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hw2 - Math 53 Homework 2 Due Wednesday in section(The...

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Math 53 Homework 2 Due Wednesday 9/8/10 in section (The problems in parentheses are for extra practice and optional. Only turn in the underlined problems.) Tuesday 8/31 – Polar coordinates Read: sections 10.3, 10.4. Work: 10.3: (11), 17 , 19 , (25), 29 , 30 , (31), (37), (51), 53 , 63 , (69), (77), 83 . 10.4: (5), 7 , 23 , (31), 35 , (41), 45 , (47). (for 10.3 #83: either follow the book’s hint and compute tan φ first; or argue carefully that, using a suitable rotation, it is enough to consider the case θ = 0.) Bonus problem (extra credit): p. 672 problem 4. Thursday 9/2 – Vectors, dot product Read: sections 12.1, 12.2, 12.3. Work: 12.1: (5), (7), (11), 13 , (21), (27), 31 , 39 . 12.2: (3), (5), (15), 17 , (23), (25), 29 , (31), (37), 39 , 45 . 12.3: (1), (11), 19 , 23 , (25), (27), (34), 35 , (39), (45), (51), 56 , (60). Problem 1 below. Problem 1. The eight vertices of a cube centered at (0 , 0 , 0) of side length 2 are at ( ± 1 , ± 1 , ± 1). a) Find the four vertices of the cube, starting with (1 , 1 , 1), that form a regular tetrahedron. Confirm your answer by finding the length of an edge and explaining
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