help-0

[twilit ibex]

Damn 😦

Where did you observe it?

[sage summit]

just run your computer at it

[twilit ibex]

Yourself?

Do you have a code?

[sage summit]

nope

[twilit ibex]

haha

damn

but what did you do?

Like, do you have any instructions?

For the algorithm that is

• but damn, that is really interresting. Because the first branch goes up to infinity, even then there are more primes on the 5 branch than the first...

That must really indicate something

(obviously)

Because the 5 branch has endings on some of its branches, so they stop.

But the first branch will produce infinitely.

Also instinctively, since there are only those 2 ways, one would think 50/50. But if it is skewed by a lot something must lie in that about primes.

[sage summit]

of the primes less than 1000

[twilit ibex]

Do we have any sort of number system based on the number 5?

Like we have hexadecimal?

ohhh...

[sage summit]

there are only 5 that don't go through 5

[twilit ibex]

So if we go above 1000 we don't know?

[sage summit]

113,151,227,401,953

[twilit ibex]

ha, nice

[sage summit]

all the others go through 5

and really idk why we are restricting to primes

[twilit ibex]

What do you mean?

[sage summit]

there is no reason to restrict to primes

[twilit ibex]

Because I want to know why some branches produce primes and others not

what else would you look for?

[sage summit]

the same is true if we don't restrict

[twilit ibex]

?

More NUMBERS go through 5 than 16?

[sage summit]

just look at all numbers, primes and nonprimes

yes

[twilit ibex]

Ah...

oh

But is it proportional?

[sage summit]

proportional to what

[twilit ibex]

I mean you might have 80% of numbers go through 5, but 90% of primes go through 5

[sage summit]

that's a tough question

[twilit ibex]

or to make it clearer 70% numbers, and 90% primes

[sage summit]

I don't know if there is an asymptotic density

[twilit ibex]

:/

But you only tested to 1000?

[sage summit]

ah I have not looked at that

(difference between prime / nonprime)

because I expect it to be completely irrelevant

[twilit ibex]

haha

you keep indirectly dissing my work

[sage summit]

I went a lot further once

[twilit ibex]

Still the same result?

[sage summit]

I don't remember how much

yeah I think

[twilit ibex]

Ah okay

[sage summit]

but also it was not clear if the limit for the asymptotic density existed

[twilit ibex]

hmmm

I will have to research that

Or

just what that actually entails

[sage summit]

well

if you could somehow come up with an asymptotic density for 5 or 32

chances are you could go and do the same for every split

[twilit ibex]

yeah

But

[sage summit]

and that would be pretty big news

[twilit ibex]

wouldn't my stems-and-branches system be a problem for that?

[sage summit]

I'm not sure what that means

[twilit ibex]

then I would need a way to merge branches

I am doing the inverse

so f.ex

32 is on the branch that has its stem at 1.

Because then I can write all numbers as a sequence of...

Let me see if I can write it correctly:

x +1 = n^(0+1) + n^(n+1) + n^(n_2+1)...

Basically I am looking for the data that is encoded in the numbers

[sage summit]

the asymptotic density of the set of powers of 2 is 0

[twilit ibex]

like 5 is 3 +2

Oh, is that what is it called?

Also n^0 is only for odd numbers

[sage summit]

5 = 3 + 2 looks more like numerology than any real maths

[twilit ibex]

ahah

Yes, but not really

Or

Basically...

Hmm... It might be numerology I don't know.

But it just seems like there must be some data encoded in the stems or the first numbers of each branch? Because as I said stem + first number in the branch = first number in the next branch.

Also there is a symbiosis of some kind between 2 being the base of all odd numbers and 3 being the lowest non-even prime.

And that any odd = 2^n+ 1

Not that 3 and 2 have magical powers, just that they're the base of all of this. So maybe there is some sort of mechanism that makes it tick like that.

Most of the base 10 numbers also originate from 5. It wouldn't be impossible to imagine, that they can make up most numbers with this algorithm.

• because you know, every number consists of the base 10

[sage summit]

yeah just stop

[twilit ibex]

😦

why?

[sage summit]

when you say base 10 you know you have left the realm of useful mathematics

[twilit ibex]

but why?

[strong furnace]

what du heck is going on here

[sage summit]

because if you had 7 fingers, would all of our maths break and collapse ?

[dense scaffold]

I have a question

I'm going thru my old set of quizzes rn

Can somebody help?

[twilit ibex]

No, but if all numbers were made of the 7 fingers, and our branches went through those numbers. Most of our primes are through these branches. And most of our numbers are also through these.

There just seems to be a coincidence, that is worth exploring

I can't formulate myself correctly :/

[strong furnace]

my bad lol I read that as note that 2 and 3 have magical powers

[twilit ibex]

haha I think Zef did too

[dense scaffold]

How'd you do that

That's cool

[twilit ibex]

It is just our system is based on 2 and 3

and 5, which has the most primes and numbers coincidentally IS 2 and 3

[dense scaffold]

Ugh

[twilit ibex]

Spain, we're in the middle of something here. You might have a better chance of getting help if you ask in anothe rchannel 🙂

• but is there any number system based on the number 2 or 3 or 5?

like hexadecimal

stupid me, there is it is called penta-decimal

[robust spindle]

thats base 16

[twilit ibex]

Yeah, just read that 😦

[robust spindle]

im sure bases 1-20 exist

and some after that exist too

[twilit ibex]

Well I will just have to look for those then.

I guess I should go back to looking at the branches now.

Thanks for the help @sage summit , will definetly look into that density thing.

[robust spindle]

Why is Collatz conjecture unproven anyway?

[twilit ibex]

No idea

Haha, not trying to prove it either

I think it is because it is an algorithm. It is very much not a priori based logic-system.

But as you can see from my use of big and general words, I should not be trusted to be your main source.

[knotty garnet]

Because its too hard to prove

[knotty garnet]

algorithms can be a priori, wat

do you know what a priori means

[twilit ibex]

Yes I believe I do.

