Let i=∫∫d(x2−y2)dxdy, where

d={(x, y): 3≤xy≤6,0≤x−y≤7,x≥0,y≥0}

show that the mapping u=xy, v=x−y maps d to the rectangle r=[3,6]×[0,7].

(a) compute ∂(x, y)/∂(u, v) by first computing ∂(u, v)/∂(x, y).

(b) use the change of variables formula to show that i is equal to the integral of f(u, v)=v over r and evaluate.

(a)∂(x, y)/∂(u, v)=

(b)i=

Asquare picture with sides of 32 inches is to be mounted on a square mat with sides of 52 inches. find the area of the mat that will remain uncovered by the picture.

Tom is the deli manager at a grocery store. he needs to schedule employee to staff the deli department for no more that 260 person-hours per week. tom has one part-time employee who works 20 person-hours per week. each full-time employee works 40 person-hours per week. write and inequality to determine n, the number of full-time employees tom may schedule, so that his employees work on more than 260 person-hours per week. graph the solution set to this inequality.

The radius of a sphere is 3 inches. which represents the volume of the sphere?