Question

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!

Answer 1

Can you answer the following? Write a formula for the length of the fence (using x & y).

Answer 2

Would that be 3600=x+x+y? The last one C(x)=3.50(x+3600/x) but I am not sure.

Answer 3

It can be rewritten as 3600 = 2x + y.

How would you write y in terms of x?

Answer 4

3600-2x=y?

Answer 5

correct

Answer 6

So does that make the answer the third one down C(x)=3.50(2x+3600/x)?

Answer 7

and is there a number that can be plugged in to check to see if the function is correct?

Answer 8

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.

Answer 9

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:
\[\Large p = x + x + y = 2x + \frac{{3600}}{x}\]

Answer 10

area*

Answer 11

@KJ4UTS

Answer 12

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?

Answer 13

so, we have:
\[\Large C\left( x \right) = 3.50p = ...?\]

Answer 14

so, what is the right option?

Answer 15

@Michele_Laino the right option looks like the third one down C(x)=3.50(2x+3600/x)?

Answer 16

correct!

Answer 17

Thank you :)

Answer 18

:)