/sqt/ - Stupid Questions Thread, Stealing Last OP Edition

It's been a while since I've had to use multivariable calculus and I'm having trouble setting up this double integral (in 1. (a)).

I know 0 < X < 10 - Y < 10 defines the region (domain) of interest, and that if we ignore X we have 0 < 10 - Y < 10. Since 10 - Y < 10 we have that Y > 0, and 0 < 10 - Y implies Y < 10.
Would the region of integration then be (x,y) in R^2 such that x is in (0, 10 - y), y in (0, 10)? and then I would use these as my limits of integration, integrating with respect to y first?

Oh, and would it be easier (and correct) to evaluate a) P( X > Y) as

P( X > Y) = 1 - P(X < Y)?

No, absolute convergence implies convergence (while the reverse is not true). That means the radius of convergence of (ii) might be bigger than the one of (i). I think the answer to both is r=3 though

(Absolute convergence implies convergence since |an| >= an for all an, and if the bigger series converges, so does the smaller one)

Shouldn't u be in K? And shouldn't the point be to show that u is algebraic over F, not in the fucking field extension????!?!?! belrtvwykiu egrstw

what's Veeky Forums's opinion on 3blue1brown? based or normie-tier?

People who make posts like yours are generally gigalow IQ wheelchair-stuck mouthbreathers who struggle with not drowning in their own spit. You won't be doing any topology without people like 3blue1brown making "normie-tier" videos. Keep watching, my dude.

Is there a formula for testing whether or not a number is an integer?

Heard the latest Waking Up podcast with Sam
Harris and Charles Murray recently and it got
me interested in the book The Bell Curve.

Is there a decent updated version of this book
which adds interesting new discovery/research
to complement the book itself in an introduction
chapter or something?

Why did a man of Stephen Jay Gould's caliber get triggered by this book anyway?

>Shouldn't u be in K?
probably

>And shouldn't the point be to show that u is algebraic over F, not in the fucking field extension????!?!?!
probably

> Is there a formula for testing whether or not a number is an integer?
if floor(x)=x, if sin(x*pi)=0... etc.

Gould was a fraud and his book The Mismeasure if Man is literally libel against the dead. Morton's experiments were even reconducted and shown to have no bias. It isn't surprising that Gould, who has clearly demonstrated he places his ideologies over scientific investigation, would be triggered by such research - most especially because the authors make themselves clear on how their findings should affect our public policies. If it were up to Gould, research into such questions would be forbidden, which is a shame: public policy notwithstanding, physical anthropology and modern human evolution are both very interesting.

How do you become a normie?

EE sophomore, what should i be learning for finding internships?

Do the floor and ceiling functions have any interesting formulas?

Are you going into sophomore year or junior year? It really depends on what courses you can take. With power courses you can easily find open internship positions. I did electromagnetic/RF courses junior year that helped me get a nice internship with relocation package and everything. Just think of companies that you are interested in and see what they do/need and take classes related to that if you can. Also list any class or outside projects that may be relevant on your resume or cover letter.

So I come from a computer science background and need to learn the math required to understand some advanced physics like Schrodinger's Equation (PDEs) and Quantum Chromodynamics (Group Theory). From what I can gather, knowing the mathematics is probably the most important step in understanding these topics, and that's mainly where I'm lacking.
My mathematical understanding stops at Calc II, Bayesian Statistics, and Discrete Mathematics. Are there any self-study guides out there for working my way up to the math needed to delve into these physics topics?
I usually can gain a decent understanding of a topic if presented with proofs and an intuitive explanation in a textbook and some challenging problems to work through, although video courses wouldn't be bad either. I've looked on MIT's opencourseware, but i'm not sure what the best progression of topics should be from my current understanding.

Because space can and does expand much faster than the speed of light.

On en.wikipedia.org/wiki/Gauss–Seidel_method
in "An example for the matrix version" are the lines "We want to use the equation... in the form". Why? Why we want? And later, in "An example for the equation version" I also saw two version with and without using T and C.

If b is in aH (the coset), is it then fair to say bH is contained in aH?

no

Aren't they equal, though? b in aH means b = ah_1, so bH = { ah_1*h | h in H }, but h_1 * h, where h goes through all of H is just all of H again, hence bH = { ah | h in H}.

IF YOU SAY I AM WRONG I WILL FUCK YOU UP

>If b is in aH (the coset), is it then fair to say bH is contained in aH?
why would b ∈ aH imply bH ∈ aH, that makes no sense

Suppose that I have two numbers a and b such that their gcd is not 1.

Suppose then I compute
gcd(a,b+1)
gcd(a,b+2)
gcd(a,b+3)
...

