help-0

[jagged imp]

arcsin is only the inverse for part of the sine function

so taking arcsin of both sides only gives you a little bit of what you want

cuz there are infinitely many values of x that might give sinx some value

but arcsin as a function can only output one of them

like if i asked you to solve sinx=1/2

and you told me x=arcsin(1/2)

that would be a solution for sure

but x=arcsiun(1/2)+2pi would also be a solution

and arcsin(1/2)+4pi and so on

[smoky barn]

can someone help my friend find the error in this

[alpine sable]

how can i create a graph out of this

y= 2x + 3

3x= y- 2

[rigid smelt]

you have to make sure that the square root is also not negative, or so in another way of saying 2-x>=0

[rigid smelt]

this is a linear equation, so plug in two number and then draw a line connecting those points

and next time choose a free channel

[clever tapir]

this is without graphing so i need help

[outer elm]

you solve it once positive and once negative

[ionic jewel]

one negative and one positive

[clever tapir]

Like set the right side positive and negative

[outer elm]

1. 3x-6 = 4x
2. 3x-6 = -4x

[clever tapir]

alright thanks

[alpine sable]

someone pls explain wth is this bc i've forgotten it

[hidden horizon]

hmm

[jagged imp]

what the exclamation mark means?

or the binomial coefficient?

[hidden horizon]

Bro it means factorial

[jagged imp]

.... i am aware of that

i was asking them what they wanted explained

[alpine sable]

im dying y'all are like 🤓 and im like 🤪

[hidden horizon]

Do u know that n! = n x (n-1)!

[alpine sable]

...

[hidden horizon]

example 3! = 3 x 2!

both will yield answer 6

[alpine sable]

what does ! all about

bc idk

[hidden horizon]

oh

[alpine sable]

no

[hidden horizon]

oh damn

wait then

@alpine sable https://www.youtube.com/watch?v=pxh__ugRKz8 watch this

[alpine sable]

omfg ok thx gotta go and prepare my grave for my brain

i hate this i gave up

[clever tapir]

I thought in varient points were at f(x) = +- 1
why am I only given one option

[hidden horizon]

BRUH

[upper kayak]

@alpine sable factorial of n just means all numbers from 1 to n multiplied

3! (pronounced three factorial) means 3 x 2 x 1

all numbers from 1 to 3, multiplied

5! = 5 x 4 x 3 x 2 x 1

[alpine sable]

bro....

like

[upper kayak]

?

[alpine sable]

um

[upper kayak]

what?

[alpine sable]

i dont even know wth is n all about

[upper kayak]

n can be any number

[alpine sable]

oh

[upper kayak]

pick any number and call it n

factorial of 🍎 where 🍎 is any number, just means all whole numbers from 1 upto 🍎 , multiplied

[alpine sable]

so what value mean here like i dont get it and how n get included here tho

[upper kayak]

factorial of 7 means all whole numbers from 1 upto 7, multiplied

which is just 1 x 2 x 3 x 4 x 5 x 6 x 7

so it's 11 factorial

divided by 5 factorial times 3 factorial

so what is 11 factorial

[floral karma]

can anyone recommend any videos or advice on how to do quadratic equations

[upper kayak]

https://www.khanacademy.org/math/algebra/x2f8bb11595b61c86:quadratic-functions-equations

[floral karma]

thanks

[upper kayak]

👍

@alpine sable do you understand now

[alpine sable]

absolutely not

[upper kayak]

ok look

3! is just another way of writing 3 x 2 x 1

[alpine sable]

im not like u i hate math i gave up

[upper kayak]

that's the way it's defined

that's a stupid thing to do

it's a simple idea

when i say 4!

i mean 4 x 3 x 2 x 1

when i say 6!

i mean 6 x 5 x 4 x 3 x 2 x 1

do you see the pattern?

it's really simple

so i can write 11! as 11 x 10 x 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1

[alpine sable]

so like 30 x 12 x 2

[upper kayak]

no

pick any number

keep it small

[alpine sable]

6

[upper kayak]

ok

the factorial of 6, which is written as 6!, is the number you get when you multiply all the numbers from 1 to 6 together

what are the numbers from 1 to 6

[alpine sable]

6 5 4 3 2 1

[upper kayak]

yeah

multiply them together

what do u get

[alpine sable]

30 x 12 x 2?

[upper kayak]

oh yeah

taht's another way of writing that

same thing

you got it

but in your case it's simpler to leave 11! it as 11 x 10 .... x 2 x 1

let's replace 11! with that

$\frac{11 \times 10 \times 9 \times 8 \times 7 \times 6 \times 5 \times 4 \times 3 \times 2 \times 1}{5!3!}$

[ocean seal]

gang

[upper kayak]

now what is 5!

oh no

@alpine sable

[alpine sable]

um

[floral karma]

120

[upper kayak]

the factorial of a number is all the numbers from 1 to that number, multiplied

[alpine sable]

oh

[upper kayak]

5 x 4 x 3 x 2 x 1

[floral karma]

= 120

[upper kayak]

which is 120, but i'm going to leave it like that

[alpine sable]

oh now i get it now im genius even for once

[upper kayak]

$\frac{11 \times 10 \times 9 \times 8 \times 7 \times 6 \times 5 \times 4 \times 3 \times 2 \times 1}{(5 \times 4 \times 3 \times 2 \times 1) \times 3!}$

[ocean seal]

gang

[upper kayak]

now rewrite 3!

$\frac{11 \times 10 \times 9 \times 8 \times 7 \times 6 \times 5 \times 4 \times 3 \times 2 \times 1}{(5 \times 4 \times 3 \times 2 \times 1) \times (3 \times 2 \times 1)}$

[ocean seal]

gang

[upper kayak]

now you can cancel

drop the parentheses

[scenic crystal]

why we take least common multiple while comparing and adding two unlike denominator fractions?

[alpine sable]

okay ty @upper kayak

[upper kayak]

👍

https://www.khanacademy.org/math/cc-fifth-grade-math/imp-fractions-3/imp-adding-and-subtracting-fractions-with-unlike-denominators/v/adding-fractions-with-unlike-denominators-introduction

@scenic crystal

[alpine sable]

wait one more

how about if the numbers are like this

like 2!3!4!

