Gravel is being dumped from a conveyor belt at a rate of25ft³/min, and its coarseness is such that it forms a pile in the shape of a cone whose base diameter and height are always equal. How fast is the height of the pile increasing when the pile is15ft high? (Round your answer to two decimal places.)

A plane flying horizontally at an altitude of2mi and a speed of500mi/h passes directly over a radar station. Find the rate at which the distance from the plane to the station is increasing when it is5mi away from the station. (Round your answer to the nearest whole number.)

mi/h

If a snowball melts so that its surface area decreases at a rate of7cm²/min, find the rate at which the diameter decreases when the diameter is12cm.

cm/min

A street light is mounted at the top of a 15-ft-tall pole. A man 6 ft tall walks away from the pole with a speed of7ft/s along a straight path. How fast is the tip of his shadow moving when he is35ft from the pole?

ft/s

Two cars start moving from the same point. One travels south at48mi/h and the other travels west at20mi/h. At what rate is the distance between the cars increasingthreehours later?

mi/h

A boat is pulled into a dock by a rope attached to the bow of the boat and passing through a pulley on the dock that is 1 m higher than the bow of the boat. If the rope is pulled in at a rate of 1 m/s, how fast is the boat approaching the dock when it is9m from the dock? (Round your answer to two decimal places.)

m/s

Gravel is being dumped from a conveyor belt at a rate of25ft³/min, and its coarseness is such that it forms a pile in the shape of a cone whose base diameter and height are always equal. How fast is the height of the pile increasing when the pile is15ft high? (Round your answer to two decimal places.)

ft/min

The top of a ladder slides down a vertical wall at a rate of0.675m/s. At the moment when the bottom of the ladder is3m from the wall, it slides away from the wall at a rate of0.9m/s. How long is the ladder?

m