

This was already answered, but in case this helps, let's look at an example and see if it's even clearer what x in D means. Suppose D is the set of positive integers. Then the set you attached a screenshot for is the set {(1, f(1)), (2, f(2)), (3, f(3)), ...}. Make sense?

[pastel schooner]

I see what does the E mean?

Thats the main thing I am curious about

[dark granite]

it means x is in D. x is a member of D. x is an element of the set D. These are all equivalent things.

[pastel schooner]

Ah!

That makes sense. Is there a name of that symbol?

[sly mantle]

$\in$

[ocean seal]

Dreadful Encore of Twisted Karma

[dark granite]

uh it's "element of" but that's how you code it in LaTeX^

[pastel schooner]

thank you

[dark granite]

You're welcome!

This channel is open for questions

[analog nymph]

why is 3(c) multiplied by 4

[dark granite]

this is because there are 4 suits, so choose 1 of the 4 for which we'll have all 4 cards within that suit

[analog nymph]

ohhh

bruhhh i am dumb

thx !

[dark granite]

You're welcome!

[gleaming sandal]

Hey

Did I solve this one right?

Ty in advance

[vague coral]

I didn't understand a single thing of what you did

why did you take y = 2x - 1/3

[gleaming sandal]

oh I see. My sleep depriviation is showing now. Mb I see it I did it fully wrong

[vague coral]

sleep is important

[grand comet]

How do I calculate finance rate pls?

<@&286206848099549185>

[thorn sundial]

can you guys help me with this

[grand comet]

1.83 hours

[minor anchor]

200/109.2813 hours

but.... that doesn't really make sense

doesn't include acceleration at the start of the race

[grand comet]

How to calculate finance rate? <@&286206848099549185> real quick

[thorn sundial]

thx

i need help with this

[grand comet]

640 x .12

[thorn sundial]

i got 76.8

[grand comet]

Me too

[thorn sundial]

is that right?

[grand comet]

Yea

Because .12 is 12 percent

[thorn sundial]

genius. i never knew that i appreciate that

[grand comet]

Easiest way to do it tbh

[thorn sundial]

💪💪💪

[grand comet]

How to calculate finance rate

[grand comet]

<@&286206848099549185>

[thorn sundial]

need help

i got b

[grand comet]

I think it’s c

Here’s my explanation

[thorn sundial]

listening

[grand comet]

The parenthesis is the first number and the second number is the x outside the parenthesis so the sum is 48? What do you think

[thorn sundial]

Sound correct

let me try what you mentioned

[thorn vortex]

It is c

[thorn sundial]

yea it's c thank you both

[grand comet]

I’ve never seen an equation like that

Worded that way

How to calculate finance rate? <@&286206848099549185>

[grand comet]

If I finish this I’m done with school @everyone who can solve this?

[thorn sundial]

this is 574 cm right?

[grand comet]

58 lol

[thorn sundial]

wth😭😭 i was hecka of

[median tendon]

How can the length of one side be bigger than the perimeter...

All the side length add up to the perimeter

[grand comet]

This man 😭

[alpine sable]

anyone know

how to do uh 19

ik im supposed to use chain law

not sure how tho in this case since dy/du is just 1

[thorn sundial]

how do i solve this

[alpine sable]

this feels like a test but

[thorn sundial]

no it's not

[alpine sable]

hey @thorn sundial what grade are u in, just a question

[thorn sundial]

y

[alpine sable]

this seems like a 6th grade question

lol

[thorn sundial]

😭 am i that slow

i j needed help

[alpine sable]

sorry lol

maybe its just cuz im old

50 miles

you solve the question by doing it like this

50x = 40(x+1/4)

then 50x = 40x +40/4
50x - 40x = 10
10x = 10

x = 1

[buoyant kayak]

no need for dy/du at all, just treat the root as a power and use power rule + chain rule

[alpine sable]

oh shit

thank you so much

[buoyant kayak]

👍

[thorn sundial]

would this be 525?

[alpine sable]

can you explain what brought you to think it was 525?

i just wanna see ur thinking process

not an attack

[thorn sundial]

80= 35 * 15

[alpine sable]

80 is not 35 times 15

not in any dimension

[thorn sundial]

alr

[alpine sable]

when the takes the train it takes 15min right?

and the train goes 80 miles an hour?

[thorn sundial]

yea

[alpine sable]

an hour has how many minutes? @thorn sundial

[thorn sundial]

60

[alpine sable]

ok

so wouldn't it be 80 x 15/60

[thorn sundial]

that's 15 over 60?