Is there some kind of bound on how long I'd have to keep going to find an integer of the form b+c such that gcd(a,b+c) = 1 ?

in other words, put the shit into wolfram alpha bc thats what my calc 3 professor told us to do lmao

FUCKING
RESPOND

i would say that having the intuition to come upon the solution yourself is 1000x more useful than reading over the derivations and trying to memorize them. recently i've been reading this book called " How To Solve It " by George Polya and he has a list of steps for approaching any problem through heuristic reasoning. mainly though coming up with the solution yourself is immensely more satisfying than regurgitating information. good luck user

Why do symmetric matrices always have real eigen values?

Please someone help. I got P(X>Y)= 1/2 for the first, which makes sense since f(x, y) is constant, must integrate to 1 over the whole region, and we are concerned with half of it. But I'm stuck on part (b).

I know the marginal distribution of Y is

[math] \int^{\infty}_{-\infty}f(x,y)dx [/math]

but i'm not sure what the limits of integration should be. Will they be x = 0 to x = 10 - y?

Give me a quick rundown on these topics Veeky Forums

What is the weirdest usage of the modular function in an equation?

which modular function...?

oops, meant the modulo operation.

Basically, wondering if there are any equations that have it mixed in with a ton of other operations. Wondering because the equations I have seen are all really simple.

en.wikipedia.org/wiki/Ramanujan's_congruences
en.wikipedia.org/wiki/Kronecker's_congruence
en.wikipedia.org/wiki/Kummer's_congruence

How hard is it to get into grad school for EE at UIUC, UMich, Berkeley, and other top tier schools that aren't Stanford/MIT/Caltech level but are still great? I have a 3.85 gpa and plan to keep it there. Have research through SMART program labs.

I don't really have a question.

I just wanted to share that I'm going to horribly fail my linear algebra test tomorrow so I don't feel as bad with myself.
When all we do on class is calculate determinants and solve simple eq systems and then the test throws a curveball with shit I can't even fucking read and even less prove, that's where I throw the towel.
If you wonder how I know that, we were given unsolved old tests to practice, and they all share the same characteristic of being marginally more complex than anything we've seen in class.

>tfw you're a brainlet
>no face cause too ashamed

Greetings Veeky Forums,

was watching video on dimensions and when they explained imaginary numbers they explained it like you see in the first two graphs in the left of the picture.

the way they presented it made me wonder. If you follow the reasoning that [math]\sqrt-1[/math] is just a quarter turn, then what do you call eighth turns, sixteenth turns, and so on until you reach 1 again? what would the algebra look for systems with smaller and smaller turns? what would the algebra look like if you had "continuous" turning? what would a "continuous" imaginary number look like?

not homework or highschoo just a curious NEET.

>what do you call eighth turns, sixteenth turns, and so on until you reach 1 again?
en.wikipedia.org/wiki/Root_of_unity

makes sense

Yes it's fair.

Indeed, choose any bh in bH. By hypothesis we have b=ah', for h' in H. Then bh=(ah')h=a(h'h) which is an element of aH.

Kek

Why is this ok?

Replying to myself, but I found a good resource if anyone else is interested
hbpms.blogspot.com/

anybody knows a good list or a book with an OK variation of exercises about Vectors in Phyiscs (high school)? I'm getting somewhat stomped by this subject but now I'm motivated to dominate it!

ty in advance

>how do I show that
[eqn]\frac{k^{2}}{k^{3}-1} \geq \frac{1}{k} [/eqn]

but what if k is negative?

Walk me through this.

Let's say I predict 8 out of 10 events correctly. Each event has a 50% chance of occurring.

I can get the standard deviation with [math]\sqrt{5*(1-0.5)}[/math], which means I was ~2 standard deviations off.

How do I get a p-value from there?

Hartog Mechanics maybe?
I rarely check the exercise section, but it's my favorite first book for mechanics.

Walk me through this.

Let's say I predict 8 out of 10 events correctly. Each event has a 50% chance of occurring.

I can get the standard deviation with sqrt(5 * (1 - 0.5)) = 1.581, which means I was ~2 standard deviations off.

How do I get a p-value from there?

k^3 >= k^3 - 1

Multiply both sides with [math]k\cdot(k^3-1)[/math] (this works unless k=0 or k=1, in which case one of the sides of the equation is undefined, otherwise k^4-k is guaranteed to be positive, and therefore the inequality still holds)

Then you get [math]k^3 \ge k^3 - 1 \equiv 0 \ge -1[/math]

I thought not every function has an anti derivate

all continuous functions do

Oh, and that is assuming k is an integer. If k is real, for any k between 0 and 1, the formula does not hold (the multiplication does not work since k^4-k is negative then)

What's the antiderivative of f(x) = abs(x)

x*sqrt(x^2)/2

wolframalpha.com/input/?i=Integrate[Abs[x]]

Does sound wave have a weight?

Yes

You don't

Elaborate. Please.

How can you write that awkward stage of definite integration when you found the average integral but haven't plugged and subtracted yet?

You'd have some long formula for y(x), but now you want to signify somehow that that's what the original expression equals to so you can keep the equality chain.

