ug-maths-physics

[tawdry gull]

if i can i would

😂

[vestal swift]

can this be proven using the epsilon-N thing also

i did the ez way la but just curious haha

[tawdry gull]

honestly, series better dont use epsilon-N stuff

just stick to normal method

[vestal swift]

for sequence then use right ?

[tawdry gull]

yes

there are times when u use epsilon-N stuff in series

but most of the time not really

[vestal swift]

if i rlly need to, and a series converges then lim a_n = 0, then i use the epsilon-N thing or epsilon delta?

both also can ? coz kinda confusing when to use which one

[tawdry gull]

delta is used for functions...

[vestal swift]

Then here they are using epsilon-N twice?

For N_1 and N_2 😭

[tawdry gull]

kind of yeah

[vestal swift]

um so if I have a limit in terms of a_n and another limit in terms of a_n, when I do the epsilon-N thing I still use the same epsilon? Just change the N isit?

[tawdry gull]

use same epsilon

ur objective is to get <eps

[vestal swift]

but this q got 2 epsilon tho so i cant rlly tell need to change epislon or N :')

[tawdry gull]

you just set eps' to be in terms of eps

u dont actually need to define eps' and its ok

example like this

no need to write eps'

just straight away use the eps you want

[vestal swift]

Wait where the eps /B+A* come from ah :')

Why suddenly got A* and B*

[tawdry gull]

just some definitions

thats from my hw :v

no need to care what they are

the point is that u dont need to define eps'

[vestal swift]

if i don't define then just ce' then done?

[tawdry gull]

write e/(|c|+1) straight away instead of e'

[vestal swift]

Isn't it sort of defining also

[tawdry gull]

yeah

but u only have 1 epsilon

:b

[vestal swift]

As in the very beginning replace isit?

But how to know which eps to pick tho

It's not vv intuitive 😭

[tawdry gull]

sketch the proof first

then u know what to pick

proof is not always one try and then get answer

have to make a sketch then write the actual proof

[rancid schooner]

a context where sketch does not refer to graph 😄

[vestal swift]

got example ah

[tawdry gull]

the one i sent lol

i didnt know i need /B+A*

then i found out that i need

so just divide by B+A*

the trick is just to assume it's just eps

then at the end u get some constant*eps

[vestal swift]

But I don't see where the A*+B come from 😭😭

[tawdry gull]

so just divide by eps

[tawdry gull]

if u wanna know where it come from u have to read the continuation...

read from the bottom

[rancid schooner]

nice proof

[tawdry gull]

heres an interesting problem for u to do @rancid schooner

[rancid schooner]

AlexV can only do simple problems

[tawdry gull]

it is a simple problem

[rancid schooner]

A-Level problems :)

[tawdry gull]

it's not that hard to do

[rancid schooner]

maybe he should rename himself ALevxV 😄

[vestal swift]

how come |A_n-A| and |B_n-B| share the same eps?

[tawdry gull]

as defined here

[vestal swift]

So this comes before the first pic u sent?

[tawdry gull]

after

i alrdy defined A* and B* in the previous question

it's the sum of |an| and |bn|

[vestal swift]

But u need the proof in the next page to know that it's eps/ (A*+B) right nani 😭

[tawdry gull]

thats why i said

sketch the proof first

[rancid schooner]

nice question!

[tawdry gull]

i told you so 🙄

[tawdry gull]

making the proof =/= writing the proof

[vestal swift]

So it's like you actually write the one on the next page then go back and fill up the blanks? 😭

[tawdry gull]

yes exactly

LOL

[vestal swift]

I could never 😭

[tawdry gull]

thats how it is in real analysis 🫠

[vestal swift]

That's a problem for next year's me

😭😭

[tawdry gull]

there will be more epsilon stuff coming

so better get used to it from now

[vestal swift]

is this ur RA hw or Calc

[tawdry gull]

technically

this is calc

[vestal swift]

FML

I CANT EVEN CALC

[tawdry gull]

by hkust honors

this is honors calc

[vestal swift]

cant imagine how badly ill get fcked by RA

[tawdry gull]

normal calc doesnt have this

[vestal swift]

oh

got honors RA? :')

[tawdry gull]

yes

[vestal swift]

GG

[tawdry gull]

honors RA is a typical masters degree RA

[vestal swift]

is ur honors calc=normal RA

[tawdry gull]

yes

intro to RA

[vestal swift]

"intro"

[tawdry gull]

good luck with RA

:b

it is not easy for sure... 🫠

[vestal swift]

Idc I just need to worry abt calc now

😭😭

[tawdry gull]

your regular calc is harder than our regular calc

[vestal swift]

Hmm which part

[vestal swift]

This isn't in our notes

[tawdry gull]

our regular calc doesnt have the analysis aspect

[vestal swift]

But the sqrt q thing is

[tawdry gull]

no epsilon delta stuff

[vestal swift]

This was 2021 finals

[tawdry gull]

really?

[vestal swift]

Ye epsilon-N right whoops

[vestal swift]

Yes

[tawdry gull]

those stuff are discussed in our lectures 😭

then exam

[vestal swift]

It was the hardest q on the paper

[tawdry gull]

we need to do epsilon-delta-N proof

yes three of them at once

[vestal swift]

WTF

[tawdry gull]

my midterm just now

few weeks ago

[vestal swift]

I want ur brain 😭😭

[tawdry gull]

have epsilon-delta-N-B proof

🫠

[vestal swift]

Tf is B

K imma rot

[tawdry gull]

limit as x goes to infty

x>B

[vestal swift]

I pray that I will never touch that for my degree

[tawdry gull]

u actually might for RA 😂

[main topaz]

Uhh--- why u guyz tryna scare mee

[rancid schooner]

All thanks to Weierstrass. One of the two guys whose pics came out in your exam 😄

[idle rain]

Gave +1 rep to The_Pierrot#5106

[vestal swift]

I thought only alkali scares you

Lame joke k bye

[vestal swift]

Now I know not to underestimate the difficulty of maths mcq

[vestal swift]

6b math gods?

[tawdry gull]

this one is actually challenging lol

i finally got it

limit comparison test is useful here

but it's not easy to find out what to compare with

[vestal swift]

TEACH ME UR WAYS

[vestal swift]

Last year's finals 😭

[rancid schooner]

Study session by πerrot!

