Find M_x,M_y , and $\bar{x}$ $\bar {y}$ ) for the Lamina of Uniform Density

question 2

Multiple Choice

Find M_x,M_y , and ( $\bar{x}$ , $\bar {y}$ ) for the lamina of uniform density $\rho$ text bounded by the graphs

• A)
• \(\begin{array} { l }
• M _ { x } = \frac { 1,024 } { 5 } , M _ { y } = 0 \\
• \bar { x } = \frac { 112 } { 13 } , \bar { y } = \frac { 7 } { 3 }
• \end{array}\)
• B)
• \(\begin{array} { l }
• M _ { x } = \frac { 128 } { 5 } \rho\\ , M _ { y } = \frac { 8,192 } { 11 } \rho \\ \bar { x } = \frac { 112 } { 13 } , \bar { y } = \frac { 14 } { 5 }
• \end{array}\)
• C)
• \(\begin{array} { l }
• M _ { x } = \frac { 1,024 } { 5 } \rho , M _ { y } = \frac { 8,192 } { 11 } \rho , \\
• \bar { x } = \frac { 112 } { 11 } , \bar { y } = \frac { 14 } { 5 }
• \end{array}\)
• D)
• \(\begin{array} { l }
• M _ { x } = \frac { 512 } { 5 } \rho\\ , M _ { y } = \frac { 8,192 } { 11 } \rho \\
• \bar { x } = \frac { 112 } { 11 } , \bar { y } = \frac { 7 } { 3 }
• \end{array}\)
• E)
• \( M_{x}=0, M_{y}=\frac{8,192}{11} \rho \)
• \( \bar{x}=\frac{112}{9}, \bar{y}=\frac{56}{3} \)

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Definitions:

Incremental Analysis

An analytical approach that focuses only on those costs and revenues that change as a result of a decision.

Break-even Point

The point at which total revenues equal total costs, resulting in no net loss or gain for the business.

Fixed Costs

Costs that do not vary with the volume of production or sales, such as rent, salaries, and insurance, providing stability to a company's expense structure.

Variable Costs

Expenses that vary directly with the volume of production or sales.