A woman was painting her nails before going out to dinner. Before she started, she realized that she could take no more than 20 minutes to finish. If it takes 0.23 minutes to paint each nail, and the paint takes 15 minutes to dry, then what is the maximum amount of nails she will be able to paint before time runs out?

Amass weighing 16 pounds stretches a spring 8/3 feet. the mass is initially released from rest from a point 2 feet below the equilibrium position, and the subsequent motion takes place in a medium that offers a damping force that is numerically equal to 1/2 the instantaneous velocity. find the equation of motion if the mass is driven by an external force equal to f(t)=cos(2t).