Motion of a Liquid In Exercises 17 and 18, the motion of a liquid in a cylindrical container of radius 3 is described by the velocity field F(x, y, z). Find
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Calculus
- Use Stokes theoremarrow_forwardhow do i solve the attached calculus problem?arrow_forwardConsiser the position-dependent force F = (5 z)i + (2 y² + 5)j+ (5 æy+ 3xz+ 5x + 3z)k, acting on a particle. a. Find the work done, W, by the force as the particle moves from the point (x, y, z) = (0,0,3) to the point (x, y, z) = (2, 1, 7) along the following paths: i. the path defined by the position vector r = 2 ti +t°j+ (3+4t)k, for 0 < t < 1; W = sin (a) f Ω a ii. the path defined by the straight line x = 2 y, z = 2 x + 3. W =arrow_forward
- U (x, y) 4c(y + 1)i + xyj, and V(x, y) = Consider two vector fields in the xy plane, given in the Cartesian coordinates as: cyi - xj, where c is a constant. Find where in the xy plane the vectors of these two fields are parallel to one another, and where they are mutually orthogonal. =arrow_forwardUse Green's Theorem to find the work done by the force field F(x, y) = Vgi + Væj on a particle that moves along the stated path. The particle moves counterclockwise one time around the closed curve given by the equations y = 0, x = 7, and y = 9 NOTE: Enter the exact answer. Warrow_forwardHeat flux in a plate A square plate R = {(x, y): 0 ≤ x ≤ 1, 0 ≤ y ≤ 1} has a temperature distribution T(x, y) = 100 - 50x - 25y.a. Sketch two level curves of the temperature in the plate.b. Find the gradient of the temperature ∇T(x, y).c. Assume the flow of heat is given by the vector field F = -∇T(x, y). Compute F.d. Find the outward heat flux across the boundary {(x, y): x = 1, 0 ≤ y ≤ 1}.e. Find the outward heat flux across the boundary {(x, y): 0 ≤ x ≤ 1, y = 1}.arrow_forward
- Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:Cengage