Answer: A pond forms as water collects in a conical depression of radius a and depth h
Chapter 2, Problem 18(choose chapter or problem)
A pond forms as water collects in a conical depression of radius a and depth h. Suppose that water flows in at a constant rate k and is lost through evaporation at a rate proportional to the surface area. (a) Show that the volume V(t) of water in the pond at time t satisfies the differential equation dV/dt = k (3a/h) 2/3 V2/3 , where is the coefficient of evaporation. (b) Find the equilibrium depth of water in the pond. Is the equilibrium asymptoticallystable?(c) Find a condition that must be satisfied if the pond is not to overflow
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