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Problem 43 Hard Difficulty

A manufacturer of corrugated metal roofing wants to produce panels that are 28 in. wide and 2 in. high by processing flat sheets of metal as shown in the figure. The profile of the roofing takes the shape of a sine wave. Verify that the sine curve has equation $ y = \sin (\frac{\pi x}{7}) $ and find the width $ w $ of a flat metal sheet that is needed to make a 28-inch panel. (Use your calculator to evaluate the integral correct to four significant digits.)

Answer

$L \approx 29.36$ inches.

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Video Transcript

he has clearance. So when you married here, So we have we're gonna draw our metal roof. So why is equal to sign? Hi ex over a seven. So it represents the sheep off the metal roof. It has to have an amplitude of one since the thickness is too. In the period of four. Since we're defining 28 by two when we see that it satisfies both of these conditions. The period to pine divided by kind, divided by seven, which is equal to 14 pie. The amplitude is indeed one. So we're gonna go on to our blink formula, which is from 0 to 28. We have f of X is equal to sign with pi X over seven so the derivative is equal to pi co sign of pi X over seven over seven. So our equation for W It's from the integral from 0 to 28 square root of one plus hi co sign of pi X over a seven over seven square D X. When we use the calculator, we get 29.37 dreary 36 Excuse me