Stitz-Zeager_College_Algebra_e-book

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Unformatted text preview: 8π 5 ≈ 0.309 + 0.951i ≈ −0.809 + 0.588i ≈ −0.809 − 0.588i ≈ 0.309 − 0.951i √ √ 7. p(x) = x12 − 4096 = (x − 2)(x +2)(x2 +4)(x2 − 2x +4)(x2 +2x +4)(x2 − 2 3x +4)(x2 +2 3+4) 11.8 Vectors 11.8 859 Vectors As we have seen numerous times in this book, Mathematics can be used to model and solve real-world problems. For many applications, real numbers suﬃce; that is, real numbers with the appropriate units attached can be used to answer questions like “How close is the nearest Sasquatch nest?” There are other times though, when these kinds of quantities do not suﬃce. Perhaps it is important to know, for instance, how close the nearest Sasquatch nest is as well as the direction in which it lies. (Foreshadowing the use of bearings in the Exercises, perhaps?) To answer questions like these which involve both a quantitative answer, or magnitude, along with a direction, we use the mathematical objects called vectors.1 Vectors are represented geometrically as directed line segments where the magnitude of the vector is taken to be the length of the line segment and the direction is made clear with the use of an arrow at one endpoint of the segment. When referring to vectors in this text, we shall adopt2 the ‘arrow’ notation, so the symbol v is read as ‘the vector v ’. Below is a typical vector v with endpoints P (1, 2) and Q (4, 6). The point P is called the initial point or tail of v and the point Q is called the terminal point or head of...
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