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:

Inventory Turnover

A ratio showing how many times a company's inventory is sold and replaced over a specified period, indicating the efficiency of inventory management.

Days' Sales In Inventory

Days' sales in inventory is a financial ratio that shows how many days, on average, it takes for a company to turn its inventory into sales, indicating inventory management efficiency.

Return On Common Stockholders' Equity

A measure of a company's profitability that shows how much profit is generated with the money shareholders have invested.

Net Income

The amount of profit left over after all expenses and taxes have been subtracted from total revenues.