Final answer:
X varies inversely with the square of Y. When Y = 3, X = 4. Find X when Y = 6.
Step-by-step explanation:
The question involves understanding inverse variation. In an inverse variation, the product of the two variables remains constant. This means if X varies inversely as the square of Y, then X * Y^2 is constant. Given that when Y=3, X=4, we can find the constant by calculating 4 * 3^2 which equals 36. This constant is used to find X when Y is 6.
We set up the equation with the new values X * 6^2 = 36. Solving for X gives us X = 36 / 6^2, which simplifies to X = 1. This shows that when Y is doubled from 3 to 6, X is reduced to a quarter of its original value, demonstrating inverse square relationship.
To solve this problem, we can use the inverse variation formula: X = k/Y^2, where k is the constant of variation. We are given that when Y = 3, X = 4. We can use this information to solve for k as follows:
X = k/3^2
4 = k/9
k = 36
Now we can use the value of k to find X when Y = 6:
X = 36/6^2
X = 36/36
X = 1