a) \(R_{12}=R_1+R_2=1+2=3\left(\Omega\right)\)

\(R_{tđ}=\dfrac{R_{12}.R_3}{R_{12}+R_3}=\dfrac{3.3}{3+3}=1,5\left(\Omega\right)\)

b) \(U=U_{12}=U_3=6V\)

\(I_{12}=I_1=I_2=\dfrac{U_{12}}{R_{12}}=\dfrac{6}{3}=2\left(A\right)\)

\(I_3=\dfrac{U_3}{R_3}=\dfrac{6}{3}=2\left(A\right)\)

c) \(P=\dfrac{U^2}{R}=\dfrac{6^2}{1,5}=24\left(W\right)\)

\(500cm^2=0,05m^2\)

\(p=\dfrac{F}{S}\Rightarrow F=p.S=500.0,05=25\left(N\right)\Rightarrow P=F=25N\)

\(P=10m\Rightarrow m=\dfrac{P}{10}=\dfrac{25}{10}=2,5\left(kg\right)\)

\(A=2\left(1+2\right)+2^3\left(1+2\right)+...+2^{2009}\left(1+2\right)=2.3+2^3.3+...+2^{2009}.3=3\left(2+2^3+....+2^{2009}\right)⋮3\)

Điện trở của bếp điện:

\(P=\dfrac{U^2}{R}\Rightarrow R=\dfrac{U^2}{P}=\dfrac{110^2}{400}=30,25\left(\Omega\right)\)

Nhiệt lượng cần thiết để đun sôi lượng nước trên:

\(Q=mc\Delta t=1.4200.\left(100-10\right)=378000\left(J\right)\)

\(\Rightarrow\left(x^2-2x+2-1\right)^2=0\Rightarrow\left(x^2-2x+1\right)^2=0\Rightarrow\left[\left(x-1\right)^2\right]^2=0\Rightarrow x-1=0\Rightarrow x=1\)

a) Áp dụng định lý Pytago:

\(BC^2=AB^2+AC^2\Rightarrow AC=\sqrt{BC^2-AB^2}=\sqrt{10^2-6^2}=8\left(cm\right)\)

Áp dụng tslg:

\(cosB=\dfrac{AB}{BC}=\dfrac{6}{10}=\dfrac{3}{5}\)

b) Áp dụng HTL :

\(\dfrac{1}{AH^2}=\dfrac{1}{AB^2}+\dfrac{1}{AC^2}\Rightarrow AH=\sqrt{\dfrac{1}{\dfrac{1}{AB^2}}+\dfrac{1}{\dfrac{1}{AC^2}}}=\sqrt{\dfrac{1}{\dfrac{1}{6^2}+\dfrac{1}{8^2}}}=4,8\left(cm\right)\)

Áp dụng tslg:

\(cosBAH=\dfrac{AH}{AB}=\dfrac{4,8}{6}\Rightarrow\widehat{BAH}\approx37^0\)

\(=x\left(x-5\right)-\left(x-5\right)=\left(x-5\right)\left(x-1\right)\)

\(\left(a+b+c\right)^2=a^2+b^2+c^2\Leftrightarrow a^2+b^2+c^2+2\left(ab+bc+ac\right)=a^2+b^2+c^2\)

\(\Leftrightarrow2\left(ab+bc+ac\right)=0\Leftrightarrow ab+bc+ac=0\Leftrightarrow bc=-ab-ac\)

\(\dfrac{a^2}{a^2+2bc}=\dfrac{a^2}{a^2+bc-ac-ab}=\dfrac{a^2}{\left(a-c\right)\left(a-b\right)}\)

CMTT: \(\left\{{}\begin{matrix}\dfrac{b^2}{b^2+2ca}=\dfrac{b^2}{\left(b-a\right)\left(b-c\right)}\\\dfrac{c^2}{c^2+2ab}=\dfrac{c^2}{\left(c-a\right)\left(c-b\right)}=\dfrac{c^2}{\left(a-c\right)\left(b-c\right)}\end{matrix}\right.\)

\(\Rightarrow A=\dfrac{a^2}{\left(a-c\right)\left(a-b\right)}+\dfrac{b^2}{\left(b-a\right)\left(b-c\right)}+\dfrac{c^2}{\left(a-c\right)\left(b-c\right)}=\dfrac{a^2\left(b-c\right)-b^2\left(a-c\right)+c^2\left(a-b\right)}{\left(a-b\right)\left(b-c\right)\left(a-c\right)}=\dfrac{\left(a-b\right)\left(b-c\right)\left(a-c\right)}{\left(a-b\right)\left(b-c\right)\left(a-c\right)}=1\)

\(\Rightarrow2x^2+6x-2x^2=30\Rightarrow6x=30\Rightarrow x=5\)