document.write( "Question 832030: A rectangular window measures 54 inches by 24 inches. There is an a = 14-inch wiper blade attached by a b = 5-inch arm at the center of the base of the window, as shown in the figure below. If the arm rotates 120°, approximate the percentage of the window's area that is wiped by the blade. (Round your answer to one decimal place.) \n" ); document.write( "

Algebra.Com's Answer #501845 by math-vortex(648) $\"\"$ $\"About$

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document.write( "Hi, there--\r\n" );
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document.write( "THE PROBLEM:\r\n" );
document.write( "A rectangular window measures 54 inches by 24 inches. There is an a = 14-inch wiper blade attached by \r\n" );
document.write( "a b = 5-inch arm at the center of the base of the window, as shown in the figure below. If the arm rotates \r\n" );
document.write( "120°, approximate the percentage of the window's area that is wiped by the blade. (Round your answer to \r\n" );
document.write( "one decimal place.)\r\n" );
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document.write( "A SOLUTION:\r\n" );
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document.write( "Find the area of the rectangle window.\r\n" );
document.write( "Let L be the length of the window.\r\n" );
document.write( "Let W be the width.\r\n" );
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document.write( "The area is length times width, 54 * 24 = 1296 square inches.\r\n" );
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document.write( "Find the area of window swept by wipers.\r\n" );
document.write( "The radius of the wiper is 14 inches. It wipes 120 degrees. This is one-third of a circle because \r\n" );
document.write( "120/360 = 1/3\r\n" );
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document.write( "The area of one-third of the circle is \r\n" );
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document.write( "We want the percentage of the window that is swept by the wiper.\r\n" );
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document.write( "[area swept by wiper] / [area of window] * 100 = [percentage of window area swept by wiper]\r\n" );
document.write( " percent.\r\n" );
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document.write( "Hope this helps! Feel free to email if you have any questions about the solution.\r\n" );
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document.write( "Good luck with your math,\r\n" );
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document.write( "Mrs. F\r\n" );
document.write( "math.in.the.vortex@gmail.com\r\n" );
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