19 A curve has equation $$y ^ { 3 } \mathrm { e } ^ { 2 x } + 2 y - 16 x = k$$ where \(k\) is a constant. The curve has a stationary point on the \(y\)-axis.
Determine the value of \(k\)
2 A gardener stores rainwater in a cylindrical container. The container has a height of 130 centimetres.
The gardener empties the water from the container through a hose.
The hose is attached 5 centimetres from the bottom of the container.
At time \(t\) minutes after the hose is switched on, the depth of water, \(h\) centimetres, in the container decreases at a rate which is proportional to \(h - 5\) Initially the container of water is full, and the depth of water is decreasing at a rate of 1.5 centimetres per minute.