1) ĐKXĐ: \(x\ge0\)

\(pt\Leftrightarrow2x=25\Leftrightarrow x=\dfrac{25}{2}\left(tm\right)\)

2) \(=\sqrt{\dfrac{\dfrac{1}{4}}{9}}=\dfrac{\dfrac{1}{2}}{3}=\dfrac{1}{6}\)

3) \(=\sqrt{225a^2}=15a\left(do.a\ge0\right)\)

4) \(=2y^2.\dfrac{x^2}{2\left|y\right|}=\left[{}\begin{matrix}x^2y\left(y>0\right)\\-x^2y\left(y< 0\right)\end{matrix}\right.\)

a) \(\Rightarrow\left|x\right|=\dfrac{16}{5}\Rightarrow\left[{}\begin{matrix}x=\dfrac{16}{5}\\x=-\dfrac{16}{5}\end{matrix}\right.\)

b) \(\Rightarrow\left[{}\begin{matrix}x+1=6\\x+1=-6\end{matrix}\right.\)\(\Rightarrow\left[{}\begin{matrix}x=5\\x=-7\end{matrix}\right.\)

c) \(\Rightarrow S=\varnothing\left(do.\left|x\right|\ge0\forall x\right)\)

d) \(\Rightarrow\left|x+\dfrac{3}{4}\right|=\dfrac{1}{2}\Rightarrow\left[{}\begin{matrix}x+\dfrac{3}{4}=\dfrac{1}{2}\\x+\dfrac{3}{4}=-\dfrac{1}{2}\end{matrix}\right.\)\(\Rightarrow\left[{}\begin{matrix}x=-\dfrac{1}{4}\\x=-\dfrac{5}{4}\end{matrix}\right.\)

e) \(\Rightarrow\left|x+\dfrac{4}{15}\right|=\dfrac{8}{5}\Rightarrow\left[{}\begin{matrix}x+\dfrac{4}{15}=\dfrac{8}{5}\\x+\dfrac{4}{15}=-\dfrac{8}{5}\end{matrix}\right.\)

\(\Rightarrow\left[{}\begin{matrix}x=\dfrac{4}{3}\\x=-\dfrac{28}{15}\end{matrix}\right.\)

\(\Leftrightarrow2x=50\Leftrightarrow x=25\)

Diện tích tiếp xúc 2 bàn chân là: \(S=2\times2=4\left(cm^2\right)=0,0004\left(m^2\right)\)

Áp suất bạn đó tác dụng lên sàn nhà:

\(p=\dfrac{F}{S}=\dfrac{P}{S}=\dfrac{10m}{S}=\dfrac{10.40}{0,0004}=1000000\left(Pa\right)\)

\(A=P.t=100.30.4.60.60=43200000\left(J\right)\)

1) Ta có: \(\Rightarrow a//b\Rightarrow\widehat{A_1}+\widehat{B_2}=180^0\)(trong cùng phía)

\(\Rightarrow\widehat{B_2}=180^0-132^0=48^0\)

2) \(\dfrac{a}{2}=\dfrac{b}{3}=\dfrac{c}{5}=k\Rightarrow\left\{{}\begin{matrix}a^2=\left(2k\right)^2=4k^2\\b^2=\left(3k\right)^2=9k^2\\c^2=\left(5k\right)^2=25k^2\end{matrix}\right.\)

\(\Rightarrow a^2+b^2+c^2=4k^2+9k^2+25k^2\Rightarrow38k^2=152\)

\(\Rightarrow k^2=4\Rightarrow k=\pm2\)

\(\Rightarrow a=2k=\pm4\)

\(R_{23}=\dfrac{R_2.R_3}{R_2+R_3}=\dfrac{8.24}{8+24}=6\left(\Omega\right)\)

\(R_{tđ}=R_1+R_{23}=14+6=20\left(\Omega\right)\)

\(I=\dfrac{U}{R_{tđ}}=\dfrac{24}{20}=1,2\left(A\right)\)

\(P=U.I=1,2.24=28,8\left(W\right)\)

ĐKXĐ: \(a,b\ne0\)

Áp dụng t/c dtsbn:

\(\dfrac{a}{b}=\dfrac{b}{10}=\dfrac{10}{a}=\dfrac{a+b+10}{b+10+a}=1\)

\(\Rightarrow\left\{{}\begin{matrix}b=10.1=10\\a=\dfrac{10}{1}=10\end{matrix}\right.\)\(\Rightarrow a+b=10+10=20\)

ĐKXĐ: \(b,d\ne0,c\ne\pm d\)

Áp dụng t/c dtsbn:

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

\(\dfrac{a^{2k}+b^{2k}}{c^{2k}+d^{2k}}=\dfrac{a^{2k}-b^{2k}}{c^{2k}-d^{2k}}=\dfrac{a^{2k}+b^{2k}-a^{2k}+b^{2k}}{c^{2k}+d^{2k}-c^{2k}+d^{2k}}=\dfrac{2b^{2k}}{2d^{2k}}=\dfrac{b^{2k}}{d^{2k}}\left(2\right)\)

\(\left(1\right),\left(2\right)\Rightarrow\dfrac{a^{2k}}{c^{2k}}=\dfrac{b^{2k}}{d^{2k}}\Rightarrow\dfrac{a^{2k}}{b^{2k}}=\dfrac{c^{2k}}{d^{2k}}\Rightarrow\dfrac{a}{b}=\pm\dfrac{c}{d}\left(đpcm\right)\)