[upper kayak]

it's just 2 factorial multiplied by 3 factorial multiplied by 4 factorial

calculate tehm

you don't have to keep them expanded here because there's no canceling

just calculate the value directly

the first one is 2 x 1

which is just two

rewrite the thing as

$2 \times 3!4!$

[ocean seal]

gang

[upper kayak]

maybe verbal explanations arent helping you

i'll just list the first few factorials

try to catch on the pattern

[alpine sable]

did i get it right?

[upper kayak]

1! = 1
2! = 1 x 2
3! = 1 x 2 x 3
4! = 1 x 2 x 3 x 4
5! = 1 x 2 x 3 x 4 x 5
6! = 1 x 2 x 3 x 4 x 5 x 6

hopefully you can see how that goes

[alpine sable]

so im correct on this one?

[upper kayak]

no

[alpine sable]

...

[upper kayak]

2! = 1 x 2 = 2
3! = 1 x 2 x 3 = 6
4! = 1 x 2 x 3 x 4 = 24

2!3!4! = 2 x 6 x 24

= 288

[alpine sable]

im so confused

[upper kayak]

what are you confused about

[alpine sable]

isn't it like u gonna times the 2 numbers

and next and next

till the final or summ

[upper kayak]

2!3!4! means 2 factorial times 3 factorial times 4 factorial

2 factorial is 2 x 1 = 2

3 factorial is 3 x 2 x 1 = 6

4 factorial is 4 x 3 x 2 x 1 = 24

[alpine sable]

no bc i was looking the value of 12!

or whatever it is

[upper kayak]

where did you get 12! from

[upper kayak]

oh

that's a different problem

[alpine sable]

.

[upper kayak]

well yeah your answer is correct

[alpine sable]

oh thank god my gosh u gave me a heart attack

[upper kayak]

lol

[alpine sable]

so when this kind of looking form or whatever that line is the way i answer the 12! is now different when it comes to this one?

[upper kayak]

it's not different

[alpine sable]

oh

[upper kayak]

you just replace 11! by 11 x 10 x 9 x 8.... x 2 x 1

because they're the same thing

[alpine sable]

n! = 1 x 2 x 3 ...... x n

what's the dot for

[upper kayak]

i didn't write out the whole thing

[alpine sable]

say what there are more

wtf

[upper kayak]

no

11! is 11 x 10 x 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1

i don't feel like typing that out everytime

so i put dots there

[alpine sable]

ahh

ok wait let me try to solve this one

[upper kayak]

ok

[alpine sable]

did i get it right im just bruh idk @upper kayak

[upper kayak]

almost

it's 120 x 6

not 120 / 6

it's 5! multiplied by 3!

[alpine sable]

oh

now? im right? right?

is the line is /?

[upper kayak]

yeah

[alpine sable]

relieved

[upper kayak]

👍

[alpine sable]

11 x 10 x 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1 / 5 x 4 x 3 x 2 x 1 * 3 x 2 x 1

= 11 x 10 x 9 x 8 x 7

Cancel no dude

1 to 5 will be cancelled

[verbal tundra]

Won't you still have a 3! In the bottom part?

[upper kayak]

yeah

[alpine sable]

He did $3! ^ 2$

[ocean seal]

sshaagar

[verbal tundra]

Ah, I thought that since he removed both the 3! and the square power, he had removed it entirely

[alpine sable]

did i get it right?

[upper kayak]

no

[alpine sable]

grrrr

[upper kayak]

4! is 4 x 3 x 2 x 1 = 24

that is correct

but 5! is 5 x 4 x 3 x 2 x 1

= 120

[alpine sable]

now?

[upper kayak]

you did the multiplication on 5! wrong

5th line is incorrect

[alpine sable]

ok wait

now?

[upper kayak]

20 x 6 is not 160

[alpine sable]

oh wait my eyes are wrong lol it's 120

[upper kayak]

yeah

5! = 120

[alpine sable]

im just so confused lookin' on these numbers

[upper kayak]

haha

you're in for a ride then

what grade are u in

[alpine sable]

now what does it mean

[alpine sable]

4th year high school

[upper kayak]

no idea how that works

i mean your school system

[alpine sable]

junior high

[upper kayak]

this is a combinatorics problem, the answer is 6!

i can't explain why, don't ask

[alpine sable]

ok lol

👍 6!

thx

is there a shortcut to do this or summ?

[upper kayak]

calculate factorials?

not really

not that i'm aware of, at least

[alpine sable]

forget it i'll just 1 by 1 lol

[upper kayak]

for factorials greater than 6! i'd just get a calculator

[alpine sable]

what grade are u in?

[upper kayak]

and when they're in fractions, just expand them and cancel

irrelevant

[alpine sable]

ok

[upper kayak]

oh yeah back to your grade

?remindme 4 years

[alpine sable]

...

[upper kayak]

!remindme 4 years

[alpine sable]

4 years what.....

[upper kayak]

i want to see your reaction in math class 4 years later

[alpine sable]

wait no...

i mean

it's hard to lose u after what u did

ty for helping me

[upper kayak]

👍

[alpine sable]

why am i feeling sad lol

[sullen echo]

Hello! I'm looking for some help with my calculus hw

I have no idea what to do with this

Given options are:
15
45
75
225

[summer quiver]

Hard question. The only thing I can think of so far is that $\int_0^1 f(x)dx = 0$ so $\int_0^{10} f(x) dx = \int_1^{10} f(x) dx$

[ocean seal]

iateawalrus

[summer quiver]

I have no idea tho

[frozen hare]

Integrating both sides, we get $$\int_{-a}^{a+1} f(x) + \int_{-a}^{a+1} f(-x) = -(a+1)^3/9 - (-(-a)^2/9)$$

[ocean seal]

findingsouth

[sullen echo]

The first term of left side is 0, and using integration by substitution the equation becomes $$\int\limits_{-a-1}^{a}{f(x)dx}=\frac{-3a^2-3a-1}{9}$$

[ocean seal]

- Neo - (Inactive until July)

[sullen echo]

I wonder if this could be useful 🤔

[strong furnace]

have you guys solved it yet?

[sullen echo]

Nope

[strong furnace]

I have an idea

that should work

consider the function as addition of two functions

an odd function and even function

first condition is even part *2

and 2nd condition relates the integral of odd part and even part

and we have the even part

does that make sense?

