The $-50+5mm$ is then retreated in a second stage DMS circuit and $85\%$ of the con Pyrolusite is recovered in the sinks at an SG of $4\mathrm{.}53.$

Determine:

$2\mathrm{.}1$ The $\%Si{O}_2$ in the feed

$2\mathrm{.}2$ The $\%Si{O}_2$ in the first float fraction

$2\mathrm{.}3$ The grade of $Mn{O}_2$ in the second stage feed

$2\mathrm{.}4$ The bath density in the final stage DMS

$2\mathrm{.}5$ The overall Mn recovery to the final sinks fraction from the initial feed