Verify that the divergence theorem is true for the vector field f on the region e. give the flux. f(x, y, z) = 5xi + xyj + 2xzk, e is the cube bounded by the planes x = 0, x = 2, y = 0, y = 2, z = 0, and z = 2.

The rumpart family is building a new room onto their house. the width of the new room will be 16 feet. the length of the room will be 4% greater than the width. write an expression to find the length of the new room. what will be the area of this new room?

The volume of gas a balloon can hold varies directly as the cube of its radius. imagine a balloon with a radius of 3 inches can hold 81 cubic inches of gas. how many cubic inches of gas must be released to reduce the radius down to 2 inches?

If, while training for a marathon, you ran 60 miles in 2/3 months, how many miles did you run each month? (assume you ran the same amount each month) write your answer as a whole number, proper fraction, or mixed number in simplest form. you ran __ miles each month.