help-26

[smoky sparrow]

https://mathalino.com/reviewer/derivation-of-formulas/derivation-of-formula-for-volume-of-a-frustum

Yes, it can be found by similarity of the solids

[median egret]

Thanks

[smoky sparrow]

No worries

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[neon iron]

Friends have a 1/3 probability to lie, three independent friends say it’s raining

[neon iron]

What prob it’s raining

P(rain | one friend rain) = 2/3

P(rain | three friends rain) = ?

Is P(rain and three friends rain) = 2/3^3 ?

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[worthy pecan]

Hi, can anyone assist with this problem? I have no idea where to begin

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[molten crystal]

the original integral had bounds -2 2

and since it's simmetric and would give zero area, he just uses half of it.

i don't understand why we do that. it's not the same integral, since one of them result zero

[loud oasis]

there are two important types of symmetry:

1. odd functions, f(-x) = -f(x)
   odd functions integrate to 0 on a symmetric interval
2. even functions, f(-x) = -f(x)
   even functions integrate to double on a symmetric interval

in this case, the function is a product of 2 odd functions (t and sin t) which gives an even function

[molten crystal]

ahhhh

ok ok

understood now

thank you

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[rapid wedge]

Not sure if I got b right

[rapid wedge]

For b, x would equal 0.1 so I just plugged it in to L(x) from the previous part

lmk if u cant read my handwriting

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[rapid wedge]

no

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[north canyon]

By vieta's formulae, $a+b+c = 3, ab + bc + ca = 2, abc = 1. \ P(a) + P(b) + P(c) = 6, P(2) = 11, P(abc) = P(1)$

[thorny flame]

Normed

[north canyon]

How do I find P(1) here?

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[bold wave]

just started learning this stuff, can't seem to understand how the final integral is x^2-2. i understand how x^2 came into place but dont know how the -2 got there

[sterile finch]

The -2 is not correct.

[bold wave]

wouldn't it be something like x^2-x?

[sterile finch]

Yes.

[bold wave]

ah alr, thats the solution my teacher gave me so gotta speak to him abt that

thank u

[sterile finch]

yw

[bold wave]

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[sterile finch]

Is your teacher German? Their x's can look like 2s.

[bold wave]

no, he is american lol

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[heavy junco]

how would I do this question??

[heavy junco]

btw this is NOT a test question

this is a practice test

[brisk blaze]

Find the roots, test values between them on a numberline, make sure to check multiplicity

[heavy junco]

oh so I can use synthetic division solve and then done?

oh wait you said number line

wait

wdym by a number line?

[brisk blaze]

Yes division, then put all roots on a number line and plug in values between them to see if they are neg

[heavy junco]

like hwo would I use it

oh

so the answer

is negative

the end answer

[brisk blaze]

If your roots are 2,4,6

(Test 1)—2—(test 3)—4—(test 5)—6–(test 7)

And then use interval notation to display when it’s net

[heavy junco]

so would it be negative when x > 5 to infinity?

I got x+2^2

(x+2)^2

and (x-5)

[heavy junco]

wait how can I tell if a function is negative and positive in certian areas?

I remember that there's a certain rule where it's a positive or negative

for the power of the equation how exactly does it work?

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[wooden osprey]

what have you tried?

[sullen herald]

i need help with b

[wooden osprey]

what have you tried?

[sullen herald]

nothing

well

everything i tried

i get wrong

I want to use a method which uses trig ratios

[wooden osprey]

i think you can actually dissect the whole thing

$a\sin B\cos^2B$

[thorny flame]

fungi

[wooden osprey]

do you see anything special in this equation?

[sullen herald]

well, so far, i see that sinb = qr/qb

so qr = qbsinb

[sullen herald]

a x sinb x cosb x cosb

[wooden osprey]

what does asinb equal?

[sullen herald]

idk

[wooden osprey]

have you tried thinking?

[sullen herald]

i would assume sin b = AC/a, howevr, its not a right angle triangle

so would I use sine rule

wait

nvm

its pc

asinb is PC

[wooden osprey]

look at angle B not as an angle of triangle ABC, but as another triangle

[sullen herald]

is it pc?

[wooden osprey]

yes

[sullen herald]

PC x cos^2b = QR?

so how do i prove it

@wooden osprey ?

[wooden osprey]

what does angle B also equal?

[sullen herald]

wait i think

i goit it

finally

Thanks fungi

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[nocturne urchin]

Could someone help me by explaining a step process of how to solve this?

[solid island]

is the answer $2sec^{2x}$?

[thorny flame]

oh? jean

[nocturne urchin]

the website says its -4

[solid island]

-4 just -4?

or -4 something?

[nocturne urchin]

-4

[nocturne urchin]

I used a calculator online to find the answer but if possible id like to know why and how to get the answer

[solid island]

all right

you have to convert sec to $\frac{1}{cosx}$

[thorny flame]

oh? jean

[solid island]

then use the rule of $(a - b)^2 = a^2 - 2ab + b^2)$ in both sides

[thorny flame]

oh? jean

[solid island]

in the right should be positives

[nocturne urchin]

ah okay

[solid island]

can you keep yourself

or you need more help

[nocturne urchin]

so would the equation transform into this $(cosx-1/cosx)^2-(cosx+1/cosx)^2$?

