SOLUTION: The graph of y = n ( 16−x2 ) is shown.
http://imgur.com/sBaSvn9
If the shaded area is equal to 86, find the value of n.
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-> SOLUTION: The graph of y = n ( 16−x2 ) is shown.
http://imgur.com/sBaSvn9
If the shaded area is equal to 86, find the value of n.
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Question 972516: The graph of y = n ( 16−x2 ) is shown.
http://imgur.com/sBaSvn9
If the shaded area is equal to 86, find the value of n. Found 2 solutions by rothauserc, Alan3354:Answer by rothauserc(4718) (Show Source):
You can put this solution on YOUR website! y = n ( 16−x2 ) where n is a constant
y = 16n - nx^2
this is a parabola that opens downward
0 = 16n - nx^2
-nx^2 = -16n
for n not equal to 0
x^2 = 16
x = 4 or -4 for y = 0
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now integrate
y = 16n - nx^2
let Z stand for integral
Z 16n - nx^2 = 16nx - (nx^3/3)
evaluate integral for x = 4 and x = -4
86 = 16n*4 -(n4^3/3) - ((16n(-4)) - (n(-4)^3/3))
86 = 64n - (64n/3) - (-64n) - (-64n/3)
86 = 64n -(64n/3) +64n - (64n/3)
86 = 128n -128n/3
258 = 384n -128n
258 = 256n
n = 258 / 256 = 1.0078125
n is approx 1
You can put this solution on YOUR website! y = n(16-x^2)
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x-ints are -4 & +4
INT(x) = n*(16x - x^3/3) (Ignore the C)
Area = INT(4) - INT(-4) = 86
86 = n
86 = n
86 = n = n*256/3
n = 86*3/256 = 129/128
