3 The equation of a curve is such that \(\frac { \mathrm { d } y } { \mathrm {~d} x } = \frac { 1 } { 2 } x + \frac { 72 } { x ^ { 4 } }\). The curve passes through the point \(P ( 2,8 )\).
- Find the equation of the normal to the curve at \(P\).
- Find the equation of the curve.
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The diagram shows the shape of a coin. The three \(\operatorname { arcs } A B , B C\) and \(C A\) are parts of circles with centres \(C , A\) and \(B\) respectively. \(A B C\) is an equilateral triangle with sides of length 2 cm . - Find the perimeter of the coin.
- Find the area of the face \(A B C\) of the coin, giving the answer in terms of \(\pi\) and \(\sqrt { 3 }\).