help-23

[split kayak]

I hope it makes sense that we are interested in a

since its our d²x / dt²

[bright bough]

yes

i think i get it now

thank youu

[split kayak]

Well, by rewriting the expression, we get:
$$-4(x+\frac{dx}{dt})=\frac{d^2x}{dt^2} \implies \frac{d^2x}{dt^2} +4\frac{dx}{dt} + 4x = 0$$

[split kayak]

Or, in terms more common to Diff. Equations

,, y'' + 4y' + 4y = 0

[split kayak]

This is our governing equation of motion, now we want our initial conditions for velocity (y') and position (y)

Which we know is t=0 -> y = a, y' = 0

taken from here

Solving now boils down to your experience with DEs

[safe radish]

@bright bough Has your question been resolved?

[safe radish]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• Do not immediately ping people or roles. After 15 minutes, feel free to ping <@&286206848099549185> once.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[hoary seal]

why is len(a) next to sin(theta)?

[hoary seal]

ik why there should be sin(theta) because it follows the same concept from unit circle

[primal bone]

Because the area of a parallelogram definitionally is the base times the perpendicular height

[open wedge]

and according to trig

[primal bone]

But if you're given the sloped length (or vector) here, a, ...

[little gorge]

heh

[hoary seal]

wdym?

[open wedge]

the side that's tilted by some bit

[primal bone]

First, do you agree with this?

[hoary seal]

I just want to know why len(a) is multiplied to sin(theta)

[open wedge]

bc of trig

you see that there's a right triangle right?

[hoary seal]

yes

[primal bone]

So the perpendicular height has length |a| times sin(theta), just from trig on this orange triangle

[hoary seal]

Yeah I understand but I don’t see how it’s derived from the orange triangle

[delicate zodiac]

Uk how sin theta is opposite by hyp

Damn got caught lacking

BASICALLY

Since hyp is a

And u only want opposite

U multiple sin theta with |a|

[safe radish]

@hoary seal Has your question been resolved?

[safe radish]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• Do not immediately ping people or roles. After 15 minutes, feel free to ping <@&286206848099549185> once.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[latent oasis]

I want proof of this series can you all explain it simply

[desert juniper]

the proof is actually quite complex, it's called Basel's problem

[latent oasis]

Ik that...

But I am ready to listen whatever it is...

I badly need the proof 😩

[quiet plume]

And there's like dozens of different such proofs

[desert juniper]

there's like half a dozen in the wikipedia page for Basel problem

they are also all well beyond me

it was also beyond Euler, even when he had confirmed the value

[slender sierra]

yessssss

[cunning pasture]

It's not simple. If you want to be rigorous, it's not that simple.

[latent oasis]

....

[cunning pasture]

Which grade are you in?

[latent oasis]

Grade 11

[slender sierra]

ehh why do u need this stuff so early gang

[latent oasis]

And I have it in my book

[slender sierra]

🤨 which book

[astral glacier]

Is it in your book as something to prove or just as a fun fact

[latent oasis]

My book

[desert juniper]

,rotate

[slender sierra]

oh jee adv obv

[latent oasis]

In a problem

[latent oasis]

Mm..

[desert juniper]

you dont need the proof for that

[astral glacier]

God damn it

[slender sierra]

jst ask teacher dude

[latent oasis]

He just yapping stuff 😭

[desert swan]

Which coaching do u go?

[latent oasis]

I don't get it

[astral glacier]

Not the place for jee conversations

[latent oasis]

I go to jee coaching in a school

[astral glacier]

Anyway

[slender sierra]

😔

[astral glacier]

Let's solve the problem

[latent oasis]

Mm

[slender sierra]

haha fr

[desert juniper]

what's jee?

[astral glacier]

Look at the terms that are being removed

[latent oasis]

Sure that would help

[astral glacier]

Felix I'll explain in hlounge

Let's not open that can of worms

[latent oasis]

It's joint entrance exam one of the toughest exams in the world holds top 3 and then advanced is top 2

[slender sierra]

my teacher tried in the euler approach

[astral glacier]

Again, not relevant to the channel

[astral glacier]

^^

[latent oasis]

Pls let's solve the problem

[slender sierra]

ion rem wht it was but idk it seemed good when he explained it

[astral glacier]

Toosie if you aren't gonna contribute, I'm gonna ask you very nicely to not flood the channel with unhelpful messages

[latent oasis]

Idk

[astral glacier]

Write out the terms that are being removed

[latent oasis]

Like the even ones right ?

[astral glacier]

Yes

[latent oasis]

Mm.. and then

[astral glacier]

Write them as a sum

What does that look like

[astral glacier]

Good

[latent oasis]

Mm next

[astral glacier]

Well no actually

We have three series

The original series

One with the even terms

[latent oasis]

....

Mm

[astral glacier]

And one with the odd terms

[latent oasis]

Mmm

[astral glacier]

And what we have is

Odd terms = original - even terms

Now look at the even terms series

[latent oasis]

Mmm

Mm

[astral glacier]

Do you observe anything interesting

[latent oasis]

What is it...?

[slender sierra]

oooo i do

[astral glacier]

Good, don't spoil it for op

...

[latent oasis]

What is it...?

Idk 😭

[slender sierra]

sory

[astral glacier]

Well here's the strategy

You know exactly one thing

Anything else, you have to relate to that one thing somehow

You know the value of the original series

What you want is the sum of the odd terms

You have odd = original - even

[latent oasis]

Mm I have it

[astral glacier]

Now the idea is that we wanna turn the even series into something we know

Can we do that

[slender sierra]

dude r u a teacher or smthin

u goated fr

[latent oasis]

And what is it i can do ?

