parametrization of the surface z = 3x² + 8x, ymbolic notation and fractions where needed.

Q: Describe and sketch the surface x + 2y + 3z = 6

A: Given

Q: Find the area of the surface. The portion of the plane z = 24 - 3x - 2y in the first octant

A: ⇒Given:-  Equation of plane                      z=24-3x-2y  in 1stoctant In intercept form,…

Q: Describe the surface whose equation is 2x2 + 2y? + 2z² – 3x – 5y + 7z – 2 = 0. NOTE: Enter the exact…

A:

Q: Find the points on the surfacex - yz = 9 that are closest to the origin. Enter your answers in order…

A: The given surface is: x2-yz=9⇒x2-yz-9=0   ............(1) We have to find the points on the given…

Q: Classify the quadric surface. z2 = x2 + y? %3D O ellipsoid O hyperboloid of one sheet O hyperboloid…

A: The solution are next step

Q: Find the area of the surface. The part of the hyperbolic paraboloid  z = y2 − x2  that lies between…

A:

Q: 10. у %3D /5 — х, 3 <x < 5

A:

Q: Describe the surface of 4z2 – 4x² – y = 4 - |

A: The general equation of a  hyperboloid on two sheets is given by x2a2-y2b2-z2c2=1 notice that there…

Q: Find the area of the surface. The part of the surface z = 9 + 5x + 2y2 that lies above the triangle…

A:

Q: Reduce the equation to one of the standard forms, classify the surface, and sketch it. Label at…

A: y2=16+x2+z2

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 exact area of the surface obtained by rotating the curve about the x-axis. y = sqrt*(1+5x)…

A:

Q: Find an equation which describes the surface created by rotating (r, x, 0) around the r-axis. Note…

A: Our Aim is to find an equation which describes the surface created byrotating (x,x,0) around the…

Q: Find the area of the surface.The part of the surface 2y + 4z − x2 = 5 that lies above the triangle…

A:

Q: Classify the quadric surface. 16x2-y2 + 16z2 = 4 %3D O hyperboloid of one sheet O hyperbolic…

A: Given quadric surface is 16x2-y2+16z2=4

Q: Find an equation of the surface of revolution obtained by revolving the plane curve 4x² – y² = 4…

A: The given equation of plane curve is 4x2-y2=4. Since the plane curve is rotated about x-axis,…

Q: Classify and sketch the surface x − y2 − 4z2 = 0.

A: The surface is given as x-y2-4z2=0. Rewrite the equation x-y2-4z2=0 as follows. x-y2-4z2=0x=y2+4z2…

Q: Find the area of the surface generated by revolving the curve y = / 2x - x , 0.75<x<1.75, about the…

A:

Q: Determine the area of the surface. The part of the surface z=1+3x+2y^2 lying on the triangle with…

A:

Q: 2. 4x2 – 25y² – z² = 100 -

A:

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

A:

Q: Identify the surface defined by x - y – 4x + z² +6= 0 O hyperboloid of two sheets O elliptic cone O…

A:

Q: Classify the quadric surface. x2-y2 + z = 0 O elliptic paraboloid O hyperbolic paraboloid O…

A: The objective is to classify the quadric surface.  The graph is given below.

Q: the solid cut from the first octant by the surface z = 81-x2-y

A:

Q: Describe the surface whose equation is 20+ 2y + 2z-3x-5y+ 7z – 2 = 0. NOTE: Enter the exact answers.…

A: Equation of the surface is : 2x2+2y2+2z2-3x-5y+7z-2=0 We need to Center and Radius of the given…

Q: The area of the surface obtained by rotating the curve y = v64-x2, -2 <x < 2 about the x-axis is

A:

Q: Classify the quadric surface. z2 = x2 + y2 9 O elliptic paraboloid O hyperboloid of two sheets O…

A: Classify the quadric surface.

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: Classify the quadric surface given by equation  and  determine its standard  form. x2 + y2 + 2z2 −…

A: The quadric surface given to us is: x2+y2+2z2-2xy+4xz+4yz=16 This is compared to the general form of…

Q: Find the area of the surface generated by revolving the curve about each given axis. x = 8t, y = 7t,…

A:

Q: Find the area of the surface. The part of the surface  2y + 4z − x2 = 5  that lies above the…

A: According to the given information, it is required to find the area of the surface.

Q: Classify the quadric surface. 4x2-y?- z2 = 1 O hyperboloid of one sheet O hyperbolic paraboloid O…

A: The objective is to classify the quadric surface.

Q: Find the area of the surface. The surface cut from the “nose” of the paraboloid x = 1 - y2 - z2 by…

A:

Q: Classify the surface: 1– x = 3y² + 4z² O Elliptic paraboloid O sphere O Ellipsoid O Plane O cone

A: In this question we have to classify the surface.

Q: Find an equation for the surface consisting of all points that are equidistant from the point (-4,…

A:

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: 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: Describe the surface whose equation is 2x² + 2y² + 2z² – x – 5y + 7z – 2 = 0. - NOTE: Enter the…

A:

Q: Classify the quadric surface. x2 z = y2 16 ellipsoid O elliptic cone elliptic paraboloid O…

A:

Q: Classify the quadric surface. 9x2 + 3y2 − 6z2 = 54

A:

Q: Find the points on the surface y = 9 + xz that are closest to the origin. (x, y, z) = (smaller…

A:

Q: Calculate the centroid coordinates of quarter circle (x² + y² = a*) in the quadrant, use Cartesian…

A:

Q: Find the area of the surface generated by revolving the curve y = /2x-x, 0.75sxs1.25, about the…

A: We know that area of surface generated by revolving the curve y=f(x) from x=a to x=b , about x-axis…

Q: Find the points on the surfacex - yz = 9 that are closest to the origin. Enter your answers in order…

A: Given:         x2-yz=9 Using Lagrange multipliers, The distance from any point to the origin is:…

Q: Classify the surface: 1- x = 3y2 + 422 O Ellipsoid O cone O Elliptic paraboloid O Plane sphere

A:

Q: Find the area of the surfaces The surface cut from the “nose” of the paraboloid x = 1 - y2 - z2 by…

A: The surface cut from the '' nose '' of the paraboloid x=1-y2-z2 by the yz plane .…

Q: Describe the surface whose equation is 2x2 + 2y? + 2z² – 9x – y + 3z – 2 = 0. - - NOTE: Enter the…

A: The given equation is 2x2+2y2+2z2-9x-y+3z-2=0

Q: Find the area of the surface. The part of the surface  2y + 4z − x2 = 5  that lies above the…

A:

Q: Find the area of the surface obtained by rotating the curve y2 = 4x + 4 0<x<8 about the x-axis? %3D

A: