Simplify the expression \(log_{10}18 - log_{10}2.88+log_{10}16\)
31.12
3.112
2
1
Correct answer is C
\(log_{10}18 - log_{10}2.88+log_{10}16\\
=log_{10}18 - log_{10}\left(\frac{288}{100}\right)+log_{10}16 = log_{10}\left(\frac{18\times 16}{1}\times \frac{100}{288}\right)\\
=log_{10}\left(\frac{288\times 100}{288}\right)=log_{10}100=log_{10}10^2=2log_{10}10=2\)
33
8
7
0
Correct answer is C
\(7\frac{1}{2}-\left(2\frac{1}{2}+3\right)\div\frac{33}{2}\\
=\frac{15}{2}-\left(\frac{5}{2}+\frac{3}{1}\right)\times\frac{2}{33}\\
=\frac{15}{2}-\left(\frac{5+6}{2}\right)\times \frac{2}{33}=\frac{15}{2}-\frac{11}{2}\times \frac{2}{33}=\frac{15}{2}-\frac{1}{3}\\
=\frac{45-2}{6}=\frac{43}{6}\)
Simplify \(\frac{5}{\sqrt{3}}-\frac{3}{\sqrt{2}}\)
\(\frac{1}{6}(5\sqrt{3}-3\sqrt{2}\)
\(\frac{1}{6}(15\sqrt{3}-6\sqrt{2}\)
\(\frac{1}{6}(3\sqrt{2}-\sqrt{3}\)
\(\frac{1}{6}(10\sqrt{3}-9\sqrt{2}\)
Correct answer is D
\(\frac{5}{\sqrt{3}}-\frac{3}{\sqrt{2}}=\frac{5\sqrt{2}-3\sqrt{3}}{\sqrt{6}}\\
=\frac{5\sqrt{2}-3\sqrt{3}}{\sqrt{6}} \times \frac{\sqrt{6}}{\sqrt{6}}Rationalize\\
\frac{\sqrt{6}(5\sqrt{2}-3\sqrt{3})}{6}\\
\frac{5\sqrt{12}-3\sqrt{18}}{6}=\frac{10\sqrt{3}-9\sqrt{2}}{6}\\
\frac{1}{6}(10\sqrt{3}-9\sqrt{2})\)
Correct 0.04945 to two significant figures
0.040
0.049
0.050
0.49
Correct answer is B
0.04945 \(\approxeq\) 0.049. (to 2 sig. figs)
36o
44o
46o
54o
Correct answer is D
θ= angle of depression of the point from the top of the wall
\(tan\theta = \frac{7}{5}=1.4; \theta = tan^{-1}(1.400)\
\theta = 54.4^{\circ}; \theta = 54^{\circ}\) to the nearest degree
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