Mass In Exercises 25-28, find the total mass of the wire with density
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Calculus, Early Transcendentals
- ange Use Newton's Second Law of Motion to find the force required so that a particle of mass 2 iao position r(t) = (t², t“, sin(2t)) %3D u Select one: a. (2, 12t2,-4 sin(20)) b. (4, 24t2, -8 sin(2t;, C. 28 d. 24 e. (2t, 4t3, 2 cos(2t))arrow_forwarddivĒ = 0 divĤ = 0 1 ƏĦ curlĒ c ðt 1 DỂ curlĦ - c ət Using Maxwell's equations, show 1 ²Ē c2 Ət² (V · V)Ẽ =arrow_forwardUse spherical coordinates. Let H be a solid hemisphere of radius 5 whose density at any point is proportional to its distance from the center of the base. (Let K be the constant of proportionality.) (a) Find the mass of H. (b) Find the center of mass of H. (Assume the upper hemisphere of a sphere centered at the origin.) (x, y, z) = ( (c) Find the moment of inertia of H about its axis Iz =arrow_forward
- how do i solve the attached calculus problem?arrow_forwardSubject-advance mathsarrow_forwardEvaluate the circulation of G = xyi + zj + 4yk around a square of side 4, centered at the origin, lying in the yz-plane, and oriented counterclockwise when viewed from the positive x-axis. Circulation = Jo F. dr =arrow_forward
- Evaluate the circulation of G = xyi+zj+7yk around a square of side 9, centered at the origin, lying in the yz-plane, and oriented counterclockwise when viewed from the positive x-axis. Circulation = Prevs So F.dr-arrow_forwardCalc 3arrow_forward100 cm 180 cm 130 cm Figure Q3 (a): Right-angle triangular roofarrow_forward
- Determine the distance to the centroid of the beam's cross-sectional area; then determine the moment of inertia about the x' axis.arrow_forwardConsider the vector-valued function r(t) = cos ti + sin tj + In(cos t)k. (a) Find the vectors T, N, and B of r at the point P = (1,0,0). (b) Find the tangential and normal components of the acceler- ation of r at the point P = (1,0,0).arrow_forwardUse Stokes' Theorem to find the circulation of F = 5yi + 3zj + 6xk around a circle C of radius 7 centered at (5, 2, 7) in the plane z = 7, oriented counterclockwise when viewed from above. Circulation = [² с F. dr =arrow_forward
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