If T = 2π√(L/G), make G the subject of the formula. Hence, find the value of G to the nearest whole number when T = 45, L = 8 and π = 3.142.

a) To make G the subject of the formula T = 2 sqrt((L)/(G)): Step 1: Divide both sides by 2. (T)/(2) = sqrt((L)/(G)) Step 2: Square both sides of the equation. ((T)/(2))^2 = (L)/(G) (T^2)/(4^2) = (L)/(G) Step 3: Rearrange the equation to solve for G. G = (L)/(T^2)4^2 G = (4^2 L)/(T^2) The formula with G as the subject is G = (4^2 L)/(T^2). Step 4: Substitute the given values T=45, L=8, and =3.142 into the formula. G = (4 × (3.142)^2 × 8)/((45)^2) G = (4 × 9.872164 × 8)/(2025) G = (315.909248)/(2025) G ≈ 0.15600456 Step 5: Round the value of G to the nearest whole number. G ≈ 0 The value of G to the nearest whole number is 0. b) Let C be the cost per person and N be the number of guests. The cost per person is partly constant (k) and partly varies inversely as the number of guests (N). This can be written as: C = k + (m)/(N) where k and m are constants. Step 1: Use the given information to form two equations. For 24 persons, the cost is N800.00: 800 = k + (m)/(24) (1) For 18 persons, the cost is N1200.00: 1200 = k + (m)/(18) (2) Step 2: Solve the system of equations for k and m. Subtract equation (1) from equation (2): (1200 - 800) = (k + (m)/(18)) - (k + (m)/(24)) 400 = (m)/(18) - (m)/(24) Find a common denominator for 18 and 24, which is 72. 400 = (4m)/(72) - (3m)/(72) 400 = (m)/(72) m = 400 × 72 m = 28800 Step 3: Substitute the value of m into equation (1) to find k. 800 = k + (28800)/(24) 800 = k + 1200 k = 800 - 1200 k = -400 So the formula for the cost per person is C = -400 + (28800)/(N). Step 4: Find the cost per person for 42 persons. Substitute N = 42 into the formula: C = -400 + (28800)/(42) C = -400 + 685.71428... C = 285.71428... Step 5: Round the cost to the nearest naira. C ≈ N286 The cost per person for 42 persons to the nearest naira is N286. 3 done, 2 left today. You're making progress.