Calculate the circulation, \int_c\vec f\cdot d\vec r, in two ways, directly and using stokes' theorem. the vector field \vec f = 5 y\vec i - 5 x\vec j and c is the boundary of s, the part of the surface z = 16 -x^2-y^2 above the xy-plane, oriented upward.

What term makes it inconsistent y=2x - 4 ?

Afarmer has a large field that is x feet in length. he wants to fence in a rectangular section in the middle of the field , leaving a length of 100 feet of open field behind each end of the fenced rectangle. he also wants the width of the fenced-in space to be 100 feet less than its length. find the expressions to represent the length and width of the fenced section of the field

Statements reasons 1. ab ? cd; ad ? bc 1. given 2. ac ? ac 2. reflexive property 3. ? adc ? ? cba 3. ? 4. ? dac ? ? bca; ? acd ? ? cab 4. cpctc 5. ? dac and ? bca are alt. int. ? s; ? acd and ? cab are alt. int. ? s 5. definition of alternate interior angles 6. ab ? cd; ad ? bc 6. converse of the alternate interior angles theorem 7. abcd is a parallelogram 7. definition of parallelogram what is the missing reason in step 3?