KJ4UTS
  • KJ4UTS
A farmer wants to fence in a rectangular field that encloses 3600 square feet. One side of the field is along a river and does not require fencing. The fencing costs $3.50 per foot. Express the total cost C(x) of the fencing (in dollars) as a function of x. Please explain. Thank you!
Mathematics
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SOLVED
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katieb
  • katieb
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KJ4UTS
  • KJ4UTS
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anonymous
  • anonymous
Can you answer the following? Write a formula for the length of the fence (using x & y).
KJ4UTS
  • KJ4UTS
Would that be 3600=x+x+y? The last one C(x)=3.50(x+3600/x) but I am not sure.

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More answers

anonymous
  • anonymous
It can be rewritten as 3600 = 2x + y. How would you write y in terms of x?
KJ4UTS
  • KJ4UTS
3600-2x=y?
anonymous
  • anonymous
correct
KJ4UTS
  • KJ4UTS
So does that make the answer the third one down C(x)=3.50(2x+3600/x)?
KJ4UTS
  • KJ4UTS
and is there a number that can be plugged in to check to see if the function is correct?
anonymous
  • anonymous
I'm sorry I knew how to do this, but at the moment I'm blanking out. If it comes to me, I'll try to post.
Michele_Laino
  • Michele_Laino
Hint: the are of your field is: xy=3600, so we have: y=3600/x then the perimeter \( \large p \) that has to be fenced is: \[\Large p = x + x + y = 2x + \frac{{3600}}{x}\]
Michele_Laino
  • Michele_Laino
area*
Michele_Laino
  • Michele_Laino
@KJ4UTS
anonymous
  • anonymous
I should have asked earlier what is the formula for the area, to which the answer is A = l x w => 3600 = x(y) So y = 3600/x So I think that you are correct Perimeter = 2x + (3600/x) So cost = 3.5 [2x (3600/x)] Can someone verify this?
Michele_Laino
  • Michele_Laino
so, we have: \[\Large C\left( x \right) = 3.50p = ...?\]
Michele_Laino
  • Michele_Laino
so, what is the right option?
KJ4UTS
  • KJ4UTS
@Michele_Laino the right option looks like the third one down C(x)=3.50(2x+3600/x)?
Michele_Laino
  • Michele_Laino
correct!
KJ4UTS
  • KJ4UTS
Thank you :)
Michele_Laino
  • Michele_Laino
:)

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