Question : The value of $\frac{(0.013)^3+(0.007)(0.000049)}{(0.007)^2+0.013(0.013-0.007)}$ is ______.
Option 1: 0.06
Option 2: 0.02
Option 3: 0.07
Option 4: 0.04
Correct Answer: 0.02
Solution :
$\frac{(0.013)^3+(0.007)(0.000049)}{(0.007)^2+0.013(0.013-0.007)}$
= $\frac{(13)^3+7^{3}}{(7^2 + 13^{2} - 7 × 13)×1000}$
Use $(a^{3} + b^{3}) = (a + b)(a^{2} + b^{2} – ab)$
So, $\frac{(0.013)^3+(0.007)(0.000049)}{(0.007)^2+0.013(0.013-0.007)}$
= $\frac{(7 + 13)(7^{2} + 13^{2} – 7 × 13)}{(7^{2} + 13^{2} - 7 × 13) × 1000}$
= $\frac{20}{1000}$
= 0.02
Hence, the correct answer is 0.02.
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