A three $-$ phase, $60-Hz,$ six$-$pole, wye$-$connected induction motor is rated at $20hp,$ and $440V.$ The motor operates at rated conditions and a slip of $5\%.$ The friction and windage losses $250W,$ and the core losses are $225W,$ neglect stray losses and find the following:

a$)$ Shaft speed.

b$)$ Rotor input power

c$)$ Load torque.

d$)$ Induced torque.

e$)$ Rotor copper losses.

f$)$ The speed of the motor at half load.