\(=\frac{1.2\left(1+2.2+3.3+4.4+5.5\right)}{3.4\left(1+2.2+3.3+4.4+5.5\right)}\)

\(=\frac{1.2}{3.4}=\frac{1}{6}\)

\(\frac{1.2+2.4+3.6+4.8+5.10}{3.2.2+2.3.4.2+3.3.6.2+4.3.8.2+5.3.10.2}\)=\(\frac{1}{3.2+3.2+3.2+3.2+3.2}\)=\(\frac{1}{30}\)

vậy bt trên =\(\frac{1}{30}\)

tk nhé

1. \(\frac{\left(0,6\right)^5}{\left(0.2\right)^5}=\left(\frac{0.6}{0.2}\right)^5=\left(3\right)^5=243\)

2.\(\frac{6^3+3.6^2+3^3}{-13}=\frac{6^2\left(6+3\right)+3^3}{-13}=\frac{6^2.9+3^2.3}{-13}\)

\(\Leftrightarrow\frac{6^2.9+3^2.3}{-13}=\frac{3^2.39}{-13}=3^2.\left(-3\right)=-27\)

Bạn ashura nhầm mũ mẫu dưới rồi

\(\dfrac{1.2+2.4+3.6+4.8+5.10}{3.4+6.8+9.12+12.16+15.20}\)

\(=\dfrac{1.2\left(1^2+2^2+3^2+2^4+2^5\right)}{3.4\left(1^2+2^2+2^3+2^4+2^5\right)}=\dfrac{2}{12}=\dfrac{1}{6}\)

3.5 h)

\(\int x\ln \left (\frac{x+1}{1-x}\right)dx=\int x(\ln(x+1)-\ln (1-x))dx=\int x\ln (x+1)dx-\int x\ln (1-x)dx\)

Xét \(\int x\ln (x+1)dx\). Đặt \(\left\{\begin{matrix} u=\ln (x+1)\\ dv=xdx\end{matrix}\right.\Rightarrow \left\{\begin{matrix} du=\frac{dx}{x+1}\\ v=\frac{x^2}{2}\end{matrix}\right.\)

\(\Rightarrow \int x\ln (x+1)dx=\frac{x^2\ln (x+1)}{2}-\frac{1}{2}\int \frac{x^2}{x+1}dx\)

\(=\frac{x^2\ln (x+1)}{2}-\frac{1}{2}\int \left(x-1+\frac{1}{x+1}\right)dx\)

\(=\frac{x^2\ln (x+1)}{2}-\frac{1}{2}\left(\frac{x^2}{2}-x+\ln |x+1|\right)+c\)

Tương tự, \(\int x\ln (1-x)dx=\frac{x^2\ln (1-x)}{2}-\frac{1}{2}\left (\frac{x^2}{2}+x+\ln |1-x|\right)+c\)

Do đó \(\int x\ln\left (\frac{x+1}{1-x}\right)dx=\frac{x^2\ln \left (\frac{x+1}{1-x}\right)}{2}+x-\frac{1}{2}\ln \left (\frac{x+1}{1-x}\right)+c\)

3.5 g)

Đặt \(\left\{\begin{matrix} u=\ln^2x\\ dv=\sqrt{x}dx\end{matrix}\right.\Rightarrow \left\{\begin{matrix} du=\frac{2\ln x}{x}\\ v=\frac{2\sqrt{x^3}}{3}\end{matrix}\right.\)

\(\Rightarrow \int \sqrt{x}\ln ^2xdx=\frac{2\sqrt{x^3}\ln ^2x}{3}-\frac{4}{3}\int \sqrt{x}\ln xdx\)

Xét \(\int \sqrt{x}\ln xdx\)

Đặt \(\left\{\begin{matrix} m=\ln x\\ dn=\sqrt{x}dx\end{matrix}\right.\Rightarrow \left\{\begin{matrix} dm=\frac{dx}{x}\\ n=\frac{2\sqrt{x^3}}{3}\end{matrix}\right.\)

\(\Rightarrow \int \sqrt{x}\ln xdx=\frac{2\ln x.\sqrt{x^3}}{3}-\frac{2}{3}\int \sqrt{x}dx\)

