help-0

[alpine nacelle]

@craggy elbow the non integers solutions are +-sqrt(2), +-sqrt(6), +-sqrt(12)

and +- sqrt(20)

you have to use that x² is an integer

[craggy elbow]

assume as integer?

[alpine nacelle]

let x be a solution of floor(x)ceil(x) = x², then floor(x)ceil(x) is an integer by definition

so x² is an integer

[craggy elbow]

yes

[alpine nacelle]

so a non integer x which is a solution, is of the form +-sqrt(k) with k some integer

now you only have to prove that there are only 4 such k

2, 6, 12, 20

[craggy elbow]

why 4

[alpine nacelle]

because I'm hopping that they are not solutions more difficult to find lol

what you're trying to solve for x non integer, is equivalent to finding x such that
a < x < a+1 and x² = a(a+1)

for an integer a (which is floor(x))

[craggy elbow]

so is that always a condition?

[alpine nacelle]

let me check 2 sec

I mean yeah it's equivalent but I'm not sure how to check I have every sol

x² = a²+2a{x}+{x}² = a²+a
{x}²+2a{x}-a = 0

aaaah annoying pb

[craggy elbow]

maybe im just annoying coz i dont get it

😔

[alpine nacelle]

oh no there are more solutions

+- sqrt(90) works too

eeehhh I hate my life rn

at least you know that some square roots are solutions and others are not

[craggy elbow]

yes

does this make any sense to you

[alpine nacelle]

your last line is wrong

no sorry, the line before

[craggy elbow]

it shud be equal to 0

[alpine nacelle]

otherwise yeah the idea is good, your a is what we call fractional part

[craggy elbow]

yea the 0.something

[alpine nacelle]

that's what I was writing {x}

[craggy elbow]

so now using the last line i have to find the solutions?

i will have to test every a and b value

[alpine nacelle]

I noted a the floor and {x} the frac part

you have the same equation written differently

'cause your b is 1-a

And then I was thinking about solving for frac part

and find some condition on it

[alpine sable]

istead of taking as b can we take it as (x-a)+1

[alpine nacelle]

(x-a)+1 is the ceil, if you define a as the frac part

b is 1-a in his sub

[alpine sable]

ohhk

i understood

well both are same

[craggy elbow]

i think its b = 1+ a?

or no...

how did you get b = 1-a

[alpine nacelle]

for x non integer, ceil(x) = floor(x)+1 = x-a+1 = x+b

b = 1-a

[craggy elbow]

😅

[alpine nacelle]

it's really annoying I don't get if you're supposed to answer with mathematica or Idk lol, solving it is a pain

[craggy elbow]

i dont need mathematica for the 3rd and 4th one

[alpine nacelle]

we found an overset of the solutions but argh

[alpine sable]

well i got it in the form of -((a^2)+a)/(2a-1)

so a is not 0.5

[alpine nacelle]

yes but this is obvious, a number that has 0.5 has a frac part won't have a integer square

[alpine sable]

yes

mostly all of them will be irrational right

if not all

[alpine nacelle]

we found an overset of solutions already

either x is an integer, as all integers are solutions, either x is equal to +-sqrt(k) for some integer k

as x² is an integer

[alpine sable]

ok, so i just found the algebraic function of the decimal part of a that can define x.

[alpine nacelle]

now we just need to find the set of possible k

a way to get them all

[craggy elbow]

😬

[alpine sable]

,help

[ocean seal]

I can't DM you! Do you have DMs disabled?

Sep 22, 2021, 7:59 AM

[alpine sable]

,help

[ocean seal]

A brief description and guide on how to use me was sent to your DMs!
Please use ,list to see a list of all my commands, and ,help cmd to get detailed help on a command!

[obsidian terrace]

can anyone give me some method to factorize polynomials with 2 variables?

[alpine sable]

what is the degree of the polynomial

[obsidian terrace]

2 and 3

[alpine sable]

0

[obsidian terrace]

nah dont worry

[alpine sable]

degree 2, can you send the general form of quadratic polynomial with two variables.

<@&268886789983436800> please help

[sly mantle]

b&

[alpine sable]

he was speaking stuff like this

i took a screen shot

[craggy elbow]

i think he got banned

alrdy

[alpine sable]

ohh ok

cool

[sly mantle]

the msgs were deleted upon ban

[alpine sable]

ok i thought he was the one who deleted them so i posted

[obsidian terrace]

great, how about degree 3

[alpine nacelle]

@craggy elbow I think you can't do any better than solving {x}²+2floor(x){x}-floor(x) = 0 for {x} and adding floor(x) to the sol, it should give the entire set by def

[alpine sable]

umm i actually don't remember general form of polynomials in degree 2 and 3, so i am asking

fine i will google

[alpine nacelle]

but it's not satisfying

it doesn't really generate the sol

[alpine sable]

is it like this ax2 + bxy + cy2 + dx + ey + f = z

[craggy elbow]

i really think it has infinite solns

[alpine nacelle]

it has, it is an infinite set

but don't you need to specify which set ?

because it is Z U S, for S = {+-sqrt(k), k a certain set of integers}

[craggy elbow]

its just asking for the solution

[alpine nacelle]

yeah, the set of solutions is all integers union some square roots

but saying there are infinite solutions doesn't say which ones

so depending on what the teacher expect maybe you can avoid the pain I guess

OMG I'M SO DUMB

ebjfebfezf

[craggy elbow]

i think i just wasted your and my time

[alpine nacelle]

I figured it out

nah

[alpine sable]

doing math, no waste time.

[alpine nacelle]

the square roots that works are all sqrt(n(n+1))

I think

it's the exact set of roots that works

n integer

and so the set of solutions of the equations is Z union {+-sqrt(n(n+1)) | n in N}

but is it true

it should be

yes it explains the sol at least

and it is exact because n < sqrt(n(n+1)) < n+1

I'm so dumb srly

[alpine sable]

that is called too much

you are the one who solved it

why do you call yourself dumb

[craggy elbow]

yea

[alpine nacelle]

because we just had to square root floor(x)(floor(x)+1)

at least we've done it, that's the most important part

[alpine sable]

this is not hello channel go to chill

[craggy elbow]

You've done it

|| but tbh i didnt understand 1 thing 🏃‍♂️ ||

[alpine nacelle]

if x isn't an integer then your equation is equivalent to floor(x)(floor(x)+1) = x²
so x = +- sqrt(floor(x)(floor(x)+1))

and floor x is an integer, so we have an overset of the solutions at least, now we just need to check that x = sqrt(n(n+1)) gives a sol

and because it does, {+-sqrt(n(n+1)) | n in N} is the exact set of non integer sol

[craggy elbow]

so is this wrong

[alpine nacelle]

it's not wrong, it was equivalent

and not an easier way to see the problem

but it's still useful to check for equivalences

always a good habit

[alpine sable]

well, i kept the graph of x(x+1)=y^2 in desmos, then i find it very hard to find any kind of solution

is there any way to find solutions to that

because it is not a polynomial it is very hard for me to think of any way.

[alpine nacelle]

well x(x+1)=y^2 isn't linked to our problem right here
to find x that are sol, you would just x²+x-y² = 0

[alpine sable]

both are same right

arent they

you just re arrange them

[alpine nacelle]

what do you call both ?

[alpine sable]

aah

yes

thanks

[alpine nacelle]

I mean yeah but then you discriminant etc
or you write y = sqrt...

it's another curve

[alpine sable]

but if i draw the graph some weird x is coming out.

[alpine nacelle]

the 2nd one is the graph I would expect

the first one must be the same, zoomed out

I guess

[alpine sable]

yes

i zoomed it out

[alpine nacelle]

it's the expected behavior of y² = x(x+1)

as x(x+1)~x² as x -> infinity

[summer mica]

hi why is lim inf 1/x =0 but divergent

[placid zinc]

lim (as x approaches 0) 1/x does not exist

[summer mica]

i meant when x appr. infinity

not 0

[high cobalt]

Hello can anyone help me with my math homework?

[alpine sable]

umm chat bots again, who is doing this.

[high cobalt]

What chat bots?

[alpine sable]

not you

not you

[high cobalt]

Oh Ok

[alpine sable]

sorry wrong channel

[high cobalt]

No Problem

[obsidian terrace]

you should send it here and someone might help you

[ember mural]

how to check a multi-variable function continuous at a point?there're infinity way to approach a point, how should i show its Continuity?

[alpine sable]

how to find area and perimeter

[latent juniper]

connect the ends of the recatngle

it'll be easier

[alpine sable]

yeh

i make it a rectangle and a semi circle

[latent juniper]

ye then calculate areas of both and add

[alpine sable]

and perimeter part

also add them ig?

[craggy elbow]

same thing add

[latent juniper]

yes

[alpine sable]

:O

tysm

ok wait 1sec

whats the formulae of perimeter of a semi circle

[craggy elbow]

circle is 2pi r

[latent juniper]

semi is pi r+2r

[snow plume]

to calculate SS i need to find the mean, but what am I finding the mean of?

this is all the info i get

[craggy elbow]

pi*r + d

[latent juniper]

yea

[alpine sable]

and i am sure that the diameter of semicircle is 4 so r is 2

[latent juniper]

yes

[alpine sable]

ok so i use pi*r + d?

tysm

[latent juniper]

can someone help me w q8

[gray gorge]

What's the shape of the patch of grass it can reach

[latent juniper]

i think its a square field

[gray gorge]

Why do you think so?

[latent juniper]

cuz its a square in the figure

[marble sparrow]

can someone help me with this question?

how do I solve this?

and this one as well?

[latent juniper]

umm i havent learnt this yet

im sorry

[vale wigeon]

@marble sparrow this channel appears to be busy. let's move somewhere else.

[marble sparrow]

sure, where should i move to?

[vale wigeon]

#help-6 is free right now

[alpine sable]

@latent juniper ok so i am done i found the area of that given shape , but the perimeter come always wrong do you know why?

[latent juniper]

lemme calculate

[alpine sable]

take your time

[latent juniper]

did you take pi as 3.14?

@alpine sable

[alpine sable]

yes 3.142

the perimeter of semi circle is correct

10.3

but the prob is with rectangle

[latent juniper]

oh

i think perimeter of circle is 10.28

oh you rounded it off to 10.3

[alpine sable]

yes true

[latent juniper]

p of rectangle si 2(l+b)= 2(9+3)= 2x12=24

oh now i understand whats the issue

personal dms?

[alpine sable]

sure

A question a question!!

👀

[gritty latch]

[alpine sable]

1-cos theta / 1+ cos theta

The answer is :- (cosec theta - cot theta) ^2

@alpine sable @gritty latch Can anyone gimme the solution if anyone free?

[alpine sable]

sorry pal i didnt to that study part

[fading zephyr]

try multiplying top and bottom by 1 - cos theta and see what happens

[alpine sable]

No problem

[alpine sable]

Okei wait

[fading zephyr]

i would also recommend you only actually carry out the multiplication in the denominator

[alpine sable]

Just in denominator?

[fading zephyr]

multiply top and bottom, but only expand the denominator

[alpine sable]

Then it came up :-
(1-cos theta) ^2/1-cos^2 theta

[fading zephyr]

yep

now, you might recognize 1 - cos^2 theta

ring any bells?

[alpine sable]

Oh yes

[fading zephyr]

what can you substitute that for

[alpine sable]

The denominator :- sin^2 theta

[alpine sable]

🤔🤔

[fading zephyr]

you sure that's a minus there?

[alpine sable]

Yes there is

It is the question

[fading zephyr]

(1 + cos x) (1 - cos x) = 1 - cos ^2 x = sin^2 x

[alpine sable]

Yes

[fading zephyr]

mhm

so we have (1 - cos x)^2 / sin^2 x

[alpine sable]

Yes

[fading zephyr]

mhm

it's done

that's ((1 - cos x)/ sin x)^2

[alpine sable]

It's the answer

[fading zephyr]

yes

you figure out the rest, it's already done

[alpine sable]

Just need to simplify? Now

Okei then tnq. I'll do it

[fading zephyr]

what is cosec x? what is cot x? in terms of sin and cos

you'll see it

[rocky cape]

yo

[alpine sable]

The answer will be 1 I guess @alpine sable

[rocky cape]

How can I solve this ?

[fading zephyr]

it's not 1, wtf

[rocky cape]

just realised my question was a quadratic

soz

[carmine girder]

could someone explain

[rocky cape]

Yo i dont understand how to do this

i factorised

5x^4(x^4 - 25x) = 0

but idk wat to do anymore

[alpine sable]

Nope it's not

[alpine sable]

Wait lemme try

The answer is :-
5x^5(x^3 - 25)

bruh

@crude flax

help or sussy

what is x tho

[latent juniper]

i can do that

[crude flax]

is that haese mathematics?

Lol

[alpine sable]

bruh

Uh what are the new chances if I skip the common tier 😅

idk man

[short widget]

Question

[alpine sable]

help

x

find

wrong

F

how find x

bruh what

[carmine lion]

what am i doing wrong here?

i checked sqrt(2+2cost) on the calc with some values

its the same as 2cos(t/2)

but how do i prove this

cos(a)cos(b) - sin(a)(sin(b)

@umbral dune

this is occupid

this channel

[split oriole]

use double angle formula

[carmine lion]

OH MY

oops wrong channel

[split oriole]

$\sqrt{2+2\cos x} =\sqrt{2}\sqrt{1+\cos x}$\ $\sqrt{2}. \sqrt{2\cos^{2}(\frac{x}{2})}$

[ocean seal]

Algebra

[agile fulcrum]

is this a legal way to find constant C?
1 = A(x-4)(x-1) + B(x-4)^2(x-1) + C(x-4)^3
let x = 1
C=-1/27
is this acceptable?
because apparently its wrong

C is supposed to be -1/9

nvm i see the problem

[carmine lion]

thanks

i get it now

[alpine sable]

hey can someone teach me the basics on angles

like how to calculate the interior and exterior

[rocky atlas]

Interior and exterior of what

There is wall seperating outside of your house and inside of your house. If you don't name that wall, how do we know whose interior and exterior you're asking.

[alpine sable]

no

[lament igloo]

do u mean co-interior angles

[alpine sable]

I mean calculating the interior and exterior

of an angle ig

[lament igloo]

like this?

[rocky atlas]

Can you show the question?

[alpine sable]

that too

[lament igloo]

well both angles combined will always = 180

[alpine sable]

I dont have a question i just need to learn cuz I wasn't there when they taught it

[lament igloo]

so if the bottom angle was 40 for example

the top would be 180 - 40

= 140

[alpine sable]

Of a triangle

[rocky atlas]

Oh

Exterior angle= sum of two opposite interior angles

If that's what you're asking

[alpine sable]

oh

I understand

[rocky atlas]

It should be in your book too

[alpine sable]

[rocky atlas]

You don't take the angle beside the exterior

You take Opposite of that - the two other angles and add 'em to get the value equivalent to your exterior angle

[alpine sable]

so you add the inside angle and you subtract from the outside?

[rain path]

77+33

[rocky atlas]

Your wordings are confusing

The Sum of inside angles are 180 degree

Obviously when you substract them from outside angle you get inside angle if that's what your question asks.

If that's what you meant lol

[alpine sable]

yuh

how does what's on the left become what's on the right? I got how to decompose numbers but I don't know how to make them into radicals

[cinder sorrel]

i have done this before but forgot what to do

[alpine sable]

like turn whole number into sqrt k form?

i guess

ah

ok so for 32

think about factors of 32

i guess

16 and 2 is the biggest factor that has one square number: 16

square root of 16 is 4

so its written as 4 root 2 as the answer

@alpine sable if this explanation is too vague i can write down a better explanation if u need

yeah but how do five 2s make 4v2

2•2V2?

but not 2V2•2

@alpine sable

[restive hill]

Can anyone help me?

[frank linden]

5x(3-6x)-4x you can Help me plz / 5x²-4(3-7x)

[oak chasm]

@alpine sable Well, it's a square root.

That's the second root.

So, you have to move the factors out in matching groups of two.

[granite tinsel]

5x(3-6x)-4x
=15x-30x²-4x
= 11x-30x²
Maybe

[alpine sable]

what about for example 40 (2, 2 2, 5)

[oak chasm]

You have five 2s.

sqrt(2⁵)

You match two of them up and that group can leave.

sqrt(2² · 2³)
2sqrt(2³)

You match 2 more of them up, and they can leave.

2sqrt(2² · 2¹)
2·2sqrt(2¹)

You only have 1 left, so it can't leave.

4sqrt(2).

[alpine sable]

bow does it work

[oak chasm]

sqrt(40)
sqrt(2³ · 5¹)

You match two 2s and they can leave.

sqrt(2² · 2¹ · 5¹)
2 sqrt(2¹ · 5¹)

You can't match up any more because you only have 1 of everything left.

2 sqrt(10).

Cube roots do groups of 3 because it's the 3rd root. And so on with the other roots.

Does that make sense?

[alpine sable]

so it becomes 8v5

[oak chasm]

No, you took out one group of 2s.

So there's one 2 in front.

And you left in a 2 and a 5.

So there's 10 inside.

Let's do it without exponents.

[alpine sable]

i don't understand anything

[oak chasm]

You got 40 = 2 · 2 · 2 · 5, right?

[alpine sable]

yes

[oak chasm]

OK, so now we're doing the square root.

[vivid ginkgo]

yes

[oak chasm]

The square root is the secord root.

[vivid ginkgo]

yes

[alpine sable]

why

[oak chasm]

Well, squaring is the second power, right?

x²

[vivid ginkgo]

yes

[alpine sable]

so its the second 2?

[oak chasm]

No, it's the second root.

[alpine sable]

wheres that

[oak chasm]

I don't understand the question.

It doesn't have a location.

[vivid ginkgo]

yes

[oak chasm]

@vivid ginkgo Please stop interrupting.

[vivid ginkgo]

ok

sorry

[alpine sable]

what's the second root

[oak chasm]

OK, let me explain.

You have exponents.

x², x³, x⁴, x⁵.

You've seen exponents, right?

[alpine sable]

yes i get it now

[oak chasm]

OK, roots also have a number.

[ocean seal]

Chai T. Rex

[oak chasm]

Have you seen those before?

[alpine sable]

mhm

[ocean seal]

Chai T. Rex

[oak chasm]

The invisible number is 2.

[alpine sable]

why

[ocean seal]

Chai T. Rex

[oak chasm]

Because they started out with square roots, so they used the root symbol for those.

Then they said we want to take more roots than just the square root.

So, they put the root number they're taking on the upper left corner of the root symbol.

[ocean seal]

Chai T. Rex

[oak chasm]

Does that make sense?

[alpine sable]

yeah

so how do I root-alize 40

with 2 2 2 5

[oak chasm]

OK, so we're taking the 2nd root (the 2 is the number in the upper left corner of the root with the square root).

So, the 2nd root means groups of 2.

The 5th root would be groups of 5.

But we're doing the 2nd root.

So it's groups of 2.

Does that make sense?

[alpine sable]

yes

[oak chasm]

OK, so 2, 2, 2, 5

That's two different numbers, 2 and 5.

Let's do the 2s first.

We need groups of 2 since it's the 2nd root.

So, we get a group of 2: 2, 2, 2, 5.

See how I've picked a group of two 2s?

[alpine sable]

yes

[oak chasm]

OK, so each group I find of a number, I put one of that number in front of the square root.

I found one group, so one 2 in front.

2 sqrt(2 · 5)

See how the one 2 came out in front because I had one group of 2s?

[alpine sable]

yes

[oak chasm]

OK, now I have 2, 5 inside.

[alpine sable]

why

[oak chasm]

Can I get a group of two 2s?

Why what?

[alpine sable]

why are 2 and 5 inside

[oak chasm]

Because I take the group out of the inside.

I had that group of 2s: 2, 2, 2, 5.

It gets taken away from the numbers inside the square root.

So, I have 2, 2, 2, 5 left.

2, 5 after I remove them.

That group is gone.

Does that make sense?

[alpine sable]

yes

[oak chasm]

OK, so it's like this.

We found a group of two 2s.

We get rid of that group from the inside of the square root.

[alpine sable]

waiot

[oak chasm]

It's one group, so we put one 2 in front.

[alpine sable]

so are u doing surds or prime factorisation @alpine sable

👁️

[oak chasm]

sqrt(2 · 2 · 2 · 5)
sqrt(2 · 2 · 2 · 5)
2 sqrt(2 · 5)

The group moves out of the square root and it gets combined into just one 2.

Does that make sense?

[alpine sable]

yeah

[oak chasm]

OK, now we have 2 and 5 in the square root still.

Can we get a group of two 2s from 2, 5?

[alpine sable]

no

@alpine sable are u doing surds

[oak chasm]

Right, there's only one 2 left, so that's not enough to get two of them.

[alpine sable]

or what exactly do u need help with

[oak chasm]

Can we get a group of two 5s?

[alpine sable]

no

[oak chasm]

Right. So we can't get any of the remaining numbers out of the square root, so they're trapped there.

[alpine sable]

yes

hmm

[oak chasm]

So, we have 2 sqrt(2 · 5)

And then we just multiply.

2 sqrt(10).

Does that make sense?

[alpine sable]

so it's 4v10

[oak chasm]

No.

[alpine sable]

2v10

[oak chasm]

When we took the group of two 2s out, it got combined into one 2 on the outside.

So, there's only one 2 on the outside.

[alpine sable]

2√10

2v10

[oak chasm]

Right.

[alpine sable]

ok

i got it

are u in gd9

[oak chasm]

This same thing works for cube roots (the 3rd root, so use groups of three) and all the other roots.

You just use groups of whatever root number you're working with.

10th root, use groups of ten.

[alpine sable]

what do i do after i got 2/1-cosec^2theta

[oak chasm]

OK, so csc²(θ) = 1/sin²(θ)

[alpine sable]

hmm

[ocean seal]

Chai T. Rex

[alpine sable]

oh

lmaooo i forgot how to do it 😩

wait

nvm

[alpine sable]

what do you mean 3th 4th... roots?

whats the difference

what if i want 3th root with 40

with?

do u mean of

of

cube root of 40??

[oak chasm]

OK, so you have:

cbrt(40)
cbrt(2 · 2 · 2 · 5)

Two different numbers there, 2 and 5.

Let's do the 2s.

It's the 3rd root, so we do groups of three.

Is there a group of three 2s?

[alpine sable]

wtf square root cube root..

whats the difference

[oak chasm]

The number is different.

[ocean seal]

Chai T. Rex

[alpine sable]

square root is second root
cube root is third root
the others are just fourth root, fifth root etc

mhm

[oak chasm]

The square root tells you what number you can square to get 40.

Like the square root of 9 is 3 because 3 squared is 9.

The cube root tells you what number you can cube to get 40.

Like the cube root of 27 is 3 because 3 cubed is 27.

So it undoes the exponent so to speak.

3 cubed is 27.

If you want to get the 3 back, you take the cube root of 27.

5⁴ is 625.

If you want to get the 5 back, you take the fourth root of 625.

It undoes the exponent.

Does that make sense?

[alpine sable]

what about 500

2 2 5 5 5

[oak chasm]

Right, which root?

[alpine sable]

square

[oak chasm]

sqrt(2 2 5 5 5)

We have two different numbers there: 2 and 5.

Let's do the 2s.

2nd root, so groups of two.

[alpine sable]

is it 10v5

[oak chasm]

Yes.

That's right.

[alpine sable]

wow im good

[oak chasm]

Yes, once you get it, it's not so bad.

[alpine sable]

👁️ oh so it was surds the whole time

whats a surd

its like

[alpine sable]

this

[oak chasm]

A surd is an irrational number.

[alpine sable]

thats called surd form

ah

yeee

have u learned the surd rules yet?

laws

[oak chasm]

And if you get numbers trapped in the square root, like 10 sqrt(5) has 5 trapped there, then 10 sqrt(5) is a surd.

[alpine sable]

i dont get irrational numbers
cant 10v5 be written as
10v5

1

??

[oak chasm]

Rational means integer over integer.

Ratio is number over number.

[alpine sable]

ah ok

[oak chasm]

Rational number is integer over integer.

[alpine sable]

basically irrational numbers are decimals that dont terminate

[oak chasm]

No, they don't repeat.

1/3 doesn't terminate, but it repeats forever.

[alpine sable]

oh right

[oak chasm]

0.333333 has 3 repeating.

,calc 1/7

[ocean seal]

Result:

0.14285714285714

[oak chasm]

1/7 has 142857 repeating forever, so it's rational.

[alpine sable]

ah i see

:O

Any genius in here that knows how to invert

(1-(1-x)^g+x^g)/2

for the range of 0<=x<=1?

[oak chasm]

@alpine sable Try doing cbrt(500).

[alpine sable]

wolfram fails sadly

what's cbrt

cube root

[oak chasm]

@alpine sable That's going to be hard because you have exponents and addition.

[alpine sable]

ah

5v2?

[alpine sable]

So best to give up on it then?

[alpine sable]

square root= 2nd root
cube root= third root

[oak chasm]

@alpine sable Almost.

You have two 2s trapped in there.

[alpine sable]

2v5

[oak chasm]

cbrt(500)
cbrt(2 2 5 5 5)
cbrt(2 2 5 5 5)
5 cbrt(2 2)

Can't take any more out.
5 cbrt(4)

Does that make sense?

[alpine sable]

ah yes

[oak chasm]

@slender stump Sorry, this channel is busy.

[alpine sable]

it for example i take 320 (160, 2) can it be both 2v160 and 160v2

[oak chasm]

Nope, when you take a group out, it reduces to one item.

So, there will be less things outside than inside.

[alpine sable]

so 160v2

[oak chasm]

Nope, use the method.

Keep factoring.

[alpine sable]

idk

no I mean 160, 2 is possible right?

how do you put it

[oak chasm]

For factoring it, yes, but not for square root result.

Like 320 does equal 2 · 160.

So, that's partly done factoring.

But sqrt(320) is not 2 sqrt(160) because you need to take out the 2s in groups of two.

So, you have to get two 2s to get a group.

So, let's do it that way.

sqrt(320)
sqrt(2 · 160)
sqrt(2 · 2 · 80)
2 sqrt(80)

[alpine sable]

320 = 2 2 2 2 2 2 5 = 6v5?

[oak chasm]

Nope, you have 3 groups of 2s, right?

They multiply together, not add.

It's not (2 + 2 + 2)sqrt(5)

[alpine sable]

ah ok

so 8v5

[oak chasm]

Right!

[alpine sable]

oh huh that seems cool

i never learned it that way lmao

[oak chasm]

There's a faster way.

It's more complex.

[alpine sable]

how 👁️

[oak chasm]

You get the factorization.

2⁶ · 5¹

We use exponents.

[alpine sable]

oh

[oak chasm]

Now, from grade school, there's a way to divide two numbers and get a quotient and remainder.

Like 5 divided by 2 is 2r1.

[alpine sable]

ye

[oak chasm]

2 with a remainder of 1.

Do you remember that?

[alpine sable]

ye LMAO

[oak chasm]

OK, so you do that with each exponent.

[alpine sable]

whaaa

[oak chasm]

The 2 exponent is 6.

We're doing the 2nd root.

[alpine sable]

yes

[oak chasm]

6 divided by 2 is 3r0

[alpine sable]

ye

[oak chasm]

3 will be the exponent outside the square root.

0 will be the exponent inside the square root.

Outside gets the quotient.

Inside gets the remainder.

[alpine sable]

oh

[oak chasm]

The exponent on 5 is 1.

We're doing the 2nd root, so we divide by 2.

1 divided by 2 is 0r1.

[alpine sable]

uh

[oak chasm]

The exponent is 0 outside and 1 inside.

[alpine sable]

👁️ are u sure this method is faster

[oak chasm]

Yes, since you don't have to count groups.

[alpine sable]

i just guess the factors lol

[oak chasm]

So, we get 2³ · 5⁰ sqrt(2⁰ · 5¹)

8 sqrt(5)

[alpine sable]

ah

[oak chasm]

This method is faster if you have large exponents, I guess.

Like if you can see how many groups there are at a glance, that's fine.

Otherwise, maybe dividing is faster than grouping things up.

[alpine sable]

mmmmm

[oak chasm]

(2¹⁰³ · 3⁴)^(1/5)

[alpine sable]

👁️

[oak chasm]

2²⁰ (2³ · 3⁴)^(1/5)

That's the fifth root.

[alpine sable]

oh yeah indices law

[oak chasm]

Roots can be written as exponents by using the reciprocal of the root number.

[alpine sable]

yee

[oak chasm]

There's one more thing in simplifying.

[alpine sable]

whats that

[oak chasm]

Sixth root of 3⁹

That's 3 (3³)^(1/6), right?

[alpine sable]

🤨

oh

ok nvm yeah

[oak chasm]

(3³)^(1/6) = 3^(3/6) = 3^(1/2)

So, sixth root of 3⁹ is 3 sqrt(3).

[alpine sable]

ah

😭 my indices is so bad

[oak chasm]

Sometimes the GCD of the exponents left in the root and the root number can be used to reduce the exponents and the root number.

[rose fulcrum]

(3^9)^(1/6) = 3^(9/6) = 3^(3/2)
So 6th root of 3^9 is 3^(3/2)?

[oak chasm]

GCD(3, 6) = 3, so you get exponents of 3/3 and root number of 6/3.

@rose fulcrum Yes.

[rose fulcrum]

So its sqrt(3) cubed

[oak chasm]

Right, or 3 sqrt(3).

[rose fulcrum]

Not 3 sqrt 3

[oak chasm]

,w 3 sqrt(3) = sqrt(3)^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]

They're both correct.

[rose fulcrum]

Oh kk my bad

[oak chasm]

(sqrt(3))³ = sqrt(3) · sqrt(3) · sqrt(3)

[alpine sable]

3^2*3=√27

[oak chasm]

Combine the first two sqrt(3)s.

[rose fulcrum]

Oh yeah obviously haha

[oak chasm]

3 sqrt(3).

[alpine sable]

,w (sqrt(3))³ = sqrt(3) · sqrt(3) · sqrt(3)

[ocean seal]

Results provided by WolframAlpha

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

Requested by milk129#7389

[alpine sable]

woah

[oak chasm]

Yep, exponents just tell you how many copies of the base to multiply together.

[alpine sable]

this texit thing is cool

also do u know where i can learn latex

is there like a textbook or smth i have to read

[oak chasm]

You can read the pinned messages in #latex-help and ask questions there (test in #latex-testing).

[alpine sable]

oo

[gilded aurora]

help me with this pls 🥺

[burnt cliff]

cube is 3 time or just the normal cube

[gilded aurora]

just normal cube

[burnt cliff]

ok

[alpine sable]

where have i seen that question before

,w [(1/2)X]-5

[ocean seal]

Results provided by WolframAlpha

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

Requested by milk129#7389

[gilded aurora]

this question ?

[alpine sable]

hmm

im not that great at math so im not gonna tell u what i think my answer is

🥶

[gilded aurora]

oh, im too mate, failed 2 time T_t

this 3rd and last wish i got 😦

[alpine sable]

failed what

😥

[gilded aurora]

in math university

[alpine sable]

f

[gilded aurora]

im interested in computer 😦 idk why they included this subject 😦 maybe needed for future

[alpine sable]

oo

[alpine sable]

for you to search the question on it 😈

🤭 researching

[gilded aurora]

:/

this what i have got so far :(((

[alpine sable]

21 = 3 7 = 3v7?

no

you cant get 21 into surd form

i think

why

21 is irrational

well

sqrt 21

surds is irrational root but of a rational number

[oak chasm]

@alpine sable Remember to group them up before taking them out.

[alpine sable]

theres no group

ukw

my math vocab is just horrendous

🥲

[oak chasm]

sqrt(21)
sqrt(3 · 7)

No groups of two, so they're stuck there.

sqrt(21) is the simplified form.

[alpine sable]

you cant simplify √21

yes

[oak chasm]

You can't always change it.

[alpine sable]

ah

ok

:(

[oak chasm]

If there aren't going to be any groups, you can't rescue anyone out of the square root.

[alpine sable]

i didnt know that

[oak chasm]

@gilded aurora How did you get 0 with two dice?

Oh, difference.

[minor willow]

is this channel occupied?

[alpine sable]

@minor willow i think so

[safe vine]

do you normally simplify probabilites?

[alpine sable]

wait if sth like this cant be factorised do i use quadratic formula? And what if it could be factorised?– do i then use factorisation or the quadratic formula

[vale wigeon]

you can use the quadratic formula on any quadratic equation if you want

whether it was nicely factorable or not

[oak chasm]

All quadratics can be factorized if you're OK with complex numbers.

[alpine sable]

how do i calculate hard percentages on paper

for example 62% of 25

[oak chasm]

OK, % is /100.

62% of 25
62/100 · 25

Now, the 25 cancels with the 25 in the 100.

62/4

31/2

Does that make sense?

[alpine sable]

mhm

what if it was 26

100 and 26 dont cancel

wouldnt that be much harder to cculate

[oak chasm]

A bit.

62% of 26

62/100 · 26

[alpine sable]

multiply 62 and 26 and shift decimal point to the left by 2

[oak chasm]

(62 · 26)/100

[minor willow]

no

[oak chasm]

Now the 62 has a 2, the 26 has 2.

The 100 has two 2s.

(31 · 13)/25

After you cancel the 2s.

Then there's no more cancelling because 31 and 13 are primes and the only primes 25 has are 5.

So, you multiply 31 and 13.

[alpine sable]

what about 27

[oak chasm]

403/25

62% of 27
62/100 · 27
(62 · 27)/100
There's one 2 in the top that can cancel with a 2 in the bottom.

(31 · 27)/50

837/50

[alpine sable]

this is much better wow thanks

[oak chasm]

Yes, that's the way to get the decimal answer.

Mine is the way to get an exact answer.

[vale wigeon]

not that it matters much since the decimals in these cases are all terminating...

[oak chasm]

Well, that's true.

I suppose mine is the way to get a reduced fraction.

[quick echo]

is there a way to simplify this even further?

[glass lichen]

not really

[alpine sable]

how??

[oak chasm]

Well, you'll get a(x - q)(x - r).

a is the coefficient of x² you start with.

q and r are the solutions you get from the quadratic formula.

[alpine sable]

wait so is the imaginary number used in the quadratic formula

[oak chasm]

Well, the quadratic formula has a square root.

If the number in it is negative, you get an imaginary number.

[alpine sable]

ah

[oak chasm]

That's added or subtracted to the real number outside the square root to give you complex number.

[alpine sable]

kk

[quick echo]

what is the formula for directrix when the ellipse center is not at the origin?

i tried adding and subtracting a^2/c to the vertices but its not working :/

[wary stream]

This is a simple Google search

[quick echo]

i cant really find it .-.

its not equal ;-;

center is at (1,-2)

a^2/c = 2sqrt10

[alpine sable]

What do i need to know to solve work on ordinary differential equations

We started them today and all is just confusing. Can’t tell the difference between dy/dx and y’. And I have no idea what kinda solution we look for

Are there some basics I gotta review for this?

whats the quadratic formula

[lime harness]

@alpine sable

[wary stream]

You realize that you can Google this

[alpine sable]

its too complicated

[glass lichen]

google isnt complicated

[wary stream]

How?

[alpine sable]

everyone on google is explained in a hard way

i mean the first results are always wikipedia

[oak chasm]

@alpine sable Use Khan Academy instead.

They have good explaining videos.

[alpine sable]

whats +
_

[wary stream]

Don't go to wikipedia, go to the images

[alpine sable]

±

[glass lichen]

plus minus

[oak chasm]

@alpine sable ± means you have two numbers. In one, you add. In the other, you subtract.

3 ± 2 has two results: 3 + 2 and 3 - 2.

[alpine sable]

ahh yeah makes sense

[alpine sable]

Where to start

[glass lichen]

???

wdym

[hexed solar]

Can anyone please help me solve a question?

[glass lichen]

You want to know about the quad formula... so look up.. the quad formula on Khan

[wary stream]

If you're referring to quadratic formula, they have a search bar to search things up on their site

[alpine sable]

ah ok

[wary stream]

No, no one, in a math server, knows how to solve a question \s

[oak chasm]

@alpine sable It's in their algebra 1 course: https://www.khanacademy.org/math/algebra. Go to the "Quadratic functions & equations" section.

It's in there.

If you're not ready for that yet, you can go to earlier sections and learn until you're ready.

Here's the exact video: https://www.khanacademy.org/math/algebra/x2f8bb11595b61c86:quadratic-functions-equations/x2f8bb11595b61c86:quadratic-formula-a1/v/using-the-quadratic-formula?modal=1.

[desert moon]

Could anyone please explain how I should get the power series for 2x/(e^(2x)-1)

What ive tried so far is doing 2x * (1 + (-e (2x))^-1
Getting the power series for (1+x)^-1 and substituting x= (-e^(2x)) into the power series

What i get is something that kinda converges to the function at negative x but not positive x

By l hopital rule i know that f (x->0) is 2

Since undefined for x=0

[burnt wharf]

@mathsJo bhi kardega iss question ko mann jaunga
Waise mughse bhi nhi bann rha

Challenge to alll

[alpine sable]

Tree on right doesn't seem to be AVL unless I'm wrong and drunk af

node 5 has balance factor of 2 no?

[dusk tiger]

So I have a problem in my math hw.

Consider the points (-5,0) and (0,3). Plot the points and find the distance between them. Give your answer both in exact form and as a decimal approximation.

What’s decimal approximation?

[oak chasm]

Child subtrees differ in height by at most one. Child subtrees of 5 are height 2 and 0.

@dusk tiger They mean to write it in decimal with only so many digits.

Like π can be written in decimal as 3.14.

That's only three digits.

So, it's a decimal approximation.

[dusk tiger]

Ok that makes sense lol. Thanks

[oak chasm]

No problem.

[alpine sable]

I thought you would need a single right rotation to balance a tree like this

my brain 😳

[oak chasm]

Yes, that would work.

[alpine sable]

I have to do 10 questions within 2 hours, it’s midpoint and distance formula, anyone help please?

[oak chasm]

Well, the midpoint is the average for each component.

[alpine sable]

Yes

[oak chasm]

So, -7 is the average of -6 and Bₓ.

[alpine sable]

Alright

[oak chasm]

Write the formula for the average.

(-6 + x)/2 = -7

[alpine sable]

Alright

[oak chasm]

Then get x.

Then do the same for y.

[alpine sable]

Okay

I can’t do it

:/

[oak chasm]

Which part?

[alpine sable]

Doing it for Y

[oak chasm]

OK, so you have two endpoints.

[alpine sable]

Yeah

[oak chasm]

Those two endpoints have y components.

[alpine sable]

Yeah Y coordinates

[oak chasm]

-3 and y where y is B's y component.

Now take the average of them.

[alpine sable]

How do I get the average?

[oak chasm]

OK, an average is where you add the things together.

Then you divide by the count of the things.

We have two things.

So, we divide by 2.

(-3 + y)/2

I added -3 and y together.

Then I divided by how many things I added together.

Does that make sense?

[alpine sable]

Alright I’ll try it

Yea

this is where i get always confused... where did 4b go in all of this??

[oak chasm]

4b had 5b subtracted from it.

[alpine sable]

didn't 5b subtract 5

[oak chasm]

4b - 5b
(4 - 5)b [distributive property]
-1b
-b

Nope, the second line has 5b being subtracted from both sides.

So, you have 4b - 5b on the left.

Undistribute the b.

4b - 5b
(4 - 5)b

Then do the work in the parentheses.

-1b

Then we don't write 1 as a coefficient.

-b

Are you still stuck on it?

[alpine sable]

also how do you choose the numbers to add or subtract in an equation? did it have to necessarily be 5b

[oak chasm]

Well, we want all the b terms on one side.

So, we need to get rid of the b term on the left side or the b term on the right side.

That way, there will only be a b term on one side.

Does that make sense so far?

[alpine sable]

yeah

[oak chasm]

4b + 5 = 1 + 5b

Now, we can subtract the 4b term from the left side to get rid of it.

Or we can subtract the 5b term from the right side to get rid of it.

They chose to get rid of the 5b on the right.

Let's do it the other way.

Let's get rid of the 4b on the left.

4b + 5 = 1 + 5b
4b + 5 - 4b = 1 + 5b - 4b

I've subtracted 4b from both sides.

After we combine like terms, we get:

5 = 1 + b

Does that make sense?

[alpine sable]

yeah

thanks

[oak chasm]

Then we want to get the non-b terms on the other side.

So, we get rid of the 1 term on the b's side.

5 - 1 = 1 + b - 1

4 = b

We get the same answer they did.

We just did it a different way.

[alpine sable]

👍

[rich ivy]

How so I get the zeros for this? I got 7,0 but it’s supposed to be something else

[ocean seal]

beanz

[grim tree]

guys help me please T-T,
determine the value of:

[alpine sable]

what about this? where did that 6r go

literally disappeared

[oak chasm]

-4(x + 1)² + 16 = 0

Divide both sides by -4.

(x + 1)² - 4 = 0

Move the 4 to the other side.

(x + 1)² = 4

Take the square root of both sides.

|x + 1| = 2

And then go from there.

Does that make sense?

[rich ivy]

so it’s 1,0?

[oak chasm]

Nope.

Where do you go from |x + 1| = 2?

[rich ivy]

subtract 1 from 2

[oak chasm]

Nope, the 1 is stuck in an absolute value right now.

[rich ivy]

uhh idk

[oak chasm]

You can't do anything to stuff stuck in a function.

OK, so |x + 1| = 2 has x + 1 negative or nonnegative, right?

If x + 1 is negative, then the absolute value will change its sign.

If it's not, then it won't.

So, we have two things:

-(x + 1) = 2
x + 1 = 2

Does that make sense?

Maybe an easier way to figure it out is that absolute value gives you the number with the sign gone.

If |x + 1| gives you 2, then x + 1 must be -2 or 2.

So,

|x + 1| = 2
x + 1 = ±2

[oak chasm]

Well, the right side has two r terms, -3r and 6r.

-3r + 6r
(-3 + 6)r
3r

[alpine sable]

ah so you also can calculate before starting the madness... equations have so many layers

[frosty cypress]

how would i solve this im so stuck lol

[oak chasm]

@alpine sable Yep, simplifying either side can be done any time.

@frosty cypress Factor the quadratic.

You can.

The process can be called either factoring or factorizing.

[frosty cypress]

And then what would I do?

[oak chasm]

OK, so get the range for x.

[frosty cypress]

The absolute value is confusing

[oak chasm]

|x - 1| < 0.1

[frosty cypress]

From the first equation?

[oak chasm]

Yes.

[frosty cypress]

Yeah for that one i got 0.99<x<1.1

[oak chasm]

I get 0.9 < x < 1.1

Hmm, let's go back.

[frosty cypress]

Yes

[oak chasm]

What did you get when you factored the quadratic?

[frosty cypress]

i got (x-1)^2

[oak chasm]

Good.

So, we want to know the interval for x - 1.