help-0

[fickle pier]

yes

[vale wigeon]

add m copies of n together to get mn

e.g. 6 * 19 = 19+19+19+19+19+19

[fickle pier]

it can also be the other way around as well right?

[vale wigeon]

yes

[lilac vault]

need a bit help

what's the alpha symbol means ?

proportion?

[raven lodge]

lost how do we factorise?
is it like
log(x)*log(y)+2log(x)?

[queen shale]

How do you make this in index

[vale wigeon]

what do you mean by "make in index"?

[cunning crow]

latex?

[vale wigeon]

$3^{-1/3} = \frac{1}{\sqrt[3]{3}}$ i think this might be what you're looking for

[ocean seal]

Ann

[queen shale]

Ah

Thx

[analog locust]

from a single matrix transformation

can it be possible that there exist more than one non-linearly dependent eigenvectors??

[raven lodge]

Hi could I dm you for help 🙂

[sharp sable]

It's question number 8 Pls help

<@&286206848099549185> i think its okey to tag

[minor crypt]

use

$\frac{y_2-y_1}{x_2-x_1}=2$

[ocean seal]

Axhraf

[alpine sable]

,iam studying

[ocean seal]

Gave you the studying! selfrole.

[sharp sable]

thats gradient

then what's after that @minor crypt

[minor crypt]

try to find a

[alpine sable]

,iam advanced

[ocean seal]

Gave you the Advanced selfrole.

[minor crypt]

by doing basic algebra

[sharp sable]

like an equation

[minor crypt]

yes

[sharp sable]

hmm

[alpine sable]

,iam talks

[ocean seal]

Gave you the Talks selfrole.

[sharp sable]

also is there like online free lessons about this

i found some on youtube

[minor crypt]

[sharp sable]

@minor crypt thanks

🙂

[minor crypt]

you only really need to know:

y=mx+q

where m=gradient and q=y-intersect

[sharp sable]

ohh

yeah i do know that

[minor crypt]

and $m=\frac{y_2-y_1}{x_2-x_1}$

[ocean seal]

Axhraf

[sharp sable]

ok

[velvet oyster]

Hi..

I have some thing to ask

Do you know how to find the center nucleus of the fan shape?

[alpine sable]

Wot

what fan shape

what centre nucleus

[velvet oyster]

The normal fan shape

[alpine sable]

Got like the question to show me

like take a screenshot or picture of it

and upload it here

[velvet oyster]

Ok wait for minits

Oh..Wait

I gat it!

@alpine sable Sorry for takeing time.

I don't know why but I gat it

[alpine sable]

wot

[harsh parrot]

What is the correct answer out of the 4 according to you?

How is it onto?

I understand why its not one to one

But not why its not onto

Range of the function will be a set of even integers while codomain is set of integers so range != codomain?

ahhhhhhhhhhhh

My brain

Thanks a lot man!

[alpine sable]

why did you leave?

[flat pecan]

hmmm, theory doubt: why is this true? Im especially confused from the first to second step: If i have a function f which associate each number N to either 0 or 1, shouldnt its cardinality be 2 x N ? Why do we get 2 ^N?

ù

@modest radish

[modest radish]

okay

so

lets say i have a finite set

of cardinality N

errr

M

to avoid confusion

[flat pecan]

lets say cardinality 3

i have a function which maps {1,2,3} ->{1,2}

[modest radish]

okay let X={1,2,3}

sure

lets use 0,1

not 1,2

[flat pecan]

kk

[modest radish]

okay so how many do you think there are

[flat pecan]

isnt its combination total 6? {1,0}{2,0}{3,0},{1,1}{2,1}{3,1}

[modest radish]

no

so for each element of X

i get to choose 0 or 1

[flat pecan]

yes

[modest radish]

thats 2 choices for 1, 2 choices for 2 , 2 choices for 3

these dont sum

they multiply

do you see why?

[flat pecan]

n

no

i dont see any other options than the 6 i listed above

[modest radish]

well lets build a function

okay so I make a choice for 1

okay i dont want to write the options once we compute it listing them all can be an exercise for you

so in order to define such a function

we can draw it as a tree

uh can i draw this on my phone

ill try

I cannot

okay ill find an image

ignore the labels here

each “level” in this pyramid is a us choosing either 0 or 1

for each element of X

[flat pecan]

yes i know where you are getting to but thats not what this function is

why would you combine them

each choice is separate

[modest radish]

yes!

separate choices multiply

[flat pecan]

yes but theyre not related

[modest radish]

but they are all distinct

once i choose 0 or 1 for f(1)

its a different function

than if i made the other choice

[flat pecan]

hmmm can i give you some context on where this is from so that you can understand my doubts

[modest radish]

here

actually

i can write them all down for you

im going to write them like

101

[flat pecan]

no i know where you are getting at

u dont need to

[modest radish]

where the first number is f(1)

[flat pecan]

just gimme a sec

[modest radish]

and then the second is f(2)

and the third is f(3)

000,001,011,111,010,110,101,100

all distinct functions

and there arent any others

[flat pecan]

so basically its an algorithms course and we are making a bijection from each possible turing machine to natural numbers. The professor wants to show that the number of problems that there are, are much greater than the number of bijections (N), and as such many problems cannot be solved by algorithms and TM in generals

[modest radish]

lets not get more abstract

[flat pecan]

but thing is, given that each bijection is a turing machine

[modest radish]

do you agree that clearly its not 6?

[flat pecan]

yes but this is crucial

[modest radish]

slow steps

please

do you agree w what I said so far now?

