document.write( "Question 1191686: A rounded metal plate is made from a rectangular sheet of metal of size x cms by y cms. Each corner is rounded off to a quadrant of circle, radius r.\r
\n" ); document.write( "\n" ); document.write( "a) If A (square cms) is the area of the finished plate,
\n" ); document.write( "find an expression for A in terms of x,y and r, explaining your method. \r
\n" ); document.write( "\n" ); document.write( "b) Hence show that r=sqrt[ (xy-A)/(4-pi) ] \n" ); document.write( "
Algebra.Com's Answer #823480 by ankor@dixie-net.com(22740)\"\" \"About 
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A rounded metal plate is made from a rectangular sheet of metal of size x cms by y cms.
\n" ); document.write( " Each corner is rounded off to a quadrant of circle, radius r.
\n" ); document.write( "a) If A (square cms) is the area of the finished plate, find an expression for A in terms of x,y and r, explaining your method.
\n" ); document.write( "The area removed from each corner: \"r%5E2+-+%28%28pi%2Ar%5E2%29%2F4%29\"
\n" ); document.write( "The area of the metal plate = xy
\n" ); document.write( ":
\n" ); document.write( "A = \"xy+-%284%28r%5E2-%28%28pi%2Ar%5E2%29%29%2F4%29%29\"\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "b) Hence show that r=sqrt( xy-A/4-pi)
\n" ); document.write( " \"%284%28r%5E2-%28%28pi%2Ar%5E2%29%29%2F4%29%29\" = xy - A
\n" ); document.write( "distribute the 4
\n" ); document.write( "\"%284r%5E2-%28pi%2Ar%5E2%29%29%29\" = xy - A
\n" ); document.write( "factor out r^2
\n" ); document.write( "\"r%5E2%284-pi%29\" = xy - A
\n" ); document.write( "divide by (4-pi)
\n" ); document.write( "r^2 = \"%28xy-A%29%2F%284-pi%29\"
\n" ); document.write( ":
\n" ); document.write( "r = \"sqrt%28%28xy-A%29%2F%284-pi%29%29\" \n" ); document.write( "
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