Show that if the vector field f = pi + qj + rk is conservative and p, q, r have continuous first-order partial derivatives, then the following is true. ∂p ∂y = ∂q ∂x ∂p ∂z = ∂r ∂x ∂q ∂z = ∂r ∂y . since f is conservative, there exists a function f such that f = ∇f, that is, p, q, and r are defined as follows. (enter your answers in the form fx, fy, fz.)

Fiona races bmx around a circular dirt course. if the radius of the course is 70 meters, what is the total distance fiona covers in two laps of the race? a. about 30,772 meters b. about 15,386 meters c. about 879.2 meters d. about 439.6 meters e. about 219.8 meters23 points hurry

Graph the equationy= x+3[tex]y = x + 3[/tex]

Amajor grocery store chain is trying to cut down on waste. currently, they get peaches from two different distributors, whole fruits and green grocer. out of a two large shipments, the manager randomly selects items from both suppliers and counts the number of items that are not sell-able due to bruising, disease or other problems. she then makes a confidence interval. is there a significant difference in the quality of the peaches between the two distributors? 95% ci for pw-pg: (0.064, 0.156)