A rectangle is inscribed in a semicircle \r\n" );
document.write( "of radius 2. If the variable x represents \r\n" );
document.write( "half the length of the rectangle, express \r\n" );
document.write( "the area of the rectangle as a function of x.\r\n" );
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document.write( "Since x represents half the length of the\r\n" );
document.write( "rectangle, the length of rectangle = 2x\r\n" );
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document.write( "Let y represent the height of the rectangle. \r\n" );
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\r\n" );
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document.write( "Then the Area of the rectangle is\r\n" );
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document.write( "Area = length × width\r\n" );
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document.write( " A = (2x)y\r\n" );
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document.write( " A = 2xy\r\n" );
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document.write( "However we must now express y in terms of x.\r\n" );
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document.write( "Draw in a radius (which equals 2) from the \r\n" );
document.write( "center of the semicircle to the upper right\r\n" );
document.write( "corner of the rectangle:\r\n" );
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document.write( "
\r\n" );
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document.write( "Use the Pythagoren theorem on the right triangle:\r\n" );
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document.write( "x² + y² = 2²\r\n" );
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document.write( "x² + y² = 4\r\n" );
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document.write( " y² = 4 - x²\r\n" );
document.write( " ______ \r\n" );
document.write( " y = Ö4 - x²\r\n" );
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document.write( "So substitute this for y in\r\n" );
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document.write( " A = 2xy\r\n" );
document.write( " ______\r\n" );
document.write( " A = 2xÖ4 - x²\r\n" );
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document.write( "Edwin
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document.write( "![\"\"](\"/images/stars/stars-13.gif\")
