C'sthe closed path that consists first of the line y- z, trom (0,0) to (2,4), then of the straight line from (2,4) to (0,6), and then the striaght line from 10.4) to (0,01, as shown in the Figure below. The path is in the presence of a vctor field given by F = 7zyi + 6z²j. (24) Calculate the line integral S.F • dg along the three curves. Curve 1, where y = : Curve 2, where y= -z+6: Curve 3, where z = 0: Total along the three curves: S. F• dg= Note: round all answers to 2 decimal places. Use Green's Theorem to evaluate the line integral f. v • dr, around the closed curve Coriented clockwise. Use a yertical slice. de dzdy dy f, y • dp =

Q: 12) Show (P,t,') 으(KDO) Hint: f. 12 →K, fa)=]

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Q: 20) For each vector field F, evaluate the circulation along the curve C consisting of the portion of…

A: Step 1:Step 2:Step 3:Step 4:

Q: Find the divergence of the field F. F = - 4x5i + 2y5j-8z5k OA. - 4x4 +2y4 -8z4 OB. 20x4 +10y4 - 40z4…

A: To find the divergence of the field F.F=-4x5i+2y5j-8z5k

Q: Given the 2-D vector field : G(x, y) = (2y)î + (x)j and the triangular curve T : line segments from…

A: Given: G→x,y=2yi^+xj^ Triangular curve T, line segments from point A0,0 to point B4,0 to point D4,2…

Q: 1. This question concerns the field F(x, y) = (1,x). a) Plot field F in the window [-2, 2] × [-2,2].…

A:

Q: 1. Match the following DE's with the correct slope field. a) y' = xy-1 b) y' = x² + y? -3 c) y' =…

A: Solution for a: y'=xy-1 Slop field is Solution for b: y'=x2+y2-3 Slop field is

Q: Plz give correct solution. Suppose T in L(F^2) and dim E(3, T) = 2. Prove that T is invertible.

A: The transformation is :  The aim is to prove that "T" is invertible.

Q: Which vector field would generate this graph? 0( - y, – a) O (y, z) O (x, – y) 0( - 1, y)

A: We check the given vector field one by one. First one is fx,y=-y,-x Now, for point 1,1 we see that…

Q: Match each vector field with its graph. ? 1. F(x, y) = x² + yj ? ? 2. H(x, y) = x² - yj 3. G(x, y) =…

A:

Q: (a) (b) Let V = F" and let A EMnxn (F), F is complex field. Prove that (x, y) = (4¹x, y) for all x,…

A:

Q: To calculate from elliptic curves we will use a simple approximation. For example, consider the…

A: Consider, the curve is y² = x3 + 17. The points are given by P=-1,4 and Q=2,5.

Q: 1. Use isoclines to sketch the direction field for y' = x+ 2y and sketch the solution curve that…

A:

Q: Suppose (B - C) D = 0, where B & C are m x n matricies and D is invertible. Show that B = C.

A: Given that  (B-C)D =0 here B and C are m×n matrices

Q: Show that Sa fdx + gdy = Sa - (16x*y²dx + 8yxʻdy) is independent of path: (10,5) –2) (10,5) ,-2) 4…

A: We are given a line integral as follows : ∫1, -210, 5 fdx+gdy=∫1, -210, 5 -(16x3y2dx+8yx4dy)   First…

Q: Suppose C is the curve from (0, 0) to (2, 0) to (2, 3) to (0, 3) to (0, 0). Find the work done by…

A:

Q: Consider the vector field v(z) = i+ i+4k . a) Calculate fu• dr , where l' is the straight line from…

A: We’ll answer the first part of this question since due to complexity. Please submit the question…

Q: Let Compute дw -(-2,-2) = -(-2,-2) = მs дw St W = 2xy - 2yz + 3xz, x = st, y = est, z = t² =

A:

Q: 6. Find the circulation of the field F(x, y) = -yi + x²j along the closed elliptical path x² + = 1…

A:

Q: 6. A mountaineer is She begins her jo (a) Calculate th

A: Directional derivative at point is obtained by derivation of the function at x and y variables or…

Q: 2x 2y Consider the vector field F = |x² + y2’ x² + y² (a) If C1 is the unit circle x² + y² = 1,…

A: Compute the circulation and flux using parameterization:  ∮C1Fdr=∮C12xx2+y2,2yx2+y2·dx,dy…

Q: Therefore, div(curl G) = sin(y) – sin(y) + 8 = Since div(curl G) is different from 0, we conclude…

A: Given that:div(curl G)=siny-siny+8=