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9. Let E be the tetrahedron with vertices: (0,0,0), (3,2,0), (0,3,0), (0, 0, 2). E is bounded by four planes: z = 0, x = 0, -2x + 3y = 0, 8 2 3 13,2,0) (a) V(E)= (b) Average of f(x, y, z) = x+2y- zon E is: 2x + 6y +9z = 18.

9. Let E be the tetrahedron with vertices: (0,0,0), (3,2,0), (0,3,0), (0, 0, 2). E is bounded by four planes: z = 0, x = 0, -2x + 3y = 0, 8 2 3 13,2,0) (a) V(E)= (b) Average of f(x, y, z) = x+2y- zon E is: 2x + 6y +9z = 18.

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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Please answer Part B.

Sure, here's a transcription suitable for an educational website: --- **Problem 9** Let \( E \) be the tetrahedron with vertices: \( (0, 0, 0) \), \( (3, 2, 0) \), \( (0, 3, 0) \), \( (0, 0, 2) \). \( E \) is bounded by four planes: \( z = 0 \), \( x = 0 \), \( -2x + 3y = 0 \), \( 2x + 6y + 9z = 18 \). **(a)** \( V(E) = \) **Diagram Explanation:** The diagram shows a 3D coordinate system with the x, y, and z axes. A tetrahedron is drawn with its vertices labeled, including the coordinate (3, 2, 0). **(b)** Average of \( f(x, y, z) = x + 2y - z \) on \( E \) is: --- The diagram includes an illustration of the tetrahedron in 3D space, clearly showing its orientation and the labeled vertex (3, 2, 0) on the xy-plane with a height reaching the z-axis. The axes x, y, and z are labeled accordingly. The problem asks to calculate the volume of the tetrahedron and find the average of a given function over it.
Transcribed Image Text:Sure, here's a transcription suitable for an educational website: --- **Problem 9** Let \( E \) be the tetrahedron with vertices: \( (0, 0, 0) \), \( (3, 2, 0) \), \( (0, 3, 0) \), \( (0, 0, 2) \). \( E \) is bounded by four planes: \( z = 0 \), \( x = 0 \), \( -2x + 3y = 0 \), \( 2x + 6y + 9z = 18 \). **(a)** \( V(E) = \) **Diagram Explanation:** The diagram shows a 3D coordinate system with the x, y, and z axes. A tetrahedron is drawn with its vertices labeled, including the coordinate (3, 2, 0). **(b)** Average of \( f(x, y, z) = x + 2y - z \) on \( E \) is: --- The diagram includes an illustration of the tetrahedron in 3D space, clearly showing its orientation and the labeled vertex (3, 2, 0) on the xy-plane with a height reaching the z-axis. The axes x, y, and z are labeled accordingly. The problem asks to calculate the volume of the tetrahedron and find the average of a given function over it.
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