Unit mixed practice: areas, rates and accumulation Problem set B Answers

125/6 = 20.8

250/3 = 83.3

1. (a) P = (6, 24)
2. (b) 36

44/3 = 14.7

\(f(x)=15x^2 - \frac{10}{x^2}\)

1. (a) x = 1.59 and x = 4.41
2. (b) 1.32

\(k=0.2\); 23.3 litres

250 litres

1. (a) 29.4 millilitres
2. (b) about 30.0 millilitres
3. (c) The rate is not defined at \(t=0\) and is very large just after it, so the model fails at the start. (Or: the ice would all melt in a finite time, but the model goes on for ever.)

1. (a) \(\int_0^{36}\frac{t^2}{60}\,dt\)
2. (b) 259 tonnes
3. (c) The total mass of grain loaded into the silo in the first 36 hours: 259 tonnes.
4. (d) 26.2 hours

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