Evaluate § F · ds, where F = 2x(x+y)i + (x² + xy + y?)j and the positively-oriented curve C encloses the square with vertices (0,0), (1, 0), (1, 1) and (0, 1).

Q: Construct a linear map L(z)=az+b that will send the imaginary y-axis to the line v=-u.

A: we have to constract a linear map that maps the y-axis to the line v=-u Basically we have to…

Q: Draw v = [ 4/1 ] and w = [ -2/2 ] and v+w and v-w in a single xy plane.

A:

Q: Q5) Find the coefficients a, b,c and d such that the curve defined by; y = ax3 + bx² + cx + d,…

A:

Q: Find a parametric representation of a straight line passing through (1,2,1) in the direction of…

A:

Q: Find the midpoint of points A(-8,2)and B(-5,-5) graphically.

A: Explanation: Plot the points A and B on the graph. Then draw a horizontal line from A and Vertical…

Q: Describe the traces of the curve x2 + 9z2 = 9 in the vertical planes (those parallel to the…

A: The traces of a surface are the cross-sections created when the surface intersects a plane parallel…

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A: Given:- In the xy-plane, line k intersects the y-axis at the point (0, -6) and passes through the…

Q: must use linear algebra to find the parametric equations of a line of intersection in R3 for x1 + x2…

A:

Q: If (x1, yı) and (x2, y2) are distinct points in the plane, show that y 1 1 =0 X1 x2 y2 is the…

A: If (x1, y1) and (x2, y2) are distinct points in the plane, to show that  xy1x1y11x2y21 =0 is the…

Q: Consider the projection from the origin of the straight line y + x = 2 on a straight line y + 2x =…

A: Graph formed by

Q: Show that the point (x0 , y0) closest to the origin on the line ax+ by =c has coordinates

A: Distance between x0, y0 and origin (0, 0) is, D=x0-02+y0-02D=x02+y02D2=x02+y02f=x02+y02…

Q: Show that the curves 2x2 + 3y2 = 5 and y2 = x3 are orthogonal.

A: To show that the two curves are orthogonal.

Q: calculate S S, y³ dA where Ris the vertex of the triangle (0, 2), ( 1,1) and (3, 2)|

A: In this question we have to calculate the following integral.

Q: Construct a linear map L(z) = az + 6 that will send the imaginary y-axis to the line v = - u

A:

Q: Find the equation of the orthogonal of the set of the x² + (y + c)² = C² curves:

A: Given the family of curves is x2+(y+c)2=c2,here c is the parameter.