help-0

[wide tartan]

you'll get (3/4) / (1/2)

[upbeat pilot]

why?

[wide tartan]

yeah here is what is going on visually:

[upbeat pilot]

oh, because it is 1x^2

[wide tartan]

yeah

[upbeat pilot]

ok

[wide tartan]

okay so now we can simplify (3/4)/(1/2)

[upbeat pilot]

3 / 2

[wide tartan]

and how do we divide fractions? well we flip the bottom one and multiply them.

yeap

yep

[upbeat pilot]

Ok

But

i thought i had to make 3 / 4 and than make 1 / 2

[wide tartan]

why?

I think you did it just fine

[upbeat pilot]

(3/4)/(1/2)

When I have a fraction / fraction, i have just to simplify all the things?

[wide tartan]

you're allowed to simplify everything yes

and you want to in this case

[upbeat pilot]

but if i make the first fraction, the second fraction and then make the fraction with the result of both fractions i will get the same answer?

[wide tartan]

yes, you'll get 2 - 1/2

in the end

if you're saying what I think you're saying

[upbeat pilot]

but it wouldn't be 3/4

so when i have fraction/fraction i have to simplify

[wide tartan]

no it wouldn't be 3/4

[upbeat pilot]

alright then

[wide tartan]

sorry what is "it" here?

[upbeat pilot]

2 - 1/ 2

[wide tartan]

no 2 - 1/2 is 4/2 - 1/2 = 3/2

[upbeat pilot]

ok

that makes sense

thank you very much

have a great day

[wide tartan]

u2

[upbeat pilot]

.close

[lone heart]

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[frail ingot]

Problem:
For a circle with a given radius, and 2 points present within that circle
Point 1: is always centered at 0,0 within the circle
Point 2: is dynamic, can be positioned anywhere within the bounds of the circle
The objective is to move P2 towards P1 following a given (arbitrary) trajectory
So the value I'm looking for is the next step, the dx and dy from where the point currently is, to where it needs to be
Complications:
The origin of P2 (it's last position or its trajectory's intersection with the circle) is unknown
The intersection between the trajectory and the circle is the origin
Specifications:
In this case, the trajectory is a sin curve

does anyone have an idea on the steps I need to take to resolve this problem?

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[frail ingot]

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[raven crag]

5 < x < 7

x < 4 < 6

[summer dirge]

this is redundant! if x is less than 4, it's always less than 6

[raven crag]

alright

x < 4

(y < 4) ⋀ (y^2 < 9)

y is less than four
the square of y is less than 9, so
y is less than 3, or less than -3

(y < 4) ⋀ ((y < 3) ⋁ (y < -3))

A ⋀ (B ⋁ C)

not sure how to draw this relationship with arrows of category theory

A ⋀ A can be written as AA, which is an identity function (?), as it equals to itself, or A

i don't know if B ⋁ C is an exclusive or, or an inclusive or

if y is less than 3, then y is less than 3
if y is less than -3, then y is less than -3

A -> A

B -> B

if (y = 2), then (y^2 = 4) ∴ (y^2 < 9)
if (y = -100), then y^2 = 10000 ∴ y^2 ≮ 9

values between -3 and 3 return True for y^2 < 9

a < y < b

-3 < y < 3

(y < 4) ⋀ (-3 < y < 3)

[raven crag]

(y < 4) is redundant,
because (y < 3),
∴ (-3 < y < 3)

(x ≥ 0) ⋀ (x ≤ 0)
x is both greater and less than 0, and it is 0, at the same time, therefore x is 0

this can be written as x = 0

this is the mathematical world, in which everything is nothing

and where nothing is everything

0 < π < 10
π is greater than 0, but less than 10

7 ≤ p < 12

• p is less than 12, and it is greater than, or equal to 7
• 7 is less, or as much as p, while p is not so much as 12

[lone heart]

@raven crag Has your question been resolved?

[raven crag]

5 < x < 7
Five is not as much as something, while something is shy of seven.

x < 4
an unknown value is related to a number

3 > y > -3
There is a relation R 3 R y, and y R -3, so ∃ 3 R -3

x = 0

this is from Joyner, D Adventures in Group Theory

[raven crag]

φ1 ⋀ φ2 → q
can be written as p → q
p is a conjunction, and a conjunction is true, when both φ1, and φ2 statements are true

i don't yet know how to relate φ1 to φn

data:

• objects: a collection ob C of statements
• arrows: for statements p, q ∈ ob C, a collection C(p, q) of arrows arrow from p to q

structure:

• identities: for any statement p ∈ ob C, an identity arrow identity arrow from p to p
• composition: for any statements p → q → r, a composite arrow g o f: p → r

[lone heart]

@raven crag Has your question been resolved?

[raven crag]

properties:

• unit laws: for any arrow p to q, f after 1p = f = 1q after f
• associativity: for any arrows a -> b -> c -> d, (h o g) o f = h◦(g◦ f)

[raven crag]

Conjunction

φ1
φ2
...
φn
∴ φ1 ∧ φ2 ∧ . . . ∧ φn

i don't understand what shows the transitivity of conjunctions, and how to show that an infinity of premises are true

<@&286206848099549185>

φ1 ∧ φ2 ∧ . . . ∧ φn what are different strategies to show this conjunction is true?

specialisation

p ∧ q
∴ p

φn has to be true for the conjunction to be true

in fact, every premise has to be true

proof by induction

• base case: prove ϕ1 is true
• inductive hypothesis: assume ϕ1 ∧ ϕ2 ∧ … ∧ ϕk is true for some k
• inductive step: show that if ϕ1 ∧ ϕ2 ∧ … ∧ ϕk is true, and ϕk + ϕk+1​ is true, then ϕ1 ∧ ϕ2 ∧ … ∧ ϕk ∧ ϕk+1 is true
• conclusion: by induction, ϕ1 ∧ ϕ2 ∧ … ∧ ϕn is true for all n

this completes the proof using mathematical induction

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[spare aurora]

How can i start doing addition and subtraction faster

[near chasm]

by doing more addition and substractions

you can find some addition and substaction worksheets from the internet and stuff

[tight pier]

You can do addition faster by multiplication.

