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a: \(A=\dfrac{5}{4}\cdot\dfrac{11}{3}\cdot\dfrac{-1}{11}=\dfrac{-5}{12}=\dfrac{-25}{60}=\dfrac{-50}{120}\)
b: \(B=\dfrac{3}{4}\cdot\dfrac{1}{12}\cdot\dfrac{2}{3}=\dfrac{1}{24}=\dfrac{5}{120}\)
c: \(C=\dfrac{5}{4}\cdot\dfrac{1}{15}\cdot\dfrac{2}{5}=\dfrac{2}{60}=\dfrac{1}{30}=\dfrac{4}{120}\)
\(D=-3\cdot\dfrac{-7}{12}\cdot\dfrac{1}{-7}=-\dfrac{1}{4}=\dfrac{-30}{120}\)
Vì -50<-30<4<5
nên A<D<B<C
a: \(A=\dfrac{5}{4}\cdot\dfrac{11}{3}\cdot\dfrac{-1}{11}=\dfrac{-5}{12}=\dfrac{-25}{60}=\dfrac{-50}{120}\)
b: \(B=\dfrac{3}{4}\cdot\dfrac{1}{12}\cdot\dfrac{2}{3}=\dfrac{1}{24}=\dfrac{5}{120}\)
c: \(C=\dfrac{5}{4}\cdot\dfrac{1}{15}\cdot\dfrac{2}{5}=\dfrac{2}{60}=\dfrac{1}{30}=\dfrac{4}{120}\)
\(D=-3\cdot\dfrac{-7}{12}\cdot\dfrac{1}{-7}=-\dfrac{1}{4}=\dfrac{-30}{120}\)
Vì -50<-30<4<5
nên A<D<B<C
ta có: \(\frac{-7}{8}=-0,875;\frac{-2}{3}=-0,6\)
\(\frac{-3}{4}=-0,75;\frac{-18}{19}=-0,94;\frac{-27}{28}=-0,96\)
\(\Rightarrow\frac{-2}{3}>\frac{-3}{4}>\frac{-7}{8}>\frac{-18}{19}>\frac{-27}{28}\)
\(A=2^{100}-2^{99}+2^{98}-2^{97}+...+2^2-2\)
\(2A=2^{101}-2^{100}+2^{99}-2^{98}+...+2^3-2^2\)
\(2A+A=2^{101}-2\)
\(A=\frac{2^{101}-2}{3}\)
\(B=\frac{1}{3}+\frac{1}{3^2}+\frac{1}{3^3}+...+\frac{1}{3^{99}}\)
\(3B=1+\frac{1}{3}+\frac{1}{3^2}+...+\frac{1}{3^{98}}\)
\(3B-B=1-\frac{1}{3^{99}}\)
\(B=\frac{1-\frac{1}{3^{99}}}{2}\)
\(A=2^{100}-2^{99}+2^{98}-2^{97}+...+2^2-2\)
\(2A=2^{101}-2^{100}+2^{99}-2^{98}+...+2^3-2^2\)
\(2A+A=\left(2^{101}-2^{100}+2^{99}-2^{98}+...+2^3-^2\right)+\left(2^{100}-2^{99}+2^{98}-2^{97}+...+2^2-2\right)\)
\(3A=2^{101}-2\)
\(A=\frac{2^{101}-2}{3}\)
Chúc bạn học tốt ~
a) 5x . ( 53) 2 = 625
5x . 56 = 625
mà 625 = 54
Suy ra : x + 6 = 4
x = 4 - 6
x = -2
b) (-3/4 )3x - 1 = 256/81
(-3/4 )3X - 1 = (-3/4)-4
SUY RA : 3X - 1 = -4
3X = -4 + 1 = -3
X = -3 : 3
X = -1
C ) (8x - 1 )2n+1 = 52n+1
SUY RA : 8X - 1 = 5
8X = 5 + 1
8 X = 6
X = 6 : 8
X = 3/4
d) (x - 2/9 )2 = 4/9
mà 4/9 = 2/32
SUY RA : x - 2/9 = 2/3
x = 2/3 + 2/9
x = 24/27
Câu e mình không bít làm bn chịu khó suy nghĩ nha !
a )
Ta có :
\(\hept{\begin{cases}\frac{x}{5}=\frac{y}{6}\\\frac{y}{8}=\frac{z}{7}\end{cases}\Rightarrow\hept{\begin{cases}\frac{x}{20}=\frac{y}{24}\\\frac{y}{24}=\frac{z}{21}\end{cases}}}\)
và \(x+y-z=69\)
ADTCDTSBN , ta có :
\(\frac{x}{20}=\frac{y}{24}=\frac{z}{21}=\frac{x+y-z}{20+24-21}=\frac{69}{23}=3\)
\(\Rightarrow\hept{\begin{cases}\frac{x}{20}=3\\\frac{y}{24}=3\\\frac{z}{21}=3\end{cases}\Rightarrow\hept{\begin{cases}x=3.20=60\\y=3.24=72\\z=3.21=63\end{cases}}}\)
Vậy ...
b )
Ta có :
\(5y=72\Rightarrow y=\frac{72}{5}=14,4\)
\(\Rightarrow x=14,4.3:2=21,6\)
và \(3x+5y-7z=30\)
Thay vào làm tiếp :
c )
\(\frac{x-1}{2}=\frac{y+3}{4}=\frac{z-5}{6}\)
\(=\frac{3\left(x-1\right)}{6}=\frac{4\left(y+3\right)}{16}=\frac{5\left(z-5\right)}{30}\)
\(=\frac{3x-3}{6}=\frac{4y+12}{16}=\frac{5z-25}{30}\)
\(=\frac{5z-25-\left(3x-3\right)-\left(4y+12\right)}{30-6-16}\)( ADTCDTSBN )
\(=\frac{5z-25-3x+3-4y-12}{8}=\frac{5z-3x-4y-34}{8}\)
\(=\frac{50-34}{8}=\frac{16}{8}=2\)
\(\Rightarrow\hept{\begin{cases}\frac{x-1}{2}=2\\\frac{y+3}{4}=2\\\frac{z-5}{6}=2\end{cases}\Rightarrow\hept{\begin{cases}x-1=2.2=4\\y+3=2.4=8\\z-5=2.6=12\end{cases}\Rightarrow}\hept{\begin{cases}x=5\\y=5\\z=17\end{cases}}}\)
Vậy ...
Áp dụng tính chất dãy tỉ số bằng nhau
\(\frac{x}{5}=\frac{y}{7}=\frac{z}{9}=\frac{x-y+z}{5-7+9}=\frac{315}{7}=45\)
suy ra: x/5 = 45 => x = 225
y/7 = 45 => y = 315
z/9 = 45 => z = 405
\(1\frac{2}{3};\frac{3}{4};0,4;\frac{1}{5};0;-0,675\)