Problem 7. A spherical raindrop evaporates at a rate proportional to its surface area.Write down a differential equation for the volume of the raindrop as a function of time.Atid.(^,^JALg4691

The volume of a spherical raindrop is given by V(t) = 4/3 * π * r^3, where r is the radius of the…

Answered: Problem 7. A spherical raindrop…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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When you use a spray can and press the valve at the top, you decrease the pressure of the gas in the can. This decrease of pressure causes the volume of the gas in the can to increase. Because the gas needs more room than is provided in the can, it expands in spray form through the small hole near the valve. In general, if the temperature is constant, the pressure, P, of a gas in a container varies inversely as the volume, V, of the container. The pressure of a gas sample in a container whose volume is 8 cubic inches is 12 pounds per square inch. If the sample expands to a volume of 22 cubic inches, what is the new pressure of the gas?
Problem 6. A cylindrical container with a diameter of 3 meters is being filled with water. The water is flowing into the container at a rate of 5m³/s. How fast is the water moving up the side of the container?
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Assign variables and restate the following problem in terms of known and unknown derivatives (but do not solve it): How fast is the volume of a cube increasing if its side increases at a rate of 0.5 cm/s?

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Problem 7. A spherical raindrop evaporates at a rate proportional to its surface area. Write down a differential equation for the volume of the raindrop as a function of time.