Answer: Cable Tension In Exercises 89 and 90, use the figure to determine the tension in

Chapter 10, Problem 89

(choose chapter or problem)

Areas of Simple Closed Curves  In Exercises 87–92, use a computer algebra system and the result of Exercise 83 to match the closed curve with its area. (These exercises were based on “The Surveyor’s Area Formula,” by Bart Braden, College Mathematics Journal, September 1986, pp. 335–337, by permission of the author.)

(a) \(\frac{8}{3}ab\)                        (b) \(\frac{3}{8}\pi a^2\)                    (c) \(2\pi a^2\)

(d) \(\pi ab\)                                       (e) \(2\pi ab\)                                          (f) \(6\pi a^2\)

Cardioid: \((0\ \leq\ t\ \leq\ 2\pi)\)

\(x=2a \cos t-a \cos 2t\)

\(y=2a \sin t-a \sin 2t\)

Text Transcription:

8/3 ab

3/8 pi a^2

2pi a^2

pi ab

2pi ab

6pi a^2

(0 leq t leq 2pi)

x=2a cos t - a cos 2t

y=2a sin t - a sin 2t