Solve the Problem $\mathrm { A } ( \mathrm { r } ( \mathrm { t } ) ) = 9 \pi \mathrm { t } ^ { 2 }$

question 403

Multiple Choice

Solve the problem.
-An oil well off the Gulf Coast is leaking, with the leak spreading oil over the surface of the gulf as a circle. At any time t, in minutes, after the beginning of the leak, the radius of the oil slick on the surface is r(t) = 3t ft. Find
The area A of the oil slick as a function of time.

• A) \(\mathrm { A } ( \mathrm { r } ( \mathrm { t } ) ) = 9 \pi \mathrm { t } ^ { 2 }\)
• B) \(\mathrm { A } ( \mathrm { r } ( \mathrm { t } ) ) = 9 \mathrm { t } ^ { 2 }\)
• C) \(\mathrm { A } ( \mathrm { r } ( \mathrm { t } ) ) = 9 \pi \mathrm { t }\)
• D) \(\mathrm { A } ( \mathrm { r } ( \mathrm { t } ) ) = 3 \pi \mathrm { t } ^ { 2 }\)

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Definitions:

Implicit Association Test

A psychological assessment tool designed to measure the strength of an individual's automatic association between mental representations of objects or concepts.

Attitudes

Mental and emotional entities that predispose an individual to respond in a particular way to objects, people, and situations.

Feelings

Emotional states or reactions that are subjectively experienced by individuals, often triggered by external events or internal thoughts.

Neuroticism

A personality trait involving a long-term tendency to be in a negative emotional state, characterized by moodiness, anxiety, and emotional instability.