The plane y + z = 7 intersects the cylinder x2 + y2 = 41 in...

The plane

y + z = 7

intersects the cylinder

x² + y² = 41

in an ellipse. Find parametric equations for the tangent line to this ellipse at the point

(4, 5, 2).

(Enter your answer as a comma-separated list of equations. Let x, y, and z be in terms of t.)

Solutions

Expert Solution

milcah answered 1 year ago

Next > < Previous

Related Solutions

The plane x+y+z= 24 intersects the cone x2+y2= z2 in an ellipse. The goal of this...

The plane x+y+z= 24 intersects the cone x2+y2= z2 in an ellipse. The goal of this exercise is to find the two points on this ellipse that are closest to and furthest away from the xy-plane. Thus, we want to optimize F(x,y,z)= z, subject to the two constraints G(x,y,z)= x+y+z= 24 and H(x,y,z)= x2+y2-z2= 0.

The plane x + y + 2z = 12 intersects the paraboloid z = x2 +...

The plane x + y + 2z = 12 intersects the paraboloid z = x2 + y2 in an ellipse. Find the points on the ellipse that are nearest to and farthest from the origin. nearest point (x, y, z) = farthest point (x, y, z) =

The paraboloid z = 8 − x − x2 − 2y2 intersects the plane x =...

The paraboloid z = 8 − x − x2 − 2y2 intersects the plane x = 4 in a parabola. Find parametric equations in terms of t for the tangent line to this parabola at the point (4, 2, −20). (Enter your answer as a comma-separated list of equations. Let x, y, and z be in terms of t.)

Let F(x,y,z) = < z tan-1(y2), z3 ln(x2 + 1), z >. Find the flux of...

Let F(x,y,z) = < z tan-1(y2), z3 ln(x2 + 1), z >. Find the flux of F across S, the top part of the paraboloid x2 + y2 + z = 2 that lies above the plane z = 1 and is oriented upward. Note that S is not a closed surface.

Consider the unit sphere x2 +y2 +z2 = 1 and the cone (z+√2)2 = x2 +y2....

Consider the unit sphere x2 +y2 +z2 = 1 and the cone (z+√2)2 = x2 +y2. Show that these surfaces are tangent where they intersect, that is, for a point on the intersection, these surfaces have the same tangent plane

Solve: y' = (y2-6y-16)x2 y(4) = 3

Let F(x, y, z) = z tan−1(y2)i + z3 ln(x2 + 8)j + zk. Find the...

Let F(x, y, z) = z tan−1(y2)i + z3 ln(x2 + 8)j + zk. Find the flux of F across S, the part of the paraboloid x2 + y2 + z = 28 that lies above the plane z = 3 and is oriented upward. S F · dS =

Let D be the region bounded by the paraboloids z = 8 - x2 - y2...

Let D be the region bounded by the paraboloids z = 8 - x2 - y2 and z = x2 + y2. Write six different triple iterated integrals for the volume of D. Evaluate one of the integrals.

Let H be the hemisphere x2 + y2 + z2 = 66, z ≥ 0, and...

Let H be the hemisphere x2 + y2 + z2 = 66, z ≥ 0, and suppose f is a continuous function with f(4, 5, 5) = 5, f(4, −5, 5) = 11, f(−4, 5, 5) = 12, and f(−4, −5, 5) = 15. By dividing H into four patches, estimate the value below. (Round your answer to the nearest whole number.) H f(x, y, z) dS

Let F= (x2 + y + 2 + z2) i + (exp( x2 ) + y2) j...

Let F= (x2 + y + 2 + z2) i + (exp( x2 ) + y2) j + (3 + x) k . Let a > 0 and let S be part of the spherical surface x2 + y2 + z2 = 2az + 15a2 that is above the x-y plane and the disk formed in the x-y plane by the circular intersection between the sphere and the plane. Find the flux of F outward across S.

Subjects