(a) Simplify : \(\frac{\frac{1}{2} of \frac{1}{4} \div \frac{1}{3}}{\frac{1}{6} - \frac{3}{4} + \frac{1}{2}}\).
(b) Given that \(\sqrt{x} = 10^{\bar{1}.6741}\), without using calculators, find the value of x.
Show Answer Show Explanation Explanation (a) \(\frac{\frac{1}{2} of \frac{1}{4} \div \frac{1}{3}}{\frac{1}{6} - \frac{3}{4} + \frac{1}{2}}\) Numerator - \(\frac{1}{2} \times \frac{1}{4} \div \frac{1}{3} = (\frac{1}{2} \times \frac{1}{4}) \div \frac{1}{3}\) \(\frac{1}{8} \times 3 = \frac{3}{8}\) Denominator - \(\frac{1}{6} - \frac{3}{4} + \frac{1}{2} = \frac{1}{6} - (\frac{3}{4} - \frac{1}{2})\) \(\frac{1}{6} - (\frac{3 - 2}{4}) = \frac{1}{6} - \frac{1}{4}\) \(\frac{2 - 3}{12} = \frac{-1}{12}\) \(\therefore \frac{\frac{1}{2} \times \frac{1}{4} \div \frac{1}{3}}{\frac{1}{6} - \frac{3}{4} + \frac{1}{2}} = \frac{3}{8} \div \frac{-1}{12}\) \(\frac{3}{8} \times -12 = \frac{-9}{2}\) = \(-4.5\) (b) \(\sqrt{x} = 10^{\bar{1}.6741}}\) Squaring both sides, we have \(x = (10^{\bar{1}.6741}})^{2}\) \(x = 10^{\bar{1}.3482}\) (checking antilogarithm) \(x = 0.2229\)