It's fast to do 15 x 10 than add 15 ten times itself

[spare aurora]

no like for example

73+99

i wanna be faster by doing that

[tight pier]

Oh

[spare aurora]

Yeah

[hearty hazel]

theres too many things you could say

[tight pier]

I usually give up

[spare aurora]

isn't there a way to do addition and subtraction faster

like a method

[hearty hazel]

add the tens

then add the ones

or just use a calculator idk what to tell u

[dawn glade]

9+3 = 12 put 2 in the second place then 7+9 and add the one from soo 172

[dawn glade]

i think they wanna be faster at doing it from head

[hearty hazel]

like from 73 + 99 --> (70 + 90) + (9 + 3) = 160 + 12 = 172

[empty cedar]

practice is probably a good way to start

[spare aurora]

Exactly

[hearty hazel]

is basically the strat i use

[near chasm]

put them down like this and start from right to left

[dawn glade]

then follow this

[dawn glade]

.

[dawn glade]

.

[hearty hazel]

but just yeah just flesh out some addition questions

[empty cedar]

for subtraction good luck lo

[hearty hazel]

for this i'd go 28 - 20 + 1

[dawn glade]

tbh i add while substracting as well lmao

[near chasm]

oh i see

[dawn glade]

i do 19 + 1 and 20 + 8 so 9

lmao

[near chasm]

yeah if you are trying to do stuff on your head you can round the numbers and do the multiplication

[near chasm]

or you can put them under like this to the paper then do the calculation which will minimize the amount of things you need to think

if it make sense

[lone heart]

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[cinder parcel]

What are some examples of functions that are Lebesgue integrable but not Riemann integrable? Except the Dirichlet function on rationals and non rationals

[minor pier]

Thomae's function

[lone heart]

@cinder parcel Has your question been resolved?

[cinder parcel]

@minor pier thanks but it is still a derivative of dirichlet function and very similar. I am looking for some entirely different example

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@cinder parcel Has your question been resolved?

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@cinder parcel Has your question been resolved?

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@cinder parcel Has your question been resolved?

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[sick oracle]

como consigo falar em um canal em portugues?

[manic agate]

falando

mas a maioria da rapaziada aaqui é gringa

joga no tradutor ou a imagem do problema que eles podem te ajudar

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[upbeat pilot]

how do i find the answer

<@&286206848099549185>

[exotic belfry]

do you know the intercept theorem (AKA thales theorem)?

[upbeat pilot]

No

[exotic belfry]

maybe with this picture?

[upbeat pilot]

I'll search later, but I don't know yet

[exotic belfry]

As E is a midpoint, so AE is half of DC, the intercept theorem says now that GA is half of GD. (in your example)

[upbeat pilot]

Sure

[exotic belfry]

you can do the same with F.

[upbeat pilot]

With E too

[exotic belfry]

so you get a relation from GH to AD.

[upbeat pilot]

so ad is half of gh

[exotic belfry]

no.

[upbeat pilot]

why

[exotic belfry]

ad is a half of GD.

[upbeat pilot]

oh

that makes sense

but why ad is not half of gh

[exotic belfry]

AD is half of GD, GH is bigger then GD, so AD cant be the half of both.

[upbeat pilot]

oh

of course ha

what i am thinking here is

gea + ief + aefd + fdh = gih

i think i can do something with this information

[exotic belfry]

thats true, but you are overcomplicating it. its much easier

[upbeat pilot]

oh, really

[exotic belfry]

you need a ratio of two areas. first think about the formalas for this two areas.

[upbeat pilot]

triangle = b * h / 2

parallelogram = b * h

[exotic belfry]

yes, but you should keep in mind that the b and the h are different. to solve your example you need the ratio of the two b and the two h.

lets start with the b.

what is b in the parallelogram and what in the triangle

[upbeat pilot]

triangle = gh

parallelogram = ad

[exotic belfry]

well, now we need a relation gh:AD

[upbeat pilot]

1/3

ad * 3 = gh

[exotic belfry]

well. now about the h.

[upbeat pilot]

3/4

the parallelogram h is 1/4 bigger than the triangle h

yes

[exotic belfry]

now put all together.

[upbeat pilot]

are we talking about sum?

1/4 + 1/3 = 7/12

it is division right

[exotic belfry]

lets say the traingle is b1 x h1/2 and the parallelogram is b2 x h2

[upbeat pilot]

ok

[exotic belfry]

if you tka the ratio triangle / parallelogram you get b1 / b2 times h1/h2 times 1/2

b1/b2 was ,,,
h1/h2 was ,,,

[upbeat pilot]

1/3 / 2/3 * 3/4 / 1/4 * 1/2 = 3/4

[exotic belfry]

b1/b2 was 3
h1/h2 = 3/4

so you get 3 times 3/4 times 1/2

[upbeat pilot]

wait, b1/b2 = 3?

[exotic belfry]

you said this.

so gh/ad = 3

[upbeat pilot]

ok

9/8

[exotic belfry]

👍

[upbeat pilot]

ok

can you tell me how did you discovered that?

[exotic belfry]

what exactly?

[upbeat pilot]

I didn't know what i had to do to discover the result, but you did it so fast

[exotic belfry]

its only intercept theorem.

and practice.

[upbeat pilot]

all that we did was the intercept theorem?

[exotic belfry]

yes to get gh/ad = 3 you use the intercept theorem twice. once for the left side (with E) and then for the right side (with F.)
and then once for the height (if you use the line EF)

so 3x intercept theorem. thats all.

)ok, 4 times there is one hidden application)

[upbeat pilot]

what is this hidden application?

[exotic belfry]

in fact you need it alos for the height twice.

[upbeat pilot]

for half of bcfe right?

[exotic belfry]

exactly.

[upbeat pilot]

just to remember, we firstly discovered the b of both polygons, then the height of both polygons, discovered the area of both and divided?

