A jet engine is to be designed for an altitude of \(12,000 \mathrm{~m}\), where the atmospheric pressure is \(19.3 \mathrm{kPa}\). The jet nozzle has a supersonic exit Mach number and is perfectly expanded. The stagnation pressure and temperature of the gas are \(100 \mathrm{kpa}\) and \(600{ }^{\circ} \mathrm{C}\). The flow rate of gas is \(45 \mathrm{~kg} / \mathrm{s}\). Calculate the throat area, exit area, and exit velocity. Use \(k=1.4\) and \(R=260 \mathrm{~J} / \mathrm{kg} \cdot \mathrm{K}\) for the gas.