[tawdry gull]

using $(\sqrt{a_n}-\frac{1}{n^p})^2 \geq 0$, determine the values of $p$ such that $\sum \frac{\sqrt{a_n}}{n^p}$ converges. Use this for your limit comparison test

[round siren]

The πerrot

[tawdry gull]

of course, under the assumption that sum a_n converges

[vestal swift]

So p>½ then choose p= ¾?

[tawdry gull]

sure

[vestal swift]

Thank u math god 🫡

[idle rain]

Gave +1 rep to The_Pierrot#5106

[tawdry gull]

alrdy get?

[vestal swift]

Then by LCT the limit goes to zero right

[tawdry gull]

yes thats it

[vestal swift]

SMART AF

that is VERY BIG BRAIN

[tawdry gull]

technically only few lines proof 🤪

[vestal swift]

I asked my tutor

His solution too hard

[tawdry gull]

can i see?

[vestal swift]

HAHAHHA

NEXT LEVEL BRUH

[tawdry gull]

first assumption alrdy wrong tho...

take $a_n$ to be $\frac{1}{n}$ whenever $n=2^k$ and $\frac{1}{n^2}$ otherwise

[round siren]

The πerrot

[tawdry gull]

so sum a_n is a convergent series

@vestal swift

[vestal swift]

Kenmore understand :')

[tawdry gull]

it's bounded above by $\sum \frac{1}{2^n}+\sum \frac{1}{n^2}$

[round siren]

The πerrot

[vestal swift]

But still overall sum less than \sum 1/n right?

[tawdry gull]

overall sum ofc is always less than 1/n cuz 1/n diverges to +infty anyway 😂

so anything convergent is always going to be less than \sum 1/n........

[vestal swift]

Ok thank u big brain math god 😭

[idle rain]

Gave +1 rep to The_Pierrot#5106

[tawdry gull]

👍

[vestal swift]

How to even think of this during the exam

[tawdry gull]

i had to search up some ideas 😂

and then i came up with that

u cant even search that question online...

[vestal swift]

Ya I know

[tawdry gull]

like, i didnt find any stackexchange on that specific question

[vestal swift]

coz that's exactly what I did ahahha

[tawdry gull]

so just found some ideas

then make the solution up with them

[vestal swift]

Oops accidentally pressed

[tawdry gull]

🤨🤨🤨

[vestal swift]

Very fucked up finals

[stuck rapids]

So scary..

[rancid schooner]

Share your finals

[idle rain]

Help needed <@&597104882482413589>

[stoic pelican]

are you allowed to use a GCD for this question?

[stoic pelican]

I think its a divergent series

[blazing wraith]

what is gcd @stoic pelican ?

[blazing wraith]

so use divergent test?

howww

[stoic pelican]

graphical calculator

[blazing wraith]

nono

can’t

[stoic pelican]

I see

well I am not quite sure how to solve this

but with whatever limited knowledge I have

I think of the following stratergy

since 2^(n+1) will always remain larger than 2^n + 1

[round siren]

HRH LordFoogThe2st

[stoic pelican]

the term will always be larger than 1 and thereby always a divergent series

*divergent sum

[blazing wraith]

ohhh so by divergent test, since we know the sum will be always be larger than one, then this is divergent? @stoic pelican

[stoic pelican]

I think so :(

consider the following geometric sum

$$\sum_{n = 1}^{\infty} (a)^n$$

[round siren]

HRH LordFoogThe2st

[blazing wraith]

ahhhh here

[stoic pelican]

if $|a| > 1$, then the series would always be divergent

[round siren]

HRH LordFoogThe2st

[blazing wraith]

yep yep

[stoic pelican]

in this case

[blazing wraith]

so our r is inside the bracket

okay it’s alright how about from the graph side?

[stoic pelican]

$\frac{2^{n+1}}{2^n + 1}$ is always a positive number and is always more than 1 for $n \in N$

[round siren]

HRH LordFoogThe2st

[stoic pelican]

wait I'll send an ss of the graph

[blazing wraith]

oki

divergent test is about if you get the lim is 0, then convergent or divergent, otherwise it’s divergent correct right ?

[stoic pelican]

I think so

For any value of x > 0

2^{x + 1} is larger than

2^x + 1

Which means that their fraction —>

[round siren]

HRH LordFoogThe2st

[stoic pelican]

my analysis might be wrong tho

I am not 100% sure

[blazing wraith]

how is this more than one ? @round siren

@stoic pelican

[stoic pelican]

Because the numerator is always larger than the denominator

Look at the graph

The blue line (aka the numerator)

Is always larger than the denominator

(Aka the red line)

But….

If you don’t want to use a GCD

You can always prove it by induction

[blazing wraith]

and what’s induction 😅

[blazing wraith]

if it’s divergent, then the lines should be going towards each other right

[stoic pelican]

Away from one another

[rancid schooner]

For cooking dinner

[blazing wraith]

okay thank you!!

[idle rain]

Gave +1 rep to HRH LordFoogThe2st#7752

[stoic pelican]

Its a method of proving mathematical statements

just like direct proofs

and proof by contradiction

there is something called proof by induction

where you prove a value for the base step

and then go on to show that the value would be true for any other value k

[stoic pelican]

Also yay my first rep in UG

[blazing wraith]

oki oki

[tawdry gull]

Just show that the sequence doesnt converge to 0 => divergence

Cuz convergent series implies that the sequence converges to 0

[vestal swift]

Root test can? @tawdry gull

[tawdry gull]

Root test inconclusive

Term test is enough

[vestal swift]

Wait doesn't it give 2 😭
n√a_n = lim 2^(n+1)/(2ⁿ+1)
Then div by 2ⁿ top and bottom? So limit is 2 😭

[tawdry gull]

Eh, yeah thats possible too then lol

[blazing wraith]

so is it convergent or divergent? @vestal swift @tawdry gull

[tawdry gull]

Diverge

[blazing wraith]

but limit is 2????

[tawdry gull]

Have u learned term test or root test before?

[blazing wraith]

what’s term test again??

i don’t remember term test, but root test yes

[tawdry gull]

Convergent series means that the sequence must converge to 0

So if the sequence does not converge to 0, the series diverges

[tawdry gull]

Root test >1 means diverges no?

[rancid schooner]

@tawdry gull please consider doing a study session on series and convergence. Many people will be interested.

