Z varies directly with x <span>so, let z = kx (k is some constant) </span> <span>now, since when z = 1/2, x = 1/3 </span> <span>we get, 1/2 = k/3, so k = 3/2 </span> <span>so, we get z = 3x/2 </span>
<span>z varies inversely with the product of r^2 and y </span> <span>so, z = c/(y * r^2) (c is some constant) </span> <span>again, when z = 1/2, y = 1/5 and r = 3 </span> <span>so, we get, 1/2 = c/(9/5), so c = 9/10 </span> <span>so, we get z = 9/(10*y*r^2) </span>
<span>the above two functions model the variations </span>
<span>does this make sense ? hopefully this is right!</span>