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