3. Let D be the solid enclosed by the planes x = 0, y = 0, z=x+3y, and z = 2 5 4x-2y. (a) Determine the volume of D. Use integration rather than a geometric argument, and express your answer as a single fraction. (b) Determine the z-coordinate of the centroid of D (the center of mass assuming constant density). Use integration rather than a geometric argument, and express your answer as a single fraction. You do not need to find any other coordinates.

Advanced Engineering Mathematics
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ISBN:9780470458365
Author:Erwin Kreyszig
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3. Let D be the solid enclosed by the planes x = 0, y = 0, z=x+3y, and z =
2 5 4x-2y.
(a) Determine the volume of D. Use integration rather than a geometric argument, and express your
answer as a single fraction.
(b) Determine the z-coordinate of the centroid of D (the center of mass assuming constant density).
Use integration rather than a geometric argument, and express your answer as a single fraction.
You do not need to find any other coordinates.
Transcribed Image Text:3. Let D be the solid enclosed by the planes x = 0, y = 0, z=x+3y, and z = 2 5 4x-2y. (a) Determine the volume of D. Use integration rather than a geometric argument, and express your answer as a single fraction. (b) Determine the z-coordinate of the centroid of D (the center of mass assuming constant density). Use integration rather than a geometric argument, and express your answer as a single fraction. You do not need to find any other coordinates.
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