document.write( "Question 1055329: You plan to make an open box by cutting equally sized squares
\n" ); document.write( "from each corner of a 10-inch by 12-inch rectangular piece of
\n" ); document.write( "material and then folding up the flaps. This is illustrated below.
\n" ); document.write( "You need the open box to contain 80 cubic inches of liquid. You
\n" ); document.write( "can do this by removing corners that are each 1 inch by 1 inch.
\n" ); document.write( "However, the box will then be too wide to fit where you need to
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Algebra.Com's Answer #670564 by Edwin McCravy(20062) $\"\"$ $\"About$

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document.write( "Cut out a square of x inches by x inches out of each \r\n" );
document.write( "side of the length and width, which leaves flaps of \r\n" );
document.write( "10-2x inches and 12-2x inches and when they are folded \r\n" );
document.write( "up the height of the box will be x:\r\n" );
document.write( "    ______\r\n" );
document.write( " __|______|__\r\n" );
document.write( "|  |      |  |10-2x\r\n" );
document.write( "|__|______|_x|\r\n" );
document.write( "   |______|\r\n" );
document.write( "     12-2x\r\n" );
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document.write( "Use the Volume formula\r\n" );
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document.write( "LWH = V\r\n" );
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document.write( "(12-2x)(10-2x)x = 80\r\n" );
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document.write( "Multiply that out and get\r\n" );
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document.write( "4x^3-44x^2+120x-80 = 0\r\n" );
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document.write( "Divide through by 4\r\n" );
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document.write( "x^3-11x^2+30x-20 = 0\r\n" );
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document.write( "We are told that x=1 is a solution.  So we use synthetic\r\n" );
document.write( "division to factor it:\r\n" );
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document.write( "1 | 1 -11  30 -20\r\n" );
document.write( "  |     1 -10  20\r\n" );
document.write( "    1 -10  20   0\r\n" );
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document.write( "So the left side of\r\n" );
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document.write( "x^3-11x^2+30x-20 = 0\r\n" );
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document.write( "factors as\r\n" );
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document.write( "(x-1)(x^2-10x+20) = 0\r\n" );
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document.write( "The quadratic doesn't factor so we solve it by\r\n" );
document.write( "the quadratic formula and get the solutions\r\n" );
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document.write( "Using the - we have  which is about 2.7639\r\n" );
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document.write( "Using the - we have  which is about 7.2361\r\n" );
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document.write( "We have to ignore the 2nd answer because if we cut out a square\r\n" );
document.write( "that big we could not make a box, because 7.2361 is more than\r\n" );
document.write( "half of the 10 inch side.\r\n" );
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document.write( "Answer: cut out a square of size  by .\r\n" );
document.write( "or 2.7639 inches by 2.7636 inches.\r\n" );
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document.write( "Edwin

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