Turn over 33 Question 11 continued _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ (Total for Question 11 is 7 marks) 34 12. y R O x Figure 3 The curve shown in Figure 3 has parametric equations x = 6 sin t        y = 5 sin 2t        0  t  2 π The region R, shown shaded in Figure 3, is bounded by the curve and the x-axis. (a) (i) Show that the area of R is given by 2 2 0 60sin cos d π t t t ∫ (3) (ii) Hence show, by algebraic integration, that the area of R is exactly 20 (3) y M O x N 4.2 Figure 4 Part of the curve is used to model the profile of a small dam, shown shaded in Figure 4. Using the model and given that ● x and y are in metres ● the vertical wall of the dam is 4.2 metres high ● there is a horizontal walkway of width MN along the top of the dam (b) calculate the width of the walkway. (5) _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________