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Viktor [21]
2 years ago
15

You have 576 feet of fencing to enclose a rectangular plot of land. Find the dimensions of the rectangular plot that would maxim

ize the area. List the smaller number first.
Mathematics
1 answer:
stiv31 [10]2 years ago
5 0

Answer:

The dimension that maximizes area is 144ft by 144ft

Step-by-step explanation:

Given

P = 576 -- perimeter

Required

The dimension that gives maximum area

Perimeter is calculated as:

P= 2 * (L + W)

So, we have:

2 * (L + W) = 576

Divide through by 2

L + W = 288

Make L the subject

L  = 288 -W

Area is calculated as:

A = L * W

Substitute L  = 288 -W

A = (288 - W) * W

Open bracket

A = 288W - W^2

Differentiate A with respect to W

A' = 288 - 2W

Set to 0 to calculate W

288 - 2W = 0

Collect like terms

2W = 288

Divide by 2

W = 144

Recall that:

L  = 288 -W

L = 288 - 144

L = 144

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Start by writing the system down, I will use y to represent f(x)

y=x^2-5x+3\wedge y=-3

Substitute the fact that y=-3 into the first equation to get,

-3=x^2-5x+3

Simplify into a quadratic form (ax^2+bx+c=0),

x^2-5x+6=0

Now you can use Vieta's rule which states that any quadratic equation can be written in the following form,

x^2+x(m+n)+mn=0

which then must factor into

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And the solutions will be m,n.

Clearly for small coefficients like ours 5,6, this is very easy to figure out. To get 5 and 6 we simply say that m=3, n=2.

This fits the definition as 5=3+2 and 6=2\cdot3.

So as mentioned, solutions will equal to m=3, n=2 but these are just x-values in the solution pairs of a form (x,y).

To get y-values we must substitute 3 for x in the original equation and then also 2 for x in the original equation. Luckily we already know that substituting either of the two numbers yields a zero.

So the solution pairs are (2,0) and (3,0).

Hope this helps :)

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2 years ago
A straight line is drawn through the intersection of the two diagonals of a parallelogram. Prove that it exactly divides the par
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Answer:

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Step-by-step explanation:

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The measure of two supplementary angels, s and t, are the ratio of 7:3. Find the value of s
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10x=180

/10     /10

x=18

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7(18)=126

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Step-by-step explanation:

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<h2><u><em>nonagon, 9 sides</em></u></h2>

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