document.write( "Question 1109658: A trough at the end of a gutter is meant to direct water away from a house. The homeowner makes the trough from a rectangular piece of aluminium that is 20 in long and 12 in wide. he makes a fold along the two sides a distance of x inches from the edge:\r
\n" ); document.write( "\n" ); document.write( " write a function to represent the volume in terms of x? what is max volume?
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Algebra.Com's Answer #724651 by ankor@dixie-net.com(22740)\"\" \"About 
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A trough at the end of a gutter is meant to direct water away from a house.
\n" ); document.write( " The homeowner makes the trough from a rectangular piece of aluminium that is 20 in long and 12 in wide.
\n" ); document.write( " he makes a fold along the two sides a distance of x inches from the edge:
\n" ); document.write( " write a function to represent the volume in terms of x? what is max volume?
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\n" ); document.write( "End of the trough looks like this. x= the height; w = the width
\n" ); document.write( "x|_w_|x
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\n" ); document.write( "From the information given we know
\n" ); document.write( "2x + w = 12
\n" ); document.write( "or
\n" ); document.write( "w = (12-2x)
\n" ); document.write( "the volume
\n" ); document.write( "V = 20 * x * w
\n" ); document.write( "replace w with (12-2x)
\n" ); document.write( "V = 20x(12-2x)
\n" ); document.write( "V(x) = -40x^2 + 240x is the function
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\n" ); document.write( "Max area occurs at the axis of symmetry: x=-b/(2a); where a=-40, b= 240
\n" ); document.write( "x = \"%28-240%29%2F%282%2A-40%29\"
\n" ); document.write( "x = +3 in for max volume
\n" ); document.write( "Find the vol when x = 3
\n" ); document.write( "V(3) = -40(3^2) + 240(3)
\n" ); document.write( "V(3) = -360 + 720
\n" ); document.write( "V(3) = 360 cu\in is max vol
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