To compute the flux ∮ F → . n ^ d s of F → ( x , y ) = 〈 3 x , 2 y 〉 across the circle given by x 2 + y 2 = 9 using vector form of Green’s theorem.

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Answer 1

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Chapter 18.1, Problem 38E

To determine

To compute the flux $\oint \vec{F} . \hat{n} d s$ of $\vec{F} (x, y) = 〈 3 x, 2 y 〉$ across the circle given by $x^{2} + y^{2} = 9$ using vector form of Green’s theorem.

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A net is dipped in a river. Determine the flow rate of water across the net if the velocity vector field for the river is given by v=(x-y,z+y+7,z2) and the net is decribed by the equation y=1-x2-z2, y20, and oriented in the positive y- direction. (Use symbolic notation and fractions where needed.)

The figure shows the vector field F (x,y) = {2xy,x2 } and three curves that start at (1,2) and end at (3,2). (a) Explain why∫c F. dr has the same value for all the three curves. (b) What is this common value?

5) Find the flux of F = (-2y, -x) on the circle of radius 2 centered at the origin. Use the vector field grapher shown in class and cut and paste the vector field here. Before you calculate the flux do you expect your answer to be positive, negative, or zero?

Answer 2

Question

Chapter 18.1, Problem 38E

To determine

To compute the flux $\oint \vec{F} . \hat{n} d s$ of $\vec{F} (x, y) = 〈 3 x, 2 y 〉$ across the circle given by $x^{2} + y^{2} = 9$ using vector form of Green’s theorem.

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Answer 3

Question

Chapter 18.1, Problem 38E

To determine

To compute the flux $\oint \vec{F} . \hat{n} d s$ of $\vec{F} (x, y) = 〈 3 x, 2 y 〉$ across the circle given by $x^{2} + y^{2} = 9$ using vector form of Green’s theorem.

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Answer 4

Question

Chapter 18.1, Problem 38E

To determine

To compute the flux $\oint \vec{F} . \hat{n} d s$ of $\vec{F} (x, y) = 〈 3 x, 2 y 〉$ across the circle given by $x^{2} + y^{2} = 9$ using vector form of Green’s theorem.

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Answer 5

Chapter 18.1, Problem 38E

To determine

To compute the flux $\oint \vec{F} . \hat{n} d s$ of $\vec{F} (x, y) = 〈 3 x, 2 y 〉$ across the circle given by $x^{2} + y^{2} = 9$ using vector form of Green’s theorem.

Answer 6

Chapter 18.1, Problem 38E

To determine

To compute the flux $\oint \vec{F} . \hat{n} d s$ of $\vec{F} (x, y) = 〈 3 x, 2 y 〉$ across the circle given by $x^{2} + y^{2} = 9$ using vector form of Green’s theorem.

Answer 7

Chapter 18.1, Problem 38E

To determine

To compute the flux $\oint \vec{F} . \hat{n} d s$ of $\vec{F} (x, y) = 〈 3 x, 2 y 〉$ across the circle given by $x^{2} + y^{2} = 9$ using vector form of Green’s theorem.

Answer 8

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Answer 9

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Answer 10

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Answer 11

Ch. 18.1 - Prob. 1PQ Ch. 18.1 - Prob. 2PQ Ch. 18.1 - Prob. 3PQ Ch. 18.1 - Prob. 4PQ Ch. 18.1 - Prob. 5PQ Ch. 18.1 - Prob. 1E Ch. 18.1 - Prob. 2E Ch. 18.1 - Prob. 3E Ch. 18.1 - Prob. 4E Ch. 18.1 - Prob. 5E

To compute the flux ∮ F → . n ^ d s of F → ( x , y ) = 〈 3 x , 2 y 〉 across the circle given by x 2 + y 2 = 9 using vector form of Green’s theorem.

Solution Summary: The author calculates the flux of F ( x, y ) = 3x, 2y, across the circle enclosing region D using the vector form of Green's theory.

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To compute the flux $\oint \vec{F} . \hat{n} d s$ of $\vec{F} (x, y) = 〈 3 x, 2 y 〉$ across the circle given by $x^{2} + y^{2} = 9$ using vector form of Green’s theorem.

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Chapter 18 Solutions

To compute the flux ∮ F → . n ^ d s of F → ( x , y ) = 〈 3 x , 2 y 〉 across the circle given by x 2 + y 2 = 9 using vector form of Green’s theorem.

Solution Summary: The author calculates the flux of F ( x, y ) = 3x, 2y, across the circle enclosing region D using the vector form of Green's theory.

Videos