Moving to another question will save this response.Question 16Using Green's Theorem, compute the counterclockwise circulation of F around the closed curve C.F = xy i + x j; C is the triangle with vertices at (0, 0), (2, 0), and (0, 8)883648A Moving to another question will save this response.O O O

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Answered: Using Green's Theorem, compute the…

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter11: Topics From Analytic Geometry

Section: Chapter Questions

Problem 41RE

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Using Green's Theorem, compute the counterclockwise circulation of F around the closed curve C. F = sin 3y i + cos 7x j; C is the rectangle with vertices at (0, 0),(pi/7,0),(pi/7,pi/3) and (0,pi/3) a) 0 b) 2/3π c) - 2/3π d) -4/3 π
Using Green's Theorem, compute the counterclockwise circulation of F around the closed curve C. F= xyi+ xj; C is the triangle with vertices at (0,0), (10,0), and (0,2)
Divergence and flux from graphs Consider the followingvector fields, the circle C, and two points P and Q.a. Without computing the divergence, does the graph suggest that thedivergence is positive or negative at P and Q? Justify your answer.b. Compute the divergence and confirm your conjecture in part (a).c. On what part of C is the flux outward? Inward?d. Is the net outward flux across C positive or negative? F = ⟨x, y2⟩
In the spring equation F = k x, the spring force, F is called Group of answer choices an independent variable none of the above a dependent variable
Using Green's Theorem, compute the counterclockwise circulation of F around the closed curve C.F = xy i + x j; C is the triangle with vertices at (0, 0), (7, 0), and (0, 4)
Divergence and flux from graphs Consider the followingvector fields, the circle C, and two points P and Q.a. Without computing the divergence, does the graph suggest that thedivergence is positive or negative at P and Q? Justify your answer.b. Compute the divergence and confirm your conjecture in part (a).c. On what part of C is the flux outward? Inward?d. Is the net outward flux across C positive or negative? F = ⟨x, x + y⟩
(a) Find the minimum and maximum xcoordinates of points on the cardioid r =1−cosθ.(b) Find the minimum and maximum ycoordinates of points on the cardioid in part (a).
using laplace transformation the solution of the following D.E y''+y=3 with y(0)=0 , y'(0)=2 is:
Stream function and vorticity The rotation of a threedimensional velocity field V = ⟨u, v, w⟩ is measured by the vorticity ω = ∇ x V. If ω = 0 at all points in the domain, the flow is irrotational.a. Which of the following velocity fields is irrotational:V = ⟨2, -3y, 5z⟩ or V = ⟨y, x - z, -y⟩?b. Recall that for a two-dimensional source-free flow V = ⟨u, v, 0⟩ , a stream function ψ(x, y) may be defined such that u = ψy and v = -ψx. For such a two-dimensional flow, let ζ = k ⋅ ∇ x V be the k-component of the vorticity. Show that ∇2ψ = ∇ ⋅ ∇ψ = -ζ.c. Consider the stream function ψ(x, y) = sin x sin y on the square region R = {(x, y): 0 ≤ x ≤ π, 0 ≤ y ≤ π}. Find the velocity components u and v; then sketch the velocity field.d. For the stream function in part (c), find the vorticity function ζ as defined in part (b). Plot several level curves of the vorticity function. Where on R is it a maximum? A minimum?
Curve C for the following vector space using Green's theorem, with the curve 1 ≤ r ≤ 2, 0 ≤ θ ≤ π being the boundary of the region defined by polar coordinate inequalities. Calculate the flux through it.
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