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DENIUS [597]
3 years ago
11

Which transformations could be performed to show that

Mathematics
1 answer:
andre [41]3 years ago
3 0

Answer: a 180 degree rotation about the origin, then a dilation by a scale factor of 1/3

Step-by-step explanation:

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A rancher wants to fence in an area of 1000000 square feet in a rectangular field and then divide it in half with a fence down t
frosja888 [35]

The shortest length of the fence used by the rancher in a rectangular field of 1000000 square feet is 4899 ft.

<h3>What is the area of a rectangle?</h3>

The area of a rectangle is a region enclosed in four corners where two opposite sides are equal. The area of the rectangle is mathematically expressed as:

Area of a rectangle = length(x) × breath(y)

1000000 sq.ft = (x) × (y) ---- (1)

However, to determine the fencing, we have:

Length of fencing = 2x + 2y  

  • since the rectangle has four sides and opposite sides are equal

Suppose we use the x-direction to estimate the region where the fencing is located, we have:

Length of fencing = 2x + 2y + x

Length of fencing = 3x + 2y ---- (2)

From equation (1), make (y) the subject of the formula and replace the value of y with equation (2)

The Length of fencing is:

\mathbf{L = 3x - 2( \dfrac{1000000}{x})}

\mathbf{\dfrac{dL}{dx} = 3 - \dfrac{2000000}{x^2} = 0}

\mathbf{ x^2= \dfrac{2000000}{3} }

\mathbf{ x= \dfrac{1000\sqrt{2}}{\sqrt{3}} }

\mathbf{x = \dfrac{1000 \sqrt{6}}{3}}

Now, if we replace the value with equation (1), then y will be:

\mathbf{y = \dfrac{1000000}{\dfrac{1000 \sqrt{6}}{3}} }\\ \\  \\ \\ \mathbf{y = \dfrac{3000 }{\sqrt{6}}}

\mathbf{x =500\sqrt{6}}

Now, the shortest length of the fencing can be computed by using the equation (2):

L = 3x + 2y

\mathbf{L = 3( \dfrac{1000  \sqrt{6}}{3}) + 2(500 \sqrt{6})}

\mathbf{L =1000  \sqrt{6} + 1000 \sqrt{6}}

\mathbf{L =2000  \sqrt{6} }

\mathbf{L \simeq 4899 \ ft}

Learn more about the area of a rectangle here:

brainly.com/question/25292087

6 0
2 years ago
What is the product of (2x - 5)(2x + 5)2 ?
m_a_m_a [10]
8x^2-50 is your answer hopes this helps
6 0
2 years ago
Read 2 more answers
HELP I NEED HELP ASAP
lawyer [7]

Answer:

i think is B hope it helped sos if its wrong

Step-by-step explanation:

6 0
2 years ago
Can you help with #15 please on fractions
Verdich [7]
The answer is C because a fraction is part of the whole, therefore making. The answer less than the whole number
7 0
3 years ago
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A system of equations has 1 solution. If 4x – y = 5 is one of the equations, which could be the other equation?
Stells [14]
Y=-4x+5 I believe you just rewrite the equation like this
7 0
3 years ago
Read 2 more answers
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