Determine which families of grid curves have u constant and which have v constant.u constanteach grid curve lies in a plane z =ky that includes the x-axisthe grid curves lie in the vertical plane y =(tan (u))xeach grid curve is a circle of radius |u| in the horizontal plane z =sin(u)each grid curve is a vertically oriented circleeach grid curve is a circle of radius (1 - Ju|) in the horizontal plane z = ueach grid curve is a helixv constanteach grid curve is a circle contained in the vertical plane x =sin(v) parallel to the yz-planethe vertical planes y= kx through the z-axisO a straight line in the plane z = v which intersects the z-axisthe grid curves run vertically along the surface in the planes y = kxthe grid curves are the spiral curvesO the grid curves lie in a horizontal plane Match the equation with its graph.r(u, v) = u cos(v) i + u sin(v) j + v kZAOIOIIZAZAOIVOIIOvOVI

Consider the surface r⇀u,v=ucosvi^+usinvj^+vk^ The parametric equations are, x=ucosvy=usinvz=v The…

Answered: Match the equation with its graph. r(u,…

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Match the equation with its graph. r(u, v) = u cos(v) i + u sin(v) j + v k

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 29E

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Question

Determine which families of grid curves have u constant and which have v constant.
u constant
each grid curve lies in a plane z =
ky that includes the x-axis
the grid curves lie in the vertical plane y =
(tan (u))x
each grid curve is a circle of radius |u| in the horizontal plane z =
sin(u)
each grid curve is a vertically oriented circle
each grid curve is a circle of radius (1 - Ju|) in the horizontal plane z = u
each grid curve is a helix
v constant
each grid curve is a circle contained in the vertical plane x =
sin(v) parallel to the yz-plane
the vertical planes y
= kx through the z-axis
O a straight line in the plane z = v which intersects the z-axis
the grid curves run vertically along the surface in the planes y = kx
the grid curves are the spiral curves
O the grid curves lie in a horizontal plane

Match the equation with its graph.
r(u, v) = u cos(v) i + u sin(v) j + v k
ZA
OI
OII
ZA
ZA
OIV
OII
Ov
OVI

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