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3 years ago

Sienna has 80 yards of fencing to enclose a rectangular area. Find the dimensions that maximize the enclosed area. What is the m

aximum area?

Mathematics

1 answer:

Lubov Fominskaja [6]3 years ago

7 0

$2x+2y=80\ \ \ /:2\\\\2x:2+2y:2=80:2\\\\x+y=40\ \ \ /-x\\\\y=40-x\ \ \ (D_x:x\in(0;\ 40))$

$Area=xy\\\\substitute\ y=40-x\\\\Area=x(40-x)=-x^2+40\\(it's\ quadratic\ function\ where\ a=-1;b=40;c=0)\\\\vertex\ of\ parabola:p=\frac{-b}{2a}\to p=\frac{-40}{2\cdot(-1)}=\frac{-40}{-2}=20-it's\ max\\\\x=20\ then\ y=40-20=20\\\\Answer:dimensions\ of\ rectangular\ is\ 20\ yd\ \times\ 20\ yd,\\and\ area\ is\ 20^2=400\ yd^2.$

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kozerog [31]

Answer:

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Step-by-step explanation:

The parameters given are;

The number of chairs = 8 × 10 = 80 chairs

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Sitting arrangements of parents = Alone or to one other person

Therefore;

The maximum number of parents on a row = 1 + 1 + 0 + 1 + 1 + 0 + 1 + 1 + 0 + 1 = 7

Hence when the rows have the maximum number of parents occupying the seats we have for the 8 rows;

7 + 7 + 7 + 7 + 7 + 7 + 7 + 7 = 56

But there are only 54 parents, therefore, up to the 7th row will have 7 parents while the 8th row will have only 5 parents to make the possible sitting arrangement to be as follows;

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The sitting arrangement for the 8th row is therefore

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Hence there will be three empty seats in the 8th row making the largest possible number of adjacent empty chairs in a single row = 3.

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3 years ago

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Nutka1998 [239]

(1.6 * 10^3) * (3.0 * 10^-6) =
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4.8 / 10^3 =
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4 years ago

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y_1=4 \\ \\
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MrRissso [65]

Length of blue cloth is 60 inches , length of gold cloth is 48 inches and length of white cloth is 72 inches.

a.

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Answer:

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