[sullen echo]

I get this one

[sullen echo]

But not this

[summer quiver]

If we create a variable b = a + 1/2

Then I think it becomes truly even

Or rather

Odd

Wait maybe not +1/2

[frozen hare]

It's a - 1/2

[strong furnace]

if you write f(x)=O(x)+E(x) for 2nd condition then split the integral using sum rule take integral of O(x) to other side then split the integral at x=a for O(x) the remaining part would be 0 by some integral rule or basic symmetry so now we have integral for a to a+1 for any O(x) which can be evaluated via the integral of E(x) which we know and we have to get the sum of all these integrals a,a+1 so that we have 0,10

[summer quiver]

-1/2 yeah

[frozen hare]

I've tried that but there's no function in the form b(x - 1/2)^3

The x^2 term matches but the constant term doesn't

[strong furnace]

ping me if you don't understand this or you think this does not work

[gilded smelt]

Hey guys, can anyone please assist me with this question

[summer quiver]

Try setting the limit = to L, then taking the ln of both sides. Remember that ln(ab) = ln(a) + ln(b)

[gilded smelt]

What you mean =L ?

[summer quiver]

Set $\lim_{x \to 0^+} \left[ xe^{\frac{1}{\sqrt{x}}} \right] = L$

[frozen hare]

Using the symmetry, the key is to write f(x) = p(x - 1/2)^3 + q(x - 1/2) which fulfils the second integral property

[ocean seal]

iateawalrus

[frozen hare]

Comparing coefficients, c = (-1/4)b and b = 1/9

And now you can integrate from 0 to 10

[gilded smelt]

Ive never seen that before but go on

[summer quiver]

So you want to find L

Take the natural log of both sides

[frozen hare]

And the answer is 225

[summer quiver]

$\ln \left( \lim_{x \to 0^+} \left[ xe^{\frac{1}{\sqrt{x}}} \right] \right) = \ln(L)$

[ocean seal]

iateawalrus

[summer quiver]

$\Rightarrow \lim_{x \to 0^+} \left[\ln (xe^{\frac{1}{\sqrt{x}}}) \right] = \ln(L)$

[ocean seal]

iateawalrus

[summer quiver]

Then use log properties

[frozen hare]

I mean q = (-1/4)p and p = 1/9 - that's it

[sullen echo]

I did it!

Thank you for helping me out so much!

[strong furnace]

well done

findingsouth has a solution as well

based on symmetry and polynomial function

[frozen hare]

ah the csat

fighting fighting and keep practicing

[sullen echo]

It's quite different from csat
This test is for those who lived in overseas for at least 3 years

And each college makes its own tests

[frozen hare]

oh ok

[sullen echo]

Anyways, thanks for encouraging me

[frozen hare]

its korean so i thought it was the csat, but anyways

[alpine sable]

i need help please im stuck on a question about trigometric functions

[strong furnace]

[alpine sable]

its due in like an hour ohelp would be amazing

[alpine sable]

oh ok hol up ill just send it

,rotate

[alpine sable]

2x + pi/3 = pi/6

$2 \times x + \frac{\pi}{3} = \frac {\pi}{6}$

[ocean seal]

sshaagar

[alpine sable]

i dojnt really understand that

can you explain?

[alpine sable]

i dont understand that

thats ie like

way out of my league

[alpine sable]

yo

Simply solve this

$2 \times x + \frac{\pi}{3} = \frac {\pi}{6}$

[ocean seal]

sshaagar

[alpine sable]

can you show the steps please? @alpine sable

[timid wind]

can someone explain matrices to me

[civic crypt]

what about them?

[alpine sable]

$n \pi - \frac{\pi}{12$

[ocean seal]

