Initially there are 350 litres of water in a tank - HSC - SSCE Mathematics Advanced - Question 15 - 2024 - Paper 1

Now substitute ( t = 40 ) into the volume equation derived from the initial condition:

First, integrate to find ( V ):

[ V = 300t - \frac{7.5t^2}{2} + C ]

Substituting ( t = 0 ) gives:

[ V(0) = 350 \implies 350 = 300(0) - \frac{7.5(0)^2}{2} + C \implies C = 350 ]

So, the equation for ( V ) becomes:

[ V = 300t - 3.75t^2 + 350 ]

Now, substituting ( t = 40 ):

[ V = 300 \times 40 - 3.75 \times 40^2 + 350 ]
[ V = 12000 - 6000 + 350 ]
[ V = 12000 - 6000 + 350 = 6350 ]\

The volume of water in the tank when ( \frac{dV}{dt} = 0 ) is ( 6350 ) litres.