[thorny flame]

NotAMuffin

[solid island]

yeah

so you can cancel cos when you apply (a+b)^2 rule

[nocturne urchin]

Then i should factor each equation into the binomial form and solve?

[nocturne urchin]

no thank you so much. Seeing it like that made it click

Im pretty behind with a test tmr so im rushing homework and so lost lol thank you

you cleared up a lot regarding this topic

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[pseudo tiger]

how was this factorisation done

i know that z^2 +4=0 has roots 2i and -2i

[orchid charm]

What's the question

Like what do you need help with

[pseudo tiger]

how is (z^2 +4)^2 = (z+2i)^2*(z-2i)^2

[orchid charm]

It's just diffrence of squares

Do you know what that is?

[pseudo tiger]

let me googel it

[opal vault]

nono

[opal vault]

as you said, z^2 + 4 has roots 2i and -2i

[orchid charm]

Oh wait Im stupid

[opal vault]

so $z^2 +4 = (z-2i)(z+2i)$

[orchid charm]

I didn't see the i

[thorny flame]

rafilou2003

[pseudo tiger]

but that applied when z^2 -4

not z^2 +4

right

[orchid charm]

Just ignore me I shouldn't be doing math this late

[pseudo tiger]

lol at me is 10AM

[opal vault]

so $(z^2+4)^2 = ((z-2i)(z+2i))^2$

[thorny flame]

rafilou2003

[neon iron]

,, (z^2 +4)^2 = \9[\big]{(z+2i)(z-2i)}^2 = (z+2i)^2(z-2i)^2

[orchid charm]

It's 1:30 am for me

[pseudo tiger]

but this applied to z^2 -4 no?

[opal vault]

no

$z^2 +4 = z^2 - (2i)^2$

[thorny flame]

rafilou2003

[pseudo tiger]

this is what i i foundi google

oh

yes makes sense then

thankyou

[pseudo tiger]

at least you live in usa

i hope

[orchid charm]

Yes I do

Gl with math

[pseudo tiger]

thank you

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[jade thunder]

what the heck is σ(Y)

[south island]

the sigma algebra on Y

[jade thunder]

But Y is a measurable function it’s not a measurable space

Y doesn’t have a σ-algebra

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[opal vault]

it does, it's $\sigma(Y) = {Y^{-1}(B), B\in \mathcal{B}(\bR)}$

[thorny flame]

rafilou2003

[opal vault]

it's the set of Y-measurable sets in Omega

It's also the smallest sigma-algebra in Omega that makes Y measurable

@jade thunder if there's anything left to clarify, ping

[jade thunder]

So it’s the smallest (by inclusion) sigma algebra on the domain of Y that makes Y measurable?

@opal vault

[opal vault]

yes

[jade thunder]

Ok that resolves my problem

I will march on from here thank you

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[solid island]

hi, im doing integrations by part

[solid island]

with this problem

here i found u, du, dv, and v

then replace but if i go further

i wont obtain the same result as the book say

this is the answer the book say

any ideas?

if i keep working on it this is what i have

[remote agate]

I think you dont need integration by parts

[solid island]

yeah i thought the same

[remote agate]

you can probably do u sub for 2x³+4 and just forcefully represent everything in u

[solid island]

doing change of variables?

[remote agate]

yes

[solid island]

but u = 2x^3 + 4 then du = 6x^2

not possible

because of the x^5

[remote agate]

do what you did just now by splitting x^5 into x^3 and x^2

the x^2 gets removed because of the substitution and the x^3 can be in terms of u

[solid island]

this you mean?

i think i did it

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[topaz reef]

I don't follow where the inequality comes from

I get that (a-b)^2 > 2ab

[sudden vapor]

can you prove that a^2 + b^2 > 2ab

[topaz reef]

Yeah

It's greater than zero and move it over

[sudden vapor]

well if you can prove that then obviously this is true

[topaz reef]

I dont see it

Not obvious to me

[sudden vapor]

(a^2 + b^2 + a^2 + b^2) > (a^2 + b^2 + 2ab)

if a^2 + b^2 > 2ab

a^2 + b^2 + a^2 + b^2 being equal to 2(a^2 + b^2)

[topaz reef]

Okay so because of this, we can use it to say since 2ab is in (a+b)^2

[pearl fog]

isnt it $\geq$

[thorny flame]

Skill_Issue

[sudden vapor]

oop yeah if a=b

[topaz reef]

Okay i think I get it, thanks.

