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Further applications of differentiation — Question 378

Original QCE Vault practice · 6 marks

Q378 · Practice questionTechnology-activeComplex unfamiliar6 marks

QUESTION 378 (6 marks)

For 0≤t≤120\leq t\leq12, a reservoir level is modelled by H(t)=7+3sin⁡(πt/6)H(t)=7+3\sin(\pi t/6) metres, where tt is measured in hours. An alarm sounds only when the level is above 99 m and rising at more than 11 m/hour. An engineer claims that the alarm will sound for at least 2020 minutes during this period. Evaluate the reasonableness of the claim.
a)
Use mathematics to justify your evaluation.
[6 marks]
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