[flat pecan]

yes i know where you are getting to

its more like i dont make sense of it in the context its in

[modest radish]

idk if thats true

i dont think you do

[flat pecan]

i do trust me

[modest radish]

anyway, my point here is simply that the 2N claim

doesnt make sense

because even for finite sets

its much larger than times 2

to see the infinite claim

i have a very different explanation

which it would help if you could be more patient about

[flat pecan]

its fine its not where im having issues understanding

[modest radish]

i am addressing your original question

as to why those functions are in bijection w powerset

[flat pecan]

yes its been addressed thanks

i got it now, but i dont make sense of the context

[modest radish]

okay go ahead if#g

ig*

[flat pecan]

ok so did you understand the part i posted about turing machines b4?

or should i explain it more

[modest radish]

I dont understand your phrasing

what two things are you comparing

[flat pecan]

natural numbers to turing machines

[modest radish]

okay sure

[flat pecan]

we are enumerating all possible turing machines with natural numbers

[modest radish]

okay

[flat pecan]

so, the professor wants to show that the cardinality of this enumeration (which would be N) is much less than the number of problems

[modest radish]

problems?

do you just mean P(N)

[flat pecan]

i mean like anything that needs to be solved

[modest radish]

that makes no sense

mathematically

[flat pecan]

let me make it more specific

[modest radish]

if by problem you mean “subsets of N”

then I understand

[flat pecan]

less than the number of functions which can be formed

each turing machine represents a function

[modest radish]

there are fewer turing machines than binary functions on N

[flat pecan]

yes

[modest radish]

is that the claim?

okay

[flat pecan]

yes

[modest radish]

i agree

[flat pecan]

so what im missing is

if turing machines map what we just discussed above

[modest radish]

can you he more specific

[flat pecan]

doesnt it just need to map each number individually to be able to map the combination?

[modest radish]

or at least more formal

[modest radish]

yes

[flat pecan]

so we map each natural number to either 0 or 1

[modest radish]

okay

[flat pecan]

lets stop for a moment and consider each individual bijection

[modest radish]

?

i think you are using the term bijection incorrectly

[flat pecan]

like natural number 3 to 0 {3,0}

[modest radish]

?

[flat pecan]

the natural number 3 gets mapped to 0

[modest radish]

thats not a bijection

[flat pecan]

why not?

[modest radish]

what do you think bijection means?

[flat pecan]

a mapping that is one to one

a function which relates each member of a set S (the domain) to a separate and distinct member of another set T

[modest radish]

i think you are misinderstanding the term one to one hahaha

okay sure

not quite

[flat pecan]

how am i misunderstanding?

[modest radish]

a bijection has to be injective (every element goes to a unique one) and surjective (every element in the target gets hit by something)

but you dont describe an individual value f(3)=1 as a “bijection”

[flat pecan]

ok thanks

lets not call it a bijection but just a mapping then

[modest radish]

sure

[flat pecan]

at this point my question is, if theres a turing machine able to consider these individually

why do we consider 010101

[modest radish]

what does that mean

please try to write longer sentences and explain yourself better

[flat pecan]

like why do we consider all distinct possibilities and put them together

instead of just considering the distinct possibilities alone

[modest radish]

Again I dont know what you mean

[flat pecan]

like from before, if there are turing machines able to solve the 6 cases i proposed initially

[modest radish]

8

[flat pecan]

.

[modest radish]

there are 8 cases to the original thing

as i showed you

[flat pecan]

yes

yes

but if a turing machine can do those 6

[modest radish]

stop saying words like “do”

explain what you mean lol

[flat pecan]

the turing machine can represent that function

[modest radish]

sure

[flat pecan]

then it should be able to represent the combinations as well

which would be 8

[modest radish]

what combinations

[flat pecan]

2^3

001

010

111

[modest radish]

i agree all 8

can be expressed by a tm

[flat pecan]

yes so the cardinality of functions of a turing machine is just 2N

i dont get why 2^n

[modest radish]

NO

the cardinality is 2^3

[flat pecan]

you see where Im confused tho?

yes it is

[modest radish]

not even a little bit

its 2^n

not 2n

if you dont understand that we have to go back

like i wanted to anyway

[flat pecan]

yes im not doubting that xd

[modest radish]

you just said this

and you are putting very little effort into explaining yourself

[flat pecan]

yes i meant the cardinality that the turing machine needs, sorry english is not my home language

im studying in another language as well

what i mean is, if a turing machine can represent those 2N functions, then it should be able to represent the full cardinality of 2^N

[modest radish]

why

what

those 6 you wrote the first time

are not enough

to get the other 8

you need 8 machines

[flat pecan]

ok i think i get it

thanks

[modest radish]

get the other 2*

uh

youre welcome ig

[alpine sable]

how would you find the area of the region of all points less than 2 units away from the parabola y=x^2 where -3<x<3 ?

https://www.desmos.com/calculator/ccy5vrvgr1
this is what i have so far

[carmine ermine]

ew

[lone cargo]

i have a question (kinda dumb):
Did someone or Euclid himself prove the parallel postulate or people just consider it is right ?

[alpine sable]

can you repost it in an unoccupied channel?

[sick kelp]

Can someone explain to me like mid point, magnitude,

[worn elbow]

Hey, ya'll hoping some new friends can help with mean, median, mode, and some other fun calculations.

[gleaming granite]

[worn elbow]

I should ask the specific questions from my homework?

[gleaming granite]

yes sirr

[worn elbow]

Sorry, new and adjusting.

is a girl

[gleaming granite]

uhh

yes mammm

[worn elbow]

Loool

All good.

Find the grade point average: four classes with the credit worth: 4,5,3,5 and the grades: A, B, B, C.

Possi, go have your fun, buddy. LOL

[viral rampart]

you'll need the equivalents of A, B, and C

oki :3

[worn elbow]

A-4.0, B-3.0 and C-2.0

I'll hit you up for next week's homework tomorrow or so.

[viral rampart]

so (4*(4.0)+5(3.0)+3(3.0)+5(2.0))/(4+5+3+5)

[viral rampart]

sure :3

[worn elbow]

You can't resist me.

[viral rampart]

I can't resist math

xD

[minor crypt]

[viral rampart]

we're frens

lol

[minor crypt]

oh :(

I have friends too 🧢

[alpine sable]

pls help, i lost sanity trying to solve it

[vague gate]

I forgot bearings the minute I stepped out of precalc

Im sorry

[wary stream]

My step process is use law of sines to find either AC or CB then respectively finding AD or BD using law of sines again then pythagorean theorem for CD

[alpine sable]

but how will i find AC or CB if i dont know CD? sin α = CD/AC

[wary stream]

Law of sines to find AC or CB

Use the full triangle

[full dome]

can someone tell me if my answer for this is correct? i need to find unknown angle which I got 13.38.

[alpine sable]

the issue is that ABC is not rectangular triangle

[wary stream]

Law of sines works with any triangle @alpine sable

[viral rampart]

a/sin(A)=c/sin(C)

[viral rampart]

^

[full dome]

ok

[wise jewel]

hey can someone explain to me how "(bc)i + (ad)i = (bc + ad)i" ???