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[dapper kernel]

I'm so confused on how to do this

[dapper kernel]

I'm so stupid

Any help would be greatly appreciate

[burnt fox]

To find area,find lets find area of triangle and rectangle indivdually then add them up at the end to find the total area

For triangle use the formula (base x height)/2

[dapper kernel]

Alright

[burnt fox]

For rectangle use the formula (base x height)

[dapper kernel]

Thanks

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[unique pewter]

Does anyone have a suggestion where can I start studying integral? Maybe some notes or examples. (I just started Calculus a week ago, I learned some basic derivative rules)

[lucid junco]

youtube

khan academy

[terse nest]

organic chemistry tutor

[lucid junco]

openstax

[unique pewter]

Hmm thanks, does anyone have a example sheets?

I searched some but they are kinda weird things

[lucid junco]

example sheet?

wdym

[terse nest]

pauls online math notes has some

if youre referring to example problems with solutions that walk you through

but theres many more

[unique pewter]

Thank uu

That'll do the work

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[molten vine]

$\lim_{x\to +\infty} \frac{f(x)}{g(x)} \text{ doesn't exist} \implies f=\Theta(g)$ ?

[thorny flame]

Adam Chebil

[meager dawn]

f can be x sin(x) and g could be 1

then f isn’t theta(g) but the limit of f/g doesn’t exist

in fact, f isn’t Theta(g) nor is it O(g) nor is it Omega(g)

[molten vine]

then it's what ? 😅

[meager dawn]

doesn’t have to be any of them. functions can be weird like that

sometimes there is just no name for it, notice that all of the definitions for complexity classes require something to happen for all x > x_0

[molten vine]

so we can't compare them ?

[meager dawn]

and sometimes none of those conditions hold

[meager dawn]

depends on what you mean by compare

[molten vine]

i mean compare the growth rate of the functions

[molten vine]

so if i find lim f/g undefined then how do i know that it's big theta or not big theta
use the formal definition ??

[meager dawn]

yeah you just sort of can’t. there are (literally) uncountably many functions that are not in any of the three classes

[meager dawn]

most of the time yes

[molten vine]

got it thnx 👍

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[molten vine]

.reopen

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✅

[molten vine]

btw are complexity classes comparing the growth rate or the order of magintude

i alwas get confused by the 2 as some resources use the term growth rate and some use order of magnitude

[meager dawn]

both terms are slightly misleading, in a sense complexity classes measure both of these things “asymptotically”, in order for g to be O(f) and f to not be O(g) f has to be growing way faster all the time (after some initial segment), and as a result f is said to be “growing faster” in a sense. in fact the thing that we really care about if we’re gonna talk about the complexity class of a function is the order of magnitude at large inputs, where “large” doesn’t have a real meaning

because comparing the complexity of two functions usually comes from wanting to compare algorithms to solve problems of varying input sizes

and so we care about the amount of time that it takes to solve our problem as we scale it up

[molten vine]

if we care about the order of magnitude why deos wikipedia use the term growth rate ?

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

[meager dawn]

because growth rate is an indicator of magnitude at high inputs

[molten vine]

so growth rate and order of magnitude mean the same thing ? 🤔

[meager dawn]

no

i didn’t say that!

it’s hard to give a really clear answer because you’re asking me why people use one term or the other, to be clear i am giving a guess as to why some people use one over the other, and then you’re asking me why wikipedia specifically uses this one, and i just should say that that person probably has a different philosophy about pedagogy than i do

you are allowed to think about growth rate if you want to and it won’t hinder your understanding as long as you understand the definitions of big O and Omega and Theta well

and then later you can build your own philosophy surrounding these things once you have worked with them a lot, and just take note of when people say growth rate and when people say order of magnitude, and then decide for yourself when to say which things (which will take time). You’ll find a lot of the time that people say growth rate for functions because talking about the order of magnitude is a bit awkward, since order of magnitude refers to numbers, but i find it weird to talk about growth rate because it’s one step removed from what we want to talk about, and both perspectives are fine

[molten vine]

honestly, i don't even know the difference between growth rate and order of magnitude 😅

[meager dawn]

order of magnitude usually is about numbers

[molten vine]

and growth rate ?

[meager dawn]

and growth rate is a convenient way to talk about functions, but then at some point when you plug in a number, that will tell you about the order of magnitude of f(n)

[molten vine]

so the order of magnitude compares f(x) and g(x) for bigger values of x
and growth rate compares the speed of which both functions grow ?

[meager dawn]

yeah in a sense

and big O notation is sort of weird because some people will tell you it’s about the first thing and some will tell you that it’s about the second thing

but really it’s just a definition to help you think about what happens at the right of the graph :P

[molten vine]

yeah u're right

thank youuu

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[meager dawn]

yw

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[stuck tapir]

i need help badly, i've been trying for a while and cant seem to get thhe answer

[stuck tapir]

i've got it down to this but when i try going past it turns out wrong

[burnt fox]

why dont you try squaring from here itself?

[stuck tapir]

i get that

unless im squaring wrong

[burnt fox]

its whole squared

[stuck tapir]

wdym

[burnt fox]

we are squaring on both sides

[stuck tapir]

how is (1+root x+1)^2 become 1+2root(x+1)+(x+1)

[burnt fox]

(a+b)^2 formula

a^2+b^2+2ab

[stuck tapir]

so root x+1 still counts as B?

