In Exercises 55–58, F is the velocity field of a fluid flowing through a region in space. Find the flow along the given curve in the direction of increasing t. 55. F = -4xyi + 8yj + 2k r(t) = ti + t²j + k, 0

In Exercises 55–58, F is the velocity field of a fluid flowing through a region in space. Find the flow along the given curve in the direction of increasing t. 55. F = -4xyi + 8yj + 2k r(t) = ti + t²j + k, 0

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

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Question

In Exercises 55–58, F is the velocity field of a fluid flowing through a
region in space. Find the flow along the given curve in the direction of
increasing t.
55. F = -4xyi + 8yj + 2k
r(t) = ti + t²j + k, 0<t<2
56. F = x²i + yzj + y²k
r(t) = 3tj + 4tk, 0<t< 1
57. F %3D (x — 2)і + xk
r(t)
= (cos t)i + (sin t)k, 0<ts
58. F = -yi + xj + 2k
r(t) = (-2cos t)i + (2 sin t)j + 2tk,
0 <t< 2m
%3D

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