Bonus: Find the coordinates for the point in the xy-Plane.
Compute the Jacobian for the transformation and. Bonus: Find the coordinates for the point in the...
Compute the Jacobian J(u, v) for the following transformation. x = 4u, y= - v J(u, v) = (Simplify your answer.)
Q20 (5 pts). Solve the system u x 2y and vx + y for x and y and find the Jacobian( 2. Find the volume of the region R using this transformation (u,v) Q20 (5 pts). Solve the system u x 2y and vx + y for x and y and find the Jacobian( 2. Find the volume of the region R using this transformation (u,v)
Question 6 (3 points) a -- 2 points) Find the Jacobian of the transformation the shear transformation: x = au + bv + cw, y=dy + ew, and z fw, where a, b, c, d, e, and f are positive real numbers, and describe the how the volume of the unit cube in uvw coordinates compares to the volume of its transformation in Cartesian coordinates. = b -- 1 point) State one example of a practical application shown in lecture...
Compute the jacobian: 26) Compute the Jacobian: x=u+5 and y= u-v 15 26) Compute the Jacobian: x=u+5 and y= u-v 15
z = 2w/u Find the Jacobian of the transformation. x = Bulv, y = 4v/w, 6400w a(u, v, w) UVW a(x, y, 2) 640 Need Help? Read It Watch it Talk to a Tutor
Solve the following relations for x and y, and compute the Jacobian J(u,v). u=x+3y, v = 5x + 4y x=y=0 (Type expressions using u and v as the variables.) Choose the correct Jacobian determinant of T below. a A. J(u, v) = du - 4u + 3v a 11 - 4u+ 3v 11 a O B. J(u,v) = -4u + 3v 11 a (5u-v dy du Mal . (517") i (517) (507°) (-44*34) dic (547) OC. Jusv) = m (...
(1 point) Suppose a change of coordinates T:R2→R2T:R2→R2 from the uvuv-plane to the xyxy-plane is given by x=4v−3u−1, y=1+4u+2v.x=4v−3u−1, y=1+4u+2v. (a) Find the absolute value of the determinant of the Jacobian for this change of coordinates. ∣∣∣∂(x,y)∂(u,v)∣∣∣=∣∣∣det|∂(x,y)∂(u,v)|=|det ⎡⎣⎢⎢[ ⎤⎦⎥⎥] ∣∣∣=|= (b) If a region D∗D∗ in the uvuv-plane has area 7.047.04, find the area of the region T(D∗)T(D∗) in the xyxy-plane. Area = A
5. (15 points) Let X, Ybe random variables with joint density Consider the transformation V=-X + Y (a) Compute the formula for the inverse transform T-1. (b) Compute the Jacobian J of T-1. (c) Determine the joint density function for U, V Be sure to consider the domain 5. (15 points) Let X, Ybe random variables with joint density Consider the transformation V=-X + Y (a) Compute the formula for the inverse transform T-1. (b) Compute the Jacobian J of...
11. Consider the parabolic coordinate system (u, v) related to the Cartesian coordi- nates (r, y) by х — 2иv, y — u? — u? for (и, v) € [0, оо) х [0, оо) 1 u = 1, u 2' (a) Sketch in the ry-plane the curves given u = 2. Then sketch in 1 v = 1, v = 2. Shade in the region R the xy-plane the curves given v = 2' bounded by the curves given by...
(1 point) Consider the transformation T : x = sau - Sov, y = ou + A. Compute the Jacobian: d(xy) d(u,v) = B. The transformation is linear, which implies that it transforms lines into lines. Thus, it transforms the square S :-50 su < 50, -50 SV < 50 into a square T(S) with vertices: T(50, 50) =( T(-50, 50) =( T(-50, -50) =( T(50, -50) =( C. Use the transformation T to evaluate the integral Stor? + y2...