document.write( "Question 82752: i need to write a proportion that indicates that 50% of a number is 17.\r
\n" ); document.write( "\n" ); document.write( "I also need to find two integers whose sum is 12 and whose product is a maximum. \r
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Algebra.Com's Answer #59571 by ankor@dixie-net.com(22740)\"\" \"About 
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i need to write a proportion that indicates that 50% of a number is 17.
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\n" ); document.write( "We know that 50% indicates a relationship of 1:2 or 1/2
\n" ); document.write( "Therefore:
\n" ); document.write( "\"1%2F2\" = \"17%2Fx\"
\n" ); document.write( "Cross multiply & find x
\n" ); document.write( "1x = 2*17
\n" ); document.write( "x = 34
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\n" ); document.write( "I also need to find two integers whose sum is 12 and whose product is a maximum.
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\n" ); document.write( "Let the two integers be x and (12-x); their product:
\n" ); document.write( "x(12-x) = 12x - x^2
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\n" ); document.write( "-x^2 + 12x = 0; a quadratic equation
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\n" ); document.write( "Find the max by finding the axis of symmetry: x = -b/(2a)
\n" ); document.write( "In our equation a = -1; b = 12:
\n" ); document.write( "x = -12/(2(-1)
\n" ); document.write( "x = -12/-2
\n" ); document.write( "x = 6, obviously the two integers are 6 & 6
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\n" ); document.write( "You can find the vertex using x = 6
\n" ); document.write( "-6^2 + 12(6) =
\n" ); document.write( "-36 + 72 = + 36 is the max
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\n" ); document.write( "If you graph it, it's easy to see
\n" ); document.write( "\"+graph%28+300%2C+200%2C+-2%2C+15%2C+-10%2C+50%2C+-x%5E2%2B12x%29+\"
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\n" ); document.write( "One of the integers is on the horizontal axis, the max product on the vertical\r
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