A​ hot-air balloon is 190 ftabove the ground when a motorcycle​ (traveling in a straight line on a horizontal​ road) passes directly beneath it going 30 mi/hr (44 ft/s​). If the balloon rises vertically at a rate of 13 ft/s​ what is the rate of change of the distance between the motorcycle and the balloon 7 seconds later? Let x be the horizontal distance from balloon to motorcycle, y be the vertical distance from the balloon to the road, and z be the distance between the motorcycle and the balloon.  Write an equation relating x, y, and z. Answer the following question Find the rate of change of the distance between the motorcycle and the balloon after 7 seconds.