[burnt fox]

yep

[stuck tapir]

for the right side?

[burnt fox]

yes

now again try to simplify the experssion

[stuck tapir]

do i sqaure again to get rid of the root?

[burnt fox]

yes

[stuck tapir]

ya idk

[burnt fox]

from this step

make sqrt function on one side

then the non sqrt on other side

then square both sides

you will get a quadratic eqn i feel

[stuck tapir]

from that?

whatever i gotta get ready for class and take the exam, if i cant do this im so cooked

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[candid sandal]

Hi

[candid sandal]

The question is "Among all isosceles triangles with a perimeter of 40 cm, determine the one that maximizes the volume of the solid of revolution obtained by rotating triangle ABC around its base AB, and give the lengths of this triangle."

I dont know what I have to do exactly

Can someone help me pls

[mint crescent]

Do yk what 3D shape is formed when you rotate?

If not, figure that out

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[royal sky]

to find volume of integration

[royal sky]

whats the differnce between disk and washer

[next harness]

washer = larger disk volume - smaller disk volume, normally

[royal sky]

sah ty

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[foggy bloom]

can i get help with this. done similar ones i want to say. but do not even know where to begin with this one

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<@&286206848099549185>

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[zenith sonnet]

Hi I wanted to check if my result is correct for 1) specifically the last one

I can translate the text for you:

1. The following bases B1, B2, B3 of the vector spaces IR2 are given, IR3, IR4:

(...)

Furthermore, let two linear maps f : IR2 → IR3 and g : IR3 → IR4 be as follows are defined:

(...)

Determine the following three representation matrices: (...)

[zenith sonnet]

maybe I determined the previous 2 matrices wrong, maybe there is a online calculator or sth that can check it, hopefully my result is correct otherwise every other is wrong lmao

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[zenith sonnet]

I think i need to calculate that way: AB3,B4(g) * AB2,B3(f) to get AB1,B3(g o f)?

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[wraith forge]

wasnt there a rule for x+2a*x-2a?

[wraith forge]

😔

[royal sky]

Are you talk in t about factorization

[wraith forge]

im talking about polinoms

[royal sky]

Factorization is for polynomials 😭

[wraith forge]

ye

that

😔

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[fleet nacelle]

A circle whose center M is tangent to the x-axis at point A. Point O is the origin of the axes (like in the sketch).
The circle intersects the y-axis at points B and D. Given A(8,0), D(0,16)
How can I find the rates of point M?
I've tried everything I know and I am not finding anything

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[fleet nacelle]

anyone going to help i really need it
i know xM is 8 since it's tangent to the x axis at A but i don't know how to find yM

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[dreamy roost]

tangent is perpendicular to radius -> MA and OE are perpendicular to each other.

[dreamy roost]

You may let M = (8, k), and solve k by DM = MA (def. of radius)

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[jade walrus]

what am I doing wrong here? i keep getting my answer as 322
procedure:
<8 4> + <9 4> + <9 5>
=> <8 4> + <10 5>
=> 8!/(4!4!) + 10!(5!5!)
=> 322

[jade walrus]

<a b> being the representation of the binomial coefficient

[acoustic pecan]

just probably means of two terms

youre adding 3

[grim sable]

You don't need to add the <9 4> and <9 5>

one coefficient from that polynomial is fine

its a pretty badly phrased question though

[jade walrus]

oh okay

yeah that makes sense

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[tall hearth]

Hi

[tall hearth]

.close

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[tall hearth]

Nvm

.close

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[chilly haven]

i need help with this

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[polar torrent]

@chilly haven this looks like chemistry. it would also be helpful to translate into English 🙂

[chilly haven]

ok thx

We can assume

its kinetic i have this and i need to integrate this equation

i need W

weigth of catalyst

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[scenic flare]

Without gathering sufficient chemistry information, what in this equation is considered constant?

if you can tell us which variables are constant related to x & W and what "dx" and "dW" represent we can guide you solving it :]

I think many coming along were mostly confused by it being chemistry and insufficient information about the equation

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[fallow condor]

The answer is just C right?

[fair thorn]

yes

[iron vine]

maybe

[lofty salmon]

is this a test?

[fair thorn]

wait, hang on

[iron vine]

yes

[fair thorn]

*thinks*

[fallow condor]

.close

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[fair thorn]

...

[iron vine]

lol

[fair thorn]

<@&268886789983436800>

is fine

[lofty salmon]

[fair thorn]

we can get them banned

[lofty salmon]

huh

why

[fallow condor]

wait wat i do

[thorn briar]

mind explaining?

[lofty salmon]

arbitrarily pinging mods with no reason for getting them banned huh

[fair thorn]

not really no

[thorn briar]

so... do so

[fair thorn]

not saying they should get banned

just sus

[iron vine]

i think they pinned a moderator bc of the question

[fair thorn]

bc when we asked

they immediately closed the channel

that's all im saying

bit sus is all

[thorn briar]

they closed the channel after getting an answer...

