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Make K the subject of the relation T = \(\sqrt{\frac{TK - H}{K - H}}\)


Question

Make K the subject of the relation T = \(\sqrt{\frac{TK - H}{K - H}}\)

Options

A) K = \(\frac{H(T^2 - 1)}{T^2 - T}\)

B) K = \(\frac{HT}{(T - 1)^2}\)

C) K = \(\frac{H(T^2 + 1)}{T}\)

D) K = \(\frac{H(T - 1)}{T}\)

The correct answer is A.

Explanation:

T = \(\sqrt{\frac{TK - H}{K - H}}\)

Taking the square of both sides, give

T2 = \(\frac{TK - H}{K - H}\)

T2(K - H) = TK - H

T2K - T2H = TK - H

T2K - TK = T2H - H

K(T2 - T) = H(T2 - 1)

K = \(\frac{H(T^2 - 1)}{T^2 - T}\)


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Dicussion (1)

  • T = \(\sqrt{\frac{TK - H}{K - H}}\)

    Taking the square of both sides, give

    T2 = \(\frac{TK - H}{K - H}\)

    T2(K - H) = TK - H

    T2K - T2H = TK - H

    T2K - TK = T2H - H

    K(T2 - T) = H(T2 - 1)

    K = \(\frac{H(T^2 - 1)}{T^2 - T}\)

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