Recent content by Sethric

Correct.

You will need to go all the way to pi for phi. Your theta bounds are correct. You don't need to worry about visualizing it - you know the volume differential: \int dV = V

You are missing a sine in your volume differential. Otherwise, what is the question? What work have you done on it so far?

No, mass is not a vector. Your two vectors will be a unit vector pointing in the direction of the ramp and a weight vector pointing down. The weight vector will have a magnitude of (9.8)(15) = 147 (Newtons, if it matters).

The reason you get a vector is that you are looking at a projection along a vector. In this case, you would be multiplying your scalar projection by a unit vector in that direction. Just because your terms matched the magnitude of a cross product, does not mean you have a cross product. You...

Umm, that is the correct answer, but not the correct method. You shouldn't need the cross product. You defined mass as a vector, and then gravity as a vector, and then said they point in different directions. That is incorrect. Mass is a scalar, force from gravity is a vector. You want to find...

There should be a double sum there, with a sum over k from k = 0 to n. Then you should be able to just solve what that sum would be.

The way I have seen this is: In a more generalized form in first order (y' = f(x, y)), if there exists a solution that serves as a boundary between two classes of solutions to the differential equation that behave differently, then that solution is called a separatrix. I don't think I have seen...

I see, you are talking about part 1. Well then, use your initial values. You know that the form will be y = y0 e-ct. You know that y0 = 240. Next, y4 = .4*240 = 96. That can solve for c.

Have you considered trying L'Hospital's Rule?

Try writing out the amount of the drug in the body at each time. At time t0, there will be 240 mg. At t=4 there will be 240 mg (next dose) + .4*240 mg (last dose). At t=8, 240 mg (next dose) + .4*240 mg (previous dose) + .4*.4*240 mg (first dose). What does the pattern look like? Can you write...

Hmm, weird. OK. Then you will want to find the projection of the force due to gravity on a vector that points down the ramp. That will require a dot product. Recall projections?

It would be easier to think of this in forces. The frictional force would be equivalent to the component of the force due to gravity that would point down the ramp, since they must cancel. Break gravity down to find that. Are you required to use a dot product here?

Try proof by contradiction. Assume that there exists an upper bound less than 2.

Partially correct. Assuming the center is a non-trivial proper subgroup of your p-group, then it is, by definition, normal - meaning your p-group is not simple. And it is required to be non-trivial. However, your center need not be a proper subgroup. If your center is the entire p-group...