help-0

[drifting basin]

Because in one of those you wrote it as 3x^3

[vapid oak]

yeah that was a mistake

[drifting basin]

Yeah okay all good

[velvet condor]

:v it doesnt mean that you cannot calculate it

[vapid oak]

i mean i suppose but that would insinuate x and y are imaginary

[velvet condor]

theres no need to solve for x and y

69 and 6969

i randomly chose those numbers :v

[median tendon]

Do you isolate x^4 and y^4 for each of equations to one side then sub it into the equation you want to be calculated and then somehow things get simplified?

[velvet condor]

i havent tried that

[vapid oak]

I think that OP just made some random equations and wants to solve them, I don't think there are any nice answers

[velvet condor]

i can think of "nice" numbers:))

brb

[median tendon]

Either really difficult or some weird trick to simplify it

[vapid oak]

maybe try using 1 lol

here's my view: the solutions no matter what will be imaginary, that doesn't mean that x^4 + y^4 is tho

[velvet condor]

true:o

i encountered with problems like that

so i came up with this thing

[velvet condor]

an example would be

[vapid oak]

ok yeah theres no way we'd be able to find that

[velvet condor]

bruh

[vapid oak]

these are the solutions

wolfram alpha'd it

[velvet condor]

what is wolfram alpha doing.....

[vapid oak]

bro im sorry. if you make up a random system of equations you arent just going to get some nice integer solutions.

[velvet condor]

actually

the real a

is the solution

others idk how wolfram managed to get that

[vapid oak]

i dont even understand what youre saying im sorry

[velvet condor]

so uh im going to cook dinner too so ill just post the hint here if u want
||square both equations and add them up :D||

brb....

[vapid oak]

i think your algebra may be incorrect

how does squaring both equations give you anything close to the solution?

[median tendon]

With a quick glimpse, I dont see how either the x^12 or y^12 can be cancelled with that

[vapid oak]

i think when they said square the equations, they literally just double the powers in the equation and nothign else.

didnt even square the -3

because thats the only way you could possibly get the desired equation

[velvet condor]

no..... bro

it is
||(x^4+y^4)^3||

[rigid smelt]

it definitely isnt

clear (x^4+y^4)^3 has a +3x^4y^4(x^4+y^4) term when expanded

[rigid smelt]

and notice that if you square both of the equations, there is noway a +3x^4y^4(x^4+y^4) would be in there

i mean if it would, there is definitely another term that wont be cancelled out

[velvet condor]

its x^2y^4 bro

you read the wrong one

:P

[median tendon]

Ok there are too many versions of this written down xD

[velvet condor]

i agree

:v

[median tendon]

But yeah it does turn out to be equal

[rigid smelt]

something is really wrong, (a+b)^2 expanded is giving 3 terms and hence when added the two equations together, you get in total of 6 terms, (a+b)^3 expansion gives 4 terms

[velvet condor]

...

[rigid smelt]

clearly (x^6-3x^2y^4)^2 + (y^6 - 3x^4y^2)^2 does not have any terms cancelled out

im sure i didnt

[rigid smelt]

idk, but thats the logic, lemme write it out on papers then

[median tendon]

Terms don't get cancelled out, but u do get some terms with same coefficient and so u can add them

[rigid smelt]

well you cant turn a 6-term expression into a 4-term expression iwthout cancelling two of the terms out

[rigid smelt]

idk but im writing to see if something cancels

[median tendon]

This is the expanded form

Clearly u go from 6 terms to 4 terms without cancelling

[rigid smelt]

oh wait nvm, something did cancel out

factoring 3x^4y^4 from all of the terms except x^12 + y^12 will give -2(x^4+y^4)+3(x^4+y^4)

but yeah, my point still stand, you cant go from a 6-term expression to a 4-term expression without cancelling something

[median tendon]

Look at that pic above

[rigid smelt]

i know

[median tendon]

There are 6 terms

[rigid smelt]

im not saying it doesnt factor to (x^4+y^4)^3

im saying that you cant go from a 6-term expression to a 4-term expression without cancelling something

[median tendon]

And u can add terms together to make it 4 terms

[rigid smelt]

trust your algebra and not the computer, to make expression with 6 terms into an expression with 4 terms, you MUST cancel something out

[vernal igloo]

why do all the points on a line satisfy the equation?, like how did it come to that?

[rigid smelt]

for example with something like x^2 + xy + y^2 + 1 can be rewritten as (x+y)^2 + 1 -xy, observe that in the end, the amount of terms the two expression have are equal

so basically, something DID cancel out, its just that i didnt see it

[median tendon]

For example, 9x^4y^8-6x^4y^8=3x^4y^8 there is no cancellations here, right?

[rigid smelt]

idk, there might be

lemme just read thru that

[median tendon]

Its just addition

[rigid smelt]

well technically something

9x^4y^8 - 6x^4y^8 cancels with each other and introduce another term which is 3x^4y^8

gosh writing these powers close together hurts my head

[median tendon]

That's a strange way to think about imo

[rigid smelt]

im just saying, to turn some kind of expression with more terms into an expression with less term, there is some algebraic cancelling, either by division, subtracting, addition or simply multiplication

i guess cancel is a bad word to use

"simplify" should fit more

[median tendon]

When I think about 'cancellations' I think about something like this x/x where x gets cancelled out causing the state to not be observable

[pearl marlin]

I have one question

[velvet condor]

ask

[pearl marlin]

How get honourable batch on my profile?

[velvet condor]

bruh

so irrelevant

its hypersquad.......

[pearl marlin]

Should i move to discussion group for its answer?

[covert berry]

How do I prove
$$gcd(p^a−1,p^b−1)=p^{\gcd(a,b)}−1$$
, where $p$ is a prime number, and $a,b∈\mathbb{N}^{+}$?

