Let C be the closed, piecewise smooth curve formed by traveling in straight lines between the points (0,0,0), (2,0,4), (3,2,6), (1,2,2), and back to the origin, in that order. (Thus the surface S lying interior to C is contained in the plane z=2x.) Use Stokes' theorem to evaluate the integral: ∫C(zcosx)dx+(x2yz)dy+(yz)dz.

The length of a field is 100 yards and its width is 75 yards. if 1 inch represents 25 yards, what would be the dimensions of the field drawn on a sheet of paper?

Ascientist studied a population of workers to determine whether verbal praise and/or tangible rewards affect employee productivity. in the study, some workers were offered verbal praise, some were offered tangible rewards (gift cards, presents, and some were offered neither. the productivity of each participant was measured throughout the study by recording the number of daily tasks completed by each employee. which inference might the scientists make based on the given information? a.) the number of daily tasks completed by each employee may influence the dependent variable, which is whether the employee receives verbal praise, tangible rewards, or neither. b.) verbal praise and/or tangible rewards may influence the independent variable, which is the number of daily tasks completed by each employee. c.) verbal praise and/or tangible rewards may influence the dependent variable, which is the number of daily tasks completed by each employee. d.) the dependent variables, which are verbal praise and tangible rewards, may influence the number of daily tasks completed by each employee.

Consider the enlargement of the pentagon. what is the value of x, rounded to the nearest tenth? 2.1 centimeters 3.3 centimeters 7.0 centimeters 15.0 centimeters