Answer to Question #64600 in Calculus for John

Question

7. A helicopter takes off from a point 80 m away from an observer located on the
ground, and rises vertically at 2 m/s. At what rate is elevation angle of the
observer’s line of sight to the helicopter changing when the helicopter is 60 m
above the ground.

8. An oil slick on a lake is surrounded by a floating circular containment boom.
As the boom is pulled in, the circular containment boom. As the boom is
pulled in, the circular containment area shrinks (all the while maintaining the
shape of a circle.) If the boom is pulled in at the rate of 5 m/min, at what
rate is the containment area shrinking when it has a diameter of 100m?

9. Consider a cube of variable size. (The edge length is increasing.) Assume that
the volume of the cube is increasing at the rate of 10 cm3/minute. How fast
is the surface area increasing when the edge length is 8 cm?