Solve for h. -98 = -7h h =

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

Luba_88 [7]

The dimensions for the plot that would enclose the most area are a length and a width of 125 feet.

In this question we shall use the first and second derivative tests to determine the optimal dimensions of a rectangular plot of land. The perimeter ( $p$ ), in feet, and the area of the rectangular plot ( $A$ ), in square feet, of land are described below:

$p = 2\cdot (w+l)$ (1)

$A = w\cdot l$ (2)

Where:

$w$ - Width, in feet.
$l$ - Length, in feet.

In addition, the cost of fencing of the rectangular plot ( $C$ ), in monetary units, is:

$C = c\cdot p$ (3)

Where $c$ is the fencing unit cost, in monetary units per foot.

Now we apply (2) and (3) in (1):

$p = 2\cdot \left(\frac{A}{l}+l \right)$

$\frac{C}{c} = 2\cdot (\frac{A}{l}+l )$

$\frac{C\cdot l}{c} = 2\cdot (A+l^{2})$

$\frac{C\cdot l}{c}-2\cdot l^{2} = 2\cdot A$

$\frac{C\cdot l}{2\cdot c} - l^{2} = A$ (4)

We notice that fencing costs are directly proportional to the area to be fenced. Let suppose that cost is the maximum allowable and we proceed to perform the first and second derivative tests:

FDT

$\frac{C}{2\cdot c}-2\cdot l = 0$

$l = \frac{C}{4\cdot c}$

SDT

$A'' = -2$

Which means that length leads to a maximum area.

If we know that $c = 8$ and $C = 4000$ , then the dimensions of the rectangular plot of land are, respectively:

$l = \frac{4000}{4\cdot (8)}$

$l = 125\,ft$

$A = \frac{(4000)\cdot (125)}{2\cdot (8)} -125^{2}$

$A = 15625\,ft^{2}$

$w = \frac{15625\,ft^{2}}{125\,ft}$

$w = 125\,ft$

The dimensions for the plot that would enclose the most area are a length and a width of 125 feet.

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8 0

2 years ago

The diameter of a round dinner plate is 10 inches. What's the area of the plate?

Anni [7]

Lets say pi is 3.14
The area of a circle is: pi*radius squared
The radius is half the diameter so it is 5 inches.
3.14*5 squared 2
3.14*25
78.5inches squared

3 0

3 years ago

Read 2 more answers

For each of the following situations, indicate what the general impact on the Type II error probability will be:

Paraphin [41]

Answer:

Step-by-step explanation:

Hello!

The type II error is committed when you fail to reject a false null hypothesis.

The probability associated with this type of error is symbolized as β.

a. The alpha level is increased.

α and β are two probabilities that are closely related in such a way that if alpha is decreased, beta automatically increases and vice versa when the sample size n is predetermined.

If you increase α then the probability of committing type II error (β) decreases.

b. The "true" population mean is moved farther from the hypothesized population mean.

If the true population mean is moved away from its hypothesized value, then the probabilities of "keeping" a false null hypothesis are bigger.

c. The alpha level is decreased.

This is the inverse situation from a. If you decrease α then, β is automatically increased.

d. The sample size is increased.

If the sample size "n" is left free, it can be shown that by increasing the sample size, both α and β decrease. In practice, α is fixed and β is calculated with several possible sizes of n. Finally choosing as sample size the one that minimizes or gives a reasonable value of β.

I hope it helps!

3 0

3 years ago

A pair of jeans cost $32 last year this year they cost $38 what was the percent increase? PLEASE ANSWER NEED HELP!

garik1379 [7]

Answer:

18.75%

Step-by-step explanation:

percent increase = $\frac{increase}{original cost}$ × 100%

Increase in cost = $38 - $32 = $6

percent increase = $\frac{6}{32}$ × 100% = $\frac{6(100)}{32}$ = 18.75%

5 0

3 years ago

How would you convert 276 yards to inches?

valentinak56 [21]

Answer:

9936 inch.

Step-by-step explanation:

Note the measurements:

1 Yard = 3 Feet

1 Feet = 12 Inch

1 Yard = 3 Feet = (12)(3) Inches = 36 Inches; 1 Yard = 36 Inches

Multiply 276 with 36

276 x 36 = 9936

9936 inches is your answer.

~

6 0

3 years ago