\(=\frac{2\ln x.\sqrt{x^3}}{3}-\frac{4\sqrt{x^3}}{9}+c\)

Do đó \(\int \sqrt{x}\ln^2xdx=\frac{2\ln ^2x.\sqrt{x^3}}{3}-\frac{8\ln x.\sqrt{x^3}}{9}+\frac{16\sqrt{x^3}}{27}+c\)

3.6c)

Đặt \(\sqrt{2-5x}=t\Rightarrow x=\frac{2-t^2}{5}\)

Khi đó \(\int x\sqrt{2-5x}dx=\int \frac{t(2-t^2)}{5}d\left (\frac{2-t^2}{5}\right)=\frac{2}{25}\int t^2(t^2-2)dt\)

\(=\frac{2}{25}\left (\frac{t^5}{5}-\frac{2t^3}{3}\right)+c\)

3.6 d)

Đặt \(\left\{\begin{matrix} u=\ln (\sin x)\\ dv=\frac{dx}{\cos ^2x}\end{matrix}\right.\Rightarrow \left\{\begin{matrix} du=\frac{\cos x}{\sin x}dx=\frac{dx}{\tan x}\\ v=\tan x\end{matrix}\right.\)

\(\Rightarrow \int \frac{\ln(\sin x)}{\cos^2x}dx=\tan x\ln (\sin x)-\int dx+c=\tan x\ln (\sin x)-x+c\)

a) \(P=U.I\Rightarrow I=\dfrac{P}{U}=\dfrac{75}{220}=\dfrac{15}{44}\left(A\right)\)

b) \(A=P.t=75.30.4.60.60=32400000\left(J\right)=9\left(kWh\right)\)

c) Tiền điện phải trả: \(9.2000=18000\left(đồng\right)\)

Bài 1

a) \(\dfrac{3}{8}+\dfrac{5}{8}=\dfrac{8}{8}=1\)             

b) \(\dfrac{3}{4}+\dfrac{-7}{16}=\dfrac{12}{16}+\dfrac{-7}{16}=\dfrac{5}{16}\)

c) \(2\dfrac{17}{20}-\dfrac{1}{2}+3\dfrac{3}{20}=\dfrac{57}{20}-\dfrac{1}{2}+\dfrac{63}{20}\)\(=\dfrac{47}{20}+\dfrac{63}{20}=\dfrac{110}{20}=\dfrac{11}{2}\)

d) \(\dfrac{2}{3}-2\dfrac{1}{8}+\dfrac{7}{24}=\dfrac{2}{3}-\dfrac{17}{8}+\dfrac{7}{24}=\dfrac{16}{24}-\dfrac{51}{24}+\dfrac{7}{24}=\dfrac{16-51+7}{24}=\dfrac{-28}{24}=\dfrac{-7}{6}\)

Bài 2 :

a) \(x-\dfrac{7}{4}=3\)

\(x=3+\dfrac{7}{4}\)

\(x=\dfrac{19}{4}\)

b) \(x-\dfrac{1}{2}=\dfrac{4}{16}\cdot\dfrac{8}{3}\)

   \(x-\dfrac{1}{2}=\dfrac{2}{3}\)

  \(x=\dfrac{2}{3}+\dfrac{1}{2}\)

 \(x=\dfrac{5}{6}\)

c) \(\dfrac{15}{11}\div x=\dfrac{45}{22}\)

             \(x=\dfrac{15}{11}\div\dfrac{45}{22}\)

            \(x=\dfrac{2}{3}\)

d) \(\dfrac{8}{3}-2x=\dfrac{8}{5}-1\)

    \(\dfrac{8}{3}-2x=\dfrac{3}{5}\)

           \(2x=\dfrac{8}{3}-\dfrac{3}{5}\)

           \(2x=\dfrac{31}{15}\)

            \(x=\dfrac{31}{15}\div2\)

           \(x=\dfrac{31}{30}\)

vì ít hơn anh 10 tuổi nên em hiện nay đang là 10 tuổi

bạn ơi đề hỏi gì vậy để mình trả lời nhé

hỏi năm nay em bao nhiêu tuổi