ASSIGNMENT 2·12 There are two parts to this assignment. The first part is on WeBWorK — the link is available on the course webpage. The second part consists of the questions on this page. You are expected to provide full solutions with complete arguments and justifications. You will be graded on the correctness, clarity and elegance of your solutions. Your answers must be typeset. They must be stapled, with your name and student number at the top of each page. 1. Consider two ships which are joined by a cable attached to each ship at the water line. Suppose the two ships are 200 metres apart, with the cable stretched tight and attached to a pulley which is anchored halfway between the ships at a depth of 45 metres. If one ship moves away from the other at 3 km/h, how quickly is the other ship moving after one minute? 2. Let z be the y-intercept of the linear approximation to ex at a. (Note that z may be written as a function dz of a.) Now suppose a itself is a function of time, with da dt = 3. Find dt when a = 2, and explain in plain English what your answer describes. 3. Come up with an expression describing your projected final grade g as a function of your confidence level l. Now suppose your confidence increases exponentially between now and the final exam. Determine the rate at which g will be increasing at the moment you write the exam. You should describe your constants and variables carefully, and defend any additional assumptions you make.