If $z$ varies inversely as $w$, and $z=10$ when $w=9$, find $z$ when $w=3$. \[ z=\square \]

Step 1 ：The problem states that $z$ varies inversely as $w$. This means that the product of $z$ and $w$ is a constant. We can express this relationship as $zw = k$, where $k$ is the constant of variation.

Step 2 ：Given that $z=10$ when $w=9$, we can substitute these values into the equation to find the constant of variation: $10*9 = k$, so $k = 90$.

Step 3 ：Now we know that $zw = 90$ for all values of $z$ and $w$.

Step 4 ：We are asked to find the value of $z$ when $w=3$. We can substitute $w=3$ into the equation and solve for $z$: $z*3 = 90$, so $z = 90/3$.

Step 5 ：\(\boxed{z = 30}\)