1. Optimization: An internet company is laying cable in an area with underground utilities. Two subdivisions marked as points P and Q are located on opposite sides of Willow Creek, which is 100 m wide. The company has to connect point P and Q with cable, where Q is on the north bank of Willow Creek, 1200 m east of P. It costs $40/m to lay cable underground and $80/m to lay cable under water. What is the least expensive way to lay the cable? [7 Marks] Q Willow Creek S R 2. Derivatives: a) Differentiate the following and do not simplify: f (x) = sin(cos(4*)) [2 Marks] b) In a research laboratory, a dish of bacteria is infected with a particular disease. The equation N(d) = (15d)e ' models the number of bacteria, /, that will be infected in d days. How many days before the maximum number of bacteria will be infected? Determine the maximum number of bacteria that will be infected. Round your final answer to 2 decimal places. [4 marks] 3. Vectors: Given a = 3, b = 2 and a + b = 4.84. Determine |a - b . Diagram required for full marks. Round final answer to 2 decimal places. [4 marks]