I need help on number 11
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The dimensions of the rectangular pen should be 15 by 20 feet and the maximum area is 1200 square feet.
Let the area be y .
Area = (base) × (height)
Base = 2x
Height = h
Let the area of the rectangular pens be y .
∴ y = 2xh
Perimeter of all the fencing = 4x+3h
∴ 4x+3h = 120
now we solve for h
3h = 120-4x
h = 40 - 4/3 x
Now we will substitute this value in the above first equation:
y = 2xh
or, y = 2x (40 - 4/3 x)
or, y = 80x - 8/3 x²
Now for the maximum area we have to find the first order differentiation of y
now,
dy /dx = 80 - 16/3 x
At dy/dx = 0 we get the value of x for which y is maximum.
80 - 16/3 x = 0
or, - 16/3 x = -80
or, x = 15 feet
Hence height = 40 - 4/3 x = 40 - 20 = 20feet
Maximum area = 2xh = 2×15×40 = 1200 square feet
The dimensions of the rectangular pen should be 15 by 20 feet and the maximum area is 1200 square feet.
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(7x + 4)(7x + 4) and (x – 9)(x – 9) are Perfect square trinomial. (5x + 3)(5x – 3) and (–3x – 6)(–3x + 6) shows the Difference of squares.
<h3>What is a perfect square?</h3>A perfect square is a number system that can be expressed as the
square of a given number from the same system.
The following are the answers
(5x + 3)(5x – 3) Difference of squares
(7x + 4)(7x + 4) is a Perfect square trinomial
(2x + 1)(x + 2) has Neither a difference of squares nor a perfect square trinomial.
(4x – 6)(x + 8) has Neither a difference of squares nor a perfect square trinomial.
(x – 9)(x – 9) is Perfect square trinomial
(–3x – 6)(–3x + 6) = Difference of squares.
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