document.write( "Question 543147: A 36 inches piece of string is cut into two pieces. one piece is used to form a circle while the other is used to form a circle. how should the string be cut so that the sum of the area is a minimum \n" ); document.write( "
Algebra.Com's Answer #354781 by lwsshak3(11628)\"\" \"About 
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A 36 inches piece of string is cut into two pieces. one piece is used to form a circle while the other is used to form a circle. how should the string be cut so that the sum of the area is a minimum.
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\n" ); document.write( "let x=length of first piece of string
\n" ); document.write( "36-x=length of second piece of string
\n" ); document.write( "..
\n" ); document.write( "x=2πr=circumference of first circle
\n" ); document.write( "r=x/2π
\n" ); document.write( "area=πr^2=π*(x/2π)^2=πx^2/4π^2=x^2/4π
\n" ); document.write( "..
\n" ); document.write( "36-x=2πr=circumference of second circle circle
\n" ); document.write( "r=36-x/2π
\n" ); document.write( "area=πr^2=π*(36-x/2π)^2=π(36-x^2/4π^2=(36-x)^2/4π
\n" ); document.write( "..
\n" ); document.write( "Add areas:
\n" ); document.write( "x^2/4π+(36-x)^2/4π
\n" ); document.write( "x^2/4π+(1296-72x+x^2)/4π
\n" ); document.write( "(2x^2-72x+1296)/4π
\n" ); document.write( "differentiate:
\n" ); document.write( "f'(x)=(4x-72)/4π=0
\n" ); document.write( "4x-72=0
\n" ); document.write( "4x=72
\n" ); document.write( "x=18
\n" ); document.write( "..
\n" ); document.write( "f\"(x)=4/4π=(1/π)>0
\n" ); document.write( "Therefore, 18 is x min
\n" ); document.write( "ans:
\n" ); document.write( "The string should be cut exactly in half with each piece 18 inches in length. \n" ); document.write( "
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