Find the Centroid of the Region Bounded by the Graphs $$y = 9 - x ^ { 2 } , \quad y = 3 - x$$

question 131

Multiple Choice

Find the centroid of the region bounded by the graphs of the given equations.
$$y = 9 - x ^ { 2 } , \quad y = 3 - x$$

• A) \(\left( \frac { 5 } { 2 } , \frac { 1 } { 2 } \right)\)
• B) \(\left( \frac { 1 } { 2 } , \frac { 5 } { 2 } \right)\)
• C) \(\left( 5 , \frac { 1 } { 2 } \right)\)
• D) \(\left( \frac { 1 } { 2 } , 5 \right)\)

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Definitions:

Variable Expenses

Costs that vary in direct proportion to changes in a business activity's level, such as sales volume or production quantity.

Break-even Point

The point at which the amount of products sold or produced matches the total costs, leading to neither a profit nor a loss.

Margin of Safety

The difference between actual or expected sales and the breakeven sales, indicating the amount by which sales can drop before the business incurs a loss.

Percentage of Sales

A financial metric or method that relates various income statement accounts as a percentage of sales, often used for analysis or forecasting.