One hundred meters of fencing is available to enclose a rectangular area next to a river. Give a function A that can represent the area that can be enclosed in terms of x.
Function : A =
Answer
x2 +
Answer
x
Hard to say. What's x supposed to be?
To find a function A that represents the area that can be enclosed in terms of x, we can start by visualizing the problem. We are given 100 meters of fencing, which is used to enclose a rectangular area next to a river. Let's assume that the side parallel to the river has a length of x meters.
Since we are enclosing a rectangular area, we need two equal sides perpendicular to the river and two sides parallel to the river. Since the total length of fencing is 100 meters, the two sides perpendicular to the river each have a length of (100 - 2x) / 2 meters.
The area of a rectangle is given by multiplying its length and its width. In this case, the length of the rectangle is x meters and the width is (100 - 2x) / 2 meters.
Therefore, the function A that represents the area that can be enclosed in terms of x is:
A = x * (100 - 2x) / 2
Simplifying this function gives:
A = (100x - 2x^2) / 2
A = 50x - x^2
So the function A = 50x - x^2 represents the area that can be enclosed based on the length x.