[lofty salmon]

that's not suspicious, they got their question answered.

[fair thorn]

...?

[fair thorn]

alr, mb

[thorn briar]

.

[iron vine]

what

[thorn briar]

i was quoting you for reference

[lofty salmon]

you dont have to spoonfeed the answers tho, try explaining them instead.

[iron vine]

oh

mb

[lofty salmon]

@fair thorn

[fair thorn]

?

yea i was going to do that

that's why i said "wait hang on"

[iron vine]

my fault

[lofty salmon]

that still not explains it.

[fair thorn]

??

bro

he's gone now

[lofty salmon]

you provided the answer first, we don't want them to give away answer actually to help them to arrive at a answer.

[fair thorn]

dude

i know how this server works

but he closed the channel before i could send

why are you berating me on this

i have already mentioned that i was going to explain

[lofty salmon]

you don't.

[fair thorn]

...??

[lofty salmon]

you just move on.

[fair thorn]

jesus chr7st

are you really going to start an argument on this

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[mental hatch]

Why are there bounds for x?

[ivory sorrel]

Arcsin is an inverse function

an inverse function needs to satisfy certain properties

namely, it has to be one one and onto

[mental hatch]

And the function is inverse to the original one as long as f(x) = y is true?

[ivory sorrel]

wdym

[mental hatch]

f^-1(y) = x is inverse to original f as long as f(x) = y

[ivory sorrel]

yes

but sin is periodic

so we chose a principal branch

[mental hatch]

I don't get why

[ivory sorrel]

Because sin isn't one one is it?

[mental hatch]

I mean, why exactly -90 <= x <= 90 ?

[ivory sorrel]

we just chose it as the range of sin in -90 to 90 is -1 to 1

[mental hatch]

Still don't get why we chose this range

[ivory sorrel]

as in why -90,90

and not 90,270?

convention

[mental hatch]

Okay, thank you

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[loud oasis]

the intervals for inverse trig functions are usually chosen as whichever interval contains 0

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[topaz reef]

So i was thinking something along the lines of this

For any x thats an interior point there is a open ball that is less than r

I went like this for any x thats an interior point we have $ d(x,z) \geq |d(x,y) - d(y, z)| \geq d(x,y) - d(y,z)$

i then decided that $d(y,z) < \varepsilon$ where $\varepsilon = d(x,y) - r$ which when plugged in gives r,

Thus showing that its an open ball, and then the compliment which is the boundry points closed by def

[thorny flame]

RealTek

[topaz reef]

and the reason for me choosing that to be epsilon is because for any y in d(x,z) there will be an open ball contained in d(x,z)

kunda shows the interior is a subset of the boundry points too (i think right?)

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[hollow bramble]

Greetings.

Solve the:

36 * cos(x+cos(x)) * cos(x-cos(x)) +9 = π²

Thanks.

[hollow bramble]

Sorry for camera

[neon iron]

I would first try to convert it into a single function

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<@&286206848099549185>

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[violet relic]

I dont have time to finish rn, but it may help you

with:

[thorny flame]

Info

[violet relic]

You have:

[thorny flame]

Info

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[hollow bramble]

Okie

[hollow bramble]

Anyway, thanks for your help

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[nimble vault]

im confused on how you would draw G7

ive calculated the edges according to the definition

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[hidden spear]

I'm supposed to use a calculator with this but I forgot how to get there and my calculator isn't working so I can only use an app I found so I can't figure out how to get to where I need on it.

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[thorny flame]

Ransik

[woeful drift]

https://tenor.com/view/shrek-you-thought-wrong-donkey-gif-14966485

it's always chain rule

consider just ln(x), you can use the chain rule on this too

it just turns out that d/dx(x) = 1

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[hoary quiver]

Hi could i get some help please.

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[weak quiver]

3. also why is it in the step immediately after that, they just rearrange the triple integral order completely?

[gentle comet]

in physics we often rearrange the order of integrals. In math though, we usually have to to some work beforehand to prove we can do that. The conditions necessary is a certain continuity of the functions we manipulate. In physics this continuity is always assured, so we can rearrange the order as we please

[weak quiver]

this is a calculus course, we dont really cover concepts related to physics as its not assumed we have a physics background

thats strange lol

[gentle comet]

1 and 2. Are you confused about the integration boundaries ?

[stone verge]

order of integration doesn't matter

[weak quiver]

yeah i understand every single boundary except the one 0 to pi

[gentle comet]

are you familiar with the spherical base we use in physics ?

[verbal raft]

he's not asking about physics

why are you so insistent on applying situational physics stuff to this

[gentle comet]

to understand the boundaries, you have to visualize the spherical base

[weak quiver]

so i can move around any of those three integrals, do them in any any order, and id get the correct answer?

[stone verge]

yes but you need to make sure an outer integral have "free bounds"

[weak quiver]

so the order does matter?

