Homework11 Homework11: Problem 1 Previous Problem Problem List Next Problem (1 point) A road perpendicular to a highway leads to a farmhouse located 2 mile away. An automobile traveling on the highway passes through this intersection at a speed of 55mph. How fast is the distance between the automobile and the farmhouse increasing when the automobile is 3 miles past the intersection of the highway and the road? The distance between the automobile and the farmhouse is increasing at a rate of 45.76 miles per hour. Previous Problem Problem List Next Problem (1 point) A hot air balloon rising vertically is tracked by an observer located 2 miles from the lift-off point. At a certain moment, the angle between the observer's line-of-sight and the horizontal is % , and it is changing at a rate of 0.1 rad/min. How fast is the balloon rising at this moment? 4/15 miles/min Previous Problem Problem List N[ d g (elel[Sy)] (1 point) If the radius of a sphere is increasing at a constant rate of 5 cm/sec, then the volume is increasing at a rate of = 180pi cm?® /sec when the radius is 3 cm. dv. dV dr Hint: — = —— - —, and the volume of a sphereis V' = Lop3. dt dr dt . R (1 point) Qil spilled from a ruptured tanker spreads in a circle whose area increases at a constant rate of 8 mi> /hr. How rapidly is radius of the spill increasing when the area is 4 mi2? The radius is increasing at = (2/sqrt(pi)) mi/hr. (1 point) A plane flying with a constant speed of 24 km/min passes over a ground radar station at an altitude of 14 km and climbs at an angle of 20 degrees. At what rate is the distance from the plane to the radar station increasing 5 minutes later? The distance is increasing at 23.8678 km/min. (1 point) A spherical balloon is inflated so that its volume is increasing at the rate of 2.4 ft3 /min. How rapidly is the diameter of the balloon increasing when the diameter is 1.8 feet? The diameter is increasing at 0.472 ft/min. (1 point) A conical water tank with vertex down has a radius of 14 feet at the top and is 23 feet high. If water flows into the tank at a rate of 10 ft? /min, how fast is the depth of the water increasing when the water is 14 feet deep? The depth of the water is increasing at 0.04383 ft/min.
