CONCURS #023
16.03.2022, ora 20:00Problema 1 [300 puncte]
$Calculati\ suma\ primelor\ 100\ de\ zecimale\ ale\ numarului\ \frac{20}{3}.$
Problema 2 [400 puncte]
$Calculati\ suma\ solutiilor\ ecuatiei\ |2\cdot x-7|=99.$
Problema 3 [500 puncte]
$Daca\ |x-9|+|y-16|=0,\ aflati\ media\ geometrica\ a\ numerelor\ x\ si\ y.$
Problema 4 [600 puncte]
$Un\ patrat\ are\ diagonala\ de\ lungime\ 24\cdot \sqrt{2}.\ Aflati\ aria\ patratului.$
Problema 5 [700 puncte]
$In\ triunghiul\ ABC\ avem\ AB=12,\ AC=18,\ BC=24,\ iar\ AD\ bisectoare,\ $
$D \in BC.\ Aflati\ BD. $
Problema 6 [800 puncte]
$Aflati\ numarul\ divizorilor\ lui\ 33^{33}.$
Problema 7 [900 puncte]
$O\ fetita\ ia\ dintr-o\ cutie\ de\ fiecare\ data\ mai\ multe\ bomboane\ decat\ luase\ data\ precedenta.$$In\ total\ in\ 5\ dati\ ea\ a\ luat\ 31\ bomboane.\ Cate\ bomboane\ a\ luat\ a\ patra\ oara\ daca\ prima$
$data\ a\ luat\ de\ trei\ ori\ mai\ putine\ decat\ a\ cincea\ oara?$
Problema 8 [1000 puncte]
$Determinati\ cel\ mai\ mic\ numar\ natural\ A\ astfel\ incat\ exista\ exact\ 2022\ numere$$naturale\ B,\ astfel\ incat\ 2\leq \frac{A}{B} \leq 3.$