Let R be the region in the first quadrant bounded above by the curve y = 2 - x2and bounded below by the line y = x. Suppose the shell method is used to determine the volume of the solid generated by revolving R about the y-axis. What is the radius of a cylindrical shell at a point x in [0, 2]?Evaluate the integral.

Consider the function represented by the equation 1/2 j + 1/4 k equals 3 which shows the equation written in function notation with j as the independent variable

Quick! a survey of 57 customers was taken at a bookstore regarding the types of books purchased. the survey found that 33 customers purchased mysteries, 25 purchased science fiction, 18 purchased romance novels, 12 purchased mysteries and science fiction, 9 purchased mysteries and romance novels, 6 purchased science fiction and romance novels, and 2 purchased all three types of books. a) how many of the customers surveyed purchased only mysteries? b) how many purchased mysteries and science fiction, but not romance novels? c) how many purchased mysteries or science fiction? d) how many purchased mysteries or science fiction, but not romance novels? e) how many purchased exactly two types of books?

When george started his current job, his employer told him that at the end of the first year, he would receive two vacation days. after each year worked, his number of vacation days will double up to five work weeks (25days) of payed vacation. how many vacation days will he have in 4 years