[exotic belfry]

yes

[upbeat pilot]

we done this, but we could find the area first and then divide the areas right?

[exotic belfry]

you dont know the areas, as you dont know the exact value of e.g. AD. you only know ratios and you are asked for a ratio.

[upbeat pilot]

(( b1 * h1 ) / 2 ) / (b2 * h2) = b1 / b2 times h1/h2 times 1/2?

[exotic belfry]

( ( b1 * h1 ) / 2 ) / (b2 * h2) = b1 / b2 times h1/h2 times 1/2?

[upbeat pilot]

yes

ok

that is it

thank you

[exotic belfry]

youre welcome

[upbeat pilot]

.close

[lone heart]

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[hidden oyster]

is the concept of infinity binary?

[lone heart]

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[hidden oyster]

.close

is the concept of infinity binary?

[merry depot]

what do you mean by binary?

[hidden oyster]

like it sounds weird, but i watch like anime and people say a specific character has boundless power, like infinite power.

But how does it work that he punshes weakly then

[limpid turret]

You should reopen if you plan to keep asking for help

[hidden oyster]

oh how?

[limpid turret]

.reopen

[hidden oyster]

.reopne

.reopen

[limpid turret]

oh

!msgdel

[lone heart]

The original post of this help channel has been deleted, and it will abruptly close and possibly lock. (This is irreversible.) Please claim a new channel, and don't delete the first message of any future channel you claim.

[cinder tundra]

This channel cannot be reopened

[hidden oyster]

i just typed "hi" and then deleted it, i didnt know how that works

[cinder tundra]

Anyways, the question does not make sense in my head

[hidden oyster]

no let me explain

imagine you have infinite power, like actually boundless power

[limpid turret]

Open a new channel

[hidden oyster]

how

[limpid turret]

#❓how-to-get-help

[cinder tundra]

Like you did with this one

[livid sage]

we applying anime logic to real life with this one

[limpid turret]

!occupied

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[hidden oyster]

is the concept of infinity binary?

[merry depot]

you're gonna have to give some context to this question....

[empty cedar]

whar

[hidden oyster]

imagine having infite power in your arms, can you punsh weak then?

[merry depot]

what do you mean 'can you punish weak'?

[limpid turret]

punsh weak?

punch?

[empty cedar]

i mean very big strong guys with big muscles can lift up big weights but can also lift up a pencil so

i suppose yes

[hidden oyster]

like can you just slap someone light

[merry depot]

sure

[cinder tundra]

Control of strengh is a different thing

[hidden oyster]

but with infinite power? you cant just say something is fewer infinite or can you?

[cinder tundra]

Infinite is not a number

[limpid turret]

That's a subjective question, and not really mathematical. But to answer your question, there's two ways to look at it:
If you have infinite strength, then

1. Every action you do will be some percentage of your total power, so every action will have infinite power, or...
2. Strength is a reservoir you draw from, and if that reservoir is infinitely deep, then you can output strength at any level you desire

Which outcome depends on the anime writing team

[merry depot]

so, if this person moves at all they must use all of their strength with every movement?
taking one step explodes the planet?

[hidden oyster]

thats what im saying, either you have infinite strength or you have not

[cinder tundra]

You cannot have infinite strengh cause

[empty cedar]

where does math come into this other than the word "infinite"

[cinder tundra]

Have is measurable

Infinite is not with measurable things

[hidden oyster]

but if we would put it in real life

[limpid turret]

then it's nonsense because infinite strength does not exist in real life

[hidden oyster]

theoretical?

[cinder tundra]

Neither

[hidden oyster]

space is infinite right?

[cinder tundra]

How do you know?

[hidden oyster]

i dont know, thats why im asking to make sure

[empty cedar]

This is quite the mathematical conundrum

I have a marvelous proof of everything you said but its too short to write in this discord message

[cinder tundra]

Strengh is measured with energy in the end

[merry depot]

infinite space and infinite energy are different things.

[cinder tundra]

Energy cannot be infinite

[limpid turret]

Physicists are presently unsure whether space exists beyond the known universe (which is finite in size)

[limpid turret]

!redir

[lone heart]

This channel is only for on-topic discussion. Please take casual conversation to #discussion or #chill.

[hidden oyster]

if i just put an x for energy there are infinite numbers for it or arent there?

[cinder tundra]

Number is not equal to energy

[limpid turret]

yes, but that does not mean energy is infinite. And the amount of energy is still bounded

[cinder tundra]

You can say the same with potatoes

[hidden oyster]

what is the bound then? what is the final number for it?

[limpid turret]

Not quite. Potatoes are discrete, but energy is a continuum

[limpid turret]

total energy of the universe. Whatever that is (assuming current cosmological theories are more-or-less correct)

[cinder tundra]

My potatoes help in math a lot

[hidden oyster]

cant you go out of bounds then theoretically

cant you just take a higher number for you

[limpid turret]

you make it sound so easy

[hidden oyster]

we say the final number is like 7, and now you just say 8 or something. or maybe 7.1

[limpid turret]

"can't I just exceed the total energy of the universe?"

[hidden oyster]

yea why not

[limpid turret]

because that's everything

[hidden oyster]

doesnt "everything" contain infinity?

[limpid turret]

not necessarily

depends on what "everything" is

[cinder tundra]

Noop

[merry depot]

because if energy is finite, then that's the cap.
If i say there's 10 people in a room, you can't just say "what if I talk to 11 of them"
it doesn't make sense. There are only 10.
If there is X 'amount of energy' in the universe, you can't just say "what if I use X+1 energy"

[cinder tundra]

Natural numbers are infinity but they dont contain all real numbers

[limpid turret]

You're confusing "infinite" and "bounded". There are infinitely many numbers between 0 and 1, but each of those numbers is still bounded above by 1 and below by 0

[hidden oyster]

another person can join the conversation though.

[merry depot]

not if there's only 10 people in the room.

