document.write( "Question 531784: The volume of a rectangular box is 6 ft^3 more than twice the volume of a cube. The length of the box is 2 ft more than the length of an edge of the cube its width is equal to the length of an edge of the cube; and its height is 1 ft more than the length of an edge of the cube. What are the dimensions of the box and the cube? \n" ); document.write( "
Algebra.Com's Answer #350667 by ankor@dixie-net.com(22740)\"\" \"About 
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The volume of a rectangular box is 6 ft^3 more than twice the volume of a cube. The length of the box is 2 ft more than the length of an edge of the cube its width is equal to the length of an edge of the cube; and its height is 1 ft more than the length of an edge of the cube. What are the dimensions of the box and the cube?
\n" ); document.write( ":
\n" ); document.write( "let x = the side of the cube
\n" ); document.write( "Write an equation for each statement:
\n" ); document.write( "\"The volume of a rectangular box is 6 ft^3 more than twice the volume of a cube.\"
\n" ); document.write( "L * W * H = 2x^3 + 6
\n" ); document.write( ":
\n" ); document.write( "\" The length of the box is 2 ft more than the length of an edge of the cube\"
\n" ); document.write( "L = x + 2
\n" ); document.write( ":
\n" ); document.write( "\"its width is equal to the length of an edge of the cube;\"
\n" ); document.write( "W = x
\n" ); document.write( ":
\n" ); document.write( "\"its height is 1 ft more than the length of an edge of the cube.\"
\n" ); document.write( "H = x + 1
\n" ); document.write( ":
\n" ); document.write( "Substituting for L,W,H
\n" ); document.write( "(x+2)*x*(x+1) = 2x^3 + 6
\n" ); document.write( "x(x^2 + x + 2x + 2) = 2x^3 + 6
\n" ); document.write( "x(x^2 + 3x + 2) = 2x^3 + 6
\n" ); document.write( "x^3 + 3x^2 + 2x = 2x^3 + 6
\n" ); document.write( "Combine like terms on the left
\n" ); document.write( "x^3 - 2x^3 + 3x^2 + 2x - 6 = 0
\n" ); document.write( "-x^3 + 3x^2 + 2x - 6 = 0
\n" ); document.write( ":
\n" ); document.write( "Graph this equation, there are two positive solutions but x=3 is an integer
\n" ); document.write( "\"+graph%28+300%2C+200%2C+-6%2C+5%2C+-10%2C+10%2C+-x%5E3+%2B+3x%5E2+%2B+2x+-+6+%29+\"
\n" ); document.write( ":
\n" ); document.write( "What are the dimensions of the box and the cube?
\n" ); document.write( " x = 3 inches the side of the cube
\n" ); document.write( "then
\n" ); document.write( " L = 3+2 = 5 inches
\n" ); document.write( " W = 3 inches
\n" ); document.write( " H = 3+1 = 4 inches
\n" ); document.write( ":
\n" ); document.write( ":
\n" ); document.write( "Check this
\n" ); document.write( "5*3*4 = 2(3^3) + 6
\n" ); document.write( "60 = 2(27) + 6 \n" ); document.write( "
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