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3 years ago

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Consider the following problem: A farmer with 750 ft of fencing wants to enclose a rectangular area and then divide it into four

pens with fencing parallel to one side of the rectangle. What is the largest possible total area of the four pens? (a) Draw several diagrams illustrating the situation, some with shallow, wide pens and some with deep, narrow pens. Find the total areas of these configurations. Does it appear that there is a maximum area? If so, estimate it. (b) Draw a diagram illustrating the general situation. Let x denote the length of each of two sides and three dividers. Let y denote the length of the other two sides. (c) Write an expression for the total area A in terms of both x and y. A = (375− 5 2y)y

1 answer:

gregori [183]3 years ago

6 0

Answer and step-by-step explanation:

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

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The midpoint of GH is M( 6,-4). One endpoint is G(8,-2). Find the coordinates of endpoint H.

Finger [1]

Using the midpoint formula, the coordinates of endpoint H are (4, -6).

<h3>The Midpoint Formula</h3>

The midpoint formula is given as: $(x_m, y_m) = (\frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} )$

<em>Where</em>,

$(x_m, y_m)$ = coordinates of the midpoint

$(x_1, y_1)$ = coordinates of the first point

$(x_2, y_2)$ = coordinates of the second point

Given the following:

$(x_m, y_m)$ = M( 6,-4)

$(x_1, y_1)$ = G(8,-2)

$(x_2, y_2)$ = H(?, ?)

Plug in the values into the midpoint formula

$M(6, -4) = (\frac{8 + x_2}{2}, \frac{-2 + y_2}{2} )$

Solve for the x-coordinate and y-coordinate separately

$6 = \frac{8 + x_2}{2}$

Multiply both sides

$6 \times 2 = 8 + x_2\\\\12 = 8 + x_2\\\\12 - 8 = x_2\\\\4 = x_2\\\\\mathbf{x_2 = 4}$

$-4 = \frac{-2 + y_2}{2}\\\\-8 = -2 + y_2\\\\-8 + 2 = y_2\\\\-6 = y_2\\\\\mathbf{y_2 = -6}$

Therefore, using the midpoint formula, the coordinates of endpoint H are (4, -6).

Learn more about midpoint formula on:

brainly.com/question/13115533

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2 years ago

Workout the area of the quarter of a circle with a radius of 8

QveST [7]

Answer:

$16\pi$

Step-by-step explanation:

We need to find 1/4 of the area of a circle with a radius of 8

Let r be radius

Area of a circle = $r^{2} \pi$

Substitute r with 8

Area of a circle = $8^2\pi =64\pi$

Now, to find 1/4 of the area, we can create an equation $\frac{64\pi }{4}={16\pi$

The answer is $16\pi$

Hope this helps :)

Have a spectacular day!

3 0

2 years ago

Read 2 more answers

Consider a value to be significantly low if its z score less than or equal to minus−2 or consider a value to be significantly hi

den301095 [7]

Answer:

Test scores of 10.2 or lower are significantly low.

Test scores of 31 or higher are significantly high

Step-by-step explanation:

Z-score:

In a set with mean $\mu$ and standard deviation $\sigma$ , the zscore of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

In this problem, we have that:

$\mu = 20.6, \sigma = 5.2$

Significantly low:

Z-scores of -2 or lower

So scores of X when Z = -2 or lower

$Z = \frac{X - \mu}{\sigma}$

$-2 = \frac{X - 20.6}{5.2}$

$X - 20.6 = -2*5.2$

$X = 10.2$

Test scores of 10.2 or lower are significantly low.

Significantly high:

Z-scores of 2 or higher

So scores of X when Z = 2 or higher

$Z = \frac{X - \mu}{\sigma}$

$2 = \frac{X - 20.6}{5.2}$

$X - 20.6 = 2*5.2$

$X = 31$

Test scores of 31 or higher are significantly high

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3 years ago

Check my proof? Two diagonals of a parallelogram bisect each other?

SIZIF [17.4K]

Your proof is correct and very well done

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3 years ago

Write a linear function f with the values f (-1) = 5 and f (3) = 4.<br> A function is f(x) =

Drupady [299]

Answer:

Step-by-step explanation:

Since we have points (-1,5) and (3,4) we can find the slope m of y=mx+b

m=(y2-y1)/(x2-d1)=(5-4)/(-1-3)=1/-4=-1/4 so we have

y=-x/4+b, using point (3,4) we can solve for the y intercept, b.

4=-3/4+b, b=19/4, so the line is

y=(-x+19)/4

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2 years ago