PokiSquad Financial Advisor

$n \pi - \frac{\pi}{12$
```Compilation error:```! File ended while scanning use of \frac .
<inserted text> 
                \par 
<*> 706863150682603532.tex
                          
I suspect you have forgotten a `}', causing me
to read past where you wanted me to stop.
I'll try to recover; but if the error is serious,
you'd better type `E' or `X' now and fix your file.```

[scenic flame]

hi

helpp, find the derivative

[proud burrow]

@scenic flame what's the question

[scenic flame]

am finding the second derivative

[scenic flame]

i think i've done something wrong in the middle, dunno but i don't know how to move on

[proud burrow]

Is it f''(y)

[summer quiver]

The second derivative of what?

What is the original function

[scenic flame]

yes

[proud burrow]

So you want to find 3rd derivative

[proud burrow]

So which derivative you have to find 1st Or 2nd

[scenic flame]

yes but I can't move on since I haven't done the 2nd yet

[proud burrow]

So you have to find 3rd derivative

[scenic flame]

this is the second

[summer quiver]

First, simplify the second term in the expression. Turn it into $2x^{-\frac{1}{4}}$

[ocean seal]

iateawalrus

[summer quiver]

Makes it easier imo

[proud burrow]

So first derivative will be 6x^-1/2-1/2x-5/4

[summer quiver]

Asrar do you know latex?

[proud burrow]

Then second will be -3x^-3/2 -5/8x^-9/8

No what's latex

[summer quiver]

This is $6x^{-\frac{1}{2}} - \frac{1}{2}x^{-\frac{5}{4}}$

[ocean seal]

iateawalrus

[summer quiver]

The formatting code I'm writing

[proud burrow]

Hey how this bot writes the equation

[summer quiver]

Second derivative is $-3x^{-\frac{3}{2}} + \frac{5}{8}x^{-\frac{9}{4}}$

[ocean seal]

iateawalrus

[proud burrow]

Yeah that's the same I told

[summer quiver]

No, it isn't

[summer quiver]

You wrote -5/8, it's +5/8
Also you wrote -9/8 in the exponent of the second term, and it's -9/4

[scenic flame]

is this the final answer?

care to share the solution please?

[summer quiver]

What is the question asking

Third derivative?

[scenic flame]

to find the derivative of this

hello?

[vagrant cobalt]

what do you need help with

,w second derivative 9x^(2/3)+2x^(-1/4)

[ocean seal]

Results provided by WolframAlpha

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

Requested by usernamephobic#0544

[scenic flame]

solution please

[vagrant cobalt]

,w first derivative 9x^(2/3)+2x^(-1/4)

[ocean seal]

Results provided by WolframAlpha

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

Requested by usernamephobic#0544

[vagrant cobalt]

it's power rule only

both times

, sorry, I can't type the whole solution

[alpine sable]

does anybody know how to prove by mathematical induction that 2304 divides 7^2n - 48n - 1 for any n >= 2

?

[hollow owl]

hi How I calc a?

[alpine sable]

Have you learnt arc measures?

cause I can only think of arc measures when It comes to this

afk

[hollow owl]

yes

[alpine sable]

actually

wait

a will be half of angle O

so if you can find angle O

you can find A

just flew right over my head

[hollow owl]

but the arnt on the same arc

they

[lilac dragon]

find β then γ then you can find α

[gray isle]

you could consider the central reflex arc

[hollow owl]

b is 135

gama is 67.5

[lilac dragon]

yep then use that α+γ=180°, cyclic quadrilateral thm

[hollow owl]

112.5?

right answer?

[lilac dragon]

yeah I believe so

curious as to @gray isle 's method now though

[gray isle]

determine the measure of the red arc

alpha will be half of that by inscribed angle theorem

[lilac dragon]

prove for n=2, then assume it's true for n=k and use that to prove that it would then be true for n=k+1

[lilac dragon]

ah neat, I wouldn't have thought of that

[alpine sable]

yeah, I have no idea how to do that, lmao. is it too hard?

[lilac dragon]

plug in n=2 and the expression is equal to 2304 so this is true. then assume that
7^(2k) – 48k – 1
is divisible by 2304. then plug in n=k+1 and manipulate

one sec I'm a little busy I'll do it in a min if you're still stuck

[alpine sable]

thanks, I'll try that in the meanwhile

[celest jungle]

How do I graph a parable in r^3?

Given the roots (0,0,0) (x,y,z) and its vertex

Im quite confident that the equation involves doing it in r^2 and then integrating that plane into the space

so its the latter that concerns me

This plane is always perpendicular to the plane xy

[lilac dragon]

alright back now, I'll write up how I'd do it but I'm doing this on the fly so idk how long it'll take

[alpine sable]

it's all right, it's not like i need it immediately, take ur time. it'd help me a lot. 🙂

[lilac dragon]

assume divisible by 2304 when n=k. then take n=k+1:
7^(2k+2) – 48(k+1) – 1
= 49×7^(2k) – 48k – 48 – 1
= 48[7^(2k) – 1] + 7^(2k) – 48k – 1.
since 7^(2k) – 48k – 1 is divisible by 2304 by hypothesis we can simply ignore it here. also, notice 2304 is just 48^2 so we are reduced to showing that
7^(2k) – 1
is divisible by 48. can prove this by induction (within the induction lol). true for k=1, just equals 48. assume true for k=j. then for k=j+1:
7^(2j+2) – 1
= 49×7^(2j) – 1
this is divisible by 48 if and only if it is still divisible by 48 when we add 48, which yields:
49×7^(2j) – 49
= 49×(7^(2j) – 1)
which is 49×(a multiple of 48) so is divisible by 48. in turn then, this completes the proof

that was a pretty gnarly induction lmao. perhaps there's a less brute-ish way to solve it, but if there is, I didn't spot the trick.

[alpine sable]

thanks a lot, adam. 🙂 i'll read it carefully and see if i understand it correctly

[worldly whale]

Gush

Guys

If y= x-2 and x=2 then the value of y will be?

[lilac dragon]

no worries, and I'm glad you're planning on digesting it. perhaps try replicating it without looking at it if you've got time to kill to cement your understanding

[lilac dragon]

y will be 0

[worldly whale]

Oh thx

[lilac dragon]

np

[worldly whale]

I'm confused bout this

And have a math exam tmrw

[lilac dragon]

where exactly are you struggling?

at which step

[worldly whale]

IX

I'm bad at ratios

[lilac dragon]

I mean, where in IX

[worldly whale]

Simplifying and ratio

[lilac dragon]

the ratio is just 360g:120g, both of which are divisible by 120

360=120×3 so the ratio can be simplified to 3:1

that's for part b

[worldly whale]

Thx

[lilac dragon]

try to apply the same reasoning to get a

[worldly whale]

Btw why x 3?

[lilac dragon]

360=120×3
120=120×1

I'm not really sure what you're asking about here

[worldly whale]

Oh ok

Thx

[muted raft]

[7^{2(k+1)}-48(k+1)-1 = 7^2 \cdot 7^{2k}-48k-49 = 7^2(7^{2n}-48n-1) +48^2k]

[ocean seal]

