Power lines A power line is attached at the same height to

Chapter 6, Problem 67

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Power lines A power line is attached at the same height to two utility poles that are separated by a distance of 100 ft; the power line follows the curve f 1x2 = a cosh1x>a2. Use the following steps to find the value of a that produces a sag of 10 ft midway between the poles. Use a coordinate system that places the poles at x = {50. a. Show that a satisfies the equation cosh150>a2 - 1 = 10>a. b. Let t = 10>a, confirm that the equation in part (a) reduces to cosh 5t - 1 = t, and solve for t using a graphing utility. Report your answer accurate to two decimal places. c. Use your answer in part (b) to find a and then compute the length of the power line.