The maximum weight that a rectangular beam can support varies jointly as its width and the square of its height and inversely as its length. If a beam one half foot wide, one half foot high, and 16 feet long can support 30 tons, find how much a similar beam can support if the beam is three fourths foot wide, one third foot high, and 11 feet long.

The formula for the lateral area of a right cone is la = rs, where r is the radius of the base and s is the slant height of the cone.which are equivalent equations?

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.

If cos(2x) = tan^2(y), show that cos(2y) = tan^2(x).