Samantha bought a $65.99 purse. She used a 15%
discount. How much did she pay? Write 2 different
expressions to solve the problem below.

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.

1. find the area of the unshaded square 2. find the area of the large square 3. what is the area of the frame represented by the shaded region show

Amachine part consists of a half sphere and a cylinder, as shown in the figure. the total volume of the part is π cubic inches.