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0,3mol chứ nhỉ?

a. \(2Al+6HCl\rightarrow2AlCl_3+3H_2\uparrow\left(1\right)\)

\(FeO+2HCl\rightarrow FeCl_2+H_2O\left(2\right)\)

\(Fe_2O_3+6HCl\rightarrow2FeCl_3+3H_2O\left(3\right)\)

b. Theo phương trình \(n_{Al}=\frac{2}{3}n_{H_2}=0,2mol\) và \(n_{HCl\left(1\right)}=0,6mol\)

\(\rightarrow m_{FeO}+m_{Fe_2O_3}=35,8-0,2.27=30,4g\)

Đặt \(\hept{\begin{cases}n_{FeO}=x\\n_{Fe_2O_3}=y\end{cases}}\)

\(\rightarrow72x+160y=30,4\left(1\right)\)

Theo phương trình \(2x+6y=n_{HCl\left(2+3\right)}=1,6.1-0,6=1\left(2\right)\)

Từ (1) và (2) suy ra x = 0,2 và y = 0,1

\(\rightarrow m_{FeO}=0,2.72=14,4g\) và \(m_{Fe_2O_3}=0,1.160=16g\)

\(\rightarrow\%m_{FeO}=\frac{14,4}{35,8}.100\%\approx40,22\%\)

\(\rightarrow\%m_{Fe_2O_3}=\frac{16}{35,8}.100\%\approx44,69\%\)

c. Theo phương trình \(n_{AlCl_3}=0,2mol\) và \(n_{FeCl_2}=0,2mol\) và \(n_{FeCl_3}=0,2mol\)

\(\rightarrow m_{\text{muối}}=0,2.133,5+0,2.127+0,2.162,5=84,6g\)

Ta có: \(5x^2+10yz\le5\left(x^2+y^2+z^2\right)=9x\left(y+z\right)+18yz\)\(\Leftrightarrow5x^2\le9x\left(y+z\right)+8yz\le9x\left(y+z\right)+2\left(y+z\right)^2\)\(\Leftrightarrow5\left(\frac{x}{y+z}\right)^2-9\left(\frac{x}{y+z}\right)-2\le0\Leftrightarrow\left(\frac{5x}{y+z}+1\right)\left(\frac{x}{y+z}-2\right)\le0\)

\(\Rightarrow\frac{x}{y+z}\le2\)(Do \(\frac{5x}{y+z}+1>0\forall x,y,z>0\)) 

\(\Leftrightarrow x\le2\left(y+z\right)\Leftrightarrow x+y+z\le3\left(y+z\right)\)

\(\Rightarrow P\le\frac{2x}{\left(y+z\right)^2}-\frac{1}{\left(x+y+z\right)^3}\le\frac{4\left(y+z\right)}{\left(y+z\right)^2}-\frac{1}{\left(3y+3z\right)^3}\)

\(=\frac{4}{y+z}-\frac{1}{27\left(y+z\right)^3}\)

Đặt \(\frac{1}{y+z}=t\)thì \(P\le4t-\frac{1}{27}t^3-16+16=-\frac{1}{27}\left(t-6\right)^2\left(t+12\right)+16\le16\)

Vậy MaxP = 16 khi \(\left(x,y,z\right)=\left(\frac{1}{3},\frac{1}{12},\frac{1}{12}\right)\)

Gọi số học sinh khối 6 là x ( 400 \(\le\) x \(\le\) 450 ) 

Theo bài ra ta có :

 x chia hết cho 6 ; x chia hết cho 10 ; x chia hết cho 12 

=> x \(\in\) BC( 6;10;12) 

ta có : 

6 = 2.3

10=2.5 

12= 2² .3 

=> BCNN(6;10;12) = 2².3.5 = 60 

=> BC(6;10;12) = B(60) = { 0 ; 60 ; 120; 180; 240 ; 300;360;420 ; .....} 

mà  400 \(\le\) x \(\le\) 450 nên => x= 420 

Vậy số học sinh khối 6  của trường đó là: 420 học sinh 

vch CTV này lớp 6 à :D 

mình chưa học nhé

ĐKXĐ : \(\hept{\begin{cases}x\ge0\\x\ne4\\x\ne9\end{cases}}\)

\(=\left(\frac{\left(\sqrt{x}+2\right)\left(\sqrt{x}-2\right)}{\left(\sqrt{x}-3\right)\left(\sqrt{x}-2\right)}-\frac{\left(\sqrt{x}+3\right)\left(\sqrt{x}-3\right)}{\left(\sqrt{x}-3\right)\left(\sqrt{x}-2\right)}\right)\div\frac{1}{2\left(\sqrt{x}-2\right)}\)

\(=\left(\frac{x-4}{\left(\sqrt{x}-3\right)\left(\sqrt{x}-2\right)}-\frac{x-9}{\left(\sqrt{x}-3\right)\left(\sqrt{x}-2\right)}\right)\times\frac{2\left(\sqrt{x}-2\right)}{1}\)

\(=\left(\frac{x-4-x+9}{\left(\sqrt{x}-3\right)\left(\sqrt{x}-2\right)}\right)\times\frac{2\left(\sqrt{x}-2\right)}{1}\)

\(=\frac{5}{\left(\sqrt{x}-3\right)\left(\sqrt{x}-2\right)}\times\frac{2\left(\sqrt{x}-2\right)}{1}\)

\(=\frac{5\times2\left(\sqrt{x}-2\right)}{\left(\sqrt{x}-3\right)\left(\sqrt{x}-2\right)}=\frac{10}{\sqrt{x}-3}\)

\(\left(\frac{\sqrt{x}+2}{\sqrt{x}-3}-\frac{\sqrt{x}+3}{\sqrt{x}-2}\right):\frac{1}{2\sqrt{x}-4}\)

\(=\left(\frac{x-4}{\left(\sqrt{x}-3\right)\left(\sqrt{x}-2\right)}-\frac{x-9}{\left(\sqrt{x}-3\right)\left(\sqrt{x}-2\right)}\right):\frac{1}{2\sqrt{x}-4}\)

\(=\frac{5}{\left(\sqrt{x}-3\right)\left(\sqrt{x}-2\right)}.\frac{2\left(\sqrt{x}-2\right)}{1}\)

\(=\frac{10\left(\sqrt{x}-2\right)}{\left(\sqrt{x}-3\right)\left(\sqrt{x}-2\right)}=\frac{10}{\sqrt{x}-3}\)