[gentle comet]

not as carelessly as you do now. for more info you can check out Fubini's theorem

the order does matter, but in most cases the conditions needed are respected

you are not, he is agreeing with me. You can not move the order of integration a priori

[stone verge]

like the inner bounds cannot depend on the outer bounds

on the LHS you have a numeric value

whereas the RHS is meaningless

in your case all bounds are constant

so you can separate them

yes i messed up

it was with dx at dy and yeah oops

[weak quiver]

what?

ok ill look back on this in a second i gotta digest all of this being said

[stone verge]

ill send an easier example

you can do that when the bounds of the outer integral are not a functions of a variable that is in the inner integral

forget this

im just gonna send a short "proof"

the conditions are, the function is separatable and the bounds are constants (numbers)

[weak quiver]

yeah i looked up fubini's theorem, i get it, just dont understand how it applies here, trying to wrap my head around it.

[stone verge]

yeah fubinni is stronger cuz works for non separatable functions

ok anyways

phi opens from 0 to pi

do you see why

[weak quiver]

i know phi is between 0 and pi, i looked into that as well when looking into a spherical base so my first question is also answered

just want to know why there was this black magic moving around of integrals now

[gentle comet]

because the bonds are constant

the integration bounds being constant, and not depending on one another, you can seperate the triple integral into 3 single integrals

[stone verge]

if you still have doubts here's what you can do by taking out constants

this looks like a mess but lets review it by parts

the inner integral is with respect to p

so everything that doesn't depend on p is a constant

you take that out

... okay i don't think i need to explain that

its just repeat that step

a bunch of times

[weak quiver]

so excuse my complete bewilderment

[stone verge]

ok

[gentle comet]

its ok, stuff like this can become confusing quite quickly

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[bleak bough]

I am trying to solve the subset problem. I am given a set of integer positive numbers and a number S. I need to find a subset where the sum of every element = S.

I want to transform this sum of subset problem into another which is the sum of square.

So I will be given the same set of positive numbers but this time I wanna know if we can partition the set into K sets where the squared sum of every subset added together <=S

[bleak bough]

So I need to transform an instance of the Sum of subset problem into an instance of the Sum of Square

Here is an example

The answer of the subset problem would be {6,5,3}

because 6+5+3 = 14

Now from the same set I need to find an S and K value

K would be the number of subset I can make where the squared sum of each subset added together would be <= S

i only need to find S and K

[gleaming reef]

oh the original problem is trivial if you consider partial sums

you can get O(n)

just compute partial sum and it becomes similiar to two sum

[bleak bough]

currently doing that

[bleak bough]

what do you mean the partial sum?

[gleaming reef]

think about it like this

if we keep track of the curr sum

in a[x]

if we do a[y] - a[x] = sum of elements between x and y

[bleak bough]

ok so a[x] would hold the sum of x + x-1 + x-2....

not the index but value

[gleaming reef]

yeah wait tho give me a second

[scenic flare]

a[y] - a[x] would be sum from x+1 to y in your case right

[bleak bough]

ok thank you bro

i have been trying some stuff since 9 am

[gleaming reef]

I think ur just thinking about this problem wrong

it is not a hard problem per say

it's literally just two sum reworded

[scenic flare]

is the problem you want to reduce onto with the input set fixed? meaning you can't transform the set

& is it the sum of the values² or the (sum of the values)²

[bleak bough]

I can transform the set, but from my understanding, the teacher only test that both set are satisfiable or not

[gleaming reef]

that's the idea

where pref[0] = 0

I guess it becomes pref[R+1] - pref[L}

[bleak bough]

ok so

[gleaming reef]

but once you have this logic down

it becomes very very eays

[bleak bough]

But what would the partial sum represent?

I don't really understand why we calculate the partial sum because anyway we would go through the entire set no?

[gleaming reef]

oh I'm misunderstanding

this is a dynamic problem question

this is not a subarray

this is subset

just consider recursion and memoization here

I'm so sorry

[gleaming reef]

my method would work for subarray

for the subset problem you would have to use DP

[scenic flare]

I won't intervene with the penguin's neat approach,
my CS approach with transforming the input would be to simply set K=2, S=S², and add an element to the set equal to 2S² - sum of squares

[bleak bough]

yeah DP I have to prove next why it's a DP

ok let me try

[gleaming reef]

if you want a hint, I found something from online

"So we will create a 2D array of size (n + 1) * (sum + 1) of type boolean. The state dp[i][j] will be true if there exists a subset of elements from set[0 . . . i] with sum value = ‘j’. "

[scenic flare]

the first or second problem?

[bleak bough]

Both, the problem is a lot bigger

I have the partition problem also to transform into the same thing im trying to get here

so the idea is to prove that partiton is DP

and that subset is DP

to prove that subset of squared sum is also DP

[scenic flare]

hm yeah I think that matrix can be crunched :3

[bleak bough]

ok thanks let me try

[bleak bough]

the 2S^2

is the original value of S?

or the one squared

[scenic flare]

let's denote them K1 S1

for the original

[bleak bough]

yep

[scenic flare]

K1, S1 are given

[bleak bough]

K1 isnt given

only S1

[scenic flare]

nvm K1 doesn't exist

K = 2

S2 = 2S1²

[bleak bough]

K can be 2, since in the sum of subset since you would have one that solve the problem and one that dont

[scenic flare]

New Input Set = Old Input Set U {2S1²-sumOfSquares}

[bleak bough]

2S1^2?