[alpine sable]

distributive property

[alpine sable]

https://tenor.com/view/mind-blow-galaxy-explode-boom-fireworks-gif-5139389

i got it

thank you so much, @wary stream

gonna repost my question since it got pushed back

how would you find the area of the region of all points less than 2 units away from the parabola y=x^2 where -3<x<3 ?
https://www.desmos.com/calculator/ccy5vrvgr1
this is what i have so far

<@&286206848099549185>

[wise jewel]

@alpine sable but then wouldnt it be (ibic) + (aidi) ?

[alpine sable]

i(bc+ad)=i(bc)+i(ad)

[wise jewel]

so then from i(bc) + i(ad) there are two i's

wouldnt it be 2i (bc + ad) ?

[alpine sable]

no

lets say you have 3(7)+3(9)

its the same as 3(7+9)

not 2*3(7+9)

[wise jewel]

ohhhhhhhhh

you're right

im just stupid and ig the variables messed up my way of thinking LOL

ty!!

[alpine sable]

If in the expansion (2 x + 5)^10 the greatest term is equal to the middle term for x belongsto(a, b) then maximum value of 12|b – a| equals to (where a, b belongs to R+)

help

[wanton dune]

how should i represent those symbols on paper? just "Q" and "R"?

[alpine sable]

it doesn't hurt to add a few lines to make it clearer what you're representing

usually for the reals we use IR instead of that whole relining

[glass lichen]

$\bQ$ i just add the 2 lines in the O part, and the | for $\bR$

[ocean seal]

Mosh

[alpine sable]

okay no yeah, i guess you can google it for a look on how it is usually drawn

[wanton dune]

i think you provided me with some useful answers

[alpine sable]

hello, where did 10 in power of 3/2 go? why is there 3/2 instead of 10 in power of 3/2?

[acoustic wharf]

get a common denominator in the second factor and then multiply by the conjugate

[vague gate]

The 10s cancel out

Thank you

[acoustic wharf]

you could then factor out an x-3

and get your limit by direct substitution

[acoustic wharf]

because... that's the definition of log; log_10(10^r)=r

[alpine sable]

ah yeah

thank you

very much

[acoustic wharf]

👍

[wispy swan]

If anyone could help me with this problem, much appreciateed

[acoustic wharf]

what's the problem though exactly?

just substitute x+dx and x into the expressions and simplify

i used h here instead of deltax

@wispy swan

[wispy swan]

ay thank you @acoustic wharf

[acoustic wharf]

👍

my turn now

can anyone help me with this question:
"an urn contains p red balls and q black ones, n are randomly picked. in how many ways can we get h red ones and k black ones?"

the answer is apparently (pChooseh)*(qChoosek)

but i dont fully understand how that's the answer

[glass lichen]

order the n are picked doesnt matter, so you need to pick h from the p red, then k from the q black

so (pCh)*(qCk)

[alpine sable]

It's two combinations

[acoustic wharf]

hmm

[wispy swan]

lag I feel like this should be an easy one lol. I might as well ask

[acoustic wharf]

whats the domain of f

is it the positive real numbers or all of the real numbers?

[wispy swan]

Doesnt say! wish I knew. I believe all of the real numbers

[acoustic wharf]

your answer is probably correct

[wispy swan]

or is it x+4 😮

[fresh terrace]

Not a question specifically about maths but is further maths gcse such a thing in the uk if anyone knows?

[acoustic wharf]

nooo

[acoustic wharf]

to this

[wispy swan]

ok ok

[alpine sable]

try with x=-1

f^(-1)(f(x))=x

[acoustic wharf]

yeah yeah but they probably arent doing rigorous math anyway

[glass lichen]

no inverse for f exists unless the domain is restricted

since x^4 is not injective on R

[acoustic wharf]

yep

[wispy swan]

I got the answer right! wo

[acoustic wharf]

see

[vital drift]

By using the points, (3,1) and (20,9), would the approximate slope and y-intercept be y = 0.4 + 0?

[wanton dune]

What those symbols before "-2" and after "+infinite" mean?

[solar pebble]

yeah it is

it's not really cared about tho

[glass lichen]

context?

[wanton dune]

x>2

[glass lichen]

ok so it's an interval

[wanton dune]

yes

[glass lichen]

<> just means unbounded then

typically it'd be $x\in (-2,\infty )$

[ocean seal]

Mosh

[wanton dune]

so, when we have this kind of notation (-2, +2) for example, it means that the interval will not cointain neither -2 and 2, right?

[glass lichen]

$x\in (-2,2) \iff {x\in\mathbb{R}|-2<x<2}$

[ocean seal]

Mosh

[wanton dune]

ow, understand

Is the contrary possible. For example, )2, -2(?

[wanton dune]

And what is the name of this symbol, for sure?

[glass lichen]

that's not a thing

american intervals are () for unbounded, [] for bounded.
International just replaces unbounded with ][

[ionic jewel]

I'll be real international unbounded looks way worse but makes way more sense

[fresh terrace]

Do you know any differences in terms of outcomes between doing the higher maths paper and the further maths one?

I am sure both are 1-9.

[wanton dune]

Understood

[unkempt sigil]

im not sure if I did this correctly. If im wrong, please tell me where i made the mistake

[alpine sable]

What DA hek?

[glass lichen]

ignore it, random troll

[pulsar aspen]

I don't think you inverted that csc into sin correctly.

[alpine sable]

Fine can you help me in a little doubt?

[pulsar aspen]

ALso, you are supposed to solve it algebraically, not using a calculator.

[unkempt sigil]

ow i see

[unkempt sigil]

wdym?

[alpine sable]

Are you done?

[pulsar aspen]

I meant, you are not supposed to use a calculator.

[unkempt sigil]

not yet lol

[uncut monolith]

help pls

[alpine sable]

Stop its busy and booked as well

Lol

Infinite😏

[unkempt sigil]

owh so i use radicals then instead of decimals?

[alpine sable]

You wanna feud with me lad? You already killed my girlfriend as well

I have to prove value of a equation in a+b√3
But my answer is coming in form of a-b√3

[pulsar aspen]

Yes. If you did that correctly, the answer should be a special angle.

wdym?