[tawdry gull]

Many = maximum 3

[rancid schooner]

I’m sure there will be more

[vestal swift]

@blazing wraith

[vestal swift]

I want real analysis or multivariable calc

[blazing wraith]

do you have full notes for all of the test? hahaha cuz my lecturer only gave my hand written ones 😢

[blazing wraith]

yep yep correct, so then this question we use root test??

[blazing wraith]

i am interested

[vestal swift]

Idk for your uni but we only use like 5
Integral test
Limit comparison test
Comparison test
Ratio test
Root test

[blazing wraith]

oooo

still share for me thank youu

i have more

geometric test, alternating series test

[vestal swift]

Yea that too

[blazing wraith]

but these 2 easy to remember

[vestal swift]

Nth term test ?

P series

[blazing wraith]

yes p series

[vestal swift]

I got ptsd from my calc finals

[blazing wraith]

what’s that again?

:(

[vestal swift]

Idk if it's against privacy policy to share them here HAHHA

[blazing wraith]

and i just started calc 2 and struggling with the tests

[vestal swift]

Maybe I'll dm u

[blazing wraith]

oki

tysm pls dm me

[vestal swift]

To show divergence

[tawdry gull]

root test or term test is fine

[rancid schooner]

maths major?

[blazing wraith]

no

[blazing wraith]

okie

[blazing wraith]

@rancid schooner @tawdry gull @vestal swift how to do this ?

@stoic pelican

[tawdry gull]

find the value?

[stoic pelican]

Hello there

I have no idea 😭

[blazing wraith]

don’t know how to cancel 🥲

[rancid schooner]

Anything missing from the second term?

[blazing wraith]

nevermnd

i think the question is wrong

[rancid schooner]

I thought so

[vestal swift]

HAPPY BIRTHDAY TO THE MATH GOD @tawdry gull

[tawdry gull]

🫠

thank youu

[vestal swift]

Have a great birthday π

[tawdry gull]

yes i had a great one :'D

[rancid schooner]

Happy birthday @tawdry gull !

[rancid schooner]

How do you know it’s his birthday?

[vestal swift]

Ig story HAHAHHA

[rancid schooner]

So you re an IG fan of πerrot :)

[vestal swift]

I just follow him and I have no life so I watch everyone's stories

His stories too much math

[rancid schooner]

did πerrot do anything mathematical for his birthday?

[tawdry gull]

nothing 🤪

[rancid schooner]

zero

very mathematical

did you have a circular birthday cake?

do you know how to cut a slice of cake and keep it fresh by not exposing the insides?

the mathematician/statistican francis galton actually wrote a paper/article showing a method of doing that. very clever.

https://galton.org/essays/1900-1911/galton-1906-cake.pdf

[rancid schooner]

in practice this works well only if your cuts are very accurate and perpendicular to the table, otherwise the two pieces won't fit perfectly.

having tried it myself 😄

[main topaz]

Interesting question

(haven't been able to solve it tho)

[tawdry gull]

Are u sure it’s just n+4 instead of 3^(n+4) ??

[blazing wraith]

it’s actually n+2 only , copied from my friend handwriting

already solved

[tawdry gull]

Oh i see

Okay then

[tawdry gull]

By finding function, find the closed form?

[rancid schooner]

What’s the answer?

[rancid schooner]

From one of your exams?

[stuck rapids]

@tawdry gull happy birthday!!!

Geniuss!!

[tawdry gull]

Homework

[tawdry gull]

Thank youu 🙏🙏

[idle rain]

Gave +1 rep to Crystopotato#7951

[rancid schooner]

Very clever question.
Surprising pattern.
Nice.

||= 1 + 2(1/2+1/4+1/8+…) = 3||

[verbal nova]

@tawdry gull happy birthday, master

[main topaz]

Most probably yes, this is from IYMC 2018 and they don't release the answers to the final questions so no idea what the answer is

[tawdry gull]

Thank youu 🙏🙏

[idle rain]

Gave +1 rep to Brave#5303

[long aurora]

wait this is actually really cool

how'd you find out about it?

[long aurora]

did it work at the end?

[rancid schooner]

😊

[rancid schooner]

read about it online sometime

[rancid schooner]

haha yes but the challenge, as mentioned above, is to ensure that both cuts are parallel

and ideally perpendicular to the table

[long aurora]

my hands are too shaky for that, it wouldnt work for me 😦

[rancid schooner]

a good maths problem would be to calculate the volume of cake cut out each time, for a certain given thickness of cut.

[long aurora]

what shape is a slice of cake

does it have a specific formula for its volume or would you need to derive it yourself

[rancid schooner]

probably have to do an integral 😄

[long aurora]

area of the triangle base into the height

[long aurora]

noo too complex

just basic V=A*L

[rancid schooner]

assume zero height, so what's the area cut out each time.

[long aurora]

...bye

[rancid schooner]

maybe someone can write a short python code to compute that. a nice problem for numerical analysis.

[long aurora]

ill keep that in mind for when i start undergrad

[rancid schooner]

@tawdry gull A variation on your question:
Evaluation the following, where a ≥ 2 is a positive integer.

[rancid schooner]

Birthday present for you 😄

[tawdry gull]

a+1?

based on my old working 🤪

[rancid schooner]

well when a=3, S=2 😄

[rancid schooner]

Hint: That is actually correct, for the numerator 😄

[toxic cape]

why is this C?

[idle rain]

Help needed <@&597104882482413589>

[rancid schooner]

See answer in #a2-further-maths-pure

[toxic cape]

yup

checked

[long aurora]

@rancid schooner what’s your favorite dish

Or kind of cuisine

[rancid schooner]

that is a trick maths question

[long aurora]

Then.. what’s the probability of asian cuisine being AlexV’s favorite?

[uncut edge]

Ramen 😄

[wary crow]

been stuck on this for the longest of time

but it seems too hard to ask on the A2 math channel so i thought id leave my last hopes with an undergrad solving it

[rancid schooner]

show your workings?

