Factor the Trigonometric Expression and Simplify $1 - \sin ^ { 3 } x$

question 108

Multiple Choice

Factor the trigonometric expression and simplify.
- $1 - \sin ^ { 3 } x$

• A) \(( 1 - \sin x ) \left( 1 - 2 \sin x + \sin ^ { 2 } x \right)\)
• B) \(( 1 - \sin x ) ^ { 3 }\)
• C) \(( 1 - \sin x ) \left( \cos x + \sin ^ { 2 } x \right)\)
• D) \(( 1 - \sin x ) \left( 1 + \sin x + \sin ^ { 2 } x \right)\)

Determine the average product under given conditions.

Identify the relationship between marginal product, total product, and average product.

Understand the principle of diminishing marginal returns.

Explain the behaviors of marginal, average, and total products as inputs vary.

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Definitions:

Acquired Characteristics

Traits that are gained by an organism after birth as a result of external influences or its own actions, not inherited genetically.

Lysenko

A controversial figure in the history of Soviet biology, Trofim Lysenko rejected Mendelian genetics in favor of his own agricultural theories, leading to widespread agricultural disaster.

Natural Selection

A fundamental mechanism of evolution where organisms better adapted to their environment are more likely to survive and reproduce.

Evolutionary Theory

A scientific theory that explains the diversity of life on Earth by proposing that life evolves over time through processes of natural selection and genetic variation.