document.write( "Question 1137042: Can someone please help? \r
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\n" ); document.write( "The length is twice as long as the width. The height is 4 inches greater than the width. The volume is 48 cubic inches.\r
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Algebra.Com's Answer #754878 by ikleyn(52866) $\"\"$ $\"About$

You can put this solution on YOUR website!
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document.write( "Let x be the width.\r\n" );
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document.write( "Then the length is 2x  and the height is (x+4).\r\n" );
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document.write( "The volume equation is\r\n" );
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document.write( "    x*(2x)*(x+4) = 48.\r\n" );
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document.write( "    2x^2*(x+4) = 48\r\n" );
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document.write( "    x^2*(x+4) = 24\r\n" );
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document.write( "By the \"trial and error\" method, x= 2.\r\n" );
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document.write( "The plot below shows that the guessed solution x = 2 is UNIQUE.\r\n" );
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document.write( "    \r\n" );
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document.write( "    Plot y = x*(2x)*(x+4) (red) and y = 48 (green)\r\n" );
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document.write( "Also, notice that the function  f(x) = x*(2x)*(x+4) is monotonic over positive x, so the uniqueness of the solution \r\n" );
document.write( "is OBVIOUS even without the plot.\r\n" );
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document.write( "ANSWER.  The width is 2 in;  the length is  2*2 = 4 in;  the height is (2+4) = 6 in.\r\n" );
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document.write( "CHECK.    2*4*6 = 48.    ! Correct !\r\n" );
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