Let's analyze the given problem and find the exact values for $x$ and $y$ step by step.

Given:

1. $s = 9$
2. $x = 4.5$
3. $y = 9 \sqrt{32}$

Step 1: Simplify $x$

The value of $x$ is already given as $x = 4.5$. Therefore: $x = 4.5$

Step 2: Simplify $y$

The expression for $y$ is $y = 9 \sqrt{32}$. Start by simplifying $\sqrt{32}$: $\sqrt{32} = \sqrt{16 \cdot 2} = \sqrt{16} \cdot \sqrt{2} = 4 \sqrt{2}.$ Substitute $\sqrt{32} = 4 \sqrt{2}$ into $y$: $y = 9 \cdot 4 \sqrt{2} = 36 \sqrt{2}.$

Thus, the exact value of $y$ is: $y = 36 \sqrt{2}.$

Final Answer:

$x = 4.5, \quad y = 36 \sqrt{2}.$

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Would you like a more detailed breakdown or have further questions? 😊
Here are 5 related questions to consider:

1. How can you simplify other square root expressions like $\sqrt{50}$ or $\sqrt{72}$?
2. If $x$ and $y$ were variables, how would their values change with different $s$?
3. What does $\sqrt{32}$ represent geometrically?
4. How would you convert $36 \sqrt{2}$ to a decimal approximation?
5. How can you rationalize the denominator in expressions like $\frac{1}{\sqrt{32}}$?

Tip: Simplifying square roots is easier if you first factor the number into primes!