page 06 MARKS 8. (a) Express cos sin x x − 2 ° ° in the form ( ) cos k x a − °, k a > < < 0, 0 360. (b) Hence, or otherwise, find (i) the minimum value of cos sin x x − 6 ° 3 ° and (ii) the value of x for which it occurs where x ≤ < 0 360. 9. A sector with a particular fixed area has radius x cm. The perimeter, P cm, of the sector is given by P x x = + 128 2 . Find the minimum value of P. 10. The equation ( ) x m x m + − + = 2 3 0 has two real and distinct roots. Determine the range of values for m. 11. A supermarket has been investigating how long customers have to wait at the checkout. During any half hour period, the percentage, P %, of customers who wait for less than t minutes, can be modelled by ( ) kt P e = − 100 1 , where k is a constant. (a) If 50% of customers wait for less than 3 minutes, determine the value of k. (b) Calculate the percentage of customers who wait for 5 minutes or longer. 4 1 2 6 4 4 2