Answered: Consider the surface S given by: 4x2 +…

Consider the surface S given by: 4x2 + 4z2 = (1+ y)?, Osys2.Compute: (a) a normal vector at each point on the surface, and (b) the area of S. Show the details of your work.

Algebra and Trigonometry (MindTap Course List)

4th Edition

ISBN:9781305071742

Author:James Stewart, Lothar Redlin, Saleem Watson

Publisher:James Stewart, Lothar Redlin, Saleem Watson

Chapter9: Vectors In Two And Three Dimensions

Section9.6: Equations Of Lines And Planes

Problem 2E

See similar textbooks

Related questions

Q: Find the area of the surface generated by revolving the curve = V¤ + 3, 4 < y <7

Q: What is the normal vector, n for S is a surface of x +y² +z² = 36 in the first octant? %3D

Q: Find the standard equation of the sphere with center (−3, 2, 4) that is tangent to the plane given…

A: Radius (r) will be the distance from the center to the tangent plane. That is the distance between…

Q: Find a vector tangent to the curve of intersection of the surfaces given by x² + y² + z² = 1 and 2²…

Q: State the equstion of the yz plane

A: We have to find equation of yz plane

Q: Find a unit vector normal to the surface x^3- xyz + z^3 = 1 , at the point (1, 1, 1)

A: To find the unit normal vector to the surface x3-xyz+z3=1 at the point 1, 1, 1

Q: Find a vector which is tangent to the curve of intersection of the surfaces z = x² – y? and xyz + 30…

A: We will find out the required tangent vector.

Q: Find equation of line normal to plane 3x + 2y- z = 5 and pass through Drigin point.

Q: Find parametric equations for the normal line to the surface z= 3x2 + 10y2 at the point (2, 1, 22).…

A: Given the equation of surface z=3x2+10y2

Q: Find a vector equation of the normal line (the line orthogonal to the surface) for the surface…

Q: Find the area of the surface obtained by rotating the curve y = 4x + 4, 0 < x< 8, about %3D the…

A: To find- Find the area of the surface obtained by rotating the curve y2 = 4x + 4, 0 ≤ x ≤ 8, about…

Q: The vector (x, 2y, –3z) is normal to the surface x2 + 2y? – 32 – 4 = 0 at any point (x, y, z). - - -

A: Let's find.

Q: Find for the equations for tangent plane and normal line at P,on the given surface 2 х2 — Зху — у?…

Q: Calculate the normal vector, n for the surface z=5-x-y with upward orientation.

A: We have to find the normal vector.

Q: Find the points on the surface 6x² + y² – 3z² = 4 where the tangent plane to the surface is parallel…

A: We need to find points of intersection.

Q: Use the method of Lagrange multiplier to find the 3D vector lying on the intersection of hyperplanes…

A: let u=x i+y j+z k be a 3D vector lying on the intersection of hyperplanes x+y=2 and y+z=4 that has…

Q: Evaluate Curlv-ñ, where v = 2xyi + (x-2y)j+xzk and ñ is a unit vector normal to the surface shown in…

Q: The centroid of an obtuse triangle is outside the triangle. true or false?

A: solution ======== The centroid is the concurrent point of the three medians in a triangle. It is the…

Q: Find a vector function that represents the curve of the intersection of the two surfaces. The…

Q: Find the normal vector to the surface z = xe™Y at the point (2,0, 2).

Q: Find a parametrization of the circle of radius 5 parallel to the yz-plane with center (-1, 4, 6).

A: The general form of a parametrization of the circle of radius r parallel to yz-plane with center…

Q: A point moves along the intersection of the elliptic paraboloid z = 3x² + 5y² and the plane y = 4.…

A: We are given the curve Z=3x2+5y2 and y=4 Now we know that the rate of change is simply derivative…

Q: The normal vector to the tangent plane for the surface x²y³ z = 8, at the point (-1, 2, 1) is: 2 3…

Q: Find a vector normal to the surface x2 + y2 - z² = 18 at P = (3, 5, 4). %3D

Q: Find a vector parametrization for the intersection of the plane x + y+z = 3 and the cylinder x² + z2…

A: solution given below..

Q: Find the points on the surface ry + yz + zr - r - z = 0 where the tangent (5) plane is parallel to…

Q: A body of mass 6 kg moves in a (counterclockwise) circular path of radius 6 meters, making one…

Q: find the points on the surface + z² = 1 that have their tangent plane perpendicular to the vector…

A: For tangent plane of the surface f(x,y,z)=k at a given point normal vector to tangent plane will be…

Q: Let S be the surface parametrized by R (u, v) =< u, uv, uv

A: It is given that, the parametrized surface is R(u,v)=u, uv, uv2, 0≤u≤2, 0≤v≤3. We have to calculate…

Q: A thin plate of constant density is to occupy the triangular region in the first quadrant of the…

Q: A point moves along the intersection of the elliptic paraboloid z = 9x + 7y and the planex = 1. At…

Q: Find the centroid of the surface formed by the revolution of cardioid r = a(1 + cose) about the…

A: Given equation of cardioid, r=a1+cosθ Let the centroid be x,y.

