Science:Math Exam Resources/Courses/MATH110/December 2014/Question 09 (a)

MATH110 December 2014

  •  Q1 (a)  •  Q1 (b)  •  Q1 (c)  •  Q1 (d)  •  Q2 (a)  •  Q2 (b)  •  Q2 (c)  •  Q3 (a)  •  Q3 (b)  •  Q3 (c)  •  Q3 (d)  •  Q3 (e)  •  Q4 (a)  •  Q4 (b)  •  Q4 (c)  •  Q5 (a)  •  Q5 (b)  •  Q5 (c)  •  Q6 (a)  •  Q6 (b)  •  Q6 (c)  •  Q7 (a)  •  Q7 (b)  •  Q7 (c)  •  Q8 (a)  •  Q8 (b)  •  Q8 (c)  •  Q9 (a)  •  Q9 (b)  •  Q10  •  Q11  •  

   Other MATH110 Exams

  •  December 2011  •  December 2010  •  April 2012  •  April 2011  •  December 2012  •  April 2013  •  December 2013  •  April 2014  •  December 2014  •  December 2015  •  April 2017  •  April 2016  •  December 2016  •  December 2017  •  April 2018  •  

Question 09 (a)

When a pebble is thrown into a pond, circular ripples form on the water surface. Suppose ${\textstyle r(t)}$ is the radius, in centimetres, of one such ripple at ${\textstyle t}$ minutes after the pebble falls into the water, and ${\textstyle A(r)}$ is the surface area of a ripple of radius ${\textstyle r}$. (a) Which of the following statements best explains the meaning of the composite function ${\textstyle A(r(t))}$? (i) The radius of the ripple, in centimetres, at time ${\textstyle t}$ minutes. (ii) The area of the ripple, in square centimetres, of radius ${\textstyle r}$ centimetres. (iii) The area of the ripple, in square centimetres, at time ${\textstyle t}$ minutes. (iv) The function ${\textstyle f}$ 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 ${\textstyle t}$ minutes.

Make sure you understand the problem fully: What is the question asking you to do? Are there specific conditions or constraints that you should take note of? How will you know if your answer is correct from your work only? Can you rephrase the question in your own words in a way that makes sense to you?

If you are stuck, check the hint below. Consider it for a while. Does it give you a new idea on how to approach the problem? If so, try it!

Hint
What are input and output of the composition function $A(r(t))$?

Checking a solution serves two purposes: helping you if, after having used the hint, you still are stuck on the problem; or if you have solved the problem and would like to check your work. If you are stuck on a problem: Read the solution slowly and as soon as you feel you could finish the problem on your own, hide it and work on the problem. Come back later to the solution if you are stuck or if you want to check your work. If you want to check your work: Don't only focus on the answer, problems are mostly marked for the work you do, make sure you understand all the steps that were required to complete the problem and see if you made mistakes or forgot some aspects. Your goal is to check that your mental process was correct, not only the result.

Solution
Found a typo? Is this solution unclear? Let us know here. Please rate my easiness! It's quick and helps everyone guide their studies. Observe that the input of $A(r(t))$ is time $t$ (min) and the output is the area (square centimetres) of a ripple. Therefore, $A(r(t))$ represents the area of the ripple, in square centimetres, at time ${\textstyle t}$ minutes. Answer: $\color {blue}(iii)$,