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ASSIGNMENT 1 for SECTION 001 There are three parts to this assignment. Part A is to be completed online before 7:00 a.m. on Friday, September 17. Part B and Part C, which require full solutions, are to be handed in at the beginning of class on the same date. Part A [10 marks] This part of the assignment focuses on fundamental skills and computations. It can be found online, labelled A1, at webwork.elearning.ubc.ca — sign in using the MATH110 001 2010W button. Part B [5 marks] This part of the assignment is drawn directly from the course texts. It focuses on mathematical exposition; you will be graded primarily on the clarity and elegance of your solutions. From the Just-In-Time text, complete the following questions: section 3.2, question 24; and section 4.2, question 18. Part C [15 marks] This part of the assignment consists of more challenging questions. You are expected to provide full solutions with complete arguments and justifications. 1. Prove Pythagoras’ theorem in a way different than the one shown in class. (One possible method: calculate the area of the following shape in two ways.) c a b 2. Consider the graph of the distance between Earth and the planet nearest to it, as a function of time. Is the graph continuous? Put another way, is the graph a single, unbroken curve? 3. A quadratic curve is a curve of the form y = ax2 + bx + c where a, b and c are real numbers, with a not equal to zero. A cubic curve is a curve of the form y = Ax3 + Bx2 + Cx + D where A, B, C and D are real numbers, with A not equal to zero. What is the maximum number of times a quadratic curve might intersect a cubic curve?