In ∆MNO, MN = 6 units, MO = 4 units and NO = 12 units. If the bisector of angle M meets NO at P, calculate NP.

Find the tangent to the acute angle between the lines 2x + y = 3 and 3x - 2y = 5.

From a point P, the bearings of two points Q and R are N67ºW and N23ºE, respectively. If the bearing of R from Q is N68ºE and PQ = 150m, calculate PR

Find the area bounded by the curve y = x(2-x). The x-axis, x = 0 and x = 2.