Chapter 6 - Section 6.7 - Variation and Problem Solving - Exercise Set - Page 398: 35

$k=4.212$

Since $y$ varies inversely as the square of $x$, then, $ y=\dfrac{k}{x^2} .$ Substituting the given values of the variables, then the value of $k$ is, \begin{array}{l} 0.052=\dfrac{k}{9^2} \\\\ 0.052=\dfrac{k}{81} \\\\ 0.052(81)=k \\\\ 4.212=k \\\\ k=4.212 .\end{array}