\(\left(\frac{1}{3}+\frac{1}{2}\right):\frac{3}{5}+\left(\frac{1}{6}-\frac{7}{10}\right):\frac{3}{5}\\\left(\frac{1}{3}+\frac{1}{2}\right).\frac{5}{3}+\left(\frac{1}{6}-\frac{7}{10}\right).\frac{5}{3}\)=>\(\frac{5}{3}.\left(\frac{1}{3}+\frac{1}{2}\right)+\left(\frac{1}{6}-\frac{7}{10}\right)\)=>5/3.3/10=1/2

Vận tốc ca nô khi xuôi dòng là :

21 + 3 = 24 ( km/h )

Vận tốc ca nô khi ngược dòng là :

21 - 3 = 18 ( km/h )

trong cùng 1 thời gian thì quãng đường tỉ lệ thuận với vận tốc nên :

\(\frac{18}{24}=\frac{30}{x}\Rightarrow x=\frac{24.30}{18}=40\)

Vậy ...

\(\left(-\frac{2}{7}+\frac{1}{5}\right):\frac{9}{35}+\left(\frac{4}{5}-\frac{5}{7}\right):\frac{9}{35}\)

\(=\left(-\frac{2}{7}+\frac{1}{5}+\frac{4}{5}-\frac{5}{7}\right):\frac{9}{35}\)

\(=0:\frac{9}{35}\)

\(=0\)

\(=\frac{-3}{35}\div\frac{9}{35}+\frac{3}{35}\div\frac{9}{35}\)

\(=\left(-\frac{3}{35}+\frac{3}{35}\right)\div\frac{9}{35}\)

\(=0\div\frac{9}{35}\)

\(=0\)

\(\frac{a}{b}=\frac{3}{4}\Rightarrow\frac{a}{3}=\frac{b}{4}\Rightarrow\frac{a^2}{9}=\frac{b^2}{16}\)

Từ \(\frac{a^2}{9}=\frac{b^2}{16}\)\(\Rightarrow\frac{a^2}{9}=\frac{b^2}{16}=\frac{a^2+b^2}{9+16}=\frac{36}{25}\)

\(\Rightarrow a=\frac{18}{5};b=\frac{24}{5}\)

\(\Rightarrow a.b=\frac{18}{5}.\frac{24}{5}=\frac{432}{25}=17,28\)

a : b = 3 : 4   =>  \(\frac{a}{3}=\frac{b}{4}\)=> \(\frac{a^2}{9}=\frac{b^2}{16}\)

- Theo tính chất dãy tỉ số bằng nhau, ta có: \(\frac{a^2}{9}=\frac{b^2}{16}=\frac{a^2+b^2}{9+16}=\frac{36}{25}=1,44\)

=> a = 1,44 . 3  = 4,32

       b = 1,44 . 4  = 5,76

=> a. b = 4,32 . 5,76 = 24,9

Ta có : \(\frac{2x+1}{5}=\frac{3y-2}{7}=\frac{2x+3y-1}{6x}=\frac{2x+3y-1}{12}\)

Nên : \(\frac{2x+3y-1}{6x}=\frac{2x+3y-1}{12}\)

<=> 6x = 12

=> x = 2 . 

\(\frac{2x+1}{5}=\frac{3y-2}{7}=\frac{2x+3y-1}{6x}=\frac{\left(2x+1\right)+\left(3y-2\right)}{5+7}=\frac{2x+3y-1}{12}\)

\(\frac{2x+3y-1}{6x}=\frac{2x+3y-1}{12}\)

\(\Rightarrow6x=12\)

\(\Rightarrow x=2\)

12-8.\(\left(\frac{3}{2}\right)^3\)=12-8.\(\frac{9}{8}\)=12-9=3

= 12-8*\(\frac{27}{8}\)=12-27=-15

\(\frac{2}{7}< \frac{1}{n}< \frac{4}{7}\)

\(\Rightarrow\frac{1}{3,5}< \frac{1}{n}< \frac{1}{1,75}\)

\(\Rightarrow3,5>n>1,75\)

\(\Rightarrow\)n \(\in\){ 2 ; 3 }

\(\frac{2}{7}< \frac{1}{n}< \frac{4}{7}\)

\(\Rightarrow n=2\)

(-3.15)*(-7.2)+(3.15)*12.4+4.8.(-3.15)

= ( -3,15 ) . ( -7,2 ) + ( -3,15 ) . ( -12,4 ) + 4,8 . ( -3,15 )

= ( -3,15 ) . [ ( -7,2 ) + ( -12,4 ) + 4,8 ]

= ( -3,15 ) . ( -14,8 ) 

= 46,62

đặt -3.15 chung ra ngoài