[glass lichen]

Dont crosspost

[alpine sable]

Why don't you google it

[uncut monolith]

decimals

[unkempt sigil]

w8 im confused lol

[glass lichen]

shut it, read the rules

[pulsar aspen]

1. The question is unclear
2. Why did you ping me?

[uncut monolith]

3

[alpine sable]

So can I ask now?

[unkempt sigil]

w8, decimal or radicals?

[uncut monolith]

Finding the double integral

∫∫Rf (x, y) dA

Where f (x, y) = x2 + y2

y R is the region enclosed by y = 1 / x, y = 3 / x, x2 - y2 = 1, x2 - y2 = 4, in the first quadrant

we obtain:

[pulsar aspen]

I mean you can ask, but don't ping anyone first except you specifically want to ask me about my answer.

[glass lichen]

didnt ask

[subtle mantle]

1, 50 makes 50

[pulsar aspen]

Also, please wait while Bruh Chan is still asking.

[unkempt sigil]

wait so xwtek said radicals and jamil said decimals so im kinda confuse now

[alpine sable]

XD lol I can hear you saying bruuhhhhh chan

What's this lol you gonna ban for sure still

[pulsar aspen]

his Discord name is literally Bruh Chan.

[glass lichen]

yeah he just got banned

[unkempt sigil]

lol

[subtle mantle]

You really do get some gremlins in the questions channels, very entertaining

[glass lichen]

mods were pinged in a different channel, then they felt the need to ping them individually

[uncut monolith]

OMG, the exercise is sending me

[alpine sable]

So can i ask

[unkempt sigil]

🥲

[pulsar aspen]

I think you should revise how do you get sin theta correctly first

[unkempt sigil]

aight, ima be back after, thanks

[alpine sable]

Okay so

I have to prove value of a equation in a+b√3
But my answer is coming in form of a-b√3

[uncut monolith]

[pulsar aspen]

do b really has to be positive number there?

[alpine sable]

Yes i have to prove

And I got value in negative of b so I'm kinda confuse

[pulsar aspen]

Full question please and how do you get that expression so far?

[alpine sable]

Sorry to say it equation

Its a irrational fraction

[pulsar aspen]

sorry. I mean expression.

[subtle mantle]

Conjugate memes

[pulsar aspen]

I don't think b has to be actually positive there.

[unkempt sigil]

hows this?

oh mb, ignore this till u helped devie

[alpine sable]

I see thank you!!
I just wanted to make sure ❤

[pulsar aspen]

No. I mean correct the sin theta first before finding the theta.

[unkempt sigil]

sorry but i dont see whats wrong on the sin theta 🥲

please tell me what i did wrong on the sin theta

[pulsar aspen]

you just have to flip the position the number to take the inverse.

i.e. numerator -> denumerator and denumerator -> numerator.

[unkempt sigil]

but the given is cosecant theta, doesnt that mean its 1/sin theta?

[unkempt sigil]

oh u mean i reverse them so that the negative below will be positive?

[pulsar aspen]

Yes, and you didn't calculate 1/csc theta correctly

[pulsar aspen]

No, don't change sign

[unkempt sigil]

so instead of 1/-2root3/3, it gonna be -2root3/3/1?

like this?

[pulsar aspen]

No, no.

1/(a/b) = b/a

Your answer looks like 1/(a/b)= 1/ab

[unkempt sigil]

owh i think i get what you mean now lol

like this?

sorry if im wrong again lolol

[pulsar aspen]

No, no.

1/((2v3)/3)=3/(2v3), not 1/(3/(2v3))

[unkempt sigil]

like this?

[pulsar aspen]

Yes.

[unkempt sigil]

owh haha thanks, ima try to solve it now

like this then?

[pulsar aspen]

No, such special angle should have been a fractional multiple of pi.

And 60 is way bigger than 2pi

[unkempt sigil]

uh oh, i dont think my math teacher thought us something about pi on this topic

[pulsar aspen]

sin function takes an angle in radians. So, the resulting sin^-1 is also in radians.

sin(-60) is a positive real number, for example

as 60 is (19+n)pi for a real number n element of (0, 1)

[unkempt sigil]

wait wait wait im soo confuse now lol, my math teacher didn't teach me the things ur saying so i have no idea 🥲

so basically, i did my math wrong?

[pulsar aspen]

Remember the special angles:
sin(0)=sin(pi)=0
sin(pi/6)=sin(5pi/6)=1/2
sin(pi/3)=sin(2pi/3)=sqrt(3)/2
sin(pi/2)=1

so the answer should've been -pi/3 or -2pi/3

[unkempt sigil]

this is the only spewcial triangles he gave us

[pulsar aspen]

that degrees is a unit.

Basically 1 degrees is actually pi/180

You can't omit the degrees.

[unkempt sigil]

but he didn't theach us pi answers

[pulsar aspen]

-pi/3 = -60 degrees. But you shouldn't forget the degrees.

[humble terrace]

can someone help

[unkempt sigil]

oh so their the same?

[glass lichen]

matrix addition is entry-by-entry

[pulsar aspen]

yes, but you omitted the degrees sign, which is important.

[unkempt sigil]

im sooo dumb kekw

[pulsar aspen]

That's like saying 160 m as your height

[unkempt sigil]

dam it that missing degree sparked a whole conversation which i had no idea what it about 🤣

like this then?

with the degree on 240 and 300

[pulsar aspen]

-60 degrees is definitely not the "related acute angle" here

[unkempt sigil]

wait what

does that mean that the principal angles are wrong too?

[pulsar aspen]

If I interpreted the question correctly, theta would be the larger angle, so you have to find the smaller angle for that, then you find the other triangle angles

[gray isle]

Including the degree symbols, the principal angles are correct

[unkempt sigil]

this are our reviews for this, i just based how i answered my questions off of this

[gray isle]

The related acute angle is between 0 and 90°

Which in this case would be |-60°| = 60°

[unkempt sigil]

oh but if its 60, then wouldnt that make the principal angles different?

[gray isle]

and the principal angles using that would be
180° + 60° = 240°
360° - 60° = 300°

[unkempt sigil]

oh i see i see

[gray isle]

the end result is the same

the principle angles refer to the solutions between 0 and 360°

[pulsar aspen]

Sorry, I'm not a native English speaker.