It is hard for an algorithm that wishes to cover all natural numbers to be self evidently logical

[knotty garnet]

that's not even remotely true

it also has nothing to do with a priori's definition

[twilit ibex]

We can see from using and computing the algorithm that is true for most of the cases.

But the whole problem is, that we can't logically deduce for ALL cases

[knotty garnet]

for collatz no, because it is unproven, but that doesn't mean that it isn't a priori

it sounds like you don't know what a priori means

[twilit ibex]

I do

[warped phoenix]

[twilit ibex]

It means something is self evident without having to empirically experience it

I.e you can figure out logically that the collatz conjecture should worl for all numbers eithout computing

But we can't

[knotty garnet]

how is a formal math problem, algorithm or not, not a priori then

[twilit ibex]

Because it might be at some point in the future

not now because we have no previous knowledge that makes it so

that is why we have the fampus quote "Maths is not ready for the Collatz conjecture" paraphrasing

[knotty garnet]

as far as I'm aware, there is nothing that exists that is knowledge-dependent or time-dependent a priori

[twilit ibex]

[knotty garnet]

just because we haven't proven it yet, doesn't mean it isn't a priori

[twilit ibex]

No, not necessarily

[knotty garnet]

how do you empirically experience the collatz conjecture

[twilit ibex]

but we haven't proven it because it is not a priori

[warped phoenix]

:0

[twilit ibex]

by computing and then looking at the results

[knotty garnet]

fallacious

100% fallacious

[twilit ibex]

No

.

[warped phoenix]

😳

[knotty garnet]

answer this

[twilit ibex]

I have

right now ee compute it all, but we can't deduce what comes after

[bold sand]

Hmmm..hmmm...?

[twilit ibex]

Done.

[knotty garnet]

if that is how you define "empirical experience" then you have the definition completely wrong

[twilit ibex]

No.

[knotty garnet]

yes you do LMAO

[twilit ibex]

You haven't read up on your rationalism vs empiricism

[knotty garnet]

I definitely have

[twilit ibex]

No.

[knotty garnet]

this is one of my areas of expertise

your definition for a priori is off

[twilit ibex]

No. But also, I am on the phone and I gotta go.

[knotty garnet]

this isn't a matter of debate, you're just objectively wrong in this case, because any formal math problem is a priori by definition

[twilit ibex]

It is not a priori, because we lack the frame of refference to logically deduce it.

Which is also why we have the famous quote.

[knotty garnet]

it's literally logic and math

[twilit ibex]

Yes if we have refferences

[knotty garnet]

no that has nothing to do with it being a priori

[twilit ibex]

It does

[robust spindle]

then why not call it an axiom

[twilit ibex]

That is literally the reason for why certain things can't be proven

[knotty garnet]

you are so absolutely confused

[twilit ibex]

The thing Gödel proved

[knotty garnet]

unproven math is still math

[twilit ibex]

because they're all non priori

yesss but they are only proven by demonstration

I seriously g2g

[knotty garnet]

ffs all math is proven by demonstration

it's called a proof

doesn't make it not a priori

why is there so much pseudoscience and pseudomath this morning wtf happened

[knotty garnet]

Do you know what an axiom is

[robust spindle]

I wouldn't say yes 😓

[knotty garnet]

Axioms are the basic assumptions we need to make in math in order to do anything

We don't prove them, we just automatically accept them as true because there's no other known way to prove them (in that axiomatic system)

[robust spindle]

hmm

[knotty garnet]

For example, any number equals itself

You just accept that as fact

There's no way to prove it because it's too simple

Basic logical truths, such as:

No statement can simultaneously be true and false at the same time

[robust spindle]

What about paradoxical statements then

[knotty garnet]

They are neither true nor false

They are classified as contradictions, that's the formal word to describe them

Assuming there's no way to resolve them

So you can't label the collatz conjecture an axiom

[robust spindle]

Alright

[knotty garnet]

We don't even know if it's true, so we certainly can't just automatically assume it is

[warped phoenix]

“The reflector of a flashlight is in the shape of a parabolic surface. The reflections of all rays from the light bulb to any point on the parabolic surface will all be parallel to each other. The casting has a diameter of 16 cm in a depth of 8 cm. Find the focus to determine how far the lightbulb should be placed from the vertex.”

How do I do this?

All I know is what a directrix and focus is

Is it saying the directrix is 16 cm?

[knotty garnet]

No that's the end to end length of the mirror

The parabola shaped mirror width

[warped phoenix]

Oh so the reflectors width

Hm

So now what

What’s the depth?

[ebon quail]

could someone help me

[warped phoenix]

Bruh

[knotty garnet]

In your problem it literally says 8 cm 🙂

[warped phoenix]

What is the depth though

The depth of the light?

The depth of the reflector?

[plain hare]

How do I calculate the area of 4 given points?

[twilit ibex]

Turn them into a square

or square-like shape

and see which shape it makes?

[plain hare]

But I'm writing code for this, so I can't see what shape it makes manually

[twilit ibex]

uhhh

[queen wigeon]

shoelace formula?

[cosmic socket]

There's a trick to it

[cosmic socket]

Yes this

It is like a determinant

[plain hare]

Ah okay, will try to implement that, thanks

[warped phoenix]

“Match the given Info with the equation of the parabola.”

Focus : (-2, 6), Directrix: (y - 4)

I got the equation y = 5 + (x + 2)^2/4

That’s none of the answer choices though

Can someone tell me what I did wrong?

[tropic pine]

How many 5 digits no.s are there

And how to prove if 19 and 20 are co prime no.s

In a shop, there are three electronic devices which beeps at interval of 15, 20 and 30 minutes
respectively. They beeped together at 10 a.m. At what time will they all beep together again?

[warped phoenix]

<@&286206848099549185>

[cosmic socket]

It looks correct to me

(x-(-2))^2 = 4(y-5)

[small surge]

How does this work, i understand using the indefinite integral but i don't understand what to do with the 'a' infront of both X values

[tall pumice]

good afternoon, could someone help me with math?

[small surge]

oh nevermind i got the answer

[obtuse valve]

asking polar curve surface can someone do ?

