document.write( "Question 1171508: A rectangular piece of stainless steel sheet metal measures 8 meters by 10 meters. if we are to take an open-top tank by cutting equal squares from each corner, folding up the tabs by 90 degrees, and welding the vertical edges; what size should the squares be cut to have the container hold 48 cubic meters? \n" ); document.write( "

Algebra.Com's Answer #796419 by Boreal(15235) $\"\"$ $\"About$

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\n" ); document.write( "the width will be 8-2x, where x is how much is cut in meters
\n" ); document.write( "the length will be 10-2x
\n" ); document.write( "the height will be x
\n" ); document.write( "the volume is x(80-36x+4x^2)=48
\n" ); document.write( "or 4x^3-36x^2+80x-48=0
\n" ); document.write( "or x^3-9x^2+20x-12=0
\n" ); document.write( "/1== -9== 20== -12
\n" ); document.write( "1--- -8---12----0 so the factors are (x-1)(x^2-8x+12)=(x-1)(x-6)(x-2)
\n" ); document.write( "the graph shows x=1,2,6, as well. The last is too large and leads to negative values
\n" ); document.write( "1 meter on each side would give dimensions of 8*6*1. And 2 meters on each side 4*6*2. Both of these would give 48 m^2.
\n" ); document.write( " $\"graph%28300%2C300%2C-10%2C10%2C-10%2C10%2Cx%5E3-9x%5E2%2B20x-12%29\"$ \n" ); document.write( "

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