zslya

[muted raft]

@lilac dragon @alpine sable

so no need for 2 induction

[lilac dragon]

ah that's the trick I missed then heh. well spotted

[upper kayak]

open?

i feel stupid for getting this one wrong

i reasoned that if y is the vertical side of the rectangle

2y + x + perimeter of the semicircle = 30

perimeter of the semicircle was $\frac{\pi x}{2}$

[ocean seal]

gang

[upper kayak]

so 2y + x + pix/2 = 30

solving for y gives $y = \frac{60-2x-\pi x}{4}$

[ocean seal]

gang

[upper kayak]

so the area of the semicircle is $\pi (\frac{x}{2})^2$

[ocean seal]

gang

[upper kayak]

adding that with xy should give the total area

[alpine sable]

did i make any braindead mistakes here

[upper kayak]

subbing y i get $A = \frac{2x(60 - 2x - \pi x) + \pi x^2}{8}$

[ocean seal]

gang

[upper kayak]

channel occupied

[upper kayak]

that's my answer

and it's wrong

why?

[barren torrent]

guys so i have an algebra 1 final next week and i dont rlly have a study guide
anyone have one?

[alpine sable]

khanacademy

[summer quiver]

LOL

[upper kayak]

this channel is occupied

[alpine sable]

Kk mb

[upper kayak]

delete and repost in some other channel

thanks

<@&286206848099549185>

[steady fox]

im having trouble putting this word problem into a mathematical model : How many liters of an 18% alcohol solution must be added to a 10% alcohol solution to get 20 L of a 15% alcohol solution? --can someone please explain?

[high idol]

What are differentials?

[upper kayak]

channel. occupied.

[summer quiver]

Occupied with what?

[upper kayak]

Me

[grave saddle]

f(0) = 0
f(n) = n - f(n-1)
told to find value of f(5)
I got f(5) = 3

Then im told to make a formula where n is greater or equal 0 without the use of f in the expression

and argue for it

im getting confused by the last part. what exactly do they mean? cant I just do f(n) = n? or f(n) = n^2 if they mean positives only?

[summer quiver]

Please send a picture of the question

[grave saddle]

its in danish and its text

[grand oasis]

then write english in microsoft word and capture it

or you can use latex

[wet fulcrum]

channel free?

[grand oasis]

nope

[wet fulcrum]

ok

[grave saddle]

alright sec

This pretty much it

<@&286206848099549185>

[marble zodiac]

helpers help moment

[ionic jewel]

ceil(n/2)

should continue going f(5) = 3 then 3 then 4 then 4 then 5 then 5 etc

you could show this by induction

[grave saddle]

oh

i havent been introduced to the ceilfunction yet but I see it

thats pretty cool. thanks @ionic jewel

[ionic jewel]

ceil is rounding up

short for ceiling

[copper plank]

hello , i was studying for my upcoming exam and there is a question i dont understand about linear graphs

so the question is :

Find the equation of a line -- Perpendicular to y =2x + 4 and passing through (3,7)

Thank you :>

[grave saddle]

yeah just googled it

[ionic jewel]

actually it's always something x.5 so normal rounding works too

[ionic jewel]

find the slope, take the negative reciprocal to get the slope for the new line, make it go through (3,7)

[alpine sable]

Hey does resistance affecf voltage at all?

[ionic jewel]

V=IR

So yes

[alpine sable]

So if resistance goes up voltage goes down?

[ionic jewel]

assuming current stays the same yes

[alpine sable]

well this is confusing me

because

if there is resistance

im assuming current is not the same

and since voltage is proportional to current

[alpine sable]

Voltage would go down

i think

this is confusing

[ionic jewel]

I believe your answer is right, I don't see why current would change

but also I'm not a physics guy, try #old-network physics server

[alpine sable]

also what about this, because i think the relationship is linear

because

assuming

resistivity is constant for a material

and so is L

and p=(RA)/L

then that pretty much means R=A

[late bridge]

a linear relationship between 2 variables means that one is a constant multiple of the other, and as you said, R=p(L/A), that means R is proportional to A^-1

given L and p constant

[alpine sable]

So then that would mean its R and 1/A right?

[patent hawk]

can someone please explain to me how to go from the first integral to the second one?

Please someone help me

[noble sinew]

a lot of rewriting but multiply num and denom of 1/(cos(u)+2) by sec^2(u/2)

should give you 2* sec(u/2)^2+cos(u)*sec(u/2)^2 in denom which you can rewrite to tan^2(u/2)+3 using some more rewriting (write out sec as 1/cos and tan as sin/cos and just simplify until you get the desired)

[patent hawk]

Thanks man I figured it out.

[alpine sable]

This describes a supervised learning model, where Y is a set of expected outputs for a set of inputs X. Y is conditional to X. We are trying to find the parameters Theta that maximize the numerator of the Bayes Rule. We try to simplify the term on the right.

My question is, how do I get from the second line to the third? I understand the rest.

[viral raptor]

if I have 4x+6y+9z=2019 how many answers can I have?

[noble sinew]

$P(\theta|X,Y)=\frac{P(Y|\theta,X)P(\theta|X)}{P(Y|X)}$

[ocean seal]

ScapeProf

[noble sinew]

is bayes theorem so idk what is happening

[alpine sable]

Bayes theorem

Yes it's Bayes Theorem, but for the step between line 1 and 2 you would see X and Y as one

$P(\theta|X,Y)=\frac{P(X,Y)*P(\theta)}{P(X,Y)}$

[ocean seal]

omen

[alpine sable]

P(X,Y) is irrelevant to finding argmax, so it is removed

the question is how do I get from line 2 to line 3

$P(X,Y|\theta)=P(Y|X,\theta)P(X|\theta)$

[ocean seal]

omen

[noble sinew]

then it is just \begin{align*}P(\theta|X,Y)&=\frac{P(Y|\theta,X)P(\theta,X)}{P(Y,X)}=\frac{P(Y|\theta,X)P(X|\theta)P(\theta)}{P(Y,X)} \ &=P(Y|\theta,X)P(X|\theta)P(\theta) \end{align*}

[ocean seal]

ScapeProf

[icy trail]

i've reached 4cos^2(x) - cos(x) -k = 0,
but im not sure how to simplify further? ive tried the quadratic formula but didnt get very far
thanks : )

[stuck plaza]

6-2x=8
-2x=8-6
-2x = 2
-2x/-2 = 2/-1 = -1

to check the answer

"Check a solution to an equation by substituting it into the left side
and the right side of the equation. Both sides must be equal."

6-2x = 8
6-2(-1)
6 -2x-1=8

6+2 = 8

so is this right?

[noble sinew]

by checking a solution they mean plug it in left side and simplify it then compare to right side

so 6-2x=6-2*(-1)=6+2=8

[stuck plaza]

yes so i removed the =8

[noble sinew]

so left hand side is 8 which is equal to rhs so the solution is correct

[stuck plaza]

ok so i was right cool i wasnt sure thank you

[noble sinew]

not what you did in above

you said 6-2x=8 (already assuming it is correct which is not the way to check it)

