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\n" ); document.write( "An open box is to be made from a flat piece of material 18 inches long and 5 inches wide by cutting equal squares
\n" ); document.write( "of length x from the corners and folding up the sides.\r
\n" ); document.write( "\n" ); document.write( "Write the volume V of the box as a function of x. Leave it as a product of factors, do not multiply out the factors.\r
\n" ); document.write( "\n" ); document.write( "V=\r
\n" ); document.write( "\n" ); document.write( "If we write the domain of the box as an open interval in the form (a,b), then what is a =?
\n" ); document.write( "And what is b =?
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document.write( "After folding up the sides, the height of the box will be \"x\".\r\n" );
document.write( "The length of the box will be (18-2x).\r\n" );
document.write( "The width of the box will be (5-2x).\r\n" );
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document.write( "Hence, the volume of the box will be x*(18-2x)*(5-2x).\r\n" );
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document.write( "These inequalities should be in the place\r\n" );
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document.write( "18 - 2x > 0,\r\n" );
document.write( "5 - 2x > 0,\r\n" );
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document.write( "that imply x < 2.5.\r\n" );
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document.write( "The domain of the volume function is {x| 0 < x < 2.5}, or, in the interval notation, (0,2.5).\r\n" );
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document.write( "Or a = 0, b = 2.5 inches.\r\n" );
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