[ocean seal]

whale

[crude hazel]

can I cancel out (y+1) in y(y+1) = x(y+1) + 6

[pearl marlin]

No

There is no (y+1)with 6

[alpine sable]

Euclidian algorithm

[ashen wave]

Can anyone help me understand what the symbols mean? Like the arrow and the tilde

[vague coral]

the tilde means negation if im not wrong

like you have a proposition P, ~P is the negation of P

[ashen wave]

what xD?

[vague coral]

e.g : p : I eat a banana
~p : I don't eat a banana

[ashen wave]

ohh okay thank you

[vague coral]

and the arrow means "implies"

[dim vine]

'Prove (n) = n' Sorry for the bad notation, I'm not sure how to show the single larger bracket but I'malso not sure how this works
(1)

I think it's meant to be a vector

[warped phoenix]

@glass lichen

Ok im back

heres the picture for reference again

so to find P(N), I did $0.8=\frac{P\left(N\right)\cdot 0.75}{0.75}$

[ocean seal]

TheMane3

[warped phoenix]

you would multiply both sides by 0.75, giving that P(N) = 0.60, since 0.8 isnt 0.6, it's not independent (dependent)

did i do it right 😄

[west vine]

Hello

Can someone help me with few statistics questions

for my homework

[hollow hawk]

i feel so dumb... but i need help with this..

[west vine]

you want to find the angles?

[hollow hawk]

yes

how find pi from 3t

[oak chasm]

What do you mean when you say find pi?

[west vine]

You mean find the values of T in radians?

[hollow hawk]

i just wanted to know how my lecturer got he pi with cos3t

the*

[west vine]

Do you know how to find it in agles

angles*

[hollow hawk]

why does it relate to angles

[west vine]

because the variable inside the cos is an angle

[steady fern]

hi

[hollow hawk]

hey

[steady fern]

i have a ask

[hollow hawk]

@oak chasm i just wanted to know how my lecturer got he pi with cos3t

[warped phoenix]

I got P(E) = 0.085, P(B) = 2.53, and P(E|B) = 0.215, they want to know if P(E) and P(B) are independent, and the formula for independence between two events is if P(E & B) = P(E) * P(B), then it's independent

I'm not told what P(E & B) is, so how am I supposed to know the answer?

[shell heron]

sorry

[warped phoenix]

all g lol

[shell heron]

lol

[noble sinew]

8.5 percent is equal to 21.5 percent?

[warped phoenix]

thats not what the answer is saying

if thats what u just said

[noble sinew]

it is?

the 21.5 percent is a conditional probability (can be seen by the statement "given that...")

now you are saying they are independent because the prob of earning more than 75 thousand is equal to the conditional probability

aka 8.5%=21.5%

[warped phoenix]

ugh sorry i gtg for like an hour, can we resume this when im back 🙂

[noble sinew]

you had yesterday that you knew they were independent if P(E)=P(E|B)

since not equal not independent

why are you even trying to find P(E and B)? And besides P(B) is not equal to 2.53 (a probability can't be above 1)

[vernal igloo]

why do all the points on a line satisfy the equation for that line?, like how did it come to that?

I understand that you can find points that represent a solution, but how come you can just make a line and all of the points on that line is a solution

[glass lichen]

cause a line by definition is the set of points that satisfy it

this is true for any graph of a function

[vernal igloo]

yeah, I understand that, however, did someone just go like "oh, if you were to sample all possible x's and find any y's, it would fill the gap between these 2 points and make a line"

[glass lichen]

if you sample all x values, you wont have gaps to fill

cause you'll have hit all of the numbers in R

[vernal igloo]

it forms a line because every step it increases by the same amount, right?

[glass lichen]

yes, slope is constant

[timid wind]

is this channel being used

nvm

can someone briefly explain how to do a) and b) and c), this function is kinda confusing

[vernal igloo]

so it's correct to say that it forms a line because "y increases by the same amount every step", correct?

[glass lichen]

yes, every step of the same size...

[ionic jewel]

yeah i was gonna say that's not the most formal definition but the idea is right

[vernal igloo]

of the same size?

[zenith wing]

This function doesn't appear to have any algebraic definition, so just lookat the graph itself. It's asking what g(-5) is, and if you look at x=-5 on the grid, and find where the function is, that will give you g(-5). Do the same for b, but in reverse; look for where g(x)=5 and find its x value. An inverse funciton essentially does the funciton in reverse; if you input the output of g(x), you will get x, so g^-1(g(x))=x, and g(g^-1(x))=x

[timid wind]

ah

[zenith wing]

and the definition of function is any input only outputs one value

[timid wind]

yeah ik

[zenith wing]

if the increase is always the same, that makes it linear

[zenith wing]

Just making sure ^^

[timid wind]

so i just put the function on the x=-5 online

[zenith wing]

wdym

oh

yeah

Yes

For a

[timid wind]

but what does it mean for g(-5)=

what type of answer do i put

[zenith wing]

g(x) is the function

[timid wind]

ohhhh

[zenith wing]

the wobbly "line" is g(x)

[timid wind]

it appears nothing is on the x=-5 line

[zenith wing]

accept*

[timid wind]

like for the question a) , what type of format is the answer in

[zenith wing]

It'll probably be a value

[timid wind]

value as in 1, 2, 10, etc

[zenith wing]

if you look at all points where x = -5, find where g(x) crosses it

[zenith wing]

yes

[timid wind]

g(x) does not cross it tho

[zenith wing]

Not even at one point?

[zenith wing]

I see a point where it intersects

[timid wind]

oyhh

im dumb

yes

[zenith wing]

no, sometimes it takes a bit

[timid wind]

(-5,6)

[zenith wing]

You're not dumb

yes

[timid wind]

ah so its 6 then

ty

[zenith wing]

Yes

Your welcome ^^

[timid wind]

and for b i just take the answer from a and try and find it

[zenith wing]

Well yes and no

because it's asking for what value of x does g(x)=5

[timid wind]

wait its just where 5 interacts

[zenith wing]

so instead of looking at a vertical line you're looking at a horizontal line

[timid wind]

so 0 and -3

[zenith wing]

Ye

Wait a second that's a piecewise function

[timid wind]

pieceise?

piecewise?

wait it is

[zenith wing]

Made of pieces of defined funcitons

[timid wind]

made of parabola and 2 lines

[zenith wing]

yeah it just isn't defined

Yes

I just saw that

Although it doesn't appear that you'll need that knowledge for this problem

[timid wind]

yea

[zenith wing]

But it's still cool to see

[timid wind]

so how do i find domain and range for the inverse

i already drew it

[zenith wing]

May I see the drawing?

