A ring-shaped region is shown below.
Its inner radius is 18in, and its outer radius is 22in.
Find the area of the shaded region.
Use 3.14 for π. Do not round your answer.

In trapezoid efgh, m∠hef=(4x2+16)∘ and m∠gfe=(5x2+12)∘. find the value of x so that efgh is isosceles.

Sarah took the advertising department from her company on a round trip to meet with a potential client. including sarah a total of 11 people took the trip. she was able to purchase coach tickets for $280 and first class tickets for $1280. she used her total budget for airfare for the trip, which was $6080. how many first class tickets did she buy? how many coach tickets did she buy?

Find the volume of the solid obtained by rotating the region enclosed by the curves y=1x and y=7^-x about the x-axis. (use symbolic notation and fractions where needed.) volume =