Final answer:
The value of m varies inversely as the square of n. Given m = 6 when n = 3, we can find the constant k. Then, for m = 13.5, we can solve for the positive value of n.
Step-by-step explanation:
The value of m varies inversely as the square of n. This can be written as the equation m = k/n^2, where k is a constant.
Given that when n = 3, m = 6, we can substitute these values into the equation to find the value of k. So, 6 = k/3^2 = k/9. Solving for k, we get k = 54.
Now, let's find the value of n when m = 13.5. Substituting the values into the equation, we have 13.5 = 54/n^2. Solving for n, we get n^2 = 54/13.5 = 4. Taking the positive square root of both sides, we find that the positive value of n is 2.