Bird Nguyen

04/05/2023 · Elementary School

Paraffin is stored in a tank with a horizontal base. At time \( t \) minutes, the depth of paraffin in the tank is \( x \mathrm{~cm} \). When \( t=0, x=72 \). There is a tap in the side of the tank through which the paraffin can flow. When the tap is opened, the flow of the paraffin is modelled by the differential equation \[ \frac{\mathrm{d} x}{\mathrm{~d} t}=-4(x-8)^{\frac{1}{3}} \text {. } \] (i) How long does it take for the level of paraffin to fall from a depth of 72 cm to a depth of 35 cm ? (ii) The tank is filled again to its original depth of 72 cm of paraffin and the tap is then opened. The paraffin flows out until it stops. How long does this take?