Ta có \(\dfrac{1}{2^2}< \dfrac{1}{1.2};\dfrac{1}{3^2}< \dfrac{1}{2.3};...;\dfrac{1}{2022^2}< \dfrac{1}{2021.2022}\)

cộng vế với vế 

\(\dfrac{1}{2^2}+\dfrac{1}{3^2}+...+\dfrac{1}{2022^2}< 1-\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{3}+...+\dfrac{1}{2021}-\dfrac{1}{2022}\)

\(=1-\dfrac{1}{2022}=\dfrac{2021}{2022}\)

Vậy ta có đpcm 

Câu 7:

a, \(Fe+H_2SO_4\rightarrow FeSO_4+H_2\)

\(CuO+H_2SO_4\rightarrow CuSO_4+H_2O\)

b, \(n_{H_2}=\dfrac{2,24}{22,4}=0,1\left(mol\right)\)

Theo PT: \(n_{Fe}=n_{H_2}=0,1\left(mol\right)\)

\(\Rightarrow\left\{{}\begin{matrix}\%m_{Fe}=\dfrac{0,1.56}{10}.100\%=56\%\\\%m_{CuO}=44\%\end{matrix}\right.\)

c, \(n_{CuO}=\dfrac{10-0,1.56}{80}=0,055\left(mol\right)\)

Theo PT: \(n_{H_2SO_4}=n_{Fe}+n_{CuO}=0,155\left(mol\right)\)

\(\Rightarrow C\%_{H_2SO_4}=\dfrac{0,155.98}{100}.100\%=15,19\%\)

d, Theo PT: \(\left\{{}\begin{matrix}n_{FeSO_4}=n_{Fe}=0,1\left(mol\right)\\n_{CuSO_4}=n_{CuO}=0,055\left(mol\right)\end{matrix}\right.\)

\(\Rightarrow\left\{{}\begin{matrix}m_{FeSO_4}=0,1.152=15,2\left(g\right)\\m_{CuSO_4}=0,055.160=8,8\left(g\right)\end{matrix}\right.\)

Câu 8:

a, \(CuCO_3+2HCl\rightarrow CuCl_2+CO_2+H_2O\)

b, \(n_{CO_2}=\dfrac{3,36}{22,4}=0,15\left(mol\right)\)

Theo PT: \(n_{CuCO_3}=n_{CO_2}=0,15\left(mol\right)\)

\(\Rightarrow\left\{{}\begin{matrix}\%m_{CuCO_3}=\dfrac{0,15.124}{20}.100\%=93\%\\\%m_{CuCl_2}=7\%\end{matrix}\right.\)

c, \(n_{HCl}=2n_{CO_2}=0,3\left(mol\right)\)

\(\Rightarrow C_{M_{HCl}}=\dfrac{0,3}{0,2}=1,5\left(M\right)\)

Bài 6: 

a, \(SO_2+Ca\left(OH\right)_2\rightarrow CaSO_3+H_2O\)

b, \(n_{SO_2}=\dfrac{1,12}{22,4}=0,05\left(mol\right)\)

Theo PT: \(n_{Ca\left(OH\right)_2}=n_{CaSO_3}=n_{SO_2}=0,05\left(mol\right)\)

\(\Rightarrow C\%_{Ca\left(OH\right)_2}=\dfrac{0,05.74}{100}.100\%=3,7\%\)

c, \(m_{CaSO_3}=0,05.120=6\left(g\right)\)

Bài 2 : (1) liên kết ; (2) electron ; (3) liên kết ; (4) : electron ; (5) sắp xếp electron

Bài 4 : 

$\dfrac{M_X}{4} = \dfrac{M_K}{3} \Rightarrow M_X = 52$

Vậy X là crom,KHHH : Cr

Bài 5 : 

$M_X = 3,5M_O = 3,5.16 = 56$ đvC

Tên : Sắt

KHHH : Fe

Bài 9 : 

