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Farmer F1 owns triangular land with vertices P(0, 0), Q(1, 1) and R(2, 0). Farmer F2 takes the region lying between segment PQ and a curve y = xⁿ (n > 1). If the area F2 takes equals exactly 30% of the area of triangle PQR, find n.
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Correct answer: 4
Solution
The area between y = x and y = xⁿ on [0,1] equals 1/2 - 1/(n+1); setting it equal to 0.30 (30% of the unit-area triangle) gives n = 4.
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