Oh wait

Okay so

[timid wind]

inverse is just down the y=x line

i think

symmetrical

[zenith wing]

A refleciton, yes

[timid wind]

yes

but domain and range i cant find cuz idk the function notation

[zenith wing]

f(x)=x is its own inverse

same with f(x)=1/x

Wait

Ye

anyways

[timid wind]

is domain just all the x points

[zenith wing]

Yes

It's the set of all possible values of x

[timid wind]

but arent there infinite x points technically

ohhhh

[zenith wing]

make sure to use open bounds and closed bounds appropriately. there appears to be no open bounds to this, though

[timid wind]

but then how would i write it

confusion

[zenith wing]

How I was taught was something like this:
D:[min-x-inc,max-x-exc)

exc is excluded (open)

inc is included (closed)

[timid wind]

hmmmm

[zenith wing]

Just replace min/max-x-inc/exc with your min and max values of x

similar thing for range, but range is for y values

[timid wind]

ah

[zenith wing]

so for instance the domain of f(x)=sqrt(x) would be D:[0,infinity)

[vernal igloo]

right, so it forms a line because y increases by the same amount every step, i guess that would be correct to say

[zenith wing]

Yes, your question has been answered like 5 times, that is correct

[warped phoenix]

`yeah thats what i thought but 0.8 * 2.53 does equal 0.215, anyway, im looking for P(E & B) because the questions asks if P(E) and P(B) are independent, right? If it was asking for If P(E) and P(E|B) then the question would be "Are the events 'earns more than $75,000 a year' and 'earns more than $75,000 a year given that they have a bachelors degree'", right?

But instead its asking if "earns more than 75,000" P(E) and "having a bachelors degree" P(B) is independent

not the former

[vivid slate]

Think anyone could help me out with A and C ? Just need to know how to set it up <@&286206848099549185>

[noble sinew]

read this https://www.probabilitycourse.com/chapter1/1_4_1_independence.php (would honestly recommend whole chapter 1)

and doesn't make sense to ask if E and E|B are independent - that isn't a thing.

[warped phoenix]

that site says "Two events A and B are independent if and only if P(A∩B)=P(A)P(B)."

[noble sinew]

Then P(A|B)=P(A)

like you also knew yesterday but somehow not now

[warped phoenix]

The question doesn't have a given anywhere though

it doesnt say "are events "blah blah blah" and "blah blah blah given etc." independent

[noble sinew]

"earns more than 75000 per year given that"

there certainly is given that in the text

[warped phoenix]

i mean in the question asking 4 independence

there's no given

[noble sinew]

If they were independent then P(E|B)=P(E)

thats a condition

[warped phoenix]

if P(E|B) = P(E) is true, then yes those two are independent, but that doesn't make events P(E) and P(B) independent right?

[noble sinew]

then P(E) and P(B) are independent

[noble sinew]

read the whole page (preferably more of chapter 1) (for example whole 1.4) then come back

1.2 useful to visualise probability

[remote lodge]

can someone tell me how to go about doing this

either i wasn't paying attention or my teacher is bad at teaching

[timid wind]

can someone explain what a bearing of 210, or 245

means

in angle math

never mind i got it

[zenith wing]

You can distribute the sqrt(5)

although that may make it worse

[vivid slate]

Anyone able to help me out with this?

[remote lodge]

do you wanna see the answers?

[zenith wing]

sure

[zenith wing]

ask in a different channel for now

[remote lodge]

honestly not trying to "cheat" i just have no clue how to do this

[zenith wing]

Nothing looks too bad about those answers

[remote lodge]

it's a multiple choice question

[zenith wing]

Yes

I know

[remote lodge]

but how would i solve the problem

[zenith wing]

I'm trying to figure out if my immediate response would be wrong

so I can help you get to the correct answer better

[remote lodge]

oh alright

[wary stream]

Distribute the $\sqrt{5}$ to all the elements in the parentheses

[ocean seal]

dldh06

[wary stream]

Then simplify, if necessary

[remote lodge]

how would i distribute?

[wary stream]

Do you know how to distribute in general?

[zenith wing]

(a*sqrt(b))*(c*sqrt(d)) = ac*sqrt(bd)

[remote lodge]

in general yes

but not with this type of work

[wary stream]

So if you have x(x + 2), what would that be, if you distributed?

[remote lodge]

x + 2x?

[zenith wing]

Close but not quite

[remote lodge]

x2

[zenith wing]

x^2, yes

[wary stream]

It would be $x(x+2) \equiv (x * x + 2 * x)$

[ocean seal]

dldh06

[wary stream]

Correct?

[zenith wing]

So my initial answer was correct, but ye just distribute the radical

[remote lodge]

ok so if i did it would be this on right?

[zenith wing]

Looks right to me

wait

no

[wary stream]

No, not correct

[zenith wing]

10*sqrt(5) != 5*sqrt(2)

[wary stream]

Apply the distribution technique, I just showed you

So $\sqrt{5}(10 - 4\sqrt{2})$

[ocean seal]

dldh06

[wary stream]

How would you distribute that? Like the x(x + 2) example

[warped phoenix]

ok i read the page

im back

[remote lodge]

5sqrt2 - 4sqrt10

not sure how to work the bot so hope you understood that

[white girder]

I can help

parzival

[wary stream]

Not quite

[remote lodge]

if you'd like to

[wary stream]

How are you obtaining $5\sqrt{2}$?

