$(20pts)$ Some wastewater with a dissoved oxygen of $2m\frac{g}{L},7-$day BOD of $380m\frac{g}{L}($BOD reaction rate coefficient $k_L$ of $\frac{0\mathrm{.}21}{?}$ day$)$ is discharged to a river at a rate of $3\mathrm{.}5\frac{m^3}{s}.(1)$ Calculate the ultimate BOD of the waste before discharge to the river $(5$ pts $.(2)$ Assuming instantaneous mixing after discharge, calculate DO $(5pts$ AND the ultimate BOD $(7pts)$ of the river water after it has received the waste. The river has a flow rate of $20\frac{m^3}{s}$ and a background DO of $9m\frac{g}{L}$ and ultimate BOD of $1\mathrm{.}0m\frac{g}{l}$ upstream of the waste discharge. $(3)$ What is the Oxygen Deficit $(3$ pts$)?$