Algebra.Com's Answer #51894 by ankor@dixie-net.com(22740)![\"\"](\"/images/stars/stars-13.gif\")  
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An open box with a square base is required to have volume of 10 cubic ft.
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document.write( "a) Express the amount A of material used to make such a box as a function of the length x of a side of the square base.
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document.write( "Base area * height = 10 cu ft
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document.write( "x^2 * h = 10
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document.write( "h = 10/x^2 is the height
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document.write( "Area of the 4 sides:
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document.write( "4(x*h)
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document.write( "Replace h with (10/x^2)
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document.write( "4(x*10/x^2)
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document.write( "Simplify:
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document.write( "4(10/x)
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document.write( "Area of the 4 sides = 40/x
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document.write( "Total area:
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document.write( "A = x^2 + 40/x
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document.write( "b) How much material is required for a base 1 foot by 1 foot?
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document.write( "A = 1^2 + (40/1)
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document.write( "A = 41 sq ft
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document.write( "c) How much material is required for a base 2 feet by 2 feet?
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document.write( "A = 2^2 + (40/2)
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document.write( "A = 24 sq ft
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document.write( "d) Graph A=A(x). For what value of x is A smallest?
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document.write( "A = x^2 + (4/x)
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document.write( "Looks like the min area is x ~ 2.7 ft for an area of about 22 sq ft
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