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4 years ago

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SCALCET8 4.7.011. Consider the following problem: A farmer with 950 ft of fencing wants to enclose a rectangular area and then d

ivide it into four pens with fencing parallel to one side of the rectangle. What is the largest possible total area of the four pens

1 answer:

kaheart [24]4 years ago

6 0

Answer:

For any rectangle, the one with the largest area will be the one whose dimensions are as close to a square as possible.

However, the dividers change the process to find this maximum somewhat.

Letting x represent two sides of the rectangle and the 3 parallel dividers, we have 2x+3x = 5x.

Letting y represent the other two sides of the rectangle, we have 2y.

We know that 2y + 5x = 750.

Solving for y, we first subtract 5x from each side:

2y + 5x - 5x = 750 - 5x

2y = - 5x + 750

Next we divide both sides by 2:

2y/2 = - 5x/2 + 750/2

y = - 2.5x + 375

We know that the area of a rectangle is given by

A = lw, where l is the length and w is the width. In this rectangle, one dimension is x and the other is y, making the area

A = xy

Substituting the expression for y we just found above, we have

A = x (-2.5x+375)

A = - 2.5x² + 375x

This is a quadratic equation, with values a = - 2.5, b = 375 and c = 0.

To find the maximum, we will find the vertex. First we find the axis of symmetry, using the equation

x = - b/2a

x = - 375/2 (-2.5) = - 375/-5 = 75

Substituting this back in place of every x in our area equation, we have

A = - 2.5x² + 375x

A = - 2.5 (75) ² + 375 (75) = - 2.5 (5625) + 28125 = - 14062.5 + 28125 = 14062.5

Step-by-step explanation:

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2 years ago

Answer the following questions

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Answer:

1. $2 \frac{2}{7}$

2. $2 \frac{1}{3}$

3. $\frac{5}{12}$

4. $8 \frac{2}{3}$

5. $\frac{2}{3}$

Step-by-step explanation:

<h2> $1. \: \: 2 \frac{2}{3} \div 1 \frac{1}{6}$ </h2>

$\frac{8}{3} \div \frac{7}{6}$

$\frac{8}{3} \times \frac{6}{7}$

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$\frac{8 \times 2}{7}$

$\frac{16}{7}$

$2 \frac{2}{7}$

<h2> $2. \: \: 6 \frac{2}{3} \div 2 \frac{6}{7}$ </h2>

$\frac{20}{3} \div \frac{20}{7}$

$\frac{20}{3} \times \frac{7}{20}$

$\frac{1}{3} \times 7$

$\frac{7}{3}$

$2 \frac{1}{3}$

<h2> $3. \: \: 4 \frac{1}{6} \div 10$ </h2>

$\frac{25}{6} \div \frac{10}{1}$

$\frac{25}{6} \times \frac{1}{10}$

$\frac{5}{6} \times \frac{1}{2}$

$\frac{5}{6 \times 2}$

$\frac{5}{12}$

<h2> $4. \: \: 6 \frac{1}{2} \div \frac{3}{4}$ </h2>

$\frac{13}{2} \div \frac{3}{4}$

$\frac{13}{2} \times \frac{4}{3}$

$13( \frac{2}{3} )$

$\frac{13 \times 2}{3}$

$\frac{26}{3}$

$8 \frac{2}{3}$

<h2> $5. \: \: 3 \frac{3}{4} \div 5 \frac{5}{8}$ </h2>

$\frac{15}{4} \div \frac{45}{8}$

$\frac{15}{4} \times \frac{8}{45}$

$\frac{1}{4} \times \frac{8}{3}$

$\frac{2}{3}$

<h3>Hope it is helpful...</h3>

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3 years ago

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