3 11 Prove that the tangent to the curve y = e" , at the point where x = 2, passes through the origin. 2 x 2 e [5 marks] ax ely = = e z( z ) dxt = 25 sec Areac = = (ts) h 60 09 IS (2T+25) 600 = (+25+7 *15 N I= 27.5s Particles of mass 3m and 5m and are attached to either side of a vertical pulley by a light inextensible string, The system is released from rest. Show that a, the acceleration in the system, is given by a = - g ms 2, and find the tension in the string. [5 marks] of8 A heavy stone is dropped into a very deep lake. The speed, s m s" , of the stone at a time, t s, after it hits the water is modelled by this function. s(1) = 20(1-e-2) a Sketch the function s() indicating any asymptotes. [2 marks] s msb At what time will the stone have reached three quarters of its final speed? [2 marks] C Do you think that the function provides a realistic model of the speed of the stone. You must a reason for your answer [1 mark] No hasn't takento accent our resistance 9 A garden is in the shape of a triangle ABC The side lengths AB = 12 m and BC = 15 m. 12 The angle between sides AB and BC is 640 64 a Find the length AC and the area of the garden. [4 marks] AC = AB + BCA garden is in the shape of a triangle ABC 11 The side lengths AB = 12 m and BC = 15 m. 12 The angle between sides AB and BC is 640 C a Find the length AC and the area of the garden. IS [4 marks] AC = AB + BC - 2 ABBC COSABC AC = 12 + 15 - 2(11 12 ) ( 15)COS64 = 211 186 3872 AC= 14. 53m (usp) Area = + absne = 2 (12) (15 ) Sha4 = 80. 9 an ( 350) A gardener covers the surface of the garden evenly with top soil. If top soil costs $30 per cubic metre and the gardener spends $150 on top soil, find the depth of the soil. [2 marks] 150 - 5 en 30 vol = areax reight 5 = 80. 9xh h= 0. 00 2 M