Basic Maths: Test 31

$\frac{{{\left( 4.5 \right)}^{3}}+{{\left( 1.7 \right)}^{3}}+{{\left( 2.8 \right)}^{3}}-3\times 4.5\times 1.7\times 2.8}{{{\left( 4.5 \right)}^{2}}+{{\left( 1.7 \right)}^{2}}+{{\left( 2.8 \right)}^{2}}-4.5\times 1.7-1.7\times 2.8-2.8\times 4.5}$ $\begin{align} & =\frac{\left( 4.5+1.7+2.8 \right)\,\left( {{4.5}^{2}}+{{1.7}^{2}}+{{2.8}^{2}}-4.5\times 1.7-1.7\times 2.8-2.8\times 4.5 \right)}{{{\left( 4.5 \right)}^{2}}+{{\left( 1.7 \right)}^{2}}+{{\left( 2.8 \right)}^{2}}-4.5\times 1.7-1.7\times 2.8-2.8\times 4.5} \\ & =4.5+1.7+2.8=9 \\ \end{align}$

$\begin{align} & 0.006\times 0.07\times 0.026\div \left( 0.13\times 0.0003 \right) \\ & =0.006\times 0.07\times 0.026\div \left( 0.000039 \right) \\ & =0.006\times 0.07\times \frac{0.026}{0.000039} \\ & =\frac{0.00001092}{0.000039}=0.28 \\ \end{align}$. 

$\begin{align} & \left[ \frac{1}{28}+\frac{1}{70}+\frac{1}{130}+\frac{1}{208} \right]\div {{\left( \frac{3}{4} \right)}^{2}} \\ & =\left[ \frac{1}{4\times 7}+\frac{1}{7\times 10}+\frac{1}{10\times 13}+\frac{1}{13\times 16} \right]\times {{\left( \frac{4}{3} \right)}^{2}} \\ & =\frac{1}{3}\left[ \frac{1}{4}-\frac{1}{7}+\frac{1}{7}-\frac{1}{10}+\frac{1}{10}-\frac{1}{13}+\frac{1}{13}-\frac{1}{16} \right]\times \frac{16}{9} \\ & =\frac{1}{3}\left[ \frac{1}{4}-\frac{1}{16} \right]\times \frac{16}{9} \\ & =\frac{1}{3}\times \frac{12}{64}\times \frac{16}{9}=\frac{1}{9} \\ \end{align}$

$\begin{align} & =\frac{2.68\left( 60 \right)}{\left( 6.34+3.66 \right)\,\left( 6.34-3.66 \right)} \\ & =\frac{2.68(60)}{10\times 2.68}=6 \\ \end{align}$

$\begin{align} & \frac{{{\left( 0.05 \right)}^{2}}-{{\left( 0.02 \right)}^{2}}}{0.05-0.02} \\ & \left[ U\sin g\,\,\,{{a}^{2}}-{{b}^{2}}=\left( a+b \right)\left( a-b \right) \right] \\ & =\frac{\left( 0.05+0.02 \right)\,\left( 0.05-0.02 \right)}{0.05-0.02} \\ & =0.05+0.02=0.07 \\ \end{align}$