PART TWO
ai Using mathematical tables, find: 2sin63.35º
ii Using mathematical tables, find: log cos 44.74º
iii Find the value of k given that log k - log(k - 2) = log 5
b) Use logarithm tables to evaluate: \(\frac{3.68^2 \times 6.705}{\sqrt{0.3581}}\)
ai From the four-figure/ mathematical table 2sin63.35º = 2(0.8938) = 1.7876
ii. From the four-figure/ mathematical table, log cos 44.74º = log 0.7103 = \(\bar{1}\).8515
iii. log k - log(k - 2) = log 5 = log \(\frac{\text{k}}{k - 2}\) = log 5 (law of logarithms)
log \(\frac{\text{k}}{k - 2}\) = log 5
\(\frac{\text{k}}{k - 2}\) = 5
cross multiply
5(k - 2) = k
5k - 10 = k
5k - k = 10
4k = 10
k = \(\frac{10}{4}\) = \(\frac{5}{2}\).
b. \(\frac{3.68^2 \times 6.705}{\sqrt{0.3581}}\) = 151.8. See the steps in the diagram above.
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