[astral glacier]

Well look at it

Does anything jump at you

[latent oasis]

Nothing I am just tripping 😵‍💫

[slender sierra]

ooo yes

[astral glacier]

Toosie- not a teacher, but have taught some classes before

[astral glacier]

It's fine

Write out a few terms of the even series

Then write out a few terms of the original series

[latent oasis]

Mm I did

[astral glacier]

See if you see anything

[latent oasis]

Idk...

Wait a minnn

[stable zephyr]

oh icl i also wanna know this

[slender sierra]

omg a prodigy 😭

[latent oasis]

I get it....

[delicate zodiac]

Are you trying to show the Euler method for the solution?

[astral glacier]

Nice

I'm not sure what the Euler method is lmao

[latent oasis]

If we take that 1/2 square common we get the original series....

Right ,m

[astral glacier]

Yes

[latent oasis]

Yay

[astral glacier]

So now we have odd = original - even

[latent oasis]

Mm

[astral glacier]

And even = 1/4 * original

So we are done

[delicate zodiac]

It's the one with the taylor series of sinx and the infinite product thing

[latent oasis]

Wait lemme solve and tell ya

[astral glacier]

Oh god no lmao

[stable zephyr]

can anyone recap the proof told again

i also wanna know

[astral glacier]

I'm trying to get this kid his answer, I'm not gonna even try to explain Basel

[stable zephyr]

im another jee aspirant 😭

[astral glacier]

We didn't prove it actually

[stable zephyr]

oh

[astral glacier]

You lack the tools for this

[delicate zodiac]

Ohhh 💔

[astral glacier]

The proof is nowhere near accessible

[latent oasis]

It is pi square / 8 ???

[astral glacier]

At this stage at least

[astral glacier]

Good

[slender sierra]

yes taylor was the way i was taught

[latent oasis]

But my solution key is kinda wierd...

[astral glacier]

What does it say

[slender sierra]

../6

[stable zephyr]

what exactly do we need to learn

[latent oasis]

Here

[stable zephyr]

cuz this looks like a question from sns 🥀

[astral glacier]

Solve for x

[slender sierra]

taylor series

[stable zephyr]

well ik taylor series

like expansions of certain functions

the imp 1s

[astral glacier]

I'd say just read through the wikipedia tbh

Either way, there's better uses for your time if you're a jee aspirant

[slender sierra]

expansions r taught in inverse trigo chapter

[astral glacier]

Basel series is absolutely not one of them

[latent oasis]

Why though 😭

[astral glacier]

Anyway, solving this for x gives you your solution

[latent oasis]

How ? Cryo

[stable zephyr]

we are on applications of derivatives man

[astral glacier]

Because x is the value of the odd sums

Velt and Toosie, I'm gonna ask y'all to move to #study-discussion

Or some other social channel

[stable zephyr]

sorry

!!

[latent oasis]

.... But how does adding even and odd give you pi square / 6. + X

[astral glacier]

Anyway Aaron, you want the value of the sum of the odd terms. That is what your answer key denotes as x

[astral glacier]

Uh no that's not what it's saying

It's saying odd = x, even = 1/2²*π²/6

[latent oasis]

It clearly says that see

[slender sierra]

wait which class u in or which collage year

[astral glacier]

And the full series is π²/6

[latent oasis]

See second line

It says even and odd together are pi square / 6 + x

Thats not true

[astral glacier]

Oh right

That's a typo then

[astral glacier]

Should be this

[stable zephyr]

judging from his answers he looks like hes in college

[desert swan]

He's in 11th

Preparing for jee

[stable zephyr]

talking about zavier i think

[desert swan]

Mbbb

[astral glacier]

Lmao I saw those you two

Idm y'all talking here when Aaron isn't here, I just don't like flooding the channel and making it hard for him to see the relevant messages

Bit too personal to just say in a public server lol

[stable zephyr]

you giving jee?

[astral glacier]

Let's just say I'm not in college

I do maths for the heck of it

[slender sierra]

damnit a math prodigy

[stable zephyr]

bro

[astral glacier]

No lmao

[stable zephyr]

look at his role, postgraduate maths

[astral glacier]

That's not what a prodigy is

Postgrad math isn't related to your education, it's related to the level of maths you do

[slender sierra]

yes 🥀 its in 4 days

[astral glacier]

Good luck

[stable zephyr]

ye meaning like you're def not in college

[astral glacier]

Anyway @latent oasis you still here?

[slender sierra]

we shud leave this help chanel

[stable zephyr]

jee adv xD gl man i still have 1 more year

[stable zephyr]

yea

[slender sierra]

jst gonna do math phy and pray to god

[stable zephyr]

cuz i went in 12th just now

[slender sierra]

aaron left 🥀

[delicate zodiac]

Lowkey

I feel like jee takes the fun out of math

Like sure

Some questions are amazing

But like

[stable zephyr]

it does actually

[delicate zodiac]

The amount of memorization you need kinda defeats the purpose of what math is about

[slender sierra]

lets go to #discussion

[delicate zodiac]

Bet

[slender sierra]

frrrrr

i hate jee mains

i enjoyed solving sameer bansal and stuffff but jee mains ruined it all

[stable zephyr]

come to #study-discussion btw

[safe radish]

@latent oasis Has your question been resolved?

