$1-29.$ An actuator used in a prosthetic arm can produce different amounts of force by changing the voltage of the power supply. The force and voltage satisfy the linear relation $F=kV,$ where $V$ is the voltage applied and $F$ is the force produced by the prosthetic arm. The maximum force the arm can produce is $50\mathrm{.}0$ N when supplied with $10$ V $.$

$($a$)$ Find the force produced by the actuator when supplied with $6\mathrm{.}0$ V $.$

$($b$)$ What voltage is needed to achieve a force of $5\mathrm{.}0$ N $?$

$($c$)$ Using the results of parts $($a$)$ and $($b$),$ sketch the graph of $F$ as a

function of voltage $V.$ Use the appropriate scales and clearly label the slope and the results of parts $($a$)$ and $($b$).$

$1-38.$ To determine the concentration of a purified protein sample, a graduate student used spectrophotometry to measure the absorbance given in the table below:

$\backslash$table$[[c(\frac{g}{m}l),a$