$M_Z = \dfrac{5,312.10^{-23}}{1,66.10^{-24}} = 32(đvC)$

Vậy Z là lưu huỳnh, KHHH : S

Bài 10  :

a) $PTK = 22M_{H_2} = 22.2 = 44(đvC)$

b) $M_{hợp\ chất} = X + 16.2 = 44 \Rightarrow X = 12$
Vậy X là cacbon, KHHH : C

Bài 11 : 

a) $PTK = 32.5 = 160(đvC)$

b) $M_{hợp\ chất} = 2A + 16.3 = 160 \Rightarrow A = 56$
Vậy A là sắt

c) $\%Fe = \dfrac{56.2}{160}.100\% = 70\%$

Bài 12 : 

a) $M_{hợp\ chất} = R + 1.4 = M_O = 16(đvC) \Rightarrow R = 12$

Vậy R là nguyên tố cacbon, KHHH : C

b) $\%C = \dfrac{12}{16}.100\% = 75\%$

Bài 13 : 

a) $PTK = 32M_{H_2} = 32.2 = 64(đvC)$

b) $M_{hợp\ chất} = X + 16.2 = 64 \Rightarrow X = 32$
Vậy X là lưu huỳnh, KHHH : S

bán kính thân cây: 0,6 : 2 = 0,3m

Thể tích cây gỗ: 6 x 3,14x0,3x0,3 = 1,6956 (m³)

Giá tiền mua 1m³ gỗ là:

1271700 : 1,6956 = 750000 (đồng)

1 was given

2 have repaired

3 had finished

4 isn't reading

5 had talked

1 was found

2 are always

8 ko có từ

9 have become

10 had met

11 aren't

12 arrives

13 is repairing

14 was built

15 had finished

16 will stay

=>(10x+45)=9,5*5,1=48,45

=>10x=3,45

=>x=69/200

Câu 1: A

Câu 2: D

Câu 3: B

Câu 4: C

Bài 1:

a) 

\(A=\left(\frac{4\sqrt{x}}{\sqrt{x}+2}-\frac{8x}{(\sqrt{x}-2)(\sqrt{x}+2)}\right):\left(\frac{\sqrt{x}-1}{\sqrt{x}(\sqrt{x}-2)}-\frac{2(\sqrt{x}-2)}{\sqrt{x}(\sqrt{x}-2)}\right)\)

\(=\frac{4\sqrt{x}(\sqrt{x}-2)-8x}{(\sqrt{x}-2)(\sqrt{x}+2)}:\frac{\sqrt{x}-1-2(\sqrt{x}-2)}{\sqrt{x}(\sqrt{x}-2)}=\frac{-4x-8\sqrt{x}}{(\sqrt{x}-2)(\sqrt{x}+2)}.\frac{\sqrt{x}(\sqrt{x}-2)}{-\sqrt{x}+3}\)

\(=\frac{-4\sqrt{x}(\sqrt{x}+2)}{(\sqrt{x}-2)(\sqrt{x}+2)}.\frac{\sqrt{x}(\sqrt{x}-2)}{3-\sqrt{x}}=\frac{-4x(\sqrt{x}-2)}{(\sqrt{x}-2)(3-\sqrt{x})}=\frac{4x}{\sqrt{x}-3}\)

b)

Ta có:
\(m(\sqrt{x}-3).A>x+2025\)

\(\Leftrightarrow 4xm>x+2025\Leftrightarrow x(4m-1)>2025\)

\(\Leftrightarrow 4m-1>\frac{2025}{x}\Leftrightarrow m>\frac{1}{4}(\frac{2025}{x}+1)\) với mọi $x>9$

\(\Leftrightarrow m> \max \frac{1}{4}(\frac{2025}{x}+1), \forall x>9\Leftrightarrow m>56,5\)

Bài 2:

a) 

\(\left\{\begin{matrix} 4x-3y=19\\ 2x+3y=11\end{matrix}\right.\Rightarrow 6x=30\Rightarrow x=5\)

\(y=\frac{4x-19}{3}=\frac{4.5-19}{3}=\frac{1}{3}\)

b) 

\(3x^2-20x+12=0\Leftrightarrow (x-6)(3x-2)=0\)

\(\Rightarrow \left[\begin{matrix} x=6\\ x=\frac{2}{3}\end{matrix}\right.\)