Question

Farmer Ed has 850 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, find the length and width of the plot that will maximize the area. What is the largest area that can be​ enclosed?

Answer 1

So hmm notice the picture below

skipping the river side, the perimeter is then, w + w + l

now, we know the Ed has 850m of fence, so we know the perimeter of that plot will be 850

thus 850 = w + w + l

$\bf 850=2w+l\implies 850-2w=l \\\\\\ \textit{area of a rectangle}\\\\ A=lw\qquad l=850-2w\implies A(w)=850w-2w^2$

take the derivative of A(x) and zero it out, check the critical points for any minima, bearing in mind that "w" cannot be greater than 850, or less than 0, that is, it has to be a critical point between (0, 850)

Answer 2

The largest area that can be​ enclosed = 90312.5 m²

Further explanation

Quadratic function is a function that has the term x²

The quadratic function forms a parabolic curve

The general formula is

f(x) = ax² + bx + c

where a, b, and c are real numbers and a ≠ 0.

The parabolic curve can open up or down determined from the value of a. If a is positive, the parabolic curve opens up and has a minimum value.

If a is negative, the parabolic curve opens down and has a maximum value

The formula for finding the coordinates of the maximum and minimum points of the quadratic function is the same.

The maximum / minimum point of the quadratic function is

$(- \frac {b} {2a}, - \frac {D} {4a})$

Farmer Ed will make a fence by the river

The total length of the entire fence is 850 meters

From the attached picture, you will get that

fence width = 2x

fence length = 850 -2x

So the area of ​​the fence formed is:

length x width = area = (850-2x) x

area = 850x-2x²

From this we get the quadratic function = -2x²+ 850x

so we get the maximum value because the value a <0 (a = -2)

we look for the value x = -b / 2a = width of the fence

x = -850 / 2.-2 = 212.5

so the length of the fence = 850 - 2,212.5 = 425

The area will be : 212.5 x 425 = 90312.5 m²

Learn more  

domain of the function

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the inverse of the ƒunction  

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F (x) = x2 + 1 g (x) = 5 - x

htps://brainly.com/question/2723982

Keywords : fencing, farmer, Quadratic function