Problem 1. Let x = f (y) be continuous and positive on the interval [0, 6]. Revolve f (y) about the y-axis to form a container, no top. Suppose that the container is filled with water which then evaporates at a rate proportional to the area of the surface of the water. Show that the water level drops at a constant rate. (Hint: Let V(t) be the volume of water at time t and h(t) be the water level at time t, then we know V'(t) = ka f²(h(t)) for some constant k. Try to show h'(t) is some constant independent of t.) y A b x = f(y)
Problem 1. Let x = f (y) be continuous and positive on the interval [0, 6]. Revolve f (y) about the y-axis to form a container, no top. Suppose that the container is filled with water which then evaporates at a rate proportional to the area of the surface of the water. Show that the water level drops at a constant rate. (Hint: Let V(t) be the volume of water at time t and h(t) be the water level at time t, then we know V'(t) = ka f²(h(t)) for some constant k. Try to show h'(t) is some constant independent of t.) y A b x = f(y)
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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