[hidden oyster]

yea, but there is a 2, and after that there is a 3

[limpid turret]

I'm talking about only the numbers between 0 and 1

I'm giving you a hypothetical scenario

[hidden oyster]

what if there would appear some other person for some reason, how does infinity work then?

[limpid turret]

If you're going to ignore that, then anything can be anything you want it to be

[hidden oyster]

yea im talking about the concept of infinity

[merry depot]

then sure. If you break the rules of the universe then yeah, whatever you want is possible.

[limpid turret]

(which is very common for manga writers tbh)

[hidden oyster]

is there anything infinite in the universe? what about time?

[limpid turret]

Start here then
https://www.amazon.com/Elements-Set-Theory-Herbert-Enderton/dp/0122384407

[hidden oyster]

i dont have 46 euros

[merry depot]

nope, assuming our models are somewhat accurate, the heat death of the universe is inevitable.

[limpid turret]

But what if you had infinity euros??

[hidden oyster]

is time influenced by heat or is heat meant metaphorically?

[hidden oyster]

i couldnt pay then

[merry depot]

Like, if youre solution to any problem is "What if we just change the rules" then sure. What you're saying will work, because you're going to change the rules to make it work.
So in response, yes your infinitely powerful person can touch lightly because he stores his infinite power in a different dimension until he needs it. How? The rules I changed to make it work like that.

[limpid turret]

Time is influenced by gravitational forces, heat is a macroscopic measurement of internal molecular motion that sums to zero net motion. They're unrelated

[hidden oyster]

but how does infinity work then irl

[limpid turret]

Infinity is an abstract concept. It's not something you're just going to find in your backyard

[hidden oyster]

yea i know

[limpid turret]

It's not like you look under your couch and you find "2" laying there

[hidden oyster]

infinity is so interessting

cant i just say infinity + 1?

[limpid turret]

Infinity is an abstract concept related to sets. A set is infinite if it is not finite. A set is finite if its elements can be mapped bijectively to some set {1, 2, ..., n}

[limpid turret]

You can say whatever you want. You can say sdesdftgfdrfvcfrtgfvfr

Is it useful? Probably not

If you want to say something useful, then no, infinity+1 doesn't really have any mathematical value

[hidden oyster]

does infinity have a value?

[limpid turret]

depends on how you define "value"

Is infinity a number? No

There are infinitely many numbers though

[hidden oyster]

i think it is many numbers

yea

[limpid turret]

It is not

The closest you can get to saying "infinity has value" is if you consider cardinality (or limits), which requires set theory (or real analysis)

[hidden oyster]

do you understand Infinity?

like if you think of infinity can you imagine in your mind what it is?

[limpid turret]

I think of infinity as one of two things

1. The cardinality of a set is infinite if and only if it is not finite
2. A sequence approaches infinity if it has no upper bound.

[hidden oyster]

but a lower bound?

so is infinity able to be bounded?

[limpid turret]

A sequence approaches -infinity if it has no lower bound

[limpid turret]

no. But infinitely many elements can be bounded (e.g. all the numbers between 0 and 1)

[hidden oyster]

i think i get it now, thanks

.close

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[ocean seal]

kisnar

kisnar

[lone heart]

@alpine sable Has your question been resolved?

[tight pier]

I would split the integral and use sub for the right one and for the left it looks partial fraction decomposition will help

[lone heart]

@alpine sable Has your question been resolved?

[tight pier]

ye

[ocean seal]

𝔸dωn𝓲²s

[tight pier]

It's not allowed with products/quotients

but with sums/differences it is

In that regard it's linear

For the left I give the hint x = 1 is a root

yea so you can write the denominator as linear factors

and apply partial fraction decomp

we can also do it together

hmm ok

up to you

I would do with you the left one

the right one is managble with sub

So the first thing I would do is write the denominator as factors

taking the hint that x = 1 is a root I would do long division or some like that

(x³ + x² - 2) : (x-1)

Let's assume you did that to save time

You would get this (x-1)(x^2+2x+2)

yes!

[ocean seal]

kisnar

[tight pier]

yes!

Now notice that the other linear factor has complex roots

So what we would do using partial fraction decomp

$\frac{x^2+4}{(x-1)(x^2+2x+2)} = \frac{A}{x-1} + \frac{Bx+C}{x^2+2x+2}$

[ocean seal]

𝔸dωn𝓲²s

[tight pier]

First step

yes!

the linear form Bx+C is used only for complex roots

now

2nd step is to multiply both sides by the denominator

$\frac{x^2+4}{(x-1)(x^2+2x+2)} = \frac{A}{x-1} + \frac{Bx+C}{x^2+2x+2} \quad \big | \cdot (x-1)(x^2+2x+2)$

[ocean seal]

𝔸dωn𝓲²s

[tight pier]

Some things will cancel out

$x^2+4 = A(x^2+2x+2) + (Bx+C)(x-1)$

[ocean seal]

𝔸dωn𝓲²s

[tight pier]

yes

it's like just a line

commando line

ok good!

[tight pier]

So we at this

Now we want to do coefficient comparison

to find A, B and C

familiar with that method?

exactly!

We would need three eq. here

ok sure if you want to

yea no problem

i dont do it like but it's ok!

$x^2+4 = Ax^2+2Ax+2A + Bx^2-Bx+Cx-C$

[ocean seal]

𝔸dωn𝓲²s

kisnar

[tight pier]

yes!

yes!

yea if we look at 2nd and 3rd eq.

sure!

(A,B,C) = (1,0,-2)

yes!

yes

,,\int \frac{1}{x-1} : \dd x - \int \frac{2}{x^2+2x+2} : \dd x

[ocean seal]

𝔸dωn𝓲²s

[tight pier]

The right one is a bit tricky

any idea?

ok good

,,\int \frac{1}{x-1} : \dd x -2 \int \frac{1}{x^2+2x+2} : \dd x

[ocean seal]

𝔸dωn𝓲²s

[tight pier]

sine we got something with x² in the denom

what would that kinda resemble

do you know an integral with the form 1/x^2+...

yes!!

