1) 2 boats leave a dock at the same time. one boat travels south at 30 mi/H and the other travels east at 40 mi/H. After half an hour, how fast is the distance between the boats increasing? 2) A spherical balloon is inflated at a rate of 10 cm^3/min. At what rate is the diameter of the balloon increasing when the balloon has a diameter of 5 cm? 3) A rope is attached to the bottom of a hot air balloon that is floating above a flat field. If the angle of the rope to the ground remains 65 degrees and the ropes pulled in at 5 ft/s, how quickly is the elevation of the balloon changing? 4) Water flows into a conical tank at a rate of 2 ft^3/min. If the radius of the top of the tank is 4 feet and the height is 6 feet, determine how quickly the water level is rising when the water is 2 feet deep in the tank. 5) A jet flying at 450 mi/H and traveling in a straight line at a constant elevation of 500 feet passes directly over a spectator at an air show. How quickly is the angle of elevation (between the ground and the line from the spectator to the jet) changing 2 seconds later? 6) A man whose eye level is 6 feet above the ground walks toward a billboard at a rate of 2 ft/s. The bottom of the billboard is 10 feet above the ground, and it is 15 feet high. The man's viewing angle is the angle formed by the lines between the man's eyes and the top and bottom of the billboard. At what rate is the viewing angle changing when the man is 30 feet from the billboard