91Ó°ÊÓ

\(-8 y^2+2=x\)

Simplify the expression. Write your answer using only positive exponents. \(\left(z^2\right)^{-3}\)

\(\sqrt[6]{\frac{g^6 h}{h^7}}\)

The maximum hull speed \(v\) (in knots) of a boat with a displacement hull can be approximated by \(v=1.34 \sqrt{\ell}\), where \(\ell\) is the waterline length (in feet) of the boat. Find the inverse function. What waterline length is needed to achieve a maximum speed of \(7.5\) knots?

Elastic bands can be used for exercising to provide a range of resistance. The resistance \(R\) (in pounds) of a band can be modeled by \(R=\frac{3}{8} L-5\), where \(L\) is the total length (in inches) of the stretched band. Find the inverse function. What length of the stretched band provides 19 pounds of resistance?

\(2 y^2=x-4\)

Simplify the expression. Write your answer using only positive exponents. \(\left(\frac{3 x}{2}\right)^4\)

\(\sqrt[8]{\frac{n^{18} p^7}{n^2 p^{-1}}}\)

The Beaufort wind scale was devised to measure wind speed. The Beaufort numbers \(B\), which range from 0 to 12 , can be modeled by \(B=1.69 \sqrt{s+4.25}-3.55\), where \(s\) is the wind speed (in miles per hour). $$ \begin{array}{|c|c|} \hline \text { Beaufort number } & \text { Force of wind } \\ \hline 0 & \text { calm } \\ 3 & \text { gentle breeze } \\ 6 & \text { strong breeze } \\ 9 & \text { strong gale } \\ 12 & \text { hurricane } \\ \hline \end{array} $$ a. What is the wind speed for \(B=0\) ? \(B=3\) ? b. Write an inequality that describes the range of wind speeds represented by the Beaufort model.

\(x+8=\frac{1}{5} y^2\)