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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.

Respuesta :

Answer:

C(x) = [tex]\$3.50(\frac{x^2+7200}{x})[/tex]

Step-by-step explanation:

Data provided in the question:

Area of the field = 3600 square feet

Fencing charges = $3.50 per foot

Let the side along the river be 'x' feet and the other side of the 'B'

now,

Area of rectangle = Bx = 3600 square feet

or

B = [tex]\frac{3600}{x}[/tex] feet

and total length to be fenced = x + 2B

therefore,

Total cost of fencing = Fencing charges × total length to be fenced

or

Total cost of fencing = $3.50 × ( x + 2B )

substituting the value of B from (1)

Total cost of fencing, C(x) = [tex]\$3.50(x+2\times\frac{3600}{x})[/tex]

or

C(x) = [tex]\$3.50(\frac{x^2+7200}{x})[/tex]

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