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tester [92]
3 years ago
13

Wyoming is an approximately square-shaped state. The area of Wyoming is 97,818 square miles. To the nearest mile, how long is on

e side of Wyoming?
Mathematics
1 answer:
BartSMP [9]3 years ago
5 0

The formula for area of a square is Area = side^2.

You are given the area, so now you have 97,818 = Side^2.

To find Side, take the square root of both sides:

Side = √97818

Side = 312.76 miles.

Rounded to the nearest mile is 313 miles.

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Answer:

Steve should use:

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Step-by-step explanation:

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\text{Side length of the Square,} s= \dfrac{52-x}{4}

\text{Area of the Square},s^2= \left(\dfrac{52-x}{4}\right)^2=\dfrac{(52-x)^2}{16}=\dfrac{x^2-104x+2704}{16}

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Area=\dfrac{16x^2+\pi(x^2-104x+2704)}{16\pi}\\=\dfrac{16x^2+\pi x^2-104\pix+2704\pi}{16\pi}\\=\dfrac{x^2(16+\pi)-104\pi x+2704\pi}{16\pi}\\=\dfrac{x^2(16+\pi)}{16\pi}-\dfrac{104\pi x}{16\pi}+\dfrac{2704\pi}{16\pi}\\A=\dfrac{x^2(16+\pi)}{16\pi}-6.5x+169

This is the function of a parabola which opens up.

To find where A is minimum, find the axis of symmetry.

$Using \: x=-\frac{b}{2a}

a=\dfrac{16+\pi}{16\pi}, b=-6.5\\ x=-\dfrac{-6.5}{2(\dfrac{16+\pi}{16\pi})}=8.53\:Inches

Steve should cut the wire so that the length of wire used to make a circle is 8.53 Inches.

Length of wire used to make the square =52-8.53=43.47 Inches

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