Find the Mass of the Lamina That Occupies the Region $D$

question 1

Multiple Choice

Find the mass of the lamina that occupies the region $D$ and has the given density function, if $D$ is bounded by the parabola $x = y ^ { 2 }$ and the line $y = x - 2$ .
$$\rho ( x , y ) = 3$$
Select the correct answer.

• A) \(\frac { 3 } { 2 }\)
• B) 2
• C) 27
• D) \(\frac { 27 } { 2 }\)
• E) None of these

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Definitions:

Marginal Cost

The increase in cost resulting from the production of one additional unit of a product or service.

Fixed Costs

Costs that do not change with the level of output or production, such as rent, salaries, and insurance premiums.

Total Cost

The complete sum of all expenses incurred in the production of goods or services, including fixed and variable costs.

Break-even Quantity

The volume of sales at which total revenues equal total costs, resulting in neither profit nor loss.