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liubo4ka [24]
3 years ago
14

A farmer is constructing a rectangular pen with one additional fence across its width. Find the maximum area that can be enclose

d with 360 yards of fencing
Mathematics
1 answer:
konstantin123 [22]3 years ago
7 0

The maximum area of the pen is the highest area the pen can have

The maximum area is 16200 square yards

Let the dimension be x and y.

So, the perimeter is given as:

\mathbf{P = 360}

Because it has one additional fence, the perimeter is calculated as:

\mathbf{2x + y = 360}

Make y the subject

\mathbf{y = 360 - 2x}

The area is calculated as:

\mathbf{A = xy}

Substitute \mathbf{y = 360 - 2x}

\mathbf{A = x(360 -2x)}

Expand

\mathbf{A = 360x -2x^2}

Differentiate

\mathbf{A' = 360 -4x}

Set to 0

\mathbf{360 -4x = 0}

Rewrite as:

\mathbf{4x = 360}

Divide both sides by 4

\mathbf{x = 90}

Substitute 90 for x in \mathbf{A = 360x -2x^2}

\mathbf{A = 360 \times 90 - 2 \times 90^2}

\mathbf{A = 16200}

Hence, the maximum area is 16200 square yards

Read more about maximum areas at:

brainly.com/question/11906003

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Answer:

Step-by-step explanation:

#4 part A= D

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Your question only states parrallelogram ABCD is shown, so I assume you only wanted those answers, GL

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A grandsons age in years is equal to his grandfather's age in years. The difference of the grandsons age in years and the grandf
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The age of the grandson is 7 years and the grandfather is 84 years if the grandson's age in months is equal to the age of grandpa in years and the difference in age is 77.

<h3>What is a linear equation?</h3>

It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.

If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.

Let's suppose the age of the grandsons is x years and

age of the grandfather's age is y years

Here some data are misprinted, so we are assuming the grandson's age in months is equal to the age of grandpa in years and the difference in age is 77.

Then according to the problem:

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y -x = 77 (as difference in age is 77)

After solving both equations, we get:

x = 7 years and y = 84 years

Thus, the age of the grandson is 7 years and the grandfather is 84 years if the grandson's age in months is equal to the age of grandpa in years and the difference in age is 77.

Learn more about the linear equation here:

brainly.com/question/11897796

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