So here

we would like to get something like x² + 1

in the denominator

not quiet

we complete the square

do you know that?

ok so

for x² + 2x what key number would we need

to complete it

or do you understand my question haha

yes!

so

we can basically rewrite 2 = 1+1

,,\int \frac{1}{x-1} : \dd x -2 \int \frac{1}{x^2+2x+\textcolor{cyan}{1+1}} : \dd x

[ocean seal]

𝔸dωn𝓲²s

[tight pier]

yea luckily!

imagine there wasn't a 1

like imagine

(x+2)² + 4

we would need to factorize 4

like

4((x+2)²/4 + 1)

and pull 1/4 as a constant

(x+2)²/4 + 1 = ((x+2)/2)² + 1

just so you know for the exam

[tight pier]

but here luckily it works out to

,,\int \frac{1}{x-1} : \dd x -2 \int \frac{1}{(x+1)^2+1} : \dd x

[ocean seal]

𝔸dωn𝓲²s

[tight pier]

yea you can!

,,\int \frac{1}{x-1} : \dd x -2 \int \frac{1}{u^2+1} : \dd u

[ocean seal]

𝔸dωn𝓲²s

[tight pier]

yes

-2

is missing

as a factor

ok

good

I think you're good now

the left is self explantory I think

ok good

and the root integral is sub

video?

As a hint: try u = 1-x²

hmm

maybe

but seems too lengthy

yea then you have

,,\int x^3\sqrt{u} : \dd x

[ocean seal]

𝔸dωn𝓲²s

[tight pier]

We need to replace dx too

yes

u = 1-x²

diff. both sides wrt x

u' = du/dx = -2x

dx = du/-2x

,,-\frac{1}{2}\int x^2\sqrt{u} : \dd u = -\frac{1}{2}\int (1-u)\sqrt{u} : \dd u

[ocean seal]

𝔸dωn𝓲²s

[tight pier]

x² can be written as 1-u because of the substitution u = 1 - x²

And then the rest should be managble

using power rules

if you expand it too

[ocean seal]

𝔸dωn𝓲²s

[tight pier]

yea

here it also makes sense to expand

[ocean seal]

𝔸dωn𝓲²s

\begin{gather*}
-\frac{1}{2}\int u^{\frac{1}{2}} - u^{\frac{3}{2}}\: \dd u
\end{gather*}

kisnar

[tight pier]

the left, correct?

u^1/2

yea!

aside from the + C but yeah

ye

ye

yeyeye 🥱

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[lone heart]

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[terse oak]

is there a tool for solving differential equations
at least give the answers cuz i'm solving some and I dont have the solutions so I dont know whether I'm doing it correct or not

[lone heart]

Please don't occupy multiple help channels.

[gray isle]

wolfram probably will

[terse oak]

https://www.wolframalpha.com/widgets/view.jsp?id=2a84a9a88db90cb062de7f46923eb601

u mean this?

[gray isle]

yes

[terse oak]

its tweaking, i gave it a simple equation and it gave no response

just typed the equation again in output 😭

[lone heart]

@terse oak Has your question been resolved?

[lone heart]

@terse oak Has your question been resolved?

[lone heart]

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[strange fractal]

excuse me

[strange fractal]

which one is rates of change in my textbook

when i check 3A its quadratics

[pseudo ice]

How do you mean “rates of change”? Do you have an example of what you’re looking for?

[strange fractal]

ohh

sry i meant

sequences and series

oh

chapter 15

[gray isle]

15

[strange fractal]

thx

.close

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[inner pawn]

a boy draws from a lot which has 6 balls inside numbered 1-6, if he tries to guess what number he gets every time he draws a lot not repeating a number twice, then the probability that be guesses all the lots wrong is?

[fervent spire]

I think of derangements but theres probably a much better approach

[cedar juniper]

After 1 lot are we putting the ball back?

[fervent spire]

We could also do case work

[fervent spire]

Principles of Inclusion and Principle type

[lone heart]

@inner pawn Has your question been resolved?

[inner pawn]

No

Whats done is done

[fervent spire]

Derangement it is then

[inner pawn]

Oh right right

Derrangement of 6 things

So its D6/6!????

[rose sigil]

it's equivalent to a derangement problem because making your guesses after each draw offers no advantage over making your 6 guesses before the game starts

[inner pawn]

Yep yep

so like

Total cases are 6! Right

And i use formally for derrangement of 6 things

So itz D6/6!

?

[rose sigil]

yep

[inner pawn]

Thanks a lot!!!

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[covert scarab]

does someone know physics here i have a doubt in physics

[wraith stratus]

post your doibert sir

[limpid turret]

!da2a

[lone heart]

No need to ask “Can I ask…?” or “Does anyone know about…?”—it’s faster for everyone if you just ask your question! See https://dontasktoask.com/

[covert scarab]

my bad

basically if i have a cavity inside a insulating solid sphere....the electric field comes out to be some value (densityX vector connecting centre / 3 epsilonnot)....but if i assume a gaussian surface .. the electric fields comes out to be 0 .... why is it so

[limpid turret]

densityX: $\rho_X$? epsilonnot I'm sure is $\epsilon_0$

[ocean seal]

SWR

[ancient temple]

Your question isnt making much sense in its current form

[slender gull]

He's using X for multiplication lol

[covert scarab]

just ignore the formula

[hushed locust]

gaussian surfaces only really work to find electric field magnitude if the setup is very symmetrical

[covert scarab]

no bro .. u can assume gaussion surface as you wish

it can be of any shape

[slender gull]

But not necessarily find the electric field.

