(b) Use Green's theorem to calculate the circulation of F around the triangle with verticcs (2,0), (0,3), (–2,0) oricnted counterclockwisc where F = (2.x² +3y)i+ (2.r + 3y²)j.

Q: Find the curl, the divergence and the potential (if it exists) of F = (2x + y², 2ry + 3y²z*, 4y°z³)

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Q: Use Stokes' Theorem to find the circulation of F = 4yi + 4zj+ 3xk around the triangle obtained by…

A: We have to find ∫CF→·dr→ using Stokes'sTheorem

Q: A sodium ion (Na+) moves in the xy-plane with a speed of 2.90 ✕ 103 m/s. If a constant magnetic…

A:

Q: Determine the parametric equations of the flow lines for the velocity vector field, v, where v =…

A: The given velocity vector is v=yi+xj. To Find: parametric equations for flow lines of the above…

Q: Find the circulation f V. dR, where V = yi + (x² + y²)j + (x + y)k, and C' is the triangle with…

A: In this question we will find the circulation of

Q: 219. The diagram at right shows a rectangular solid, two of whose vertices are A = (0, 0, 0) and…

A:

Q: 1. Let R and b be positive constants. The vector function r(t) = (R cost, R sint, bt) traces out a…

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Q: Suppose F(x, y) = (x² + 6y, 2x − 2y²). Use Green's Theorem to calculate the circulation of around…

A:

Q: An Eulerian flow field is described in Cartesian coordinates by V = 4i+xzj+5y3tk. (a) Is it…

A: According to bartlrby guidelines we have to answer only first three subparts please upload the…

Q: Evaluate /| cos(x? + y²) dA, where D is the D disk x? + y <I Select one: a. -n O b. A O c. O O d. 2…

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Q: Let F (8xy, 3y, 8z). = The curl of F = (000). Is there a function f such that F = V f? ☐ (y/ (y/n)

A: Step 1: Step 2: Step 3: Step 4:

Q: 1. Obtain the directional derivative of: a.. f(x,y) = x²-4x³y² at the point (1,-2) in the direction…

A: Step 1:

Q: F(1, y.:)= (x², 2x²y*, 5yz*) Given: Find (a) div F (b) curl F

A:

Q: 1. Let U(x, y, z) be the scalar function: U(x,y,z) = xy/z+yz/x +zx/y a. Find VU b. curl (V U)

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Q: 7. For the vector-valued function √t-1 ln(2t - 1) t² - 1 r(t) = (VI- t-1 2 COS πt rt), (t (t = 1):…

A: Let us solve above problem

Q: Suppose F 2.xz + 3y²) ay + (4yz²) az. (a) Calculate fLL F dS, where S is the shaded surface in…

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Q: Let F = . [F Use Stokes' Theorem to evaluate F.dr, where C is the triangle with vertices (7,0,0),…

A: Given,             F→=4x+y2, 8y+z2, 9z+x2, Use Stokes' Theorem to find:                ∫CF→·dr→,…

Q: Find the flux of F = z²k upward through the part of the sphere æ² + y² + z² = a² in the first octant…

A: Given vector field is  F=z2k to find the flux through sphere x2+y2+z2=a2 in the first octant.

Q: Suppose that f(x, y) is continuous on D= {(z,y) |r² + y² ≤y, x>0} and satisfies Find f(x, y).…

A: We are given a relation, f(x,y) = 1-x2-y2-8π∬f(x,y)dx dy over D Where D=(x,y)|  x2+y2≤y

Q: (- 4,3). a) Let f(x, y)= x²y°. Find the directional derivative of f at P(-1,1) in the direction of ū…

A: a)

Q: Suppose F(x, y) = x² + y²j and C is the line segment segment from point P = (-3,-4) to Q = (-3, 1).…

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Q: Use Stokes' Theorem to find the circulation of F = 2yi + 3zj + 7xk around the triangle obtained by…

A: Here we have to solve the given problem using stokes' theorem.

Q: Compute the curl of F = (3y2, ay, 22).

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Q: Let f = (r +2ryz)i+( + 2xy)j+ (+ 2xyz)k. Find j at (1.0, 1). (a) divergence of

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Q: Calculate the divergence and the curl of this vector function.

A: “Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: ar(t) = cos(-10t)i+sin(-10t)j-10tk, compute A. The velocity vector v(t) = B. The acceleration vector…

A:

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.