Find the Centroid of the Region Bounded by the Graphs $$y = | x | \sqrt { 16 - x ^ { 2 } } , \quad y = 0 , \quad x = - 4 , \quad x = 4$$

question 59

Multiple Choice

Find the centroid of the region bounded by the graphs of the given equations. $$y = | x | \sqrt { 16 - x ^ { 2 } } , \quad y = 0 , \quad x = - 4 , \quad x = 4$$

• A) \(\left( \frac { 5 } { 16 } , 0 \right)\)
• B) \(\left( \frac { 16 } { 5 } , 0 \right)\)
• C) \(\left( 0 , \frac { 5 } { 16 } \right)\)
• D) \(\left( 0 , \frac { 16 } { 5 } \right)\)

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Definitions:

Natural Selection

A process by which species adapt to their environment as individuals with beneficial traits survive and reproduce more successfully than others.

Behaviourism

A theory of learning based on the idea that all behaviors are acquired through conditioning, initiated by interactions with the environment.

John Watson

An American psychologist often cited as one of the founders of behaviorism, emphasizing the importance of observable behaviors over internal phenomena like thoughts and feelings.

Conscious Experience

The subjective awareness of one's thoughts, feelings, and environment, often contrasted with unconscious processes.