$($Show work and steps. Circle$/$box final answers$)$ Problem $5$

For the system shown in the figure below, M$\_($i$)=2\mathrm{.}0,$A$\_($i$)=20\mathrm{.}0$cm$^(2),$ throat area $=15\mathrm{.}0$cm$^(2),$ shock area $=22\mathrm{.}0$cm$^(2),$ and exit area $=25\mathrm{.}0$cm$^(2).$ With the working fluid being the air behaving as a calorically perfect gas with constant $\backslash$gamma $=1\mathrm{.}4,$ Assume steady, quasi$-$one$-$dimensional flow, and calorically perfect gas.

a