[tex] \large \bold{SOLUTION:} [/tex]
[tex]5.)\: d = k\sqrt{q_1 q_2} [/tex]
[tex] \textsf{When }q_1 = 1, d = 5,\textsf{and }k = 4[/tex],
[tex] \begin{aligned} d &= k\sqrt{q_1 q_2} \\ 5 &= 4\sqrt{1\cdot q_2} \\ 5 &= 4\sqrt{q_2} \\ \frac{5}{4} &= \frac{\cancel{4}\sqrt{q_2}}{\cancel{4}} \\ \frac{5}{4} &= \sqrt{q_2} \\ \quad\quad \left(\dfrac{5}{4}\right)^2 & = (\sqrt{q_2})^2 \\ q_2 &=\frac{25}{16} \\ q_2 &\approx \boxed{1.5625}\quad\textit{Answer} \end{aligned} [/tex]
[tex]6.)\: r = \sqrt{\dfrac{V}{3.14h}} [/tex]
[tex]\textsf{When }V = 15 \textsf{ and }h = 12,[/tex]
[tex] \begin{aligned} \quad \quad r &= \sqrt{\frac{V}{3.14h}} \\ r &= \sqrt{\frac{15}{3.14(12)}} \\ r &= \sqrt{0.3981} \\ r &\approx \boxed{0.63}\quad\textit{Answer} \end{aligned} [/tex]
[tex]7.)\: s = \pi r \sqrt{r^2 + h^2} [/tex]
[tex]\textsf{When }s = 364.25\textsf{ and }r = 5.75,[/tex]
[tex] \begin{aligned} 364.25 &= \pi (5.75)\sqrt{5.75^2 + h^2} \\ \frac{364.25}{5.75\pi} &= \frac{\cancel{5.75\pi}\sqrt{33.0625 + h^2}}{\cancel{5.75\pi}} \\ \frac{364.25}{5.75\pi} &= \sqrt{33.0625 + h^2} \\ \quad \quad \left(\frac{364.25}{5.75\pi}\right)^2 &= \left(\sqrt{33.0625 + h^2}\right)^2 \\ 406.5965 &= 33.0625 + h^2 \\ h^2 &= 406.5965 - 33.0625 \\ h^2 &= 373.534 \\ h &=\sqrt{373.534} \\ h &\approx \boxed{19.33}\quad\textit{Answer} \end{aligned} [/tex]
[tex] \blue{\mathfrak{\#CarryOnLearning}} [/tex]
