Prove that a hyperbola is an equilateral hyperbola if and only if e=2e=\sqrt{2}e=2.
Solve the equation.
e2lnx=9e^{2 \ln x} = 9 e2lnx=9
Ecology The air temperature affects how quickly water evaporates from a particular reservoir. The amount of water that evaporates from the reservoir each day for various temperatures in degrees Fahrenheit is shown in the table below as acre-feet (af).
Temperature (∘F) (af) 40800601640702060852690\begin{array}{|c|c|} \hline \text { Temperature }\left({ }^{\circ} \mathbf{F}\right) & \text { (af) } \\ \hline 40 & 800 \\ \hline 60 & 1640 \\ \hline 70 & 2060 \\ \hline 85 & 2690 \\ \hline \end{array} Temperature (∘F)40607085 (af) 800164020602690
Describe the meaning of the slope of this line in the context of this problem.
For the following exercise, perform the operations. Express answers in reduced form.
aa2−9+1a−3\dfrac{a}{a^2-9}+\dfrac{1}{a-3} a2−9a+a−31