124quiz6solutions

124quiz6solutions - Math 124 Quiz 6 Oct. 27, 2006 Name: 1)...

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Math 124 Quiz 6 Oct. 27, 2006 Name: 1) A woman at a point A on the shore of a circular lake with radius 2 miles wants to arrive at the point C diametrically opposite A on the other side of the late in the shortest possible time. She can walk around the shore of the lake at the rate of 4 miles per hour and row a boat at 2 miles per hour. At what angle θ (see diagram) should she launch her boat to minimize time? Solution: (ON NEXT PAGE) 1
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This problem is tricky to be sure, so I felt it was reasonable to walk about the room and give people hints here and there. We begin by constructing a function for the total time it takes to complete her journey from point A to point B . This needs to be a function of the angle θ . This involves finding the distances involved as functions of θ . Let x represent the distance she needs to row. Using cosine, we see that cos( θ ) = x 4 (This is because any triangle inscribed in a circle with one side on a diameter is a right triangle.) So, x = 4 cos( θ
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124quiz6solutions - Math 124 Quiz 6 Oct. 27, 2006 Name: 1)...

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