Solve the system u=2x-y v= 3 x+2y, for x and y in terms of u and v then find the value of Jacobian σ(x, y)/σ(u, v). Find the image under the transformation of the triangular region with the vertices (0,0) ,(2,4), and (2, -3) in the x, y plane. Sketch the transformed region in uv plane. The function for x in terms of u and v is x=?

Find the coordinates of point x that lies along the directed line segment from y(-8, 8) to t(-15, -13) and partitions the segment in the ratio of 5: 2.

Suppose a store sells an average of 80 cases of soda per day. assume that each case contains 24 cans of soda and that the store is open 10 hours per day. find the average number of soda that the store sells per hour.

If p(x) is the total value of the production when there are x workers in a plant, then the average productivity of the workforce at the plant is a(x) = p(x) x . (a) find a'(x). a'(x) = xp'(x) − p(x) x a'(x) = xp'(x) − p(x) x2 a'(x) = p'(x) − p(x) x a'(x) = xp'(x) − p'(x) x2 a'(x) = p'(x) − xp(x) x2 why does the company want to hire more workers if a'(x) > 0? a'(x) > 0 ⇒ a(x) is ; that is, the average productivity as the size of the workforce increases. (b) if p'(x) is greater than the average productivity, which of the following must be true? p'(x) − xp(x) > 0 p'(x) − xp(x) < 0 xp'(x) − p'(x) > 0 xp'(x) − p(x) < 0 xp'(x) − p(x) > 0