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1) \(\dfrac{1}{4}x-\dfrac{1}{3}=\dfrac{-5}{9}\)
\(\Rightarrow\dfrac{1}{4}x=-\dfrac{2}{9}\Rightarrow x=-\dfrac{8}{9}\)
2) \(2^{x-3}-3.2^x=-92\)
\(\Rightarrow2^x\left(2^{-3}-3\right)=-92\)
\(\Rightarrow2^x.\dfrac{-23}{9}=-92\)
\(\Rightarrow2^x=32\Rightarrow x=5\)
...\(a=\left[\left(\left(50-1\right):1+1\right):2\right]\left(50+1\right)=25.51=1275\)
\(...a1=\left[\left(\left(98-35\right):3+1\right):2\right]\left(35+98\right)=11.133=1463\)
\(A=\dfrac{1}{3}+\dfrac{1}{3^2}+\dfrac{1}{3^3}+\dfrac{1}{3^4}+...+\dfrac{1}{3^{99}}\)
\(\Rightarrow\dfrac{A}{3}=\dfrac{1}{3^2}+\dfrac{1}{3^3}+\dfrac{1}{3^4}+...+\dfrac{1}{3^{100}}\)
\(\Rightarrow A-\dfrac{A}{3}=\dfrac{2A}{3}=\left(\dfrac{1}{3}+\dfrac{1}{3^2}+\dfrac{1}{3^3}+...+\dfrac{1}{3^{99}}\right)-\left(\dfrac{1}{3^2}+\dfrac{1}{3^3}+\dfrac{1}{3^4}+...+\dfrac{1}{3^{100}}\right)\)
\(\Rightarrow\dfrac{2A}{3}=\left(\dfrac{1}{3^2}-\dfrac{1}{3^2}\right)+\left(\dfrac{1}{3^3}-\dfrac{1}{3^3}\right)+...+\left(\dfrac{1}{3^{99}}-\dfrac{1}{3^{99}}\right)+\left(\dfrac{1}{3}-\dfrac{1}{3^{100}}\right)=\dfrac{1}{3}-\dfrac{1}{3^{100}}\)
\(\Rightarrow2A=3\cdot\left(\dfrac{1}{3}-\dfrac{1}{3^{100}}\right)\)
\(\Rightarrow\text{A}=\dfrac{1-\dfrac{1}{3^{99}}}{2}\)
\(\Rightarrow A=\dfrac{1}{2}-\dfrac{1}{2.3^{99}}< \dfrac{1}{2}\)
\(2^3. 4^2 . 5^3 \)\(= 8 . 16 . 125 = 16000\)
\(9.3^3.\dfrac{1}{81}.3^3=\left(9.81\right)\left(\dfrac{1}{81}.81\right)=729\)
\(3^2.5^2\left(\dfrac{2}{3}\right)^2=9.25.\dfrac{2^2}{3^2}=9.25.\dfrac{4}{9}=100\)
\(\left(\dfrac{1}{3}\right)^2.\dfrac{1}{3}.9^2=\dfrac{1}{9}.9.\dfrac{1}{3}.9=3\)
\(2^3.4^2.5^3=\left(2^3.5^3\right).4^2=10^3.4^2=1000.16=16000\)
\(9.3^3.\dfrac{1}{81}.3^2=\left(9.\dfrac{1}{81}\right).\left(3^3.3^2\right)=\dfrac{1}{9}.3^5=\dfrac{3^5}{3^2}=3^3=81\)
\(3^2.5^2.\left(\dfrac{2}{3}\right)^2=5^2.\left[3^2.\dfrac{2^2}{3^2}\right]=5^2.2^2=10^2=100\)
\(\left(\dfrac{1}{3}\right)^2.\dfrac{1}{3}.9^2=\left(\dfrac{1}{3}\right)^2.\left(\dfrac{1}{3}.9^2\right)=\dfrac{1}{9}.\dfrac{9^2}{3}=\dfrac{9}{3}=3\)
A) -15,5 x 20,8 +2,5 x 9,2 -15,5 x 9,2 + 3,5 x 20,8
=-15,5 x 20,8 + 2,5 x 9,2 + -15,5 x 9,2 +3,5 x 20,8
=[20,8x(-15,5+3,5)]+[9,2x(2,5+-15,5)]
=[20,8x(-12)]+[9,2x(-13)]
=-249,6+-119,6
=-369,2
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