The surface σ shown in the accompanying figure on the next page, called a M o ¨ b i u s s t r i p , is represented by the para-metric equations x = 5 + u cos υ / 2 cos υ y = 5 + u cos υ / 2 sin υ z = u sin υ / 2 Where − 1 ≤ u ≤ 1 and 0 ≤ υ ≤ 2 π . (a) Use a CAS to generate a reasonable facsimile of this surface. (b) Use a CAS to approximate the location of the centroid of σ (see the definition preceding Exercise 33).
The surface σ shown in the accompanying figure on the next page, called a M o ¨ b i u s s t r i p , is represented by the para-metric equations x = 5 + u cos υ / 2 cos υ y = 5 + u cos υ / 2 sin υ z = u sin υ / 2 Where − 1 ≤ u ≤ 1 and 0 ≤ υ ≤ 2 π . (a) Use a CAS to generate a reasonable facsimile of this surface. (b) Use a CAS to approximate the location of the centroid of σ (see the definition preceding Exercise 33).
Precalculus: Concepts Through Functions, A Unit Circle Approach to Trigonometry (4th Edition)
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