(a) Using mathematical tables, find ; (i) \(2 \sin 63.35^\circ\) ; (ii) \(\log \cos 44.74^\circ\);
(b) Find the value of K given that \(\log K - \log (K - 2) = \log 5\);
(c) Use logarithm tables to evaluate \(\frac{(3.68)^{2} \times 6.705}{\sqrt{0.3581}}\)
Verified Correct Answer: .
Step-by-Step Mathematical Solution
(a)(i) \(\sin 63.35^\circ = 0.8938\)
\(2 \sin 63.35^\circ = 2 \times 0.8938 = 1.7876\)
(ii) \(\log \cos 44.74^\circ = \bar{1}.8514\)
(b) \(\log K - \log (K - 2) = \log 5\)
\(\log (\frac{K}{K - 2}) = \log 5\)
\(\therefore \frac{K}{K - 2} = 5 \implies K = 5(K - 2)\)
\(K = 5K - 10 \implies 10 = 5K - K = 4K\)
\(K = 2\frac{1}{2}\)
(c) \(\frac{(3.68)^{2} \times 6.705}{\sqrt{0.3581}}\)
No
Log
\((3.68)^{2}\)
\(0.5658 \times 2 = 1.316\)
\(6.705\)
\(0.8264 = 0.8264\)
= \(1.9580\)
\(\sqrt{0.3581}\)
\(\bar{1}.5540 \div 2 = \bar{1}.7770\)
\(151.7\)
\(\gets 2.1810\)
\(\therefore \frac{(3.68)^{2} \times 6.705}{\sqrt{0.3581}} = 151.7\)
Source: Myschool Past Questions Archive (Record #54526)