1. **State the problems:** - Isolate $\beta_0$ in $\beta_0 = 2l + 2w$ - Isolate $A$ in $A = \pi r^2$ - Isolate $x$ in $\frac{x}{A} = xy$ 2. **Isolate $\beta_0$:** Given $\beta_0 = 2l + 2w$, it is already isolated. So, $$\beta_0 = 2l + 2w$$ 3. **Isolate $A$:** Given $A = \pi r^2$, $A$ is already isolated. $$A = \pi r^2$$ 4. **Isolate $x$ in $\frac{x}{A} = xy$:** Start with: $$\frac{x}{A} = xy$$ Multiply both sides by $A$ to eliminate the denominator: $$\cancel{A} \times \frac{x}{\cancel{A}} = xy \times A$$ which simplifies to: $$x = Axy$$ Now, subtract $Axy$ from both sides: $$x - Axy = 0$$ Factor out $x$: $$x(1 - Ay) = 0$$ Divide both sides by $(1 - Ay)$ (assuming $1 - Ay \neq 0$): $$\frac{x \cancel{(1 - Ay)}}{\cancel{(1 - Ay)}} = \frac{0}{1 - Ay}$$ which simplifies to: $$x = 0$$ **Final answers:** - $\beta_0 = 2l + 2w$ - $A = \pi r^2$ - $x = 0$