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Pani-rosa [81]
3 years ago
9

Please help me with this problem :)

Mathematics
1 answer:
myrzilka [38]3 years ago
7 0

Answer:

9/25

Step-by-step explanation:

36/100 = 9/25

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Find the dimensions of a rectangle (in m) with area 1,000 m2 whose perimeter is as small as possible. (Enter the dimensions as a
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The perimeter of the rectangle is the sum of its dimensions

The dimensions that minimize the perimeter are \mathbf{10\sqrt{10 },10\sqrt{10 }}

The area is given as:

\mathbf{A = 1000}

Let the dimension be x and y.

So, we have:

\mathbf{A = xy = 1000}

Make x the subject

\mathbf{x = \frac{1000}{y}}

The perimeter is calculated as:

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Substitute \mathbf{x = \frac{1000}{y}}

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Set to 0

\mathbf{ -\frac{2000}{y^2} + 2 = 0}

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\mathbf{ -\frac{2000}{y^2}  = -2}

Divide both sides by -1

\mathbf{\frac{2000}{y^2}  = 2}

Multiply y^2

\mathbf{2000  = 2y^2}

Divide by 2

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Take square roots of both sides

\mathbf{y = \sqrt{1000 }}

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Substitute \mathbf{y = \sqrt{1000 }} in \mathbf{x = \frac{1000}{y}}

\mathbf{x = \frac{1000}{\sqrt{1000}}}

\mathbf{x = \sqrt{1000}}

\mathbf{x = 10\sqrt{10 }}

Hence, the dimensions that minimize the perimeter are \mathbf{10\sqrt{10 },10\sqrt{10 }}

Read more about perimeters at:

brainly.com/question/6465134

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whats the question

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