A600-kg car is going around a banked curve with a radius of 110 m at a steady speed of 24.5 m/s. what is the appropriate banking angle so that the car stays on its path without the assistance of friction

The centripetal force tending to take the car off track is
[(600 kg)(24.5 m/s)^2]/(110 m) = 3274.09 N

Let the banking angle be x.
Then the restorative force on the car is
(600 kg)(9.8 m/s^2)sin(x) = 5880sin(x) N

For dynamic equilibrium,
5880sin(x) = 3274.09
sin(x) =  0.5568
x = arcsin(0.5568) = 33.8°

33.8°