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3 August, 18:20

The polynomial 3x ^ 3 - 16x ^ 2 + 31x - 20 the area of a trapezoidal desktop. Of the bases of the x ^ 3 - 5x the height of the trapezoid? Hins: Use long division, what is trapezoid represented by the expressions trapezoid

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  1. 3 August, 20:29
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    Step-by-step explanation:

    Given:

    Area = 3x^3 - 16x^2 + 31x - 20

    Base:

    x^3 - 5x

    Area of trapezoid, S = 1/2 * (A + B) * h

    Using long division,

    (2 * (3x^3 - 16x^2 + 31x - 20)) / x^3 - 5x

    = (6x^3 - 32x^2 + 62x - 40)) / x^3 - 5x = 6 - (32x^2 - 92x + 40) / x^3 - 5x = 2S/Bh - Ah/Bh

    = 2S/Bh - A/B

    = (2S/B * 1/h) - A/B

    Since, x^3 - 5x = B

    Comparing the above,

    A = 32x^2 - 92x + 40

    2S/B = 6

    Therefore, h = 1
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