Consider the vector field F (x+ y)i + (x² + y²)j What is the downward flux across the line segment from (0,0) to (-10,0)? (a) For (F N) ds, r(t) = E for 0

Elementary Linear Algebra (MindTap Course List)
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Chapter7: Eigenvalues And Eigenvectors
Section7.CM: Cumulative Review
Problem 15CM
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Consider the vector field F =
(x + y)i + (x2 + y²)j. What is the downward flux across the line segment from (0,0) to (–10,0)?
(a) For
(F N) ds,
r(t) =
Z for 0 <t < .
F(r(t)).
Σ
N =
Σ
ds
E dt
|(F N) ds =
(b) And so,
Consider again the vector field F
(x + y)i+ (x2 + y² )j _What is the downward flux across the line segment from (9,0) to (0, –9)?
%3D
(a) For
(F · N) ds,
r(t) =
E for 0 <t < 1
F(r(t))
Σ
N =
Σ
ds =
E dt
(b) And so,
(F N) ds
Σ
Transcribed Image Text:Consider the vector field F = (x + y)i + (x2 + y²)j. What is the downward flux across the line segment from (0,0) to (–10,0)? (a) For (F N) ds, r(t) = Z for 0 <t < . F(r(t)). Σ N = Σ ds E dt |(F N) ds = (b) And so, Consider again the vector field F (x + y)i+ (x2 + y² )j _What is the downward flux across the line segment from (9,0) to (0, –9)? %3D (a) For (F · N) ds, r(t) = E for 0 <t < 1 F(r(t)) Σ N = Σ ds = E dt (b) And so, (F N) ds Σ
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