Question

va rog sa faceti ex 2 si 5 din exercitiile de mai sus
DAU COROANA !​

Answer 1

 

$\displaystyle\bf\\2)\\(a,~b,~c)~d.p.~(3;~6;~9)\\\\\frac{a}{3}=\frac{b}{6}=\frac{c}{9}=k\\\\a=3k\\b=6k\\c=9k\\a+b+c=72\\3k+6k+9k=72\\18k=72\\\\k=\frac{72}{18}\\\\k=4\\\\a=3\times4=12\\b=6\times4=24\\c=9\times4=36\\\\Descompunem~numerele:\\12=2^2\times3\\24=2^3\times3\\36=2^2\times3^2\\\\cmmdc=2^2\times3~~~(puterile~comune~la~exponentul~cel~mai~mic)\\cmmdc=4\times3=12\\\\cmmmc=2^3\times3^2~~~(toate~puterile~la~exponentul~cel~mai~mare)\\cmmmc=8\times9=72$

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$\displaystyle\bf\\5)\\a)~Complementul~unghiului~de~16^o37'~este:\\90^o-16^o37'=\\=89^o60'-16^o37'=73^o23'\\\\b) \textbf{Bisectoarea este dreapta care imparte un unghi in 2 parti egale.}\\\\c)~\textbf{Triunghiu echilateral este triunghiul care are toate laturile egale.}\\\\d)~\textbf{Doua cercuri sunt congruente atunci cand au razele egale.}\\\\e)~|-3|=3$

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$\displaystyle\bf\\f)\\\\\frac{x}{y}=\frac{2}{3}~~~Cat~este~\frac{2x+1}{3y+2}~?\\\\x=2k~~si~~y=3k\\\\\frac{2x+1}{3y+2}=\frac{2\times2k+1}{3\times3k+2}=\frac{4k+1}{9k+2}\\\\k~~nu~se~poate~simplifica.\\Eroarea~vine~de~la~o~greseala~de~transcriere~a~fractiei.\\\\Daca~fractia~ar~fi:~~~\frac{2x+y}{3y+x}~atunci~se~poate~rezolva.$

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$\displaystyle\bf\\Rezolvare:\\\\\frac{2x+y}{3y+x}=~~(Simplificam~fortat~fractia~cu~y)\\\\\\=\frac{~~\dfrac{2x+y}{y}~~}{\dfrac{3y+x}{y}}=\\\\\\=\frac{~~\dfrac{2x}{y}+\dfrac{y}{y}~~}{\dfrac{3y}{y}+\dfrac{x}{y}}=\frac{~~2\times\dfrac{x}{y}+\dfrac{y}{y}~~}{3\times\dfrac{y}{y}+\dfrac{x}{y}}=\frac{~~2\times\dfrac{2}{3}+1~~}{3\times1+\dfrac{2}{3}}=\\\\\\=\frac{~~\dfrac{4}{3}+1~~}{3+\dfrac{2}{3}}=\frac{~~\dfrac{4+1\times3}{3}~~}{\dfrac{3\times3+2}{3}}=\frac{~~\dfrac{7}{3}~~}{\dfrac{11}{3}}=\frac{7}{11}$

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$\displaystyle\bf\\g)\\2x+1=0\\3y-2=7\\x\cdot y=?\\Rezolvare:\\2x+1=0\\2x=-1\\\\x=-\frac{1}{2}\\\\3y-2=7\\3y=7+2\\3y=9\\y=\frac{9}{3}=3\\x\cdot y=-\frac{1}{2}\times3=-\frac{3}{2}\\\\\\h)\\Comparam~numerele:\\-2\sqrt{3}~~cu~~-3\sqrt{2}\\\\Ridicam~la~puterea~a~2-a~partea~fara~semn~a~numerelor.\\\\-\Big(2\sqrt{3}\Big)^2=-12\\\\-\Big(3\sqrt{2}\Big)^2=-18\\\\-12 >-18\\\\-2\sqrt{3}~>~-3\sqrt{2}\\\\\implies~~Afirmatia~din~enunt~este~FALSA$