1. The problem presents multiple equations, but per instructions, we will solve only the first one: $$y = \frac{x}{\sqrt{w_0}}$$. 2. This equation expresses $y$ as a function of $x$ and a constant $w_0$. The square root in the denominator means $w_0$ must be positive. 3. To understand the behavior of $y$, note that for fixed $w_0$, $y$ is directly proportional to $x$. 4. If you want to solve for $x$ in terms of $y$ and $w_0$, multiply both sides by $\sqrt{w_0}$: $$y \sqrt{w_0} = x$$ 5. This isolates $x$: $$x = y \sqrt{w_0}$$ 6. This is the simplest form; no further simplification is needed. Final answer: $$x = y \sqrt{w_0}$$