A river, running between parallel banks, is 20 m wide. The depth, y y\,y metres, of the river measured at a point x x\,x metres from one bank is given by the formula
y=110x(20−x),0≤x≤20. y = \frac{1}{10}x\sqrt{(20-x)}, \quad 0 \leq x \leq 20. y=101x(20−x),0≤x≤20.Complete the table below, giving values of y y\,y to 3 decimal places.
| xxx | 0 | 4 | 8 | 12 | 16 | 20 |
|---|---|---|---|---|---|---|
| yyy | 0 | 2.771 | 0 |
Use the trapezium rule with all the values in the table to estimate the cross-sectional area of the river.
Given that the cross-sectional area is constant and that the river is flowing uniformly at 2 m s-1, estimate, in m3\text{m}^3m3, the volume of water flowing per minute, giving your answer to 3 significant figures.
