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15 1.4 1.3 {10 points) 1.2 1.1 1-0.8 -0.4 0 0.2 0.4 0.6 0.8 1 We discussed in class that a freely hanging rope forms a catenary (see problem 53 on page 379), represented here by Hz) 2 cosh: . In other circumstances {see problem 41 on page 513) a hanging rope forms a parabola. It's natural to ask by how much these two curves differ. The Figure above shows both curves. As you can tell, the difference is very small. Let y 2 p(1') dene the parabola satisfying p[z') = cosh), 2' = 71, 0, 1. To nd 13(2) 2 0.32 + ba: + c solve a suitable linear system. You get 13(2) = 0.54x"2+1 and maxASzgl |cosha= p[a:)l = 0.00945 - The positive value of z where this maximum deviation occurs is .1: = 0.66475 . To compute the maximum deviation you have to solve a nonlinear equation. I used Newton's Method

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