Find the Mass of the Lamina Described by the Inequalities $x \geq 0$

question 94

Multiple Choice

Find the mass of the lamina described by the inequalities $x \geq 0$ and $3 \leq y \leq 3 + \sqrt { 9 - x ^ { 2 } }$ , given that its density is $\rho ( x , y ) = 7 x y$ . (Hint: Some of the integrals are simpler in polar coordinates.)

• A) \(\frac { 2,079 } { 8 }\)
• B) \(\frac { 16 } { 6,237 }\)
• C) \(\frac { 8 } { 2,079 }\)
• D) \(\frac { 2,457 } { 8 }\)
• E) \(\frac { 6,237 } { 16 }\)

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Definitions:

Mitochondrion

An organelle found in large numbers in most cells, involved in energy production.

Axons

Long nerve fibers that transmit signals from the body of a neuron to other cells.

Dendrites

The branched projections of a neuron that receive electrochemical signals from other neurons and conduct them toward the cell body.

Cell Wall

A rigid layer lying outside the plasma membrane of the cells of plants, fungi, and bacteria, providing structure and protection.