Find the gradient of \(xy^{2} + x^{2} y = 4xy\) at the point (1, 3).
The position vectors of P, Q and R are \(11i + j, 5i + \frac{13}{3}j\) and \(2i + 6j\) respectively.
(a) Show that P, Q and R lie on a straight line.
(b) Find the ratio of \(|\overrightarrow{PQ}| : |\overrightarrow{QR}|\)
A committee of 3 is formed from a panel of 5 men and 3 women. Find the :
(a) number of ways of forming the committee ;
(b) probability that at least one woman is on the committee.
The table shows the distribution of the lengths of 20 iron rods measured in metres :
| Length (m) | 1.0 - 1.1 | 1.2 - 1.3 | 1.4 - 1.5 | 1.6 - 1.7 | 1.8 - 1.9 |
| Frequency | 2 | 3 | 8 | 5 | 2 |
Using an assumed mean of 1.45, calculate the mean of the distribution.
Find the direction of the resultant of the forces in the diagram.