[safe radish]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• Do not immediately ping people or roles. After 15 minutes, feel free to ping <@&286206848099549185> once.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[old matrix]

context: i was watching some olympiad exercises in my country and i came across this one which i was interested in but have no idea of how to solve. the problem says "Prove that a natural number n¨ is divisible by 9, if and only if, the sum of its digits is a multiple of 9". could it be something like: n : 9 = x and d+c+b...= s where S is the sum of the digits and x is a natural number?

[arctic raven]

a number $n=a_\ell a_{\ell-1}\cdots a_1a_0$ is really just [n=\sum_{k=0}^\ell a_k\cdot 10^k]

[flat frigate]

Flip

[arctic raven]

in base 10

[old matrix]

is K the digits?

[arctic raven]

sure

if you say the 0th (rightmost) digit is a_0, and the ell-th (leftmost) digit is a_ell

[arctic raven]

well no, the digits are the a_k's

but they are indexed by 0 <= k <= ell

[old matrix]

ohh okay okay

and so basically when you subtract their digits it will give n = 0 (mod 9)?

[arctic raven]

prove it

[old matrix]

oh wait

.close

[safe radish]

Channel closed

Closed by @old matrix

Use .reopen if this was a mistake.

[plush spruce]

why close the channel mid conversation lol

nice name btw

[arctic raven]

maybe they saw the idea

and didn't want to be spoiled further

[plush spruce]

nice point xD

[safe radish]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• Do not immediately ping people or roles. After 15 minutes, feel free to ping <@&286206848099549185> once.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[real imp]

how do i do

[safe radish]

What step are you on?
1. I don't know where to begin.
2. I have begun but got stuck midway.
3. I got an answer but I was told that it's wrong.
4. I got an answer and would like my work checked.
5. I have a question about someone else's work/solution.
6. I have completed the problem and don't need help anymore. Thank you.
7. None of the above

[real imp]

1

[tardy mango]

Since you're already given quite a few interior angles, I'd try to find the ones you're not given in terms of x.

Then consider what facts you might know about the interior angles of a polygon

[real imp]

(n-2) x 180

[tardy mango]

mhm that's relevant

[whole hill]

Wassup again bro!!

[median sand]

I would just find the sum of all interior angles in that polygon first, intuitively.

[safe radish]

@real imp Has your question been resolved?

[real imp]

i ifugred it out

i figured out

[real imp]

sir.

[safe radish]

Channel closed

Closed by @real imp

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• Do not immediately ping people or roles. After 15 minutes, feel free to ping <@&286206848099549185> once.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[glass sparrow]

hello can someone help me with this question

[glass sparrow]

i don't understand how to get the anti diff graph of that

[safe radish]

@glass sparrow Has your question been resolved?

[median sand]

Define the function.

In (x-a)(x-b)(x-c) form.

Ah wait, let me think about it.

[quiet plume]

You're given quite a lot of information about the derivative of f.
What does it mean for f if f'(x) = 0? Can you classify those points on f somehow?
What about points where f' attains a maximum (or a minimum? What does that say?
Can you tell where f is increasing/decreasing from the graph?
What about when it's concave up or down?

[median sand]

Also given that f'(x) is a cubic, then there is one chance that f(x) is a quartic.

[safe radish]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• Do not immediately ping people or roles. After 15 minutes, feel free to ping <@&286206848099549185> once.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[regal iron]

hello i have attempted so many times but i still cannot (for the life of me) figure out how to find periods in a sinusoidal function. at all. how do i find it from a given equation?!
i missed every question on my test regarding periods and my exam is friday and i have no idea how to find them. pls help

[regal iron]

i get
period = 2pi times b

but what’s b?? and when do i have to like flip it into the equation? why??

[tardy mango]

b is the coefficient of the variable, and b should also be positive.

[regal iron]

here’s the question i’m trying to solve

so if x (t) is being multiplied by 1/2

that’s b right?

[tardy mango]

mhm b is 1/2

[summer coral]

period is defined as 2pi / |B|, where B is the value in Acos(Bt)

[tardy mango]

That’s another way you can define it

Anyway channel is yours

[regal iron]

so
period = 2pi • 1/2

period = pi/2?

but then do i flip that Something Something reciprocal to be 2/pi??

my teacher always says i have to flip it

is my math wrong on that

[summer coral]

its 2pi divided by 1/2

[regal iron]

wait

that would be

just pi

right

[summer coral]

$\frac{2\pi}{\frac12}$

[flat frigate]

Krish

[regal iron]

i’m tryna do this in my head

wait it would be 4pi

[summer coral]

which is equivalent to $2\pi \cdot \frac{1}{\frac12}$, or $2\pi \cdot \frac21$

[flat frigate]

Krish

[regal iron]

so 4pi

[summer coral]

yes but does that make sense how we flipped it?

[regal iron]

and then would you take the reciprocal of it? so it would be 1/4pi?

wait we already flipped it?!

[summer coral]

no, the period is just 4pi

[regal iron]

I swear my math teacher said i had to use the reciprocal of it

[summer coral]

maybe they were talking about dividing by a fraction, but we did take the reciprocal when dividing by that 1/2.

