Solve the Problem $\delta ( x , y , z ) = x + y + z$

question 387

Multiple Choice

Solve the problem.
-Find the center of mass of a tetrahedron of density $\delta ( x , y , z ) = x + y + z$ bounded by the coordinate planes and the plane $\frac { x } { 5 } + \frac { y } { 4 } + \frac { z } { 8 } = 1$ .

• A) \(\bar { x } = \frac { 110 } { 51 } , \bar { y } = \frac { 28 } { 17 } , \bar { z } = \frac { 200 } { 51 }\)
• B) \(\bar { x } = \frac { 55 } { 34 } , \bar { y } = \frac { 21 } { 17 } , \bar { z } = \frac { 50 } { 17 }\)
• C) \(\bar { x } = \frac { 55 } { 51 } , \bar { y } = \frac { 14 } { 17 } , \bar { z } = \frac { 100 } { 51 }\)
• D) \(\bar { x } = \frac { 22 } { 17 } , \bar { y } = \frac { 84 } { 85 } , \bar { z } = \frac { 40 } { 17 }\)

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Definitions:

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