Consider the paraboloid z=x2+y2. The plane 2x−2y+z−7=0 cuts the paraboloid, its intersection being a curve. Find...
Consider the paraboloid z=x2+y2. The plane 2x−2y+z−7=0 cuts the paraboloid, its intersection being a curve. Find "the natural" parametrization of this curve. Hint: The curve which is cut lies above a circle in the xy-plane which you should parametrize as a function of the variable t so that the circle is traversed counterclockwise exactly once as t goes from 0 to 2*pi, and the paramterization starts at the point on the circle with largest x coordinate. Using that as your starting point, give the parametrization of the curve on the surface.
c(t)=(x(t),y(t),z(t)), where
x(t)=
y(t)=
z(t)=
Homework Answers
Add Answer to:
Consider the paraboloid z=x2+y2. The plane 2x−2y+z−7=0 cuts the
paraboloid, its intersection being a curve. Find...
C is the curve of intersection of the paraboloid z (++y and the plane z 2x+2. 2. Evaluate [ F -dr using Stokes' Theorem. Choose the simplest surface with boundary curve C and orient it upward....
C is the curve of intersection of the paraboloid z (++y and the plane z 2x+2. 2. Evaluate [ F -dr using Stokes' Theorem. Choose the simplest surface with boundary curve C and orient it upward.
C is the curve of intersection of the paraboloid z (++y and the plane z 2x+2. 2. Evaluate [ F -dr using Stokes' Theorem. Choose the simplest surface with boundary curve C and orient it upward.
10. Stokes' Theorem and Surface Integrals of Vector Fields a. Stokes' Theorem: F dr- b. Let S be the surface of the paraboloid z 4-x2-y2 and C is the trace of S in the xy-plane. Draw a sk...
10. Stokes' Theorem and Surface Integrals of Vector Fields a. Stokes' Theorem: F dr- b. Let S be the surface of the paraboloid z 4-x2-y2 and C is the trace of S in the xy-plane. Draw a sketch of curve C in the xy-plane. Let F(x,y,z) = <2z, x, y?». Compute the curl (F) c. d. Find a parametrization of the surface S: G(u,v)- Compute N(u,v) e. Use Stokes' Theorem to computec F dr
10. Stokes' Theorem and Surface Integrals...
-y-2x 2+2y de If - 1 + xy + y2 + x2 = 0 and it...
-y-2x 2+2y de If - 1 + xy + y2 + x2 = 0 and it is known that day find all coordinate points on the curve where x = -1 and the line tangent to the curve is horizontal, or state that no such points exist.
10. Stokes Theorem and Surface Integrals of Vector Fields a Stokes Theorem:J F dr- b. Let S be the surface of the paraboloid z 4-x2-y2 and C is the trace of S in the xy-plane. Draw a sketch of cu...
10. Stokes Theorem and Surface Integrals of Vector Fields a Stokes Theorem:J F dr- b. Let S be the surface of the paraboloid z 4-x2-y2 and C is the trace of S in the xy-plane. Draw a sketch of curve C in the xy-plane. Let F(x,y,z) = <2z, x, y, Compute the curl (F) c. d. Find a parametrization of the surface S: G(u,v)ーーーーーーーーーーーーー Compute N(u,v) e. Use Stokes' Theorem to compute Jc F dr
10. Stokes Theorem and Surface...
1. (1 point) Find the arc-length parametrization of the curve that is the intersection of the elliptic cylr 1 and the plane z-2y = 7. Use s as the arc length parameter with s = 0 corresponding to...
1. (1 point) Find the arc-length parametrization of the curve that is the intersection of the elliptic cylr 1 and the plane z-2y = 7. Use s as the arc length parameter with s = 0 corresponding to the point (0, 1.9) oriented counter-clockwise as seen from above Spring 2016)
1. (1 point) Find the arc-length parametrization of the curve that is the intersection of the elliptic cylr 1 and the plane z-2y = 7. Use s as the arc...