[crisp sleet]

Thank you man

[alpine sable]

abi hangi sinif konu bu

ben kucugum

[obtuse valve]

üniversite 1 mat 2

[alpine sable]

iyimis abi kolay gelsin

[obtuse valve]

eyvallah hocam

[slim bone]

Help

[alpine sable]

,rccw

[alpine sable]

@slim bone have you tried anything so far?

[minor elbow]

area of circle =pi *r^2

so 6p-8pi=pi*(7x+9)^2

@slim bone

someone help me with this q plz

idk what to do

<@&286206848099549185>

[warped phoenix]

someone please help

how do i further simplify this?

[strong furnace]

damn it I wrote down the answer thing but deleted instead of posting lol

[minor elbow]

lol wha

[strong furnace]

negative reals multiplication in inequality reverses the order

[plain dawn]

this looks similar to an amc 10a problem. Maybe (x^2 + 3- 2)/x^2 + 3

[warped phoenix]

whats amc 10a

[plain dawn]

oh its a math competition lol

[warped phoenix]

oh lol

[minor elbow]

no but i just made it so that x_1+3x_3>=2x_2

[warped phoenix]

@plain dawn well the answer was $1 - \frac {2} {x^2+3}$

[ocean seal]

TheMane3

[warped phoenix]

and im curious how the hell they got that

[plain dawn]

yeye

bc x^2 + 3 - 2 / x^2 + 3 right

[minor elbow]

ah

[plain dawn]

so thats just x^2 + 3 / x^2 + 3 + -2/x^2 + 3

[minor elbow]

split x^2+3 into x^2+1+2

[strong furnace]

since I am lazy , I will just specify what I mean for some non zero x in S x1-2x2+3x3>=0 then ax1-2ax2+3x3<=0 for a <0

[warped phoenix]

$x^2 + 3 / x^2 + 3 + -2/x^2 + 3$

[ocean seal]

TheMane3

[strong furnace]

by non zero I mean non zero vector

[plain dawn]

ye that

[minor elbow]

bro there are people talking about 2 questions at once

its getting confusing

[warped phoenix]

^

[minor elbow]

dude can you move to diff channel plz

[alpine sable]

help

[mellow canyon]

how does this process work? Why does theta become isolated when you take the inverse of tan, and why does the inverse move to the other side?

[ocean seal]

Julian42

[blissful tinsel]

oh wait

$\tan^{-1}(\tan(\theta)) = \theta$

[ocean seal]

Julian42

[blissful tinsel]

so if you apply $\tan^{-1}$ to both sides you and up with your second expression

[ocean seal]

Julian42

[blissful tinsel]

not to confuse $\tan^{-1}$ with $\frac{1}{\tan(\theta)}$

[ocean seal]

Julian42

[placid zinc]

Simply because that's what tan^-1 is.
If tan(θ) = x
Then θ = tan^(-1)(x)

[rugged latch]

can anyone help with a physics question?

i kind of understand F = G * (m1 * m2) / r^2

i don't understand how that force is distributed between the two objects

like, I get that the sun is so massive that its pull towards the earth is negligable

but it exists

in the case of Pluto/Charon it's more obvious, both planets revolve around a common center of mass outside of either body

[finite spindle]

yes

[rugged latch]

thanks @finite spindle

hey wait....

[finite spindle]

what was the question again?

[rugged latch]

how does one determine the distribution of the attractive force?

is it a ratio of their masses?

[alpine sable]

the attractive force is towards both objects center of mass

[finite spindle]

and the force is equal on both objects

[rugged latch]

...processing...

[finite spindle]

equal but in exact opposite directions

[rugged latch]

okay, thanks! That makes sense

[warped phoenix]

Can someone walk me through step by step on factoring and simplifying this rational expression?

[sage jacinth]

factor by grouping

[warped phoenix]

how?

i did the denominator first, and factored it to $\frac{x^3+2x^2+3x+6}{\left(x+2\right)\left(x+4\right)}$

[ocean seal]

TheMane3

[sage jacinth]

there are 4 numbers on the top, so you can factor in groups of 2

[warped phoenix]

so make it $\frac{\left(x^3+2x^2\right)+\left(3x+6\right)}{\left(x+2\right)\left(x+4\right)}$?

[ocean seal]

TheMane3

[sage jacinth]

yes

now factor each pair on the top

[warped phoenix]

that makes it $\frac{x^2\left(x+2\right)+3\left(x+2\right)}{\left(x+2\right)\left(x+4\right)}$

[ocean seal]

TheMane3

[sage jacinth]

yes

[warped phoenix]

do i cancel out the (x + 2)

[sage jacinth]

now let u = (x+2)

[warped phoenix]

u?

[sage jacinth]

yea

the letter

[warped phoenix]

huh

ok

[sage jacinth]

im just doing this to make it simpler, but you generally dont need it

[warped phoenix]

hmm

alright

so then $\frac{ux^2+3u}{u\left(x+4\right)}$

[sage jacinth]

so the top is x^2*u + 3u --> (x^2+3) * u = (x^2+3)(x+2) because u = x+2

[ocean seal]

TheMane3

[sage jacinth]

or you factor out x+2 from both pairs and then cancel out afterward

yea

now you can just add like terms

and then resub and cancel

[ocean seal]

(バカ) baka

[solar pebble]

@warped phoenix is this channel finished?

or question

[warped phoenix]

yes

[solar pebble]

ok, thanks

now I have a question

why do $\frac{x+4}{x+5}$ and $\frac{x+4}{x+4}$ render differently shaped graphs? what's so significant about the $1$ difference?

It's obvious that they cancel out, but why doesn't that allow +4/+5 to cancel?

[ocean seal]

Xetrov

[solar pebble]

there we go

[queen wigeon]

well one is a rational function and one is a line with a hole at x=-4

[solar pebble]

I suppose you could say $\frac{x+4}{x+5} = \frac{x+5 - 1}{x+5} = \frac{1}{x+5} - \frac{x+5}{x+5} = \frac{1}{x+5} - 1$

[ocean seal]

Xetrov

[solar pebble]

nvm I had a brain fart

which is why a reciprocal is formed

sorry, stupid question

[kind helm]

Can graphs touch the asymptotes?

