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Ksenya-84 [330]
1 year ago
8

A farmer wants to fence an area of 13.5 million square feet in a rectangular field and then divide it in half with a fence paral

lel to one of the sides of the rectangle. Let y represent the length (in feet) of a side perpendicular to the dividing fence, and let x represent the length (in feet) of a side parallel to the dividing fence. Let F represent the length of fencing in feet. Write an equation that represents F in terms of the variable x.
Mathematics
1 answer:
denis23 [38]1 year ago
4 0

Answer:

  F = 3x +(2.7×10^7)/x

Step-by-step explanation:

The formulas for area and perimeter of a rectangle can be used to find the desired function.

<h3>Area</h3>

The area of the rectangle will be the product of its dimensions:

  A = LW

Using the given values, we have ...

  13.5×10^6 = xy

Solving for y gives ...

  y = (13.5×10^6)/x

<h3>Perimeter</h3>

The perimeter of the rectangle is the sum of the side lengths:

  P = 2(L+W) = 2(x+y)

<h3>Fence length</h3>

The total amount of fence required is the perimeter plus one more section that is x feet long.

  F = 2(x +y) +x = 3x +2y

Substituting for y, we have a function of x:

  F = 3x +(2.7×10^7)/x

__

<em>Additional comment</em>

The length of fence required is minimized for x=3000. The overall size of that fenced area is x=3000 ft by y=4500 ft. Each half is 3000 ft by 2250 ft. Half of the total 18000 ft of fence is used for each of the perpendicular directions: 3x=2y=9000 ft.

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Answer:

volume = 10m^3

Step-by-step explanation:

This shape is called a rectangular prism. The formula for finding the volume of this prism is: volume = L * W * H

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3 years ago
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Xelga [282]

Answer:

30(x+1)/(x+7)

Step-by-step explanation:

This is not a rational expression because denominator has a domain of which it can be undefined.

To rationalize multiply by the reciprocal of the denominator (1/6+1/x+1)

___<u>5___ </u>*(6)(x+1) --> _____<u>30(x+1)_____</u> --><u> 30x+1</u>_ --> <u>30x+1</u>

1/6+1/x+1   *(6)(x+1)--> 6(x+1)/6 + 6(x+1)/(x+1) --> (x+1)+6 --> x+7

Final Answer: 30(x+1)/(x+7)



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Answer:

5 gallons

Step-by-step explanation:

3/4 + 6/8 + 20/8 + 1

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