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a/ Gọi A là giá trị của biểu thức trên
\(\Rightarrow A=\frac{1}{10}+\frac{1}{15}+\frac{1}{21}+...+\frac{1}{120}\)
\(\Rightarrow A=\frac{2}{20}+\frac{2}{30}+\frac{2}{42}+...+\frac{2}{240}\)
\(\Rightarrow A=2\left(\frac{1}{20}+\frac{1}{30}+\frac{1}{42}+...+\frac{1}{240}\right)\)
\(\Rightarrow\frac{A}{2}=\frac{1}{20}+\frac{1}{30}+\frac{1}{42}+...+\frac{1}{240}\)
\(\Rightarrow\frac{A}{2}=\frac{1}{4.5}+\frac{1}{5.6}+\frac{1}{6.7}+...+\frac{1}{14.15}+\frac{1}{15.16}\)
\(\Rightarrow\frac{A}{2}=\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}+\frac{1}{6}-\frac{1}{7}+...+\frac{1}{14}-\frac{1}{15}+\frac{1}{15}-\frac{1}{16}\)
\(\Rightarrow\frac{A}{2}=\frac{1}{4}-\frac{1}{16}\)
\(\Rightarrow A=\frac{3}{16}.2=\frac{3}{8}\)
b/ 0,2 x 317 x 7 + 0,14 x 3520 + 33,1 x 14
= 0,2 x 317 x 7 : 10 x 10 + 0,14 x 3520 + 33,1 x 100 x 14 : 100
= 0,2 x 317 x 0,7 x 10 + 0,14 x 3520 + 33,1 x 100 x 0,14
= ( 0,2 x 0,7) x 317 x 10 + 0,14 x 3520 + 3310 x 0,14
= 0,14 x 3170 + 0,14 x 3520 + 3310 x 0,14
= 0,14 x ( 3170 + 3520 + 3310)
= 0,14 x10000
= 1400
Hứa r, k mik nha!
a, 14 : (0,4 + \(\dfrac{0,16}{x}\)) = 7
0,4 + \(\dfrac{0,16}{x}\) = 14 : 7
0,4 + \(\dfrac{0,16}{x}\) = 2
\(\dfrac{0,16}{x}\) = 2 - 0,4
\(\dfrac{0,16}{x}\) = 1,6
\(x\) = 0,16 : 1,6
\(x\) = 0,1
b, 520 + 7,5 x 4 = \(x\) + \(\dfrac{174}{50}\) + 50
520 + 30 = \(x\) + 3,48 + 50
\(x\) + 53,48 = 550
\(x\) = 550 - 53,48
\(x\) = 496,52
a, 7/5 : x + 3/2 = 16/3
7/5 : x = 16/3 - 3/2
7/5 : x = 23/6
x = 7/5 : 23/6
x = 42/115
b, x : 1/5 + 1/7 = 3/5 . 18/21
x : 1/5 + 1/7 = 18/35
x : 1/5 = 18/35 - 1/7
x : 1/5 = 13/35
x = 13/35 . 1/5
x = 13/175
c, x - 1 và 1/3 : 2 = 5/7
x - 4/3 : 2 = 5/7
x - 4/3 = 5/7 . 2
x - 4/3 = 10/7
x = 10/7 + 4/3
x = 58/21
d, x + 2 và 3/5 . 1/6 = 35/36
x + 13/5 . 1/6 = 35/36
x + 13/5 = 35/36 : 1/6
x + 13/5 = 35/6
x = 35/6 - 13/5
x = 97/30
e, ( x + 3/2 ) : 2 = 7/10 + 1/5
( x + 3/2 ) : 2 = 9/10
x + 3/2 = 9/10 . 2
x + 3/2 = 9/5
x = 9/5 - 3/2
x = 3/10
\(a.\left(y.100-0,7357\right):0,01=0,55+15,88\)
\(\Leftrightarrow\left(100y-0,7357\right):0,01=16,43\)
\(\Leftrightarrow100y-0,7357=0,1643\)
\(\Leftrightarrow100y=0,9\)
\(\Leftrightarrow y=\frac{9}{1000}\)
\(b.14:\left(0,4+\frac{0,16}{y}\right)=7\)
\(\Leftrightarrow0,4+\frac{0,16}{y}=2\)
\(\Leftrightarrow\frac{0,16}{y}=1,6\)
\(\Leftrightarrow x=0,1\)
\(c.520+7,5.4=y+\frac{175}{5}+30\)
\(\Leftrightarrow520+30=y+65\)
\(\Leftrightarrow550=y+65\)
\(\Leftrightarrow y=485\)
=0.16/x=1.6
\(\Rightarrow\)x= 0.16/1.6
\(\Rightarrow\)x=0.1
3/4 x 8/9 x 15/16 x ... x 99/100 x 120/121 = 3 x 8 x 15 x 99 x 120/ 4 x 9 x 16 x 100 x 121
= ( 1 x 3 ) x ( 2 x 4 ) x ( 3 x 5 ) x ... x ( 9 x 11 ) x ( 10 x 12 ) / ( 2 x 2 ) x ( 3 x 3 ) x ( 4 x 4 ) x ... x ( 10 x 10 ) x ( 11 x 11 )
= ( 1 x 2 x 3 x ... x 10 ) x ( 3 x 4 x 5 x ... x 12 ) / ( 2 x 3 x ... x 11 ) x ( 2 x 3 x ... x 11 ) = 12/11x2 = 6/11
a/7/9(1/4+3/4)=7/9.1=7/9
b/13/9(16/5-14/5+3/5)=13/9.1=13/9
34cm=34/100m
524mm=524/1000m
70mm=70/1000=7/100m
a/7/9(1/4+3/4)=7/9.1=7/9
b/13/9(16/5-14/5+3/5)=13/9.1=13/9
34cm=34/100m
524mm=524/1000m
70mm=70/1000=7/100m
\(a.\)
\(14:\left(0,4+\frac{0,16}{x}\right)=7\)\(=>0,4+\frac{0,16}{x}=14:7\)
\(=>0,4+\frac{0,16}{x}=2=>\frac{0,16}{x}=2-0,4\)
\(=>\frac{0,16}{x}=1,6=>0,16:x=1,6\)
\(=>x=0,16:1,6=>x=0,1\)
Vậy \(x=0,1\)