Sketch the curve of intersection of the surfaces. The paraboloids z = x² + y² and z = 25 – x – y². %3D y

Q: Find the area of the surface. The part of the paraboloid x = y^2 + z^2 that lies inside the cylinder…

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Q: Identify and sketch the surfaces y = - (x2 + z2)

A: Given Data The equation of curve surface is y=-(x²+z²)   The sketch of the surface equation is,

Q: Sketch the surface..........CYLINDERS............. x2 + y2 = 4

A: x2+y2=4 Now, rewrite the above surface for the function as, z=fx,y. z=fx,y=4-x2-y2

Q: Calculate the surface area of the following: the cap cut from the sphere r² + y² + z² = 3 by the…

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Q: (b) Sketch the trace of the surface z = 2x? – y? when x = -1. Label your axes, and give the…

A: Given surface is  z=2x2-y2          (i) By putting x=-1 in (i), the surface becomes z=2-y2 The graph…

Q: What is the equation of the surface revolved about the x-axis for z? – xz = In x + 3x? A. y? + z? =…

A: Given that z2-xz=lnx+3x The objective is to write the equation of the surface revolved about x axis.…

Q: 10. The part of the paraboloid x = y² + z² that lies inside the cylinder y² + z² = 9

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Q: Find the exact area of the surface obtained by rotating the curve about the x-axis. x3 y = 2 1 6x' 2

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Q: Find the exact area of the surface obtained by rotating the curve about the x-axis. =x²+²x≤x≤1 3x 2…

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Q: Find the points on the surface y = 4 + xz that are closest to the origin. (х, у, 2) (smaller…

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Q: Describe and sketch the surface (x2/16) + (y2/9) + z2 = 1

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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 of surface which is z2-xz=lnx+3x. This equation is a quadratic equation for z.…

Q: Find the area of the portion of the paraboloid z=x^2+y^2 that lies inside the cylinder x^2+y^2=4.

A: Given that ,  paraboloid   z=x2+y2 cylinder        x2+y2=4

Q: Find the area of the surface cut from the paraboloid x² + y² -z = 0 by the plane z = 6. The surface…

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Q: Find the exact area of the surface obtained by rotating the curve about the x-axis. y = V8 - x, 25…

A: given, y=8-x  ,2≤x≤8  the graph is

Q: Evaluate yds where S is the surface = x + 2y?, 0 <a < 1, 0<y S 2

A: Consider the surface, z = x + 2y²

Q: Use traces to sketch and identify the following surface 25x² + 4y? + z² 100.

A: Given: The surface 25x2+4y2+z2=100.

Q: Find the exact area of the surface obtained by rotating the curve about the x-axis. y = V6 - x, 4 <…

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

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Q: ` What is the shortest distance from the surface xy + 9x + z² = 76 to the origin? distance =

A: z2+9x+xy=76z2=76-9x-xy   ---- Eq 1Let P(x,y,z) be a point on the given surface. We know that…

Q: Evaluate .(x+y² +=?) dS, where S is the portion of the paraboloid x=5+y² + z? contained within the…

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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: Sketch the section of the surface at y= 0. 4. + 9 36

A: Given the equation4x2+9z2=36

Q: Describe the shape of the surface: x? + y2 = 9. How would you describe the curve of the intersection…

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

A: “Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: Sketch the surface r = 2y? + 32².

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Q: Match the equation with the surface it defines. f(x, y) = -√√x²+12 X O O O stisk 3

A: Note that, according to Bartleby guidelines, we can answer only the first question in the case of…

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: Find an equation for the surface obtained by rotating the line z = 2x about the z-axis. + x²) b. z?…

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Q: Sketch the section of the surface at y=0. z = /2+x² + y?

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Q: Check whether the given surface (x – a)² + (y – b)² + (z – c)? 16 is developable or not. -

A: Given surface(x-a)2+(y-b)2+(z-c)2=16orz=c+16-(x-a)2-(y-b)2If the surface is developable…

Q: sketch the given surface. y 2+ z 2 = 1

A: To sketch: The surface y2+ z2 =1 Concept used: The general equation of the cylinder whose base…

Q: Write the equation x +z* - (y- 1) = 0 in cylindrical sy stem. W hich surface does it represent? Give…

A: Given :            The equation x2 + z2 - (y - 1)2 = 0   To write the given equation in…

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

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Q: What is the shortest distance from the surface xy + 6x + z² = 48 to the origin? distance =|

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Q: The solid S above the surfaces 22 = + y? and below r +y +(2 - 5)2 = 25. 2 + y² + (2 - 5) = 25

A: Solution is below.

Q: (a) Find the area of the surface generated by the given curve about x-axis y = Vx , 18 x< 4

A: Note: According to Bartleby guidelines; for more than one question asked only the first one is to be…

Q: Describe and sketch the surface y2 + z2 = 9

A: the given equation represents the cylinder where it forms the circle as the base on yz plane and is…

Q: Sketch the portion of the surface that lies in the first octant: y = z. 0.15 0.a 0.1 0. 0.15 0.18

A: To sketch the portion of the surface y=z that lies in the first octant. The sketch of y=z is:

Q: Find the area of the surface. The part of the sphere x2 + y2 + z2 = 4z that lies inside the…

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Q: (A) Find the surface area of the portion of the half ball with radius a which cuts off by the…

A: Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: 3. Find the area of the surface cut from the paraboloid x? + y +z = 2 by the plane y = 0.

A: Here we have to find the area of the surface cut from the paraboloid x2+y+z2=2 by the plane y=0.

Q: Find an equation for the surface generated by revolving the curve about the y-axis. y = 2x , (z = 0)…

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

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

A: Given equation is y2+z2=16

Q: Use traces to sketch and identify the following surface 25x2+4y2+z2=100

A: Ellipse is a closed curve around 2 focal points such that for every point on that curve, the sum of…

Q: Describe and sketch the surface y = z2

A: Solution: Consider the given surface y = z2 On the y z-plane, it represents a parabola that opens in…

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

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