Find the mass M of a fluid with a constant mass density flowing across the paraboloid z = 36-x² - y², z ≥ 0, in a unit of time in the direction of the outer unit normal if the velocity of the fluid at any point on the paraboloid is F = F(x, y, z) = xi + yj + 13k. (Express numbers in exact form. Use symbolic notation and fractions where needed.) M = Incorrect 31740π. Feedback Use A Surface Integral Expressed as a Double Integral Theorem. Let S be a surface defined on a closed bounded region R with a smooth parametrization r(r, 0) = x(r, 0) i+ y(r, 0)j + z(r, 0) k. Also, suppose that F is continuous on a solid containing the surface S. Then, the surface integral of F over S is given by F(x, F(x, y, z) ds = ´= ا³. Recall that the mass of fluid flowing across the surface S in a unit of time in the direction of the unit normal n is the flux of the velocity of the fluid F across S. M = 0₂² F-ndS F(x(r, 0), y(r, 0), z(r, 0))||I, X Io|| dr dº
Find the mass M of a fluid with a constant mass density flowing across the paraboloid z = 36-x² - y², z ≥ 0, in a unit of time in the direction of the outer unit normal if the velocity of the fluid at any point on the paraboloid is F = F(x, y, z) = xi + yj + 13k. (Express numbers in exact form. Use symbolic notation and fractions where needed.) M = Incorrect 31740π. Feedback Use A Surface Integral Expressed as a Double Integral Theorem. Let S be a surface defined on a closed bounded region R with a smooth parametrization r(r, 0) = x(r, 0) i+ y(r, 0)j + z(r, 0) k. Also, suppose that F is continuous on a solid containing the surface S. Then, the surface integral of F over S is given by F(x, F(x, y, z) ds = ´= ا³. Recall that the mass of fluid flowing across the surface S in a unit of time in the direction of the unit normal n is the flux of the velocity of the fluid F across S. M = 0₂² F-ndS F(x(r, 0), y(r, 0), z(r, 0))||I, X Io|| dr dº
Functions and Change: A Modeling Approach to College Algebra (MindTap Course List)
6th Edition
ISBN:9781337111348
Author:Bruce Crauder, Benny Evans, Alan Noell
Publisher:Bruce Crauder, Benny Evans, Alan Noell
ChapterA: Appendix
SectionA.2: Geometric Constructions
Problem 9P: A soda can is made from 40 square inches of aluminum. Let x denote the radius of the top of the can,...
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