Farmer ed has 7000 meters of fencing and wants to enclose a rectangular plot that borders on a river. if farmer ed does not fence the side along the river, what is the largest are that can be enclosed?

Let

x--------> the length side of the rectangular plot (assume side along the river)

y------> the width side of the rectangular plot

we know that

the perimeter of the rectangular plot is equal to

so

Clear variable y

-------> equation

The area of the rectangular plot is

------> equation

substitute equation in equation

we know that

To find the larger area that can be enclosed------> Find the vertex of the quadratic equation

The quadratic equation is a vertical parabola open down

so

the vertex is a maximum

using a graphing tool

see the attached figure

the vertex is the point

that means

For

the largest area is

Find the value of y

the dimensions of the rectangular plot are

therefore

the answer is

The largest area that can be enclosed is

you would need to know all the numbers that are on there

step-by-step explanation:

answer: domain and range mean all possible values of x and y that could be substituted to the inequality. a solution means all possible values that make the inequality statement true. so while the range is still all real numbers, the solution is the shaded area, for which y will always be greater than the line of the function.