[ancient temple]

You can, but if the field isnt constant over the whole surface you wint be able to pull it out of the integral

[reef pier]

you can make any arbtirary gaussian surface, sure, but unless you feel like actually calculating the surface integral over the varying electric field, you better abuse some symmetries

[hushed locust]

well gaussian surfaces can be any shape and any location, but assuming a constant electric field magnitude and direction on that surface (which is usually how they're used) is a much more stringent requirement

[covert scarab]

see in this case i am assuming gaussian surface to be exactly the size of cavity where there is no charge

[hushed locust]

the we can with confidence say that the flux through that surface is 0, since there is no charge enclosed... and nothing more, since we can (and do) find that the electric field comes in one one side and out the other, adding up to a net 0 flux

[reef pier]

yeah so you're getting a 0 electric field inside the cavity (expected since there's no enclosed charge)

[covert scarab]

yes exactly but in reality there is some electric field inside it

[hushed locust]

it's not true that electric field inside a cavity is 0 if that cavity is not centered, the setup is probably something like this (in which case the electric field is uniform and nonzero)

[covert scarab]

so e.ds =0
e=0 then

[hushed locust]

that doesn't follow. flux can be positive or negative, so how can you know the positive and negative don't just cancel out?

in fact that's often how gaussian surfaces work

[covert scarab]

oh so you are saying that the integral of ds is actually making 0 not the E?

[hushed locust]

yes. the only way we can conclude the electric field is actually 0 from that is if we can be sure the electric field has some particular symmetry properties

[covert scarab]

ok i got it but 1 more question arises

if it is so then why electric field inside a uniform shell is 0

i can assume the gaussian surface of exactly of its size

then integral of ds is non zero?

[hushed locust]

generally we only consider gaussian spheres of either larger or smaller radius than the shell, because charge "exactly on the surface" doesn't fit nicely with gauss' law

[covert scarab]

well not exactly of its size but like nearly of its size

[hushed locust]

well anything smaller and the charge is not enclosed, so the flux must be 0. we know that if the spheres (gaussian and physical) are perfectly concentric, and charge is uniformly distributed, then the electric field due to those charges on the sphere's surface must only point inward or outward (since no direction is any different from any other direction, along the surface)

[ancient temple]

Because in this case, you actually respected the symmetry of the sphere, by choosing a spherical surface. In such a case the field will be CONSTANT over the surface, which allows us to write:$\int E \cdot ds = 0 \implies E \int ds =0 \newline \implies E(4\pi r^2)=0 \implies E=0$

[covert scarab]

ooh i got it

[ocean seal]

quickdoom

[covert scarab]

thanks a lot

[hushed locust]

yeah in the conducting sphere case, no direction is any different from any other direction (other than inwards vs outwards), so the electric field can't possibly point in any direction or vary in any direction than radially. but if the surface is not totally concentric that whole argument falls apart

[covert scarab]

oh wait if i assume the cavity exactly at centre of the uniform insulated sphere then will it be 0? due to symmetricity

[hushed locust]

yes

[covert scarab]

thanks @hushed locust

[hushed locust]

which agrees with the previous result that the magnitude of the field inside any cavity is proportional to the vector pointing from the center of the sphere to the center of the cavity, that vector is now just 0

[covert scarab]

ohh yeah that can be also said

.close

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[covert scarab]

hello guys i have a conceptual problem about e. what is exactly e and why its differentiation is e

[rose sigil]

$e^x = 1 + x + \frac{x^2}{2!} + \frac{x^3}{3!} + \frac{x^4}{4!} + \cdots$

[ocean seal]

slayla

[rose sigil]

differentiating this termwise you’ll see we get the same thing back

[covert scarab]

ok

but what is e

[rose sigil]

wdym?

it’s a real number

[covert scarab]

what is the value?

[rose sigil]

there are different ways to look at it

[rose sigil]

one is e = e^1 here

[rose sigil]

this limit is another

[covert scarab]

i didnt understand

[earnest saddle]

This is good explanation of why e^x is derivative of e^x

Try to differentiate both sides

RHS is just a polynomial, so it will be easy to differentiate

Then you will get de^x/dx = e^x

[covert scarab]

ohk

thanks

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[flat loom]

Five young athletes were awarded prizes for sports achievements. The first one received PLN 1024, and each subsequent one received 𝑝% more than the previous one. The fifth athlete received 2,500 zlotys. Determine the amounts of the awards of the other three (from the lowest). how to solve it?

[wraith stratus]

oh

pln/ zloty is a currency

[buoyant basin]

isnt it just 1024 * x^4 = 2500 ; solve for x and calculate 1024 * x^1 , 1024 * x^2 and 1024 x^3

[rustic ruin]

this but x=1+p (i think so anyways)

to solve for p

[flat loom]

y

i think its a string, either arithmetic or geometric

[buoyant basin]

what is the task asking for? just the amounts of the other three?

or what does (from the lowest) mean

[lone heart]

@flat loom Has your question been resolved?

[flat loom]

The sum of the five initial expressions of a convergent geometric sequence is equal to LaTeX: 1Frac{40}{81}
1
40
81
. The sum of all the expressions of this sequence is from it by LaTeX: {frac{1}{162}
1
162
greater. Calculate the quotient of this sequence. Round the result to 2 decimal places.

[lone heart]

@flat loom Has your question been resolved?

[lone heart]

@flat loom Has your question been resolved?

[lone heart]

@flat loom Has your question been resolved?

[lone heart]

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[thorn nymph]

Help I tried so many times what's the value of x

[wet harness]

!status

[lone heart]

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

[safe vine]

show working pls

[wet harness]

5! = 120 so thats 1 on rhs

[earnest saddle]

I saw this question the other day

[safe vine]

lol what

[wet harness]

Also. 25^0 = 1

[rustic current]

HELP GUTS

GUYS

[safe vine]

yo

[safe vine]

take a new help channel

[wet harness]

Bro foreseen the future !

[rustic current]

idk how to do that

[safe vine]

wtf

what is happening

[thorn nymph]

Pls help us

[wet harness]

Same !

[earnest saddle]

someone posted it here

[safe vine]

show your working

so we can help

[rustic current]

u got me?

