Find the volume of the largest rectangular box with edges parallel to the axes that can be inscribed in the ellipsoid 7² 2 y² + 81 25 + 64 =1 Hint: By symmetry, you can restrict your attention to the first octant (where z, y, z 20), and assume your volume has the form V = 8zyz. Then arguing by symmetry, you need only look for points which achieve the maximum which lie in the first octant. Maximum volume:
Find the volume of the largest rectangular box with edges parallel to the axes that can be inscribed in the ellipsoid 7² 2 y² + 81 25 + 64 =1 Hint: By symmetry, you can restrict your attention to the first octant (where z, y, z 20), and assume your volume has the form V = 8zyz. Then arguing by symmetry, you need only look for points which achieve the maximum which lie in the first octant. Maximum volume:
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter6: The Trigonometric Functions
Section6.7: Applied Problems
Problem 58E
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![Find the volume of the largest rectangular box with edges parallel to the axes that can be inscribed in the ellipsoid
72 y² 22
+ + = 1
25 64
81
Hint: By symmetry, you can restrict your attention to the first octant (where z, y, z ≥ 0), and assume your volume has the form V = 8zyz. Then arguing by symmetry, you need only look
for points which achieve the maximum which lie in the first octant. Maximum volume:](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fb40b6873-57d9-434d-ac29-d6d174612f1c%2Fe5559900-75db-447a-a67c-b2dbf7d75db7%2Fj5z4fas_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Find the volume of the largest rectangular box with edges parallel to the axes that can be inscribed in the ellipsoid
72 y² 22
+ + = 1
25 64
81
Hint: By symmetry, you can restrict your attention to the first octant (where z, y, z ≥ 0), and assume your volume has the form V = 8zyz. Then arguing by symmetry, you need only look
for points which achieve the maximum which lie in the first octant. Maximum volume:
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