So, I didn't know about principal angle as we called it differently

[unkempt sigil]

so the real answer of the equation is -60 but since it says 0<theta<360, we make it to absolute value?

[unkempt sigil]

its cool bro, thanks for the help

[gray isle]

no,

Wrong interpretation

[unkempt sigil]

but the answer of the theta is -60 tho right, we just change it to 60?

[gray isle]

taking the arcsin of (-sqrt(3)/2) gets you -60°

however the related acute angle would be 60°

[unkempt sigil]

oh so the negative is positive because its the acute angle itself

[gray isle]

uh yeh.

[unkempt sigil]

thank you my bruh

[gray isle]

when finding the related acute angle,
it'd be more reliable to take the absolute value of the ratio before applying the inverse trig ratio

[unkempt sigil]

oh i see

[gray isle]

though it doesn't really matter for sin and tan,
its quite useful when working with cosine

[unkempt sigil]

thanks for being patient with me guys 😁

[unkempt sigil]

noted

[spice crypt]

how do I prove there's only a finite amount of ways to decompose some positive integer into a sum of multiples of 2 and 3?

it's pretty much showing the diophantine equation $2x+3y=n$ for some $n\in\mathbb{N}$ has only finitely many solutions for $x,y\in\mathbb{N}$

[ocean seal]

(𒀭)

[spice crypt]

pretty sure the diophantine equation solves to something like $x=2m+n$ and $y=-(3m+n)$ for some $m\in\mathbb{Z}$ over integers but I'm not sure where to go from there

[ocean seal]

(𒀭)

[ionic jewel]

Since $x\leq \frac n2$ and $y\leq\frac n3$, and $x,y \in\bN$, assuming n is finite, there are only a finite number of integers between 0 and n, so there can at most be $\frac n2 \cdot \frac n3$ solutions.

[ocean seal]

bunny

[ionic jewel]

since n/2*n/3 is finite if n is finite

[spice crypt]

oh, cool

thanks!

[rancid citrus]

Hey, I have a question.
How to notate, write a conjunction point of two linear functions?

Specifically, I have two linear functions,
y=¾x+½
y=-2x+17
and I found that their conjunction point is (6, 5), but I don't know how to mathematically notate the conjunction.

Should it be like
y=¾x+½ ∩ y=-2+17 = (6, 5)

Also my English terminology in math isn't the best, so I hope I'm clear

Please try asking your question in an other room, I'm already waiting for an answer to my question.

Could I just give each of them a "name"?
A=y=¾x+½
B=y=-2+17
And then simply write A ∩ B = (6, 5) ?

[covert berry]

yeah

denote lines with lowercase instead i think

like a, b , d , m , etc

[rancid citrus]

Aha, ok. I think that's correct because "lines" that go infinitely are marked with lowercase letters.

Thanks a bunch.

[covert berry]

I assume you were writing a whole essay to disagree with that

Because that doesn't look like what you would take several minutes to write

😂

np

[rancid citrus]

I was just trying to remember what that "line" is called in English. 😅😅 In my native language it literally translates as "straight"

[covert berry]

Are you asian

[rancid citrus]

Nope, from the Balkans

[covert berry]

ah ok

good luck

[rancid citrus]

Thanks for that too, I am just now preparing for a final exam after finishing primary school of 8 years. It's in 3 days

[raven briar]

Could someone help me to solve this problem?

In a game, there are two players, A and B, who take turns tossing a fair coin. The winner of a round is the first person to get a head. The loser of a round of the game goes first in the next round. To win the game, a player must be the first to win 3 rounds. If A goes first, what is the probability that they win?

[pulsar aspen]

Try to find out the probability of winning the first round first

[raven briar]

i've figured that out

it's 2/3 for A and 1/3 for B

[pulsar aspen]

Good, since the games is first 3 wins, the maximum number of wins is 5 rounds

[pulsar aspen]

Now lets look at each games, ignore the labelling AB, only first/second. What is the probability of a configuration wins?

[raven briar]

what do you mean by a 'configuration'?

[pulsar aspen]

example: 11001 (1 = second, 0 = first)

Then you find out how to map AB representation to first/second representation

[raven briar]

so would i have to consider every configuration possible?

e.g. 000, 111, 1000 and so on?

@pulsar aspen

so if 0 represents winning a round for A and 1 represents a loss

would i just consider 000, 1000, 0100, 0010, 11000, 10100, 10010, 01010

[pulsar aspen]

Well, not quite

Assume 0 is first player win, 1 second player win, A for a win, B for b win,

1. How do you map (bijectively) a string from AABAB to a string like 01000?

2. How do you determine a probability for an event like 01000?

[raven briar]

could i have another hint?

@pulsar aspen

[pulsar aspen]

Prepend the 01000 with 1 and group by pattern 1 + repeating 0. What does it relate to the winning condition?

[raven briar]

could you just explain the solution? i don't really understand what you mean

[pulsar aspen]

Assume that 0 = first player win, 1 = second player win. For a game configuration, prepend 1. Group by pattern 10*, Then we get a series of integer:
a0, b0, a1, b1, ...

Now sum a and b together, so we get
a = a0 + a1 + ...
b = b0 + b1 + ...

Now, a+b=6.

Probably I will solve it later. But for now, I have an important business.

[raven briar]

ok thank you

[vernal prawn]

is this chat taken

[viral patio]

there's a very sneaky way to do this

[shut yoke]

general term formula is
un=u1+(n−1)d

i dont want to do it sneaky, i dont understand it and will run into it next year

[viral patio]

okay, i will give you the sneaky answer and the non-sneaky answer

[viral patio]

1. Sneaky answer
   S_n is the sum of the first n terms of the arithmetic sequence u_1 + u_2 + ... u_n
   so S_1 is the sum of just the first time, i.e. S_1 = u_1
   so plug n = 1 and see which of them agree - in this case, only one remains

[shut yoke]

oh

general term is the same as u_1 right

[viral patio]

the general term is u_n
the first term is u_1

[shut yoke]

i plugged it into the top one and got
s_1 = 1/4(3-1)

the very top one not one of the options

[viral patio]

yup, what does that simplify to?

(also please reply to my messages so i get ping'd)

[shut yoke]

sorry
1/4*2

[viral patio]

which simplifies to?

