The density of atmosphere (measured in kilograms/meter3) on a certain planet is found to decrease as altitude increases (as measured from the planet's surface). What type of relationship exists between the altitude and the atmospheric density, and what would the atmospheric density be at an altitude of 1,291 kilometers?

Amerry-go-round of radius r, shown in the figure, is rotating at constant angular speed. the friction in its bearings is so small that it can be ignored. a sandbag of mass m is dropped onto the merry-go-round, at a position designated by r. the sandbag does not slip or roll upon contact with the merry-go-round. how would you rank the following different combinations of m and r on the basis of the angular speed of the merry-go-round after the sandbag "sticks" to the merry-go-round from largest to smallest. a) m = 10kg, r = 0.25r b) m = 20kg, r = 0.25r c) m = 10kg, r = 0.50r d) m = 10kg, r = 1.0r e) m = 15kg, r = 0.75r f) m = 40kg, r = 0.25r