Find a transformation
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- Let G(u, v) = (2u + v, 7u + 3v) be a map from the uv-plane to the xy-plane. Describe the image of the line through the points (u, v) = (1, 1) and (u, v) = (1, –1) under G in slope- intercept form. y =arrow_forwardDue in 15 hoursarrow_forwardIntegrate (x + y) dA, where R = {(x, y):0 < x < 2, x < y < x + 4}. Use the transformation x = 2u and y = 4v + 2u. Hint: Sketch the given region R and then the new region in the uv plane.arrow_forward
- Evaluate the circulation of G = xyi + zj + 4yk around a square of side 4, centered at the origin, lying in the yz-plane, and oriented counterclockwise when viewed from the positive x-axis. Circulation = Jo F. dr =arrow_forwardConsider the transformation x =r cos 0, y=r sin 0, z = z from cylinderical to rectangular coordinates, a(x, y, z) a(r, 0, z) * where r > 0. Find 1 -rarrow_forwardEvaluate the circulation of G = xyi+zj+7yk around a square of side 9, centered at the origin, lying in the yz-plane, and oriented counterclockwise when viewed from the positive x-axis. Circulation = Prevs So F.dr-arrow_forward
- Let G(u, v) = (5u + 2v, 5u + 9v) be a map from the uv-plane to the xy-plane. Calculate Jac(G) = d(x,y) a(u,v)* (Use decimal notation. Give your answer as a whole number.) Jac(G) =arrow_forwardSketch a diagram of the linear map G that maps the rectangle R = [0, 1]×[0, 1] inthe uv-plane to the parallelogram P in the xy-plane with vertices (0, 0),(2, 2),(1, 4),and (3, 6). Draw the rectangle in the uv-plane on the left and its image P in thexy-plane on the right, with an arrow labeled G in the middle. Find the map G(u, v) = (x(u, v), y(u, v)) explicitly. Set up, but do not evaluate an integral in u and v to calculate Z ZRxy dA.arrow_forwardUse the cross product to find the area of the portion of the plane defined by z = x + y which lies above the square [0, 1] x [0, 1] in the xy-plane. Draw a picture.arrow_forward
- Find the centroidarrow_forwardFind the region in w- plane which is image of the region 1 < z| < 2 in z- plane with the transformation f(z)= %3D z-1arrow_forwardGraph the solid that lies between the surface z= 2xy/( x2 + 1) and the plane z =x + 2y and is bounded by the planes x =0 x= 2 y = 0 and y=4 x=-1, y =0 and y =4arrow_forward
- Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:Cengage