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elena-14-01-66 [18.8K]
3 years ago
9

a garden is to be laid out in a rectangular area and protected by a chicken wire fence. What is the largest possible area of the

garden if only 100 running feet of chicken wire is available for the fence?
Mathematics
2 answers:
dangina [55]3 years ago
5 0
The largest possible area for a given amount of material enclosing a rectangle will always be a perfect square with each side being one quarter of the amount of material.

The proof is:

M=2x+2y, solve for y

y=(M-2x)/2

A=xy, and using y from above...

A=(Mx-2x^2)/2

dA/dx=(M-4x)/2

d2A/dx2=-2

Since acceleration is always negative, when velocity is zero, it will be at an absolute maximum for A(x)

dA/dx=0 when M-4x=0, 4x=M, x=M/4

So the maximum area occurs when x=M/4, and from earlier:

y=(M-2x)/2  then use x=M/4 in this and get:

y=(M-M/2)/2

y=(2M-M)/4=M/4  so x=y=M/4, a perfect square.

So for your particular example...

M=2x+2y and M=100

100=2x+2y

50=x+y

y=50-x

Now:

A=xy, using y found above...

A=50x-x^2

dA/dx=50-2x

d2A/dx2=-2  so an absolute maximum occurs when dA/dx=0

dA/dx=0 when 50-2x=0, 2x=50, x=25...

and from earlier, y=50-x, using x from above y=50-25=25

so y=x=25

So the maximum area with 100 feet of fencing is 25^2=625ft^2
sergejj [24]3 years ago
4 0
I believe that 25*25=625 and that is the biggest area
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Answer:

A function f(x) is said to be periodic, if there exists a positive real number T such that f(x+T) = f(x).

You can also just say: A periodic function is one that repeats itself in regular intervals.

Step-by-step explanation:

The smallest value of T is called the period of the function.

Note: If the value of T is independent of x then f(x) is periodic, and if T is dependent, then f(x) is non-periodic.

For example, here's the graph of sin x.  [REFER TO PICTURE BELOW]

Sin x is a periodic function with period  2π  because  sin(x+2π)=sinx  

Other examples of periodic functions are all trigonometric ratios, fractional x (Denoted by {x} which has period 1) and others.

In order to determine the period of the determined graph however, just know that the period of the sine curve is the length of one cycle of the curve. The natural period of the sine curve is 2π. So, a coefficient of b=1 is equivalent to a period of 2π. To get the period of the sine curve for any coefficient b, just divide 2π by the coefficient b to get the new period of the curve.

Hopefully this helped a bit.

6 0
3 years ago
440 divided by 2/5 please
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The answer for this question is 1,100
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PQ has a midpoint of M. the coordinates of M are (-4, 7) and the coordinates of P are (2, 13). What are the coordinates of Q?
Natali5045456 [20]

Using the midpoint formula, the coordinates of Q are: <em>A. (-10, 1)</em>

<h3>What is the Midpoint Formula?</h3>
  • Midpoint formula is given as, M(x, y) = (\frac{x_2 + x_1}{2} , \frac{y_2 + y_1}{2})

Thus, given that:

  • M is the midpoint of PQ.
  • M (-4, 7)
  • P (2, 13).

Therefore:

M(-4, 7) = (\frac{2 + x_1}{2} , \frac{13 + y_1}{2})

Solve for x-coordinate of P:

-4 = 1/2(2 + x1)

2(-4) = 2 + x1

-8 = 2 + x1

-8 - 2 = x1

x1 = -10

Solve for y-coordinate of P:

7 = 1/2(13 + y1)

14 = 13 + y1

y1 = 1

Therefore, using the midpoint formula, the coordinates of Q are: <em>A. (-10, 1)</em>

<em />

Learn more about the midpoint formula on:

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3 0
2 years ago
Help :C The question is the picture !
hjlf

Answer:

35

Step-by-step explanation:

28/4=7

5x7=35

so the missing value is 35

Hope i helped have a great day ( or night )!

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