Consider the vector field f(x, y, z) = (4yz, y2 4xz, 4xy) (15 pts) a. show that this vector field is conservative b. find the potential function associated with this conservative vector field. c. calculate the circulation of this vector field around the curve given by the intersection of the cone 4=n/4 and the sphere p = 1. you may use the results of part a. or b. and integration theorems if it

Suppose that 3% of all athletes are using the endurance-enhancing hormone epo (you should be able to simply compute the percentage of all athletes that are not using epo). for our purposes, a “positive” test result is one that indicates presence of epo in an athlete’s bloodstream. the probability of a positive result, given the presence of epo is .99. the probability of a negative result, when epo is not present, is .90. what is the probability that a randomly selected athlete tests positive for epo? 0.0297

The graph of a function f(x)=(x+2)(x-4). which describes all of the values for which the graph is negative and increasing? all real values of x where x< -2 all real values of x where -2

Miguel has 334 baseball cards and 278 football cards. he says, i have 612 cards in all. is that reasonable? explain using the words round and estimate.