GIVEN: a>0, The surface, 2: x+y+z = a, x ≥ 0, y ≥ 0, z ≥ 0. Consider the 3D field: F (x+y, z, y - x) Orient the surface so that its normal vector to it has a positive z- component. Here is the canonical parameterization of 22: D:D, P(x, y) = (x, y, a- x - y) where D = {(x, y) = 0 ≤ x ≤ a 0 ≤ y ≤ a- FIND: The flux of F through 2 with the given orientation. A X Ω F = Add extra pages, as needed. A = (a,0,0) B=(0, a,0) C = (0,0,a) B (x + y, z, y - x) Y
GIVEN: a>0, The surface, 2: x+y+z = a, x ≥ 0, y ≥ 0, z ≥ 0. Consider the 3D field: F (x+y, z, y - x) Orient the surface so that its normal vector to it has a positive z- component. Here is the canonical parameterization of 22: D:D, P(x, y) = (x, y, a- x - y) where D = {(x, y) = 0 ≤ x ≤ a 0 ≤ y ≤ a- FIND: The flux of F through 2 with the given orientation. A X Ω F = Add extra pages, as needed. A = (a,0,0) B=(0, a,0) C = (0,0,a) B (x + y, z, y - x) Y
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
please please please anwer super super fast its really important and urgent also please try to write clear and neat
this is not a graded question
![[20] (2)
GIVEN: a>0, The surface, Q2: x+y+z = a, x ≥ 0, y ≥ 0, z ≥ 0.
Consider the 3D field: F= (x, 2x, 3x)
Orient the surface so that its normal vector has a positive z- component.
FIND: The flux of F through 2 with the given orientation.
Parameterization of D:
D = PROJ, &:D Q
xy
= {(²₂₂) |0 ≤ y ≤a-x}
$(x,y)=(x, y, a-x-y)
⇒
= (1,0,-1) canonical
*y = (0,1,-1)
⇒ x = (1,1,1)
=
parameterization
A
a
J
A = (a,0,0)
B = (0, a, 0)
C = (0,0,a)
F = (x, 2x, 3x)
D=A
B
y=a-x
a
FLUX = √ F•áŠ = √ (2,22,32)-(1,1,1) dedy
= √₂ 6x dx dy = 65 ª 1 * x² dyd
бу
a
a
6 ["²x (2-x) b = 6 √ ² x ² + ax de
6 [ - ‡ a³ + + a²³²]
3
Y](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F4295bf62-da14-49f1-b3bf-6e678bc68de3%2Fbbede9e8-266f-4bdb-af23-08a2381127b8%2Fhshcyri_processed.jpeg&w=3840&q=75)
Transcribed Image Text:[20] (2)
GIVEN: a>0, The surface, Q2: x+y+z = a, x ≥ 0, y ≥ 0, z ≥ 0.
Consider the 3D field: F= (x, 2x, 3x)
Orient the surface so that its normal vector has a positive z- component.
FIND: The flux of F through 2 with the given orientation.
Parameterization of D:
D = PROJ, &:D Q
xy
= {(²₂₂) |0 ≤ y ≤a-x}
$(x,y)=(x, y, a-x-y)
⇒
= (1,0,-1) canonical
*y = (0,1,-1)
⇒ x = (1,1,1)
=
parameterization
A
a
J
A = (a,0,0)
B = (0, a, 0)
C = (0,0,a)
F = (x, 2x, 3x)
D=A
B
y=a-x
a
FLUX = √ F•áŠ = √ (2,22,32)-(1,1,1) dedy
= √₂ 6x dx dy = 65 ª 1 * x² dyd
бу
a
a
6 ["²x (2-x) b = 6 √ ² x ² + ax de
6 [ - ‡ a³ + + a²³²]
3
Y
![[10] (5)
: x + y + z = a, x ≥ 0, y ≥ 0, z ≥ 0.
(x + y, z, y - x)
Orient the surface so that its normal vector to it has a positive z - component.
GIVEN: a>0, The surface,
Consider the 3D field: F
Here is the canonical parameterization of Q:
Þ:D →
→ Ω, Φ(x, y)
(x, y, a- x - y)
where D = x, y
=
=
0 ≤ x ≤ a
0 ≤ y ≤a-
FIND: The flux of F through
with the given orientation.
A
X
Ω
Add extra
pages, as
needed.
A = (a,0,0)
B = (0,a,0)
C = (0,0, a)
B
F = (x+y, z, y - x)
Y](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F4295bf62-da14-49f1-b3bf-6e678bc68de3%2Fbbede9e8-266f-4bdb-af23-08a2381127b8%2Fqfipd4w_processed.jpeg&w=3840&q=75)
Transcribed Image Text:[10] (5)
: x + y + z = a, x ≥ 0, y ≥ 0, z ≥ 0.
(x + y, z, y - x)
Orient the surface so that its normal vector to it has a positive z - component.
GIVEN: a>0, The surface,
Consider the 3D field: F
Here is the canonical parameterization of Q:
Þ:D →
→ Ω, Φ(x, y)
(x, y, a- x - y)
where D = x, y
=
=
0 ≤ x ≤ a
0 ≤ y ≤a-
FIND: The flux of F through
with the given orientation.
A
X
Ω
Add extra
pages, as
needed.
A = (a,0,0)
B = (0,a,0)
C = (0,0, a)
B
F = (x+y, z, y - x)
Y
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 3 steps with 2 images
Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
