Final answer:
When y varies inversely as the squared of x, the equation is y = k/x^2. To find k, we substitute the given values and solve for it.
Step-by-step explanation:
Inverse variation is a relationship between two variables in which one variable increases as the other decreases, and vice versa, in a way that the product of the two variables remains constant.
When y varies inversely as the squared of x, the equation can be written as y = k/x^2, where k is a constant. We are given that y = 25 when x = 3, so we can substitute these values into the equation to solve for k:
25 = k/3^2
25 = k/9
To solve for k, we can multiply both sides of the equation by 9:
25 * 9 = k
225 = k
Therefore, the value of k is 225.