Question

The base of the closed cubelke surface shown here is the unit square in the planeThe four sides in the planes x, y, and y1. The top is an arbitrary smooth surface whose identity is unknown LetF- 23k and suppose the award of Frough Side Ais and through Side Bis-Can you conclude anything about the outward fough the top version for your answer Choose the correct answer below and recessary in the answer box to complete your choice O A Yes, the wrough the top can be called (Type an integer or action) O Youtward a rough the top is posive, but cannot be called O the outward us through the top is negative, but it cannot be cold way OD. No. The word fux trough the top cannot be determined without itsety Give reasons for your answer OA by the Divergence Theorom, the outward fuxis Side A and Bhaves 1 and 3.rospectively and the sides haves of the bottom hos fux-3 OB. By the Divergence Theorem, the award fx is 0. Side A and Sie have fures and respectively, and all other side aves of Oc. By the Divergence Theorem, the outwardlux is 3 Side A and have fun and - 3, espective, and the sides opposite have fues of 0. The bottom of 3 OD. The outward flux through the top crot be determined without its dry

Answer 1

Since gif (x! + (-2y) +44(2+3) =I-2+1 EO, the sum of the Ontured flines the tone sides, the bottom acon dvso. and top munt Eaud SSS E dre Sad Soul Vie dve jaso o dve we are giun the fluxes B, so if acean the three covedinak ove sides A -and ve lan find the fluxes planes then we will be able to calculate the flux aceon the top. Bottom ; 2=0, ñ - K ss F. ñ dr = 11 E. (-6ldo ss-(2+3) dady Bottom Bottom T Bottom: 2=0 -3 Area (unit sauce) - y=0, Left side o =) The fiun acrou n=-5 the left side in --] 1 - To Fol-J) = 2y=0 in 0. ñ=-;-) E-ñ = FiscX0 Back side: x=0 The Flux across Il Fods = (Hlux ae vous top + bottom + Falto faceff left fright) Islody ndiq balle side is also o - E-3 +1-3 toto F = 6-1=5 al ross top surface = 5 Flux