O) Use Stokes' Theorem to evaluate F. dr where F(x, y, z) = xyi + j + xyk and C is the curve of intersection of the hyperbolic paraboloid z = y2 - x and the cylinder x2 + y? = 1 oriented counterclockwise as viewed from abo (b) Graph both the hyperbolic paraboloid and the cylinder with domains chosen so that you can see the curve C and the surface. 1.0 1.0 05 0.5 -0.5 -0.5 -10 -10 -1.0 10 10 0.5 05 -0.5t -10 -1.0 -1.0 (c) Find parametric equations for C and use them to graph C. (Enter your answer as a comma-separated list of equations. Let x and y be in terms of t where osts 2m.)
O) Use Stokes' Theorem to evaluate F. dr where F(x, y, z) = xyi + j + xyk and C is the curve of intersection of the hyperbolic paraboloid z = y2 - x and the cylinder x2 + y? = 1 oriented counterclockwise as viewed from abo (b) Graph both the hyperbolic paraboloid and the cylinder with domains chosen so that you can see the curve C and the surface. 1.0 1.0 05 0.5 -0.5 -0.5 -10 -10 -1.0 10 10 0.5 05 -0.5t -10 -1.0 -1.0 (c) Find parametric equations for C and use them to graph C. (Enter your answer as a comma-separated list of equations. Let x and y be in terms of t where osts 2m.)
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter11: Topics From Analytic Geometry
Section11.4: Plane Curves And Parametric Equations
Problem 53E
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Equations and inequalities describe the relationship between two mathematical expressions.
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Please solve (c) using the provided answers for (a) & (b) in the screenshot. Handwriting is preferred. Thanks!
Transcribed Image Text:(a) Use Stokes' Theorem to evaluate
F. dr where F(x, y, z) = x?yi + j + xyk and C is the curve of intersection of the hyperbolic paraboloid z = y2 - x2 and the cylinder x2 + y2 = 1 oriented counterclockwise as viewed from above.
F. dr = T
(b) Graph both the hyperbolic paraboloid and the cylinder with domains chosen so that you can see the curve
C and the surface.
1.0
1.0
0.5
0.5
0.0
-0.
-0.5
-1.0
-1.0
1.0
1.0
0.5
0.5
-0.5
-0.5
-10
-10
-1.0
-1.0
-0.5
-0.5
00
00
0.5
0.5
1.0
1.0
1.0
1.0
0.5
0.5
0.0
-0.5
-0.5
-1.0,
-1.0
1.0
1.0
0.5
0.5
Z0.0t
-0.5
-0.5
-10
-10
-1.0
-1.0
-05
-0.5
00
0.0
0.5
05
1.0
1.0
(c) Find parametric equations for C and use them to graph c. (Enter your answer as a comma-separated list of equations. Let x and y be in terms of t where osts 27.)
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