$(10)$

One alternative for operating an activated sludge plant is to waste the bacterial population directly from the reactor instead of from the recycle line $($see schematic$).$

$($a$)$ points$]$ Considering that the fundamental definition of ${}_c$ is: $7$

${}_c-=\frac{\text{T}\text{o}\text{t}\text{a}\text{l}\text{b}\text{i}\text{o}\text{m}\text{a}\text{s}\text{s}in\text{s}\text{y}\text{s}\text{t}\text{e}\text{m}}{\text{R}\text{a}\text{t}\text{e}of\text{b}\text{i}\text{o}\text{m}\text{a}\text{s}\text{s}\text{r}\text{e}\text{m}\text{o}\text{v}\text{a}\text{l}}$

show that ${}_c$ is independent of the mixed liquor volatile suspended solids concentration in a "reactor$-$wasted" system. You may safely ignore biomass contained in the settling tank and recycle line and assume $x_e$ is negligible. system vs$,$ the conventional recycle wasted system. Describe it$.$