Stokes’ Theorem for evaluating surface integrals Evaluate the line integral in stokes’ Theorem to determine the value of the surface integral ∬ s ( ∇ × F ) ∙ n dS . Assume n points in an upward direction. 21 . F = 〈 y , z − x , − y 〉 ; S is the part of the paraboloid z = 2 − x 2 − 2 y 2 that lies within the cylinder x 2 +y 2 =1.
Stokes’ Theorem for evaluating surface integrals Evaluate the line integral in stokes’ Theorem to determine the value of the surface integral ∬ s ( ∇ × F ) ∙ n dS . Assume n points in an upward direction. 21 . F = 〈 y , z − x , − y 〉 ; S is the part of the paraboloid z = 2 − x 2 − 2 y 2 that lies within the cylinder x 2 +y 2 =1.
Solution Summary: The author evaluates the surface integral value by obtaining line integral in Stokes' theorem.
Stokes’ Theorem for evaluating surface integrals Evaluate the line integral in stokes’ Theorem to determine the value of the surface integral
∬
s
(
∇
×
F
)
∙ndS. Assume n points in an upward direction.
21. F =
〈
y
,
z
−
x
,
−
y
〉
;
S is the part of the paraboloid z = 2 − x2 − 2y2 that lies within the cylinder x2+y2=1.
Quantities that have magnitude and direction but not position. Some examples of vectors are velocity, displacement, acceleration, and force. They are sometimes called Euclidean or spatial vectors.
Robbie
Bearing Word Problems
Angles
name:
Jocelyn
date: 1/18
8K
2. A Delta airplane and an SouthWest airplane take off from an airport
at the same time. The bearing from the airport to the Delta plane is
23° and the bearing to the SouthWest plane is 152°. Two hours later
the Delta plane is 1,103 miles from the airport and the SouthWest
plane is 1,156 miles from the airport. What is the distance between the
two planes? What is the bearing from the Delta plane to the SouthWest
plane? What is the bearing to the Delta plane from the SouthWest
plane?
Delta
y
SW
Angles
ThreeFourthsMe MATH
2
Find the derivative of the function.
m(t) = -4t (6t7 - 1)6
Find the derivative of the function.
y= (8x²-6x²+3)4
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