Math 221

Homework #1

Instructions. This is due on September 7 at the beginning of class. It is worth 20 points. Late papers lose 4 points if turned in by 8:00 Monday morning, plus 3 points per additional day late. You must work by yourself, but feel free to consult with me. Explain what you did and why you did it: good explanations are essential! Your paper should have an introduction, a main body and a conclusion. Start early, ask questions and do well.

Problems. Work exercises 31, 33 and 34 on page 733. This gives you 4 Scramblers to compare: example 2.1 and these three exercises. Which do you think is the best ride? Give pros and cons of each ride.

As discussed in exploratory exercise 1 on page 734, a general Scrambler is given by the equations

x = r cos t + sin kt

y = r sin t + cos kt

Find values of the radius r and speed k to produce a better Scrambler. Explain what you like about your ride and why it would fun.