$6\mathrm{.}30$ A variable$-$geometry supersonic convergent$-$divergent inlet is to be designed for an isentropic operation $($in the started mode$)$ at $M_D=2\mathrm{.}6.$ Calculate

a$.$ the inlet design contraction ratio $\frac{A_1}{A_{th}}$

b$.$ the percentage opening of the throat $\frac{A_{th}^{\text{'}}-A_{th}}{A_{th}}$ needed to start the inlet

c$.$ the throat Mach number in the open position, $M_{th}^{\text{'}}$