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

9/2 = 4.50

128/3 = 42.7

1. (a) P = (4, 8)
2. (b) 32/3 = 10.7

123/4 = 30.8

\(f(x)=12x^3 + \frac{3}{x^2}\)

1. (a) x = 1.39 and x = 8.61
2. (b) 14.2

\(k=0.5\); 34.7 grams

1350 kg

1. (a) 43.5 millilitres
2. (b) about 46.0 millilitres
3. (c) The rate is not defined at \(t=0\) and is very large just after it: the model cannot be used from the start.

1. (a) \(\int_0^{45}\frac{t^2}{40}\,dt\)
2. (b) 759 m³
3. (c) The total volume of water drained from the cellar in the first 45 minutes: 759 m³.
4. (d) 36.3 minutes

32/3 = 10.7