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Page 2 Question 2 (a) For matrixA = (4 1 2 3) , ifg(X) = X2 + 4x + 2, what is the answer to g(A)? (b) Using algebra, nd the solution to the system of inequalities below y S 5 3x y + 19 2 x2 8x (c) What is peculiar about the slope of a function before and after a point of inection as compared with the slope before or after a maximum or minimum point? (d) Suppose that the satifaction received from a number of rides taken on a roller coaster 2x+1 3x+4 0.5 is given by the function SCX) = 200 ( ) , where S is the satisfaction received and X is the number of rides taken. (i) Find the rate at which the satisfaction changes with respect to the number of rides taken. Question 3. (a) A project management consultant estimated that if a particular project was completed, it years after completion, N thousand persons would benefit directly from the project, where t3 N(t) =4.5t2 +16t, 0 s t s 10 For what value of t, will the largest number of people receive direct benefits? (b) A clothing manufacturer makes trousers, skirts and blouses. Each trouser requires 20 minutes ofcutting time, 60 minutes of sewing time and 5 minutes ofpackaging time. Each skirt requires 15 minutes of cutting time, 30 minutes of sewing time and 12 minutes of packaging time. Each blouse requires 10 minutes of cutting time, 24 minutes of sewing time and 6 minutes of packaging time. The amount of time available for cutting, sewing and packaging is 115 hours, 280 hours and 65 hours respectively. Using either the Inverse Method or the Cram er's Rule, determine how many of each type of clothing should be made to use all available labour hours