For the following vector field, compute (a) the circulation on and (b) the outward flux across the boundary of the given region. assume the boundary curve is oriented counterclockwise. f = < x, y > ; r is the half annulus {(r, theta): 4 leq r leq 7, 0 leq theta leq pi} a. the circulation on the boundary is . (type an exact answer, using pi as needed.) b. the outward flux across the boundary is . (type an exact answer, using pi as needed.)

The manufacturer of a new product developed the following expression to predict the monthly profit, in thousands of dollars, from sales of the productwhen it is sold at a unit price of x dollars.-0.5x^2 + 22x - 224what is represented by the zero(s) of the expression? a.the profit when the unit price is equal to 0b.the unit price(s) when the profit is equal to 0c.the profit when the unit price is greatestd.the unit price(s) when profit is greatest

What is the area of a triangle with vertices at (-3 3) (-3,2) and (1,2)?

The sum of the squares of two numbers is 8 . the product of the two numbers is 4. find the numbers.