Use  inertia  to  classify  the  quadric surface  given by equation. x2 + y2 + 2z2 − 2xy − 4xz − 4yz + 4x = 8

Q: . Determine the area of the surface with parametric equations a = 2u?, y = v², z = 2uv, 0 <u < 3, 0…

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Q: Find an equation in cylindrical coordinates for the surface represented by the rectangular equation.…

A: Given rectangular equation is y = x2

Q: find a parametrization of the surface Parabolic cylinder between planes The surface cut from…

A: To find a parametrization of the surface: Given that, Between the planes z=0 &amp; z=3 Thus, 0≤z≤3…

Q: Find the angle between the two planes 6x − 3y + z = 5,  −x + y + 5z = 5 and find a set of parametric…

A: We have given the equation of planes; 6x − 3y + z = 5 −x + y + 5z = 5 Hence the normal vectors of…

Q: Find an equation in cylindrical coordinates for the surface represented by the rectangular equation…

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Q: Find the highest and lowest point of the surface z2 = x2 + y2 ,on the plane 4x – 3y + 8z = 10 %3D…

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Q: Find an equation of the surface of revolution by revolving the plane curve 3y = v(9- [(x-1)] ^2)…

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Q: find a parametrization of the surface. The paraboloid z = x2 + y2, z&lt;=4 The paraboloid z = 9 - x2…

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Q: Find an equation of the sphere with center (2, 1,−3) that is tangent to the plane x −3y + 2z = 4.

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Q: state the type of the quadric surface and describe the trace obtained by intersecting with the given…

A: Given: x2+y42+z2=1  ……1   Equation of plane is: z=14  ……2

Q: Find parametric equations for the surface obtained by rotating the curve y = 36x4 – x2, –6 <t< VI

A: Here we solve the given problem of calculus.

Q: Classify the quadric surface. x2 - y2 + z = 0 O hyperboloid of one sheet O hyperboloid of two sheets…

A: Classify the quadratic surface.

Q: Find the center C and the radius a for the sphere 1. 3x2 + 3y2 + 3z2 + 2y - 2z = 9 2. x2 + y2 + z2 -…

A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question…

Q: state the type of the quadric surface and describe the trace obtained by intersecting with the given…

A: x2+y42+ z2=1,y=5x2+y42+ z2=1

Q: Find an equation in spherical coordinates for the surface represented by the rectangular equation x2…

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Q: Sketch the curve of intersection of the surfaces. The paraboloids z = x² + y² and z = 16 – x – y.…

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Q: Find an equation in spherical coordinates for the surface represented by the rectangular equation.…

A: Solution is given below:

Q: Find parametric equations for the intersection of the planes 2x + y − 3z = 0 and x + y = 1

A: Two planes lying in 3-Dimensional plane can intersect each other at any point and that point can lie…

Q: Find an equation in cylindrical coordinates for the surface represented by each rectangular…

A: Given  x2+y2=4z2 It can be compared with the equation of elliptic cone with its axis along z-axis.…

Q: A cylindrical surface in an xyz-coordinate system is an equation that contains only two of the…

A: In this question we have to state whether the given statement is true or false.

Q: Find an equation in spherical coordinates for the surface represented by the rectangular equation.…

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Q: Find an equation in cylindrical coordinates for the surface represented by the rectangular equation…

A: Given:y2=10-z2r2=x2+y2x=r cosθy=r sinθz=z

Q: Find an equation of the surface consisting of all points P(x, y, z) that are twice as far from the…

A: Let d1 be the distance from the point 0,0,1 to the point Px,y,z and d2 be the distance from the…

Q: Use  inertia  to  classify  the  quadric surface  given by equation. y2 − z2 − 9x − 4y + 8z − 12 = 0

A: We wish to use inertia to classify the quadric surface given by the following equation:  ------(1)…

Q: Classify the surface: 1- x = 3y? + 4z2 O Plane O sphere O cone O Elliptic paraboloid O Ellipsoid

