y is directly proportional to (d+2)^2, when d=5, y=147. d^2 is inversely proportional to x^2, when d=2, x=3. Find an equation for y in terms of x
Though this question initially appears complex, it can be broken down into logical steps that make the answer straightforward to find. The two statements should be approached individually, to give an equation for y in terms and d, and another for d in terms of x. The equation for d in terms of x can be substituted into the equation for y in terms of d, to give an equation for y in terms of x
Finding the first equationy ∝ (d+2)2y = k(d+2)2147 = k X 72147 = 49kk =3y = 3(d+2)2 (1)
Finding the second equationd2 ∝ 1/x2d2 = k/x24 = k/9k = 36d2 = 36/x2d = 6/x (2)
Subsituting for the final equationSubstituting (2) into (1)y = 3((6/x)+2)2
