document.write( "Question 972516: The graph of y = n ( 16−x2 ) is shown.\r
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\n" ); document.write( "\n" ); document.write( "If the shaded area is equal to 86, find the value of n. \n" ); document.write( "
Algebra.Com's Answer #594812 by rothauserc(4718)\"\" \"About 
You can put this solution on YOUR website!
y = n ( 16−x2 ) where n is a constant
\n" ); document.write( "y = 16n - nx^2
\n" ); document.write( "this is a parabola that opens downward
\n" ); document.write( "0 = 16n - nx^2
\n" ); document.write( "-nx^2 = -16n
\n" ); document.write( "for n not equal to 0
\n" ); document.write( "x^2 = 16
\n" ); document.write( "x = 4 or -4 for y = 0
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\n" ); document.write( "now integrate
\n" ); document.write( "y = 16n - nx^2
\n" ); document.write( "let Z stand for integral
\n" ); document.write( "Z 16n - nx^2 = 16nx - (nx^3/3)
\n" ); document.write( "evaluate integral for x = 4 and x = -4
\n" ); document.write( "86 = 16n*4 -(n4^3/3) - ((16n(-4)) - (n(-4)^3/3))
\n" ); document.write( "86 = 64n - (64n/3) - (-64n) - (-64n/3)
\n" ); document.write( "86 = 64n -(64n/3) +64n - (64n/3)
\n" ); document.write( "86 = 128n -128n/3
\n" ); document.write( "258 = 384n -128n
\n" ); document.write( "258 = 256n
\n" ); document.write( "n = 258 / 256 = 1.0078125
\n" ); document.write( "n is approx 1
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