Use stokes' theorem to compute z c ~f d~s where ~f(x; y; z) = y2~i + z2~j + x~k and the curve c is the triangle in 3-space with vertices at (1; 0; 0), (0; 1; 0), and (0; 0; 1). hints: (a) for the surface s needed in stokes' theorem, use the part of the plane x + y + z = 1 that lies in the rst octant. (b) that plane can be written parametrically as (x; y) = hx; y; 1 x yi. (c) make sure you have the upward pointing normal!

Agroup of students want to create a garden. they do not know the exact measurements but they propose using a variable to represent the length and width of the garden. the length of the garden is 10 feet longer than double the width. use a single variable to write algebraic expressions for both the length and width of the garden. write an algebraic expression for the area of the garden. use mathematical terms to describe this expression.