The relationship described in the problem is a direct variation, where U varies directly as the square root of V. In direct variation, when one variable changes, the other variable changes in a specific way. The formula for this kind of relationship is:
U = k√V
where U is directly proportional to the square root of V with k being the constant of proportionality.
From the problem statement, we know that when U = 24, V = 9, and we need to find the constant of proportionality k.
Let's substitute these values into the equation:
24 = k√9
Solving for k, we find:
24 = k * 3
k = 24 / 3
k = 8
Now we have the constant of proportionality, k = 8. To find V when U = 16, we substitute U = 16 into the equation:
16 = 8√V
Solving for √V, we find:
√V = 16 / 8
√V = 2
To find V, we square both sides of the equation:
V = 2²
V = 4
Therefore, the value of V when U = 16 is 4.