Q295 · Practice questionTechnology-freeComplex familiar6 marks
QUESTION 295 (6 marks)
Water enters a tank at rate litres per minute, while water leaves at litres per minute. Initially the tank contains litres. The model applies for .
![Solid inflow graph I(t)=8+4 sin(pi t/6) on [0,12]; dashed horizontal outflow line at 6 L/min.](/qce-data/assets/methods-2026-MM26-ORIG-057-mobile.svg)
a)[3 marks]
Determine the amount of water in the tank.
b)[2 marks]
Determine all times in the interval when is stationary.
c)[1 mark]
Determine exactly.
WORKED SOLUTION
6 marksPractice marking scheme
ANSWER
a) . b) and min. c) L.
Worked solution
a) . Integrate and use .
b) Solve for arguments in . The arguments are and , giving .
c) , so .
Exact answers unless rounding is specified; equivalent forms accepted.
a) Uses inflow minus outflow.
a) Integrates correctly.
a) Uses the initial volume.
b) Solves the trigonometric equation on the domain.
b) Gives both times.
c) Gives 44 litres.
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