Question

10 si 13 repede va rog DAU COROANA

Answer 1

$\it 10)\ \ A+B+C=180^o \Rightarrow A+B+40^o=180^o|_{-40^o} \Rightarrow A+B=140^o\ \ \ \ (1)\\\\ \\ \dfrac{A}{B}= \dfrac{2}{3}\ \stackrel{derivare}{\Longrightarrow}\ \dfrac{A}{2}= \dfrac{B}{3}= \dfrac{A+B}{2+3}\ \ \stackrel{(1)}{=}\ \ \dfrac{140^o}{5}=28^o\ \ \ \ (2)\\ \\ \\ (2) \Rightarrow \begin{cases}\it \dfrac{A}{2}=28^o \Rightarrow A=2\cdot28^o=56^o\\ \\ \it \dfrac{B}{3}=28^o \Rightarrow B=3\cdot28^o=84^o\end{cases}$

_____________________________

$\it 13)\ 0,25=\dfrac{1}{4}\\ \\ \\ 0,1(6)=\dfrac{16-1}{90}=\dfrac{15^{(15}}{90}=\dfrac{1}{6}\\ \\ \\ 0,125=\dfrac{125^{(125}}{1000}=\dfrac{1}{8}$

$\it \{E,\ F,\ G\}\ i.\ p.\ \{\dfrac{1}{4},\ \dfrac{1}{6},\ \dfrac{1}{8}\} \Rightarrow \{E,\ F,\ G\}\ d.\ p. \{4,\ 6,\ 8\}\ \Rightarrow\\ \\ \\ \Rightarrow\ \dfrac{E}{4}=\dfrac{F}6{}=\dfrac{G}{8}=\dfrac{E++F+G}{4+6+8}=\dfrac{180^o}{18}=10^o\\ \\ \\ \dfrac{E}{4}=10^o \Rightarrow E=4\cdot10^o=40^o\\ \\ \\ \dfrac{F}{6}=10^o \Rightarrow F=6\cdot10^o=60^o\\ \\ \\ \dfrac{G}{8}=10^o \Rightarrow G=8\cdot10^o=80^o$