5. Consider the tetrahedron in the first octant (where each coordinate is positive) bounded above by the plane 6x + 4y + 2z = 12 (a) Sketch a graph of the shadow onto the ry-plane in the space provided. The graph need not be to scale, but number the axes so that important points can be read from the graph. Shade in the region. (b) Express the volume of the solid described above as a triple integral in the order of integration dz dy dx or dz dx dy.
5. Consider the tetrahedron in the first octant (where each coordinate is positive) bounded above by the plane 6x + 4y + 2z = 12 (a) Sketch a graph of the shadow onto the ry-plane in the space provided. The graph need not be to scale, but number the axes so that important points can be read from the graph. Shade in the region. (b) Express the volume of the solid described above as a triple integral in the order of integration dz dy dx or dz dx dy.
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 help with a and b!
Transcribed Image Text:5. Consider the tetrahedron in the first octant (where each coordinate is positive) bounded above
by the plane
6x + 4y + 2z = 12
(a) Sketch a graph of the shadow onto the ry-plane in the space provided. The graph need not
be to scale, but number the axes so that important points can be read from the graph. Shade in
the region.
(b) Express the volume of the solid described above as a triple integral in the order of integration
dz dy dx or dz dx dy.
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find the volume of the solid by evaluating your answer to part b
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