anonymous
  • anonymous
looking at a sequence of regular pentagons where each side has a lenth of 2 - one set right next to the other, in a row - how do i figure out an alg equation to represent perimeter (y) of each phase of the pattern? (x represents phase number)
Mathematics
  • Stacey Warren - Expert brainly.com
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jamiebookeater
  • jamiebookeater
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DebbieG
  • DebbieG
I'm having trouble picturing this. Do adjacent pentagons share a side?
anonymous
  • anonymous
|dw:1377711758080:dw|yes
DebbieG
  • DebbieG
OK, so in phase 1 you have 5 sides of length 2 each. Then in each additional phase, you add on 4 more sides of length 2 each, right? Another way to think of it is that the pattern for the total perimeter starts at 10 when x=1, and then from there each time you increment x by 1, you increment y by 8.... (2+8) + 8 + 8 + 8..... etc. Do you see a pattern there, that you can translate into an equation of x?

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DebbieG
  • DebbieG
(Where you would limit the domain, x, to positive integers.)
anonymous
  • anonymous
These are my options: I thought I knew the answer, but now the way you are explaining it I think I was wrong. y = 2x + 3, y = 3x + 2, y = 3x + 5, y = 6x + 4,
DebbieG
  • DebbieG
Hmmm. I think maybe I don't understand what it is asking, because none of those look right to me. Oh wait.... is y supposed to be the total outer perimeter only? I was thinking it was the total length of the "edges".... with one edge "shared" for each additional pentagon. But if it is OUTER edge only, that will change things....
DebbieG
  • DebbieG
Which IS what "perimeter" should mean....|dw:1377713936482:dw|
anonymous
  • anonymous
yea thats what the question is asking
DebbieG
  • DebbieG
OK, then I apologize, my first post was modeling something else. Now look at the pattern that you get. For x=1 you have 5 sides, so y=2(5)=10 For x=2, you add only 3 sides, because the "shared" side isn't counted for either figure. so 8 sides total, and you have y=2(8)=16. for x=3 and beyond, you will keep adding 3 sides each time.... so you have: x=3 means 11 sides so 2*11=22 x=4 means 14 sides so 2*14=28 etc. so you can use those points to find which equation works: (1, 10) (2, 16) (3, 22) (4, 28) etc... and you should be able to see which answer is correct. :)
DebbieG
  • DebbieG
In fact, you can just calculate slope (since all the equations are linear) and that should be enough to tell which is right.

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