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a: \(2^{300}=8^{100}\)
\(3^{200}=9^{100}\)
mà 8<9
nên \(2^{300}< 3^{200}\)
b: \(3^{500}=243^{100}\)
\(7^{300}=343^{100}\)
mà 243<243
nên \(3^{500}< 7^{300}\)
b: -1989/1991>-1>-2001/2000
c: 1/1000>0>-120/157
i: 2021/2020=1+1/2020
2022/2021=1+1/2021
mà 1/2020>1/2021
nên 2021/2020>2022/2021
f: 91/87>1>102/104
b: \(\left[\left(6+\dfrac{3}{5}-3-\dfrac{3}{14}\right)\cdot\dfrac{2}{5}\right]:\left(21-1.25\right)=x:\left(5+\dfrac{5}{6}\right)\)
\(\Leftrightarrow x:\dfrac{35}{6}=\dfrac{237}{175}:\dfrac{79}{4}\)
\(\Leftrightarrow x:\dfrac{35}{6}=\dfrac{12}{175}\)
\(\Leftrightarrow x=\dfrac{2}{5}\)
Ta có :
\(\frac{a}{b}=\frac{5}{6}\Rightarrow\frac{a}{b}=\frac{20}{24}\Rightarrow\frac{a}{20}=\frac{b}{24}\)\(\left(1\right)\)
\(\frac{b}{c}=\frac{8}{9}\Rightarrow\frac{b}{c}=\frac{24}{27}\Rightarrow\frac{b}{24}=\frac{c}{27}\)\(\left(2\right)\)
\(\frac{c}{d}=\frac{3}{2}\Rightarrow\frac{c}{d}=\frac{27}{18}\Rightarrow\frac{c}{27}=\frac{d}{18}\)\(\left(3\right)\)
Từ ( 1 ) ; ( 2 ) ; ( 3 ) \(\Rightarrow\frac{a}{20}=\frac{b}{24}=\frac{c}{27}=\frac{d}{18}=\frac{d-c}{18-24}=\frac{54}{-6}=-9\)
\(\frac{a}{20}=-9\Rightarrow a=-9.20=-180\)
\(\frac{b}{24}=-9\Rightarrow b=-9.24=-216\)
\(\frac{c}{27}=-9\Rightarrow c=-9.27=-243\)
\(\frac{d}{18}=-9\Rightarrow d=-9.18=-162\)
\(\Rightarrow A=a+2b+3c+4d=-180+\left(-216\right).2+\left(-243\right).3+\left(-162\right).4\)
\(=-1989\)
Bài 2:
50g nước biển chứa:
25000:1000*50=25*50=1250(g muối)
\(a:b=4:5\Rightarrow\dfrac{a}{4}=\dfrac{b}{5}\\ b:c=7:8\Rightarrow\dfrac{b}{7}=\dfrac{c}{8}\\ \Rightarrow\dfrac{a}{28}=\dfrac{b}{35}=\dfrac{c}{40}\)
2225 = (23)75 = 875 < 975 =( 32)75 = 3150 ⇒ 2225 < 3150