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3 years ago

Si al doble de 3,4 se le resta el triple de 4,3 resulta

Mathematics

1 answer:

defon3 years ago

6 0

Answer:

I would help you but I can't read the question.

Step-by-step explanation:

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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 <em>optimal</em> 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 <em>maximum allowable </em>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 <em>maximum</em> 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

What is the realationship between the area of the scales ⚖️ used in pictures ?

dlinn [17]

<h2>Explanation:</h2>

As I understand, you need to know the relationship between the area of similar figures. Two shapes are similar if we can turn one into the other by moving, rotating, flipping, or scaling, so this means we can make one shape bigger or smaller.

From math, if we call $k$ the scaling factor, then the area of one figure ( $A_{1}$ ) divided by the area of another similar figure ( $A_{2}$ ) will be equal to the scaling factor squared. In other words: