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Chapter 16 Solutions
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- answer in fraction please thanksarrow_forwardCalculate the curl of the vector g = (x−y) ax+(y+x) ay, and visualize it. Explain what does "curl of vector field" mean, in your own words. When does it equal zero?arrow_forwardA net is dipped in a river. Determine the flow rate of water across the net if the velocity vector field for the river is given by = (x - y, z + y + 9, z) and the net is decribed by the equation y = V1-x - z, y 2 0, and oriented in the positive y- direction. (Use symbolic notation and fractions where needed.) V. dS =arrow_forward
- Cal 3arrow_forward(a) Calculate the flux of the vector field F(x, y, z) = 275k through a sphere of radlus 4 centered at the origin, oriented outward. Flux = (b) Calculate the flux of the vector field F(x, y, z) = -53 +5 through a cube of side length 4 with sides parallel to the axes, oriented OL Flux =arrow_forwardCompute the flux of the vector field F = 5yi +37-5xzk through the surface S, which is the surface y = x² + 2², with x² + 2² ≤ 1, oriented in the positive y-direction. flux = You can get a hint after 2 incorrect answers.arrow_forward
- Please do all a to darrow_forwardA net is dipped in a river. Determine the flow rate of water across the net if the velocity vector field for the river is given by v = (x - y, z + y + 6, z? ) and the net is decribed by the equation y = 1 – x - z', y 2 0, and oriented in the positive y- direction. (Use symbolic notation and fractions where needed.) · dS = Incorrectarrow_forwardUse the rule of differentiation of the scalar product, to evaluate(u · v) for the following vector fields: and a) ú= Calculate the time derivatives of u and v. Represent your answers in the form i+ j+ k and v = i+ (u. v)= j+ u = eªt i + 4t² j +1 k. е k. v = 5i + sin(3t)j + cos(6t) k. b) Now calculate the time derivative of scalar product of u and v: d (u dtarrow_forward
- Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:CengageElementary Linear Algebra (MindTap Course List)AlgebraISBN:9781305658004Author:Ron LarsonPublisher:Cengage Learning