25(a) C(100) = 2600 + 80(100) = 10600(b)(i) 250n - (2600 + 80n)= 170n - 2600(ii) 170n - 2600 >= 0n >= 2600/170 n >= 15.2So, the set of n is n = 16,17,18...(iii) n = 35, profit = 170(35) - 2600 = 3350n = 200,profit = 170(200) - 2600 = 31400
30(a)(i) f(1 + 2) = f(3) = 9f(1) + f(2) = 1 + 4 = 5(ii) sinx(b)(i) C(a + b) = π(a + b) = πa + πb = C(a) + C(b)(ii) F = -kx where F is the froce of spring and k is the spring constant