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30. A growing raindrop Suppose that a drop of mist is a perfect sphere and that, through condensation, the drop picks up moisture at a rate proportional to its surface area. Show that under these circumstances the drop's radius increases at a constant rate. 31. The radius of an inflating balloon A spherical balloon is inflated with helium at the rate of 100T ft /min. How fast is the holloon n'n nodiuo ingrencing at the instant the radius is 5 ft? How

30. A growing raindrop Suppose that a drop of mist is a perfect sphere and that, through condensation, the drop picks up moisture at a rate proportional to its surface area. Show that under these circumstances the drop's radius increases at a constant rate. 31. The radius of an inflating balloon A spherical balloon is inflated with helium at the rate of 100T ft /min. How fast is the holloon n'n nodiuo ingrencing at the instant the radius is 5 ft? How

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Can you please solve number 30 and 32

198 Chapter 3 Derivatives bru a. At what rate is the water level changing when the water is 8 m deep? b. What is the radius r of the water's surface when the water is ym deep? c. At what rate is the radius r changing when the water is 8 m deep? 30. A growing raindrop Suppose that a drop of mist is a perfect sphere and that, through condensation, the drop picks up moisture at a rate proportional to its surface area. Show that under these circumstances the drop's radius increases at a constant rate. 31. The radius of an inflating balloon A spherical balloon is inflated with helium at the rate of 100T ft'/min. How fast is the balloon's radius increasing at the instant the radius is 5 ft? How sfast is the surface area increasing? Co 32. Hauling in a dinghy A dinghy is pulled toward a dock by a rope from the bow through a ring on the dock 6 ft above the bow. The rope is hauled in at the rate of 2 ft/sec. adope a. How fast is the boat approaching the dock when 10 ft of rope are out? b. At what rate is the angle 0 changing at this instant (see the figure)? Ring at edge 132 200 of dock CSLI 6!
Transcribed Image Text:198 Chapter 3 Derivatives bru a. At what rate is the water level changing when the water is 8 m deep? b. What is the radius r of the water's surface when the water is ym deep? c. At what rate is the radius r changing when the water is 8 m deep? 30. A growing raindrop Suppose that a drop of mist is a perfect sphere and that, through condensation, the drop picks up moisture at a rate proportional to its surface area. Show that under these circumstances the drop's radius increases at a constant rate. 31. The radius of an inflating balloon A spherical balloon is inflated with helium at the rate of 100T ft'/min. How fast is the balloon's radius increasing at the instant the radius is 5 ft? How sfast is the surface area increasing? Co 32. Hauling in a dinghy A dinghy is pulled toward a dock by a rope from the bow through a ring on the dock 6 ft above the bow. The rope is hauled in at the rate of 2 ft/sec. adope a. How fast is the boat approaching the dock when 10 ft of rope are out? b. At what rate is the angle 0 changing at this instant (see the figure)? Ring at edge 132 200 of dock CSLI 6!
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