A spring is such that a 5-lb weight stretches it 6 in. The 5-lb weight is attached, the spring reaches equilibrium, then the weight is pulled down 3 in. below the equilib- rium point and started off with an upward velocity of 6 ft/sec. Find an equation giving the position of the weight at all subsequent times.

The area of a circle increases at a rate of 2 cm² /s. How fast is the radius changing when the radius is 5cm? a) Draw the picture. b) Write the given and unknown derivatives in d/dt notation. c) Label the variables. d) Proceed to solve and finish the problem. Reminder, keep solutions and answer in exact form and don't forget the units on the final answer.