Find the flux of the vector field F = 〈e-z,4z,6xy) across the curved sides of the surface S = {(x, y,z): z= cos y, lys π, 0sxs4} . Normal vectors point upward. Set up the integral that gives the flux as a double integral over a region R in the xy-plane.

Acompany manufactures large valves, packed in boxes. a shipment consists of 1500 valves packed in 75 boxes. each box has the outer dimensions 1.2 x 0.8 x 1.6 m and the inner dimensions 1.19 x 0.79 x 1.59 m. the boxes are loaded on a vehicle (truck + trailer). the available capacity in the vehicle combination is 140 m3. each valve has a volume of 0.06 m3. - calculate the load factor on the box level (%). - calculate the load factor on the vehicle level (%). - calculate the overall load factor (%).