Identify the surface and find the traces 4x2 +9z2-36y%3D0 O A. None of these. O B. Paraboloid. 3. xy-trace: the lines y= ± xz-trace: the parabola x= 4y yz-trace: the parabola y = -9x %3D O C. Elliptic paraboloid. 3 y3 + xy-trace: the lines xz-trace: the parabola x2 = 4y %3D yz-trace: the parabola 2 = -9x O D. Elliptic paraboloid. xy-trace: the parabola x2 = 9y %3D xz-trace: the origin. yz-trace: the parabola z2 = 4y

Q: State the type of the quadratic surface: x^2−(y/8)^2+z^2=1 1. Hyperboloid of two sheets 2.…

A: The given question can be solved as shown in step 2.

Q: z =x' +y° +1 Y L x' +y? -z? = 1 LY

A:

Q: Identify and sketch the section of the surface at z = 0. y? 2 Type of the surface: hyperboloid of…

A:

Q: Find the area bounded by the parabola y² = 8x, the line y = x + 2, and the x-axis. A 3.33 square…

A: as per company guidelines we can solve only first question when multiple question being posted

Q: 8.2

A: We know that,

Q: 1. Given the quadric surface S2 : y = 4 – x² – 4z? 1.1 Find an equation of the trace of S2 on each…

A:

Q: 2. Given the quadratic surface S by the equation below, determine the type of surface. 2x? + 3y? +?…

A:

Q: Find the following: The traces of the surface x2 + y? + 22 = 6 in the planes parallel to the…

A:

Q: What is the equation of the surface revolved about the x-axis for z² - xz = ln x + 3x A. y² + z² =…

A: Given: The equation z2-xz=lnx+3x which is of surface and is quadratic for z.  To find: The equation…

Q: Q2/Examine the following surface for maximum, minimum, and saddle points 2 = x² + y² + xy + 4x - 4y…

A: We can use the second derivative test to find the maximum, minimum and saddle points.

Q: (a) If a > 0, find the area of the surface generated by rotating the loop of the curve 3ay = x(a –…

A: The graph of the function 3ay2=x(a-x)2.

Q: The given curve is rotated about the y-axis. Find thearea of the resulting surface.   y = 1 -x2…

A:

Q: Given the surface 9x^2 − 4z^2 = 9y. Find its traces on each coordinate plane and on the planes y=4,…

A: Solutions

Q: 10) The line x = -1+t,y = 2 +t,z 2t + 7 intersects the surface z = x2 + y?. Find the cosine of the…

A:

Q: draw and identify the graph of the following surfaces a. x² + y² = sin²z, z = [0, π]

A: Any surface in the 3D plane can be represented in the form of f(x,y,z)=0. A graphing utility can be…

Q: For the surface 4x² – y² + z² = 9, the trace y = 0 is : O Ellipse O Elliptic cone O Hyperbola O…

A: Topic = Geometry The trace is Ellipse.

Q: State the type of the quadratic surface: æ² + () + 2? = 1 1. Hyperboloid of two sheets 2.…

A: Solution ) given x2 + (y/8)2 + z2 = 1 We can write this equation  x2/12 + y2/82 + z2/12 = 1 the…

Q: A 2-D surface was found in one research group of scientists and a surface equation has been derived…

A:

Q: For the surface 4x² +2²-y²=9, classify the trace when z = 1. O line O hyperbola O ellipse O parabola

A:

Q: Identify the surface and find the traces gx2 + 4y-36z%3D0 | O A. Elliptic paraboloid. xy-trace:…

A: The given equation is: 9x2+4y2-36z=0⇒36z=9x2+4y2⇒z=x24+y29...(1) so, the given surface is an…

Q: Consider the following equation of a quadric surface. 2 x = 1-y -z a. Find the intercepts with the…

A: Given,  x=1-y^2-z^2

Q: State the type of the quadratic surface: x? - ()° + z? = 1 1. Hyperboloid of two sheets 2.…

A: Givenx2-(y4)2+z2=1Since both variables are squared and have opposite signs the conic is a hyperbola…

Q: 11. What is the equation of the surface revolved about the x-axis for 2² - xz = ln x + 3x? A. y²…

A: Introduction: When a surface is revolved around the coordinate axis, another surface is obtained. In…

Q: Name the surface and draw an accurate Graph of x² – y² – z² = 1 in R’.