Like if the domain is ]0,+inf[, 0 is a candidate to be an asymptote

But what if the domain is [0,+inf[ , is 0 a candidate?

[sage oxide]

what is a simplified exact surd

[oak chasm]

@kind helm Not a vertical asymptote, no.

[kind helm]

Thanks

[finite spindle]

isn't it a triple integral?

[crystal tiger]

@finite spindle stokes is either a double integral, or a single integral

[warped phoenix]

How would I simplify this?

I got x + 8 + 5/x - 3

What did I do wrong?

<@&286206848099549185>

Here’s what I did

[whole prairie]

Um I have a tangent line question and I don’t exactly remember the steps to solve it. I have y = (function) where x=(number)

And I have to find the equation for the tangent line to the graph

[glacial hedge]

@whole prairie dy/dx = dy/dx (function)

dy/dx at x is slope at x

so

you get

y = (dy/dx (at x)) * (x- (number)) + (function (number))

[whole prairie]

So I would put in x to get the slope then find the leftover number to get the final equation or am I thinking of the wrong thing?

[glacial hedge]

ok

lets say you have function f(x)

and dy/dx at x = m

(m is slope at x)

actually

lets use n

f(n) m = slope of f(x) at x=n

then we get

y=mx+b

now just solve for b

f(n) = m*n + b (because the line must follow (n, f(n)))

b = f(n)-m*n

so we get

[warped phoenix]

<@&286206848099549185>

[glacial hedge]

y = mx-mn+f(n)

[glacial hedge]

why? why would you ping the helpers before posting something

[warped phoenix]

Because i did post something

you don't even have to scroll up to see the bottom of my message...

[sage cloak]

Hey, does anyone knows how to prove that please?

[wraith cairn]

add 0.15 AO to both sides

[sage cloak]

Ohh yeahh true, thanks

[wraith cairn]

actually I am not sure.

oh you add 1 AO to both sides

not 0.15

[sage cloak]

0.85 OA works too

[alpine sable]

can someone walk me through this

pls

[ionic jewel]

someone did the other day

if you swap the bounds of an integral (top to the bottom, and bottom to the top) the result is flipped sign

so the result is going to be negative of the one above with flipped bounfs

@alpine sable

[alpine sable]

so the other ones are irrelevant?

[ionic jewel]

you do not need them to answer the question

[alpine sable]

oh okay

yeah thats what i was confused about

[ionic jewel]

i mean realistically you don't need any of them

,w integral from 8 to 2 of x^3

[ocean seal]

Results provided by WolframAlpha

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

Requested by 兔子#6562

[ionic jewel]

you can calculate it standalone

but they want you to use the "flip the bounds" trick

[alpine sable]

ah kk, yeah i know about that

what about for this one?

[ionic jewel]

you can split it into two integrals

[alpine sable]

would i just plug in?

[ionic jewel]

integral of x -interal of 14

and integral of 14 is just 14* the integral of 1, which is given to you as 4

so the answer is going to be split to be able to solve to (16-14(4))

[alpine sable]

oooooh okay that makes sense

i thought itd be like (16-14)(4)

[woven pollen]

what?

[supple nexus]

i need help

[woven pollen]

#1 if you have two rulers on your desk, one 13 inches long and the other 22 inches long, how long would they be end to end?

#2 if I have a piece of string and tell you its length from one end to its center is 13inches, then how long is the total string?

[glacial hedge]

Hi does anyone know how to prove this... intuatively it seems false but im not sure

wait acutlaly i htink its true but can someone confirm

?

[placid zinc]

If you suspect something could be false, try a few basic examples. What happens if f(x,y) = 1? Compute left and right, and see if they're equal

[lusty pewter]

is this correct?

[fringe yoke]

Yes

If your goal is to isolate x

[lusty pewter]

thabks

yeah it is

is this correct to isolate K?

[queen wigeon]

yes

[lusty pewter]

thanks

umm is this correct im a bit confused

[glacial hedge]

inverse of f(x,y) = 1 is undefined?

[woven flume]

you went wrong here

[lusty pewter]

oh ok

cos i have to isolate a

so im confused

[queen wigeon]

try $\frac{a-w}{a}=1-\frac{w}{a}$

[ocean seal]

mchen10

[woven flume]

yeah

[lusty pewter]

ooh ok

thanks so much

oh i got right answer with wrong working lol

[ocean seal]

Elonmosqito96

[lusty pewter]

is this correct?

[queen wigeon]

looks good

[lusty pewter]

thanks

[stray apex]

What is the percentage chance of a combaniton consisting of three buttons with no repeats being right

[ionic jewel]

there are so many things missing from this question

how many buttons

how many solutions are right?

[lusty pewter]

is this right?

[inner token]

is it true that you always have to use sums of integrals when there is a point on the curve that isn't differentiable?

[lusty pewter]

is my working correct?

[queen wigeon]

for $\frac{x-1}{3}-\frac{x+1}{4}=x$, the negative sign needs to be distributed to the x+1

[ocean seal]

mchen10

[lusty pewter]

oh yeah true

thanks

[lusty pewter]

is this working right?

[summer goblet]

7th to 8th line, why x+1 disapeared?

[alpine sable]

ik this aint maths but is this correct?

[lusty pewter]

um 28x - x = 27x and also the 1 left cos u didnt need it

i did that

@summer goblet

[summer goblet]

,w (28x+1)/(x+1)=20

[ocean seal]

Results provided by WolframAlpha

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

Requested by Eudecio#6126

[lusty pewter]

its 28x - 38 tho

[summer goblet]

I think you can not do this.

Or I am not understanding what you are doing.

You must multiply both sides by (x+1)

Them

28×-38 = 20*(x+1)

The result will be the same as what the code I wrote showed.

[lusty pewter]

y is it 28x + 1 and not 28 - 38 though

[summer goblet]

y = why ?

[lusty pewter]

yeah

[summer goblet]

I see I wrote it wrong. I am sorry.

[lusty pewter]

all good

[summer goblet]

28x - 38 = 20*(x+1)

[lusty pewter]

huh

oh yeah right

[summer goblet]

,w (28x-38)/(x+1)=20

[ocean seal]

Results provided by WolframAlpha

Click here to refine your query online
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Requested by Eudecio#6126

[lusty pewter]

alr

thanks

[summer goblet]

Do not use this tool without authorization of your teachers.

[lusty pewter]

ok i wont

so does 28x/x not equal 27x/1

[summer goblet]

no.

[lusty pewter]

ok

[summer goblet]

You must take care. Look

28x\x = 28

Because x/x = 1

[lusty pewter]

ooohhh

yeah

that makes sense

thanks

[summer goblet]

There is not any number subtracting 28x to make it become 27x

[lusty pewter]

ok yeah this is starting to make sense

thanks so much

[summer goblet]

You only can take this x+1 out of there or with fatorization with the numerator.

Or multiplying both sides by x+1

Numerator is the number above the division.

[lusty pewter]

yeah

[summer goblet]

28x-38 = 2*(14x - 18) this is fatorization.

If in an hipotetic sutuation

It was not 14x-18 there but (x+1)

Them we would have

2*(x+1)/(x+1)

It would be equal to 2

[lusty pewter]

yeah

[summer goblet]

Because equal numbers divided are equal to 1

And x+1 is equal to x+1

[lusty pewter]

yeah

thanks for the help im gonna go and try some more questions

[summer goblet]

Ok.

Good luck.

[white osprey]

ok so on the number line if we had two numbers a,b

how do you know (a+b)/2 is always right in the middle of a and b

just curious

[meager cedar]

Whats the remainder when 2222^5555 is divided by 7 , i got 6 using congruences i wanna check if i am right

Just say if the answer is wrong, dont give me the answer

[placid zinc]

@glacial hedge
Why do you need the inverse of f?

[scarlet spire]

these channels are probably so dead during summer arent they lol

[viscid blaze]

What's gamma 2/3 .4/3

[rigid smelt]

on the contrary, no, people, even on the larger scale, human, will never stop learning

[thorn kindle]

Lol

[alpine sable]

thats, a, lot, of, commas

[rugged bronze]

Im doing an aops writing problem and I'm wondering when it says due June 31 does it mean i have June 31 available to do it, or June 30 I'd the last day to do it

[alpine sable]

june 31 2021, 23:59:59 is the deadline

[red phoenix]

But june has 30 days!

[rugged bronze]

Alr thank you

[foggy cargo]

hello

how would I formulize these questions?

[red phoenix]

You know about the volume of revolution formulas?

[foggy cargo]

no I do not

ocould you explain it to me please ?

[red phoenix]

If you have some y = f(x), then the volume enclosed by the curve and the x-axis rotated about that axis

is the pi * the integral from (x_0 to x_1) of y^2 dx

[foggy cargo]

what exactly is the difference between the washer and shell method

how would the first question look like

[red phoenix]

I would ask you to graph it to get a good idea of what it's talking about

OR atleast draw a graph

And you will see the area it's talking about, and how it wants to rotate that about the line x = 4

Then you think about the formula volume = pi * integral (y_o to y_1) of x^2 dy

(this volume revolution about the y-axis is the washer method)

Howevr this formula talks about rotating about the y-axis not x = 4

But you can instead translate the graphs so you g et the same problem but about the y-axis

[placid zinc]

@foggy cargo
The difference is between:

• Slicing the solid into disks, and getting the volume of each one
• Coring the solid into hollow cylinders and getting the volume of each one

[foggy cargo]

@placid zinc there's actually a question could you solve it for me so I can udnerstand is easier?

it's almost 3 AM I want to understand this before the quizz tomorrow

[raven rover]

https://www.mathsisfun.com/calculus/solids-revolution-disk-washer.html

https://www.mathsisfun.com/calculus/solids-revolution-shells.html

https://math.libretexts.org/Bookshelves/Calculus/Book%3A_Calculus_(Apex)/07%3A_Applications_of_Integration/7.02%3A_Volume_by_Cross-Sectional_Area-_Disk_and_Washer_Methods

https://math.libretexts.org/Courses/Monroe_Community_College/MTH_211_Calculus_II/Chapter_6%3A_Applications_of_Integration/6.3%3A_Volumes_of_Revolution%3A_The_Shell_Method

[placid zinc]

@foggy cargo
Yeah go nuts

Well, I won't "solve for you" but we can talk about it

[trim loom]

some one pls help with my hw

[alpine sable]

IF ZERO IS DIVIDED BY any non zero integer then the result is

[lethal ore]

ZERO

[fervent grail]

Can we found a root of a quadratic/cubic/quartic/quintic equation using vieta ?

[vale wigeon]

assuming you meant 'find'... why do you ask?

also it's certainly a lot easier for quadratics than the higher degrees

[fervent grail]

IS THIS STATEMENT TRUE ?

Quintic formula doesn't exist

Anything above that doesn't exist

And you cant prove a formula for anything above quintic

The fact that you cannot prove the formula above quintic has been proved

[fervent grail]

I was asking this bcz quadratic has a certain formula for founding the roots certainly with cubic and quartic but is there any formula for Quintic or above powers equation

[vale wigeon]

well, no, the abel-ruffini theorem says there is no formula in radicals that solves the general quintic

where "formula in radicals" means a formula containing only the four arithmetic operations and square, cubic, 4th and 5th roots

does that answer your question?

[fervent grail]

Yup thanks
That means the bottom line is that the formula for the root of an equation exists only upto quartic equation and for Quintic and above degree equ no formula can be made

[vale wigeon]

you could say that

[fervent grail]

Thanks

[alpine sable]

thank you

Can anybody help me check if the upper equation equals to 2031?

[ocean seal]

Result:

2031

[alpine sable]

Thanks!

[mental dune]

how do I find the exact value of this expression

[dawn wraith]

I’ll give you a hint

[cobalt breach]

hmmm\

[dawn wraith]

cot(pi/2-x) = tan(x)

[cobalt breach]

first of all i dont know wat is soc, tan cot or i.

hay, can i get like a private lesson on this.

cuz i donno this thing

hEY HEY HEY

IM ASKING

A QUESTION

[mental dune]

sec

= 1/cosx

[cobalt breach]

I can GET LIKE A PRIVATE LESSON ON TAN AND COS AND LIM AND SIN

[mental dune]

oh dude

idk look it up

[proper copper]

Yo i need help

[full wasp]

[cobalt breach]

BROOOOOOO HELP ME FIRSTTTT

[dawn wraith]

What is it you need?

[cobalt breach]

WAT IS SIN LIM COS TAN

[proper copper]

Just look it up

[dawn wraith]

You haven’t heard of trigonometry at all?

[mental dune]

they are just things used in trigonometry

ratios

[cobalt breach]

in gemetry?

[mental dune]

except for lim

[cobalt breach]

WAIT IN GEMOERTY

IS IT IN GEMEOTRY

[dawn wraith]

Let alone handling limits which is in the suite of calculus

[proper copper]

I need help with that

[cobalt breach]

thats so easy

[dawn wraith]

Hold on with that

[cobalt breach]

whats x

wait

im bumb

idk wat ur even tryingto do here.

[proper copper]

Wat u mean @dawn wraith?

[dawn wraith]

I’m dealing with something at the moment, give me about a minute

[proper copper]

Sure thing

[hollow pelican]

is this none of the given answers?

[cobalt breach]

yeah he is dealing with me

STOP SENDING THINGS AND SYMBOLS

[dawn wraith]

All right I’m back

[cobalt breach]

yay

what lim cos tan

[hollow pelican]

opps sorry didnt know this channel is busy

[dawn wraith]

It’s fine bud, glad you did.

[cobalt breach]

sorry its not busy

its me

.

[dawn wraith]

@proper copper
I won’t give you an answer, but I will hand you this; you cannot insert a negative number inside of a square root and the denominator cannot be nought.

[full wasp]

yeah basically anything thats gonna give you undefined is not in the domain

[proper copper]

Right but the x seems separated from the

[dawn wraith]

Exactly

So x cannot be negative at all

But there is also another anomaly, when could the denominator be zero?

[mental dune]

@dawn wraith hey, referring to my earlier question. I googled that formula, and i understand it now. I think there might be another way to do it though, the formulas used for cot(1/pi - x) = tanx, isnt used in my math advanced course, only my math extension so I doubt it is assumed knowledge for people who dont do the extension course.

do you think there might be a different way

[dawn wraith]

pi/2*

[mental dune]

sorry for interupting

[dawn wraith]

It’s fine

[mental dune]

yeh my bad

[proper copper]

Its not √x-6 tho then that would be x>=6

[dawn wraith]

I could try, just let me finish with him

[mental dune]

thanks 🙂

[proper copper]

But its rather √x which is confusing me

[dawn wraith]

What is confusing about it?

[proper copper]

√x is basically an unknown number

Sorry but cannot find any help on the internet when it comes to this lol

[dawn wraith]

What do you mean by unknown?
A variable?

[proper copper]

Because its usually √x- or + something

Its never by itself

[dawn wraith]

Well, x cannot be negative

[proper copper]

Right

[dawn wraith]

Because you cannot substitute a negative number inside of a sqrt

So, what would be the number to nullify the denominator?

[proper copper]

All positive numbers

[dawn wraith]

Hm?

No.

What I am asking of you is to find the x that equates the denominator to 0

Basically, solve:
sqrt(x) - 6 = 0

[proper copper]

Wait so 6?

[dawn wraith]

no.

You want x, not sqrt(x)

[proper copper]

I am fried

[dawn wraith]

bruv

Anyhow

I’ll do it with you

[dawn wraith]

So after adding 6 to both sides;
sqrt(x) = 6

Squaring both side:
x = 36

Notice that the square root in a function is usually referring to an arithmetic square root which means that we ignore the negative term.

[proper copper]

What is a problem like this called? Cues I cannot find it anywhere on YouTube

[dawn wraith]

Uh, just finding domains

[proper copper]

Yes I tried looking that up but they never give an example where x is just by itself

[dawn wraith]

https://youtube.com/watch?v=djT6-YamHaA&feature=share

Here’s a video that might help you

[proper copper]

I appreciate it man.

[dawn wraith]

Anyhow, x cannot be negative, nor can it be 36.

Algebraically:
x >= 0; x ≠ 36

Anyway, I suppose that concludes it

@mental dune I’m with you lad, what do you need?

[mental dune]

same question

find the exact value

thing is with the formula u gave me

[dawn wraith]

I’ve found it lad, I used the formula I’ve told you of.

[mental dune]

in order to get that formula you use cos(a+b)

which is taught in my maths extension course

but this is intended for the other maths advanced course

[dawn wraith]

Sum of angles formula? For cosine?
Why?

[mental dune]

nah to find the cot(pi/2 - x) = tan(x)

https://socratic.org/questions/how-do-you-verify-the-identity-cot-pi-2-x-tanx

[dawn wraith]

You want to prove it?

[mental dune]

according to that

[dawn wraith]

There is no need for that at all, I’m sure a right triangle could do the trick

[mental dune]

I understand how to prove it, those formulas are taught in my extension course, but the question is from the advanced course which doesnt use those formulas

so I dont think the formula is meant to be used

You sure there isnt another way?

[dawn wraith]

I haven’t told you there isn’t another way, just give me a bit

[mental dune]

Ok thanks

@alpine sable What is that?

[dawn wraith]

Okay hold up

[mental dune]

oh

tan(a-b)

[dawn wraith]

Do you at least know that tan = sin/cos and cot = cos/sin ?

[mental dune]

wouldnt it just be the reciprocal

yes

[dawn wraith]

That’s good, do you know that:
cos(pi/2-x) = sin(x)?