I doubt you need to integrate. Just looking at the problem, note the pdf is constant. P(X>Y) is just area of the domain where X>Y times 1/50. You probably just need to calculate the area of a triangle.

>How can you write that awkward stage of definite integration when you found the average integral but haven't plugged and subtracted yet?
>You'd have some long formula for y(x), but now you want to signify somehow that that's what the original expression equals to so you can keep the equality chain.
Do you mean [math]z(x)|^b_a[/math]?

f(u)= 0, f poly of degree n. Divide by u^n.

So is it gonna be
> x^2 + 5 - x^3 |^b_a

> Find a median of an ordered sample of the first 9 whole numbers from the range of values of the function
WTF DOES THIS MEAN FFS?!

A median or the median?

>Writing a thesis on stochastic simulation and markov chain monte-carlo
>Every application seems to have a similar deterministic implementation that is often better optimized

Is Monte-Carlo a meme?

I don't fucking know it's not in fucking ENGLISH.

How THE FUCK do I integrate sqrt(-x^2 + 2)? Substitution clearly doesn't fucking work since it's just f(g(x)) without g'(x) factor.

Does anyone think richard feynman looks like the guy that reviews junk food on youtube in suit?

>How THE FUCK do I integrate sqrt(-x^2 + 2)? Substitution clearly doesn't fucking work since it's just f(g(x)) without g'(x) factor.
Substitution CLEARLY WORKS, the problem is that you want a direct answer after substituting. Try
x=Sqrt[2]*Sin[y]
and work until you get something.

Try trig subs

>x=Sqrt[2]*Sin[y]
WTF does sin have to do with it? Where does this come from ffs?

Expand PLEASE.

WTF IS UP WITH THIS WHOLE ROOT&MINUS SIGN BULLSHIT?! IT'S ALWAYS SOME FUCKERY WITH THESE TWO FFS.

>compute f(0), f(1), ... f(8) (I assume the first 9 whole numbers are 0..8, could also be -4, -3, ... 4)
>take median
>done

Well THAT'S WHAT I FUCKING DID - at least started to, and I get -3 3 5 15, so clearly it's not gonna be 0, which is the answer.

> (You)
> >x=Sqrt[2]*Sin[y]
> WTF does sin have to do with it? Where does this come from ffs?
Trig substitutions are very common. The idea is that, when you have to integrate a function of the square root of ax^2+b it is easier to use the properties of the trig functions.
Sqrt[ax^2+b]=Sqrt[b] Sqrt[(a/b)x^2+b]
substituting x=sqrt[b/a]Sin (y) this becomes
Sqrt[b] Cos(y)
and
dx=sqrt[b/a] Cos(y) dy

Therefore
Sqrt[ax^2+b]dx= (b/sqrt[a]) Cos(y)^2 dy

It's clearly the third answer though

Just try squaring both of them:
[math]-2b\sqrt b = \sqrt{-4b^3}[/math]
Then if you square both sides
[math] 4b^2 * b = -4b^3[/math]

> I assume the first 9 whole numbers are 0..8
That's the thing too, I have no fucking idea what do they mean by this.

\sqrt{-4b^3} = 2ib \sqrt{b}, which is the answer to A

Although the question does not make sense, since the first answer is also valid

That's what I meant. But for some reason the answer it the third ffs

You could write it as [math]\sqrt{-4b^3} = \sqrt4\cdot\sqrt{-b^3} = 2 \cdot \sqrt{-b^3} = -2b\cdot\sqrt{-b}[/math]

I cannot believe how RETARDED people itt are. IT'S UNDER THE ROOT FFS which means b IS NEGATIVE, which means THE ROOT OF b IS NEGATIVE. So the green answer is the only valid one.

Fucking idiots.

>WTF IS UP WITH THIS WHOLE ROOT&MINUS SIGN BULLSHIT?! IT'S ALWAYS SOME FUCKERY WITH THESE TWO FFS.
1. The - inside the square root stays in the square root. If you take it outside you get an "i", you dumbass. That's why your "obvious solution" is wrong.
2. Because the square root they are giving you is supposedly real this means that b

sqrt(2 - x^2) = sqrt(2)sqrt(1 - (x/2)^2)

Turn x/2 into z

so you have

sqrt(2)sqrt(1 - z^2)

Now do the substitution z = sint.

But where the fuck does sin come from? It has nothing to do with powers and shit that we have up to that point.

Differential Equations 1 final Thursday

I freeze up when given an equation to solve.... no idea where to start I know there isnt enough time to try every method (seperation of vars, variation of parameters, etc)

The root of 4 can be -2 and 2, so A is still a valid answer

Nice try except I solved it faster than you did You see because I'm not as slow as you, I post problems here AS I SOLVE THEM MYSELF, so it's parallel processing, which makes it faster. I don't normally ask question unless it seems literally impossible, but I have a crucially important test in less than 3 weeks, so no time to really enjoy the process.

I'm a brainlet, should I cut my losses and go for CS?