[swift jasper]

Ignore what I said actually

[regal iron]

Ok wait so

hold on let me use an example from my notes

b would be 4 right

[summer coral]

yes

[regal iron]

so it’d be
period = 2pi • 4

[summer coral]

not times 4. divided by 4

period $= \frac{2\pi}{\abs{B}}$

[flat frigate]

Krish

[regal iron]

Oh nah my teacher is 100% evil she has us doing multiplying by b

[regal iron]

i think it’s bc she taught us the formula up top where is 1/b

for some extra reason

.

Ok everything makes so much more sense now

[summer coral]

ah, then yes multiplying by 1/b is the same as dividing by "b"

[regal iron]

bc we got the answer to be pi/2 in the notes

[summer coral]

yes that is correct

[regal iron]

bc it would just be 2pi/4

= pi/2

Ok i think i blame my teacher for this

[summer coral]

multiplying something by 1/2 is the same as taking half of it, in other words

[regal iron]

bc she would tell me to flip the period into the answer

[summer coral]

calling it 1/b is probably not the best way to put it but i'd make sure to know both ways, since they're saying the same thing

[regal iron]

OKOK

TYSM!!!!

this clears up so much

[summer coral]

of course!

[regal iron]

.close

[safe radish]

Channel closed

Closed by @regal iron

Use .reopen if this was a mistake.

[safe radish]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• Do not immediately ping people or roles. After 15 minutes, feel free to ping <@&286206848099549185> once.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[regal iron]

Hello again
how do i solve this problem?

[regal iron]

i got that arccos (sqrt2/2) = pi/4

[summer coral]

work from inside to out

[regal iron]

but i’m stuck on the part that’s cot(pi/4)

i flipped it to be

tan(4/pi)

and that’s where i’m stuck

[summer coral]

yes it should be cot(pi/4) that is correct

and it should not be tan(4/pi) but you are close

how do you write cot in terms of tan?

[regal iron]

don’t you just flip it?

[summer coral]

yes, so what would cot turn into?

[regal iron]

Uhm

4/pi

[summer coral]

dont worry about the inside pi/4

if you had cot(x)

how would you write that in terms of tan?

[regal iron]

tan = 1/cot
or
cot = 1/tan

[summer coral]

yes exactly

so you know that

$\cot x = \frac{1}{\tan x}$

[flat frigate]

Krish

[summer coral]

notice in this how the "x" does not change at all

the inside argument will never change, just the function you are using.

[regal iron]

Mmm

[summer coral]

does that part make sense?

[regal iron]

Yes i think so

my brains fried from my test today LOL i think im projecting things i did on the test into this unit

[summer coral]

no worries, happens all the time.

in this case what is your "x"?

[regal iron]

does it just stay the same?

[summer coral]

yes

[regal iron]

tan (pi/4)

Now i’m wondering where da hell that’s gonna be on the unit circle

[summer coral]

forget the tan part for now, just tell me where is pi/4 on the circle?

[regal iron]

o

Wait

i’m thinking inverse

[summer coral]

ah

[regal iron]

tan (pi/4) = 1

[summer coral]

yes good!

[regal iron]

HELPME I WAS LIKE damn what ratio on the unit circle is gonna give me pi/4 hello 😩

oof that’s gonna get me so bad on the test

ik ima be mixing that up

so my answer is just 1?

[summer coral]

and since cot is 1/tan, you can say it's equal to 1/1

[summer coral]

yep!

[regal iron]

WWWW TYSM

[summer coral]

also, if you wanted another way to do it, instead of terms of tan you can directly go to sin and cos

[regal iron]

ima keep this chat open while i do my study guide… LOL

[summer coral]

since $\cot x = \frac{\cos x}{\sin x}$

[flat frigate]

Krish

[regal iron]

AH THATS TRUE

Oof

i’m hit with an area question

https://tenor.com/view/bunny-rabbit-tiktok-rabbit-not-hungry-skinny-rabbit-gif-12104320708632505949

[summer coral]

same applies for tan, just instead of cos/sin its sin/cos

[regal iron]

the area of a triangle

A = 1/2bh ?

[summer coral]

go ahead and send a picture of it if you can

[regal iron]

Dam i feel like it was smtn long af

[summer coral]

but yes the general formula for area of a triangle is 1/2 bh

[summer coral]

in this case, 1/2 bh won't help since you don't know the height

have you learned heron's formula?

[regal iron]

OOP FOUND IT

Fuck it is long

[summer coral]

yeah it can get tedious

[regal iron]

so it’d be Worlds Longest Formula SSS Triangle

[summer coral]

yes it would be exactly this

find the semi-perimeter and then plug it in to that "K" equation

[regal iron]

FREE ME FROM THIS SUPER HELLLL

[summer coral]

you'll get through it! once you learn all the fundamentals it'll get easier to apply it to all kinds of problems

[regal iron]

DATS TRUE

thankfully i’ve learned all this before

[summer coral]

unit circle is just the beginning of all advanced math :)

[regal iron]

just a matter of relearning it

[regal iron]

I lowk like the unit circle 👀

our test today was on verifying trig identities and it almost killed me tho

[summer coral]

thats good! i did too and it definitely helped knowing my way around it.

verifying trig identities is probably one of the more fun topics. you're literally given the question and answer, your job is to just find the steps in the middle

[regal iron]

HELL NAHHHH

I can’t do those questions it’s too stressful under a time limit

i don’t like how many options there are

[outer pollen]

-# isn't four options standard for MCQs?

[summer coral]

well for AP/IB exams or other state/national exams yes, but a teacher technically can be as evil as they want.

