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nadya68 [22]
2 years ago
12

A farmer wants to fence in a rectangular plot of land adjacent to the north wall of his barn. no fencing is needed along the bar

n, and the fencing along the west side of the plot is shared with a neighbor who will split the cost of that portion of the fence. if the fencing costs $12 per linear foot to install and the farmer is not willing to spend more than $3000, find the dimensions for the plot that would enclose the most area. (width, length) =
Mathematics
1 answer:
jeyben [28]2 years ago
3 0

Hi,

Let assume a the west side,

b the length of the north wall (i suppose the answer is smaller then the barn.

Cost of the fence= a*6+a*12+b*12=3000 $.

So 3a+2b=500==>b=(500-3a)/2

Area =a*b=a(500-3a)/2= 250a-3/2a²

Derivate the area ==> 250-3a=0

==> a=250/3 and b=(500-3*250/3)/2=125

Width=125 (feet)

Length=250/3=83.333 (feet)

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Determine the angle at the centre of a circle with radius 6.0 cm for an arc length of 8.0 cm.
sveta [45]

Answer:

Third option.

Step-by-step explanation:

You need to remember that the formula used to calculate the arc lenght is:

arc\ length=r C

Where "r" is the radius and "C" is the central angle in radians.

You need to solve for "C":

C=\frac{arc\ length}{r}

You know the radius and the arc lenght, therefore, you can substitute values to calculate the central angle in radians. Therefore, this is:

C=\frac{8.0cm}{6.0cm}

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3 years ago
Please help. I don't understand anything.
alina1380 [7]

Answer:

A

Step-by-step explanation:

The area of figure=Area of rectangle+Area of triangle

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2 years ago
Read 2 more answers
The feet of the average adult woman are 24.6 cm long, and foot lengths are normally distributed. If 16% of adult women have feet
nevsk [136]

Answer:

Approximately 16% of adult women have feet longer than 27.2 cm.

Step-by-step explanation:

Normal Probability Distribution

Problems of normal distributions can be solved using the z-score formula.

In a set with mean \mu and standard deviation \sigma, the z-score 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 p-value, we get the probability that the value of the measure is greater than X.

The feet of the average adult woman are 24.6 cm long

This means that \mu = 24.6

16% of adult women have feet that are shorter than 22 cm

This means that when X = 22, Z has a p-value of 0.16, so when X = 22, Z = -1. We use this to find \sigma

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

-1 = \frac{22 - 24.6}{\sigma}

-\sigma = -2.6

\sigma = 2.6

Approximately what percent of adult women have feet longer than 27.2 cm?

The proportion is 1 subtracted by the p-value of Z when X = 27.2. So

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

Z = \frac{27.2 - 24.6}{2.6}

Z = 1

Z = 1 has a p-value of 0.84.

1 - 0.84 = 0.16

0.16*100% = 16%.

Approximately 16% of adult women have feet longer than 27.2 cm.

3 0
2 years ago
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