Assignment #7

Due: 8 February,1999

1. Once again, the good ship Swine Trek is forced to save two-dimensional space: the Cylons have launched a failing mark in MA 110 along the positive y-axis, straight at the origin. Ivanova orders the ship to move along the x-axis so as to cross the path of the mark 10 units ahead of it and lock on with a tractor beam. The Swine Trek's tractor beam subsequently keeps the mark at a constant distance of 10 units from the ship while the ship continues to move along the positive x-axis. Phaicus observes that the path of the mark is always tangent to the tractor beam and finds an equation in x and y describing the path of the mark after the Swine Trek starts towing it. Find this equation! [7]

2. As you probably figured out on the last assignment, the Fibonacci numbers are given by the relations f1 = 1, f2 = 1, and fn+2 = fn+1 + fn for n > 0. Prove that

f_n = [ (1 + 5^{1/2})^n - (1 - 5^{1/2})^n ] / 5^{1/2}2^n

Bonus: Which four science-fiction TV shows are referenced in Problem 1}? [0.4]

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Maintained by Stefan Bilaniuk. Last updated 1999.12.03.