[regal iron]

wym? also w pfp

@summer coral pls tell me the answer is none of these

[outer pollen]

you mentioned not liking how many options there are, and I believe that refers to the MCQs?

[regal iron]

bc i got -sqrt3/2

[outer pollen]

if you're not, I apologize.

[regal iron]

OHHH SORRY
i meant more as in like how many paths you can take to solve the problem

so many strategies you can do

[summer coral]

it is one of them

[regal iron]

Ooof

ok so i did

[summer coral]

can you send your work?

[regal iron]

YES

[outer pollen]

er....

[regal iron]

In my defense

my teacher has never made us do this before

Idk why she’s pulling the csc sec and cot out on me 😒

mrs this was not in the notes homework or even test

https://tenor.com/view/airball-nba-brick-gif-15266795546092124798

how do i convert from arccot to arctan

[safe radish]

@regal iron Has your question been resolved?

[safe radish]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• Do not immediately ping people or roles. After 15 minutes, feel free to ping <@&286206848099549185> once.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[dim swift]

Question regarding Set Notation

My work has been overlapping with set theory as of recent, specifically non-negative integers and rationals, and I'm slightly confused as to how I should write them. I've seen and used $\mathbb Z_{\geq0}$ most of the time, but recently moved to $\mathbb N$ (With $0\in\mathbb N$), however I can't find any standard notation for positive rationals. I've wrote $\mathbb Q_{0+}$ or $\mathbb Q_{\geq0}$ but I ask if there's a better notation for all of the sets I've mentioned here, or if the notation I use is okay.

[flat frigate]

C. U. B. E.

[main mural]

positive or non-negative rationals?

[dim swift]

non-negative rationals, sorry

[main mural]

i think $\bQ_{\geq 0}$ would be the most unambiguous and widely understandable option

[flat frigate]

artemetra

[main mural]

otherwise writing ``$q \in \bQ$ where $q \geq 0$ " is also really common

[flat frigate]

artemetra

[main mural]

you can also say "let $\bQ_0$ be the set of nonnegative rationals" in the beginning of your document and reuse it later

[flat frigate]

artemetra

[dim swift]

I see

Thanks a lot!

[main mural]

of course

[dim swift]

.close

[safe radish]

Channel closed

Closed by @dim swift

Use .reopen if this was a mistake.

[safe radish]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• Do not immediately ping people or roles. After 15 minutes, feel free to ping <@&286206848099549185> once.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[echo gazelle]

Is this right

[gray zinc]

Yes good boy

[echo gazelle]

Yay thanks

[small sandal]

should probably combine them into a single fraction

it looks uglier but if this was a test question, you would get marked down on not having it fully simplified

[safe radish]

@echo gazelle Has your question been resolved?

[echo gazelle]

Is the answer for the third one correct

[echo gazelle]

I only need it for Taylor polynomial so I think it’s fine 😄

[small sandal]

ah okk

[echo gazelle]

Is there a way I can check if im correct

That’s not here

[small sandal]

whats your original f?

[echo gazelle]

1/(1+lnx)

[small sandal]

it doesn't have a solutions section for the problems your working on?

[echo gazelle]

Yah

[small sandal]

i suppose a way to check, would be to graph 1/(1+ln(x)) and the Taylor series you obtained and see if it approximates the curve after n iterations

[echo gazelle]

ahh ok thx

im also having trouble understanding the taylor remainder formula

what is the k?

[small sandal]

i haven't seen this formula, i only know how to do regular Taylor/Maclaren series things

[echo gazelle]

o ok

ill open a new channel for it then

thx so much

[small sandal]

np

[echo gazelle]

.close

[safe radish]

Channel closed

Closed by @echo gazelle

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• Do not immediately ping people or roles. After 15 minutes, feel free to ping <@&286206848099549185> once.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[desert swan]

Can somebody pls explain me part iii

[hollow dock]

Break even is when revenue=cost

[hollow dock]

The revenue is 60 per unit, so 60n in total

[desert swan]

Wdym

[hollow dock]

Which part do you not understand?

The break even part

[desert swan]

Everything

[hollow dock]

Ok, so do you know what it means to break even?

[desert swan]

Nope

[hollow dock]

Break even means what you earn is the same as what you pay

So lets say for example you set up a shop, it costs $60 for the stall and $30 for the products, to break even, you need to sell the products such that you earn back the $90

Do you get this example?

[desert swan]

Yes

[hollow dock]

So in the question, the money earned is 60 × n

Because 60 per unit and we have n units

You get that part?

[desert swan]

Yes

[hollow dock]

The money you pay is the base 10000 and for each unit sold its 40 each, so its 10000+40n

You get that part?

[desert swan]

Yes

[hollow dock]

So to break even, you equate the 2 parts together

[desert swan]

M=60n

And m=10000+40n

[hollow dock]

Yes

[desert swan]

Where m is total amount

[hollow dock]

M is the break even

[desert swan]

Isn't it the same thing?

Or not?

[hollow dock]

Basically yeah

Any other questions?

[desert swan]

Norp

Nope*

Tysm

.close

[safe radish]

Channel closed

Closed by @desert swan

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• Do not immediately ping people or roles. After 15 minutes, feel free to ping <@&286206848099549185> once.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[neon ivy]

I need a hint telescoping

$\sum_{n=1}^{\infty} \sqrt{1+\frac{1}{n^2}+\frac{1}{(n+1)^2}}$

[neon ivy]

Not sure where to start in all honesty

[flat frigate]

alistair

[neon ivy]

Wait i think i got it

[untold magnet]

What did you try

[brave wolf]

this is quite weird

it quite clearly diverges

[safe radish]

@neon ivy Has your question been resolved?

[cunning pasture]

Yes, each term is greater than 1, and so the sum is >= 1 + 1 + 1 + 1 ..... = infinity

Anyway, if you mean the sum of it till a finite value of n, it's easy; just combine the terms of the expression inside the root.
||The result is a perfect square||

[safe radish]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

[safe radish]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• Do not immediately ping people or roles. After 15 minutes, feel free to ping <@&286206848099549185> once.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[tulip flame]

i need help with this question

[safe radish]

Please don't occupy multiple help channels.

[tulip flame]

srry

how i get off other channel

[gritty kernel]

prob just close it

.close

[tulip flame]

ty

.close

[safe radish]

Channel closed

Closed by @tulip flame

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• Do not immediately ping people or roles. After 15 minutes, feel free to ping <@&286206848099549185> once.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[stone shale]

I don't have any idea how to start with this problem.

[stone shale]

Hmm?

[rancid lion]

seems like you're trying to find YG/BG

[stone shale]

Can't but

I later reqlized

[rancid lion]

it's possible

[stone shale]

But how would it help in area man?

[rancid lion]

alright so can you find the area of BFC

[stone shale]

Leme think

[rancid lion]

*BFC sorry

[stone shale]

Ohk

[rancid lion]

found it yet?

[stone shale]

Sry bro I'm onto it

Uhhh

Uhh

It'll be 1/3

?

Of ∆ABC

[rancid lion]

wrong

[stone shale]

K leme

Think

[rancid lion]

ok lemme give you the gist of the whole problem

[stone shale]

Ok

[rancid lion]

so suppose i have triangle ABC here, D is the midpoint of BC. what is the ratio between the area of ABD and ABC

[stone shale]

Gimme hint for [BFC]>

[stone shale]

Hmmm thinkin

[rancid lion]

i drew an altitude AH here

so area of ABD should be BD*AH/2

area of ABC is BC.AH/2 = 2BD.AH/2

[stone shale]

Yup leme.divide

[stone shale]

BC /BD

[rancid lion]

ok great

[stone shale]

So u meant we construct

Perpendicular

Thru GYZ?

And ABC?

[rancid lion]

you can imagine the perpendicular in your head

[stone shale]

Oh yea

I forgot I had head🥲

AB/BF

[rancid lion]

what i want you to realize here is area of ABD/ABC = BD/BC (since the 2 triangles have the same height when you drop the perpendicular from A)

[stone shale]

=

[ABC]/[BFC]?

[rancid lion]

exactly

[stone shale]

Pls wait

Maybe I could do it

on my own

[safe radish]

@stone shale Has your question been resolved?

[stone shale]

I'm onto it.

[stone shale]

I'm stuck again

What do I do

Aft

[rancid lion]

where

[stone shale]

I got [BFC] and [BEC] by that area method

[rancid lion]

alright

do you know what CG/CF=?

[stone shale]

1:3

[rancid lion]

wrong

well you got CG/GF = 2:1

[stone shale]

U asked for CF

[rancid lion]

yes

well imagine CG is 2 parts, GF is 1 part

CF = CG + GF which should be 3 parts

so CG/CF = ?

[stone shale]

This

[rancid lion]

no

[stone shale]

2/3

Mb

[rancid lion]

ok good

so you got CG/CF = 2/3

and CZ/CF = 1/2

so GZ / CF= ?

[stone shale]

Ohk

Bro imable to.get

CZ/CG =3/4

[stone shale]

..

[rancid lion]

oh cool

[stone shale]

Ik the rest ig

Wait

Same for BY/BG

now

[rancid lion]

yes you're getting there

[stone shale]

Again stuck

at

∆BGC ~∆YGZ

[stone shale]

..

[rancid lion]

alright so you have BCF

[rancid lion]

use this to get BGC

[stone shale]

Bro u Tryna BGC

[rancid lion]

from BGC and this you get BZC

[stone shale]

We ain't got BFG man

[rancid lion]

we dont need BFG here

[stone shale]

how to...

Get BGC

By BFC

[stone shale]

See diagram

Refer these points pls

[rancid lion]

well you just got this

CG/CF = 2/3

so BCG/BCF = 2/3

[stone shale]

Oh I see

Tht area thing

Here also

Applied

[rancid lion]

yea this problem is just applying the area thing many many times

[stone shale]

Ok I can now ig

[stone shale]

U meant BZC ??

[rancid lion]

yes

[stone shale]

Construction?

?

[stone shale]

Construction??

[rancid lion]

yes

you construct the segment BZ

[stone shale]

3/4

[rancid lion]

and now BZG is just BCG - BZC right?

[stone shale]

Yup

[rancid lion]

i think you can do it from here

[stone shale]

Yeah ig

[stone shale]

[BZG]/[BZC]=1/3

[rancid lion]

yes

[stone shale]

[BZG]+[ BZC]= [BGC]

But still

I'll get 2 variables

Even if I go by

[stone shale]

manipulating this

[stone shale]

...

[rancid lion]

didnt you calculate BGC already?

[stone shale]

Hold up... wait a min

[stone shale]

but in fracs

I havent got BGC relation with ABC

yet

[rancid lion]

well you can just calculate along the way

[stone shale]

Ig we will

[rancid lion]

we know ABC is 480

[stone shale]

Hmm

Okie

[rancid lion]

so according to what we got, BFC = 240

[stone shale]

How?

