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, 2 3 (3,2,0) (a) V(E)= Y (b) Average of f(x, y, z) = x + 2y - z on 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, 2 3 (3,2,0) (a) V(E)= Y (b) Average of f(x, y, z) = x + 2y - z on E is: 2x + 6y +9z = 18.
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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Question
![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: \( z = 0 \), \( x = 0 \), \( -2x + 3y = 0 \), \( 2x + 6y + 9z = 18 \).
### Diagram Description
There is a 3D coordinate system diagram showing the tetrahedron. The axes are labeled \( x \), \( y \), and \( z \). The vertices are shown at the specified coordinates. The edges and faces of the tetrahedron are drawn connecting the vertices.
(a) \( V(E) = \) [Volume of the tetrahedron space - placeholder for answer]
(b) Average of \( f(x, y, z) = x + 2y - z \) on \( E \) is: [Placeholder for computed average value]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F5dc3ef7d-848e-4463-9030-e4a43ebc2b5f%2F775bdc36-8604-454e-96c9-c25390f61591%2Fhd7iaue_processed.jpeg&w=3840&q=75)
Transcribed Image Text: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: \( z = 0 \), \( x = 0 \), \( -2x + 3y = 0 \), \( 2x + 6y + 9z = 18 \).
### Diagram Description
There is a 3D coordinate system diagram showing the tetrahedron. The axes are labeled \( x \), \( y \), and \( z \). The vertices are shown at the specified coordinates. The edges and faces of the tetrahedron are drawn connecting the vertices.
(a) \( V(E) = \) [Volume of the tetrahedron space - placeholder for answer]
(b) Average of \( f(x, y, z) = x + 2y - z \) on \( E \) is: [Placeholder for computed average value]
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