Question

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

a+b+c+d+e = 162
b=a:2⇒ a=2b

c= (a+b) :2 ⇒ 2c = a+b = 2b+b=3b⇒ 2c= 3b ⇒ c=3b/2

d = (a+b+c) :2 ⇒ 2d = a+b+c⇒ 2d = 2b +b+3b/2 = 3b+3b/2= 9b/2
⇒d= 9b/4

e= (a+b+c+d) :2⇒ 2e=a+b+c+d = 2b + b + 3b/2 +9b/4
2e = 3b + 3b/2 + 9b/4 = 12b/4 + 6b/4 + 9b/4 = 27b/4
e= 27b/8

2b+b+3b/2 +9b/4 + 27b/8=162
24b /8 + 12b/8 + 18b/8 +27b/8 = 162
81b/8 = 162
81b= 162*8
b= 162*8:81 ⇒ b=16
a=32
c=3*16:2=24⇒ c=24
d=9*16:4=36⇒ d=36
e=27*16:8=54⇒ e=54