[mental dune]

no

nah

[dawn wraith]

He’s not though

[mental dune]

Im not sure those formulas are meant to be used for the question

yeh i dont need the proof for the formula

Just need to answer that

[dawn wraith]

Yeah, that’s an option, only the question would be if he learnt the formula.

[mental dune]

actually

cos(pi/2 -x )

i do know that

that is knowledge which is know

n

[dawn wraith]

All right, we’re set then.

[mental dune]

yeh ik @alpine sable

I understand how it is derived

that formula isnt meant to be used tho

its meant for students who wont know how to do that

[dawn wraith]

I have a way for you with the formulas you had studied

Anyhow

Here we go

[mental dune]

I take 2 maths subjects - math advanced and extension. that is knowledge which i have from extension but in advanced they wouldnt know how to do that. and it is from the advanced maths textbook

anyway

@dawn wraith go on

[dawn wraith]

Bud, could you send the photo again?

[dawn wraith]

Okay

Split the fraction into two

You’d have 1 + tan(3pi/10)/cot(pi/5)

[mental dune]

yes i tried this

is there anyway to take it further?

[dawn wraith]

Yeah!

[mental dune]

thats where i stopped

[dawn wraith]

split the tangent into sin/cos, likewise for the cotangent into cos/sin

You’d eventually get:
1 + sin(3pi/10)/cos(3pi/10) ***** sin(pi/5)/cos(pi/5)

[mental dune]

ah yes

1 + (1)(1)

wait no

wait yes

[dawn wraith]

Yes.

The answer is 2.

[mental dune]

yeh I have the answers, thanks for the help

🙂

[dawn wraith]

👍🏼

[mental dune]

hang on a sec

haha sorry

sin(3pi/10)/cos(3pi/10) * sin(pi/5)/cos(pi/5)

[dawn wraith]

It’s no sweat bud

[mental dune]

how is this = to 1?

[dawn wraith]

Hold on, I’ll just write it down

And send a photo

You know what, I won’t.

I’ll just say this

[mental dune]

haha ok

[dawn wraith]

Notice:
sin(3pi/10) = sin(pi/2-pi/5) = cos(pi/5).

[mental dune]

all good

thanks

I have been a major dumbass, i kept interpreting cot(pi/2 - x) as 2-x being the denominator

[lusty pewter]

what is 1+1 @everyone

[dawn wraith]

Ah, had that one a lot

[mental dune]

but the formula is taught

just complementary angles

soz

[dawn wraith]

Yippity

[mental dune]

looking up how the formula i have been taught which is simple, can be derived was the big mistake

thanks

[dawn wraith]

Anytime.

[rich basin]

Would anyone be able to please help me at question 1

[dawn wraith]

Which

[signal portal]

hello, how would I calculate 1000 + 100 - x = y? Initially my understanding is that I will do 1000 + 100 = 1100
Then I will have 1100 - x = y
could you please guide me to understand it?

[rigid smelt]

what exactly is the original question and relationship between x and y?

[alpine sable]

Does anyone have a physics server?

ping me

[rigid smelt]

#old-network

[signal portal]

I need to solve y @rigid smelt (find the value of y)

[rigid smelt]

they you just did

you found y in terms of x

where i guess x is a constant

idk, thats all i can say from the information that is given to me

[signal portal]

I think its an algebra with 2 unknowns

so what will the y be?

[rigid smelt]

its just y=1100 - x

like i said

unless there is more context that i dont know about

[signal portal]

yes clear thank you very much

[orchid coral]

Uhmm how do you find the total number of combination?

No 18

the ans is probably false...

[vale wigeon]

,rccw

[slow pewter]

anyone can help with the second equation?

[vale wigeon]

@slow pewter channel busy please move

@orchid coral i mean, there are 9! possible numbers in this question, but you don't actually need to know that

[orchid coral]

its fine i only need to find the total combination

[vale wigeon]

you do not

[orchid coral]

then how do you solve it?

[vale wigeon]

your number needs to be divisible by 18

which is equivalent to being divisible by 9 and by 2

it's going to be divisible by 9 no matter what because the sum of its digits is 45

and for it to be divisible by 2 (i.e. even) the digit at the end must be even

you have 4 even digits to choose from and each one is equally likely to get put at the end

thus 4/9

[orchid coral]

oh alright thanks

that is suprisingly straight forward

[lethal ore]

#challenge-problems

[half pasture]

I got this problem on a test and I couldn't solve it in 4 hours: What is the largest possible volume of a parallelepiped contained in a tetrahedron of volume 1? If anyone can give a hint I would be grateful.

[vale wigeon]

this looks tricky

but i have a hunch that the answer may be 3/4

no idea how you'd prove that tho

[half pasture]

What is your example? the best I got was 2/9

[vale wigeon]

wait

i think i messed up

[half pasture]

my example is the unit cube contained in a tetrahedron with vertices (0,0,0),(3,0,0),(0,3,0),(0,0,3)

this gives 2/9 relative volume

[vale wigeon]

yeah it'd be 2/9 my bad

yeah my example boils down to that too

if we make the assumption that our parallelelpiped shares a vertex with the tetrahedron i think this is the best that can be done (and can be shown by AM-GM)

or rather, not just that it shares a vertex, but that it shares a vertex and the three edges emanating from it are contained in the tetrahedron's edges

[half pasture]

yeah probably

[vale wigeon]

can we show that any parallelepiped without that property contained inside the tetrahedron can be replaced by one that is strictly larger?

[alpine sable]

the book says angle rqs is 50 but that doesnt make sense. my calculations give me 37.5

[vale wigeon]

@alpine sable channel busy please move

(unless omri is done)

[half pasture]

like, I have no idea....

you could say I'm done, I think this problem is hard

[dawn wraith]

After a lot of thinking and semi-sketching, I think you’re right here bud

There isn’t anything else I can think of..

[golden basalt]

Pls someone help me

Solving it

[twin pine]

f(a+h)means that you put a + h instead of x is in the function f(x)

[twin pine]

So $f(a+h) = 2(a+h)^2 + 5$

[ocean seal]

andreask

[twin pine]

and then do the math

[sick lance]

1+3+5+...+(2n-1)=n^2
1+3+5+...+(4n-1)=?