[stuck plaza]

i carried over the original question is all i removed it

anyway i get it now thank you

[spring harbor]

A circle goes through B(-1,0) and is at point A (1,2) tangent to the line with equation y = 2x. What is the area of this circle?

Could someone help me out? Thanks.

[timid wind]

is there a calculator for this

pls

<@&286206848099549185>

[ionic jewel]

fermats little thm

[patent hawk]

<@&286206848099549185> someone please explain

[spring harbor]

Can you guys read #rules please?

It says ping after 15 minutes the question has been posted

[ionic jewel]

tan^2 + 1 = sec^2 = 1/cos^2

then on the bottom we have

2tan cos^2 + 2

= 2sin cos + 2

half angle sub from that

and yes rea the rules

[patent hawk]

i apologize for that, i completely forgot

[patent hawk]

thanks bunny

[timid wind]

how will that help

wth is femates little thereom

nvm ill find calcaulator

[ionic jewel]

hmm

good luck with that lmao

[timid wind]

there is

modulo arithemetic calculator

[ionic jewel]

ok

[timid wind]

ok

[quartz glen]

I need help:

• How do i solve this equation using the Simplex Method or Graphical Method or Big M Method?
• How do i convert it to its duel form?
• And How do i make a Sensitivity analysis model for it?

[tired radish]

1+1?

[alpine sable]

2

[tired radish]

okok thank you man

[alpine sable]

No problem man.

[mossy basin]

Can someone help me solve this: A,B and C are sets and i have to show steps to make left side = right:

(A − B) ∩ (A − C) = A − (B ∪ C)

[manic quail]

Isn't that just de morgan's law?

[mossy basin]

I feel like it is but the question is out of 4. So i dont know if im missing something

wouldnt it also be distritive?

[worldly oriole]

If I have to find the variance of the random variable would it be like this?

https://cdn.discordapp.com/attachments/847924576423641140/848332219008548904/b3d9d151ab5264b75461163419e33430.png

[worldly wraith]

ya

assuming 6.5 is mean

uhh i'll just ping 😔
@worldly oriole yup !

[torpid delta]

If we have

$F_{n+1} = F_n - \frac{1}{n+1} \implies \ f_{n+1} = f_n + \frac{1}{(n+1)^2}$

[ocean seal]

TC159

[torpid delta]

$\lim f_n = \frac{\pi^2}{6} + f_0$

[ocean seal]

TC159

[torpid delta]

If we have $\lim \frac{d}{dn} F_n = 0 \therefore f_0 = -\frac{\pi^2}{6}$, correct?

[ocean seal]

TC159

[torpid delta]

But $f_n = f_0 + \sum_{i=1}^{n} \frac{1}{i^2} \ \therefore F_n = -n \cdot \frac{\pi^2}{6} + \int \sum_{i=1}^{n} \frac{1}{i^2} ; ; dn + c$

[ocean seal]

TC159

[torpid delta]

Is it possible to solve that integral over values? what would that integral evaluate to at n = 1 for example, would it be -1/n, with n evaluated at 1 or n, with n evaluated at 1?

[gray gorge]

Is n an integer variable?

[torpid delta]

The idea is to have a continuous function represent the summation and therefore the function itself

so I guess no

[gray gorge]

So for example here you're summing up terms indexed with integers i until an upper bound that isn't even an integer?

[torpid delta]

I mean, I used a summation because I wanted a continuous function which would represent that summation on integer values. Similar to the gamma function and the factorial

[granite lily]

How would I do 5

<@&286206848099549185>

[gray gorge]

You might be interested in this https://en.wikipedia.org/wiki/Digamma_function?wprov=sfla1

[lone heart]

From

#❓how-to-get-help

Rule 4

If your question has not been answered for a minimum of 15 minutes, you may use the Helpers tag once. Please do not try to bump your question using this ping unnecessarily. Do not abuse this ping. Do not individually ping users with the Helpers tag without their express permission.

[torpid delta]

I've seen the digamma function previously

[gray gorge]

Then I presume you meant to write the digamma function (- the euler mascheroni constant) instead of that sum?

[torpid delta]

I'm kind of a dumb dumb

[alpine sable]

I need help with trigonometry quiz. Can anyone help me with it?

[lone heart]

From

#❓how-to-get-help

Rule 1

The help channels are solely for help with math, so feel free to post your question. Asking whether you can ask a question or if anyone knows about some specific topic is unnecessary, so please try to avoid questions of that nature.

[gray gorge]

But

If it's a graded quiz

You're not allowed to ask for help on it

[torpid delta]

if it's graded isn't it a ban motive

[alpine sable]

really?

[gray gorge]

Precisely

[torpid delta]

obviously

[alpine sable]

i did most of it i just need help with 2-3

[gray gorge]

Is it graded?

[torpid delta]

If it's graded you should stop responding lmao

either way this is the wrong thing #❓how-to-get-help

[wary stream]

If it's against academic dishonesty, right? Because some quizzes allow collaboration so it's not against rules

[gray gorge]

Collaboration with anyone?

[alpine sable]

its fine if we do get help, me and my classmates have been helping eachother out for the other quizzes, but we are all struggling with this one

[gray gorge]

Haven't heard of a quiz like that before

[alpine sable]

there are a lot of quizzes like that, and not just for math

[torpid delta]

I did that too during online classes doesn't mean that just because you think it's okay that it's really okay

👁️

[alpine sable]

the teacher knows

[torpid delta]

but it's graded??

[alpine sable]

yes and they allow us to get help with everything in the class

[gray gorge]

How's that grade worth anything

Lol

[torpid delta]

^^

[alpine sable]

?

[gray gorge]

You're allowed to use any resource

[alpine sable]

its just a quiz so its not gonna be worth that much, but you need an 80% or higher to continue with the course

[gray gorge]

That sounds more like a type of project to me

[wary stream]

During the whole covid situation, rules became more relaxed and teachers allowed collaboration on stuff like quizzes

[alpine sable]

^

so do i have permission to get help?

[torpid delta]

I've had open book tests before. Though the books weren't that much of use because there was very limited time. Note these were tests to help raise grades because everyone was doing shit

[torpid delta]

this is the wrong channel

It was occupied

[alpine sable]

sorry

[torpid delta]

It's fine

lol

[gray gorge]

Sorry, no help on graded assignments of any kind

[torpid delta]

Hmmm?

[gray gorge]

Wrong reply

[torpid delta]

Ahh

[alpine sable]

but the rules say only test or exams

it doesnt specify any other graded things

[gray gorge]

In practice, the mod team have been keeping an eye out for all graded assignments

[alpine sable]

so shouldnt that be specified in the rules than?

[gray gorge]