[shut yoke]

1/2
wait so do i plug 1 into the other and see which one solves to 1/2

[viral patio]

exactly, that's the sneaky method

[shut yoke]

oh thats not sneaky thats just understanding thats just understanding that s_1=u_1

there is another way?

[viral patio]

it's sneaky because you're taking advantage of the fact that it's multiple choice, the non-sneaky method is trying to directly find u_n

[viral patio]

the other way would be to use that:
s_n - s_(n-1) = u_n
or equivalently (might be easier to see why this is true)
s_n = s_(n-1) + u_n
since you're given the formula for s_n, you can work out s_(n-1) and subtract, giving you u_n

[covert berry]

who said lerking on discord won't teach you stuff

[alpine sable]

i have the reference point

[shut yoke]

lol im thinking

[alpine sable]

but for the normal vector

i dont have enough eqns to solve, only 2 eqns

$$4a - 3b - 5c = 0$$
$$3a + b - 3c = 0$$

[ocean seal]

ajuze

[alpine sable]

what am i missing here, where n = <a,b,c>

[shut yoke]

is it s_n - s_(n-1) = u_n

that is not writing normally

[viral patio]

am i blind or is that not the same thing as what i typed?

[shut yoke]

you are not blind lol

[viral patio]

use \ before underscore

[shut yoke]

is it s_(n-1)
or
s(n-1)

[shut yoke]

^

[viral patio]

they're the same thing, it's just notation
we wrote s_n, u_1, etc. so we should stick with s_(n-1)

[shut yoke]

do i have to use one of the two equations for finding s_n

and use what i was given in that equation

[shut yoke]

gimme a few im gonna try to figure this out

[alpine sable]

Can u help my q while she is trying @viral patio

[shut yoke]

you should prolly go to a diff channel just for convenience

[alpine sable]

I would but now I'm in a inconvenient place

(on my phone)

[sullen nova]

,w 1+1

[ocean seal]

Results provided by WolframAlpha

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

Requested by Le Vorn#7624

[shut yoke]

so i get n/2(u_1+u_n) = n/4(3n-1)

right

[viral patio]

where did u_1 + u_n come from?
i'm not sure i understand your question

[shut yoke]

s_n = n/2(u_1 + u_n)

[shut yoke]

^

[viral patio]

is that true in general? i don't know off the top of my head and i don't have pen/paper on hand to run through the calculations and verify

[shut yoke]

yah it is

its the formula

[viral patio]

okay, do you need anything more from this?

[shut yoke]

no, i get it thanks a lot

[viral patio]

🙂

[exotic mortar]

The marketing department at DIBI Ltd. have determined that the demand, at $d per unit, for a product can be
modelled by the equation, , where x is the number of units produced and sold. The total cost, $C, of
producing x items given by .
What price will yield a maximum profit?

How do I do this

[ionic jewel]

there is definitely not enough information

looks like your math formatting didn't copy

[ionic jewel]

profit = earnings - production costs

so find the profit equation and the find the max

[exotic mortar]

does the profit equation equal to (80x/sqrt x)-(200+0.2x)

[ionic jewel]

no

why is it 80x

oh

yes is it

[exotic mortar]

?

[ionic jewel]

yes your profit eqn is right

[exotic mortar]

idk how to doo the next part

[ionic jewel]

find critical point(s), then check which is a maximum

[exotic mortar]

critical points?

[fading zephyr]

are you looking at differential calculus in class?

derivatives and stuff

[ionic jewel]

assuming this is calculus, critical points are points such that the derivative equals 0 or is undefined

[exotic mortar]

Im looking at functions not deravitives

I can use a gdc btw

[ionic jewel]

what's a gdc

[exotic mortar]

graphics calculator

[ionic jewel]

oh

then just graph it and find the max

your calculator can find the max automatically (it's under some menu)

[exotic mortar]

Ok tysm

[iron jolt]

is anyone here?

[covert berry]

maybe you should just ask and someone may show up lol

[iron jolt]

if the number '1' is used to represent a THING, then that thing MUST fall under the rule of physics, and as such, the equation time=distance/speed must always be in place. if so, then how can 3x1 and 1x3 be the same exact thing if 3x1 is 3, one time , and 1 x 3 is one three times, so... 3x1= XXX, and 1x3 = X , X , X ... these two must have either been seperated in time, or space

am i wrong?

[covert berry]

wtf

[storm turret]

What does that even mean

[covert berry]

this man's crazy

i like it

[iron jolt]

multiplication can not be used to represent real life things

its flawed

thats why

[covert berry]

but i don't know what you're talking about

lol

[iron jolt]

you cant create 3 one time, and one, 3 times, and call it the same, they are fundamentally different

[covert berry]

but they're the same value

i remember a guy writing a book about flaws of equality

something like that

maths have flaws

everyone agrees

[iron jolt]

what does value mean then, because 1 plus 2, and 2 plus 1, they both combine and then, yes, it can be the same

[covert berry]

yeah, read that book

[iron jolt]

haha will do

[covert berry]

it may have the answer to your question

[iron jolt]

thanks 🙂

[covert berry]

i don't remember its name tho

uhhh

[misty pebble]

Why can I turn 1/3x^-2/3 into 1/3x^2/3?. Keeping the 1/3 is the same spot seems strange while moving the exponent and x

[gray isle]

you're gonna need some parentheses

did you mean
$$\frac13 x^{-2/3} = \frac{1}{3x^{2/3}}$$

[ocean seal]

ℝamonov

[misty pebble]

apologies

[gray isle]

exponent laws

$x^{-a} = \frac{1}{x^a}$

[ocean seal]

ℝamonov

[misty pebble]

ty

[alpine sable]

No. 7 part 2

Please help 🥺

hi

[gray isle]

,rotate

[gray isle]

what have you tried?

[onyx pier]

where does those 45 comes from??
$\frac{5}{9}+\frac{2}{3}-1\frac{1}{5} = \frac{25}{45}+\frac{30}{45}-\frac{54}{45} = \frac{1}{45}$

[ocean seal]

Rin

[gray isle]

45 is the lcm of 3 , 5 and 9

[vale wigeon]

common denominator.

[onyx pier]

i'm sorry, what is lcm??

[gray isle]

lowest common multiple

[onyx pier]

i see, so basically 9 x 3 x 5?