[ocean seal]

dldh06

[white girder]

Actually no

I mostly came here to learn and observe how you guys answer questions

Sorry I thought I had this equation in the bag

[zenith wing]

I just joined and have been answering questions like I normally do

[white girder]

Im just here to learn so just move on like im not here please

[wary stream]

What was the first step that we did with the x(x + 2) example?

[remote lodge]

distributive property

[wary stream]

And that looks like?

[remote lodge]

x2

x times x + x^2

[zenith wing]

that's not right

Still not quite right

[wary stream]

If you don't simplify, how would you distribute x(x + 2)?

So in general, $a(b + c) \equiv (a *b + a*c) $, correct?

[remote lodge]

sorry i got a quick phone call

[remote lodge]

yeah i understand

[wary stream]

So apply that concept to $x(x + 2)$

[ocean seal]

dldh06

[wary stream]

Keeping the multiplication signs too

[remote lodge]

wouldn't the x cancel out since it's a like term?

[wary stream]

Nope

It's multiplication

Distribution is normally multiplicative

[remote lodge]

ok hang on

is it xx + x2?

[wary stream]

Add in the multiplication symbols too

To make it more clear to read

[remote lodge]

x times x + x2

[wary stream]

Both terms

[remote lodge]

both terms? wdym?

[wary stream]

It would be $x * x + 2 * x$, correct?

[ocean seal]

dldh06

[remote lodge]

ohhhh ok

sorry 😅

[wary stream]

Because remember, $a(b + c) = a * b + a * c$

[ocean seal]

dldh06

[remote lodge]

ok thank you

[wary stream]

Now apply that same concept to $\sqrt{5}(10 - 4 \sqrt{2})$

[ocean seal]

dldh06

[wary stream]

No, apply the a(b + c) = (a * b + a * c) concept first

[remote lodge]

would i apply it to the sqrt2 as well?

[wary stream]

Yes

[remote lodge]

ok, not sure how i should present it to you though

feel like it would be hard to understand what i'm doing through text

[wary stream]

So the first step is distribute and getting it in the form of a * b + a * c, correct?

What would that look like?

[remote lodge]

hold on

[oblique gate]

How can I learn to read such statements (as in using the curly brackets and the "such that")?

[glass lichen]

set builder notation

[wary stream]

Yes, so far so good, but next time add in the multiplication symbols

[oblique gate]

thank you

[remote lodge]

infront of the 10 and 4?

[wary stream]

Yes, so $\sqrt{5} * 10 - \sqrt{5} * 4\sqrt{2}$

[ocean seal]

dldh06

[remote lodge]

ok, that's what i have right now

[wary stream]

So, next step, can things be simplified?

[remote lodge]

can i lower things to there GCD?

[wary stream]

There's no need to find a GCD.

When I meant simplify, combine the like terms

[remote lodge]

oh.

[wary stream]

So can you combine $\sqrt{5} * 10$?

[ocean seal]

dldh06

[remote lodge]

no?..

[wary stream]

Like is $\sqrt{5 * 10}$ a legal thing to do?

[ocean seal]

dldh06

[remote lodge]

yeah

could you make sqrt15?

[wary stream]

No

It's not a legal operation to do

[remote lodge]

ok, can i add both sqrt5?

[wary stream]

Nope

What's the difference between $\sqrt{5} * 10$ and $\sqrt{5} * \sqrt{10}$?

[ocean seal]

dldh06

[harsh swallow]

a factor of sqrt(10)

oh shit

sorry

[remote lodge]

you're fine Katherine lol

[wary stream]

One is $10\sqrt{5}$ and the other is $\sqrt{50}$, correct?

[ocean seal]

dldh06

[remote lodge]

yes

sorry. i was afk for a split second so i didn't respond very fast

[wary stream]

.

So back to that, can you combine $\sqrt{5} * 10$?

[ocean seal]

dldh06

[remote lodge]

no, the 10 would go in font of the sqrt

[wary stream]

Now, what about $\sqrt{5} * 4\sqrt{2}$?

[ocean seal]

dldh06

[tired geyser]

Two triangles are congruent if they have a pair of correspondingly proportional sides and each pair of angles adjacent to each of these sides also equal to each other?

[remote lodge]

no, but can you add sqrt5 and sqrt2 to make sqrt10 while 4 is in front?

[tired geyser]

help me please :(

[wary stream]

Not add but multiply

[remote lodge]

find an unused Question channel

and wait for a reponse

[wary stream]

Ask in a not busy channel and be patient, someone will answer you

[remote lodge]

oh ok

[tired geyser]

thanks

[remote lodge]

so would this be correct

[wary stream]

Yes

[remote lodge]

sweet!

so is this the answer?

[wary stream]

Yes

[remote lodge]

ok thank you so much @wary stream for the little tutoring session

i really appreciate it

[steel mason]

help

[alpine sable]

im a bit confused about ↑

i know that a single ↑ is squaring i think

x↑y = x^y

and that tetration would be ↑↑

[remote lodge]

how'd you type that lol

[harsh swallow]

alt code or something

[alpine sable]

and tetration with ↑↑ would look like

[harsh swallow]

$\uparrow$

[ocean seal]

Katharine

[alpine sable]

tetration: x↑↑y = x^x… y times

[harsh swallow]

yes

[alpine sable]

whats the symbol for a flipped }

and the gist of ↑↑↑ i get is basically

x↑↑↑y = x^(x↑↑y)

[inner sequoia]

how do i read these coordinate things

[harsh swallow]

first one is x

the second one is y

[inner sequoia]

wtf

but

[harsh swallow]

or function value at x

[alpine sable]

the f’s

[inner sequoia]

what does -1, f mean

[harsh swallow]

(-1, f(-1)) = point x = -1 y = f(-1)

f just means function

a function is a thing that assigns a new number to a number that you have put in

[inner sequoia]

f(-1) so x = -1?

