Non Linear models -> write an algebraic equation...i'm st

[xam2morr]

I have a question that i am having a real hard time solving.

Question: Michelle wishes to create a rectangular dog enclosure along an existing wall. She has 18m of fencing.

Complete the following table of values for all possible rectangular enclosures with whole number dimensions.

I can do that, and it's as follows:

                          Finite 
Length   Width   Area   Differences

  16       1      16                        
  14       2      28        12
  12       3      36         8
  10       4      40         4 
   8       5      40         0 
   6       6      36         4 
   4       7      28        etc.
   2       8      16

So I can pull from that (the finite differences) that the relationship is not linear. Then I had to graph it, which I had no problem with.

The part of this question i had real trouble with was:

Write an equation for area in terms of width (note: width only, no length)

I learned from a teacher that if you do finite differences for the first finite differences and they are constant, the equation will have a squared number in it, (the width) but I am so stumped from there. I was also told that you can make it like a y-mx+b eqution, if the line is linear, which it isn't.

Is there anything I can look at as far as relationships that are between width and area that work every time? Or do I have to just pretty much try and pick out a trend each time? I'm kinda in a pickle, and my exam is in less than two days. Hope you can help. Thank you!

 

[Denis]

since length = 18 less twice the width: area = w(18 - 2w)

As general case, fence = f: area = w(f - 2w)

 

[Mrspi]

Re: Non Linear models -> write an algebraic equation...i'

I have a question that i am having a real hard time solving.

Question: Michelle wishes to create a rectangular dog enclosure along an existing wall. She has 18m of fencing.

Complete the following table of values for all possible rectangular enclosures with whole number dimensions.

I can do that, and it's as follows:

                          Finite 
Length   Width   Area   Differences

  16       1      16                        
  14       2      28        12
  12       3      36         8
  10       4      40         4 
   8       5      40         0 
   6       6      36         4 
   4       7      28        etc.
   2       8      16

So I can pull from that (the finite differences) that the relationship is not linear. Then I had to graph it, which I had no problem with.

The part of this question i had real trouble with was:

Write an equation for area in terms of width (note: width only, no length)

I learned from a teacher that if you do finite differences for the first finite differences and they are constant, the equation will have a squared number in it, (the width) but I am so stumped from there. I was also told that you can make it like a y-mx+b eqution, if the line is linear, which it isn't.

Is there anything I can look at as far as relationships that are between width and area that work every time? Or do I have to just pretty much try and pick out a trend each time? I'm kinda in a pickle, and my exam is in less than two days. Hope you can help. Thank you!

Ok...let w = the width of the enclosure.
Then, the opposite side will also be w.

She has only 18 m of fencing to use, so the remaining FENCED side will have a length of 18 - 2w (the fourth side will be the wall.)

Ok...you have a rectangular enclosure with one side w and the adjacent side (18 - 2w).

the area of the enclosure is
A = w * l
A = w(18 - 2w)
A = 18w - 2w²