A quality x varies inversely as the square of y. Given that x=4, when y=3, the value of x when y=6 is

Options

A. 1
B. 2
C. 3
D. 4

Answer

To solve the problem step by step, we will follow the concept of inverse variation and use the given values to find the required result.

### Step-by-Step Solution:

1. **Understand the relationship**: The problem states that \( x \) varies inversely as the square of \( y \). This can be mathematically represented as:
\[ x = \frac{k}{y^2} \]
where \( k \) is a constant.

2. **Substitute the known values**: We are given that \( x = 4 \) when \( y = 3 \). We can substitute these values into the equation to find \( k \):
\[ 4 = \frac{k}{3^2} \]

3. **Calculate \( k \)**: Simplifying the equation:
\[ 4 = \frac{k}{9} \]
To find \( k \), multiply both sides by 9:
\[ k = 4 \times 9 = 36 \]

4. **Use the value of \( k \)**: Now that we have \( k = 36 \), we can find the value of \( x \) when \( y = 6 \). Substitute \( y = 6 \) into the equation:
\[ x = \frac{36}{6^2} \]

5. **Calculate \( x \)**: Simplifying further:
\[ x = \frac{36}{36} = 1 \]

Thus, the value of \( x \) when \( y = 6 \) is **1**.