Homework Statement
5. What is the average distance traveled by a muon with an energy of 5 GeV? 500 GeV? (assume v is approximately c)
Homework Equations
The Attempt at a Solution
I wasn't really sure where to begin with this. I was under the impression that if in both...
1. Homework Statement
Which of the following Nuclear Reactions are allowed?
A) e- + p --> \mu- + p
B) n --> p + \pi-
C) K- + p --> (anti)k0 + n
2. Homework Equations
While I don't know if there are any relevant equations, I know that there are several conservation laws that are required...
Homework Statement
Determine the equation of the following points:
(12. 270)
(14, 300)
(16, 330)
(18. 380)
Homework Equations
The Attempt at a Solution
I realized right away that this is not a linear set of points, so it wouldn't work out to just find the slope between two...
Homework Statement
\oint \frac{dz}{z^2 + z} = 0, C: abs(z) > 1
Homework Equations
\oint \frac{f(z)}{z-z_0} dz = 2i\pi * f(z_0)
The Attempt at a Solution
Under normal circumstances, I usually deal with these in the following way.
I say that F(z) = 1 (the value in the...
Homework Statement
What is the gravitational potential both inside and outside a spherical shell of inner radius b and outer radius a? Homework Equations
\Phi = -2\pi*G*\rho*\int (r'*r') \int (sin(\theta)/r) d\theta
Integration range for the first integral is from a to b, while the...
Homework Statement
Integrate:
\int \int \frac{1}{[(x_1-x_2)^2+a^2 ]^1^/^2} dx_1 dx_2
(The bounds on the first integral are [-L/2, L/2] and the second integral's bounds are the same.)Homework Equations
N/AThe Attempt at a Solution
I stared at this problem long and hard, and was hoping to...
I can say that my original function is greater than this new function, and that this new function is also divergent.
OK, I can see how your choice coincides with the way the convergence test is written. I just made the mistake of jumping the gun with this new technique =).
I want to relate it to something like
\frac{1}{\sqrt{n(n+2)}}
But to be honest I can't think of an easy way to deal with that one either...I'll continue thinking about it...thanks for correcting it though =).
Ah OK, thanks so much for your help! My professor gave us a whole list of these things to figure out, and if I'm applying the comparison test you just showed me correctly, then I shouldn't have any more problems.
Am I applying what you just showed me in the correct manner here...
Sigh.
Using your method, I got the answer in 15 seconds, as opposed to the 15 minutes my other way took.
Thanks to you, I know this is now convergent - but, for future reference, is it OK for me to make that assumption that I made towards the end of the problem?
Homework Statement
Is
\sum \frac{1}{2n(2n+1)}
convergent or divergent?
(Note that the summation is from 1 to infinity)
Homework Equations
\int f(x) dx = L, (range is from 1 to infinity)
IF
L = \infty, divergent
L < \infty, convergent.
The Attempt at a Solution
I...
Homework Statement
Show that
\sum \frac{n!}{10^n}
converges or diverges.(Note, I was unsure of how to format this via latex, so the summation is from n = 1 to infinity.)Homework Equations
The root test:
|\frac{a_n_+_1}{a_n}|
The Attempt at a Solution
a_n=\frac{n!}{10^n}...