Match each cross section to its area. a cross section passing through the diagonals of opposite
faces of a cube with edges that are 7 inches long and a
diagonal that is approximately 10 inches
a cross section parallel to the base of a cube whose edges are
8 inches long
a cross section perpendicular to the base and passing
through the diagonals of the base and opposite face of a
right rectangular prism that is 24 inches wide, 7 inches long.
and 12 inches tall and measures 25 inches along the
diagonal of the base
a cross section parallel to the base of a right rectangular prism
that is 3 inches long, 7 inches wide, and 11 inches tall

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