No one loves meh 😔

[alpine sable]

Sure

my smol Brain tells me that the answer is $(2n)^2$

🤡

[ocean seal]

PersonWithSmolBrain

[minor crypt]

the 2 outside of the brackets, no?

@alpine sable

[pearl marlin]

Use sn= n(a+l)/2

[alpine sable]

No

[minor crypt]

oh got it

[sick lance]

Lemme try

[alpine sable]

In general $1+3+ \dots+2(n)-1=n^2$

[ocean seal]

PersonWithSmolBrain

[alpine sable]

Easily provable by induction or the sum of AP formula

Here $n$ is replaced by $2n$, that’s it

[ocean seal]

PersonWithSmolBrain

[sick lance]

BRUH NOW I UNDERSTAND thank you

[ocean seal]

Edward.

[alpine sable]

This is a violation of the server rules <@&268886789983436800>

[night geyser]

wow they posted it in 4 separate channels

@heady notch do not offer money for assignment help.

are you familiar with clairaut's/schwarz's theorem?

it's quartic in n.

it's quadratic in n^2.

without any other qualifiers, "...in n" is the default

and so no, i would not call it quadratic.

[fresh bolt]

oh okay

[alpine sable]

Thank you! that helped

[ocean seal]

Edward.

[halcyon grove]

Trying to figure out how to work out this question

could anybody give me a hand?

[alpine sable]

n^0 is 1 which is constant time so that is first
∑k is n(n+1)/2 which is O(n^2)
2^lgn is just n
16^lgn is n^4

n^0 < lg(n+1)^2 < 2^lgn < 5nlgn+20n < ∑k < n^3 < 16^lgn < 2^lglgn + 3√n < 3^(2n) < (n^3+3)!

[blissful tinsel]

whats the question?

[alpine sable]

what about it?

[halcyon grove]

the screen shot i left

i'm having serious trouble working it out

[alpine sable]

what are you asking for?

zeroes?

[halcyon grove]

Just for somebody to help me figure it all out

sorry

[alpine sable]

the graph?

whats the question

[halcyon grove]

i dont really understadn it myself

[alpine sable]

are you trolling?

[halcyon grove]

Express the follwing as a single fraction in it's simplest form

[alpine sable]

thank you

[halcyon grove]

that's the question also no

[alpine sable]

so make a common denominator of a(a+4)

[halcyon grove]

right?

sorry i've been told to revise this so i'm honestly just getting the hang of it

[alpine sable]

no worries! so $\frac{2}{a}-\frac{3}{a+4}=\frac{2(a+4)}{a(a+4)}-\frac{3a}{a(a+4)}=\frac{2a+8-3a}{a(a+4)}=\frac{8-a}{a(a+4)}$

[ocean seal]

Edward.

[halcyon grove]

how in

hells name lol

[alpine sable]

ok so if you have $\frac2a$ do you agree that $\frac{2(a+4)}{a(a+4)}$ is equivalent?

[ocean seal]

Edward.

[alpine sable]

multiplying by 1 wont change values...

[halcyon grove]

right?

sorry about this

[alpine sable]

dont apologize haha

[alpine sable]

and do you agree that $\frac{3}{a+4}$ and $\frac{3a}{a(a+4)}$ are equal?

[ocean seal]

Edward.

[halcyon grove]

yeha?

[alpine sable]

again multiplying by 1 shouldnt change anything

[halcyon grove]

I believe so ?

[alpine sable]

so then you just subtract them

[alpine sable]

where is the confusion in this then

could you state the step?

[halcyon grove]

everything? honestly i got some revision papers and told to go through them but i've not really done something like this before

so i'm kinda boggled

but the answer being

[alpine sable]

break it down, we have 2a + 8 - 3a on the numerator, what does that simplify to?

[fresh bolt]

hi can i dm you

[alpine sable]

no, you can message here

[fresh bolt]

2^lglgn + 3√n

how do i simplify this

[alpine sable]

Assuming lgn is the base 2 log as is done in CS then that becomes log(n)/log(2)

Shoot I made a mistake above then

[fresh bolt]

hmm?

[fresh bolt]

yea lg is base 2 log

[alpine sable]

should be $n^0 < 2^{\lg\lg n} + \sqrt[3]{n} < \lg(n+1)^2 < 2^{\lg n} < 5n\lg n+20n < \sum k < n^3 < 16^{\lg n} < 3^{2n} < (n^3+3)!$

[fresh bolt]

also, for n^4 how do i classify it? should it be quadratic, cubic, exponential?

[ocean seal]

Edward.

[alpine sable]

quartic which ias after quadratic and cubic but before exponential

cuz quadratic is n^2
and cuz cubic is n^3
so quartic is n^4

[fresh bolt]

quartic? :O my sch never teach that tho :(

[alpine sable]

same

it's just a term

just a word

[sleek elbow]

nvm

its this

lol

[merry pendant]

My braincells

[merry pendant]

AAAAAAAAAAAAAAA

[sleek elbow]

Man im 9th grade, no idea wtf that is

[merry pendant]

0 braincells moment

[merry pendant]

Same

[alpine sable]

a depressed quartic

which is unrelated to this convo.

[merry pendant]

No its brain killer machine

[alpine sable]

seems like they applied reverse COV

i saw that technique with the jacobian in my grade school class.

to solve a double integral

but that does not mean anything to a 9th grader

[sleek elbow]

integral symbols look cool

thats all I know

[fresh bolt]

wow

theres also quintic

[sleek elbow]

I thought there isnt

🤔

[fresh bolt]

these terms

[sleek elbow]

thought it was proven that there cant be a quintic

or something

[sleek elbow]

wait that

that simple 👀

[heady notch]

Tyler and Gabe went to the arcade and played the same two games. Tyler played 5 rounds of one game and two rounds of the other for $24. Gabe played 4 rounds of each game for $30. Write two equations for the amounts the two boys spent. Then find the cost for one round of each game. PLEASE HELP