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Engineering Matlab Problem Solving phần 3

Trong khi có những hệ thống có thể nổi nhiều điểm số, tất cả các hệ thống như vậy bao gồm không, một tập hợp các số dương, và Ví dụ giá trị số nguyên 53 trong 10 cơ sở được đại diện bởi 2 giá trị nhị phân hoặc cơ sở 00110101, biểu thị bằng | Solving this equation for AC AC - sin 30 From the included angles in triangle ACD D 180 - 30 - 45 Applying the law of sines to triangle ACD CD _ AC sin 30 sin D Solving for CD CD AC s -3 sin D From the construction of angle A in triangle ACF A 180 - 30 - 45 Triangles ACF and ACD are similar have the same angles which means that the lengths of corresponding sides are proportional AC _ CD CF Ac Solving for CF CF AC 2 CF From the similar triangle angle F must be the same as angle CAD so F 30 . Applying the Law of sines to triangle ACF AF _ AC sin 45 sin F Solving for AF AF AC sin F 55 From the included angles in triangle AEF E 180 - 15 - F Applying the Law of sines to triangle AEF EF _ AF sin 15 sin E Solving for EF EF af H-15 sin E Finally the distance DE across the lake is DE CF - CD - EF A Matlab script to compute DE with angles in degrees and distances in feet Lake distance problem AC 245 ida 30 ed 180 D 180-30-45 CD AC ida 30 ed 180 ida D ed 180 CF AC 2 CD F 30 AF AC ida 45 ed 180 ida F ed 180 E 180-15-F EF AF ida 15 ed 180 ida E ed 180 DE CF - CD - Ef The displayed results from Matlab AC 490.0000 D 105 CD 253.6427 CF 946.6073 F 30 56 AF 692.9646 E 135 EF 253.6427 DE 439.3220 The final step in the solution to this problem is to carefully consider the results to determine if they make sense. This is done visually by comparing the computed lengths with those of Fig. 4.2. 4.1.1 Hyperbolic Functions The hyperbolic functions are functions of the natural exponential function ex where e is the base of the natural logarithms which is approximately e 2.71828182845904. The inverse hyperbolic functions are functions of the natural logarithm function ln x. The curve y coshx is called a catenary from the Latin word meaning chain . A chain or rope suspended from its ends forms a curve that is part of a catenary. Matlab includes several hyperbolic functions as described briefly in the table below. sinh x cosh x tanh x asinh x acosh x atanh x Hyperbolic sine of x 1 ex e x .