1. **State the problem:** We are given that $y$ is inversely proportional to $x^2$, which means $y \propto \frac{1}{x^2}$. We have a table with $y=32.4$ when $x=4$, and we need to find the missing $y$ value when $x=9$. 2. **Write the formula:** Since $y$ is inversely proportional to $x^2$, we can write: $$y = \frac{k}{x^2}$$ where $k$ is the constant of proportionality. 3. **Find the constant $k$ using the known values:** Substitute $y=32.4$ and $x=4$: $$32.4 = \frac{k}{4^2} = \frac{k}{16}$$ Multiply both sides by 16: $$k = 32.4 \times 16 = 518.4$$ 4. **Find the missing $y$ when $x=9$:** Use the formula with $k=518.4$: $$y = \frac{518.4}{9^2} = \frac{518.4}{81}$$ Calculate: $$y = 6.4$$ 5. **Answer:** The missing value of $y$ when $x=9$ is $6.4$. This shows how inverse proportionality works: as $x$ increases, $y$ decreases according to the square of $x$.