4. The shell of a spacecraft (see Figure 2) is a union of two surfaces : • S₁ is part of 2² + 4y² + 4z² = 4 where a ≤ 0. • S₂ is part of x=4-4y² - 42² where a 20. Both surfaces are oriented away from the origin. Consider the vector field F(x, y, z)=2xi + 2yj-3zk. (a) Evaluate, directly, the flux of F across S₁. (b) Evaluate, directly, the flux of F across S₂. (c) Use your findings above and the Divergence Theorem to find the volume of the spacecraft.
4. The shell of a spacecraft (see Figure 2) is a union of two surfaces : • S₁ is part of 2² + 4y² + 4z² = 4 where a ≤ 0. • S₂ is part of x=4-4y² - 42² where a 20. Both surfaces are oriented away from the origin. Consider the vector field F(x, y, z)=2xi + 2yj-3zk. (a) Evaluate, directly, the flux of F across S₁. (b) Evaluate, directly, the flux of F across S₂. (c) Use your findings above and the Divergence Theorem to find the volume of the spacecraft.
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter6: The Trigonometric Functions
Section6.6: Additional Trigonometric Graphs
Problem 78E
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![4. The shell of a spacecraft (see Figure 2) is a union of two surfaces :
• S₁ is part of 2² + 4y² + 4z² = 4 where x ≤ 0.
• S₂ is part of x = 4 - 4y² - 42² where x ≥ 0.
Both surfaces are oriented away from the origin.
Consider the vector field F(x, y, z) = 2xi + 2yj - 3zk.
(a)
Evaluate, directly, the flux of F across S₁.
(b)
Evaluate, directly, the flux of F across S₂.
(c)
Use your findings above and the Divergence Theorem to
find the volume of the spacecraft.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F96179140-ed94-42a5-b023-b8f4ee7d08b1%2F35327f2a-7816-49ac-b919-c3d521fb32f6%2F2zzsing_processed.jpeg&w=3840&q=75)
Transcribed Image Text:4. The shell of a spacecraft (see Figure 2) is a union of two surfaces :
• S₁ is part of 2² + 4y² + 4z² = 4 where x ≤ 0.
• S₂ is part of x = 4 - 4y² - 42² where x ≥ 0.
Both surfaces are oriented away from the origin.
Consider the vector field F(x, y, z) = 2xi + 2yj - 3zk.
(a)
Evaluate, directly, the flux of F across S₁.
(b)
Evaluate, directly, the flux of F across S₂.
(c)
Use your findings above and the Divergence Theorem to
find the volume of the spacecraft.
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