Numerical, Graphical, and Analytic Analysis The cross sections of an irrigation canal

Chapter 3, Problem 57

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Numerical, Graphical, and Analytic Analysis The cross sections of an irrigation canal are isosceles trapezoids of which three sides are 8 feet long (see figure). Determine the angle of elevation of the sides such that the area of the cross section is a maximum by completing the following. (a) Analytically complete six rows of a table such as the one below. (The first two rows are shown.) (b) Use a graphing utility to generate additional rows of the table and estimate the maximum cross-sectional area. (Hint: Use the table feature of the graphing utility.) (c) Write the cross-sectional area as a function of (d) Use calculus to find the critical number of the function in part (c) and find the angle that will yield the maximum cross-sectional area. (e) Use a graphing utility to graph the function in part (c) and verify the maximum cross-sectional area. yx2