At steady state, air at $200$ kPa, $380$ K$,$ and mass flow rate of $0\mathrm{.}1$ kg$/$s enters an insulated duct having differing inlet and exit cross$-$sectional areas. The inlet cross$-$sectional area is $6$ cm$2.$ At the duct exit, the pressure of the air is $100$ kPa and the velocity is $250$ m$/$s$.$ Find velocity at inlet, temperature at exit, and cross sectional area at exit. PE is negligible and the air is modeled as an ideal gas. constant C$\_$p $=1\mathrm{.}008$kJ$/$kg$*$K