[vale wigeon]

no

you do not need to multiply by 3, as 9 is already a multiple of 3

[onyx pier]

uhm.. i dont understand, what is this kind of calculation called in english? let me google it 😅

oh nvm found it

thanks!

[alpine sable]

what am i doing wrong here?

$$\frac{\delta z}{\delta v} = \frac{\delta f}{\delta x}\frac{\delta x}{\delta v} + \frac{\delta f}{\delta y}\frac{\delta y}{\delta v}$$

[ocean seal]

ajuze

[alpine sable]

i dont see where the x(3,5) = 5 and y(3,5) = 3 come into play

resolved

[ocean seal]

Hyl1s

[harsh acorn]

Can someone help me find x

[spare fern]

Notice that 5!, 7!,9! And 11! All contain 3×4

[robust dagger]

hi, so my teacher gave me this as an answer to revision, but when she moved the 20 over instead of minusing it she divided it

is this correct?

if so why?

since the 20 is on its own and clearly plused to the equation, wouldny you minus 20 from both sides

[sage summit]

absolutely not

[ruby current]

doesnt look correct

[robust dagger]

ok good

so just to clarify, the correct way to do this is
25 = -10cos(2t) + 20
5 = -10cos(2t)
-1/2 = cos(2t)
^-1cos - -1/2 = 2t
answer divided by 2 = T?

or is it -1/2 = -60 degrees
-60 degrees = cos2t
-30 degrees = cos t
find -30 degrees on unit circle for cos

4pi/6 , 7pi/6

[stark grail]

i need help😭

its about prob distribution

[dusk orbit]

Biggs

[jagged imp]

those are all solved by integrating both sides wrt x

do you have a specific one you're struggling with or..?

[jagged imp]

is Z distributed with standard normal dist?

also one of you needs to move

[stark grail]

ya

[ruby current]

P(-2.5 < Z < a) = P(Z < a) - P(Z < 2.5) = 0.6413

you can find P(Z < 2.5) from a z-score table

[jagged imp]

been a while since i worked with this but it should be doable by writing the prob on the lhs as P(-2.5<Z<0)+P(0<Z<a) and solving for a with symmetry and shit

[stark grail]

how to know whether the value a is negative or positive?

[ruby current]

so you're left with finding which value a has probability 0.6413+P(Z < 2.5)

[stark grail]

Thanksss

[jagged imp]

yeah do what tushar said it'll be simpler i'm rusty on this

[sullen nova]

halpo

H₂(g) + I₂(g) ⇄ 2HI(g) at 400⁰C

when pressure is increased

[stark grail]

Thank you

[sullen nova]

it shifts to where?

[jagged imp]

a) thats chemistry and b) There's more moles of gas on the LHS so when increasing pressure it shifts to the right to produce more products

and something about le shitters chatlier's principle and the system trying to relieve the stress placed on it for your justification

[sullen nova]

but the moles are equal

[jagged imp]

oh sorry i misread i thought there was a 2 in front of the H

[vale wigeon]

wait, why would pressure increase at all as a result of this reaction?

[jagged imp]

in that case, it doesn't affect the equilibrium position

[vale wigeon]

though i'm not very confident in my thermodynamics knowledge

but like, hm

[jagged imp]

the question is asking what happens if the pressure in the system increases

by air being pumped in or something

[sullen nova]

this is Chemical Equilibrium

[jagged imp]

not as a result of the system itself

[vale wigeon]

le vorn, why don't you post the full problem

i've known you to mangle wording before

[sullen nova]

I eat bread

[jagged imp]

fair

[misty pebble]

How do I do this?

Would it intercept in the middle? Do I need any other information?

[solar pebble]

sorry not sure, I did it 4 years ago

[sullen nova]

Le Fishe Au Chocolat

[warm rain]

Yes, you're right it will intercept in the middle as there is a minimum there (gradient is zero). You should be able to do it by looking at the gradient of the function at each side of the minimum. Remember, f'(x) will be linear.

[misty pebble]

Does the gradient of the derivative line matter? I found the solution and it doesn't include it.

[lapis imp]

Hello is this room occupied?

[subtle mantle]

Doesn’t seem to be, b0ss

[lapis imp]

Ow ok ok thanks <3

Please help i just wanna ask that if doing linear regression

Ur data needs to be normal?

[shell heron]

i need help with C

i tried factoring but that didnt work out

still got 0/0

[gray isle]

What do you have after factoring?

[shell heron]

i got x(7x - 4 - 3/x)/x(3x - 4 - 1/x)

and then i removed the x's

[lapis imp]

Sad

[gray isle]

express the numerator and denominator as products of linear factors

(similar to how I assumed you did parts a and b)

[subtle mantle]

If you’re just doing least squares regression then no I don’t think it does

[lapis imp]

Ow ok ok thanks!

[limpid stone]

what is the cartesian equation for r = 1 - sintheta

the answer is (x^2+y^2+y)^2 = x^2 + y^2

but idk how u get it

[tired fox]

a change in pressure won't lead to any shift, because there are the same number of moles of gas on both sides

[alpine sable]

Could someone help me find x? I dunno how to solve, am i supposed to take log?

[upbeat gorge]

Binomial expansion can help here

[alpine sable]

Hmm, i haven't learned that yet in class

I suppose ill leave this question for now if it has to do with binomial expansion

[wary stream]

There's an x in there?

[alpine sable]

In the powers

[wary stream]

But that's an x? Looks like an n or Greek eta with curl

[viscid basalt]

"to teach is to learn twice" does that mean teach=2learn and learn=0.5teach

[stiff wraith]

could someone help me with this

i know how to do it for numbers but im not sure how to do this with n

and how to prove :/

[glass lichen]

what have you tried?

Note the fact you have prove the answer likely means there is 1 answer for all possible n values

[stiff wraith]

tbh i dont know where to start

sorry 😦

[glass lichen]

ok well do you have a guess for what the gcd will be?

[velvet lotus]

guys i need help

[knotty sleet]

Channel occupied

[knotty sleet]

I would recommend reading up on the Euclidean algorithm

[velvet lotus]

whats 3\7 +2\3 devide 2\5-1\4

[knotty sleet]

You'll understand the general topic much better if you do that

[velvet lotus]

wheeler can u help me

with my fraxtiion question

@knotty sleet

[frank nacelle]

^

[velvet lotus]

srry

[glass lichen]

the channel wasnt occupied if they didnt respond

[wary stream]

There wasn't any activity for almost 30 minutes, so it's technically unoccupied

[knotty sleet]

Oops didn't see the time

[golden zodiac]

is anyone here good at functions?

