\(A=2\left(x^3-y^3\right)-3\left(x+y\right)^2\)

\(A=2\left[\left(x-y\right)^3+3xy\left(x-y\right)\right]-3\left[\left(x-y\right)^2+4xy\right]\)

\(A=2\left[2^3+3xy.2\right]-3\left[2^2+4xy\right]\)

\(A=2\left[28+6xy\right]-3\left[4+4xy\right]\)

\(A=56+12xy-12-12xy=56-12=44\)

\(BC^2=AB^2+AC^2=36+64=100=10^2\)

\(\Rightarrow BC=10\left(cm\right)\)

\(SinB=\dfrac{AC}{BC}=\dfrac{8}{10}=\dfrac{4}{5}\Rightarrow SinC=Sin\left(90-B\right)=CosB=\dfrac{3}{5}\)

\(CosB=\dfrac{AB}{BC}=\dfrac{6}{10}=\dfrac{3}{5}\Rightarrow CosC=Cos\left(90-B\right)=SinB=\dfrac{4}{5}\)

\(tanB=\dfrac{AC}{AB}=\dfrac{8}{6}=\dfrac{4}{3}\Rightarrow tanC=tan\left(90-B\right)=CotB=\dfrac{3}{4}\)

\(CotB=\dfrac{AB}{AC}=\dfrac{6}{8}=\dfrac{3}{4}\Rightarrow cotC=cot\left(90-B\right)=tanB=\dfrac{4}{3}\)

5,055...X_X

\(\dfrac{6}{7}< 1< \dfrac{7}{4}\Rightarrow0>-\dfrac{6}{7}>-\dfrac{7}{4}\left(1\right)\)

\(\dfrac{8}{13}=\dfrac{8.3}{13.3}=\dfrac{24}{39}< 0< \dfrac{2}{3}=\dfrac{2.13}{3.13}=\dfrac{26}{39}\left(2\right)\)

\(\left(1\right),\left(2\right)\Rightarrow-\dfrac{7}{4}< -\dfrac{6}{7}< 0< \dfrac{8}{13}< \dfrac{2}{3}\)

1,2 \(\times\) 1,4 \(\times\) 0,8 = 1,344 (m³)

Thời gian để vòi chảy đầy bể là:

   5 giờ 36 phút - 4 giờ = 1 giờ 36 phút

  Đổi 1 giờ 36 phút = 96 phút

         1,344 m³ = 1344 l

 Mỗi phút vòi chảy được số lít là: 

         1344 : 96 = 14 (l)

Đáp số: 

a, 4\(\dfrac{3}{8}\) + 5\(\dfrac{2}{3}\)

= \(\dfrac{35}{8}\) + \(\dfrac{17}{3}\)

= \(\dfrac{105}{24}\) + \(\dfrac{136}{24}\)

= \(\dfrac{241}{24}\)

b, 2\(\dfrac{3}{8}\) + 3\(\dfrac{6}{7}\) - 1\(\dfrac{1}{4}\)

= \(\dfrac{19}{8}\) + \(\dfrac{27}{7}\) - \(\dfrac{5}{4}\)

= \(\dfrac{133}{56}\) + \(\dfrac{216}{56}\) - \(\dfrac{70}{56}\)

= \(\dfrac{279}{56}\)

Đúng

Xuất sắc

100 điểm

\(\left(x+y+z\right).\left(\dfrac{1}{x+y}+\dfrac{1}{y+z}+\dfrac{1}{x+z}\right)=\dfrac{2017}{672}\)

\(\Rightarrow\left(\dfrac{x+y+z}{x+y}+\dfrac{x+y+z}{y+z}+\dfrac{x+y+z}{x+z}\right)=\dfrac{2017}{672}\)

\(\Rightarrow1+\dfrac{z}{x+y}+1+\dfrac{x}{y+z}+1+\dfrac{y}{x+z}=\dfrac{2017}{672}\)

\(\Rightarrow3+\dfrac{x}{y+z}+\dfrac{y}{x+z}+\dfrac{z}{x+y}=\dfrac{2017}{672}\)

\(\Rightarrow\dfrac{x}{y+z}+\dfrac{y}{x+z}+\dfrac{z}{x+y}=\dfrac{2017}{672}-3=\dfrac{2017}{672}-\dfrac{2016}{672}=\dfrac{1}{672}\)

\(\Rightarrow C=\dfrac{1}{672}\)