Concept explainers
Motion of a Liquid In Exercises 85 and 86, the motion of a liquid in a cylindrical container of radius 4 is described by the velocity
. Find
where S is the upper surface of the cylindrical container.
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Calculus (MindTap Course List)
- Nonuniform straight-line motion Consider the motion of an object given by the position function r(t) = ƒ(t)⟨a, b, c⟩ + ⟨x0, y0, z0⟩, for t ≥ 0,where a, b, c, x0, y0, and z0 are constants, and ƒ is a differentiable scalar function, for t ≥ 0.a. Explain why r describes motion along a line.b. Find the velocity function. In general, is the velocity constant in magnitude or direction along the path?arrow_forwardEXERCISE 5 The temperature is T degrees at any point (x, y, z) in three-dimensional space and T(x,y, z) = 1/(x² + y² + z² + 3). %3D Distance is measured in inches. (a) Find the rate of change of the temperature at the point (3, –2, 2) in the direction of the vector –2 i+3j-6k. (6) Find the direction and magnitude of the greatest rate of change of T at (3,–2,2). 14arrow_forwardDetermine the moments of inertia of the Z-section about its centroidal xo- and yo-axes. -130 mm 21 mm yo 155 mm 21 mm 21 mm -130 mm Answers: (106) mm4 i (106) mm4 i lyo IIarrow_forward
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- Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:CengageAlgebra and Trigonometry (MindTap Course List)AlgebraISBN:9781305071742Author:James Stewart, Lothar Redlin, Saleem WatsonPublisher:Cengage Learning