Let r be a relation, x a set of attributes of r, and a an attribute of r. (also, denote by xa the result of adding a to x.) define the support of x, written #x, as the number of distinct tuples in r|x (r restricted to, or projected onto, the attributes of x). prove that if x→a, then #x=#xa.

Explain the difference laminar and turbulent flow. explain it with the shear stress and the velocity profiles.

Thermal stresses are developed in a metal when its a) initial temperature is changed b) final temperature is changed c) density is changed d) thermal deformation is prevented e) expansion is prevented f) contraction is prevented

Ajournal bearing has a journal diameter of 3.250 in with a unilateral tolerance of 20.003 in. the bushing bore has a diameter of 3.256 in and a unilateral tolerance of 0.004 in. the bushing is 2.8 in long and supports a 700-lbf load. the journal speed is 900 rev/min. find the minimum oil film thickness and the maximum film pressure for both sae 20 and sae 20w-30 lubricants, for the tightest assembly if the operating film temperature is 160°f. a computer code is appropriate for solving this problem.