balancexv2174 balancexv2174
  • 02-11-2020
  • Mathematics
contestada

When eleven lines are drawn on a plane, with no three concurrent and no two parallel, how many open regions are produced?

Respuesta :

mhanifa
mhanifa mhanifa
  • 13-11-2020

Answer:

  • 22

Step-by-step explanation:

We are considering for non-parallel lines and no three intersections

Let's see how many open areas are produced by the lines on a plane

  • 1 line = 2 open areas
  • 2 line = 4 open areas
  • 3 lines = 6 open areas and 1 closed region
  • 4 lines = 8 open areas and 3 closed regions
  • 5 lines = 10 open areas and 6 closed regions

and so on

We see a pattern of 2n open areas for n lines, so

  • 11 lines = 22 open areas
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