The surface of equation + + = = 1 is: 16 A cone An ellipsoid A circular cylinder OA sphere

Q: Find the area of the surface formed by revolving the portion in the first quadrant of the graph of…

A: Rearrange the given equation to find y in terms of x and thus f(x). Plot the curve and find the…

Q: Find the area of the surface pf revolution geneeated by revolvinh about y= -2 the arc of the…

A: Given, So, x=y212=gy ⇒g'y=y6 limit of y is from 0 to 6 The formula for finding the area is,…

Q: Find an equation for the surface of revolution formed by revolving the curve in the indicated…

A: Given equation of curve is z = ln x The radius function about z axes is  r(z) = x = ez

Q: 8.2

A: We know that,

Q: Find the surface are generated when y= (x^3)/5 is revolved about the x axis on the interval…

A: Explanation of the solution is given below...

Q: Find an equation for the surface consisting of all points P for which the distance from P to the…

A: Let, P(x, y, z) be the point on required surface.

Q: Find the area of the segment of a sphere formed by revolving the graph of       y = √(r2 − x2) , 0 ≤…

A:

Q: Match the equation with the surface it defines:

A: given equation is x24+y24=z249

Q: Find the equation of the xy-trace of the sphere. (x – 2)? + (y + 4)² + (z – 6)? = 72 Sketch the…

A:

Q: What is the shape of the horizontal cross section of this solid figure? O triangle O trapezoid O…

A: Topic:- cross section of a cone

Q: Which quadric surface is represented by the equation below? 22 = 1 16 y? 4 Ellipsoid Cone Elliptic…

A:

Q: Find the surface area of the portion of the sphere generated by revolving the curve y = 1- x², 0sis…

A: y=1-x2,  0≤x≤12 Differentiating with respect to x, we get dydx=121-x2·0-2x=-x1-x2

Q: 21 y2 a. x + 1 %3D

A: The given equation is x21+y29+z24=1We know the general equation of ellipsoid is x2a2+y2b2+z2c2=1So…

Q: Identify the surface 2x² + 4y? – 1=0. A. An elliptic cylinder. B.Ahyperbolic cylinder. OC. None of…

A: We will solve the problem

Q: b. z= 4x2 + 4y²

A: The equation describes surface of elliptic paroboloid.

Q: Identify the type of surface represented by the given equation. x= - 72?, no limit on y O Cylinder O…

A: Consider the given equation, x=-7z2 This equation is of the form of parabola on the xz-axis and y…

Q: Find the center and the radius of the sphere. 2 + y2 + z2 + 4x + 5z = 0

A:

Q: cribe the surface with equation 2 +y +? + 8x + 6y + 2z - 10 = 0 surface is a sphere with center ( i…

A:

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: Write the equation for the surface generated by revolving the curve x2 - 2y2 = 1 about the y-axis.…

A:

Q: 91 a) Find an equation of the sphere with center (1,-3,-5) and tangent to xz-plane.

A:

Q: Find an equation of the sphere with center (-5, 4, 6) and radius 8. (x + 5)² + (y – 4)² + (z – 6)? =…

A:

Q: (a) What does the equation y = x represent as a curve in R?? O ellipse O cirde O hyperbola O…

A: We want to find true options.

Q: Identify the surface in the xyz coordinate system given by the equation: z=-√(4-y^2) O cylinder O…

A: Let's find.

Q: Determine the projection of the surface - y² = z on the xy-plane? (H - Ellipse Нуperbola Two…

A: To determine the projection, z = 0 x2/3 -y2 = 0

Q: Identify the type of surface represented by the given equation. x? ? z? 10 =D1 7 O Elliptical cone O…

A: Given query is to find the surface represented by given equation.

Q: What is the definition of a parabolic cylinder?

A: The parabolic cylinder functions are the solutions to the differential equation d2ydx2 + ax2 + bx +…

Q: Find the area of the surface obtained by rotating the parabola 1 0 <x < 2, about the y-axis.

A:

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: 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: Classify and sketch the surface 12x? – 3y? + 4z? = 12 What are the 3 traces? Show equations of the…

A: A quadratic surface is a hypersurface. It is nothing but the generalization of a conic section in…

Q: x + y? – 4y + 2² = 0

A: Consider the provided question, Given equation of the surface, x+y2-4y+z2=0

Q: What sort of surface is represented by the equation r = 2? Circle ) Hyperbolic Paraboloid Cone O…

A: which surface we can represent by radius that sort of surface :

Q: = V16 – x², -2<x<3, is rotated about the x-axis. Find the area of the resulting surface.

A:

Q: Sketch the surface in R' of the equation presented. 4x² + y? = 36 Interactive 3D Graph - 10…

A: The given equation is, 4x2+y2=36x29+y236=1x232+y262=1⋯⋯1 In 2D, equation (1) is a equation of a…

Q: ) Classify the equations below as one of the following types of surfaces: A. parabolic cylinder, B.…

A:

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

A:

Q: Find the surface area of the cone frustum generated by revolving the line segment y = (x/2) + (1/2),…

A: The surface area formula using integration is given by: In the question, we are given: Also x lies…

Q: Find the radius of the sphere x^2+4x+y^2 -2y+z^2-7=0

A:

Q: Consider the equation below. 16x2 + y? + 16z2 - 8y – 160z + 400 = 0 Reduce the equation to one of…

A:

Q: A group of engineers is building a parabolic satellite dish whose shape will be formed by rotating…

A:

Q: Describe and sketch the surface y2 + z = 6

A: Graph: Given surface y2+z=6 Since one co-ordinate has power 2 and other co-ordinate has power 1. So…

Q: point on the ellipsoid x2 + 2y2 + z2 = 19 wher x = 2 - 8t, y = 5 + 4t, and z = 4 - 2t. =) =(| )…

A: The equation of ellipsoid is x2+2y2+z2=19  ............. (1) and the equation of the line x=2-8t,…

Q: Find an equation which describes the surface created by rotating (1, V1,0) around the r-axis. Note…

A: Definition:   If the curve y=f(x),  a ≤ x ≤ b  is rotated about the x−axis, then the surface area is…

Q: You are given a y=sqrt(36-x^2), -3≤x≤3, curve that rotates about the x-axis. What is the area of the…

A: Given curve is y=36−x2, −3≤x≤3 and curve rotates about the x-axis. We have to find the area of the…

Q: Find the center and the radius of the sphere. x^2+y^2+z^2-6x+3z=0

A:

Q: Find the sphere’s center and radius. x2 + y2 + z2 + 10z = 0

A:

Q: Find equetion of Hhe parabole farmm an I with focus zt (3,0) and divectrix x=-3

A: Focus =  F= (3,0)  Directrix - x =-3  i.e. x+3=0

Q: Classify the quadric surface. 4x? - y2 - z2 = 1 O hyperboloid of one sheet O hyperbolic paraboloid O…

A:

Q: Identify the type of surface represented by the given equation. x? y? ? O Hyperboloid of two sheets…

A:

Estimation

A new framework of data analysis where the new statistical methods are used for interpreting the results and analyzing the data is known as estimation in statistics.