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a,
Khối lượng mol đường:
MC12H22O11 =12.MC + 22.MH + 11.MO = 12.12 + 1.22 +16.11= 342 g/mol.
b,
Trong 1 mol phân tử C12H22O11 có 12 mol nguyên tử C, 22 mol nguyên tử H, 11 mol nguyên tử O.
c,
\(\%C=\dfrac{12.12.100}{342}=42,1\%\)
\(\%H=\dfrac{1.22.100}{342}=6,4\%\)
\(\%O=100-42,1-6,4=51,5\%\)
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
\(\dfrac{b-c}{a^2+1}+\dfrac{c-a}{b^2+1}+\dfrac{a-b}{c^2+1}\\ =\dfrac{\left(b-c\right)}{\left(a+b\right)\left(a+c\right)}+\dfrac{\left(c-a\right)}{\left(b+c\right)\left(b+a\right)}+\dfrac{\left(a-b\right)}{\left(c+a\right)\left(c+b\right)}\\ =\dfrac{\left(b-c\right)\left(b+c\right)+\left(c-a\right)\left(c+a\right)+\left(a-b\right)\left(a+b\right)}{\left(a+b\right)\left(b+c\right)\left(c+a\right)}\\ =\dfrac{b^2-c^2+c^2-a^2+a^2-b^2}{\left(a+b\right)\left(b+c\right)\left(c+a\right)}\\ =0\)
\(\dfrac{b-c}{a^2+1}+\dfrac{c-a}{b^2+1}+\dfrac{a-b}{c^2+1}\)
\(=\dfrac{b-c}{a^2+ab+bc+ac}+\dfrac{c-a}{b^2+ab+bc+ca}+\dfrac{a-b}{c^2+ab+bc+ca}\)
\(=\dfrac{b-c}{a\left(a+b\right)+c\left(a+b\right)}+\dfrac{c-a}{b\left(a+b\right)+c\left(a+b\right)}+\dfrac{a-b}{c\left(c+a\right)+b\left(a+c\right)}\)
\(=\dfrac{b-c}{\left(a+c\right)\left(a+b\right)}+\dfrac{c-a}{\left(b+c\right)\left(a+b\right)}+\dfrac{a-b}{\left(b+c\right)\left(a+c\right)}\)
\(=\dfrac{\left(b-c\right)\left(b+c\right)+\left(c-a\right)\left(a+c\right)+\left(a-b\right)\left(a+b\right)}{\left(a+c\right)\left(a+b\right)\left(b+c\right)}\)
\(=\dfrac{b^2-c^2+c^2-a^2+a^2-b^2}{\left(a+b\right)\left(b+c\right)\left(c+a\right)}=0\)
\(x^3+x^2-x+2=x^3+2x^2-x^2-2x+x+2=x^2\left(x+2\right)-x\left(x+2\right)+\left(x+2\right)=\left(x+2\right)\left(x^2-x+1\right)\)
cos300=\(\dfrac{P}{T}\)
\(\Rightarrow T=\dfrac{P}{cos30^0}=\dfrac{80\sqrt{3}}{3}N\)
tan300\(\dfrac{N}{P}\Rightarrow N=P.tan30^0=\dfrac{40\sqrt{3}}{3}N\)