calculus

Find the number b such that the line y = b divides the region bounded by the curves y = 16x2 and y = 9 into two regions with equal area. (Round your answer to two decimal places.)

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  1. We want

    Int(x dy)[0,b] = Int(x dy)[b,9]

    x = 1/4 y^(1/2)

    Int(y^(1/2))[0,b] = Int(y^1/2)[b,9]

    2/3 y^(3/2)[0,b] = 2/3 y^(3/2)[b,9]

    2/3 b^(3/2) = 2/3 9^(3/2) - 2/3 b^(3/2)
    4/3 b^(3/2) = 2/3 9^(3/2)
    2b^(3/2) = 9^(3/2)
    2^(2/3) b = 9
    b = 9/2^(2/3) = 9/cbrt(4)

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