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Lilit [14]
3 years ago
6

A rectangular plot of farmland will be bounded on one side by a river and on the other three sides by a​ single-strand electric

fence. With 2400 m of wire at your​ disposal, what is the largest area you can​ enclose, and what are its​ dimensions?
Mathematics
1 answer:
wlad13 [49]3 years ago
4 0

Answer:

x = 600 m

y = 1200 m

Amax = 720000  m²

Step-by-step explanation:

Let call x the smaller side of the rectangular plot and y the largest ( we assume we have one y side bounded by a river: Then

A(p)  Area of the plot x*y

A(p) = x*y

And perimeter of the plot ( to be fenced ) is:

P(p)  = 2*x + y = 2400     ⇒  y  = 2400 - 2*x

Area of rectangular plot as function of x:

A(x) = x * ( 2400 - 2x )

Taking derivatives on both sides of the equation

A´(x) = ( 2400 - 2x ) + (-2) *x    ⇒  A´(x) = ( 2400 - 2x ) - 2x

A´(x) = 0      ⇒   2400 - 4x = 0    ⇒  4x  = 2400  

x = 600 m

And y =  2400 - 2*x

y = 2400 - 1200

y = 1200 m

And the largest enclosed area is  Amax = 1200*600

Amax = 720000 m²

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3 years ago
Filipo is building a rectangular sandbox . The length of the sandbox is 1 foot longer than twice the width of the sandbox .the p
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Answer:

Part A : D.) 2w + 2(2w+ 1) = 29

Part B : Length of the sandbox is 10 feet.

Step-by-step explanation:

Given,

Perimeter = 29 ft

We need to find the equation for the perimeter and also the length of the sandbox.

Solution,

Let the width of the sandbox be 'w'.

Now as per question said;

The length of the sandbox is 1 foot longer than twice the width of the sandbox.

So we can say that;

Length = 2w+1

Now we know that the perimeter is equal to the sum of twice of length and width.

framing in equation form, we get;

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Hence The equation used to find the width is  29=2(2w+1)+2w.

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3 0
3 years ago
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