[main topaz]

||
a) let P be (at^2,2at)
use the parametric eqs to get dy/dx and use P to get eq of tangent and then T. Ig simple lengths of line segments can help prove the equality unless there is an easier way

b) P and Q lie on line y=2at and S and T on y=0 so they are both parallel. Hence angle QPT=angle PTS. triangle PTS is isosceles so angle PTS=TPS hence done

c) let U be on line PN on opposite side of N
NPM=UPQ (vertically opp angles)
UPQ=90-QPT
so NPM=90-QPT

SPN=90-TPS=90-QPT
hence SPN=NPM
||

for reference i drew parabola opening towards positive x axis

and P a point in the first quadrant

and N on the lower end of the normal PN

and umm did b and c geometrically mainly, not sure if u wanted em to be done algebraically

[rancid schooner]

(a) Just basic coord geometry. Parabola is y²=4ax, i.e. y⋅y = 2a(x+x), so tangent at P is y⋅2at = 2a(x+at²) which reduces to ty=x+at², so T = (-at²,0)
SP=PQ follows from the definition of the parabola ie distance from focus (S) to any point on the parabola equals distance from that point to the directrix (x=-a).
(b) Using the result from (a), SPQT is a rhombus, so this result follows.
(c) Using the parabolic reflector property of the parabola, i.e. incoming rays parallel to the axis are reflected towards the focus, S, this result follows.

[main topaz]

Parabolas have interesting properties. I should give them a look

[tawdry gull]

https://math.stackexchange.com/questions/74347/construct-a-function-which-is-continuous-in-1-5-but-not-differentiable-at-2/74383#74383

[main topaz]

The ||W|| reply lmaoooooo

[vestal swift]

stupid qs, why is this not m

[tawdry gull]

Typo i think

[vestal swift]

ok thanks math god

[idle rain]

Gave +1 rep to The_Pierrot#5106

[vestal swift]

Hi math gods, how did they get a^3? :’)

[rancid schooner]

v is a unit vector. So a² + b² = 1.

[vestal swift]

OH smh I am dumb af thanks sifu

[idle rain]

Gave +1 rep to AlexV#1811

[rancid schooner]

😊

[vestal swift]

Struggling to understand calc3, y'all have any vids rec? :')

[tawdry gull]

https://www.youtube.com/playlist?list=PLHXZ9OQGMqxc_CvEy7xBKRQr6I214QJcd

@vestal swift

[vestal swift]

Is this better than the khan academy one haha

Coz that one i think was taught by 3b1b

[tawdry gull]

no idea

[rancid schooner]

Is it about div, grad, and curl?

[vestal swift]

Rn I'm learning gradient vector, directional derivatives, partial derivative and stuff like that

[rancid schooner]

Sounds like fun 😄

[toxic cape]

is b) right ?

[idle rain]

Help needed <@&597104882482413589>

[main topaz]

One into one functions are ones in which all elements in the given domain are not used right?

[toxic cape]

one -one into is not used & one-one onto is used

what is injective surjective & bijective ?

@rancid schooner could you explain ASAP 🥲

@rancid schooner please

@rancid schooner I'll give you free rep

[rancid schooner]

anything for free rep 😄
https://en.wikipedia.org/wiki/Bijection,_injection_and_surjection

[toxic cape]

@rancid schooner thanks

[idle rain]

Gave +1 rep to AlexV#1811

[toxic cape]

@rancid schooner thanks

[idle rain]

Gave +1 rep to AlexV#1811

[toxic cape]

here

[tawdry gull]

@willow flicker funny behavior going on here

[willow flicker]

What happened?

[willow flicker]

Bro don’t ping so excessively, once only was enough da

[idle rain]

User warned!

@toxic cape has been warned for pinging a user excessively while repping

[tawdry gull]

👍👍

[toxic cape]

Dude @willow flicker check here

I asked him help

He is not responding

[tawdry gull]

and you thought everyone can respond quickly?

how about just wait and not ping? pinging excessively is annoying

[tawdry gull]

and this is so pathetic lol

[tawdry gull]

I honestly don't know how he got his reputed role lol

[toxic cape]

Fine I will not ping excessively

[swift zinc]

he has a lot of reps

[tawdry gull]

💀 i see

[tawdry gull]

@rancid schooner

interesting conceptual question

the task is to briefly explain the fallacy of the student

[rancid schooner]

nice

reminds you of a quenelle

https://en.wikipedia.org/wiki/Quenelle

good opportunity to use $\oiint$ and $\iiint$ :)

[round siren]

AlexV
Compile Error! Click the reaction for more information.
(You may edit your message to recompile.)

[tawdry gull]

,preamble

[round siren]

Your current preamble. Use ,texconfig to see the other LaTeX config options!

No custom user preamble set, using the default preamble.

% Required to support mathematical unicode
\usepackage[warnunknown, fasterrors, mathletters]{ucs}
\usepackage[utf8x]{inputenc}

% Always typeset math in display style
\everymath{\displaystyle}

% Use a larger font size
\usepackage[fontsize=14pt]{scrextend}

% Standard mathematical typesetting packages
\usepackage{amsfonts, amsthm, amsmath, amssymb}
\usepackage{mathtools}  % Extension to amsmath

% Symbol and utility packages
\usepackage{cancel, textcomp}
\usepackage[mathscr]{euscript}
\usepackage[nointegrals]{wasysym}

% Extras
\usepackage{physics}  % Lots of useful shortcuts and macros
\usepackage{tikz-cd}  % For drawing commutative diagrams easily
\usepackage{color}  % Add some colour to life
\usepackage{microtype}  % Minature font tweaks

% Common shortcuts
\def\mbb#1{\mathbb{#1}}
\def\mfk#1{\mathfrak{#1}}

\def\bN{\mbb{N}}
\def\bC{\mbb{C}}
\def\bR{\mbb{R}}
\def\bQ{\mbb{Q}}
\def\bZ{\mbb{Z}}

% Sometimes helpful macros
\newcommand{\func}[3]{#1\colon#2\to#3}

Page 1/2 · May 20, 2023, 12:24 PM

[tawdry gull]

$\oiint$

[round siren]

The πerrot
Compile Error! Click the reaction for more information.
(You may edit your message to recompile.)

[tawdry gull]

need to customize your preamble to use said integral symbols

,preamble \usepackage{esint}

[rancid schooner]

,preamble \usepackage{esint}

$\oiint$

[round siren]

AlexV
Compile Error! Click the reaction for more information.
(You may edit your message to recompile.)

Your preamble request has been sent to my review team.
You will be messaged when your request is reviewed (usually around 1-2 hours, depending on availability).
If you wish to retract your submission, please use ,preamble --retract.

[rancid schooner]

$\oiint$

[round siren]

AlexV
Compile Error! Click the reaction for more information.
(You may edit your message to recompile.)