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Q: state the type of the quadric surface and describe the trace obtained by intersecting with the given…

A: The given quadratic surface is  x2+y42+z2=1 , y=0

Q: Find parametric equations for the intersection of the surfaces y = x² and 2x² + y² + 6z² = 24 and…

A: Find out the parametric equations for the intersection of the surfaces y=x2 and 2x2+y2+6z2=24…

Q: Sketch the quadric surface: r +4y2 +4z2 16. Note: The x, y, & z axes are depicted in red, green, &…

A: The given function is: x2+4y2+4z2=16

Q: Sketch the curve of intersection of the surfaces. The paraboloids z = x² + y² and z = 25 – x – y².…

A: Given that: z=x2+y2      ......(1)z=25-x2-y2      ......(2)

Q: Find the equation of spheres passing through the circle x+y+z'-6x-2z+5 =0, y = 0 and touching the…

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Q: the trace of the surface in the plane x=1?

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Q: classify the quadric surface given by equation and determine its standard form.−8x 2 − 8y2 + 10z2 +…

A: We have the quadratic surface : -8x2-8y2+10z2+32xy-4xz-4yz-24=0…

Q: Evaluate the surface z =1,0<x,y <1.

A: To solve this we will use divergence theorem.

Q: Find the area of the surface. The part of the surface z = 1 + 2x + 2y2 that lies above the triangle…

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Q: Consider the equation of the surface S given by: exyz + x3z3 − 3y4 = 9 An equation for the plane…

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Q: Find an equation in cylindrical coordinates for the surface represented by the rectangular equation.…

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Q: Find

A: We find surface area of given region.

Q: Find the surface area of the ellipse that lies on the plane z=11-3x+2y and inside the cylinder…

A: The plane z=11-3x+2y and cylinder is x2+y2=9. Obtain the partial derivatives of z=11-3x+2y:…

Q: Consider the surface x² - y² + z² = −4. A. Identify the name of the surface. B. The line…

A: We know general form of hyperboloid of two sheets is  -x2a2-y2b2+z2c2=1 where positive term is the…

Q: Find the points on the surfacex – yz = 36 that are closest to the origin. Enter your answers in…

A: Given : x² - yz = 36

Q: Classify the quadric surface. −49x2 + y2 + z2 = 49

A: Given query is to find the shape of the surface.

Q: Find an equation in cylindrical coordinates for the surface represented by the rectangular equation…

A: we have to find an equation in cylindrical coordinates for the surface represented by the…

Q: classify the quadric surface given by equation and determine its standard form.−x 2 − y2 − z2 + 4x y…

A: Given quadric Surface is         -x2-y2-z2+4xy +4xz+4yz =3 Comparing it to the general form,…

Q: Classify and Sketch the surface X2+ Zy² + Z? -4x+4y-2z+3:0

A: The given equation of the surface is x2 + 2y2 + z2 - 4x + 4y - 2z + 3 = 0.The general equation,…

Q: Find parametrizations The portion of the paraboloid y = 2(x2 + z2 ), y&lt;=2, that lies above the…

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Q: Find an equation of the surface of revolution by revolving the plane curve 3y = v(9- [(x-1)] ^2)…

A: Solution

Q: Find an equation in cylindrical coordinates for the surface represented by the rectangular equation…

A: Consider the following equation: x2+y2-2z2=5                                             ...... 1…

Q: Identify and sketch the section of the surface at z = 0. v2 = 1 25 4 16 Type of the surface: too 4 4…

A: Solve the given

Q: Find the equation of the tangent plane to the given surface at the point (0,-1,2). y = 2x2 – 2 - O y…

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Q: Parametrize the intersection of the surfaces using t = z as the parameter. (If there are multiple…

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Domain

In simple mathematics terms, a domain is defined as the space on which all the possible inputs for the function will lie. It can also be expressed as a set of departures for the required function.