Answered: 1. A wire is parametrized by (t, 5t –… | bartleby

Algebra & Trigonometry with Analytic Geometry

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter3: Functions And Graphs

Section3.1: Rectangular Coordinate Systems

Problem 22E

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Question

1. A wire is parametrized by (t, 5t – 3,3 – t2) from 0 <t< 1.
(a) The density of the wire is given by p(x, y, z) = Vī g/cm. What is the total mass of the wire?
(b) An electric field is given by E(x, y, z) = (y+ 3, 2x, 2r + z). What is the work done by the field
on an electron moving along the parametrization?

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You are now allowed to assume that the half-planes determined by the line with the equation ax+by +c = 0 correspond to the points (x, y) so that ax + by + c < 0 and ax + by + c > 0, respectively. Usingthis, show that axiom B4(i) holds. (Hint. Suppose (q, r) and (s, t) are on the same side of the given lineand that (s, t) and (u, v) are on the same side of the given line. en construct the parametrized linethrough (q, r) and (u, v). Consider the mappingλ γ7→ a(q − qλ + uλ) + b(r − rλ + vλ) + c and note that it is continuous and either increasing or decreasing. Use this fact to show that, for everyλ, γ(λ) > 0 or γ(λ) < 0, depending on which half-plane the points are on.)
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For vectors in the unit circle 11 x 11 = 1, the vectors y = Ax in the ellipse will have 11 A -l y 11 = 1. This ellipse has axes along the singular vectors with lengths = 0"1, ... , O"r (as in Figure 7.5). Expand IIA-1 Yll2 = 1 for A= [2 1; 1 2].
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