Each of these extreme value problems has a solution with both a maximum value and a minimum value. Use Lagrange multipliers to find the extreme values of the function subject to the given constraint. f(x, y) = xy; 4x2 + y2 = 8

Solve for x and y: 217x + 131y = 913; 131x + 217y = 827

The cross-sectional areas of a right triangular prism and a right cylinder are congruent. the right triangular prism has a height of 6 units, and the right cylinder has a height of 6 units. which conclusion can be made from the given information? the volume of the triangular prism is half the volume of the cylinder. the volume of the triangular prism is twice the volume of the cylinder. the volume of the triangular prism is equal to the volume of the cylinder. the volume of the triangular prism is not equal to the volume of the cylinder.

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.