I had ratios

[rancid lion]

^

you just got ABC/BFC = AB/BF = 2:1

[stone shale]

Oh man

I forgot

[stone shale]

Sry continue

[rancid lion]

from here BCG = 160

we got BZC/BCG = CZ/CG = 3/4 so BZC = 120

[stone shale]

Got it right

[rancid lion]

and now you can calculate BZG

[stone shale]

Oh

[stone shale]

Got it right too

40

[stone shale]

=BZG

BZG

[rancid lion]

alright now we're very close

[stone shale]

Done

Got it

How tomdo

Ik now

[rancid lion]

good

[stone shale]

Bro how to get [BYZ]

[rancid lion]

well if you apply all the same length ratio derivations to BE

[rancid lion]

you get BY = 3/4 BG

[stone shale]

Got it

30

[stone shale]

How to get BFG

[stone shale]

@rancid lion

[rancid lion]

you dont need BFG

[stone shale]

Bro ik

My way

Is diff

Lil

U see

[rancid lion]

have you found GYZ yet

[stone shale]

Refer here.

[rancid lion]

that's wrong

[stone shale]

Huh?

How

It's right bro

[rancid lion]

GYZ = BZG - BYZ

[stone shale]

Bruh it was this ez

I struggled diff.way

[stone shale]

Bro I swear I struggled diff.way

😭

💀

😭

.close

[safe radish]

Channel closed

Closed by @stone shale

Use .reopen if this was a mistake.

[stone shale]

Btw

[hallow otter]

Is this occupied??

[summer coral]

this is closed.

[safe radish]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• Do not immediately ping people or roles. After 15 minutes, feel free to ping <@&286206848099549185> once.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[potent oar]

i cant figure out this one

[potent oar]

like, the first step, what do i do?

[plucky elk]

should translate

[hasty steppe]

the solution to this equation is:

[golden nebula]

Would reccomend taking x less than 2 and greater than 2 and square both sides for each case

@potent oar your Italian right? Do you know trignometry?

[potent oar]

okay but once i square both sides i get x>x^2-4x+4 which... what do i do there?

[golden nebula]

Hmm. I got it. Sorry no need to square yet. Let sqrt(x) equal x-2 at some value a

[potent oar]

what? what about it?

[golden nebula]

So let's look at when x is less than a

When x is less than a

Which will be greater sqrt(x) or x-2?

[potent oar]

i...dont know what you mean... how can i know without knowing the value of a?

[golden nebula]

Just treat a as that

Treat a like a value where sqrt(x) is equal to x-2

[potent oar]

okay

[golden nebula]

So when x is less than a, which one is greater?

[potent oar]

x-2 is greater, no?

yeah it's greater

[golden nebula]

Its smaller actually

[potent oar]

how so

no wait

you're right, if x decreases, x-2 goes down faster yeah

[golden nebula]

Really sorry @potent oar but I have to cut short our conversation here. I have to go now

[potent oar]

bruh

[golden nebula]

Maybe another <@&286206848099549185> can help you

[dense lark]

Wzup

[radiant ice]

could you plug numbers in?

[potent oar]

so, if sqrt(x)=x-2 at x=a, if i decrease a, x-2 decreases faster so.... idk where this was going

[naive summit]

yo

still need someone to help

[radiant ice]

which means..?

[potent oar]

i dont know

that's why i'm here

[radiant ice]

okay let’s say

[naive summit]

alright

[radiant ice]

i make a = -1

[naive summit]

you dont need to

[radiant ice]

well i’m saying like

[dense lark]

Oo

[radiant ice]

is sqrt(-1) greater than -3 (-1 - 2)

[dense lark]

Try desmos?

[potent oar]

sqrt(-1) doesnt exist...

[naive summit]

$sqrt(x) > x-2$

[flat frigate]

jade

[dense lark]

Imaginary

[radiant ice]

well it’s i

[naive summit]

first step lets get rid of that sqrt

square both sides

[dense lark]

Squaring both sides 🗣️ 🗣️ 🗣️ 🗣️ 🔥 🔥 🔥 🔥

[potent oar]

square both sides, i get x>x^2-4x+4

[dense lark]

Next wut

[naive summit]

$x > (x-2)^2$

[dense lark]

Correcto

[flat frigate]

jade

[naive summit]

now redistribute

[dense lark]

Open nd equate???

x > x^2 + 4 -4x

[naive summit]

$0>x^2-5x+4$

[flat frigate]

jade

[dense lark]

How 5x....

[naive summit]

my wifi is poor btw itll be a bit laggy

[potent oar]

is this legal??

[naive summit]

now factor

[dense lark]

Yea

[potent oar]

dont you need to invert > to < if moving the thing to the right?

[naive summit]

@potent oar try factoring x^2-5x+4

[dense lark]

Nvm nvm

[naive summit]

subtract x from both sides

[dense lark]

Yea got it

Ddint see the 0

*didnt

[dense lark]

Not rlly

That happens when we're moving a value less than 1

[naive summit]

only if you divide both sides by -1

[potent oar]

x-1 x-4?

[naive summit]

yep

so yk the 0 property for multiplication?

[potent oar]

like, every number *0 is 0? yeah i went to elementary school

[naive summit]

we can set these both to be 0

0>(x-1)(x-4)

if x-1 is 0, then we can do 0>x-1

if x-4 is 0, we can do 0>x-4

[potent oar]

so x-1<0
x<1
x-4<0
x<4
...
so x<4 && x>=0?

cause of the root

so... B?

[naive summit]

should be right

[potent oar]

yeah okay... if that's correct than i panicked for nothing

i didnt know i could just move the x to the other side, i'm always so weary...

okay thanks

.close

[safe radish]

Channel closed

Closed by @potent oar

Use .reopen if this was a mistake.

[safe radish]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• Do not immediately ping people or roles. After 15 minutes, feel free to ping <@&286206848099549185> once.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[potent oar]

C?

[potent oar]

ignore the ln part

[round egret]

what does the last line mean

[potent oar]

pi over 2 -1 plus pi over 2

the answer, basically

[round egret]

I think that's wrong

it should be pi/2 - 1

[potent oar]

how so

isnt the integral equal to x^2*arctan(x)-x+arctan(x)?

[round egret]

$(1)^2 \cdot \arctan(1) - 1 + \arctan(1)$ is $\frac{\pi}{4} - 1 + \frac{\pi}{4}$

[flat frigate]

MxRgD

[potent oar]

why is it pi/4

isnt arctan(1) pi/2??

its not!!!

okay

woops

yeah

okay gonna make sure i remember my trigonometry during the exam... thanks

.close

[safe radish]

Channel closed

Closed by @potent oar

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• Do not immediately ping people or roles. After 15 minutes, feel free to ping <@&286206848099549185> once.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[chrome knoll]

may somebody educate me about this

[safe radish]

What step are you on?
1. I don't know where to begin.
2. I have begun but got stuck midway.
3. I got an answer but I was told that it's wrong.
4. I got an answer and would like my work checked.
5. I have a question about someone else's work/solution.
6. I have completed the problem and don't need help anymore. Thank you.
7. None of the above

[chrome knoll]

i tried

[azure harbor]

Err can you please translate the problem

[round egret]

you wrote $P = q^{n-1}$

[flat frigate]

MxRgD

[round egret]

it should be $P_n = q^{n-1} \cdot p$

[flat frigate]

MxRgD

[round egret]

because the problem states that

[round egret]

oh

[round egret]

is this the original?

[chrome knoll]

i translated it to engliush

[chrome knoll]

yea

[round egret]

it doesn't look right since here P is different

[chrome knoll]

p^n =q^n-1 =(1-p)^n-1

photo translator messed up

wait i think i see what i messed up

i think this does the job

can somebody verify if possible

[plucky elk]

,rotate

[safe radish]

@chrome knoll Has your question been resolved?

[tardy mango]

typo, you should say that q=1-p after separating it off with something like "and".

also you never found a closed form for this series

the standard trick is to let the series be S and consider qS

then ||subtract the two in a (roughly) termwise fashion||

[chrome knoll]

yeah i never figured out how

[chrome knoll]

i dont get it

do i rewrite the brackets as 1/1-q?

[tardy mango]

work with what I said for a little, you don't need to see it instantly

[chrome knoll]

im a little foggy rn ill see what i can make out

@tardy mango

i realized that it did look like an infinite sum

[safe radish]

@chrome knoll Has your question been resolved?

[dim wraith]

ru?

@chrome knoll

[chrome knoll]

da

[dim wraith]

it's well known fact

so i think they need you to prove it

you already did

so basically solved?

[chrome knoll]

i think i did

no clue

1/p is the only solution for a closed from that i can think of

[dim wraith]

,tex $\mathbb E[X]=\sum_{n=1}^{\infty} n,p,q^{n-1}=p\sum_{n=1}^{\infty}nq^{n-1}\$
using the standard series identity
$\ \sum_{n=1}^{\infty}nq^{n-1}=\frac1{(1-q)^2}\qquad(|q|<1)\$
$\mathbb E[X]=p\cdot\frac1{(1-q)^2}=p\cdot\frac1{p^2}=\frac{1}{p}$

[flat frigate]

feel_in_tears

[chrome knoll]

i got it right

[dim wraith]

but i think it's more like well known thing

[chrome knoll]

im in high school

discreet random variables and distribution rows are new to me

[dim wraith]

grade?

[chrome knoll]

10

this is from a new book aswell

[dim wraith]

do you understand what is geometric random variable now?

[chrome knoll]

much harder than the last one i was reading

[chrome knoll]

i grasped the concept

a few more practice problems wont hurt

this is my first time deriving out of context tbh

[dim wraith]

can you send book name pls

i want to read

[chrome knoll]

where r u from

[dim wraith]

russia

[chrome knoll]

toje

kazax ya

[dim wraith]

i had prob theory class but no exam

so exam about random variables was statistics

half year ago

[chrome knoll]

А Шыныбеков 10 класс Алгебра и начало анализа

[dim wraith]

there was prob spaces

[chrome knoll]

spaces of?

?

[dim wraith]

wdym of9?

[chrome knoll]

typo sorry

Anyway check that book out

its free

The books we study with at school is garbage

[dim wraith]

i mean random variable is function from prob space to R

[chrome knoll]

are u in uni

[dim wraith]

ye

[chrome knoll]

i see

[dim wraith]

or im not sure about this idk

[chrome knoll]

it should be any positive interger more than 0 and less than 1(for p)

and the x is just a variable

a discreet one

it shouldn't be negative either since mx will be negative aswell

[dim wraith]

Do you know integrals?