The diagram shows the curve \(y=1+3\sqrt{2x}\) and the line \(2y+x=16\). The curve and the line intersect at the point \(A\).
Show that the coordinates of \(A=(2,7)\).[3]
Find the shaded area bounded by the curve \(y=1+3\sqrt{2x}\), the line \(2y+x=16\) and the line \(x=18\).[4]
Area \(Z\) is bounded by the curve \(y=1+3\sqrt{2x}\), the line \(2y+x=16\) and the \(y\)-axis. To find the area \(Z\), a student writes down the formula \(\text{Area}\hspace{0.5em}Z=\displaystyle\int_a^7g(y)\,\mathrm{d}y+B\). Find an expression for \(g(y)\) and the values of \(a\) and \(B\).[3]