Relating rates - completely lost. HW due tomorrow.
We have a ton of problems due tomorrow and I can't even fathom where to begin. Here are a few problems that I think if I understand how to do, I may be able to get the rest of the problems:
1) A spherical balloon is inflated wiht helium at the rate of 100pift^3/min. How fast is the baloon's radius increasing at the instant the radius is 5 ft? How fast is the surface area increasing at that instant?
2) A balloon is rising vertically above a level, straight road at a constant rate of 1 ft./sec. Just when the balloon is 65 ft above the ground, a bicycle moving at a constant rate of 17 ft/sec passes under it. How fast is the distance between the bicycle and balloon increasing 3 sec later?
(The book gives a triangle like diagram. The baloon has a line underneath it with an up arrow that says y(t) next to it, the bicycle going right with x (t) underneath it and then the hypotenuse is s(t).