[harsh swallow]

yes

[remote lodge]

yes

[harsh swallow]

because f(x)

is the function in general

[alpine sable]

but does x↑↑↑y = x^(x↑↑y)

[harsh swallow]

f(-1) is when x = -1

[inner sequoia]

f(x) means?

[harsh swallow]

f(x) is the short way of saying

function value at x

[inner sequoia]

so the function is the line right

[harsh swallow]

yes

[alpine sable]

hello

[inner sequoia]

so if x is 5, then at x the function is 5?

[harsh swallow]

hi one sec sam

if x = 5

f(x) = f(5) = -5+3

in this case

because f(x) = -x + 3

[inner sequoia]

f(x) = -x + 3

[harsh swallow]

$x \uparrow \uparrow \uparrow y = x \uparrow \uparrow (... \uparrow \uparrow x)$ y times

[remote lodge]

@wary stream it was correct, thank you again :)

[alpine sable]

???

[ocean seal]

Katharine

[alpine sable]

still doesnt make much sense

so it would be x↑↑↑y = ((x↑↑x)↑↑x).. nested y times?

[harsh swallow]

$x \uparrow \uparrow \uparrow y = x \uparrow \uparrow (x \uparrow \uparrow(x \uparrow \uparrow(... \uparrow \uparrow x)))$ y times

[ocean seal]

Katharine

[harsh swallow]

just nested

[alpine sable]

k

[harsh swallow]

it's difficult without numbers

cuz with numbers you can actually complete the nests

you know what i mean?

[alpine sable]

i understand it but i couldnt imagine tetrating it

its confusing lol

[harsh swallow]

beeeg number

@inner sequoia

[alpine sable]

i see

what about ↑↑↑↑?

[inner sequoia]

yeah

[harsh swallow]

you needed help

[inner sequoia]

yes

i am still trying to compute wtf f(x) means

is it f*x?

[alpine sable]

would it just be that but the nested ↑↑’s were ↑↑↑‘s

[harsh swallow]

exactly that sam

now i help onecore

[wary stream]

It's just another way to denote a function

[harsh swallow]

no f(x) is shorthand for a function

[wary stream]

It's equivalent to y

[harsh swallow]

a function is just a thing that takes a number

[inner sequoia]

oh

[harsh swallow]

and gives you another number

it may be the same number

it may be 3 times the number

[inner sequoia]

so if f(x) = x+2
then y = x+2?

[harsh swallow]

maybe it's the number but - 2

[wary stream]

So f(x) = x + 1 is the same as y = x + 1

[harsh swallow]

exactly @inner sequoia

[inner sequoia]

but why is it called f(x)

[harsh swallow]

because f(x) are special cases

[wary stream]

It's to denote the function with a value input

[inner sequoia]

it says f(x) is f at x

what does f at x mean

[wary stream]

So f(x) = x + 1, if you denote like this f(5) = x + 1, then you plug in 5 for x

[harsh swallow]

it means the y value when you look at when x = something

[wary stream]

So it would f(5) = x + 1 => f(5) = 5 + 1

[harsh swallow]

f(6) is f of x = 6 | f at x when x is 6

[inner sequoia]

so f is function right

[harsh swallow]

the difference between functions f(x) = and y =

is that sometimes y =

can have multiple values for one x =

while f(x) is always only one

for every x

there is one f(x)

does that make sense

[inner sequoia]

yeah

f is output right?

[harsh swallow]

yes

[inner sequoia]

OH

[harsh swallow]

f(x) is the output

x is the input

[inner sequoia]

so f at x
means if i input x (lets say 5), then f will be at f(x) (lets say f is 20), meaning f(x)= 4x?

[harsh swallow]

perfect

[inner sequoia]

thank you

thank you

[harsh swallow]

although be careful when working backwards

as f(x) could also be x + 15

[inner sequoia]

why

[harsh swallow]

which means x = 5 and f(x) = 20

[inner sequoia]

f(x) = 20

(x) = 5

[wary stream]

Or $f(x) = \frac{100}{x}$

[ocean seal]

dldh06

[inner sequoia]

how do i tell if its addition or multiplication

[harsh swallow]

you don't have to work backwards

you will be given the f(x)

and have to calculate stuff with it

[viscid cove]

is the channel in use?

[inner sequoia]

yes

[viscid cove]

my bad

[inner sequoia]

alr now ik what function is

(−1, f(−1))

how do i read this

[harsh swallow]

If all you're given is x = 5 and f(x) = 20 you cannot figure out if it is division, multiplication or addition

you would need more information

[inner sequoia]

f(x) = −x + 3

[harsh swallow]

you read that as a point on the graph

you know the x, y graph?

[inner sequoia]

yes

but what does -1, f mean

[harsh swallow]

it is a way of writing down points on the x, y graph

(-1, f(-1)) = (x, y)

x = -1

[inner sequoia]

so x = -1, f?

and y = -1?

[harsh swallow]

x = -1

y = f(-1)

[inner sequoia]

oH

[harsh swallow]

the comma separates the x and the y

[inner sequoia]

so if x = -1

then -x = 1

and then add 3

so f(x) = 4

[harsh swallow]

yes

so now we know

(-1, f(-1)) = (-1, 4)

[inner sequoia]

f is function, and x is input

alr

so

f(x) is function at input

then

uh

f(x) = 4

oh shit thats why im confused im making problems in my head without enough data

[wary stream]

It's denote f(x) but f is an arbitrary variable. You can label it with any variable you want to. Like s(x) is valid notation too

[inner sequoia]

oh so f is just f

[harsh swallow]

f is just chosen because it means function

[viscid cove]

not a variable

[inner sequoia]

alr

so x is input

y or f(x) is output

and f is the operation correct?

[harsh swallow]

yes

[inner sequoia]

so if f(x) is 2x + 9

then what is it when its just f

[harsh swallow]

that's not allowed

because f is a function that does something to a number

to an input

so having it just loose doesn't work

[inner sequoia]

so if f were by itself would it be like a tunnel without an entrance?

