Use Stokes' Theorem to calculate the circulation of the field F around the curve C in the indicated direction.F = x2i + xyj + yk; C: the counterclockwise path around the perimeter of the rectangle in the x-y plane formed from the x-axis, y-axis , x = 2 and y = 9

A. -162
B. - 81
C. 81
D. 162


Answer: C

Mathematics

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Use the Venn diagram to list the set of elements in roster form.Find A ? B'.

A. {P, G} B. {Z, P, G, <, &, *} C. {<, *} D. {P, G, <, *}

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Find the simplest form of a second-order homogeneous linear differential equation that has the given solution.y = c1e-8x + c2e-5x 

A. D2y + 13Dy + 40y = 0 B. D2y + 13Dy - 40y = 0 C. D2y - 13Dy - 40y = 0 D. D2y - 13Dy + 40y = 0

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Simplify. Write your answer with positive exponents only.

A.  
B.  
C.
D.  

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Use a sum or difference identity to find the exact value.tan 

A. -1 - 
B. -1
C. -2 - 
D. -1 - 

Mathematics