Mathematics 2005 JAMB Past Questions - Question 16: The weight Wkg of a metal bar varies jointly as its length L meter and the square of its diameter d meters. if W=140 when d=4 2/3 and L =54. Find d in terms of W and L.

Correct Answer

A

Explanation

To find the value of d in terms of W and L, we can use the joint variation equation:W = k * L * d^2where W is the weight of the metal bar, L is the length, d is the diameter, and k is the constant of variation.We are given that W = 140 when d = 4 2/3 and L = 54. Let's substitute these values into the equation:140 = k * 54 * (4 2/3)^2To simplify the equation, we need to convert the mixed fraction (4 2/3) into an improper fraction. 4 2/3 = (4 * 3 + 2) / 3 = 14/3Now we can substitute the values into the equation:140 = k * 54 * (14/3)^2To solve for k, we can divide both sides of the equation by (54 * (14/3)^2):k = 140 / (54 * (14/3)^2)Now we have the value of k. To find d in terms of W and L, we rearrange the equation:W = k * L * d^2d^2 = W / (k * L)Taking the square root of both sides, we get:d = sqrt(W / (k * L))Now we can substitute the values of W, L, and k into the equation to find d in terms of W and L.