For each equation of a surface given in cylindrical coordinates, sketch the surface and describe it in words. (a) r=7 (b) 0 = ; 2 (c) z = 2

Q: Find parametric equations and a parameter interval for the motion of a particle in the xy-plane that…

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Q: 1. Identify the quadric surface 2. Write the equation of the traces of the quadric surface on the…

A: The equation is of form  y2-z23-x212=1  This gives a quadric surface called Hyperboloid of two…

Q: 7. The parametric equation of an ellipse is given by x = a cost, y=bsint; 0<t<2n. Determine the area…

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Q: Consider the curve C on the yz-plane with equation y?– z + 2 = 0 (a) Sketch a portion of the right…

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Q: Write an equation in general form of the tangent plane to the parametric surface at the stated…

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Q: Match the equation with the surface it defines:

A: given equation is x24+y24=z249

Q: (a) Find a spherical coordinate equations; for the sphere X²+y²+(z-1)²=1 and the surface…

A: (a)

Q: Find parametric equations for the surface generated by revolving the curve y = 1/x about the x-axis.

A: When y = f(x) is rotated about x axis, we get a surface with parametric representation is,…

Q: Let B be the surface with equation x = -1+ /y. (a) Provide a hand-drawn sketch of B. Label the…

A: We are given that B as the surface with equation x=-1+y2. For (a), Let us sketch the surface B. It…

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: Describe the surface with cylindrical equation r=6. Hint The 8 and 2 components of points on the…

A: We have to find the surface whose cylindrical equation is given by : r=6

Q: A parametric equation of the line of the intersection of the planes x - z = 0 and x – y + 2z = 0 is

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Q: Find a parametric form for the line through the point (8, –6, –3) and perpendicular to the plane 2x…

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Q: Let B be the surface with equation x =-1+ /÷y. 24 (a) Provide a hand-drawn sketch of B. Label the…

A: As per the question we are given a 2d equation as : x = -1 + √(y/2) And we have to first draw its…

Q: Sketch and identify the surface given by the equation Z=: x² +

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

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Q: Find a set of parametric equations for the curve of intersection of the cylinder (x - 1)2 + y2/4 = 1…

A: Given: The equation of cylinder is: x-12+y24=1 .....(1) The equation of paraboloid is: x2+y-22=z…

Q: escribe and sketch the surface in R*represented by the equation x + y = 2.

A: Given that - Describe and sketch the surface in R³ represented by the equation x + y = 2.

Q: The equation of a surface in spherical coordinates is ϕ = π/4. Find the equation of the surface in…

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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: 1. Find an equation for the set of points whose distance from the plane z =8 is twice the distance…

A: SOLUTION-

Q: Sketch the surface represented by the parametric equations x = cos³ t and y=sin³ t with 0st≤n/2.…

A: Given: x=cos3t and, y=sin3t we have to find the surface area by rotating about x-axix. Suppose the…

Q: Find an equation of the surface of revolution generated by revolving the plane curve about the…

A: Given:    Surface y2=z3 : about the z-axis. Find:- (a)Draw the graph of surface (b)an equation of…

Q: Find parametric equations and a parameter interval for the motion of a particle that starts at (a,…

A: (a)

Q: In each part, find an equation of the sphere with center (1, – 7, –8) and satisfying the given…

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Q: Consider the equation of the surface. 1 f (x, y) = x² + y² + 1 Identify the graph of the surface…

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

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Q: Find an equation of the surface of revolution generated by revolving the plane curve about the…

A: Given equation: x2=4y    which has to be revolved about the y-axis.

Q: Find the point at which the line given by the parametric equations below intersects the plane.…

A: Given a system of linear equations are, 2X + 4Y -3Z =-48.................(1) X = 10 +…

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Q: Consider the equation surface S in the 3D space given by the equation z = x³ – 1. Let C be the curve…

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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 an equation of the surface of revolution generated by revolving the plane curve about the…

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Q: Find an equation of the surface of revolution generated by revolving the plane curve about the…

A: It is required to find the equation of the revolution generated by revolving the given plane about…

Q: Find the first fundamental form of surface of revolution?

A: Suppose M is a surface determine by , Xu , v ⊂ E3. Suppose αt is curve on M , where t ∈ a , b. Here…

Q: Find parametric equations and a parameter interval for the motionof a particle that starts at (a, 0)…

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Q: Find the parametric equation of the intersection of the planes x + y = 1 and x + z = 2.

A: Equation of plane 1 - x+y = 1        Normal vector of plane 1 = n1 = 1,1,0…

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

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Q: Find parametric equations for the line tangent to the curve of intersection of the surfaces at the…

A: Given, the surfaces:               x+y2+2z=4,   x=1  Point: (1, 1, 1) Let         z = 1-2t

Q: Find parametric equations and a parameter interval for the motionof a particle that starts at (a, 0)…

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Q: Consider the surface defined by the equation z2 = 2x² + 4x - 6y? - 2y+ 1. %3D Find a set of…

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Q: Consider a sphere E with center at the origin and radius equal to 1, following the Beltrami-Klein…

A: Determine the parametric equation by first determining the equation of the line and then…

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Q: Find the area of the surface obtained by rotating the curve of the following parametric equations…

A: We need to find surface area.

Q: Consider the following equation of a quadric surface. y? 2 2 X + 144 144 1 144 - a. Find the…

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Q: The equation of a surface in rectangular coordinates is given. Find the equation of the surface in…

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Q: Consider the curve C on the yz-plane with equation y? – z + 2 = 0 (a) Sketch a portion of the right…

A: Given that,  Curve C parabola on the yz-plane with equation y2-z+2=0                   1 Therefore,…

Q: Describe and sketch the surface y2 + z2 = 16

A: Given equation is y2+z2=16

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

A: Given equation of curve is z2 = 4y The radius of function about y axis is  z2 = 4yz = 4yz = 2yr(y) =…

Q: 3. Find an equation of the surface of revolution generated by revolving the given plane curve about…

A: Given, Curve,z=ex in the  xz-plane about the x-axis To find an equation of surface of revolution…