Câu hỏi:

Thể tích khối bê tông ghép đó là: $12.7.2+3.3.3=195$ dm³.

$A=\frac{{{49}^{5}}{{.8}^{10}}}{{{14}^{7}}{{.49.4}^{13}}}-\frac{\frac{7}{10}-\frac{7}{12}+\frac{7}{5}}{0,8-\frac{8}{12}+\frac{8}{5}}$

$=\frac{{{7}^{10}}{{.2}^{30}}}{{{2}^{7}}{{.7}^{7}}{{.7}^{2}}{{.2}^{26}}}-\frac{7.\left( \frac{1}{10}-\frac{1}{12}+\frac{1}{5} \right)}{8.\left( \frac{1}{10}-\frac{1}{12}+\frac{1}{5} \right)}$

$=\frac{{{7}^{10}}{{.2}^{30}}}{{{7}^{9}}{{.2}^{33}}}-\frac{7}{8}$

$=\frac{7}{8}-\frac{7}{8}=0$.

Đổi $1l=1\,000\,cm^3$.

Chiều rộng của hộp sữa là:

$1000:\left( 20.10 \right)=5$ (cm)

Diện tích xung quanh của hộp sữa là:

$2.\left( 5+10 \right)$. $20=600$ (cm²)

Diện tích vật liệu dùng để làm vỏ hộp sữa là:

$600+2. 5 . 10=700$ (cm²).

Ta có $\left( \frac{1}{2}+\frac{1}{3}+\frac{1}{4}+...+\frac{1}{2022} \right)x=\frac{2021}{1}+\frac{2020}{2}+\frac{2019}{3}+...+\frac{1}{2021}$.

$\left( \frac{1}{2}+\frac{1}{3}+\frac{1}{4}+...+\frac{1}{2022} \right)x=2021+\frac{2020}{2}+\frac{2019}{3}+...+\frac{1}{2021}$

$\left( \frac{1}{2}+\frac{1}{3}+\frac{1}{4}+...+\frac{1}{2022} \right)x=\left( 1+\frac{2020}{2} \right)+\left( 1+\frac{2019}{3} \right)+\left( 1+\frac{2018}{4} \right)+...+\left( 1+\frac{1}{2021} \right)+1$

$\left( \frac{1}{2}+\frac{1}{3}+\frac{1}{4}+...+\frac{1}{2022} \right)x=\left( 1+\frac{2020}{2} \right)+\left( 1+\frac{2019}{3} \right)+\left( 1+\frac{2018}{4} \right)+...+\left( 1+\frac{1}{2021} \right)+\frac{2022}{2022}$

$\left( \frac{1}{2}+\frac{1}{3}+\frac{1}{4}+...+\frac{1}{2022} \right)x=\frac{2022}{2}+\frac{2022}{3}+\frac{2022}{4}+...+\frac{2022}{2021}+\frac{2022}{2022}$

$\left( \frac{1}{2}+\frac{1}{3}+\frac{1}{4}+...+\frac{1}{2022} \right)x=2022\left( \frac{1}{2}+\frac{1}{3}+\frac{1}{4}+...+\frac{1}{2022} \right)$

$x=2022$

$\frac{2}{7}+\left( -\frac{3}{5} \right)+\frac{3}{5}=\frac{2}{7}+\left( \frac{3}{5}-\frac{3}{5} \right)=\frac{2}{7}.$