The radius of a cylindrical tube is increasing at a rate of 2 meters per hour, and the height of the cylinder is decreasing at a rate of 5 meters per hour. At a certain instant, the base radius is 4 meters and the height is 6 meters. What is the rate of change of the volume of the cylinder at the instant? What is the ratio of the instantaneous radius to the altitude at the instant when the rate of the volume is neither increasing nor decreasing?

1. How fast is the water level rising in a rectangular fish tank whose base is 20 ft² if the tank is being filled at a rate of 0.5 ft³/min? Your answer

1. A spherical balloon is inflated so that its volume is increasing at the rate of 7 How fast is the diameter of the balloon increasing when min the radius is 3 ft? min NOTE: Enter the exact answer. Rate of change of the diameter = min 2. A conical water tower with vertex down has a radius of 14 ft at the top and is 18 ft high. If water flows into the tank at a rate of 28 ft/min, how fast is the depth of the water increasing when the water is 17 ft deep? Round your answer to two decimal places. The depth of water is increasing at a rate of ft/min. 3. An aircraft is flying horizontally at a constant height of 5000 ft above a fixed observation point (see the figure below). At a certa instant the angle of elevation is 30 and decreasing, and the speed of the aircraft is 240 mi/h. Use 1 mi=5280 ft. a) How fast is decreasing at this instant? Express the result in units of deg/s. Round your answer to one decimal place. 0 is decreasing at a rate of deg/s. b) How fast is the distance between…

10. A ladder 20 feet long leans against a building. If the bottom of the ladder slides away from the building horizontally at a rate of 2 ft./ sec. How fast is the ladder sliding down the house when the top of the ladder is 8 feet from the ground. A. -2.5825 m/s C. -7.5825 m/s B. -6.5825 m/s D. -4.5825 m/s