[rancid schooner]

so not yet

[tawdry gull]

yeah 1-2 hours i guess

$\oiint$

[round siren]

The πerrot

[tawdry gull]

@rancid schooner

$\oiiint$

[rancid schooner]

nice. but why oval rather than circular?

[round siren]

The πerrot
Compile Error! Click the reaction for more information.
(You may edit your message to recompile.)

[rancid schooner]

$\oiint$

[tawdry gull]

it's like that

[round siren]

AlexV

[rancid schooner]

nice

[tawdry gull]

$\varoiint$

[round siren]

The πerrot

[tawdry gull]

this one is circular

[rancid schooner]

$\varoiiint$

[round siren]

AlexV
Compile Error! Click the reaction for more information.
(You may edit your message to recompile.)

[rancid schooner]

$\varoiint$

[round siren]

AlexV

[rancid schooner]

nice

[unkempt hemlock]

if he is not responding, then wait. the world doesn't revolve around u 😂

[stoic pelican]

i shouldnt have taken this role

visual pollution right there

u and alex are bots I’m so convinced

[tawdry gull]

i have actuarial notations in my TeXiT preamble lol

$\Vx[t]{\itop{\group{xy}}:\angln}$

[round siren]

The πerrot

[tawdry gull]

$\premium*[t]{\Ax*{x:\angln}}$

[round siren]

The πerrot

[rancid schooner]

Nice

Annuity

[stoic pelican]

keep flexing damn🙄

[tawdry gull]

u can add it too by urself

[rancid schooner]

Now do some continued fractions

[tawdry gull]

try typing ,preamble \usepackage{actuarialsymbol}

[tawdry gull]

can be done without any new packages

[stoic pelican]

okie

[swift zinc]

i cant believe

im learning stuff like laplace transforms

and still making mistakes like adding instead of multiplying

or forgetting minus signs

or powers

[rancid schooner]

You need to put them in la right place 😄

[deft tapir]

this bot's funny

[stoic pelican]

this 'bot'

I agree tho

[young marten]

I suppose part of it is cause the speed at which it spins is constant

and also gravity pulls us down

and ig gravity is stronger than the centrifugal force

[young marten]

like if earth was to just freeze and stop spinning

then likely we would be thrown off

but since it's constant we dont ig

kinda like when you're in a car

you're travelling quite fast

and then the car crashes

you would move forward

but when the speed is constant

you feel the forces less

or when a car is accelerating

not too sure though maybe someone else can confirm

[idle rain]

Gave +1 rep to (Standard Deviation) Male#2029

[young marten]

nws

yep

im not too sure about this part though

cause it's constantly changing direction

because you have forces from other planets too

and the sun

and the earth's orbit is an ellipse

so the velocity is constantly changing

ig maybe because

it acts on

earth

and us

so it isn't felt

i doubt it's subtle

it surely isnt

how so lol

even then not too sure but idts

because it effects its orbit

and direction

that's p big

I think it's because

those forces

act on earth and us

same time

so it balances out ig

but we'll see what someone else says too

fundamentally

I think it's because

the acceleration is negligible

well

i suppose there is but

i doubt it's big

and so we don't feel it, cause we feel acceleration not speed

like need something to compare to

back to the car example

if you were travelling in a straight road

at 200km/h constantly

and outside it's all just the same thing

youd feel you're going slow

like when you're in an airplane

cruising

but if you go from 0-120 in 5s or something

then that would feel like you're going fast

[young marten]

and i suppose reason for this is the forces are greater

[young marten]

as opposed to this

yes

because you respond to change more than anything

yep

well it isn't constant

but gravity

acts on us

and ig that is stronger than any other force

that would act on us

kinda but not balances, it keeps us grounded

if that makes sense

[rugged burrow]

1+1=3

Am i correct

[idle rain]

Help needed <@&597104882482413589>

[finite spear]

The rocket used a technique called spin stabilisation to stabilise itself as it travelled upwards. Controlling the direction of a rocket during ascent is difficult as there are many factors that can produce unwanted torque (e.g. an imbalance in thrust, strong winds, etc.). This torque can quickly cause a rocket to lose control or veer off course. Rotating the rocket about its central axis helps 'balance out' these forces, improving stability.

This is similar to spinning bullets in a rifle. The barrel of a rifle has small, spiral grooves in it that rotate a bullet as it passes through the barrel, improving the accuracy of shots.
https://youtu.be/M8ODXkYaJo8

To stop the rotation (usually before the payload is deployed), a yo-yo de-spin is used. This basically involves releasing two weights tied to wrapped cables on either side of the rocket. When they're released, they unspool and fling away, taking away some of the angular momentum of the rocket. This stops/reduces the rocket's spin so that the payload can be safely deployed.

Check this video out for more on spin stabilisation and the yo-yo de-spin:
https://youtu.be/ZKAQtB5Pwq4

_ _
Here is the full video of the launch (from UP Aerospace):
https://youtu.be/ceCnJLwMdFk

At around 3:47, you can see the weights being deployed:

The theory that there is a dome around the flat Earth (which is what the video is trying to promote) and that the rocket stopped rotating because it hit the dome is clearly false. The rocket would have been destroyed had it hit such a dome.

[willow flicker]

Can someone explain what this formula for calculating center of mass (CM)? I haven’t learned summations in A level maths

[idle rain]

Help needed <@&597104882482413589>

[sour otter]

sente of mass of?

there are many objects

[willow flicker]

The overall center of mass

[vestal swift]

Math gods, I don’t get the transition 🥹 why is it 0 and not 3 😭

[topaz ridge]

Did you get that ?

It's a formula don't ask how it i just know it's a formula to calculate the coordinates of the center of mass

Oh that i can help

This is for the x coordinate

Same way we can find the coordinates for Y and Z

What we did is we multiplied each mass with their corresponding x coordinate here

I think we learned this exact thing in o levels but not with coordinates... We placed some stones/weights on a horizontal scale than used this method to calculate where the center of mass of the scale would be... It's ok if you can't recall but this is the formula

[willow flicker]

ohhh so its basically like average, but involving x, y and z coordinates right?

[topaz ridge]

Yea

[blissful niche]

So u guys are in university right ? I had a question is university more burdened and tougher then A levels like very less time to do other things .

[stark wave]

Well generally it gets harder as you continue

[vestal swift]

@ mathgods is there an alternative proof for this or this is the only way?

