USE GAS DYNAMICS TABLES TO SOLVE!!!!

$6\mathrm{.}12.$ A converging$-$diverging nozzle receives air from a tank at $100$ psia and $\backslash (600^\{\backslash$circ$\}\backslash$mathrm$\{$R$\}\backslash ).$ The pressure is $28\mathrm{.}0$ psia immediately preceding a plane shock that is located in the diverging section. The Mach number at the exit is $0\mathrm{.}5$ and the flow rate is $\backslash (10\backslash$mathrm$\{$lbm$\}/\backslash$mathrm$\{$sec$\}\backslash ).$ Determine:

$($a$)$ The throat area.

$($b$)$ The area at which the shock is located.

$($c$)$ The outlet pressure required to operate the nozzle in the manner described above.

$($d$)$ The outlet area.

$($e$)$ The design Mach number.