Find the circulation and flux of the field Bold Upper F equals x Bold i plus y Bold j around and across the closed semicircular path that consists of the semicircular arch Bold Bold r 1 (t )equals (a cosine t )iplus (a sine t )j, 0 less than or equals t less than or equals pi, followed by the line segment Bold r 2 (t )equals t Bold i, negative a less than or equals t less than or equals a. The circulation is nothing. (Type an exact answer, using pi as needed.) The flux is nothing.

The graph shows the prices of different numbers of bushels of corn at a store in the current year. the table shows the prices of different numbers of bushels of corn at the same store in the previous year. previous year number of bushels price of corn (dollars) 2 10 4 20 6 30 8 40 part a: describe in words how you can find the rate of change of a bushel of corn in the current year, and find the value. part b: how many dollars more is the price of a bushel of corn in the current year than the price of a bushel of corn in the previous year? show your work.

Solve each quadratic equation by factoring and using the zero product property. 14x - 49 = x^2

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 =