page 08 MARKS 13. An electronic device contains a timer circuit that switches off when the voltage, V, reaches a set value. The rate of change of the voltage is given by , where k is a constant, t is the time in seconds, and 0 ≤ V < 12. Given that V = 2 when t = 0, express V in terms of k and t. 14. Prove by induction that ( ) ! ! 1 1 n r r r n = = + − ∑ 1 for all positive integers n. 15. The equations of two planes are given below. (a) Verify that the line of intersection, L1, of these two planes has parametric equations (b) Let π3 be the plane with equation . Calculate the acute angle between the line L1 and the plane π3. (c) L2 is the line perpendicular to π3 passing through P (1, 3, −2). Determine whether or not L1 and L2 intersect. 5 5 2 3 4