I'll take note of it internally

Thanks for bringing it up

[gray isle]

concerns in #help-4

[torpid delta]

Anyway Digamma function was sexy, thank you for reminding me of it.
$f_{n+1} = f_n + \frac{1}{n+1} \implies \
F_{n+1} = F_n + \log(n+1) + c \implies \
F_n = F_0 + \log(\Gamma(n+1)) + c\cdot n \implies \ f_n = \frac{d}{dn} \log(\Gamma(n+1)) + c$

[alpine sable]

so you think people are using this server for just other math purposes?

[ocean seal]

TC159

[torpid delta]

👁️

[alpine sable]

not grades?

[gray gorge]

Yes?

[alpine sable]

you know how much people would be lying, i bet most of these guys are in high school lol

[torpid delta]

yeah, probably

[alpine sable]

using this to get their grades up

this is a server for people to help eachother

[wary stream]

Me and @sly mantle (sorry for the ping) discussed this like a day or two ago, and (s)he said if it's academic dishonestly, it's bannable but if the quiz states collaboration is allow, it's not academic dishonestly. Can you confirm this?

[knotty sleet]

It's ok to use it to learn

[alpine sable]

so why is it wrong for me to get help for something i am struggling on

[torpid delta]

It's mostly used for homework help

[knotty sleet]

But not to help get past exams and things of that sort

[alpine sable]

its not an exam

[gray isle]

I find no distinction between a quiz and a test

[torpid delta]

sheeeeeeeeeesh

this has turned into a huge collab

[alpine sable]

quiz is worth way less

[gray isle]

also this seems to be interesting an actual question

[torpid delta]

haven't seen something this massive since the manhattan project

[knotty sleet]

So then it won't matter if you don't do too well right

[torpid delta]

wait so it's a quiz?

[alpine sable]

yes, but it was never specified in the rules

[torpid delta]

Quizzes are obviously not allowed either

[alpine sable]

and you said graded assignments, hw is gradded

[torpid delta]

they're a type of test

[alpine sable]

graded

[knotty sleet]

It's kind of common sense

[sly mantle]

academic dishonesty is bannable

[alpine sable]

so why is it fine for hw to be allowed but not quiz

[knotty sleet]

Don't need to spell everything out explicitly😅

[gray gorge]

They're banned

[wary stream]

But if the quiz says collaboration is allowed?

[torpid delta]

Welp

[torpid delta]

you mean kicked?

[gray gorge]

No

[torpid delta]

Pretty sure that if they were banned their messages would disappear

[gray gorge]

Banned

[torpid delta]

or is it like a weird bot ban

[gray gorge]

What?

[torpid delta]

Bans used to remove your messages

[gray gorge]

You can choose not to

[torpid delta]

Wait, really?

[gray gorge]

Yes

[sly mantle]

@wary stream even so i imagine the expectation is for classmates to collab, not seek help from a whole community of helpers

[torpid delta]

Had no idea

huh, the more you learn

I find it very weird to ask for help for a quiz from people online

your classmates are always a good option to ask help for in quizzes

[gray gorge]

It is, that's why we don't have tolerance

[manic quail]

I find it very weird that you are allowed to collaborate on quizzes in any way.

[torpid delta]

Well, I don't want my friends to fail

👁️

[wary stream]

It's mainly because of the covid situation

[torpid delta]

besides, I haven't had online quizzes since I was in lockdown

so

[torpid delta]

Yeah, even with video it's very easy to be creative and cheat 👁️

Anyway this is a maths help channel.

So this is heavily off topic

[gray gorge]

Don't encourage people to perform academic dishonesty

[torpid delta]

tight

[wary stream]

This statement does raise a good question, in which we can discuss in #discussion or #math-discussion, but if you say graded assignments, what are the rules about homework? It's technically a graded assignment so people who ask for help on hw, wouldn't they technically get banned?

[gray gorge]

There's usually a distinction between graded and ungraded homework

[wary stream]

Most, if not all, hw is graded though, unless it was more of practice hw problems as prep for a quiz/exam

[ionic jewel]

Most professors I have had simply do not check homework, and just let you fail if you needed it and didn't do it.

Also have some that check for participation, which also wouldnt be a problem helping here

but yeah graded for accuracy homework is questionable, but I'm pretty sure thats the majority of what we help with anyways

[hollow peak]

Does anyone know something to graph with « letters » instead of number ? Idk if I’m clear I can show a picture in dms

[wary stream]

You can post your question here and someone would be by to assist you

[hollow peak]

Well I would like to graph this but on my computer but I have no idea how to do it since a and b are letters

[wary stream]

Graphing using what software?

[hollow peak]

I’m open to anything

i can use latex but I’ve never graphed on latex though and idk if it works with letters

[strong furnace]

Are you learning definite integrals?

I think that's just a random graph made for help in understanding

[hollow peak]

@strong furnace I have learned it last year yes

[strong furnace]

You can try to think of a function that might look like it tho

[ionic jewel]

your handwriting is neat enough to just take a picture, yeah theres some latex graphing utilities you could learn

[hollow peak]

Thank u 💓

[hollow peak]

Well this is supposed to be a proof I’m not sure my teacher would let me ‘-‘

[graceful bloom]

Hey guys

[woven scaffold]

hello how are you?

[wary stream]

Hi? Did you have a math related question to ask that you needed help on?

[graceful bloom]

Yep i had one

Im good wbu

I was studying complex no.

That topic is insane

[wary stream]

Go ahead and post the question you need help with and someone will be by to help

[graceful bloom]

No one is that good in complex stuff, everyone ignore that topic

[wary stream]

As I said, go ahead and post your question on it and whoever that understands it(you'll be surprised at the amount of people who know their stuff), will help you out

[graceful bloom]

Okay i will post it later when i will study

Thanks to server and active ppl

Hail math

[strong furnace]

It's a Troll I think

[manic quail]

what's "complex no"?

[echo pike]

can someone help me with this?

[wary stream]

Complex numbers, I believe

[manic quail]

nombers

[graceful bloom]

@manic quail well its a topic on irrational negative under sign of square root shit

[wary stream]

I believe there is a formula that relates side length with slant height. I don't recall it but a quick Google search on it will help you

[hollow peak]