[tawdry gull]

rigorously only?

i think thas alrdy the simplest way

[vestal swift]

Yes

[tawdry gull]

yeah i think only like that?

if by definition at least

[vestal swift]

Ok thank u math god 🫡

[idle rain]

Gave +1 rep to the_pierrot#0

[vestal swift]

What about this one

[stark wave]

Aww you just found it

Every kid who does thermo gets that

[buoyant notch]

wdym died by his own hand

suicide?

[stark wave]

Yep

[sour otter]

nah bro hand attempted murder

it got charged seperately

[buoyant notch]

lmao

[tawdry gull]

interesting question that came out in my finals

[flint gust]

Is this what imma be doing in uni

I am scared af

[tawdry gull]

only if u take honours courses 🤪

[sour otter]

Omg the ferrot

[strange wigeon]

what

[flint gust]

The “pie”errot

[sour otter]

No

Ferrot

[flint gust]

“Pie”errot

[sour otter]

But I called him ferrot n he never objected

[rancid schooner]

@tawdry gull How would you solve this:
Given three complex numbers a, b, and c, show that the equation of the circle passing through the three points on the complex plane is:

[rancid schooner]

would that be Fleming's Right Hand or Fleming's Left Hand?

[tawdry gull]

you're not the worst one to "mispell" my name

[rancid schooner]

in the same spirit it would be 𝜑errot :)

[sour otter]

omg yessss, 𝜑errot :)

[frigid mountain]

What can't a math major do? Support a family of four

[proper rapids]

That's the first thing u had to send @frigid mountain😂

[floral blade]

Dude come one

Okay, how about a physics major joke?

[mint tiger]

Therr were 2 channels before. You guys merged them?

[floral blade]

I can neither confirm nor deny your claim

@fickle bronze got any good books for the Fourier transform?

[fickle bronze]

Hmm not really - just lecture notes

[floral blade]

Coolio

[glass depot]

what has happened to this server

[fickle bronze]

Continued fractions

[blissful tundra]

Ayyy

[stoic pelican]

@frigid mountain see

[low dust]

test

roger

[blissful tundra]

@frigid mountain Explain yourselves

[stoic pelican]

Hey guys!

[floral blade]

Heyo!

[fickle bronze]

Hullo - ur username sounds familiar @stoic pelican

[glad oar]

Insta person

I said the same thing 😂

[fickle bronze]

Ahhh makes sense

[stoic pelican]

@fickle bronze we were friends on insta if you remember ZJ...Mo was our acquaintance...if you remember me probably by the label Photographer or Artist. I took a 6 months break from insta and then got back and contacted all my insta friends back. I contacted @znotes_revision too but no one replied. I recently got to know that a content creator handles your insta channel now...you got so big, I am so happy for yaa♥

[fickle bronze]

@stoic pelican yes I do remember! Aww okay - yeah sorry I took a break from Social Media too and let the guys handle it. Haha our Social Media following is still quite small but thank youu 💛

[stoic pelican]

Following actually don't matter because your intentions are nice and has an impact on even on a few people lives...💙 @fickle bronze

[stoic pelican]

physics =

maths =

[astral meadow]

Physics = Math + Science =
Math =

[tawdry gull]

=tex \sum_{n=1}^{\infty} \frac{1}{n^2} = \frac{\pi^2}{6}

[grave gust]

@tawdry gull there a 6 b4 that sign

And a square root

[fickle bronze]

@grave gust look at his equation, its not with pi as a subject. If u rearrange it u get the root n factor of 6. Nice LaTeX @tawdry gull 😉

[grave gust]

I totally understand everything you said

[tawdry gull]

Yes, i do LaTeX @fickle bronze

@grave gust if u were to make pi the subject, u would get just like the one u circled

[bronze latch]

Calculator 👌

[bronze latch]

Can you explain bois 😅

[silent palm]

it should be undefined, no? ∞ - ∞ = undefined @bronze latch

[bronze latch]

I found this...

But why

[silent palm]

@bronze latch bro, not the channel for this

[grave whale]

Help

<@&597104882482413589>

[grave whale]

???????????

[ivory locust]

Differentiate and find the values of x where dy/dx = 0

Then differentiate again and substitute the values you found into it

@grave whale

[grave whale]

Yeah I got it

Thanks

[zenith fjord]

@bronze latch that's true

there are different infinities

check out some videos about it

[floral blade]

Hey everyone!

I'll be working on linear and vector analysis from the 8th to 13th

Feel free to join in via VC or anything else

I'll try uploading some notes of it too

[floral blade]

-1.) https://www.youtube.com/playlist?list=PLZHQObOWTQDPD3MizzM2xVFitgF8hE_ab
0.) https://brilliant.org/courses/linear-algebra/
1.) https://www.coursera.org/learn/linear-algebra-machine-learning
2.) Advanced Engineering Mathematics - Erwin Kreyzsig
3.) Linear Algebra done right - Sheldon Axler
4.) Mathematical methods for physicists - Weber and Arfken
5.) Introduction to Linear Algebra - Gilbert Strang
6.) Appendix I, Quantum Mechanics - David Griffith
7.) Introduction to Mathematical methods - Charlie Harper
8.) http://physics-ref.blogspot.com/search/label/Linear Algebra

Stuff for linear algebra

-1 = Noob level
0 = Beginner
1 = Wannabe
Then you get better as you progress

[floral blade]

https://www.livescience.com/schrodingers-cat-can-be-peeked-at.html

[floral blade]

Hey everyone!

So I'll continually upload problem sets on everything that I'm working on

Lol

[stark wave]

@tawdry gull @fickle bronze

[tawdry gull]

I want

[floral blade]

@tawdry gull this one's for you

https://www.youtube.com/watch?v=747zoPEakZw

[tawdry gull]

i saw that alrdy haha

[floral blade]

Lol mb

[grave whale]

yo

this dude really watches math vids on youtube

🤣

[floral blade]

Yups

Why not?

