Question

A rancher plans to fence a rectangular pasture adjacent to a river. The rancher has 100 meters of fence, and no fencing is needed along the river.

Write the area A as a function of x, the length of the side of the pasture parallel to the river. What is the feasible domain of A?

Answer 1

The area A of the rectangular pasture can be written as a function of x: A = 100x - 2x^2. The feasible domain of A is 0 <= x <= 50.

Step-by-step explanation:

To write the area A as a function of x, we need to consider the dimensions of the rectangular pasture. Let's assume the length of the pasture parallel to the river is x meters. Since the pasture is adjacent to the river, the width of the pasture will be perpendicular to the river and can be represented by 100 - 2x (since we don't need fencing along the river). The area of the rectangular pasture is then A = x(100 - 2x) = 100x - 2x^2.

The feasible domain of A refers to the possible values of x that make sense in the context of the problem. In this case, x must be between 0 and 50 (half the length of the fence), otherwise, the width of the pasture would be negative or greater than 100, which is not feasible. So, the feasible domain of A is 0 <= x <= 50.