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into a lagoon, then narrows again at its mouth. See Figure below:

into a lagoon, then narrows again at its mouth. See Figure below:

Advanced Engineering Mathematics
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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2. A river follows the path y = f(x) where x, y are kilometers. Near the sea, it widens into a lagoon, then narrows again at its mouth. See Figure below: Sea River, y = f(x) (1, f(1)) (-1, f(-1)) Lagoon At the point (r, y), the depth d(r, y) of the lagoon is given by d(r, y) = 40 – 160(y – f(z))² – 40z² meters The lagoon itself is described by d(1, y) 2 0. What is the volume of the lagoon in cubic meters? HINT: use new coordinates u = 1/2, v = y – f(x) and Jacobians.
Transcribed Image Text:2. A river follows the path y = f(x) where x, y are kilometers. Near the sea, it widens into a lagoon, then narrows again at its mouth. See Figure below: Sea River, y = f(x) (1, f(1)) (-1, f(-1)) Lagoon At the point (r, y), the depth d(r, y) of the lagoon is given by d(r, y) = 40 – 160(y – f(z))² – 40z² meters The lagoon itself is described by d(1, y) 2 0. What is the volume of the lagoon in cubic meters? HINT: use new coordinates u = 1/2, v = y – f(x) and Jacobians.
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