Solve the equation: \( e^{2x} = 7 \)

Let \( R \) be the region enclosed by the graphs of \( f(x)=4 \cos (x)-3 \) and \( g(x)=4 \sin (x)-4 \). Find the length of the boundary of region \( R \). Use a calculator and round your answer to 3 decimal places.

Find the producers' surplus at a price level of \( \overline{\mathrm{p}}=\$ 64 \) for the price-supply equation below. \( \mathrm{p}=\mathrm{S}(\mathrm{x})=15+0.1 x+0.0003 \mathrm{x}^{2} \) The producers' surplus is \( \$ \square \). (Round to the nearest integer as needed.)

18. La integral de \( \int \frac{d x}{x+5}=e s: \) \( \begin{array}{ll}\text { a) } \frac{\ln |x+5|}{-5}+c & \text { b) } \frac{\ln 3}{-x}+c \\ \text { c) } \ln |x+5|+c & \text { d) } \frac{x \ln e^{-2}}{-2}+c \\ \text { A) } & \\ \text { B) } \\ \text { C) } \\ \text { D) }\end{array} \)

Let \( R \) be the region enclosed by the graphs of \( f(x)=4 \cos (x)-1 \) and \( g(x)=4 \sin (x)-2 \). Find the length of the boundary of region \( R \). Use a calculator and round your answer to 3 decimal places.

Question 17 ( 5 points) \( \begin{array}{l}\text { A turkey is taken out of the oven with an internal temperature of } 180^{\circ} \text { Fahrenheit and is } \\ \text { allowed to cool in a } 75^{\circ} \mathrm{Froom} \text {. After half-hour, the internal temperature of the turkey is } 140^{\circ} \\ \text { F. To the nearest minute, how long will it take the turkey to cool to } 100^{\circ} \mathrm{F} \text { ? }\end{array} \)