[harsh swallow]

it's more like if i were to write down an equation

like

y = x

but instead i wrote

y =

it doesn't work

does that make sense

[inner sequoia]

yes

[harsh swallow]

we can talk about y = in a way

but we cannot do mathematics with it

similarly we can talk about f

but we can only use it when it's f(x)

[remote slate]

Hi can somone explain why a rational function can only have 1 oblique asympote

[wanton vortex]

https://math.stackexchange.com/questions/1934481/why-cant-a-rational-function-have-both-a-horizontal-and-an-oblique-asymptote

[dark parcel]

Hi guys I understand how to solve this but im confused by the fs

As I solve this equation I don’t get any extra constant f, please I’m stuck

[ionic jewel]

f = 0?

[dark parcel]

Yeah but then how is there are pssquared in numerator

There’s nothing I’m doing that gives me that

Okay I found the answer I made a mistake when grouping Y(S) values mistakenly grouped one I shouldn’t have which would move on the other side of the equation given me the fs

[dark parcel]

And how about this one?

I know I multiply F(s) with Laplace of e^-2t which is 1/s+2 but when multiplying I don’t know how to get it into that form

Partial fractions?

Anyone please?

<@&286206848099549185>

[median tendon]

I think this is something that can be found in the tables

I think this might help

@dark parcel

[placid zinc]

This is incorrect. That is:
L(xy) ≠ L(x)L(y)

See Youssef's picture above

[dark parcel]

Ah yes thank you youssef for that picture and thanks kaynex

Just remember F(s) times exponential is always shifted

[dark parcel]

But why doesn’t that linear rule apply here?

[jagged imp]

<@&268886789983436800>

[median tendon]

Why would linear rule mean L(xy)=L(x)L(y)?

Linearity implies superposition, which is L(x+y)=L(x)+L(y)

And also L(cx)=cL(x), where is c is a constant

[dark parcel]

Ahhh

Yes yes right

Thanks Youssef!

[median tendon]

np

[bronze lynx]

A paintball court charges an initial entrance fee plus a fixed price per ball.
The variable p models the total price (in dollars) as a function of n, the number of balls used.
p=0.80n+5.50
What is the entrance fee?

Could someone help me with this word problem?

[median tendon]

Ok, sure
What have u tried so far, or atleast any initial thoughts on how to tackle it?

Hint: how many balls have been used when you first enter the game?

[bronze lynx]

I first thought about adding 0.80n + 5.50 to get 6.30n but then I scratched that because I knew it wasnt right
Then i tried looking for a value for n like 1, 2, 3, 4 etc. but then I realized there is no guarantee the question could accept multiple possibilities so none of those would be right

And now I'm just stuck

[median tendon]

Whats the answer to my hint?

[bronze lynx]

0....

[median tendon]

Ok, when do u pay an entrance fee?

[bronze lynx]

I am slow 🤦

5.50

[median tendon]

There we go

[bronze lynx]

It wasnt a trick question i just had to fully read the problem

And its not the first time Ive done that so thats something I have to work on

[warped phoenix]

Shouldnt it equal 3/13...?

the dog has to be brown, there are 13 brown dogs, and 3 dogs of those 13 are large, the probability that a dog is large given it's brown is 3/13...

[median tendon]

10 sounds right

[warped phoenix]

how????

[median tendon]

Cause those three are already included in the other numbers

If the three dogs are large and brown, then they must have been already included in the 5 large and 10 brown

When they say 10 brown, it doesn't mean they can't be large either

[warped phoenix]

how was i meant to know it was included

channel in use dude

ok look at this

here they do 11/23

huh?????

this channel is in use

use a different one

@median tendon and in the above self drawn diagram am i not doing the exact same thing as they're doing in the first problem

what changed

[median tendon]

Ok, let's look at the second question

23 have seen the film adaptions

23 is not put in the circle

For the first question, you are putting 10 in one of the circle, this is wrong

[warped phoenix]

why? the circle i put it in is for dogs that are only brown, of which there are 10

[median tendon]

Show me where the word 'only' appears in that question

[warped phoenix]

nowhere 😦

[median tendon]

The union is 10

[warped phoenix]

ohhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhh

🤦‍♂️

i see now

[alpine sable]

i think what u need/all so 3/12=1/4 like 10 we dont need

[warped phoenix]

the intersection is always going to be included in both figures

[median tendon]

Try drawing the circles again for q1

[warped phoenix]

ok

[warped phoenix]

😄?

[median tendon]

Yes

[warped phoenix]

ok then ill try to always remember that

that the intersection is always going to be included

never a separate thing

thus "intersection" i suppose

[median tendon]

The wording is very important

[warped phoenix]

right

ok

i see

thank you so much

[median tendon]

Np

[warped phoenix]

im having a lot of damn trouble with probability so ill be back in a bit probably hahahahahha

[median tendon]

I always hated probability too

I still do

[warped phoenix]

"what is the probability that @warped phoenix is going to open up discord again given that @warped phoenix is having issues with 99% of probability" 😂

there probably is a very specific answer to that

[alpine hound]

Ques - let the number of integers between 1 and 2021 with the property that the sum of its digits is 9 is p. find p / 2

[median tendon]

Your question implies that p=9?

[alpine sable]

$pi/2 = 2\int_{-3}^{3}\sqrt{9-x^2}$

[ocean seal]

music lounge

[glass lichen]

dont post nonsense.

if you're gonna type in the help channels be helpful not a pain

#latex-testing as well

[alpine hound]

noo , P is the no. of integers between 1 and 2021 whose sum of digits is 9

[glass lichen]

well I mean the blunt way is to just find p then find p/2

so along the lines of how many partitions of 9 exist into 4 numbers, then how many permutations of those 4 numbers give a number under 2021

[alpine hound]

ok so u r spamming

[glass lichen]

<@&268886789983436800>

[sage jacinth]

spamming in a math server, very productive

[night geyser]

thanks.

