In general, to solve the heat equation, you should use a full Fourier transform--i.e. the one where you find the Fourier coefficients associated with plane waves ei(kx±ωt). Using this you can easily deduce what the coefficients should be for the sine and cosine terms, using the identity...
The term you seem to be looking for is called the "observer effect." Terms that are also very closely related are "wavefunction collapse" and "decoherence."
Light is subject to relativistic effects; for example light is redshifted or blueshifted depending on the reference frame in which it is measured, light can bend around gravitational sources (e.g. gravitational lensing), and there are issues of simultaneity characteristic of relativity...
Well you have set this up in a very unusual form (for example, why is your lower limit 2 and your upper limit -1?), but it is a correct setup and as it turns out the integral from y=2 to y=-1 of (-y)-(2-y^2) dy is indeed 4.5. So it looks like you're having trouble with evaluating the integral...
Since the curl of the vector potential A is equal to the magnetic field B, a good way to think of it is that A circulates around any point where B is nonzero--its net circulation around a point gives the B field at that point, according to the right-hand rule. It is important to remember though...
You could do this by doing a series expansion for the numerator and looking at the limit of the leading order expression. This is a useful series expansion:
cos(x-1) ≈ 1 - (x-1)2/2! + (x-1)4/4! + ...
This is basically the definition of cosine, but you can get it through taylor expansion...
Alright I think I figured out how you got your answer vela, and I do believe it is correct for the distinguishable lines case.
You said there are 12! possible orderings for the whole group of people, and then you multiplied this by the probability that the couple is randomly placed in the...
Edit: I've gotten so confused with this problem that I want to edit this post even though vela has already responded. My fault.
Vela started his argument by saying there are 12! ways to arrange these people, but that does not try to eliminate double-counting configurations such as:
(A B C D)...
I mean, I already told you the name of the unit:
Is it a problem that the units of acceleration are meters per second squared? That is an extremely commonly used one, as in g=9.8 m/s2
Basically, the strategy for finding the units of β is to make sure all other units cancel besides one power of [x].
Since the factor of 2/3 doesn't matter (it is unitless or "dimensionless"), and you already have figured out α, we can write:
[x]=[βt3/2] = [β] [t]3/2
where the square...
Well, first you are right that the radial force outward from the axis of the cylinder should cancel on the axis of the cylinder. One way to see this is through a basic "symmetry argument." Imagine there were a radial force away from one spot on the axis.
Now imagine we rotated the problem...
Well, I was able to solve this problem. You can factor A out pretty quickly... You can easily write:
A+B = (A + A cosθ, A sinθ) = A(1+cosθ, sinθ) while A-B=(A - A cosθ, -A sinθ) = A (1-cosθ, -sinθ). Then you have:
|A+B|=73|A-B|
|A(1+cosθ, sinθ)| = 73 |A(1-cosθ, -sinθ)|
Where the bars denote...
Hmm did you edit your OP? I'm a little confused now since now your relevant equation is correct. But yes, once you make that correction, it should work out with some algebra.
Edit: Okay, now I see you edited your second post. This is quite a whirlwind of edits! Next time I'd recommend making an...