\(2\dfrac{1}{2}.x=\dfrac{5}{6}\)

\(\Rightarrow x=\dfrac{5}{6}:2\dfrac{1}{2}\)

\(\Rightarrow x=\dfrac{1}{3}\)

1/3

\(A=\left(\dfrac{1}{2}-1\right)\left(\dfrac{1}{3}-1\right)...\left(\dfrac{1}{10}-1\right)=\left(\dfrac{1-2}{2}\right)\left(\dfrac{1-3}{3}\right)...\left(\dfrac{1-10}{10}\right)=\dfrac{-1}{2}.\dfrac{-2}{3}...\dfrac{-9}{10}\)

Vì có tất cả 9 (lẻ) thừa số hạng nên A sẽ có dấu âm
\(A=\dfrac{-1}{2}.\dfrac{-2}{3}...\dfrac{-9}{10}=-\left(\dfrac{1}{2}.\dfrac{2}{3}...\dfrac{9}{10}\right)=\dfrac{-1}{10}\)

Vậy \(A=\dfrac{-1}{10}\)

bấm máy tính đê

tự tính

=\(\dfrac{\left(3^3\right)^4\times3^2}{\left(3^2\right)^3}=\dfrac{3^{12}\times3^2}{3^6}=\dfrac{3^{14}}{3^6}=3^8=6561\)

\(=\dfrac{1}{99}-\left(\dfrac{1}{1.3}+\dfrac{1}{3.5}+\dfrac{1}{5.7}+...+\dfrac{1}{97.99}\right)\) (1)

Đặt BT trong dấu ngoặc là A ta có

\(2A=\dfrac{3-1}{1.3}+\dfrac{5-3}{3.5}+\dfrac{7-5}{5.7}+...+\dfrac{99-97}{97.99}=\)

\(=1-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{5}+\dfrac{1}{5}-\dfrac{1}{7}+...+\dfrac{1}{97}-\dfrac{1}{99}=\)

\(=1-\dfrac{1}{99}\Rightarrow A=\dfrac{1}{2}-\dfrac{1}{2.99}\)

\(\Rightarrow\left(1\right)=\dfrac{1}{99}-\dfrac{1}{2}+\dfrac{1}{2.99}=\dfrac{2-99+1}{2.99}=-\dfrac{96}{2.99}\)

- 1,2 + (- 0,8 ) + 0,25 + 5,75 - 2021

= -1,3 + 0,25 + 5,75 - 2021

= -1,05 + 5,75 - 2021

= 4,7 - 2021

= -2016,3 

\(-1,2+\left(-0,8\right)+0,25+5,75-2021\)

\(=-2+0,25+5,25-2021\)

\(=-1,75+5,25-2021\)

\(=3,5-2021\)

\(=-2017,5\)

\(\dfrac{5}{9}:\left(\dfrac{1}{11}-\dfrac{5}{22}\right)+\dfrac{7}{4}.\left(\dfrac{1}{14}-\dfrac{2}{7}\right)\)

\(\dfrac{5}{9}:\dfrac{-3}{22}+\dfrac{7}{4}.\dfrac{-3}{14}\)

\(=\dfrac{-5.22}{9.3}-\dfrac{7.3}{4.14}\)

\(=-\dfrac{110}{27}-\dfrac{3}{8}=-\dfrac{961}{216}\)

\(\dfrac{5}{9}:\left(\dfrac{1}{11}-\dfrac{5}{22}\right)+\dfrac{7}{4}.\left(\dfrac{1}{14}-\dfrac{2}{7}\right)\)

\(=\dfrac{5}{9}:\left(-\dfrac{3}{22}\right)+\dfrac{7}{4}.\left(-\dfrac{3}{22}\right)\)

\(=\dfrac{5}{9}.\left(-\dfrac{22}{3}\right)+\dfrac{7}{4}.\left(-\dfrac{3}{22}\right)\)

\(=-\dfrac{110}{27}+\left(-\dfrac{21}{88}\right)\)

\(=-\dfrac{9113}{2376}\)

\(\left(1+\dfrac{1}{2}\right).\left(1+\dfrac{1}{3}\right).....\left(1+\dfrac{1}{2012}\right)\)

\(=\dfrac{3}{2}.\dfrac{4}{3}.....\dfrac{2013}{2012}\)

\(=\dfrac{2013}{2}\)

(1+1/2).(1+1/3) ... (1+1/2012)

=> 3/2 . 4/3 ... 2013/2012

=>2013/2

– Diện tích trần nhà là:
4,5 x 3,7 = 16,65 (m2)
– Diện tích 4 bức tường (hay còn gọi là diện tích xung quanh) là:
2.4,5.3 + 2.3.3,7 = 2.(4,5 + 3,7).3 = 49,2 (m2)
– Diện tích cần được quét vôi là:
16,65 + 49,2 – 5,8 = 60,05 (m2)

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