1. [5 points] Answer the following questions: a. How do you find the mass of a...
I really hope you can give me a complete answer and explain it , please don‘t Answer if you cannot I will definitely rate a good answer. thanks Show that the 3D force field is a conservative field. Find the work done against the force when moving from Write down (i) an expression for the gradient of a 3D scalar field Ф(x, y, z) and (ii) the pseudo-determinant expression for the curl of a vector field v. Then show that...
please solve all with detailed steps. thank you! Find the mass, and the center of mass of the solid cone D with density p(x, y, z) = 1 bounded by the surface z = 4- x2 + y2 and z = 0 1) 2) Evaluate dA where R is the square with vertices (0,0), (1,–1), (2,0), and (1,1) x+y+1 (Hint: use a convenient change of variables) 3) Evaluate the line integral (x - y+ 2z)ds where C is the circle...
please help me answer all 4, I need help. thank you Athin wire represented by the smooth curve C with a density (units of mass per longth) has a mass M ds. Find the mass of the wire c {xyxy=4x?, Os 55) with density px.y)-6+3xy. The mass of the wro is about (Round to one decimal place as needed.) Given the force field F, find the work required to move an object on the given oriented curve. F = (y....
please just the final answer for both Evaluate the surface Integral || 5. ds for the given vector fleld F and the oriented surface S. In other words, find the flux of F across S. For closed surfaces, use the positive (outward) orientation. F(x, y, z) = yi - xj + Szk, S is the hemisphere x2 + y2 + y2 = 4, 220, oriented downward 26.677 X Evaluate the surface integral llo F.ds for the given vector field F...
Evaluate the surface integral F dS for the given vector field F and the oriented surface S. In other words, find the flux of F across S. For closed surfaces, use the positive (outward) orientation. F(x, y, z) -xi yj+3 k S is the boundary of the region enclosed by the cylinder x2 + z2-1 and the planes y 0 and x y 2 Evaluate the surface integral F dS for the given vector field F and the oriented surface...
Evaluate the surface integralF F ds for the given vector field F and the oriented surface S. In other words, find the flux of F across S. For closed surfaces, use the positive (outward) orientation. S is the boundary of the region enclosed by the cylinder x2 + z2-1 and the planes y O and x y 3 Evaluate the surface integralF F ds for the given vector field F and the oriented surface S. In other words, find the...
21 Problem 20. Let S be the surface bounded by the graph of f(x,y)-2+y2 . the plane z 5; Os1; and .0sys1. In addition, let F be the vector field defined by F(x, y,z):i+ k. (1) By converting the resulting triple integral into cylindrical coordinates, find the exact value of the flux integral F.n do, assuming that S is oriented in the positive z-direction. (Recall that since the surface is oriented upwardly, you should use the vector -fx, -fy, 1)...
Consider the vector field F(x, y, z) = (z arctan(y2), 22 In(22 +1), 32) Let the surface S be the part of the sphere x2 + y2 + x2 = 4 that lies above the plane 2=1 and be oriented downwards. (a) Find the divergence of F. (b) Compute the flux integral SS. F . ñ ds.
Evaluate the surface integral S F · dS for the given vector field F and the oriented surface S. In other words, find the flux of F across S. For closed surfaces, use the positive (outward) orientation. F(x, y, z) = xzey i − xzey j + z k S is the part of the plane x + y + z = 7 in the first octant and has upward orientation.
Evaluate the surface integral F dS for the given vector field F and the oriented surface S. In other words, find the flux of F across S. For dlosed surfaces, use the positive (outward) orientation F(x, y, 2) _ yj-zk, sconsists ofthe paraboloid γ_x2 +22, O sys1, and the disk x2 +22 s 1.7-1. Need Help? to Tter Evaluate the surface integral F dS for the given vector field F and the oriented surface S. In other words, find the...