(a) Find center of mass of a solid of constant density bounded below by the paraboloid z=x^2+y^2 and above by the plane z=4. (b) Find the plane z=c that divides the solid into two parts of equal volume. This plane does not pass through the center of mass.

10 ! in a race, nick is 50 feet in front of jay after ten seconds. how fast can nick run, if jay can run 20 feet per second?

Witch represents the inverse of the function f(x)=1/4x-12

Problems and applications q5 four roommates are planning to spend the weekend in their dorm room watching old movies, and they are debating how many to watch. here is their willingness to pay for each film: willingness to pay (dollars) shen antonio dmitri jake first film 10 9 8 3 second film 8 7 6 2 third film 6 5 4 1 fourth film 4 3 2 0 fifth film 2 1 0 0 within the dorm room, the showing of a movie a public good. if it costs $12 to rent a movie, the roommates should rent movies in order to maximize the total surplus. suppose the roommates choose to rent the optimal number of movies you just indicated and then split the cost of renting equally. this means that each roommate will pay $ .