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[Amperzand]

That sounds super incomprehensible. :V

[MagmaMcFry]

Can anyone tell me what "occur to an even power" mean? All Google shows me are incomprehensible pure mathematics textbooks.

You left out a lot of context here, but if I need to take a guess, it's about prime factors and divisibility. For example, 3 occurs to an even power in x if you can divide 3 out of x an even number of times until it is no longer possible.

Example: x is a square number if and only if every prime occurs to an even power in x.
Way cooler example: x is the sum of two square numbers if and only if every prime that is one less than a multiple of 4 occurs to an even power in x.

[Skyrunner]

Does anyone know what the "x" in a probability density function f(x) stands for? @_@

I'm trying to prove that for X ~ U(a, b), the probability that X is less than a + (b-a)p equals p. I know this is intuitively correct, because programming and stuff, but I can't figure out how to make it a proof.

[Virex]

It's just the point at which you're evaluating the probability density.

[MagmaMcFry]

You can intuitively represent the probability density as the derivative of the probability distribution function. To prove your thing, calculate the probability of X < a + (b-a)p by integrating your density from -infinity to a + (b-a)p.

[Skyrunner]

Ah, got it!

[Vector]

-snip-

[MagmaMcFry]

Or like this:
We know a <= c and b <= d, so a+b <= c+d, which is equivalent to b-c <= d-a.

[Vector]

-snip-

[smjjames]

so much for my attempt to direct a derail here.......

[Shadowlord]

Copied and commented from another thread, somewhere in here I presumably made a mistake which I'm not immediately seeing:

This is using relativistic mass, I started with m=M0/sqrt(1-v^2/c^2) and E=m*c^2

Everywhere I wrote m below it's actually M0, the rest mass. I combined the two equations and changed the variable name to avoid confusing wolfram alpha later. Also j is E. It's named j so I can remember that it's in joules.
m/sqrt(1-v^2/c^2)*c^2=j

I was trying to solve for v:

(c^2*m)/(j)=sqrt(1-v^2/c^2)

((c^2*m)/(j))^2-1=-v^2/c^2

-v=sqrt((((c^2*m)/(j))^2-1)*c^2)

Substituting in real numbers and checking the result in W|A gave me a velocity that was both negative and, it it has been positive, far, far greater than the speed of light, which should have been impossible if I did that all correctly.
v=-sqrt((((c^2*10.89 kg)/(0.042 TJ))^2-1)*c^2)

Result of running that through on wolfram alpha:
"v = -2.33*10⁷ sqrt(1 c^2)"

[TheDarkStar]

Your math is correct but the equation is wrong. E = mc² is only true if the momentum is zero. Wikipedia tells me that you want to use is
E_kinetic = ^{(rest mass)c^2}/_{sqrt(1 - v^2/c^2)} - (rest mass)c^2.

[Shadowlord]

Ahh, thanks.

[3man75]

Some problems I've been having trouble with...

1. F of G (4); F(X) |19x^2 - 10x|; G(X) 19x - 10;

I know you have to put G into whatever x's F has like so: 19(19(4) - 10)) - 10 (19(4) - 10 (4)); After commulating that I find that the answer I get isn't part of the any of those provided. Where am I going wrong in the substitution or something else?

2. I'm doing logathrithm expressions and I'm comfortable with Logs but they also have a problem here stated as: ln 1 over e^3 = -3;

I just have no idea what do do when they say change it from log to an equivalent expression with a exponent.

I mean I do know that if you get something like log4^1 over 64 = -3 that you can change it to 4^-13 = 1 over 64.

**1 over 64 is a fraction by the way. I don't know how to do fractions on written forums. Same above When I say number over something.**

3. When they ask for the domain of a function in F(x) = log10 (x +8 over x - 6) does the 10 mean anything? I'm tempted to just say that all numbers not positive 6 , negative, or 8 are okay for x.

[TheBiggerFish]

3man75:Absolute value sign.



Do you know negative exponents?
1/e^3 = e^-3
ln(e^-3)=-3

Log base 10.  As opposed to natural log, log base e.

Like log₁₀(10^3)=3=log_e(e^3)

As for fractions, use /.

That is how you fraction.