y varies directly as w2. When y = 8, w = 2. Find y when w = 3

The given statement "y varies directly as w^2" can be written as an equation: y = k w^2 where k is a constant of proportionality. We are also given that when y = 8, w = 2. We can use this information to solve for k: 8 = k (2^2) 8 = 4k k = 2 Now that we know the value of k, we can use the equation to find y when w = 3: y = 2 (3^2) y = 18 Therefore, when w = 3, y is equal to 18. In other words, the problem is asking us to find the value of y when the value of w is changed from 2 to 3, given that y varies directly with w^2. We can use the equation y = k w^2 and the given information to solve for the constant of proportionality k. Once we have found k, we can use the equation to find y when w = 3.