Science:Math Exam Resources/Courses/MATH110/December 2014/Question 09 (a)
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Question 09 (a)
When a pebble is thrown into a pond, circular ripples form on the water surface. Suppose is the radius, in centimetres, of one such ripple at minutes after the pebble falls into the water, and is the surface area of a ripple of radius .
(a) Which of the following statements best explains the meaning of the composite function ?
(i) The radius of the ripple, in centimetres, at time minutes.
(ii) The area of the ripple, in square centimetres, of radius centimetres.
(iii) The area of the ripple, in square centimetres, at time minutes.
(iv) The function of the minutes and the area.
(v) The product of the area of the ripple, in square centimetres, by the ripple’s radius at time minutes.
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What are input and output of the composition function ?
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Observe that the input of is time (min) and the output is the area (square centimetres) of a ripple.
Therefore, represents the area of the ripple, in square centimetres, at time minutes.