[thorny sphinx]

😂

[fickle bronze]

https://writings.stephenwolfram.com/2020/04/finally-we-may-have-a-path-to-the-fundamental-theory-of-physics-and-its-beautiful/

[floral blade]

@cunning olive this is a better place to discuss

So um the equation is a differential eq

[cunning olive]

ah i seee

[floral blade]

Lemme sort this out

So um this is the equation for it

$$a = -\frac{g}{L}Sin(\theta) $$

[floral blade]

Where a is the acceleration

What you have is an equation describing a bunch of pendulums trying to oscillate at the same time

From what I can see

Also @cunning olive you can use Mathematica to simulate it

[cunning olive]

ooo yes this formula, im using it too

can you elaborate a bit on the angular velocity? @floral blade

[floral blade]

So velocity in general means the rate of change of sth

[cunning olive]

right

[floral blade]

Angular velocity is simply the rate of change of the angle

[cunning olive]

so we have 2 angular velocities here, 2 masses, 2 lengths for each of the arm respectively

[floral blade]

i.e the displacement from the normal position

Can you show me a diagram

Do we have two arms?

[cunning olive]

um one moment

[floral blade]

Suree

@cunning olive you've studied calculus right?

[cunning olive]

n-nope

[floral blade]

Ah okay

I mean it's okayy, you'll learn it sometime in the future

So um this is the general picture

[proper rapids]

Pugazh lecture through tests

wow

[cunning olive]

this is just a rough picture of how its supposed to look like, it calculates values, makes new values and plots them

[astral meadow]

Yay math and physics

[floral blade]

Yupp double pedulum

[floral blade]

https://proofwiki.org/wiki/Main_Page

@tawdry gull check it out

[astral meadow]

Did this get renamed

[floral blade]

LOL

[stark wave]

😂 😂 😂

[floral blade]

At least it's honest

[bronze latch]

Lmao

[floral blade]

https://www.youtube.com/watch?v=fCi195e9QD4

Superhuman indeed

[floral blade]

https://www.youtube.com/watch?v=hpjwotips7E

Slick intro lol

[floral blade]

❤️

[warm agate]

💙

[midnight river]

That

Was beautiful

[floral blade]

https://vimeo.com/425261787

A PhD student explains her thesis in general terms

[astral meadow]

ooh interesting

[formal stone]

Niceee

[wooden imp]

How do i get an equation of the circle with only the x and y intercepts given?

<@&597104882482413589>

[floral blade]

$$(x-h)^2 + (y-k)^2 = r^2$$

[wooden imp]

hmm... how would the x and y intercepts be used to solve the equation?

[stark wave]

you have three values to solve for three variables

[spring cedar]

when x= -3, y=0
when x= 7, y=0

[wooden imp]

alright... so, when y = 3+- square root of 30, then, x = 0?

[spring cedar]

yib

try it out, h=2, k=3 and r²=34

[wooden imp]

ok...

alright... the answer seems to be correct, but how did you get the h, k and r^2 values?

[blazing temple]

Wha is there a question

I got a ping

[spring cedar]

Use the equation above,
replace x with -3 and y with 0
(-3-h)² + (0-k)² = r²
(7-h)² + (0-k)² = r²
hence,
r² - k²= (-3-h)²
r² - k² = (7-h)²

(-3-h)²= (7-h)²

[floral blade]

Ooh okay

[wooden imp]

ah... then you expand it into quadratic form, and solve for h and k?

[floral blade]

Um no

You'll zero if you follow the last eq

You may need to iterate

[spring cedar]

h² will cut off so np

[wooden imp]

i got h as 2.

so, i'll have to the same thing for k?

[spring cedar]

yes

[floral blade]

Oh yes

Mb

[spring cedar]

do not square tho,
(3+√30 - k)² = (3-√30-k)²
do,
(3+√30 - k)= + or - (3-√30-k)

In either one, k will cut off, so use the other equation to find the value of k

[wooden imp]

i got k = 3.

[spring cedar]

Nice, now find the value of r² from any of the equations

[floral blade]

Yup

[wooden imp]

hold on... how do you get r squared?

[floral blade]

$$(x-h)^2 + (y-k)^2 = r^2$$
you use this bad boi

[floral blade]

Guys, watch out for these "Blackboard lunch type" lectures from KITP

https://www.youtube.com/watch?v=Qv-2RHekbPY

They actually breakdown advanced concepts in simple language

This is similar to the lunch talks from IAS

[wooden imp]

how do i find the centre of y = 2x-13?

<@&597104882482413589>

[spring cedar]

Do you have the final answers?

[blazing temple]

@wooden imp The tangent to a circle is always perpendicular to the radius (just a geometric property of the circle); so you want to find the equation perpendicular of y=-3x+57 passing through the point (16, 9) (use y-y1=m(x-x1)). Then that line will intersect with y = 2x-13 to give you the centre... if I'm not being stupid

[spring cedar]

m=1/3, As for perpendicular lines m1*m2=-1

[blazing temple]

Yesyes

Oh and the radius is just the distance formula from the center

[wooden imp]

here's the question (w/ the answer)

[blazing temple]

Ye so just method above and you'll get the correct answers

[floral blade]

https://www.youtube.com/watch?v=WWTvNlfkvoI

Skepticism 💯

[slender bear]

MATH IS WRONG MATH IS WRONG

SO I STUDIED SANDWITCH THEOREM TODAY OK

AND IF THE ANGLE X IS ZERO DEGREES THEN THE DENOMINATOR WOULD ALSO BE ZERO

IE NOT ONE

MATH IS WRONG MATH IS WRONG

[floral blade]

Well math is made up so that is allowed-

[slender bear]

but- i fell in love w math BEC it's never wrong

like in algebra no matter which method u take the answer is always he same as long as your math is right

[floral blade]

Well here's the thing math will do anything to be logically consistent

It's not wrong per say in this case esp

Well the trouble always comes with evaluating limits at the beginning

Like each method has a place where it works and where it doesn't

Similar case for Differential Equations

Most of them are unsolvable/don't converge

We care about convergence so we have to make up ad hoc rules sometimes

[slender bear]

i lost u after differential equations bec we're just starting in in calculus. i'll visit this again when i learn more
but what you're basically saying is i didnt prove math wrong? 😔😔😔

[floral blade]

We invent rules to be consistent that's

https://www.youtube.com/watch?v=p_di4Zn4wz4

This might help you learn differential equations

But it's good that you hate it

[slender bear]

i dont hate it sir

it's v interesting

let me watch

[floral blade]

Haffun

[woven wraith]

http://www.phidiastech.com/2020/06/physics-and-engineering-breakthroughs-in-2020/

[wooden imp]

in the case of the directrix being 4 units above the focus, does this mean that the directrix is (x+4, y+4)?