[wicked plover]

Could somebidy please help!!

I'm not sure how to input this in a formula

<@&286206848099549185>

[vapid oak]

alright so do you know the compound interest formula?

[wicked plover]

yes

[vapid oak]

so write it out using all of the information the question gives, and use P instead of the principal amount

and then solve for P

[wicked plover]

so si it

[ocean seal]

Omfish

[wicked plover]

S look

I forgot

[vapid oak]

do you have the formula anywhere in your notes, or maybe look it up online

[wicked plover]

how do i get two?

I got the formula

But how do i get two?

[vapid oak]

no i wrote the wrong thing dont worry

$10000=P(1+\frac{8}{200})^{10}$

[ocean seal]

Omfish

[vapid oak]

this is the correct formula

is there anything you dont understand?

[wicked plover]

Yea

its compounded

6 times

since its semi annualy right

[vapid oak]

no its compounded 10 times because for 5 years, it is compounded twice

[wicked plover]

Waitttttt

[wicked plover]

so is this what im supposed to have?

so its compounded two hundred times?

[vapid oak]

well yes but now is your chance to ask me some questions

no i rewrote the number $\frac{0.08}{2} as \frac{8}{200}$

[ocean seal]

Omfish

[wicked plover]

Ohhhh

[vapid oak]

because we are compounding at 8% twice a year, so to make the fraction easier to deal with i multipled both sides by 100

[wicked plover]

Ohh okok

so

would it look like this?

[vapid oak]

wait no almost

swap around the A and the 10000

because 10000 is the desired amount, and we are trying to solve for the principle amount

[wicked plover]

Ohhhh okok

i get it

thank you so much

[vapid oak]

my pleasure

[wicked plover]

so is

196000

the answer?

[vapid oak]

maybe I havent checked

[wicked plover]

Please do

[vapid oak]

that isnt what i just got

notice that your answer is bigger than 10000, theres no way you could compound and lose money to return to 10000

[wicked plover]

Oh

what is the answer?

maybe im doing something wrong?

oh

is it

[wicked plover]

19.6?

[vapid oak]

thats just a number im not sure what you want me to do with that response

[wicked plover]

uhh

[wicked plover]

does this equal

to 19.6

[vapid oak]

no

[wicked plover]

?

[vapid oak]

it equals 4563.8

[wicked plover]

how??

[vapid oak]

ok so does this make sense to you:

$10000=P(1+\frac{0.08}{2})^{20}$

[ocean seal]

Omfish

[vapid oak]

i would then divide by everything on the RHS except P

$\frac{10000}{(1+\frac{0.08}{2})^{20}}=P$

[ocean seal]

Omfish

[vapid oak]

and then chuck it into the calculator

[wicked plover]

Oh okok

Oh ok it worked

and thats how I get my answer

[vapid oak]

yep

if you are solving for P

if youre solving for A you would do the process to solve for A

[wicked plover]

What am i solving for!?!?

[vapid oak]

well in this problem you are solving for P

[wicked plover]

OH you scared me lol

damn

[vapid oak]

but im just saying that in a problem where you arent solving for p, the process will be different

like if you want to solve for T, which will never happen tho

[wicked plover]

Ohhh okok

I get it thank you so much

[vapid oak]

yay

[fair mesa]

you guys are done right? can I ask

[vapid oak]

yep

[fair mesa]

I'm struggling to find the CNF form of this expression

(¬a ^ b ^ ¬e ^ d ^ ¬c) v (a ^ ¬b ^ e ^ ¬d ^ ¬c)

Got to this point then just dunno how to proceed from then

=¬(¬(¬a ^ b ^ ¬e ^ d ^ ¬c) ^ ¬(a ^ ¬b ^ e ^ ¬d ^ ¬c)) (De Morgen’s law)
=¬((a v ¬b v e v ¬d v c) ^ (¬a v b v ¬e v d v c)) (De Morgen’s law)

[vapid oak]

either i dont know of the kind of problem youre doing or i dont understand this format

yep i dont know of this

[fair mesa]

It's boolean expression

[vapid oak]

sorry should have just ingored it then

[fair mesa]

np ill just wait for someone else

dont worry about it

[ocean seal]

Minh Baka

[manic glade]

assuming the logic here is correct, how does the phrasing look like? is it understandable? too verbose? too informal?

[alpine hound]

total 9-digit numbers whose digit sum is 4 ?

[timid zenith]

Consider a set of all polynomials with real coefficients, I wanna check if it is a field or not. I can see it satisfies all the axioms of a field except for the multiplicative inverse. For that, after multiplying a polynomial by it's multiplicative inverse, are we supposed to get the product equal to 1 or another polynomial with all coefficients equal to 1?

[alpine sable]

Can someone help me

[stuck tangle]

how did this multiplication happened?

[halcyon geode]

Seems like a mistake to me

[austere bridge]

yeah that's for sure a imstake

[primal dew]

is 1+3i odd or even?

[austere bridge]

that's not a valid question to ask for complex numbers

it's like asking if 1/2 is odd or even

[primal dew]

So i tried googling that and found:

𝑘 is odd if and only if (−1)^𝑘 = −1.
𝑘 is even if and only if (−1)^𝑘 = 1.

dont know how true that is

(i had the wrong quote)

[austere bridge]

you can define it however you'd like, but there's not much sense asking it without any context

[primal dew]

no you can't

[alpine sable]

Why not?

[primal dew]

because i could define 546789 as even

but thats not true

[austere bridge]

this is getting off topic

what's the original context of asking about 1 + 3i?

[velvet condor]

Let $(a+1)(b+1)(c+1)=69, (a+2)(b+2)(c+2)=169, (a+3)(b+3)(c+3)=269,$ calculate (a+4)(b+4)(c+4)

[ocean seal]

Minh Baka

[gray isle]

use \\ to make a new line

[vale wigeon]

depends

if you talk about something known as the Gaussian integers - which is the set of complex numbers whose real and imaginary parts are both integers - there actually is a way to talk about evenness and oddness in that context which still makes sense!

there are a couple different ways to characterize it, but in essence, to find whether a Gaussian integer is even or odd, add its real & imaginary parts and take the parity of that.

under this rule, 1+3i will be even.

a consequence of this is that, while in the integers all even numbers are multiples of 2 (and vice versa), in the Gaussian integers all even numbers are multiples of 1+i instead. (and 2 = (1-i)*(1+i) )

[willow wadi]

<@&286206848099549185>

[alpine sable]

@lime gate do u know differentiation and kinematics

[lime gate]

Dont ping me

Disrespectful 🤧

[alpine sable]

[lime gate]

I dont know it

[alpine sable]

Me searching for indian guy jo hindi me smjha de

[lime gate]

Lol

[craggy dirge]

hey i have a quick conceptual question

does order of integration matter for triple integration?

for example

i switch the (0,2pi) and (-1,1) and also the dr and dx

[alpine sable]

yes you can switch the order

in fact you have too sometimes

[noble sinew]

if the integral gives a finite answer when integrand is replaced to abs value of the integrand you can swap

[craggy dirge]

in this case i can right?

[noble sinew]

yes assuming P_B is just some constant

[craggy dirge]

aight thanks

[alpine sable]

[high palm]

need help with question 6 b

i'm a bit confused

[vale wigeon]

,rcw

[wild marten]

$P_n = \frac{3n^2 - n}{2}$ and $Q_n = n^2$ and $T_{n-1} = \frac{n(n-1)}{2}$. Now sub these values in your question and you will get the answer

[ocean seal]

Schrödinger's Smile

[alpine sable]

how am i supposed to justify?

[alpine sable]

$circle location = 2\int_{-3}^{3}\sqrt{9-x^2}$

[ocean seal]

AAAAAAAAAAAAAAA

[alpine sable]

whatt

how

https://tenor.com/view/mind-blown-amazed-explosion-space-omg-gif-10279314

[vale wigeon]

any progress so far?

[keen salmon]

nvm I found the answer

[vale wigeon]

k

[stark trail]

k

[paper oar]

k

[alpine sable]

$a = arcsin(\frac{sin(I)}{n}) - I$

[ocean seal]

DavidNickisson

[alpine sable]

I have been struggling to solve for 'I', been beating my head against the wall for the past hour

Any help would be greatly appreciated

[vapid oak]

do you want to solve for I in terms of a and n?

[alpine sable]

Yes

[vale wigeon]

this strikes me as hard if not impossible to get in closed form

where did this equation come from?

[vapid oak]

i would agree

upon graphing it, it looks like the equation is independant of a

[alpine sable]

Formula is derived from Snell's law for a very specific use case

[vale wigeon]

is there any reason why you need an exact solution for this?

[alpine sable]

That is the problem there...

[vapid oak]

would theta_2 not just be 42°?

[alpine sable]

Unfortunately not that simple

[vapid oak]

nvm i interpreted the diagram incorrectly

[vale wigeon]

so $n_1$ and $n_2$ are the refractive indices of two different materials?

[ocean seal]

Ann

[alpine sable]

Yeah, I didn't do the best job of making it clear

[alpine sable]

Correct

[vale wigeon]

does the light ray enter the n_2 material head-on?

as in, perpendicular to the surface, meaning the angle of incidence is zero?

this diagram isn't very clear

[noble sinew]

Replace 4 with n and 3 with a here. 17 comes from 4^2+1, so n^2+1 and 8 from 4 * 2, so n * 2

[vale wigeon]

lmao this is brutal

[alpine sable]

Enters at angle theta2 to the surface

[alpine sable]

Woah

[vale wigeon]

honestly i'm really struggling to make sense of your diagram

did you copy it from somewhere?

[alpine sable]

My head 😂

[vale wigeon]

yikes

okay, where did this whole setup come from

[alpine sable]

Angles of plano-convex lens and trying to figure out what angle it needs to be at the edge to refract out at 90 degrees from the normal of the flat surface

That's where it came from 😂

[vapid oak]

if Snell's Law is $n_1\cdot\theta_1=n_2\cdot\theta_2$ can I ask what's the differing factor in your diagram?

[ocean seal]

Omfish

[vale wigeon]

the law is n1 sin(θ1) = n2 sin(θ2) is it not?

[alpine sable]

Yup

[vale wigeon]

this made almost no sense

sorry but you'll have to produce a better diagrm

diagram*

[alpine sable]

That's the best I can give

I just need to figure out theta_2

[red phoenix]

This is all the information apart from n2, theta 1 and n1?

[alpine sable]

Yup

Light ray is parallel to the top normal

[ornate peak]

how do i find a differentiable function? i got the value of f(256) = 10

[fair crater]

They want f' and not f I think

If you mean how to find f', check chain rule

[ornate peak]

oh k

ty

[fallow jasper]

Could someone check for me if this is correct?

[tidal solar]

can someone pls tell me what is
2 + 2?

[vale wigeon]

is this serious or are you trolling?

[vague coral]

hes obviously trolling

[vale wigeon]

maybe i can get him to admit it outright

[fallow jasper]

$2+2=(2+1)+1=$

$\succ(2)+1=$

$\succ(\succ(2))=$

$\succ(3)=4$

[ocean seal]

Blackdeath39

[crisp grove]

nice

[jaunty lotus]

excuse me,how can i get second formula??

[vale wigeon]

chain rule

[jaunty lotus]

I see , thankyou!!

[tidal solar]

what?

[fallow jasper]

It's 4

[tidal solar]

yea that's more like an answer

thanx for telling me what 2 + 2 equals

:)

[fallow jasper]

I gave you a simple proof in case you were going to doubt that

[stable grail]

a (2,3) - 3 b (6,7) C (- 8,5) find all sides