Question 4Let H be the part of the hyperboloid with equation x2 + y? - z2 = 1 located between the planes z = -2 andz = 2. The area of H isA = T(V2 ln(2/2+3) + 12).a) Show that H can be parameterized byŘ(u, v) = V1+ v² cos(u)i+ V1+ v² sin(u) j+ v kwith 0sus 2n and -2 svs 2.a) If the surface H is oriented at the point (1,0, 0) by the normal vector ñ =1, calculate the flux of thevector field F defined byF(x,y, 2) = -yi + xj + z°kthrough H.a) if G is a vector field of constant norm and perpendicular to the surface H at any point, which is theflow of G through H ?

(a) Given surface H is part of hyparaboloid with equation x2+y2−z2=1 and −2≤z≤2Given that…

Question 4 Let H be the part of the hyperboloid with equation x² + y² - z² = 1 located between the planes z = -2 and z = 2. The area of H is A = π(√√2ln(2√2+3) +12). a) Show that H can be parameterized by R(u, v) = √√√1 + v² cos(u) i + √√1+v² sin(u)j +vk with 0 ≤us 2π and -2 ≤ v ≤ 2. a) If the surface H is oriented at the point (1,0,0) by the normal vector i = 1, calculate the flux of the vector field F defined by F (x, y, z) = −yi + xj + z³k through H. a) if G is a vector field of constant norm and perpendicular to the surface H at any point, which is the flow of G through H?

Question 4 Let H be the part of the hyperboloid with equation x² + y² - z² = 1 located between the planes z = -2 and z = 2. The area of H is A = π(√√2ln(2√2+3) +12). a) Show that H can be parameterized by R(u, v) = √√√1 + v² cos(u) i + √√1+v² sin(u)j +vk with 0 ≤us 2π and -2 ≤ v ≤ 2. a) If the surface H is oriented at the point (1,0,0) by the normal vector i = 1, calculate the flux of the vector field F defined by F (x, y, z) = −yi + xj + z³k through H. a) if G is a vector field of constant norm and perpendicular to the surface H at any point, which is the flow of G through H?

Trigonometry (MindTap Course List)

10th Edition

ISBN:9781337278461

Author:Ron Larson

Publisher:Ron Larson

Chapter6: Topics In Analytic Geometry

Section6.6: Parametric Equations

Problem 5ECP: Write parametric equations for a cycloid traced by a point P on a circle of radius a as the circle...

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