Edexcel Mathematics June 2022 · Paper 2 · Question 14

June 2022 · Paper 2 · Question 14 · 10 marks

$14. (a) Express 3 21 1 () () xx−+ in partial fractions. (3) When chemical A and chemical B are mixed, oxygen is produced. A scientist mixed these two chemicals and measured the total volume of oxygen produced over a period of time. The total volume of oxygen produced, V m3 , t hours after the chemicals were mixed, is modelled by the differential equation d dV t = 3 21 1V tt() ()−+ V  0 t  k where k is a constant. Given that exactly 2 hours after the chemicals were mixed, a total volume of 3 m3 of oxygen had been produced, (b) solve the differentia l equation to show that V = 32 1 1() ()t t− + (5) The scientist noticed that • there was a time delay between the chemicals being mixed and oxygen being produced • there was a limit to the total volume of oxygen produced Deduce from the model (c) (i) the time delay giving your answer in minutes, (ii) the limit giving your answer in m3 (2) 37 38 39$

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