The running time for movie A is 32 minutes more than twice the running time for movie B. If the running time for movie A is subtracted from triple the running time for movie B, the result is 52 minutes. Find the running times for each movie.

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.

20 solve 2(4 x + 3) < 5 x + 21. a) { x | x < 9} b) { x | x > -5} c) { x | x > -9} d) { x | x < 5}

Point a is at 12, and point d is at 56. point c is midway between a and d, and point b is midway between a and c. which of these is the coordinate of b?