Which of these is an exponential parent function? OA. f(x)=2x-2 OB. f(x) = 2x C. f(x) = 2x + 3 OD. f(x) = 24x

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

0.00147 in standard form

kondaur [170]

Answer:

1.47 times 10 to the power of -3

Step-by-step explanation:

8th grade math I'm guessing lol

7 0

3 years ago

Larry plays quarterback for the Eagles. During the team's opening football game, the Eagles have the ball 48 yards away from the

frez [133]

So take 48 then subtract 31 which would equal 17. Then add back the yards they lost. So 17+19=36

6 0

3 years ago

Read 2 more answers

The probability that a birth in the United States is male during 2018 is 0.511. Suppose a random number generator from 1 to 1,00

RideAnS [48]

Answer:

Suppose a random number generator from 1 to 1,000 is used as a statistical model to create simulated results for births in the United States during 2018. Suppose the numbers 1 to 511 represent a male birth in the United States during 2018 and 512 to 1,000 represent a female birth in the United States during 2018. Explain whether the following results

6 0

2 years ago

Read 2 more answers

Segment AB has endpoints at −2 and 12. What is the coordinate of its midpoint?

charle [14.2K]

Hi there!

$\large\boxed{5}$

Find the midpoint using the midpoint formula:

m = (p1 + p2) / 2

m = (-2 + 12) / 2

m = 10 / 2

m = 5.

3 0

3 years ago

Which of these is an exponential parent function? OA. f(x)=2x-2 OB. f(x) = 2x C. f(x) = 2x + 3 OD. f(x) = 24x​

Which of these is an exponential parent function? OA. f(x)=2x-2 OB. f(x) = 2x C. f(x) = 2x + 3 OD. f(x) = 24x