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Câu 4:
PTHH: \(Zn+S\underrightarrow{t^o}ZnS\)
Ta có: \(\left\{{}\begin{matrix}n_{Zn}=\dfrac{0,65}{65}=0,01\left(mol\right)\\n_S=\dfrac{0,384}{32}=0,012\left(mol\right)\end{matrix}\right.\)
\(\Rightarrow\) Lưi huỳnh còn dư, Kẽm p/ứ hết
\(\Rightarrow\left\{{}\begin{matrix}n_{ZnS}=0,01\left(mol\right)\\n_{S\left(dư\right)}=0,002\left(mol\right)\end{matrix}\right.\) \(\Rightarrow\left\{{}\begin{matrix}m_{ZnS}=0,01\cdot97=0,97\left(g\right)\\m_{S\left(dư\right)}=0,002\cdot32=0,064\left(g\right)\end{matrix}\right.\)
c: Ta có: \(\left(\dfrac{1}{2}\right)^{2x+1}=\dfrac{1}{8}\)
\(\Leftrightarrow2x+1=3\)
\(\Leftrightarrow2x=2\)
hay x=1
d: Ta có: \(\left(-\dfrac{1}{3}\right)^{x+3}=\dfrac{1}{81}\)
\(\Leftrightarrow x+3=4\)
hay x=1
\(A=\dfrac{2^{13}\cdot3^7}{2^{15}\cdot3^2\cdot9^2}=\dfrac{2^{13}\cdot3^7}{2^{15}\cdot3^6}=\dfrac{3}{4}\)
\(C=27\cdot\left(-\dfrac{3}{2}\right)^{-5}\cdot\left(-\dfrac{2}{5}\right)^{-4}:\left(\dfrac{2}{125}\right)^{-1}\)
\(=27\cdot\dfrac{-32}{243}\cdot\dfrac{625}{16}\cdot\dfrac{2}{125}\)
\(=\dfrac{-32}{9}\cdot\dfrac{1}{8}\cdot5\)
\(=-\dfrac{20}{9}\)
1.
a, \(\sqrt{3}sin2x+2cos^2x=0\)
\(\Leftrightarrow\sqrt{3}sin2x+2cos^2x-1=-1\)
\(\Leftrightarrow\sqrt{3}sin2x+cos2x=-1\)
\(\Leftrightarrow\dfrac{\sqrt{3}}{2}sin2x+\dfrac{1}{2}cos2x=-\dfrac{1}{2}\)
\(\Leftrightarrow cos\left(2x-\dfrac{\pi}{3}\right)=-\dfrac{1}{2}\)
\(\Leftrightarrow2x-\dfrac{\pi}{3}=\dfrac{2\pi}{3}+k2\pi\)
\(\Leftrightarrow x=\dfrac{\pi}{2}+k\pi\)
1.
c, ĐK: \(x\ne k2\pi\)
\(\dfrac{2sin\left(x+\dfrac{\pi}{6}\right)-cos2x}{cosx-1}\)
\(\Leftrightarrow\sqrt{3}sinx+cosx-cos2x=cosx-1\)
\(\Leftrightarrow\dfrac{\sqrt{3}}{2}sinx-\dfrac{1}{2}cos2x=-\dfrac{1}{2}\)
\(\Leftrightarrow sin\left(x-\dfrac{\pi}{6}\right)=-\dfrac{1}{2}\)
\(\Leftrightarrow\left[{}\begin{matrix}x-\dfrac{\pi}{6}=-\dfrac{\pi}{6}+k2\pi\\x-\dfrac{\pi}{6}=\dfrac{7\pi}{6}+k2\pi\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}x=k2\pi\left(l\right)\\x=\dfrac{4\pi}{3}+k2\pi\end{matrix}\right.\)
\(\Leftrightarrow x=\dfrac{4\pi}{3}+k2\pi\)
a: \(M=\left|x\right|+x\)
\(=\left[{}\begin{matrix}x+x=2x\left(x\ge0\right)\\-x+x=0\left(x< 0\right)\end{matrix}\right.\)
b: \(N=\left|x\right|:x=\pm1\)
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