The function f(x, y,z)equals2 x minus 8 y plus 5 z has an absolute maximum value and absolute minimum value subject to the constraint x squared plus y squared plus z squared equals 93. Use Lagrange multipliers to find these values.

Write each expression in exponential form and find its value.| ! 2 x 2 x 2 x 2

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.

(a.s."similarity in right triangles"solve for xa.) 10b.) 20c.) 14.5d.) [tex] 6\sqrt{3} [/tex]