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Bad White [126]
4 years ago
11

1.You have 150 yards of fencing to enclose a rectangular region. One side of the rectangle does not need fencing. Find the dimen

sions of the rectangle that maximize the enclosed area. What is the maximum area?
Mathematics
1 answer:
Cerrena [4.2K]4 years ago
7 0
Let the dimensions be x and y. 2 of the sides measuring x and only one of the sides measuring y should be fence. 
                                  150 = 2x + y
The area of the rectangular figure,
                                      A = xy
Substituting the y in the first equation to the second,
                                      A = x(150 - 2x)
                                   A = 150x - 2x²
Differentiate the equation and equate to zero,
                                  dA/dx = 0 = 150 - 4x
The value of x is 37.5 yard and y is equal to 75 yard. The maximum area is 2812.5 yd².
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The matrix represents the vertices of the rectangle after it is scaled by a factor of 3 is,

[ 0  12 12  0]

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<h2>We have to determine</h2>

Which matrix represents the vertices of the rectangle after it is scaled by a factor of 3?

<h3>According to the question</h3>

The vertices of the triangle are

The scale factor is 3.

<h3>The vertices of the triangle are scaled with the factor of 3 so the vertices are get multiplied by 3.</h3>

Therefore,

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\rm (0, 0), (4, 0), (4, 4) \ and\  (0, 2)\\\\ (0\times 3, 0\times 3), (4 \times 3, 0 \times 3), (4 \times 3, 4 \times 3) \ and \ (0 \times 3, 2 \times 3) \\\\ (0, \ 0), (12, \ 0), (12, \ 12), \ (0,\ 6 )

The vertices of the rectangle after it are scaled by a factor of 3.

Therefore,

The matrix represents the vertices of the rectangle after it is scaled by a factor of 3 is,

[ 0  12 12  0]

[ 0  0  12  6]

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