Lots of people work with complex numbers if you're talking about the square root of -1 being i

[ionic jewel]

turns out complex numbers get a lot harder than \sqrt{-1} = i

[torpid delta]

how do you draw that well

[wary stream]

Talent?

[ionic jewel]

practice?

[torpid delta]

How does one attain talent

[ionic jewel]

okay someone post the meme

[torpid delta]

How does one inherit practice

[wary stream]

Become an artist, but let's not get off topic in a help channel

[torpid delta]

Anyway, Geogebra

[ionic jewel]

geogebra doesnt do what s/he wants i dont think

[torpid delta]

I don't quite understand what they're trying to do.

[ionic jewel]

it doesnt offer much (besides 3d graphing) outside of desmos, which also shouldnt work

[torpid delta]

What are they trying to graph

they can create a slider for dx; Put two points A and B on the graph of the function, define a third point with coordinates (x(A)+dx, f(x(A) + dx))

[ionic jewel]

I assume they wanted the labels too but I suppose thats a good solution

[torpid delta]

I'll create a similarly looking polynomial

[wary stream]

Matlab/Octave is a good software to do all that, and mathematica

[torpid delta]

I didn't quite

understand

@wary stream

@hollow peak

what is f(cm)

is it the value of f at the lowerbound and the higher bound?

@ionic jewel

doesn't this only hold for when there are no extremes in between cm and CM

for example something like this?

[alpine sable]

heyyoo can someone help with this question?

i just need to get the steps and im good

its the forming of the equation thats troubling me

[round socket]

@hidden horizon

wanna help me

[hidden horizon]

um sorry im busy rn

[round socket]

HEY

[glass lichen]

dont ping random users. post the question in an unused channel and wait for someone to help

[round socket]

hes NOT random

hes my friend actually

so.

[glass lichen]

cool, didnt ask

[round socket]

well you assumed he was random

[glass lichen]

if you have a question, post it

stop complaining

[round socket]

well hes my bestie so

WHAT

BICH WHAT

you randomly came at me

without knowing all the facts

then i gave u the facts

[glass lichen]

are you going to use the help channel or not?

[round socket]

and u told me u didnt ask

i WAS until you randomly budged in

while I was using it.

[glass lichen]

you werent using it

[round socket]

i was.

[glass lichen]

where's the question posted then?

[round socket]

it was posted in my brain

i was getting to thaat

[glass lichen]

then you werent using the channel

[round socket]

if you couldnt tell

all up in my pussy boy

[vast blaze]

#❓how-to-get-help

[shrewd oracle]

@round socket dude...calm down, if you got a question ask it, if not then dont?

[round socket]

wat

i been calm

[shrewd oracle]

Hardly so

[round socket]

mosh been all up in my pusy

i swear!

i was just @ ing my bestie

[shrewd oracle]

Dude...

[round socket]

and mosh HAD to interfere

like helo!

[shrewd oracle]

Yeah try dm ? Its a thing

[round socket]

i dont have my bestie added as a friend yet

but thank you for the idea!

no need for the tude

[glass lichen]

shut up if you're not going to use the channel appropriatly

[round socket]

me and iamrdt go WAY back!

[glass lichen]

no one needs a random user throwing a tantrum in the help channel

[round socket]

mosh you was throwing the tantrum

dafqu u mean hoe

[wary stream]

@round socket Are you here to interrupt and cause trouble like the other day? Because if you are please stop

[round socket]

mosh LOVE budging into other peoples buisness

i swear

[glass lichen]

what's preventing you from googling the formula and using it?

[round socket]

ALL I DID WAS @ MY FREIND TO HELP ME

LOL

what is preventing me is knowing which forma to google

[glass lichen]

well clearly it's arc length of a circle in degrees

[round socket]

its not so clear for me

no need for attitude

[shrewd oracle]

Same goes both ways

[round socket]

i aint got no attitude

[glass lichen]

you do.

[wary stream]

Google arc length formula

[round socket]

ok miss "dont ping random people"

2πr (θ/360)

this is what i got!

[glass lichen]

yeah

[round socket]

now.

[glass lichen]

so use it and you're done.

[round socket]

55/360?

wait

=19.71

2πr (θ/360)=19.71

wait

[wary stream]

You do, recall the last time you were here? Causing a ruckus for hours

[glass lichen]

yes.

[round socket]

2πr (55/360)=19.71

BICH ITS BC U HAD MAD ATITDUE

for NO reason!

[glass lichen]

shut the hell up

no one cares

[round socket]

you told me good luck failing

like goodnight!

omg u are mean

OMGGG

IM REPORTING YO AZ

[shrewd oracle]

Dude just stop...

[glass lichen]

ok, go ahead

[cyan token]

what is this?

[alpine sable]

do u still ned help

[round socket]

CAN YALL STOP FLOODING MY CHANNEL

OMG

[shrewd oracle]

Someone havin a temper tantrum

[glass lichen]

you're the one flooding it

[cyan token]

I see

[glass lichen]

[round socket]

YES BC
IM USING IT

[shrewd oracle]

This is the main w channel...

Dude your gonna get banned...

[round socket]

not me!

STOP FLOODING THE CHANNEL

[shrewd oracle]

Theres 9 mods on...do you honestly think nome are watching?

[round socket]

IS THE ANSWER 20.53??

[alpine sable]

okay kid with having trouble with 8th grade math

[round socket]

dilligaf

[glass lichen]

no, missing units

[round socket]

OMG U GUYS ARE SO MEAN

FOR NO REASON WTF

now yall are making fun of me for being dumb

ok

[shrewd oracle]

Your acting rude? Ive done nothing

[round socket]

like sorry im in 8th grade

what u want me to do

skip some grades

liek HELLO!

[glass lichen]

not throw a tantrum

[alpine sable]

haahahhaah

[glass lichen]

that's what we'd like you to do

[round socket]

well i aint finna let yall boss me around

like yall are higher ups

cuz ya aint

[alpine sable]

kid is mad

[round socket]

OMG

[shrewd oracle]

Never said we were?

[round socket]

IS THE ANSWER 20.53 CM

or

whatever the units are

it dont matter since

...

[glass lichen]

radii are lengths, so yes, units of cm

[round socket]

CM

YESSSSSSS

OKAYYYY

WHY AM I LOWKIE GOOD ASF

[glass lichen]

you're not

[round socket]

CAN SOMEONE HYPE ME UP

oh.

sorry

[alpine sable]

yo shut up ugly poser

[round socket]

...

[alpine sable]

hes trolling right

[round socket]

OMG

WHAT THE HELL?

WHAT DID I DO

[glass lichen]

Next time you want help, fucking act your age and dont throw a tantrum

[round socket]

OMG

MY AGE IS 12

[glass lichen]

<@&268886789983436800>

[round socket]

I AM ACTING MY AGE

[alpine sable]

.

[shrewd oracle]

So act 12 and not 2

[round socket]

WTF?