Respuesta :
Answer:
[tex]C(w) =\dfrac{3600}{w}+36w[/tex]
Step-by-step explanation:
Let l be the length of rectangular field and w be the width of rectangular field.
Area = 100 square meter
Area of rectangular field
=[tex]=\text{Lenght}\times \text{Breadth}\\\Rightarrow l\times w = 100\\\\\Rightarrow l = \dfrac{100}{w}[/tex]
Cost of fencing = 18 dollars per meter
Perimeter of rectangle
[tex]= 2\times \text{(Length + Width)}\\=2(l + w)[/tex]
Total cost =
[tex]\text{Cost of fencing}\times \text{Perimeter of fileld}\\=18\times 2(l+w)\\\\=18\times 2(\dfrac{100}{w} + w)\\\\=36(\dfrac{100 + w^2}{w})\\\\\Rightarrow C(w) =\dfrac{3600}{w}+36w\\\\\text{where w is the width of the field}[/tex]
is the required cost function.
The total cost of the fence in terms of the width of the field is [tex]\rm C = \dfrac{3600}{w}+36w[/tex].
Given that
A rectangular field is to have an area of 100m2 and is to be surrounded by a fence.
The cost C of the fence is 18 dollars per meter in length.
We have to determine
The total cost of the fence in terms of the width of the field (use the variable 'w' for width.
According to the question
Let the total cost of the fence of the width field by W.
Area of the rectangular fence = 100 square meters.
The cost C of the fence is 18 dollars per meter in length.
Area of the rectangular field;
[tex]\rm Area = Length \times Width\\ \\ 100 = Length \times W\\ \\ L = \dfrac{100}{W}[/tex]
The perimeter of the rectangle;
[tex]\rm Perimeter = 2 \times (Length + Width)\\ \\ Perimeter = 2(L+W)[/tex]
The total cost of the fence in terms of the width of the field is,
[tex]\rm Total \ cost = Cost \ of \ fence \times Perimeter \ of \ field\\ \\ C= 18 \times 2(l+w)\\ \\ C= 18 \times 2(\dfrac{100}{w}+w)\\ \\ C = 18 \times 2(\dfrac{100+w^2}{w})\\ \\ C= 36(\dfrac{100+w^2}{w})\\ \\C = \dfrac{3600}{w}+36w[/tex]
Hence, the total cost of the fence in terms of the width of the field is [tex]\rm C = \dfrac{3600}{w}+36w[/tex].
To know more about Equation click the link given below.
https://brainly.com/question/26176817
