(a) Find the equation of the line that passes through the origin and the point of intersection of the lines \( x + 2y = 7 \) and \( x - y = 4 \). (b) The ratio of an interior angle to an exterior angle of a regular polygon is 4: 1. Find the: (i) number of sides; (ii) value of the exterior angle; and (iii) sum of the interior angles of the polygon.

(a) In the diagram above, \(\overline{PR}\) is a tangent to the circle O at Q. \(\angle\)POQ = 56º and  \(\overline{PO}\) intersect  \(\overline{SO}\) at V such that \(\angle\)SVP = 109º. Calculate: (i) \(\angle\)TQP (ii) \(\angle\)QTS

(b) Simplify \(\frac{2n^2 - 3n - 2 }{2n^2 + 3n + 1} \times \frac{n^2 - 1}{n^2 - 4}\)

(a) In the diagram above, ABT is a circle centre O. \(\overline{PQ}\) is a tangent to the circle at T and ABC is a straight line. \(\overline{TC}\) bisects \(\angle\)BTQ, \(\angle\)BAT = 44º and \(\angle\)PTA = 60º. Find \(\angle\)ACT

(b) The circumference of the base of a cylindrical tank is 11 m. The height of the tank is 3 m more than 6 times the base radius. Calculate the:

(i) radius; (ii) height; (iii) volume of the tank.