ai đó làm ơn giúp em với
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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 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) $\%Fe = \dfrac{56.2}{160}.100\% = 70\%$
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
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 $x>9$
\(\Leftrightarrow m> \max \frac{1}{4}(\frac{2025}{x}+1), \forall x>9\Leftrightarrow m>56,5\)