ASSIGNMENT 2·11 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. According to Boyle’s Law, if a quantity of gas is enclosed in a container at a constant temperature, then its pressure p and volume V are inversely proportional. Suppose that, at a certain point, the pressure in a 500 cm3 piston chamber is 200 kPa, and rising at a rate of 10 kPa/second. At what rate is the volume decreasing? 2. It is estimated that the Great Pyramid of Giza was built at a rate of around 350 m3 per day. Assuming that this rate was constant and that the pyramid was built from the ground up, how quickly was the height of pyramid increasing ten years after its construction began? 3. Determine the rate at which the shadow cast by the Ladner clock tower is lengthening, at the specific moment in the afternoon when the shadow is as long as the tower is high. Be sure to explain your solution clearly, indicating all your assumptions.