[alpine sable]

since he would be traveling 80 miles in 60 mins

yea

15 over 60

[thorn sundial]

i got 200

20*^

[alpine sable]

Yep

Since he drove for a fourth of an hour, not 7ish hours

so the final answer has to be smaller than the unit

[thorn sundial]

mmmmm alr

i see it now

[alpine sable]

yeee

same thing w the last question

[thorn sundial]

bet

it's wrong

it's not 20

😭

[alpine sable]

aul

ayo

[thorn sundial]

huh

[alpine sable]

OH

FASTER THAN HIS DRIVING

sorry im stupid i thought it was just 80mph i didnt read the question

[thorn sundial]

nah it's g

[grand comet]

That’s a hard one

[thorn sundial]

damm😭

[alpine sable]

ok for some reason i can do differential calculus but not prealgebra

lets.go

[thorn sundial]

isn't it 80?

or 35

[alpine sable]

send me your steps

[alpine sable]

hold up

why 20

no it doesn't equate to 20 nor 80

if r = 35

wait i mixed r n d up

[thorn sundial]

😭😭

[alpine sable]

nope that should be ok

ure finen

try 35

today i realised that i can't do math

[thorn sundial]

nah ur proably tired

[alpine sable]

i just woke up

and started doing mf calculus

@buoyant kayak uhh could you help me find the mistake here

the one at the extreme left

same q i sent earlier

cuz im pretty sure i messed up somewhere

[buoyant kayak]

you just forgot to subtract 1 from the power

should be -3/2 not -1/2

other than that, pretty sure that's correct

[alpine sable]

wait it was already -1/2..

shit

thats where i messed up

also, according to the answer key the 3 is supposed to be -3

[buoyant kayak]

oh yeah

power rule, multiply by -1/2

so that would turn it negative

[alpine sable]

alriiiight

thanks

[buoyant kayak]

👍

[alpine sable]

it's always these kinds of mistakes that get me lol

[fast steppe]

Question 63 is my question here. Is this not a function because either when x is 3 or -3 and y can be either 3 or -3? Since function has to be there is only one y when there is only one x value?

[clever folio]

So for your example with 3 you would agree (3,3) and (3,-3) are in W right?

The defn of a function requires any element in the domain to map to exactly one element of the codomain.

[fast steppe]

I'm also trying to understand what W is

[clever folio]

So does W map 3 to only one thing?

[fast steppe]

W stands for

[clever folio]

W is just a set right?

[fast steppe]

Yeah

[clever folio]

You could also call it a relation of course.

[fast steppe]

Does it mean when you make the graph, when you make a straight line in x axis there should be only one element that connects with y?

[clever folio]

Do you mean like the vertical line test?

Prettt sure that's what you mean.

[fast steppe]

For example this is not a function

[clever folio]

Yah that's right.

[alpine sable]

thought thar was a parabola and the notebook was sideways for a second

wait no that is a parabola

[fast steppe]

Thank you. But I'm trying to make a graph on the question 63

[clever folio]

You could do it in desmos I suppose.

It probably has some features that look a little like a square or diamond.

[fast steppe]

That clarifies that it's not a function then

[clever folio]

So the reason you want to graph, is that anything to do with that alt defn of a function ur book mentions?

[fast steppe]

No just for my personal questions

[clever folio]

Your ex with the num 3 was more than enough by the usual defn of a function.

[fast steppe]

X2 + Y2 = 4?

[clever folio]

An easy way to graph it is to notice for y>=0 that y=|x| and for y<0 y=-|x|

[clever folio]

What?

[fast steppe]

Oh I thought you meant example 3 of that question set

[clever folio]

No when you were talking about (3,y)

In W and you pointed out y could be 3 or -3.

[fast steppe]

Yes

[clever folio]

Makes sense to me.

[fast steppe]

Thanks :3

[clever folio]

I guess just be sure to make sure it's clear why (3,3),(3,-3) is a counter ex to your defn for a function though. Informally I'd just say x maps to two different things in W I suppose.

[mortal void]

is it free right now?

[rich basin]

Would anybody help me with this?

<@&286206848099549185>

[alpine sable]

@rich basinthis one?

[glass lichen]

Yes, the one they linked too

[alpine sable]

@rich basinwhich part don't you understand

i suggest first calculating the acceleration

and the equating the force with friction

[glass lichen]

I suggest waiting for them to answer your first question

[split trail]

can someone do 11-14 and teach me how to do it pls

<@&286206848099549185>

[alpine sable]

ok let's do it

[split trail]

i get questions like f(4)

[alpine sable]

do you want to join call

[split trail]

sure

[alpine sable]

mathematics call

[rich basin]

@alpine sable so what i don't understand is how can we calculate the accleration?