Tính nhanh:35,43x0,01+85,94x0,01-1,36:100=.....?.Mọi người ơi!Giải chi tiết giúp mình nhé....
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1) 2NH3 + 3Cl2 --> N2 + 6HCl
Chất khử: NH3, chất oxh: Cl2
2N-3 -6e--> N20 | x1 |
Cl20 +2e--> 2Cl- | x3 |
2) 4NH3 + 5O2 --> 4NO + 6H2O
Chất khử: NH3, chất oxh: O2
N-3 -5e--> N+2 | x4 |
O20 +4e--> 2O-2 | x5 |
3) 8Al + 3Fe3O4 --> 4Al2O3 + 9Fe
Chất khử: Al, chất oxh: Fe3O4
\(2Al^0-6e\rightarrow Al_2^{+3}\) | x4 |
\(Fe_3^{+\dfrac{8}{3}}+8e\rightarrow3Fe^0\) | x3 |
4) MnO2 + 4HCl --> MnCl2 + Cl2 + 2H2O
Chất khử: HCl, chất oxh: MnO2
Mn+4 +2e-->Mn+2 | x1 |
2Cl- -2e--> Cl20 | x1 |
5) 16HCl + 2KMnO4 --> 2MnCl2 + 2KCl + 5Cl2 + 8H2O
Chất khử: HCl, chất oxh: KMnO4
2Cl- -2e--> Cl20 | x5 |
Mn+7 +5e--> Mn+2 | x2 |
6) 3Cu + 8HNO3 --> 3Cu(NO3)2 + 2NO + 4H2O
Chất khử: Cu, chất oxh: HNO3
Cu0-2e--> Cu+2 | x3 |
N+5+3e--> N+2 | x2 |
7) 4Zn + 10HNO3 --> 4Zn(NO3)2 + NH4NO3 + 3H2O
Chất khử: Zn, chất oxh: HNO3
Zn0-2e-->Zn+2 | x4 |
N+5 +8e--> N-3 | x1 |
8) 8Al + 30HNO3 --> 8Al(NO3)3 + 3N2O + 15H2O
Chất khử: Al, chất oxh: HNO3
Al0-3e--> Al+3 | x8 |
2N+5 +8e--> N2+1 | x3 |
9) 2Al + 6H2SO4 --> Al2(SO4)3 + 3SO2 + 6H2O
Chất khử: Al, chất oxh: H2SO4
Al0-6e--> Al2+3 | x1 |
S+6+2e--> S+4 | x3 |
10) 2KMnO4 + 10FeSO4 + 8H2SO4 --> 2MnSO4 + 5Fe2(SO4)3 + K2SO4 + 8H2O
Chất khử: FeSO4, chất oxh: KMnO4
2Fe+2 -2e--> Fe2+3 | x5 |
Mn+7 +5e--> Mn+2 | x2 |
Ta có
\(a^2+1=a^2+ab+bc+ca=a\left(a+b\right)+c\left(a+b\right)=\left(a+b\right).\left(a+c\right)\\ Cmtt:b^2+1=\left(b+a\right).\left(b+c\right)\\ c^2+1=\left(c+a\right).\left(c+b\right)\)
Nên
\(\dfrac{b-c}{a^2+1}+\dfrac{c-a}{b^2+1}+\dfrac{a-b}{c^2+1}\\ =\dfrac{\left(b-c\right)}{\left(a+b\right)\left(a+c\right)}+\dfrac{\left(c-a\right)}{\left(b+c\right)\left(b+a\right)}+\dfrac{\left(a-b\right)}{\left(c+a\right)\left(c+b\right)}\\ =\dfrac{\left(b-c\right)\left(b+c\right)+\left(c-a\right)\left(c+a\right)+\left(a-b\right)\left(a+b\right)}{\left(a+b\right)\left(b+c\right)\left(c+a\right)}\\ =\dfrac{b^2-c^2+c^2-a^2+a^2-b^2}{\left(a+b\right)\left(b+c\right)\left(c+a\right)}\\ =0\)
\(\dfrac{b-c}{a^2+1}+\dfrac{c-a}{b^2+1}+\dfrac{a-b}{c^2+1}\)
\(=\dfrac{b-c}{a^2+ab+bc+ac}+\dfrac{c-a}{b^2+ab+bc+ca}+\dfrac{a-b}{c^2+ab+bc+ca}\)
\(=\dfrac{b-c}{a\left(a+b\right)+c\left(a+b\right)}+\dfrac{c-a}{b\left(a+b\right)+c\left(a+b\right)}+\dfrac{a-b}{c\left(c+a\right)+b\left(a+c\right)}\)
\(=\dfrac{b-c}{\left(a+c\right)\left(a+b\right)}+\dfrac{c-a}{\left(b+c\right)\left(a+b\right)}+\dfrac{a-b}{\left(b+c\right)\left(a+c\right)}\)
