Line segment D runs from (1, -4, 3) to (2, 0, -1). Determine how much work is done by the force field F(x, y, z) = <3y2/4, sin2(z+3), -cos2(2-y)>
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Line segment D runs from (1, -4, 3) to (2, 0, -1). Determine how much work is done by the force field F(x, y, z) = <3y2/4, sin2(z+3), -cos2(2-y)>
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- A particle starts at the point (−4, 0), moves along the x-axis to (4, 0), and then along the semicircle y = 16 − x2 to the starting point. Use Green's Theorem to find the work done on this particle by the force field F(x, y) = 5x, x3 + 3xy2 .Find the work done by the force field 2 2, , , 3 , x y z z z y z z x F in moving a particle along the line segment from (0, 2, 0) to (−4, 3, 2).Find the word done by the force field F (x,y,z)= <x-y2, y-z2, z-x2> on a particle that moves along the line segment from (0,0,1) to (2,1,0)
- Find the gradient vector field for the scalar function f(x,y)=sin(2x)cos(6y). Enter the exact answer in component form. ∇(x,y)=A particle starts at the point (-2,0), moves along the x-axis to (2,0) and then along the semicircle y=radical(4-x^2) to the starting point. Use Green’s Theorem to find the work done on this particle by the force field F(x,y) =(2x,x^3+3xy^2).Given the vector field v=⟨0,2xz+3y^2,4yz^2 ⟩. Find the line integral of the path from (0,0) to (0,1). Please show full solution legibly. Thank you!!
- Calculate for the axial force in kN at member DC of the frame shown in figure 2 using Cantilever Method. Enter absolute value and use 2 decimal places in your solution.Find the parametrization of two different curves from the point (2,4) to (3,9). Compute the work done of the vector field F=〈2xy,x2+2〉over the two curves found in part (a).Find a unit vector tangent to the curve of intersection of -x^2 - 2y^3 = z - 3 and 25/x2 - 4y - 3z^2 = - x + 6 at the point (1,1,0).
- an object is moving in 3-dimensional space with velocity vector v(t)=(sin(t),t,t^2) starting at point (0,0,1). At what point will it be after 5 times units?Suppose ƒ is differentiable at (9, 9), ∇ƒ(9, 9) = ⟨3, 1⟩, and w = (1, -1). Compute the directional derivative of ƒ at ⟨9, 9⟩ in the direction of the vector w.Find the work done in moving a particle in a force field F = 3xyi - 5xyzj + 10xk along: straight line (0,0,0) to (2,3,4) space curve x = 2t3, y = 2t2 , z = 3t3-t2 from t = 0 to t = 3 The curve defined by x2 = 4y, 3x3 = 8z from x = 1 to x=3