[scenic flare]

yes

wait just to clarify again, for the second problem, is it Sum[value²] or Sum[value]²?

[scenic flare]

what's Kc & Ci

[bleak bough]

Kc = K

K is the number of subset you can make

C is a subset

so C1 is the first subset

C2 is the second

etc

[scenic flare]

the sum of squared subset sums needs to be <= S2?

[bleak bough]

yeah

[scenic flare]

that's weird k

[bleak bough]

only

only if the original problem has a solution

[scenic flare]

ys, reduction

[bleak bough]

yup

Am i high for this to fail?

[scenic flare]

I don't code in C/C++ sry

[bleak bough]

np

ok thank you guys I will try to make it works but you have given me a lot of hope

[scenic flare]

hm it's definitely an odd mapping, is the task intended to not use input transformation?

if we have some original set with a subset equal to S1

then if we force K=2 for instance

then we need the requirement of a minimal sum of squared sums exactly if it's partitioned in a way such that one of the partitioned sets is the initial subset equal to S1

we could f.i. force that behavior

[bleak bough]

We would be able to add a number to that set

and just add that number squared to S1 for S2

no?

[scenic flare]

ok if we can add at least one number, then it'll be simpler

[scenic flare]

we can add an element which cancels the remaining sum for instance I think

[bleak bough]

these are some example set

I think your idea works

we would have the original set = S1

[scenic flare]

hm yeah what if we add -7

[bleak bough]

if we squared both of them

we cant add negative number

[scenic flare]

k

[bleak bough]

we would have original set ^2 = S1 ^2

then we had for ex 2 to the original set

to get S2 we would do

original set ^2 + 2^2 = S2

with a K = 2

wouldn't it work ?

[scenic flare]

original set² + 2² = S2?

[bleak bough]

yeah

[scenic flare]

not sure how you got to that

or rather, which element would you add to cancel the sum

[bleak bough]

the element doesnt matter

We know Sum(original set) = S1

[scenic flare]

si

[bleak bough]

If we have K =2 , we would need to have 2 sets

one would be the original set

the other would be the number we add

[scenic flare]

original subset u refer to ryt

[bleak bough]

yeah

ohhs

shit

im dumb

nvm

[scenic flare]

only a single number?

what's with the remaining ones :D

[bleak bough]

nvm doesnt work i forgot it was a subset that was =S1

[scenic flare]

yes we want the sum of the two squared sums to be minimal

if the other values get grouped together

the easiest way to achieve that to have a negative number I think

if we only take positives then hm

[bleak bough]

yup but only positive numbers are in the set

Ok the CS approach you told me earlier doesnt work

[scenic flare]

yeah because I interpreted the question differently

say our elements would sum to 20

ignoring S1 & S2

then the minimal possible sum when partitioning into two subsets

is if they're equal

[bleak bough]

yeah

[scenic flare]

so first set sums to 10, second to 10

because x² + (20-x)² is minimal at x=10

which is true for every even sum

it'll always be minimal at half the value

which means we can take the original sum S1

[bleak bough]

For the first part of the question I did the same thing

[scenic flare]

and let the other squared subset equal S1² too

[bleak bough]

I split it in half by 2

Squared the sum/2

[scenic flare]

ys, now this approach ofc only works if the initial sum is >= half of the set

if we have {1,2,3,4,5,6} S1 = 5 for instance

then it won't

since the remaining values are >5

in that case, we could repeat the process

hm alth we can't be sure if there are numbers bigger than the subset sum we desire

which makes it tricky

[bleak bough]

How could you repeat the process for the remaining values?

[scenic flare]

well if you have a sum of 30 for instance

what's the best way to split them into 3 subsets

such that the sum of square sums is minimal

[bleak bough]

10,10,10

[scenic flare]

yes

which is what we can utilise

if the sum is too big

repeatedly

[bleak bough]

so if you have a 13 7 and 10 you split the 13 in 2 half?

