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A plane with equation + ² + ² = 1 (a, b, c > 0) together with the positive coordinate planes forms a tetrahedron of volume V = abc (as shown in the Figure below) Find the plane that minimizes V if the plane is constrained to pass through a point P = (6,3,7). C=(0, 0, c) A = (a, 0, 0) The plane P B=(0, b, 0) y = 1

A plane with equation + ² + ² = 1 (a, b, c > 0) together with the positive coordinate planes forms a tetrahedron of volume V = abc (as shown in the Figure below) Find the plane that minimizes V if the plane is constrained to pass through a point P = (6,3,7). C=(0, 0, c) A = (a, 0, 0) The plane P B=(0, b, 0) y = 1

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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A plane with equation ² + ² + ² = 1 (a, b, c > 0) = together with the positive coordinate planes forms a tetrahedron of volume V Find the plane that minimizes V if the plane is constrained to pass through a point P = x C=(0, 0, c) A = (a, 0, 0) The plane B=(0, b, 0) y = 1 abc (as shown in the Figure below) = (6,3,7).
Transcribed Image Text:A plane with equation ² + ² + ² = 1 (a, b, c > 0) = together with the positive coordinate planes forms a tetrahedron of volume V Find the plane that minimizes V if the plane is constrained to pass through a point P = x C=(0, 0, c) A = (a, 0, 0) The plane B=(0, b, 0) y = 1 abc (as shown in the Figure below) = (6,3,7).
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