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:

Cataracts

A medical condition where the lens of the eye becomes progressively opaque, leading to vision impairment.

Bottom-up Processing

An approach to information processing that starts with the sensory input and builds up to the final perception.

Sensory Adaptation

Diminished sensitivity as a consequence of constant stimulation.

Sensory Receptors

Specialized cells or neuronal structures that respond to specific types of external stimuli, such as light, sound, pressure, or chemicals, sending signals to the brain.