for the first image attach please do the calculations similar to the second image attachplease please answer everything correctly I would really appreciate if you would answerthis is not a graded question [10] (4)GIVEN: Constant a > 0W is the solid cube with edge length, a.0 ≤ x ≤ aW=(x, y, z)|0 ≤ y ≤ axelo0 ≤ z ≤ a= Top face of W.The square face where z = aat every point on it.oriented with unit normalpointing away fromthe interior of W;note that n =on Q.Xñ = 2 AF = (x,- y, z)FIND: The flux of F through with out - ward normal, nflux = SF•.dSZ|ΩnΩ= top surface=Z = (0,0,1)WY [15] (3)GIVEN: constants a > 0W is the solid cube with edge length, a.0 ≤ x ≤≤ y ≤ a0 ≤z≤ aW has constant density, S, and total mass, M.Let L be the axis of about whichwe want to calculatethe moment of inertia.GIVEN: L = z-axis.FIND: The moment of inertia of W w.r.t, L, I₂(Express I in terms of a and M)NOTE: V(W) = a³I₂ = [(x² + y²) S dvW=(x, y, z) 0== 28 √ √ x²dvW= 28=||Xs [ x ² dv + S√√ y ² dSL = 2-axisaa28 √ ² √ ² √ ªz ² d z dy dzx2Ma²aa2=28 (√² x ²4x) ([² 4 ) ( ["dz):) (625 ( 1 a ²)(a)(a)52011 (10³)Maa³Z|||Note: If W is a solid of revolution about L,then the computation of I may benefitfrom the Cylindrical Transformation.WY

W is the solid cube with an edge length a W=x,y , z 0≤x≤a0≤y≤a0≤z≤a To Find: Flux ∫∫F→·dS→

GIVEN: Constant a > 0 W is the solid cube with edge length, a. 0 ≤ x ≤ a • forma {(x, y, z)|0 ≤ y ≤ a 0 ≤ z ≤ a W = Q= Top face of W. The square face where z = a at every point on it. oriented with unit normal pointing away from the interior of W; note that n = 2 on 9. Xx n = 2 F = (x, y, z) FIND: The flux of F through with out - ward normal, n flux = F.dS Ω: = top surface Z = (0,0,1) W Y

GIVEN: Constant a > 0 W is the solid cube with edge length, a. 0 ≤ x ≤ a • forma {(x, y, z)|0 ≤ y ≤ a 0 ≤ z ≤ a W = Q= Top face of W. The square face where z = a at every point on it. oriented with unit normal pointing away from the interior of W; note that n = 2 on 9. Xx n = 2 F = (x, y, z) FIND: The flux of F through with out - ward normal, n flux = F.dS Ω: = top surface Z = (0,0,1) W Y

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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