Use calculus to find the largest possible area for a rectangular field that can be enclosed with a fence that is 500 meters long.

The maximum area that can be enclosed is 15625 feet²

A rectangle is a quadrilateral in which opposite sides are equal and parallel to each other.

Let x represent the length and y represent the width. Hence:

perimeter = 2(length + width)

500 = 2(x + y)

250 = x + y

y = 250 - x

The area of a rectangle (A) = length * width

A = x * (250 - x)

A = 250x - x²

The maximum area is at dA/dx = 0, hence:

dA/dx = 250 - 2x

250 - 2x = 0

2x = 250

x = 125 feet

y = 250 - x = 250 - 125 = 125 feet

The maximum area = x * y = 125 * 125 = 15625 feet²

The maximum area that can be enclosed is 15625 feet²

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answer: .64

step-by-step explanation

set up the formula for standard deviation for this set of numbers, then simplify

8.75

how-to:

first, we need to find what we have to work with.

since i know that we have 7 (years) and 0.8 (inches), we can use these to solve and find the equation!

secondly, what you want to do, is see that we need to know how much growth out of the 0.8 inches he got in only 1 year, instead of 7 years.

let's try to divide.

7 ÷ 0.8 = 8.75