A straight line goes through the points (p, q) and (r, s), where  p + 2 = r  q + 4 = s. Find the gradient of the line.

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.

The base of a triangle exceeds the height by 9 inches. if the area is 180 square inches, find the length of the base and the height of the triangle.

60 musicians applied for a job at a music school. 14 of the musicians play both guitar and drums, 28 play drums, 18 play the guitar. what is the probability that the applicant who gets the job plays drums or guitar?