Mathematics, 21.02.2020 22:20 jaisha23
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−απ(3a/πh)2/3V2/3,whereαis the coefficient of evaporation.(b) Find the equilibrium depth of water in the pond. Is the equilibrium asymptotically stable?(c) Find a condition that must be satisfied if the pond is not to overflow.
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A pond forms as water collects in a conical depression of radius a and depth h. Suppose that water f...
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