This question builds on an earlier "rod problem": A 4-centimeter rod is attached at one end A to a point on a wheel of radius 2 cm. The other end B is free to move back and forth along a horizontal bar that goes through the center of the wheel. At timet=0the rod is situated as in the diagram at the left below. The wheel rotates counterclockwise at 3.5 rev/sec. Thus, whent=1/21sec, the rod is situated as in the diagram at the right below.

(a) LetPbe the point on the circle where the rod is attached. Write a formula for the slope of the tangent line to the circle at timetseconds: (b) Write a formula for the slope of the rod at timetseconds: (Hint: You will need to recall the formula for the x-coordinate of the rod along the x-axis) (c) Find the first time when the rod is tangent to the circle:

seconds. (d) At the time in (c), what is the slope of the rod? (e) Find the second time when the rod is tangent to the circle:

seconds. (f) At the time in (e), what is the slope of the rod?