The following table shows the period of revolution of some unknown planets of equal mass.

period of revolution

planet period of revolution
w 1.9 years
x 11.8 years

which of the following best explains which planet is farther from the sun?

a. planet w, because gravity is inversely proportional to the square of distance
b. planet x, because gravity is inversely proportional to the square of distance
c. planet x, because the sun exerts a greater gravitational force on it than on planet w
d. planet w, because the sun exerts a greater gravitational force on it than on planet x

Suppose water is leaking from a tank through a circular hole of area ah at its bottom. when water leaks through a hole, friction and contraction of the stream near the hole reduce the volume of water leaving the tank per second to cah 2gh , where c (0 < c < 1) is an empirical constant. a tank in the form of a right-circular cone standing on end, vertex down, is leaking water through a circular hole in its bottom. (assume the removed apex of the cone is of negligible height and volume.) (a) suppose the tank is 20 feet high and has radius 8 feet and the circular hole has radius 2 inches. the differential equation governing the height h in feet of water leaking from a tank after t seconds is dh dt = − 5 6h3/2 . if the height of the water is initially 8 feet, how long will it take the tank to empty? (round your answer to two decimal places.)