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. - Component B occupies the region outside the sphere r=2 cos (p) and inside the sphere r=2 with € [0, π/2]. Assume B has a uniform density of PB.. Component C is a curved wedge that lies inside the region enclosed by the cylinder (x-2)²+y²=4 and the planes z=0 and z = -y. Assume C has a uniform density of ec " ii. Sketch B and C.

. - Component B occupies the region outside the sphere r=2 cos (p) and inside the sphere r=2 with € [0, π/2]. Assume B has a uniform density of PB.. Component C is a curved wedge that lies inside the region enclosed by the cylinder (x-2)²+y²=4 and the planes z=0 and z = -y. Assume C has a uniform density of ec " ii. Sketch B and C.

Advanced Engineering Mathematics
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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Please hand sketch Component B and C

MAST20029 Engineering Mathematics Formulae Sheet 1. Change of Variable of Integration in 2D JJ₁ f(x, y) dxdy = [[ f(x(u, v), y(u, v))|J(u, v)| dudv R 2. Transformation to Polar Coordinates x = r cos 0, 3. Change of Variable of Integration in 3D [[[ f(x, y, z) dadydz 4. Transformation to Cylindrical Coordinates x = r cos 0, y = r sin 0, 5. Transformation to Spherical Coordinates 7. Work Integrals y = r sin 0, LFG 8. Surface Integrals x = r cos sin o, y = r sin sin o, z = r cos o, = = [[[_ F(u, v), w)|J(u, v, w) dudvdw [[₁, g(x, y, z) ds = S J(r,0) = 6. Line Integrals Jo f(x, y, 2) ds = ["* f(x(t), y(t), z(t)) √x'(t)² + y(t)}² + 2'(t)² dt F(x, y, z). dr = J(r, 0, z) = r = r cb dx - [² R² +F="/ F₁ F₂ dt a F. ÂdS = J(r, 0, 0) = r² sin o 9. Flux Integrals For a surface with upward unit normal, 11. F + F3 dz = [[ g(x, y, f (x, y)) √[f² + f² +1dxdy dt = SS₁₂ - ² -F₁fx - F2fy + F3 dydx
Transcribed Image Text:MAST20029 Engineering Mathematics Formulae Sheet 1. Change of Variable of Integration in 2D JJ₁ f(x, y) dxdy = [[ f(x(u, v), y(u, v))|J(u, v)| dudv R 2. Transformation to Polar Coordinates x = r cos 0, 3. Change of Variable of Integration in 3D [[[ f(x, y, z) dadydz 4. Transformation to Cylindrical Coordinates x = r cos 0, y = r sin 0, 5. Transformation to Spherical Coordinates 7. Work Integrals y = r sin 0, LFG 8. Surface Integrals x = r cos sin o, y = r sin sin o, z = r cos o, = = [[[_ F(u, v), w)|J(u, v, w) dudvdw [[₁, g(x, y, z) ds = S J(r,0) = 6. Line Integrals Jo f(x, y, 2) ds = ["* f(x(t), y(t), z(t)) √x'(t)² + y(t)}² + 2'(t)² dt F(x, y, z). dr = J(r, 0, z) = r = r cb dx - [² R² +F="/ F₁ F₂ dt a F. ÂdS = J(r, 0, 0) = r² sin o 9. Flux Integrals For a surface with upward unit normal, 11. F + F3 dz = [[ g(x, y, f (x, y)) √[f² + f² +1dxdy dt = SS₁₂ - ² -F₁fx - F2fy + F3 dydx
Component A is bounded by the planes x=0, x=2, z=-y and z= i. Sketch A and find its volume. بوعان Components B and C have different geometries and density but must be designed to have equal mass. • Component B occupies the region outside the sphere r = 2 cos(p) and inside the sphere r=2 with = [0, π/2]. Assume B has a uniform density of PB. · Component C is a curved wedge that lies inside the region enclosed by the cylinder (x-2)² + y²=4 and the planes z=0 and z = −y. Assume C has a uniform density of Pe ii. Sketch B and C. Find the volume of B and C, and the ratio PB / PC to achieve equal mass. iv. Find the flux of F across S, the surface of C, given that F(x₁412) = [2x + cosh (Sy²)] i + [zxe*_6z]; +[1 + xy² ] K V. What is the flux of F across the surface of a spherical body if F2,4₁2) = Ak , where A is a real and negative constant?
Transcribed Image Text:Component A is bounded by the planes x=0, x=2, z=-y and z= i. Sketch A and find its volume. بوعان Components B and C have different geometries and density but must be designed to have equal mass. • Component B occupies the region outside the sphere r = 2 cos(p) and inside the sphere r=2 with = [0, π/2]. Assume B has a uniform density of PB. · Component C is a curved wedge that lies inside the region enclosed by the cylinder (x-2)² + y²=4 and the planes z=0 and z = −y. Assume C has a uniform density of Pe ii. Sketch B and C. Find the volume of B and C, and the ratio PB / PC to achieve equal mass. iv. Find the flux of F across S, the surface of C, given that F(x₁412) = [2x + cosh (Sy²)] i + [zxe*_6z]; +[1 + xy² ] K V. What is the flux of F across the surface of a spherical body if F2,4₁2) = Ak , where A is a real and negative constant?
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