Answer the questions below

63. A woman at a point A on the shore of a circular lake with 71. What is the smallest possible area of the triangle that is cut radius 2 miles wants to arrive at the point C diametrically off by the first quadrant and whose hypotenuse is tangent opposite A on the other side of the lake in the shortest to the parabola defined by y = 4 - x at some point? possible time, as shown in the figure. She can walk at the rate of 4 mi/h and a row a boat at 2 mi/h. How should she proceed? 91. A painting in an art gallery has height h and is hung so that its lower edge is a distance d above the eye of an 64. An oil refinery is located on the north bank of a straight observer, as shown in the figure. river that is 2 km wide. A pipeline is to be constructed from the refinery to storage tanks located on the south bank of the river 6 km east of the refinery. The cost of laying pipe is $400,000/km over land to a point P on the north bank and $800,000/km under the river to the tanks. How far from the wall should the observer stand to get the best view? (Where should the observer stand so as to maximize the angle 0 subtended at his eye by the painting?) 69. At which points on the curve defined by y = 1 + 40x' - 3x does the tangent line have the largest slope