Question

Stii,raspunzi,nu stii te uiti si inveti.
O semidreapta[OA se roteste in jurul punctului O,parcurgand in 5 secunde un unghi de 162grade.
Cate grade au unghiurile parcurse in fiecare secunda daca fiecare unghi reprezinta jumatate din suma unghiurilor precedenta

Answer 1

Notez cu a,b,c,d si e masurile celor 5 unghiuri (in aceasta ordine).

$a+b+c+d+e=162~grade \\ \\ a=a \\ b= \frac{a}{2} \\ c= \frac{a+b}{2}= \frac{a+ \frac{a}{2} }{2}= \frac{a}{2}+ \frac{a}{4} \\ d= \frac{a+b+c}{2}= \frac{a+ \frac{a}{2}+ \frac{a}{2}+ \frac{a}{4} }{2}= a+ \frac{a}{8} \\ e= \frac{a+b+c+d}{2}= \frac{a+ \frac{a}{2}+ \frac{a}{2}+ \frac{a}{4} + a+\frac{a}{8} }{2}=a+ \frac{a}{2}+ \frac{a}{8}+ \frac{a}{16}$

$a+b+c+d+e=162 \Leftrightarrow \\ \Leftrightarrow a+ \frac{a}{2}+ \frac{a}{2}+ \frac{a}{4}+a+ \frac{a}{8}+ a+\frac{a}{2}+ \frac{a}{8} + \frac{a}{16} =162~\Leftrightarrow \\ \Leftrightarrow a(1+ \frac{1}{2} + \frac{1}{2}+ \frac{1}{4}+1+ \frac{1}{8}+1+ \frac{1}{2}+ \frac{1}{8}+ \frac{1}{16}=162~\Leftrightarrow \\ \Leftrightarrow a* \frac{81}{16}=162 \Rightarrow \boxed{a=32~(grade)}.$

Primul unghi are 32 de grade, al doilea 16, al treilea 24, al patrulea 36 si al cincilea 54.