Use either form of Green's Theorem to evaluate the following line integral. 03x y dx+ 4x y dy; C is the triangle with vertices (0,0), (9,0), and (0,5) with counterclockwise orientation Paxy °y° dy = [O dx + 4x C (Type an exact answer.)

Q: quation of the hyperb

A: Given,      z=-16

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A: The relation between spherical and rectangular coordinates in polar form is given by the following…

Q: Use Green's Theorem to compute y dx+(x³+3xy²) dy where C is the closed curve around the triangle…

A:

Q: Use the parametric equations of an ellipse, x = 3 cos (0), y = 4 sin(0), 0≤ 0 ≤ 2T, to find the area…

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Q: -1/2 1-x² xy/x² + y² dydx А.

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Q: Verify that U(x,y) = x3y - xy3 is harmonic on the complex plane.

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Q: III. Find a set of parametric equations for the curve of intersection of the cylinder (x-1)² + ² x²…

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Q: 21. Let Sech u = 3/5 , determine the values of the remaining five hyperbolic functions.

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Q: b) Evaluate the value of I = S(e³y – 3x)dx + (6xey + y)dy, where C' is the parabola - C (0, 0) to…

A: One has to solve it by Green's Theorem.

Q: Find polar coordinates (r,θ) where r < 0 and 0≤θ≤2π of(√3,−1)

A: Given point in the rectangular coordinates is 3,-1. To find the polar coordinates r,θ, where r&lt;0…

Q: Find the Curl of the function f=(3x- 2y)k ?* O 2-3) O -2i+3) O 21-3) 2i+3)

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Q: 2. Evaluate the quantity e™ for each of the given values of 0. Give your answer in rectangular form…

A: As per bartleby guidelines we only give first three questions answers.

Q: 115 Let C be the CCW triangle with vertices (-1,0), (1,0) and (0, 1). Calculate [ (xe* _y³)dx + (y³…

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Q: Find all non - zero complex numbers z satisfying z =i z.

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Q: 6. Consider F (w), a complex function of a real variable w: F (w) = (2+jw)/(3+j4w) a. Express F (w)…

A: Given: The complex function of a real variable .a) To express  in cartesian form and find it's real…

Q: f (lnx + y) dx − a² dy, where & is the rectangle with vertices (1, 1), 1. Use Green's Theorem to…

A: Let I =∮(ln x+y)dx-x2 dy, where the region is C which is a rectangle with vertices…

Q: Use the transformation u=-2.= 3y and =z to evaluate (5- Sy) de dzdy.

A: Introduction: The process of determining the area of the region under the curve is known as…

Q: 1. If 4 = xy i+yzj+zxk, find curl4 and curl curl A at points (1,2, –3).

A: Given that A = xy i + yzj + zxk and find curlA and curlcurlA at point (1,2,-3). Here i attached…

Q: enter-radius form of the equation of t

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Q: dy Consider the parametric equations x = e' -1 and y=1-t. Which of the following represents dx 1-12…

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Q: Verify that the function u(x.y) x- 3xy -5y is harmonic in the entire complex plane ,And find the…

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Q: Eliminate the parameter for the given parametric equations to write an equation in the form of y=…

A: Given x=ln t and y=et

Q: Evaluate ([cos (x – y)sin(x+ y)dA, where R is the triangle with vertices (0,0), R (-1,7), and (7,7)…

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Q: Sketch the bifurcation diagram for y = (A– 4t)y (where A is a parameter, as usual). 2

A: To find- Sketch the bifurcation diagram for y' = λ - 4t2y (where λ is a parameter, as usual)

Q: h the comp y² + 2xy)

A:

Statements and Logic

Logic is the analysis of general patterns of thoughts without regard to any specific sense of context.