Find the Center of Mass of the Lamina Bounded by the Graphs

question 68

Multiple Choice

Find the center of mass of the lamina bounded by the graphs of the equations $x = 64 - y ^ { 2 }$ and $x = 0$ for the density $\rho = k x$

• A) \(\left( \frac { 128 } { 7 } , 0 \right)\)
• B) \(\left( 0 , \frac { 128 } { 7 } \right)\)
• C) \(\left( \frac { 32 } { 7 } , 0 \right)\)
• D) \(\left( 0 , \frac { 256 } { 7 } \right)\)
• E) \(\left( \frac { 256 } { 7 } , 0 \right)\)

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Definitions:

Vein

A blood vessel that carries blood towards the heart. Most veins carry deoxygenated blood from the tissues back to the heart.

Capillary

The smallest of the body's blood vessels, connecting arterioles and venules, and playing a key role in the exchange of water, oxygen, carbon dioxide, and many other nutrients and waste substances between blood and surrounding tissues.

Inappropriately Loud Voice

Speaking at a volume that is considered excessively high for the given social or contextual setting, often leading to discomfort or disturbance.

Talking

The act of communicating verbally, using spoken words to convey ideas, thoughts, or feelings.