$.$ A three$-$phase induction motor is connected to a $450$ V$,50$ Hz supply. The motor has $8$ poles and operates with a full$-$load rotor speed of $750$ RPM$.$ The motor has a stator winding resistance of $0\mathrm{.}4$ ohms per phase, a rotor winding resistance $($referred to the stator side$)$ of $0\mathrm{.}35$ ohms per phase, and a combined leakage reactance of $5$ ohms per phase. Calculate:

a$)$ The slip of the motor.

b$)$ The rotor current frequency at full load.

c$)$ The total impedance of the rotor circuit referred to the stator side.