In a polar coordinate system, the midpoint of the line segment whose endpoints are $\left( 8, \frac{5 \pi}{12} \right)$ and $\left( 8, -\frac{3 \pi}{12} \right)$ is the point $(r, \theta).$ Enter $(r, \theta),$ where $r > 0$ and $0 \le \theta < 2 \pi.$

Afactory adds 3 red drops and 2 blue drops of coloring to white paint to make each pint of purple paint. the factory will make 50 gallons of the purple paint. how many drops of red and blue coloring will the factory need in the 50 gallon batch of purple paint.

Acertain population of bacteria demonstrates exponential growth doubles in size every 4 days. how long will it take the population to triple in size?

Identify the graph of y = ln x + 1.