Q: 3. Find the area of the surface cut from the nose of the paraboloid x = 1-y²-z² by the yz-plane. Do…

Q: Find a vector normal to the surface x2 + yz = 5 at (2, 1, 1).

Q: Find the surface area of that part of the plane 6x + 8y + z = 7 that lies inside the elliptic…

Q: The normal vector to the tangent plane for the surface xy² z³ 2 3 = -4, at the point (1, 2, -1) is:…

Q: Consider the surface given by x2 + y? + z? = a². Show that every normal line to this surface passes…

Q: Find a parametrization of the circle of radius 7 with center (5, 3, 9) in a plane parallel to the…

Q: Find the average z-coordinate of points in a hemisphere of radius 8 centered at the origin with its…

A: We have to find the average z coordinate of the hemisphere of radius 8 centered at origin with base…

Q: 4) Find the families of lines of curvature of the surface :=r+y

A: The answer is given in handwritten format --

Q: Find the surface normal vector to the surface z 4-(x +y²) at the point (1, 1,v2) by (a) Vf (b) N =…

Q: Find the surface area of that part of the plane 8x + 9y + z = 8 that lies inside the elliptic…

Q: he normal vector to the tangent plane for the surface point (1, 2, -1) is: Select one: None of them…

A: topic:- application of derivatives

Q: Find equations of the Normal plane and Osculating plane of the y = 2t, x = 2 sin 3t , z = -2cos 3t…

A: Given vector rt=2sin3t,2t,-2cos3t. Then r't=6cos3t,2,6sin3t. The given point is 0,π,-2. Now the…

Q: Find a vector function that represents the curve of intersection of the surface 4x+2y-8z^2=16 and…

A: To find a vector function that represents the curve of intersection of the surface 4x+2y-8z2=16 and…

Q: verify Stokes § = (a%-y)i - yz'i over the uppea hazf SOD Face Of the sphere =1 bounded by the

A: Given that, F→=(2x-y)i→-yz2j→-y2zk→ To verify Stoke's theorem: ∫CF→·dr→=∬Scurl F→·n^dS Here C is…

Q: Use inertia to classify the quadric surface given by equation. x2 + y2 + 2z2 − 2xy − 4xz − 4yz…

A: We have to use inertia to classify the quadratic surface given by equation. x2 + y2 + 2z2 −…

Q: Consider the surface S given by 4x2 + 4z2 = (1 + y)?, 0 < y < 2. Compute: (a) a normal vector at…

Question

Consider the surface S given by: 4x2 + 4z2 = (1 + y)2, osys2. Compute: (a) a normal vector at each point on the surface,
and (b) the area of S. Show the details of your work.

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

This is a popular solution!

SEE SOLUTION Check out a sample Q&A here

Step 1

VIEW

Step 2

VIEW

Trending now

This is a popular solution!

Step by step

Solved in 2 steps

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

$Differentiation$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, advanced-math and related others by exploring similar questions and additional content below.

Similar questions

Does the sphere x2+y2+z2=100 have symmetry with respect to the a x-axis? b xy-plane?
Which lines or line segments or rays must be drawn or constructed in a triangle to locate its a orthocenter? b centroid?
Find a vector normal to the surface 3z 3 + x 2 y - y 2 x = 1 at P =(1,-1,1) .
Find a unit vector normal to the surface x^3- xyz + z^3 = 1 , at the point (1, 1, 1)
Find a vector function that represents the curve of intersection of the surface 4x+2y-8z^2=16 and the cylinder of radius 3 wrapped around the y-axis.
The upper half of the unit sphere x2+y2+z2=1 is z=Square root of 1-x2-y2. Find its centroid?
Find a unit vector n that is normal to the surface 2z^2−x^4−y^4=1 at P=(1,2,3) that points in the direction of the xy-plane (in other words, if you travel in the direction of n, you will eventually cross the xy-plane).
Find the area of the surface, which is part of the surface z = 1 + 3x + 2y2 that lies above the triangle with vertices (0, 0), (0, 1) and (2, 1).
Given F(x, y, z) = x^2i + 2xyj + 3xzk and a region, being cut from the 1st octant by the sphere x^2 + y^2 + z^2 = 4. Sketch the region, label surfaces and find normal vectors for the surfaces.
Find a nonzero vector normal to the plane z−3(x−4) = −4(1−y) correctly.
Classify the quadric surface given by equation and determine its standard form. x2 + y2 + 2z2 − 2xy + 4xz + 4yz = 16
Let S be the surface obtained by revolving the plane curve 2x=sqrt(9−y2) about the y-axis.Obtain a vector equation for S and use it to find the equation of the tangent plane to S at the point (-1,1,-1).