MATHEMATICS 120 PROBLEM SET 9
Due November 20, 2002
For full credit, please show all work.
1. (5 marks) The line y = mx + b intersects the parabola y = x2 in points A and B. Find
the point P on the arc of the parabola between A and B that maximizes the area of the
triangle P AB.
2. (5 marks) A fence 8 ft tall runs parallel to a tall building at a distance of 4 ft from the
building. What is the length of the shortest ladder that will reach from the ground over
the fence to the wall of the building?
3. (5 marks) (Section 4.5, Problem 44) One corner of a strip of paper a cm wide is folded
up so that it lies along the opposite edge. Find the least possible length of the fold line.
4. (5 marks) Apply Newton’s method to the equation x2 − a = 0 to derive the following
square root algorithm
1
a .
xn+1 =
xn +
2
xn
√
Use this to find 10 correct to 3 decimal places.
Please read Sections 4.5-4.6 of the textbook. The recommended practice problems are:
Section 4.5, 1–44; Section 4.6, 1-14, 18–23.
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