Abcd is reflected across the x- axis, then rotated 90 clockwise about the orgin, and finally reflected across the line y= x to form a’ b’ c’ .

Matteo makes raspberry punch. the table shows how many parts ginger ale and raspberry juice to use for a batch. raspberry punch parts ginger ale 2 parts raspberry juice 3 matteo decides to add one part of raspberry juice. what is the new ratio of ginger ale to raspberry juice?

Determine whether the following statements are true and give an explanation or counterexample. bold a. when using the shell method, the axis of the cylindrical shells is parallel to the axis of revolution. bold b. if a region is revolved about the y-axis, then the shell method must be used. bold c. if a region is revolved about the x-axis, then in principle it is possible to use the disk/washer method and integrate with respect to x or the shell method and integrate with respect to y.

Pete is making decorations for a dinner party. the instructions tell him to use 9 flowers for a medium-sized decoration. complete each statement to adjust the flowers for different-sized decorations based on these instructions.