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kumpel [21]
3 years ago
5

What 4 groups invaded the Roman Empire?

Social Studies
2 answers:
Pepsi [2]3 years ago
8 0

Answer:

The Gauls. Vestal Virgins fleeing during the attack by the Gauls. ( ...

The Visigoths. Sack of Rome by the Visigoths led by Alaric I. ( ...

The Vandals. Vandals sacking Rome. ...

The Ostrogoths. ...

The Normans. ...

The Holy Roman Empire.

Explanation:

hi

Citrus2011 [14]3 years ago
3 0
The Gauls. Vestal Virgins fleeing during the attack by the Gauls. ( ...
The Visigoths. Sack of Rome by the Visigoths led by Alaric I. ( ...
The Vandals. Vandals sacking Rome. ...
The Ostrogoths. ...
The Normans. ...
The Holy Roman Empire.
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Explanation:

Let the width of the print be = x

Then the width of the page is x + (1.5+1.5) = x + 3

Let the height of the print be = y

Then the height of the page is y + (1+1) = y + 2

Given the area of the print is 81 square inches

That means, xy = 81

Therefore, y = \frac{81}{x}

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A = (x + 3)(y + 2)

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\frac{dA}{dx}=(x+3)(\frac{81}{x}+2)

\frac{dA}{dx}= \left (\frac{81}{x}+2  \right )+\left ( x+3 \right )\left ( -\frac{81}{x^{2}} \right )=0

\frac{81+2x}{x}=\frac{(x+3)(81)}{x^{2}}

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Now y = \frac{81}{x}

          = \frac{81}{11.02}

          = 7.35 inch

Therefore the dimensions of thr page for the least amount of paper is x = 11.02 inch by  y = 7.35 inch

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