<@&597104882482413589>

[blazing temple]

@wooden imp iirc, the directrix of conic sections can only be "below" the focus, and its not a point; its a line.

[wooden imp]

Find equation of parabola in standard and general forms that satisfy the condition:
Vertex (0, 0), axis horizontal and passes through (4, 2)

<@&597104882482413589>

[blazing temple]

@wooden imp Sorry for the very late reply, did you get the last question?
For this one, what I think you have to do is:
The general form of the parabola is y = 4ax^2

So you can plug in (0,0) and (4,2) into that

You'll get some simultaneous equations, then you can solve them

I think?

Nvm ignore that

I'm dumb

[wooden imp]

plugging in (0,0) would probably give out 0.

[blazing temple]

Hmm

Yeah

Lmao

I'm so sorry lol whoops

Wait no nvm yes if you plug in (4, 2) you'll get the value of a so yes

[wooden imp]

when i plug in (4,2) into (y-k)^2 = 4p(x-0), which would be the equation if the parabola were to open right (given that it meets in the horizontal axis), i get this value:

k^2-8k+16 = 8p

[blazing temple]

Yes but the vertex is (0,0), and since in the form (y-k) = 4a(x-h)^2, the vertex values of k and h are both 0

[wooden imp]

hm... how are we gonna get the p value?

[blazing temple]

Just plugging in the point (4,2) into y = 4ax^2

Oh god am I being dumb, sorry I'm not the best at this ahaha

[wooden imp]

but what does it mean when the parabola is "axis horizontal"?

[blazing temple]

Ok I think that means that its axis of symmetry is horizontal (so the x-axis)... which means I was wrong

[wooden imp]

for a moment, i was thinking "wait... i think that the axis of symmetry is not on the y axis", meaning that the parabola can open either upward or downward.

[blazing temple]

So the general form for a parabola that opens sideways (which has a horizontal axis of symmetry) with vertex (0,0) is y^2 = 4ax right.... am I remembering that right?

@wooden imp

[wooden imp]

this is what one of the powerpoints for the topic i found

[blazing temple]

Ah

So I was taught y^2 = 4ax, with a as the focal length (i.e. the distance from the focus to vertex) rather than p

So I think if you plug in the point (4, 2) into y^2 = 4px, you'll get the equation of the parabola

So;
2^2 = 4p(4)
4 = 16p
p = 1/4

Therefore the equation is y^2 = x

@wooden imp Is that right?

[wooden imp]

well, i guess this is correct....

[blazing temple]

Looll sorry I botched everything several times @wooden imp Did you still need help with that other question?

[wooden imp]

here's another one that i may need help on:
Vertex (5, 2), axis vertical and passes through (4, -2)

[blazing temple]

Ok so general form of the parabola that is vertical is

[blazing temple]

Where (h,k) is the vertex

So we know that its (5,2) so

[blazing temple]

Then plug in the point (4, -2) to get a, and then you've got the parabola

@wooden imp

[wooden imp]

is a = -1/16?

[blazing temple]

I think so

Ye checks out

[wooden imp]

so, the answer is (x-5)^2 = -1/16 y?

[blazing temple]

Nonono

The answer would be

[blazing temple]

@wooden imp

[wooden imp]

now, a last question, which is a word problem:

An arch in the form of a parabola has a height of 25 ft
and a span of 40 ft. How high is the arch at a distance 6 ft
from the center of the span?

[blazing temple]

@wooden imp Ok so here's the situation I'm imagining

So we wanna find the equation of this parabola

The x-coordinate of the parabola doesn't matter (its the same height), the y-coordinate is 25 because the height is 25, so the vertex is (0, 25)

At least that's what I've chosen for convenience

[wooden imp]

so... would a span of 40 ft be the directrix?

[blazing temple]

The "span" I think refers to the width of the parabola at the base rather than the directrix

So that means at y = 0, x = 20 and -20, giving an overall "span" of 40

Plug all that into the general equation of a parabola and you'll get the value of a, and therefore the equation of the parabola

[wooden imp]

so, i'll plug both (20,0) and (-20, 0) to get two equations?

[blazing temple]

Nonono you can choose one

[wooden imp]

i'll choose (20,0)

[blazing temple]

You'll end up with the same a value because you're squaring the x value anyways

[wooden imp]

400-40h+h^2 = 4a(0-k)

[blazing temple]

Yes and remember the vertex (h, k) is (0,25)

[wooden imp]

i got h = 20

[blazing temple]

Wait wdym

So you should have that the vertex is (0, 25) and at x=20, y=0

So

[blazing temple]

So the equation is

[blazing temple]

@wooden imp

[wooden imp]

thanks, @blazing temple.

[blazing temple]

Np!

[wooden imp]

tbh, i have never learnt about conic sections until a few weeks ago

[blazing temple]

Ye it's just a bit of practice, the stuff is pretty confusing

[wooden imp]

indeed...

[floral blade]

😂

[floral blade]

https://home.cern/news/press-release/physics/particle-physicists-update-strategy-future-field-europe

YESSSS

[floral blade]

plot are awesome-

[peak shard]

Ooh matlab quiver? 😍

[floral blade]

yesss 😍

||Mathematica actually but yee||

[thin basalt]

nice vector field

[floral blade]

yepp

[peak shard]

What's this for electric fields?

[floral blade]

just fields

I did make one for electric fields tho

Lines = electric field, Circles = potential

[peak shard]

Nice

Is it feasible to do quiver arrows and also mountaineous 3D potentials?

Can't remember if the functions works together, or maybe cuz there's just too much stuff on one plot 🤔

[thin basalt]

uhm

right

2 questions

provided that someone is actually willing to solve them

[floral blade]

umm okii

[thin basalt]

parsec's my savior

[peak shard]

My brain hurts seeing that 😂

[floral blade]

parsec's my savior
@thin basalt I haven't started ma'am, hold up 😂

lemme start

[thin basalt]

even though I'm an impatient person

but there's no need to hurry

take all the time you need

[floral blade]

passive aggressive threat I see

[thin basalt]

tHrEaTs ArE rElAtIvE

[floral blade]

😂 😂

Oh no the AdI virus

[peak shard]

=wolf integrate 1/[(x-2)^(3/2) (x+1)^(1/2)] dx

Oh woah wolfram can handle it