A: Given: The surface x 2 - y 2 - z 2 = 1     To determine: The name of the given surface and the graph…

Q: Q2/ Examine the following surface for maximum, minimum, and saddle points 2 = x² + y² + xy + 4x - 4y…

A:

Q: Q3: Find the points on the surface x^2+z^2-25=0, closest to the origin.

A: Distance formula is d2=x2+y2+z2 .......(1) From the given equation z2=25-x2 ....... (2)

Q: 1. Find the closest point of the surface ry + xz + yz = 1 to the origin. %3D

A:

Q: 9a2 + 4y? + 36z? = 36 %3D

A: given surface 9x2+4y2+36z2=36 claim- to find the trace of given surface in planes x=k , y=k , z=k ,…

Q: Consider the surface in 3D described by the equation z = x² + y? – 16. (You might want to start by…

A: We are given that z=x2+y2-16 which is an Elliptical Paraboloid. We have to describe the trace in xy…

Q: (a) What does the equation x² + y´ = 1 represent as a curve in R? (b) What does it represent as a…

A:

Q: 2? = a? + 2y?

A: Consider the given surface z2=x2+2y2 The trace in the plane x=k are z2-2y2=k2 For k=0, z2-2y2=0⇒…

Q: Q3: Find the points on the surface x^2+z^2-2=0, closest to the origin.

A:

Q: 15) Consider the following equations of quadric surfaces: a) x=+-4 b) x? - y? + z? = 4 i) Identify…

A: 15) b) The given equation is: x2-y2+z2=4...(1)

Q: Evaluate [[. (y+210 – = )aS, where S is the surface cut from the paraboloid y² +4z = 36 by the…

A: Surface integral of a function f(x,y,z) on a surface S given by z=g(x,y) ∫∫Sf(x,y,z)dS = ∫∫Df(x,y,…

Q: 28.) What surface is the graph of (x-1) =y² +z? ? (a) A cone (b) A hyperbolic paraboloid (c) A…

A: The surface is a cone with vertex at (1,0,0).

Q: 32. Which of the following is the trace of the surface in the plane y=3? * O Hyperbola O Ellipse O…

A: Given, To evaluate trace of the surface in the plane at y=3

Q: The curve y= 7,0 <x <3; is rotated about the x-axis. Find the exact area of the 3 resulting surface.

A: Given: The curve is Interval is from 0  to 3  and it is rotated about x axis

Q: Given surface A: 4x² − 9y² = 9(z² + 4) 1. Identify the type of quadric surface for A. 2. Give an…

A:

Q: x2 Consider the surface T with equation 4 (y – 3)² + 22 = 1. - 3

A:

Q: Match the equation with the surface it defines. Also, identify each surface by type. 1. x = y? - z2;…

A:

Q: Sicatch the section of the surface at y-0. 2r +z = 6 AM -8-6-4 -2 -8-6 -4 -2 2 N 6

A: Here y=0 so graph is form in xz plane This is the equation of line in xz plane For x intercept we…

Q: Identify the surface defined by the following equation. -2²-8²+²/2+ + 8x-6y=29 25 Select the correct…

A: Concept: Two Sheet Hyperboloid or Elliptic Hyperboloid : Hyperbolas or ellipses are geometric…

Q: Consider the equation below. x2 - y2 + z2 - 4x - 2y – 2z + 4 = 0 Reduce the equation to one of the…

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Q: Name the surface and draw an accurate Graph of y = x² + z² in R'.

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Q: Find the area of the surface generated by removing about the x-axis the upper half of the ellipse…

A:

Q: Evaluated the counter integral 9,+z² - z-1 dz ,where C 1. The circle z| = 0.5 2. The circle |z+1-i=…

A: Given contour integral is  ∮Cezz3+z2-z-1dz We can write it as ∮Cez(z+1)2(z-1)dz Poles of…

Q: Find the equation of the integral surface of the PDE 2y(z- 3)p+(2x- z)q = y(2x – 3) which contains…

A: Here to finding the equation of integral surface to given partial differential equation we use the…

Q: Find the area of the surface generated by removing about the x-axis the upper half of the ellipse…

A:

Q: Use traces to help identify the surface y = 9x2+25z?. O a. Hyperbolic paraboloid b. Cone O c.…

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Q: Sketch the following, and identify the surface by name. Show all your work, including all traces. x2…

A: solution given below