At the inlet of a supersonic nozzle where static temperature is 700 K and stagnation pressure is 425 kPa, the Mach number is $M_{inlet} = 0.75$ and the area is $A_{inlet} = 20 \text{ cm}^2$. Downstream, the area at the throat is $A_{throat} = 15 \text{ cm}^2$ and a normal shock forms at a location where $A = 22 \text{ cm}^2$. The exit area of the nozzle is $A_{exit} = 25 \text{ cm}^2$. Assuming ideal gas behavior of carbon dioxide ($\gamma = 1.3$, R = 188.95 J/kg K) and constant specific heats, calculate the following:
(a) static temperature at the throat;
(b) Mach number at the exit, $M_{exit}$;
(c) velocities immediately upstream and downstream of normal shock ($V_1$ and $V_2$);
(d) $P_{exit}/P_{inlet}$
