Deriving a formula question (1 Viewer)

[VenomP]

A rural water dam is to be emptied by means of a control valve. The valve operates so that the volume of the water, V litres, remaining in the dam varies with the time, t minutes, according to the equation

dV / dt = -bt, where b is a constant

i) Initially the dam contains 250 000 litres of water.

Show that after t minutes, V = 250 000 - 1/2 br^2

ii) If b =0.431, at what rate will the dam be emptying when V = 85 000 litres?

 

[lolokay]

dV = -bt.dt
V = -b*1/2 t² + K
at t=0, V = 250 000
so V = 250 000 - 1/2 bt²