UNO High School Problem of the Week Competition
Problem 9
If y varies directly as x and inversely as the square of z, and y = 1.5 when x = 2 and z =4, then find the value of z when y = .25 and x = .75.
Solution
The formula looks like this: y = kx/z^2. We know that 1.5 = k(2)/(4)^2. When we solve this for k, we see that k = 12. When we plug in the values k = 12, y = .25, and x = .75 into the equation, we get .25 = 12(.75)/z^2. When we solve this for z, we find that z = 6 or -6.
