Use stokes' theorem to evaluate c f · dr where c is oriented counterclockwise as viewed from above. f(x, y, z) = i + (x + yz)j + (xy − sqrt(z )k, c is the boundary of the part of the plane 7x + 6y + z = 1 in the first octant.

Jackie purchased 3 bottles of water and 2 cups of coffee for a family for $7.35. brian bought 4 bottles of water and 1 cup of coffee for his family for $7.15. how much does each bottle of water cost? how much does each cup of coffee cost? i need this done

Find the magnitude, correct to two decimal places, made by each of the following with positive direction of the x axis a) y= x the answer is 45° but i don’t know how

Someone answer this asap for the function f(x) and g(x) are both quadratic functions. f(x) = x² + 2x + 5 g(x) = x² + 2x - 1 which statement best describes the graph of g(x) compared to the graph of f(x)? a. the graph of g(x) is the graph of f(x) shifted down 1 units. b. the graph of g(x) is the graph of f(x) shifted down 6 units. c. the graph of g(x) is the graph of f(x) shifted to the right 1 unit. d. the graph of g(x) is the graph of f(x) shifted tothe right 6 units.