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A hot-air balloon is 170 ft above 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 10 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 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. 2 2 x² + y² = 2² Differentiate both sides of the equation with respect to t (2x) dx dt dt dz dt GOED The rate of change of the distance between the motorcycle and the balloon after 7 seconds is about (Round to two decimal places as needed.) ( √ VM M. (AA) x