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A wire, 4 meters long, is cut into two pieces. One is bent into a shape pf a square and the other into a shape of a circle.

1. If the length of wire used to make the circle is x metres, write in terms of $x$ the length of the sides of the square in metres.
2. Show the sum of the areas of the circle and the square is given by $f(x) = (\frac{1}{16} + \frac{1}{4\pi})x^{2} - \frac{x}{2} + 1$
3. How should the wire be cut so that the sum of the areas of the circle and the square is a minimum?
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