[scenic flare]

nono that'd skip the process of adding elements

the added elements would ensure that it can be split into 3

but I'm uncertain how

[bleak bough]

ahh

[scenic flare]

so if we have S1 = 10 for example, but the entire set sums to 100, then we'll need at least K=10

for an even split

[bleak bough]

Ok by using your idea i pass 4/5 test

Yeah, but if K is too big the complexity becomes too high

because the functions that checks if there is a solution is in 2^n

[scenic flare]

is there some number theory perspective we overlook

because ensuring that in the second problem it's split such that the original subset is preserved

would require an equal splitting of values I'd presume

[bleak bough]

hmmm

So we could do

K = Sum / S1
S2 = K*S1^2

[scenic flare]

don't yet see a way to ensure edge cases are covered, wish thee best of luck solving it though, am a lil tired so I gtg 🦇

[bleak bough]

ayt thanks a lto for the help

I appreciate it

[scenic flare]

What would work is adding 1's equal to the difference

which would force one partition subset to contain S1 as sum

Yeah

I'll call the initial set X

For the transformation you'd first remove all elements from X that are greater than S1

then we calc sum(X) - S1 = Delta

and we add Delta * (S1-1) ones to X

then we get the <=> implication for the reduction

because we essentially construct Delta arbitrary partitioned sets containing the remaining elements from the original set and 1's

[bleak bough]

ok you have a giga brain

[scenic flare]

and one partitioned set must be the original set equal to S1

the adding 1's part could be optimized though

given the values in the set

[bleak bough]

so then S1 would be the minimum value

[scenic flare]

depending on the runtime complexity requirements

[scenic flare]

well S1 is given

S2 = (Delta+1) * S1²

because we'll have K = Delta+1

and each partitioned set must contain a sum of S1

so the minimal possible sum is (Delta+1) * S1²

still sounds like a more theoretical approach to this reduction than a practical one, I must overlook something

[bleak bough]

ok let me try it out

[scenic flare]

If your set has n numbers which are bounded by m, then the current runtime is O(n*m)

so pseudo-polynomial runtime

since m is an input number, no input size

[bleak bough]

instead of adding 1, won't adding Delta*S1 at the end of X work

your solution works

omg

[scenic flare]

You can optimize in the added values now yes :)
you need to still ensure all other sets of sum S1 can be created

[scenic flare]

Oh I thought it'd run out of time

but it seems it's on the acceptable runtime spectrum

which suggests this problem isn't easy to optimize

[bleak bough]

My solution must be in polynomial runtime

I think your solutions is in Polynomial runtime

so it works

i will have to do a deep analysis

[scenic flare]

It's O(n*m) so sadly pseudo-polynomial :/

it's a good pseudo-polynomial but not purely polynomial

[bleak bough]

doesn't work because of the positive requirement

[scenic flare]

k

[bleak bough]

but I can use the maximum theorem to just have O(n)

[scenic flare]

well yh, theoretically a bit loose but yes

are you given a bound?

[bleak bough]

omg im dumb at the end of the document the teacher left a clue

but its pretty much what we are doing

[scenic flare]

Actually you have the integer size bound in C++ ig :D

[bleak bough]

Hint: Add two integers (possibly different) to the set, but too large to belong to the same subset. By setting the right values to these two elements as well as to the integer EcEc​, you can ensure that the answer to the partition problem is "yes" if and only if the answer to your instance of sum of squares is "yes".

yup but I dont think it will cross it

the bound

[scenic flare]

Oh yh two integers suffice, S2 should be much bigger instead

which reduces the runtime

say your set has sum 27

and S1 = 13

then we can take some arbitrary larger number (preferably magnitudes bigger)

eg 100

and we add these two elements:

100-13 = 87

100-14 = 86

And we take S2 = 2 * 100²

then it'd force a split where one of the partitions contains the subset with sum 13

I thought too narrow of how we construct S2

[bleak bough]

i dont get the 100-13 and 100-14 part

[scenic flare]

We want to construct two subsets which sum to 100

and we know there exists a subset in the original set with sum S1 = 13

and the entire set sums so 27, so the remaining values sum to 14

and if we want to force a grouping of the elements that sum to 13, we can add the elements
87 and 86

because if you now want to create a partition of two subsets which each equal 100

then you have to take 87 with the elements that sum to 13

and 86 with the others

which means O(n) runtime as we only need the sum of values

nywys gtg but you can also dm me if you stumble upon CS related questions since the density of cs students/tutors is lesser than mathematicians here clearly :]

[bleak bough]

ohhhhhh

i get it

omg

ok bro thanks a lot

you really helped me a lot

I appreciated it

[topaz sinew]

@bleak bough Has your question been resolved?

[topaz sinew]

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[woven quartz]

Hi, I would appreciate if someone can give me hints on how to solve this PDE ( the questions list is from Legendre polynomial applications )

[woven quartz]

Im stuck, as stated in the forum, in solving for theta

The ODE for R is of the Euler-Cauchy type and I think I got it right

For the procedure im using Separation of variables method with the solutions superposition principle

after the procedure this is the ODE for theta

This is ODE for r, Euler-Cauchy

with an strange solution for this type of equation imo

this is solution for R

That leads me to this uncompleted solution

Hope this clarifies what I´m doing or trying to do

[woven quartz]

I think it sould apear legendre polynomials but I dont know how

[topaz sinew]

@woven quartz Has your question been resolved?

[snow timber]

Ive searched around laplace equations and i think a change of variable of t = cos(theta) should get you to a legendre differential equation @woven quartz

[woven quartz]

yup

that does it

thanks

i did´nt notice that it was the Laplace equation for spherical coordinates with phi zero

[topaz sinew]

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• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

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