Suppose that the functions \( q \) and \( r \) are defined as follows. \[ \begin{array}{l}q(x)=x^{2}+9 \\ r(x)=\sqrt{x+8}\end{array} \] Find the following. \[ \begin{array}{l}(r \circ q)(8)= \\ (q \circ r)(8)=\square\end{array} \]

To solve the given expressions, we need to evaluate \( (r \circ q)(8) \) and \( (q \circ r)(8) \). 1. **Calculating \( (r \circ q)(8) \)**: This means we first apply \( q \) to \( 8 \) and then apply \( r \) to the result. \[ q(8) = 8^2 + 9 = 64 + 9 = 73 \] Now, we take this result and apply \( r \): \[ r(73) = \sqrt{73 + 8} = \sqrt{81} = 9 \] Thus, \( (r \circ q)(8) = 9 \). 2. **Calculating \( (q \circ r)(8) \)**: Here, we first apply \( r \) to \( 8 \) and then apply \( q \) to the result. \[ r(8) = \sqrt{8 + 8} = \sqrt{16} = 4 \] Now, we apply \( q \) to this result: \[ q(4) = 4^2 + 9 = 16 + 9 = 25 \] Therefore, \( (q \circ r)(8) = 25 \). Putting it all together, we have: \[ (r \circ q)(8) = 9, \quad (q \circ r)(8) = 25 \]