document.write( "Question 193600: Mr.Green has 8.5 by 11 inch cardboard sheets. As a class project Mr.Green asked his students make an open top box under these conditions:
\n" ); document.write( "1.) each box must be made by cutting small squares from each corner of a cardboard sheet
\n" ); document.write( "2.) The box must have a volume of 48in^3
\n" ); document.write( "3.) The amount of cardboard waste must be minimized
\n" ); document.write( "What is the approximate side length for the small squares that would be cut from the cardboard sheet? \n" ); document.write( "
Algebra.Com's Answer #145457 by ankor@dixie-net.com(22740)\"\" \"About 
You can put this solution on YOUR website!
Mr.Green has 8.5 by 11 inch cardboard sheets. As a class project Mr.Green asked
\n" ); document.write( " his students make an open top box under these conditions:
\n" ); document.write( ":
\n" ); document.write( "1.) each box must be made by cutting small squares from each corner of a cardboard sheet
\n" ); document.write( "2.) The box must have a volume of 48in^3
\n" ); document.write( "3.) The amount of cardboard waste must be minimized
\n" ); document.write( "What is the approximate side length for the small squares that would be cut from the cardboard sheet?
\n" ); document.write( ":
\n" ); document.write( "Let x = side length of the cut-out squares
\n" ); document.write( ":
\n" ); document.write( "then box dimensions will be
\n" ); document.write( "(8.5-2x) by (11-2x) by x
\n" ); document.write( ":
\n" ); document.write( "Vol
\n" ); document.write( "(8.5-2x)*(11-2x)*x = 48 cu/in
\n" ); document.write( ":
\n" ); document.write( "you can check this using x = .7
\n" ); document.write( "(11-1.4)*(8.5-1.4)*.7 = 47.7 ~ 48
\n" ); document.write( ":
\n" ); document.write( "Note that the 3rd intercept ~ 6.4 is obviously on valid
\n" ); document.write( "FOIL to find the area of the bottom
\n" ); document.write( "93.5 -17x - 22x + 4x^2
\n" ); document.write( "Multiply by the height (x) to create an equation for the vol of 48 cu/in
\n" ); document.write( "x(4x^2 - 39x + 93.5) = 48
\n" ); document.write( "4x^3 - 39x^2 + 93.5x - 48 = 0
\n" ); document.write( ";
\n" ); document.write( "Plot his equation on a graph
\n" ); document.write( "\"+graph%28+300%2C+200%2C+-4%2C+8%2C+-30%2C+40%2C+4x%5E3-39x%5E2%2B93.5x-48%29+\"
\n" ); document.write( "Choose the lowest value x intercept for mimimum waste
\n" ); document.write( "x = .70646 (found on a graphing calc)
\n" ); document.write( ":
\n" ); document.write( "You can check this on a calc
\n" ); document.write( "(8.5-1.4)*(11-1.4)*.7 ~ 48\r
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