7. (a) State Stoke's Theorem. (b) Use Stoke's theorem to evaluate curl(F)d where F(x, y, z)-< x2 sin(z), y2, xy >, and s is the part of the paraboloid z = 1-2-1/2 that lies above th...
7. (a) State Stoke's Theorem. (b) Use Stoke's theorem to evaluate curl(F)d where F(x, y, z)-< x2 sin(z), y2, xy >, and s is the part of the paraboloid z = 1-2-1/2 that lies above the xy-plane.
7. (a) State Stoke's Theorem. (b) Use Stoke's theorem to evaluate curl(F)d where F(x, y, z)-, and s is the part of the paraboloid z = 1-2-1/2 that lies above the xy-plane.
3. (a) Consider the paraboloid z = x2 + y2 Find a unit vector normal to...
3. (a) Consider the paraboloid z = x2 + y2 Find a unit vector normal to the surface of this paraboloid at the point P = (x, y, z) = (1, 2,5). (b) Consider a vector field ä = (xy2 + z)i + (xy + 2)9 + xk where, as usual, i = Î. Ì = û and k = 2 are the unit vectors. Show that a = Vº for some scalar field o.
Q3. Find the unit tangent vector to the curve (t) t, 2,1 at the points where it cuts the plane 2x = z-y. Q3. Find the unit tangent vector to the curve (t) t, 2,1 at the points where it cuts t...
Q3. Find the unit tangent vector to the curve (t) t, 2,1 at the points where it cuts the plane 2x = z-y.
Q3. Find the unit tangent vector to the curve (t) t, 2,1 at the points where it cuts the plane 2x = z-y.
EXAMPLE 4 Find the volume of the solid that lies under the paraboloid z 5x2 - 5y2, above the xy-p...
EXAMPLE 4 Find the volume of the solid that lies under the paraboloid z 5x2 - 5y2, above the xy-plane, and inside the cylinder x2 + y2-2x (x-1)2 + y2=1 or r 2 cos 8 SOLUTION The solid lies above the disk D whose boundary circle has equation x2 +y2x or, after completing the square, In polar coordinates we have x2 +y Thus the disk D is given by and x-r cos(), so the boundary circle becomes 2r cos(), or...
Begin with the paraboloid z = 22 + y2 for 0 < < 4, and slice...
Begin with the paraboloid z = 22 + y2 for 0 < < 4, and slice it with the plane y = 0. Let S be the surface that remains for y> 0 (excluding the planar surface in xz-plane) oriented downward (i.e. n3 <0). Let C be the Semicircle and the line segment in the plane z = 4 with counterclockwise orientation and F =< 2z+y, 2x + z, 2y + 2 > ZA C 4 S 2 = x2...
C is the curve of intersection of the paraboloid z (++y and the plane z 2x+2. 2. Evaluate [ F -dr using Stokes' Theorem. Choose the simplest surface with boundary curve C and orient it upward.
C is the curve of intersection of the paraboloid z (++y and the plane z 2x+2. 2. Evaluate [ F -dr using Stokes' Theorem. Choose the simplest surface with boundary curve C and orient it upward.
10. Stokes' Theorem and Surface Integrals of Vector Fields a. Stokes' Theorem: F dr- b. Let S be the surface of the paraboloid z 4-x2-y2 and C is the trace of S in the xy-plane. Draw a sketch of curve C in the xy-plane. Let F(x,y,z) = <2z, x, y?». Compute the curl (F) c. d. Find a parametrization of the surface S: G(u,v)- Compute N(u,v) e. Use Stokes' Theorem to computec F dr
10. Stokes' Theorem and Surface Integrals...
-y-2x 2+2y de If - 1 + xy + y2 + x2 = 0 and it is known that day find all coordinate points on the curve where x = -1 and the line tangent to the curve is horizontal, or state that no such points exist.
