This is super important for my grade guys can you please let me know the answer

If the farmer has 234 feet of fencing, what are the dimensions of the region which enclose the maximal area?

marissa [1.9K]

Answer: 58 ft × 58 ft

Step-by-step explanation:

Let the length of the region = x feet

And, the width of the region = y feet

Since, the perimeter of the region = 234 feet ( Given )

⇒ $2(x+y) = 234$

⇒ $x+y = 117$

⇒ $y = 117 - x$

Again the area of the region, A = xy

⇒ $A(x) = x(117-x)$

⇒ $A(x) = 117x - x^2$

By differentiating the above equation with respect to x,

⇒ $A'(x) = 117 - 2x$

For maxima or minima,

$A'(x) = 0$

$\implies 117 - 2x = 0$

$\implies -2x = -117$

$\implies x = 58.5$

Again differentiating equation A'(x) with respect to x,

We get, A''(x) = -2

Hence, For x = 58.5 A''(x) = negative

⇒ For x = 58.5 feet the area A(x) is maximum,

⇒ The length of the region having maximum area = x = 58.5 feet

And, the width of the region having maximum area = y = 117-x= 117 - 58.5=58.5 feet,

⇒ The dimension of the region having the maximum area = 58.5 ft × 58.5 ft

8 0

2 years ago

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-6(2r +8)=-10(r-3)<br> I need the work to

barxatty [35]

Answer:

r = -39

Step-by-step explanation:

So we are trying to solve the equation for r.

-6(2r + 8) = -10(r - 3)

Divide both sides by -2. (This will make distributing much easier.)

3(2r + 8) = 5(r - 3)

Distribute the 3 on the left side and the 5 on the right side,

6r + 24 = 5r - 15

Subtract 24 from both sides.

6r = 5r - 39

Subtract 5r from both sides.

r = -39

So now we have solve the equation.

I hope you find my answer and explanation to be helpful. Happy studying. :)

5 0

2 years ago

Imagine you conducted a study to look at the association between whether an expectant mother eats breakfast (or not) and the gen

mario62 [17]

Answer:

: The percentage of newborn infants who are exclusively breastfed at the time of hospital discharge.

Data Source: Rhode Island Department of Health, Center for Health and Data Analysis, Newborn Developmental Risk Screening Program Database and Maternal and Child Health Database.

Footnotes: The year indicated is the mid-year of a five-year period of data.

Step-by-step explanation:

3 0

2 years ago

Zucchini weights are approximately normally distributed with mean 08 pound and standard deviation 0.25 pound. Which of the follo

marissa [1.9K]

Answer:

The correct option is A

Step-by-step explanation:

From the question we are told that

The mean is $\mu = 0.8 \ pounds$

The standard deviation is $\sigma = 0.25 \ pounds$

Generally the the probability that a randomly selected zucchini will weigh between 0 55 pound and 13 pounds is mathematically represented as

$P(0.55 < X < 1.3) = P(\frac{0.55 - 0.8}{ 0.25} < \frac{X - \mu}{\sigma } < \frac{1.3 - 0.8}{0.25})$

=> $P(0.55 < X < 1.3) = P( -1 < Z < 2 )$

So looking the option of normal curves given in the question we see that it is option A that matches our interval

8 0

2 years ago

Misha solves the equation 3 x minus 2 (x + 3) = 4 (x minus 2) minus 7 by applying the distributive property to each side of the

Anon25 [30]

Answer:

2(x+3)=4

2x+6=4

2x=4-6

2x=-2

2x÷2

x=1

8 0

2 years ago

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