Recent content by scottie_000

Have you drawn yourself a small sketch of what the curve will look like in this case? Remember that the mean is already at 12. Also, since this is a continuous distribution, you need to find the probability that X is within a range of values: P(0<=X<=12) = P(X<=12) - P(X<=0)

The best way to write this is using \LaTeX, but that's best learned another day. What operations for finding a determinant do you know about so far? Hint: You want to try eliminating entries in one of the rows so they become 0. What about replacing the 3rd row with (3rd+2nd+1st)?

Mathematics is indeed a wonderful tool to describe the world around us. And it works as a language in which we can successfully render physics. However I like to think that mathematics is universal; the way in which we communicate does not alter what we are attempting to discover. Just my...

Anyone have any ideas? I'm sure it's very simple, but I can't think how to actually prove it

You have your equation \frac{\dot\epsilon}{\epsilon} = -3(w+1)\frac{\dot a}{a} From here you can eliminate the time-dependence \frac{d\epsilon}{\epsilon} = -3(w+1)\frac{da}{a} and this is a differential equation involving just \epsilon and a you can solve by integrating both sides

Homework Statement I am given a static spacetime line element which has the property that the metric is time independent. I am asked to calculate some of the Christoffel symbols, which I have done. The question asks to show that for an observer at rest, the four-velocity is given by V^a =...

Glad to help

^(1/3) just means cube root, so is there a button with a 3 in a square root sign?

Are you able to write down the equations of motion for a projectile in terms of s, u, v and t? These are the standard equations one uses to solve such problems If you can do this, then you need to be able to split the motion into horizontal and vertical components and solve from there. Let me...

Can you write down the relevant Maxwell equation, then change all derivatives in length and time to simple division by their charactersitic values?

Or you could just answer the entire question... Is it not better to give a few hints, so that the OP will understand how to do it themselves?

Assuming the vessel is filled with water, do you know how many litres of water is in a cubic metre? Or how many ml makes up a cubic centimetre? From there you need to be able to rearrange this equation to solve for r in terms of V

No need to worry really. You will come across it sooner or later and it's good to know

Do you know how to solve x^2 y'' + axy' + by =0 in general? Hint: Use the substitution x = e^z

Yes the answer is likely to involve R somewhere. However, your equation for the hemisphere is slightly off: can you write down the equation for a sphere of radius R in terms of x,y and z? Once you have that, it is a simple case of restricting z to be positive as you said. Also, maximizing the...