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Math 125 – Section 04 – Calculus I Lab Assignment 6 – John Tynan Due Date: October 14 Name:___________________________________ Score:______________ You must show all of your work to receive full credit. Each question is worth 5 points for a total of 30 points. 1. A spherical balloon is inflated so that its volume is increasing at the rate of 3 ft3/min. How fast is the diameter of the balloon increasing when the radius is 1 foot? 2. Suppose that we have an inverted conical water tank that has a height of 8 m and a radius of 3 m. Water is being pumped into the tank at a rate of 5 cubic meters per minute. When the water inside the tank is 4 m deep, how quickly is the height of the water in the tank increasing? How fast is the radius of the top level of the water increasing at that same instant? 3. Suppose that a kite is 400 feet in the air and remains at that height. The kite is blowing horizontally away from the owner of the kite at a rate of 12 ft/s. How quickly is the length of the string increasing when 480 feet of string is already being used? Assume the string forms a straight line. 4. A television camera is positioned 4000 feet from the base of a rocket launching pad. A rocket rises vertically and its speed is 600 feet/second when it has risen 3000 feet. If the camera is kept focused on the rocket, how fast is the camera’s angle of elevation changing when the rocket is 3000 feet high? 5. Two boats are positioned so that one is 200 miles east of the other. One boat begins moving due north at 20 mph and the other begins moving south at 30 mph. How fast is the distance between them increasing 5 hours after they begin moving? 6. A baseball diamond is a square 90 ft on a side. A player runs from first base to second at a rate of 16 ft/sec. (see page 201 in your book) At what rate is the player’s distance from third base changing when the player is 30 ft from first base? At what rate are angles θ1 and θ2 changing at that time?