# Giving u y 8 x 2 y 40 24 x 42 u 0 0 v 8 so x 3 v and

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, giving u = y + 8 x = 2 y + 40 , u = 0, 0 ≤ v 8 , so x = 3 v and y = − v x = −3 y , 0 ≤ x 24 x 42 . 24 .
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13-11-7 HW #23 Find the image of the set S under the given transformation. y = v u 3 ,
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13-11-7 HW #23 . 4. 1/1 points | Previous Answers SCalcET7 15.10.011. A region R in the xy -plane is given. Find equations for a transformation T that maps a rectangular region S in the uv -plane onto where the sides of S are parallel to the u - and v -axes as shown in the figure below. (Enter your answers as a comma-separated list of equations.) R , x 9 . y 3 . y 2 y = 7 x
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13-11-7 HW #23 5/8 Solution or Explanation R is a parallelogram enclosed by the parallel lines and the parallel lines The first pair of equations can be written as If we let then these lines are mapped to the vertical lines in the uv -plane. Similarly, the second pair of equations can be written as and setting maps these lines to the horizontal lines in the uv -plane. Boundary curves are mapped to boundary curves under a transformation, so here the equations define a transformation that maps R in the xy -plane to the square S enclosed by the lines