CONCURS #025
28.11.2022, ora 20:00Problema 1 [256 puncte]
$Calculati\ \sqrt{1}+\sqrt{4}+\sqrt{9}+...+\sqrt{100}.$
Problema 2 [312 puncte]
$Calculati\ \frac{1}{2}+\frac{1}{3}+\frac{1}{6}.$
Problema 3 [368 puncte]
$Aflati\ numarul\ divizorilor\ lui\ 540$
Problema 4 [424 puncte]
$Triunghiul\ ABC\ are\ aria\ egala\ cu\ 246,\ iar\ G\ este\ centrul\ sau\ de\ greutate.$
$Aflati\ aria\ triunghiului\ AGB.$
Problema 5 [480 puncte]
$Patratul\ ABCD\ are\ aria\ 360.\ Daca\ M\ si\ N\ sunt\ mijloacele\ laturilor\ AB,\ respectiv\ BC,$
$aflati\ aria\ triunghiului\ DMN.$
Problema 6 [536 puncte]
$Aflati\ cate\ numere\ naturale\ de\ doua\ cifre\ sunt\ divizibile\ cu\ 2\ sau\ cu\ 3.$
Problema 7 [592 puncte]
$Daca\ x\cdot (x-5)=184\ si\ y\cdot (y-5)=184,\ iar\ x\ si\ y\ distincte,\ calculati\ x^{2}+y^{2}.$
Problema 8 [648 puncte]
$Cate\ solutii\ are\ ecuatia\ |x-1|+|y-1|+|z-1|+|w-1|=2,\ unde\ x,y,z,w\in \mathbb{Z}?$