10. Stokes Theorem and Surface Integrals of Vector Fields a Stokes Theorem:J F dr- b. Let S be the surface of the paraboloid z 4-x2-y2 and C is the trace of S in the xy-plane. Draw a sketch of curve C in the xy-plane. Let F(x,y,z) = <2z, x, y, Compute the curl (F) c. d. Find a parametrization of the surface S: G(u,v)ーーーーーーーーーーーーー Compute N(u,v) e. Use Stokes' Theorem to compute Jc F dr
10. Stokes Theorem and Surface...
1. (1 point) Find the arc-length parametrization of the curve that is the intersection of the elliptic cylr 1 and the plane z-2y = 7. Use s as the arc length parameter with s = 0 corresponding to the point (0, 1.9) oriented counter-clockwise as seen from above Spring 2016)
1. (1 point) Find the arc-length parametrization of the curve that is the intersection of the elliptic cylr 1 and the plane z-2y = 7. Use s as the arc...
7. (a) State Stoke's Theorem. (b) Use Stoke's theorem to evaluate curl(F)d where F(x, y, z)-< x2 sin(z), y2, xy >, and s is the part of the paraboloid z = 1-2-1/2 that lies above the xy-plane.
7. (a) State Stoke's Theorem. (b) Use Stoke's theorem to evaluate curl(F)d where F(x, y, z)-, and s is the part of the paraboloid z = 1-2-1/2 that lies above the xy-plane.
3. (a) Consider the paraboloid z = x2 + y2 Find a unit vector normal to the surface of this paraboloid at the point P = (x, y, z) = (1, 2,5). (b) Consider a vector field ä = (xy2 + z)i + (xy + 2)9 + xk where, as usual, i = Î. Ì = û and k = 2 are the unit vectors. Show that a = Vº for some scalar field o.
Q3. Find the unit tangent vector to the curve (t) t, 2,1 at the points where it cuts the plane 2x = z-y.
Q3. Find the unit tangent vector to the curve (t) t, 2,1 at the points where it cuts the plane 2x = z-y.
EXAMPLE 4 Find the volume of the solid that lies under the paraboloid z 5x2 - 5y2, above the xy-plane, and inside the cylinder x2 + y2-2x (x-1)2 + y2=1 or r 2 cos 8 SOLUTION The solid lies above the disk D whose boundary circle has equation x2 +y2x or, after completing the square, In polar coordinates we have x2 +y Thus the disk D is given by and x-r cos(), so the boundary circle becomes 2r cos(), or...
Begin with the paraboloid z = 22 + y2 for 0 < < 4, and slice it with the plane y = 0. Let S be the surface that remains for y> 0 (excluding the planar surface in xz-plane) oriented downward (i.e. n3 <0). Let C be the Semicircle and the line segment in the plane z = 4 with counterclockwise orientation and F =< 2z+y, 2x + z, 2y + 2 > ZA C 4 S 2 = x2...
Most questions answered within 3 hours.
-
Problem 2: The Problem of Social Cost. A Rancher and Farmer live
side-by-side to each other....
asked 50 minutes ago -
a uniform bar of weight 40N is 4 meter long. weights
on 60N and 100N are...
asked 19 minutes ago -
Define Diet counceling? What are the
responsibilities of a counselor?
asked 2 hours ago -
Hey im just confused about how to put the ' A angle n' and ' S...
asked 2 hours ago -
A short essay about the WSJ article on Oreo versus Hydrox.
asked 2 hours ago -
##8. A program contains the following function definition:
##def cube(num):
##return num * num * num...
asked 2 hours ago -
find the value z of a standard Normal variable that satisfies
each of the given conditions....
asked 2 hours ago -
"banana".find('z')
Out[22]: -1
why is this -1
python 3.7
asked 2 hours ago -
Ilegal Consideration Marna Balin was involved in two automobile
accidents in which she suffered severe injures.She...
asked 2 hours ago -
Walk through the operation of QuickSort when n = 7 and the input
array is A...
asked 2 hours ago -
Answer with True or False. Argue the answers
7) The circulation of field B on any...
asked 2 hours ago -
Chase Co. uses the perpetual inventory method. The inventory
records for Chase reflected the following
Jan...
asked 2 hours ago