A Pebble Is Dropped into a Calm Pond,causing Ripples in the Form

question 28

Multiple Choice

A pebble is dropped into a calm pond,causing ripples in the form of concentric circles.The radius (in feet) of the outer ripple is $r ( t ) = 0.2 t$ ,where t is the time in seconds after the pebble strikes the water.The area of the circle is given by the function $A ( r ) = \pi r ^ { 2 }$ .Find and interpret $( A \circ r ) ( t )$ . ​

• A) \[( A \circ r ) ( t ) = 0.2 \pi t\] ; \[( A \circ r ) ( t )\] represents the area of the circle at time t.
• B) \(( A \circ r ) ( t ) = 0.2 \pi t ^ { 2 }\) ; \(( A \circ r ) ( t )\) represents the area of the circle at time t.
• C) \[( A \circ r ) ( t ) = 0.04 \pi t\] ; \(( A \circ r ) ( t )\) represents the area of the circle at time t.
• D) \(( A \circ r ) ( t ) = 0.04 \pi t ^ { 2 }\) ; \[( A \circ r ) ( t )\] represents the area of the circle at time t.
• E) \[( A \circ r ) ( t ) = 0.04 \pi t ^ { 3 }\] ; \(( A \circ r ) ( t )\) represents the area of the circle at time t.

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Definitions:

Assert

To assert a fact or conviction with confidence and vigor.

Disjunctive Syllogisms

A form of logical argument where, from two propositions, each of which could be true or false, a definite conclusion is drawn.

Suspects

Individuals thought to be involved in or responsible for a criminal activity but not yet proven guilty.

Culprit

The person or thing responsible for a fault or problem.