Use spherical coordinates.
Let H be a solid hemisphere of radius 2 whose density at any point is proportional to its distance from the center of the base. (Let K be the constant of proportionality.)
(a) Find the mass of H.
(b) Find the center of mass of H. (Assume the upper hemisphere of a sphere centered at the origin.)
(c) Find the moment of inertia of H about its axis.

Which is the equation of an ellipse with directrices at x = ±4 and foci at (2, 0) and (−2, 0)?

1yd 1 ft = 1 1/12 1 1/3 1 1/2 1 1/6

Christine wong has asked dave and mike to her move into a new apartment on sunday morning. she has asked them both, in case one of them does not show up. from past experience, christine knows that there is a 40% chance that dave will not show up and a 30% chance that mik a. what is the probability that both dave and mike will show up? (round your answer to 2 decimal places.) b. what is the probability that at least one of them will show up? c. what is the probability that neither dave nor mike will show up? (round your answer to 2 decimal places.)e will not show up. dave and mike do not know each other and their decisions can be assumed to be independent.