7. 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 (in m/s) is the boat approaching the dock when it is 7 m from the dock? (Round your answer to two decimal places.)
8. At noon, ship A is 70 km west of ship B. Ship A is sailing south at 40 km/h and ship B is sailing north at 20 km/h. How fast (in km/h) is the distance between the ships changing at 4:00 p.m.? (Round your answer to one decimal place.)
9. Water is leaking out of an inverted conical tank at a rate of 9,500 cm³/min at the same time that water is being pumped into the tank at a constant rate. The tank has height 6 m and the diameter at the top is 4 m. If the water level is rising at a rate of 20 cm/min when the height of the water is 2 m, find the rate (in cm³/min) at which water is being pumped into the tank. (Round your answer to the nearest integer.)
10. Gravel is being dumped from a conveyor belt at a rate of 35 ft³/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 (in ft/min) is the height of the pile increasing when the pile is 14 ft high? (Round your answer to two decimal places.)
11. The top of a ladder slides down a vertical wall at a rate of 0.25 m/s. At the moment when the bottom of the ladder is 5 m from the wall, it slides away from the wall at a rate of 0.6 m/s. How long is the ladder?
