A $3-$phase induction motor is connected to a voltage source withvs$($t$)=140$cos$(400$st$)$Vrms $.$The motor has Rs$=4,$R$\text{'}$r$=0\mathrm{.}5,$Xs$=2,$X$\text{'}$r$=10,$and Xm$=40.$

a$)$If the motor is spinning at a speed of $1300$rpm while operating in its normal operating range, how many poles does the motor probably have? $(5$points$)$

b$)$What is the developed torque, Tdev $,$for the motor when spinning at the speed from part a$?(10$points$)$

c$)$What are all of the possible slip values if the developed torque, T dev $,$is $6$Nm$?(10$points$)$