\(=\dfrac{\left(b-c\right)\left(b+c\right)+\left(c-a\right)\left(a+c\right)+\left(a-b\right)\left(a+b\right)}{\left(a+c\right)\left(a+b\right)\left(b+c\right)}\)
\(=\dfrac{b^2-c^2+c^2-a^2+a^2-b^2}{\left(a+b\right)\left(b+c\right)\left(c+a\right)}=0\)
gọi tổng này là một số A
ta có
A=7/4x(1/1x5+1/5x9+1/9x13+1/13x17+1/17x21)
A= 7/4x(1-1/5+1/5-1/9+1/9-1/13+1/13-1/17+1/17-1/21)
A= 7/4x(1-1/21)=7/4x20/21
suy ra A=5/3
7/1×5 + 7/5x9 + 7/9x13 + 7/13x17 + 7/17x21
= 7/4x(4/1x5 + 4/5x9 + 4/9x13 + 4/13x17 + 4/17x21)
= 7/4x(1 - 1/5 + 1/5 - 1/9 + 1/9 - 1/13 + 1/13 - 1/17 + 1/17 - 1/21)
= 7/4x(1-1/20)
= 7/4x19/20
= 133/80
Bài 2:
\(A=\frac{1}{10}+\frac{1}{40}+\frac{1}{88}+\frac{1}{154}+\frac{1}{238}+\frac{1}{340}\)
\(3A=\frac{3}{2\times5}+\frac{3}{5\times8}+\frac{3}{8\times11}+\frac{3}{11\times14}+\frac{3}{14\times17}\)
\(3A=\frac{1}{2}-\frac{1}{5}+\frac{1}{5}-\frac{1}{8}+\frac{1}{8}-\frac{1}{11}+\frac{1}{11}-\frac{1}{14}+\frac{1}{14}-\frac{1}{17}\)
\(3A=\frac{1}{2}-\frac{1}{17}=\frac{15}{34}\)
\(A=\frac{15}{34}\times\frac{1}{3}=\frac{5}{34}\)
Bài 2:
\(A=\frac{1}{10}+\frac{1}{40}+\frac{1}{88}+\frac{1}{154}+\frac{1}{238}+\frac{1}{340}\)
\(3A=\frac{3}{2\times5}+\frac{3}{5\times8}+\frac{3}{8\times11}+\frac{3}{11\times14}+\frac{3}{14\times17}\)
\(A=\frac{1}{2}-\frac{1}{5}+\frac{1}{5}-\frac{1}{8}+\frac{1}{8}-\frac{1}{11}+\frac{1}{11}-\frac{1}{14}+\frac{1}{14}-\frac{1}{17}\)
\(3A=\frac{1}{2}-\frac{1}{17}=\frac{15}{34}\)
\(A=\frac{15}{34}\times\frac{1}{3}=\frac{5}{34}\)
\(y'=\dfrac{\left(-2x+2\right)\left(x-3\right)-\left(-x^2+2x+c\right)}{\left(x-3\right)^2}=\dfrac{-x^2+6x-6-c}{\left(x-3\right)^2}\)
\(\Rightarrow\) Cực đại và cực tiểu của hàm là nghiệm của: \(-x^2+6x-6-c=0\) (1)
\(\Delta'=9-\left(6+c\right)>0\Rightarrow c< 3\)
Gọi \(x_1;x_2\) là 2 nghiệm của (1) \(\Rightarrow\left\{{}\begin{matrix}-x_1^2+6x_1-6=c\\-x_2^2+6x_2-6=c\end{matrix}\right.\)
\(\Rightarrow m-M=\dfrac{-x_1^2+2x_1+c}{x_1-3}-\dfrac{-x_2^2+2x_2+c}{x_2-3}=4\)
\(\Leftrightarrow\dfrac{-2x_1^2+8x_1-6}{x_1-3}-\dfrac{-2x_2^2+8x_2-6}{x_2-3}=4\)
\(\Leftrightarrow2\left(1-x_1\right)-2\left(1-x_2\right)=4\)
\(\Leftrightarrow x_2-x_1=2\)
Kết hợp với Viet: \(\left\{{}\begin{matrix}x_2-x_1=2\\x_1+x_2=6\end{matrix}\right.\) \(\Rightarrow\left\{{}\begin{matrix}x_1=2\\x_2=4\end{matrix}\right.\)
\(\Rightarrow c=2\)
Có 1 giá trị nguyên
Lấy (32,43 + 85,94)x 0,01-0,0136
118,37 x0.01 - 0,0136
1.1837 - 0,0136
1,701