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In this project, you play the role of a consultant to a bedding manufacturer. The manufacturer is interested in constructing a sleeping pod. In particular, you will use a number of tools from Calculus III (including optimization and parameterization) to advise the client on the construction of such a pod. The pod is to be in the shape of the ellipsoid + y² +2²=1. 1. Use a graphing utility to graph the ellipsoid in 3-space. 2. Derive a parameterization of the ellipsoid in terms of p and 8 (as in spherical coordinates). Find the volume of the ellipsoid. 3

In this project, you play the role of a consultant to a bedding manufacturer. The manufacturer is interested in constructing a sleeping pod. In particular, you will use a number of tools from Calculus III (including optimization and parameterization) to advise the client on the construction of such a pod. The pod is to be in the shape of the ellipsoid + y² +2²=1. 1. Use a graphing utility to graph the ellipsoid in 3-space. 2. Derive a parameterization of the ellipsoid in terms of p and 8 (as in spherical coordinates). Find the volume of the ellipsoid. 3

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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In this project, you play the role of a consultant to a bedding manufacturer. The manufacturer is interested in constructing a sleeping pod. In particular, you will use a number of tools from Calculus III (including optimization and parameterization) to advise the client on the construction of such a pod. The pod is to be in the shape of the ellipsoid x² + y² + = 1. 1. Use a graphing utility to graph the ellipsoid in 3-space. 2. Derive a parameterization of the ellipsoid in terms of op and 8 (as in spherical coordinates). 3. Find the volume of the ellipsoid. 4. Find the point(s) on the ellipsoid that is farthest from the origin. 5. What is the largest cube that can be inscribed in the pod?
Transcribed Image Text:In this project, you play the role of a consultant to a bedding manufacturer. The manufacturer is interested in constructing a sleeping pod. In particular, you will use a number of tools from Calculus III (including optimization and parameterization) to advise the client on the construction of such a pod. The pod is to be in the shape of the ellipsoid x² + y² + = 1. 1. Use a graphing utility to graph the ellipsoid in 3-space. 2. Derive a parameterization of the ellipsoid in terms of op and 8 (as in spherical coordinates). 3. Find the volume of the ellipsoid. 4. Find the point(s) on the ellipsoid that is farthest from the origin. 5. What is the largest cube that can be inscribed in the pod?
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