5 In this question you must show detailed reasoning. The region bounded by the \(x\)-axis, the \(y\)-axis, the line \(x = 4\) and the curve with equation \(\mathrm { y } = \frac { 15 } { \sqrt { \mathrm { x } ^ { 2 } + 9 } }\) is occupied by a uniform lamina. The centre of mass of the lamina is at the point \(G ( \bar { x } , \bar { y } )\) (see diagram).
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1. Show that \(\bar { x } = \frac { 2 } { \ln 3 }\).
2. Determine the value of \(\bar { y }\). Give your answer correct to \(\mathbf { 3 }\) significant figures.
   \(P\) is the point on the curved edge of the lamina where \(x = 3\). The lamina is freely suspended from \(P\) and hangs in equilibrium in a vertical plane.
3. Determine the acute angle that the longest straight edge of the lamina makes with the vertical.