1. Let a, b and c be 1, 1 and 9 respectively Consider the ellipsoid & given by the equations + = 1. a² 62 c² (a) Let P₁ = (±x, ±y, ±z) be the vertices of a rectangle inscribed in E. Explain why the volume of & is given by V = 8xyz. (b) Use the method of Lagrange multipliers to determine the largest possible volume of E.
1. Let a, b and c be 1, 1 and 9 respectively Consider the ellipsoid & given by the equations + = 1. a² 62 c² (a) Let P₁ = (±x, ±y, ±z) be the vertices of a rectangle inscribed in E. Explain why the volume of & is given by V = 8xyz. (b) Use the method of Lagrange multipliers to determine the largest possible volume of E.
Trigonometry (MindTap Course List)
10th Edition
ISBN:9781337278461
Author:Ron Larson
Publisher:Ron Larson
Chapter2: Analytic Trigonometry
Section2.3: Solving Trigonometric Equations
Problem 11ECP
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Question
![1. Let A, b and c be
1, 1 and 9 respectively
y²
Consider the ellipsoid & given by the equations
2²=1.
a²
6²
(a) Let P; = (±x, ±y, ±z) be the vertices of a rectangle inscribed in Ɛ. Explain
why the volume of & is given by V = 8xyz.
+
(b) Use the method of Lagrange multipliers to determine the largest possible
volume of E.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F38e693cf-3870-4eab-9920-bd211e6a8ee6%2Fc8132480-87f7-45ef-a8f7-b0fd44f01a48%2Fhxchivt_processed.png&w=3840&q=75)
Transcribed Image Text:1. Let A, b and c be
1, 1 and 9 respectively
y²
Consider the ellipsoid & given by the equations
2²=1.
a²
6²
(a) Let P; = (±x, ±y, ±z) be the vertices of a rectangle inscribed in Ɛ. Explain
why the volume of & is given by V = 8xyz.
+
(b) Use the method of Lagrange multipliers to determine the largest possible
volume of E.
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could you also do part b for this and on a piece of paper preferably.
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could please write this in on a piece of paper, so that it is easier to understand?
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