[thorn nymph]

Its on paper I cant get o myphone rn

[safe vine]

i did it already

[thorn nymph]

To take foto

[safe vine]

but like

[rustic current]

can i get the answer

[safe vine]

the goal is to teach

not to give the answer

[rustic current]

ok join call

teach me

[thorn nymph]

Pls teach

[safe vine]

just

simplify everything first

[thorn nymph]

I did

my answers are either 1 or 25

But neither work

[safe vine]

and then you do some factoring

simplify more

then you should get a quadratic

which gives you one answer

[thorn nymph]

Please give answers I will use it later to review

[rustic current]

AMBY PLSSS

[thorn nymph]

Pleeease

[safe vine]

can u type out where u got to

[thorn nymph]

i fugiured it out

its 8

[safe vine]

\sqrt[4]{64x}=\sqrt[4]{\frac{4120^{128}x^2+256120^{128}}{120^{128}}}

oh yea

it is 8

good job

$\sqrt[4]{64x}=\sqrt[4]{\frac{4120^{128}x^2+256120^{128}}{120^{128}}}$

wait what

why my latex not latex ing

[thorn nymph]

.close

[lone heart]

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[ocean seal]

Amby

[lone heart]

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[slender sorrel]

need help idk why this is wrong

[hearty quartz]

It would be nice to have graph of the functions

The issue is coming from the graphs

I will let you think about the problem

[lone heart]

@slender sorrel Has your question been resolved?

[slender sorrel]

oh the bounds are 0 to 2

wtf

[hearty quartz]

Is there any way you can get around that

[slender sorrel]

no this site is cancer

i can use y instead of w

.close

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[topaz locust]

I have a question about the tvm calculator

[topaz locust]

when i fill in all the details it comes out to that montly payment

but on the car website it comes out to almost 1k lower

theres a 5k downpayment which is why the PV is lower

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@topaz locust Has your question been resolved?

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[fresh flame]

this is what I got but im still getting the wrong answer

[near chasm]

at the last step, you forgot to derive pi*r it seems

[fresh flame]

hmm?

[near chasm]

delete that r and it should be fine

[fresh flame]

where

[near chasm]

derivative of the first term pi*r is just pi

and dr/dt of course

[fresh flame]

okay i removed the r but im still getting a bit off from the answer

answer key is saying it's 252

but im getting 207

nevermind I subbed in one wrong value

thank you so much

.close

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[leaden tusk]

Right. Ive made myself a script of the tasks ive finished, tips and tricks i got from others, etc. So id like to put the first 3 linear equations aside and move onto the 2nd part.

I remember tidbits but i cant say that im capable of doing it, so anyone knows how to solve? And id appreciate a " fool-proof" guide. Cause frankly, im an idiot at this.

[leaden tusk]

I remember a fella telling me it had 2 methods of doing it? Systems of linear equations?

-x + y = -5
3x - 2y = -12?

[empty cedar]

do you want the method which is annoying and painful when the numbers are large or the method which is confusing

[leaden tusk]

Which one is easier to understand?

And remember

[empty cedar]

lets just go with elimination

basically in elimination you have to manipulate one or both of the equations so that when you add them one of the variables cancel out

[leaden tusk]

Also, again, im a dumbass so id appreciate if we keep this as simple as possible (explaining-wise)

[leaden tusk]

Huh?

[empty cedar]

i will give my own example

x+y = 4
x-y = 6

now what happens if we add both of the equations together

[leaden tusk]

x+y + x-y?

[empty cedar]

yes

then 4+6 on the other side

[leaden tusk]

Wait

Shouldnt it be 4 - 6- wait. Oh!!
Nvm nvm. Brain fa

Fart*

So we do 4+6?

[empty cedar]

yes on the other side

so it would be

(x+y) + (x-y) = 4 + 6

now when you add (x+y) and (x-y) together the y will dissapear

since y-y = 0

[leaden tusk]

?

How exactly is only y affected and not x?

[empty cedar]

x + y + x - y = 4 + 6

(x + x) + (y - y) = 4 + 6

2x = 10

[leaden tusk]

Wait.

Ohhhhh

Its like programming. ((Kinda))

[empty cedar]

after that it should be obvious what to do

solve for x

x = 5

then pick one of the equations and solve for y by substituting x

x + y = 4

5 + y = 4

y = -1

[leaden tusk]

Ohhhh

Wait give me a example question

I wanna see if i understand

[empty cedar]

ill give one more example because theres another thing

lets say

[leaden tusk]

Oh?

[empty cedar]

2x + 2y = 4
x - y = 6

now when you add both of these equations youll notice that no variables cancel out

(2x + 2y) + (x - y) = 10

3x + y = 10

no luck

[leaden tusk]

Shouldnt it be 4x?

[empty cedar]

2x + x = 3x

[leaden tusk]

Wait no-

I misunderstood the y as x. My bas

Bad*

[empty cedar]

so what you want to do is manipulate the equations so that you can cancel out one of the variables

it sounds complicated but basically

pick one of the variables, x or y

[leaden tusk]

Ill pick x

[empty cedar]

2x + 2y = 4
x - y = 6

now make it so that when you add the two equations x cancels out

[leaden tusk]

Huh?

[empty cedar]

ill just show you

2x + 2y = 4
x - y = 6

-2[x - y = 6]
-2x + 2y = -12

basically i multiplied -2 to both sides of the equation on the bottom

[leaden tusk]

Oh wait nvm. I thought we jumped to some new task or step. Its the same task. Ok ok.

[empty cedar]

now we have

2x + 2y = 4
-2x + 2y = -12

when you add both of the equations, x will cancel out

leaving with
4y = -8
y = -1

it should be simple what to do from then

[leaden tusk]

Determine what x is?

[empty cedar]

x - y = 6

x - (-1) = 6

x + 1 = 6

x = 5

ok now you try for problem one of the thing you solved

just try your very best

[empty cedar]

.

-x + y = 5
3x - 2y = -12

[leaden tusk]

Lemme try a)

-x + y = 5
3x - 2y = -12

((Oh sorry. Scrolled up to reply and write-))

[leaden tusk]

Hmmm

[leaden tusk]

-x + y + 3x - 2y = 5 + (-12)?

[empty cedar]

if you try to do that nothing cancels out and youll be stuck

you have to manipulate one of the equations

[leaden tusk]

Uhhhh

[empty cedar]

choose a variable

an easy one

[leaden tusk]

Hmmm

-x?

[empty cedar]

x

sure

now think of a way to manipulate the equations so that x cancels out when you add it

(you have to multiply on both sides)

[leaden tusk]

Uhh

[empty cedar]

i need to go, the pentathlon is starting. Bye

[leaden tusk]

Well thanks anyway. I guess ill just wait here and think

Enjoy :3

[empty cedar]

youre getting tgere

try satch videp on it

sorru hard tp type in swimming

[leaden tusk]

Its fine

Goodbye :3

Hmm

[leaden tusk]

-x + y = 5
Multiplied by 3...
-3x + 3y = 15.
9x - 6y = -36.

...thats...not getting me anywhere tbh. Worth a shot tho.

[forest marsh]

hey hows it going ?

[empty cedar]

you dont need multiply both equations

can only be one

[leaden tusk]

Not that great. But howdy

[leaden tusk]

Oh youre still here-

[leaden tusk]

Idk i remember someone telling me to miltiply each of them.

[empty cedar]

i said multiply both side

not both equation

[forest marsh]

i'm fine waiting football to restart , struggling on the a) of the second task ?

[empty cedar]

but your idea is correct

[leaden tusk]

Yep

[forest marsh]

just multiply the first equation not the second one by 3 actually

[leaden tusk]

-x + y = 5
3x + 2y = -12.

Now multiplying the first one by 3.
-3x + 3y = 15.

Oh i think i get it

...

No i dont. I just thought id get an idea if i said that outloud

[forest marsh]

no it's 15 on the right

[forest marsh]

it works sometimes

so

[leaden tusk]

Btw

[forest marsh]

now you will have to add them to get rid of the x terms

[leaden tusk]

Lemme see if i got this right

[leaden tusk]

First we have the task.
-x + y = 5
3x + 2y = -12

We multiply the First line. AND ONLY THE FIRST LINE

By 3. ((Not sure if its always 3 but ima roll with it for now))

Then. We add the 2nd line to the first line after we multiplied it?

[forest marsh]

ok so the number who multiply depends on what you need to make the terms disapear while adding

[leaden tusk]

Oh so if its like

-x + y = number.
And the lower is
5x + 4y = number.

We multiply by 5?

[forest marsh]

add or substract both works but in this case it's more efficient to add yes

[forest marsh]

yes!

[leaden tusk]

Alright. Im getting it somewhat

Now. Back to the task-

[leaden tusk]

-3x

• 3x. Well thats 0. Which is thanos snapped

3y - 2y = y

Y = 15 - 12

Y = 3?

[forest marsh]

okay and now do you know how to find x ?

[leaden tusk]

Give me a moment

[forest marsh]

since you know y=3

[leaden tusk]

-x + y = 5

I know y is 3

..wait.

X is in negatives-

Or does that not matter

Cause if it dosent. X is 2

[forest marsh]

x is a real numbers and y too it can be negative, positive, fraction, sqrt ... everything you can imagine so there is no condition on the values of x

[forest marsh]

since you know y=3

what do you do to find x ?

[leaden tusk]

Uhhhh

Not sure tbh

-x + 3 = 5

If we follow the same rules as before

We leave the variable on one side. And put the numbers on the other?

[undone obsidian]

yes

[leaden tusk]

-x = 3 + 5 ? ((It could be subtraction or adding. I just took a shot in the dark))

[undone obsidian]

whats the eq

what u tryna solve for

[leaden tusk]

Here

[undone obsidian]

ok

[leaden tusk]

Oh. So its Subtraction?

[forest marsh]

we already end it

[leaden tusk]

Sorry <:(

[forest marsh]

you do -3 both sides yes

[undone obsidian]

y=-6 so -x+-6=5

[leaden tusk]

-x = 3 - 5?

[leaden tusk]

Huh

[forest marsh]

no you have -x +3 = 5

you substract -3 on both sides

what you get ?

[leaden tusk]

-x + 3 = 5
-3. -3?

[forest marsh]

why do ya say sorry you're learning xd

[leaden tusk]

-x = 2?

[forest marsh]

oh ok mb i just don't know what barely really means i messed up translation

didn't meant to be not kind

i wanted to say that we have reach the end of the solve

[leaden tusk]

-x + y = 5
3x + 2y = -12

We multiply by 3 cause theres 3x.

-3x + 3y = 15
3x + 2y = 12.

We add them. -3x and 3x is 0, 3y -2y is y.

15 - 12 is 3. Y= 3.

Back to the first line.
-x + 3 = 5
Subtract by 3 on both numbers.
-x = 2

Btw. How can we tell when to subtract? :0.

[forest marsh]

for the system of equations or the 3 at the end ?

[leaden tusk]

Overall

Like. Are there any requirements or signs that tell me " oh i gotta subtract"

[forest marsh]

if you have x+3=2 for example

you have a " + " on the left right ?

so when you want to get rid of it you will defeat him with a " - "

this is a questions of signs indeed

x+3=2 <===> x = 2 - 3 <====> x = -1

[leaden tusk]

So whenever theres a plus on the left

Its time to subtract?

[forest marsh]

yes

[forest marsh]

or the right

[leaden tusk]

?

[forest marsh]

imagine you have 2 = -x + 4

what do you do ?

[leaden tusk]

Subtract both numbers by 4?

[forest marsh]

yes

the things i want you understand is no matter what side it is you have to substract when it's a + and add when it's a -

[leaden tusk]

No?

[forest marsh]

?

[leaden tusk]

Bad wi fi

[forest marsh]

oh okay

[leaden tusk]

I said that making sure was i right or wron

Wrong*

[leaden tusk]

So we add when its a minus.

Subtract when its a plus

[forest marsh]

yes

all good ?