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My square orchid garden abuts my house so that the house itself forms the northern boundary. The fencing for the southern boundary costs $4 per foot, and the fencing for the east and west sides costs $2 per foot. Find the total cost of the fencing as a function of the length of a side x.

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Answer:

The total cost of the fencing as a function of side is [tex]C = 8\cdot x[/tex].

Step-by-step explanation:

Dimensionally speaking, the total cost is equal to the product of length and cost per length. Given that orchid garden has a square form, there is only an input: Side ([tex]x[/tex]), measured in feet. Therefore, the total cost of fencing is represented by the following formula:

[tex]C = (c_{west} + c_{south} + c_{east})\cdot x[/tex]

Given that [tex]c_{west} = c_{east} = 2\,\frac{\$}{ft}[/tex] and [tex]c_{south} = \$\,4\,\frac{\$}{ft}[/tex], the total cost of the fencing as a function of side is:

[tex]C = 8\cdot x[/tex]

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