Find the area of the surface. The part of the surface 2y + 4z - x2 = 5 that lies above the triangle with vertices (0, 0), (2, 0), and (2, 4)

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

A: Given

Q: Sketch the surface.......... ASSORTED ............... 4y2 + z2 - 4x2 = 4

A: Given :             The given function is 4y2 + z2 - 4x2 = 4 And can be written as,…

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: Identify and sketch the surfaces 4x2 + 4y2 + z2 = 4

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

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

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

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Q: Find the points on the surface x² −yz = 5 that are closest to the origin.

A: Let the point P be (x,y,z). The distance between the point P and origin is given by the formula…

Q: 4d. z =-x´ + y´ Name of the surface

A: The structure obtained from the given equation is more like of dome structure

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: 5. Plot the surface of 6x2 – 2.r – y?z2 = 0, for -10 <r, y, z < 10 %3D | |

A: To plot the given surface.

Q: Classify and sketch the surface 4x2 − 3y2 + 12z2 + 12 = 0.

A: Solution:Given surface4x2 - 3y2 + 12z2 + 12 = 0    — 1divide equation 1 with -12,⇒ x2-3 + y2u - z2 -…

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

A: In the question we have to find the value of area enclosed by the function of given figures.

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

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Q: 5. Find the surface area of the portion of the surface z = 2x + y? that is above the triangular…

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Q: Classify the surface: 1 – x = 3y + 4z?

A: Given :  The surface 1 - x = 3y2 + 4z2.   To classify the given surface.

Q: 3. Find the area of the part of the surface x 2z + y° - 3, that lies above the triangle in the…

A: Given, x=2z+y2-3, i.e. z=12x-y2+3. As it is known that the surface area is given as,…

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 part of the surface z = x² + 2y that lies above the triangle with vertices…

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

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Q: Find the surface area of the portion of the sphere x2 + y2 + z2 = 25 inside the cylinder x2 + y2 =…

A: Recall:  The formula of surface area is S=∫∫S1+∂z∂x2+∂z∂y2 dA

Q: Find the area of the surface. The part of the cylinder y2 + z2 = 9that lies above the rectangle…

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Q: Find the area of the surface. The surface in the first octant cut from the cylinder y = (2/3)z^(3/2)…

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

A: To identify the surface, set each variable to some constant and find what type of surface produces…

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

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Q: Find the area of the surface. The part of the paraboloid z = x² + y2 that lies inside the cylinder…

A: Area of the surface f(x ,y) above a region R of the xy-plane is given by…

Q: The figure shows the surface created when the cylinder y2 + z2 =1 intersects the cylinder x2 + z2 =…

A: It is given that, the cylinder y2 + z2 =1............... (1) intersects the cylinder x2 + z2 = 1…

Q: Explain why C lies on the surface of the cylinder x² + y² = 1.

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Q: The portion of the surface z = 2x + y2 that is above the triangular region with vertices (0, 0), (0,…

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Q: Find the area of the surface. The part of the surface z = 1 + 2x + 2y2 that lies above the triangle…

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

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Q: Find the area of the surface x2 - 2y - 2z = 0 that lies above the triangle bounded by the lines x =…

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Q: Find the area of the surface. The part of the plane z = 7 + 5x + 2y that lies above the rectangle…

A: The given equation is, z=7+5x+2y The partial derivatives are, fx=5fy=2

Q: Plot the surface of 6a2- 2x4- y?z2 = 0, for -10 <x, y, z < 10

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Q: Describe and sketch the surface 16x2 + 16y2 − 9z2 = 0

A: Given surface 16x2+16y2-9z2=0

Q: Sketch the section of the surface at y = 0. 4 2 -2 -6 -4 -6 -4 4 6. -61

A:

Q: The part of the surface z =1  + 3x+ 2y 2 that lies above the triangle with vertices (0, 0), (0, 1)…

A: Part of the surface: z=1+3x+2y2∂z∂x=3, ∂z∂y=4yVertices of the triangles are (0,0) , (0,1) , (2,1)

Q: Find the area of the surface. The portion of the paraboloid z = 16 - x - y in the first octant

A: The given surface is the portion of the paraboloid z=16-x2-y2 in the first octant. The surface area…

Q: Find the area of the surface. 12. The part of the sphere x2 + y2 + z2 = 4z that lies inside the…

A: Solution:GivenSphere:   x2+y2+z2=4zParaboloid: z=x2+y2To find the area of the…

Q: Sketch the surfaces 1. z = y2 - 1 2. 4x2 + y2 = 36

A: Using graphing calculator to sketch themz=y^2-1

Q: Q1/ Use traces to sketch and identify the surface z2 - 4x2 - y² = 4

A: Let's find.

Q: Find the area of the surface. The part of the plane z = 8 + 5x + 2y that lies above the rectangle…

A: Area of the surface z=f(x,y) A(s)=∬1+fx2+fy2f(x,y)=8+5x+2yfx=5fy=2

Q: The part of the surface z-1+ 3x + 2y that lies above the triangle with vertices (0, 0), (0, 1). and…

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

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Q: Sketch the surfaces ASSORTED x2 + y2 = z

A: we have to sketch the surface x2 + y2 = z.

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

A: Given equation is y2+z2=16