A hot-air balloon is 180 ft above the ground when a motorcycle (traveling in a straight line on a horizontal road) passes directly beneath it going 60 mi / hr (88 ft / s). If the balloon rises vertically at a rate of 12 ft /s, what is the rate of change of the distance between the motorcycle and the balloon 6 seconds later? Let x be the horizontal distance from the balloon to the 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. 0 Differentiate both sides of the equation with respect to t. dz dt The rate of change of the distance between the motorcycle and the balloon after 6 seconds is about A (Round to two decimal places as needed.)