You are given that x is directly proportional to y^3, and y is inversely proportional to \(\sqrt{z}\). If the value of x is 3 when z is 12, what is the value of x when z is equal to 75?

x =k * y^3/sqrt(z) 3 = k * y^3 /sqrt(12) x = k * y^3/sqrt(75), solve for k, x, y k =2.5, x=0.34641 and y^3 =6/5 =1.2. OR:

k=sqrt(12), x =6/5 and y^3 =3 Note : Somebody should check this! Thanks.