Let r denote the region in the first quadrant that is bounded by the y-axis, y = 2x, and is between and x^2 + y^2 = 1 and x^2 + y^2 = 2. suppose that the mass density at each point in r is inversely proportional to its distance from the origin. a. sketch r b. set-up double integrals in polar coordinates that equal the area of r, the mass of r, and the y-coordinate of the center of mass of r.

One side of a rectangle is 7 feet shorter than seven times the other side. find the length of the shorter side if we also know that the perimeter of the rectangle is 306 feet.

1yd 1 ft = 1 1/12 1 1/3 1 1/2 1 1/6

Three friends went on a road trip from phoenix, az, to san diego, ca. mark drove 50 percent of the distance. jason drove 1/8 of the distance. andy drove the remainder of the distance. 1. andy thinks he drove 1/4 of the distance from phoenix, az, to san diego, ca. is andy correct? 2. the distance from phoenix, az, to san diego, ca, is 360 miles. how many miles did each person drive? 3. solve the problem. what is the answer in total?