A farmer plans to build a 250 square feet rectangular chicken pen adjacent toher chicken coop. The coop wall will form one side of the fence but she needs tofence the otherthreesides. The fencing costs$10 per linear foot. Her math-whizdaughter determines that if the side of pen parallel to the coop wall isxft long,then the cost in dollars of fencing will be given by the functionC(x) = 10x+5000x.(a) [4 points] Use a diagram and the information provided above toshowthatthe cost function isC(x) = 10x+5000x

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oeerivona oeerivona · Answer 1 · 2021-10-04T12:00:39+02:00

The perimeter of a rectangle is the sum of twice the width and twice the length

The function that gives the cost of fencing is given from the graph by the following function;

The reason why the above function is correct is as follows:

Question: Please find attached the required diagram used to obtain the function;

The given parameters are;

Area of the square rectangle = 250 m²

Length of the side of the pen wall parallel to the coop = x

Cost of fencing per foot, c = $10

The function for the cost in dollars of fencing, C(x) = 10x + 5000

Solution:

Let y represent the length of the other side, we have;

x × y = 250

Therefore;

[tex]P = x + 2 \times \dfrac{250}{x} = x + \dfrac{500}{x}[/tex]

The total cost of the fencing, C(x) = c × P

Therefore;

[tex]\mathbf{C(x)} = 10 \times \left(x + \dfrac{500}{x} \right) = 10 \cdot x + \dfrac{5,000}{x}[/tex]

Learn more about functions here:

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