Corrugated cardboard is produced by gluing corrugated paper between at sheets of paper. A particular type of corrugated cardboard is made up of two corrugated sheets of paper glued between three at sheets of paper as shown below. (.1. 3) 3 f (1;) 2 slit) 0 The at sheets of paper are described by the horizontal lines 3/ = 0, y = 2 and y = 3. The corrugations are described by two functions f{x} and g(x} = sin(irx}+l, where all distances are measured in centimetres. a) Given that f(x) = HCOSHLY) +0, write down the values Ufa, b and c. Let d(x) = f(x) - g(x) the vertical distance between the corrugated sheets of paper. The graph of d(x) is plotted below. 3 2 O 2 4 6 8 10 12 b) Show that d(x) = TX + - COS + sin(7x) . 2 2State the period of d(x) . c)d) Determine the maximum and minimum distances between the corrugated paper, correct to three decimal places. c} Find the values of x for which d(x} : for 15 x S 5 . Give noninteger solutions correct to 3 decimal 2 places