11. A local radio station has been given the exclusive rights to promote a concert in the city’s civic arena, which seats 22 000 persons. The commission $ C for the radio station is $ 5 000 plus $ 0.50 for each of the n tickets sold for the concert.
(a) Write down the formula connecting C and n.
(b) Use the formula to calculate
(i) the commission for the radio station when 15 000 tickets are sold,
(ii)the number of tickets sold when the commission for the radio station is $ 11 250,
(iii)the maximum commission for the radio station.
12. (a) If a is directly proportional to the cube of b and that a = 54 when b = 3, find the equation relating a and b.
(b) using the equation in (a), find the value of
(i) a when b = 5,
(ii) b when a = 128.
13. In each of following, find the unknown variable without finding the proportionality constant.
(a) If h is directly proportional to the square of k and h = 8 when k = 3, find h when x = 6.
(b) If m is directly proportional to p1/2 and m = 12 when p = 16, find p when m =18.
14. If the height of a cylinder is fixed, its volume is directly proportional to the square of its radius. When the radius of the cylinder is 2 cm, its volume is 81 cm3. Find the radius of the cylinder if the volume is 506.25 cm3.
15. Given that a2is directly proportional to b3 and a = 8(3)1/2whenb = 4,
(a) find the equation connecting a and b,
(b) find the value of a when b = 3.
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