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Relate Rate Problems- HW Problems
1. Air is being pumped into a balloon at a rate of 30 cu.in/min. What
is the rate of change of the radius when the radius is 4 in.? What is the
rate of change of the surface area when the radius is 4 in.?
2. The edges of a cube are expanding at a rate of 2 in/sec. How fast is
the surface area changing when each edge is 10 in.?
3. An airplane is flying horizontally at an altitude of 4mi. and a speed
of 600 mph directly over a radar station. Find the rate of change of the
distance between the plane and the radar station 5 minutes later.
4. At noon car A is 90 miles east of its destination travelling 60mph
west. At the same time, car B is 90 miles north of that same destination
travelling 50 mph south. How fast is the distance between the two cars
changing at 1pm?
5. A spotlight on the ground shines on a wall 24 feet away. A man 6ft.
tall is walking toward the spotlight at 4 ft/sec. How fast is the length of
his shadow changing when he is 12 ft. from the wall?
Relate Rate Problems- HW Problems
1. Air is being pumped into a balloon at a rate of 30 cu.in/min. What
is the rate of change of the radius when the radius is 4 in.? What is the
rate of change of the surface area when the radius is 4 in.?
2. The edges of a cube are expanding at a rate of 2 in/sec. How fast is
the surface area changing when each edge is 10 in.?
3. An airplane is flying horizontally at an altitude of 4mi. and a speed
of 600 mph directly over a radar station. Find the rate of change of the
distance between the plane and the radar station 5 minutes later.
4. At noon car A is 90 miles east of its destination travelling 60mph
west. At the same time, car B is 90 miles north of that same destination
travelling 50 mph south. How fast is the distance between the two cars
changing at 1pm?
5. A spotlight on the ground shines on a wall 24 feet away. A man 6ft.
tall is walking toward the spotlight at 4 ft/sec. How fast is the length of
his shadow changing when he is 12 ft. from the wall?
