Show that use of the energy theorem (Problem 2) in the Lagrangian integral form of conservation of energy, d dt Vo 1 2 v · v + ε rhoo dVo = Vo (b · v + r) rhoo dVo + So (to · v − qo · no) dAo, leads to the pointwise (differential) form: rhoo ε˙ = To · ˙F + rhoo r − Div qo, where qo is the referential heat flux vector.

Afactory makes propeller drive shafts for ships. a quality assurance engineer at the factory needs to estimate the true mean length of the shafts. she randomly selects four drive shafts made at the factory, measures their lengths, and finds their sample mean to be 1000 mm. the lengths are known to follow a normal distribution whose standard deviation is 2 mm. calculate a 95% confidence interval for the true mean length of the shafts. input your answers for the margin of error, lower bound, and upper bound.