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1) The radius, r, of a circle is increasing at a rate of 2 cm/min. Find the rate of change of the area when the radius is 6cm.
2) A ladder 15 ft long leans against a vertical wall. If the lower end is being moved away from the wall at the rate of 5 ft/sec, how fast is the height of the top decreasing when the lower end is 10 ft. from the wall?
3) A balloon is rising vertically above a level, straight road at a constant rate of 1.5 ft/sec. Just when the balloon is 70 ft above the ground, a bicycle moving at a constant rate of 20 ft/sec passes under it. How fast is the distance between the bicycle and balloon increasing 3 sec. later.
please show all your work and steps!
2) A ladder 15 ft long leans against a vertical wall. If the lower end is being moved away from the wall at the rate of 5 ft/sec, how fast is the height of the top decreasing when the lower end is 10 ft. from the wall?
3) A balloon is rising vertically above a level, straight road at a constant rate of 1.5 ft/sec. Just when the balloon is 70 ft above the ground, a bicycle moving at a constant rate of 20 ft/sec passes under it. How fast is the distance between the bicycle and balloon increasing 3 sec. later.
please show all your work and steps!