I can pay a bit of money if someone can help me out

not for hw or smth just revision

having a hard time understanding it

[glass lichen]

channel is in use, #❓how-to-get-help

[golden zodiac]

ok ty

[primal bridge]

I need to draw a triangle inside of a square and make it so that all points of the triangle touches the sides of the square. I have something like this calculated with

x = r * cosθ
y = r * sinθ

but clearly this is not the solution as you can see in the image below. Last time i had math was in highschool a year ago so I don't understand everything.

does anyone know how I can achieve what I want?

ps. this is not an exercise bound to any school project.

I have to achieve something like this

[rigid smelt]

hmm

are there any other conditions?

or you just want to have a triangle inscribed in a square?

[stray sand]

what kind of functions ?

[primal bridge]

This is what i need to achieve:

Draw a series of regular polygons, one inside the other. The innermost should be an equilateral triangel, enclosed by a square, enclosed by a pentagon, etc. Let all the points of each N-polygon touch sides of the (N+1)-polygon.

[rigid smelt]

and we are supposed to do this in a cartesian plane?

hmmm

[primal bridge]

I work with a simple graphics program and need all the points of a polygon to draw it

but works like this so the topleft is the origin

[rigid smelt]

well im thinking you should start with an easy model first, something like the vertices of the triangles are to be located at the midpoints of the sides of the squares

and then to a pentagon, the vertices of the squares are at the midpoints of the sides of the pentagon

hmm why do i have a feeling the golden ratio is gonna appear somewhere in the formula

[primal bridge]

ah, thank you i will try some more things

[minor aspen]

Hopefully this is a math question; if not, lmk please:
I'm wondering how would I find an average (and RMS) value of this kind of signal, where the signal is not periodical?

Average value is the area divided by period as far as I know right now - and since there is no period here, can I even do it?

[proud burrow]

Have you got your solution

[stray sand]

nope

[proud burrow]

Ohk message me question I will help you

[stray sand]

Thanks for your good will. It was my friend's homework question. He said he had it done.

[proud burrow]

Ohk no problem

[sharp basalt]

how do you do this

[solar pebble]

And since cos is an even function :^)

f(x-pi/2) is a shift by pi/2 to the right

so it'd be A

,w sin(x-(pi/2))

and just to make sure

[ocean seal]

Results provided by WolframAlpha

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

Requested by Xetrov#0272

[solar pebble]

by no means am I qualified to give this sort of advice but if you can do numerical integration divided by the domain size

that's the typical way to do it

@wanton smelt laws of logs and conversion

[ionic jewel]

how do you take log with two bases

[solar pebble]

specifically

[ionic jewel]

never seen that

[wanton smelt]

its 1/5

0.2

[alpine sable]

some people use commas for decimals

which is weird imo

[ionic jewel]

oh

[alpine sable]

i mean it's weird cause we've never seen it like that

[ionic jewel]

then how do they write coordinates

(1.2)

[wanton smelt]

nah we use commas there too

[solar pebble]

$\log_x y= \frac{\log_a y}{\log_a x}$

[wanton smelt]

its about context

[solar pebble]

is this right?

[wanton smelt]

think so

[ocean seal]

Xetrov

[solar pebble]

don't even remember

[alpine sable]

I've seen someone use / or |

[solar pebble]

not touched logs for ages

[alpine sable]

and it was in #help-9 about 10 mins ago

[summer lava]

Hey guys I need help with a problem I'm facing when modelling a system of sets

[trail epoch]

2 (x2) is x4?

[summer lava]

So basically I have a system of a few sets (say 5), and I want to model the probability needed when choosing an item from a few sets among them

[solar pebble]

do you have the exact problem?

[wanton smelt]

a?

[summer lava]

So if I had 5 sets, each with 20 elements, and I needed to choose 1 item from 3 of said 5 sets, one of the three sets would then have 19 elements. When this is done again, if I chose 3 out of 5 sets is there a way to remember which particular set had 19 elements?

[solar pebble]

@wanton smelt to convert to a new base

[wanton smelt]

so i got log(64)/(log1-log5) now

[summer lava]

The problem I'm facing is the item is chosen randomly, so you cant really state exactly which set the item would have come from in the first place

[wanton smelt]

any base?

[solar pebble]

any

[wanton smelt]

should i pick one in particular

[solar pebble]

just as long a is the same on top and bot

I'd chose it strategically

[wanton smelt]

what would be best in this case

[solar pebble]

literally any

but probably 10

[wanton smelt]

what do I do now

[solar pebble]

or 1?

idk

[wanton smelt]

cant be 1

a>0 a=/=1

[solar pebble]

good point

brain fart

I thought the denominator would account for that but nvm

[wanton smelt]

im so confused

[solar pebble]

OOH

I'm stupid

notice 64 = 2^6

root 5 = 5^0.5

and the bases are 0.2 and 0.5

0.1* 2 and 0.1 *5

[wanton smelt]

i what

so how do i do it ⚰️

[solar pebble]

you sure?

[wanton smelt]

sure of what

[solar pebble]

you got it?

[wanton smelt]

nope

[solar pebble]

...

[wanton smelt]

i understand what youre saying but i still dont know how to solve it

[solar pebble]

oh

mb I thought you said you know how to do it

$\log_{0.2} 2^6 = 6 \frac{\log 2}{\log 0.2}$

[ocean seal]

Xetrov

[wanton smelt]

log0.5(5^(1/2))=(1/2)(log5/log0.5)?

what do I do with log2/log0.2

[solar pebble]

yes that's right

then you can simplify it

[wanton smelt]

how do I simplify it lol i havent excercised at all sorry

[solar pebble]

hold on

we're multiplying whole logs here

let me have a think :S

[wanton smelt]

lol ok ill try the next ex in the meantime

[solar pebble]

2 = 10/5

5=10/2

try that

hopefully we get some nicer numbers

[wanton smelt]

log(xy)=logx+logy?

[solar pebble]

$\frac{\log 10 - \log 5}{\log 10 - \log 500}$