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    Topics || Problems

    If \(A\) is a cross-section area of a chimney, its so-called effective area \(E\) is the smallest root of the equation \(E^2 -2AE+A^2-0.36A =0\). Solve \(E\) interms of \(A\). From the result, find \(E\) if \(A = 30\) square feet.
    Solution:

    \(E\) interms of \(A\)

    \(E^2 -2AE+A^2-0.36A =0\)

    \(E^2 -2AE+A^2 =0.36A\)

    \((E-A)^2 =0.36A\)

    \(E-A =\sqrt{0.36A}\)

    \(E =A\pm\sqrt{0.36A}\)

    If \(A = 30\)

    \(E =30+\sqrt{0.36(30)}\)

    \(E = 33.29 \: \text{ft^2}\)

    \(E =30-\sqrt{0.36(30)}\)

    \(E = 26.71 \: \text{ft^2}\)