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: Evaluate L₂Lova (4-3²) dydx -√4-x² by using polar coordinates.

A:

Q: Use Green's theorem to calculate §. -y² dx + xy dy where C is the vertex triangle (1,3), (4,0) and…

A: Consider the given integral. I=∮c-y2dx+xydy The green theorem is defined as, ∮cPdx+Qdy=∬R∂Q∂y−∂P∂x…

Q: 3x, - 2x, + 4X3 = 1 X, + X2 - 2x3 = 3 2x, - 3x, + 6x3 = 8 Select one: O a. x,=1,x,=3, x,=1 O b.…

A: From Cramer's rule,                                  If , ∆=0 then given system has no solution.

Q: Find the slope of the tangent in the positive x-direction to the surface z = 3x - 6xy at the point…

A: We have to find the partial derivative with respect to x

Q: Find three different parametrizations of the graph of y = x3.

A:

Q: Compute sin z dz , where a is the piece of the parabola with equation y= a?, which lies between the…

A:

Q: I need a 3d sketch of the equation  Z=x+xsiny+xy

A: z=x+xsiny+xy

Q: Generate a 3D plot based on the equation z=sin(x) +cos(y), both x and y range from 0 to 2 pi. Please…

A: [x,y]=meshgrid(0:2*pi); z=sin(x)+cos(y); surf(x,y,z)

Q: Evaluate  ∫C (3y + exsinx) dx + (8x - ln(y3+2)) dy, where C is the circle x2 + y2 = 9  with positive…

A:

Q: Evaluate | exp(-2²)dx, using an iterated integral and polar coordinates.

A: Using Cartesian coordinates to polar coordinates.

Q: [ 64–x² 64-x²-y 2x? dzdydx. Use cylindrical coordinate to evaluate La LIe4-r2 So

A:

Q: Evaluate f" Na-*) /x² + y² dydx, using polar coordinate. -a

A:

Q: particle started at A(1,0) circled the origin once  an d returned toA(1,0) .what were the change in…

A: Given: A particle started at A(1,0) circled the origin once  and  returns to A(1,0)

Q: (b) Let w = 1+ j. Determine w giving your answer in rectangular form.

A:

Q: Write √x+y²+2x-y=3 +y²+2x−y=3 as a polar equation r = f(0).

A: Write in Polar equation

Q: 9-y² 2. Evaluate the integral (2.x + y) dady by converting to polar 9-y? Coor- dinates.

A:

Q: Find the points of intersection between r =2 cos20 andr=- %3D 1- cose

A: To find the intersection point two curve we have to find r,θ by solving given curve.

Q: Find a parametric function for the intersection of r – 3y + 4z = 0 and a? + y² = 9.

A:

Q: Let f(2) = . Use the polar form of the Cauchy-Riemann equations to determine where f is…

A:

Statements and Logic

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