32. 34. = 35. x-y- 36. 16x 16y- 162' 1 37. 25 38. 4x + 2y +- 4 39. z-x +y - 2x - 4y +4 (a) y-x - -1 In Exercises 33-40, sketch the quadric surface. 33. z-y +x -0 (b) y +x - ? 1 (x- 2)+ (y +1)* + 1. 40. 4

Q: Explain why the curve of intersection of the surfaces x + 3y? – 2z2 + 2y = 4 and 2x? + 6y? – 4z2 –…

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Q: Find the minimum distance from the point (5, 0, 0) to the paraboloid z = x2 + y2. (Give your answer…

A: Given:    z = x2 + y2  Point: ( 5, 0, 0 )

Q: Sketch the surface..........CYLINDERS.............x2 + 4z2 = 16

A: Here we have to draw the surface of cylinder having equation  x2+4z2=16

Q: 3. Identify and sketch the surface given by z = 16-y²; 0 ≤ y ≤ 2; 0≤x≤ 4. in 3-space, include ALL…

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Q: Sketch the surfaces 1. 9x2 + y2 + z2 = 9  2. 4x2 + 9y2 + 4z2 = 36

A: Using graphing calculator to graph them. 9x^2 + y^2 + z^2 = 9

Q: 7. Sketch the surface 15zs9-x' - y² and x'+y' <1

A: To find:

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

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Q: Identify and sketch the section of the surface at x = 0. 25x + 4y? – 16z = 0 %3D Type of the…

A: Question is solved.

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: Compute the surface area of the ellipse that lies on the plane z=11-3x+2y and inside the cylinder…

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

A: Given:  And can be written as,  Therefore, The obtained function is in the form of Hyperboloid…

Q: What is the total length of the curve of intersection of the surfaces x2 + y2 + z2 = 4 and y2 + 2z2…

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Q: Find the points on the surface xy2z3=2 that are closest to the origin.

A: Given, xy2z3=2We have to find the point on the given surface that are closest to origin.let the…

Q: Determine the maximum highest point (x, y,=) the surface on z = 1+ 4x + 4y- x* - y*

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Q: Sketch the surface: x + 2y + 3z = 12.

A: First find the intersection of plane with axis then draw the plane.

Q: Sketch the curve of intersection of the surfaces. The ellipsoid 2x + 2y² + z² 24 and the paraboloid…

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Q: Sketch the surfaces 1. x2 + y2 = 4  2. x2 + 4z2 = 16

A: The given surfaces are sketched using online 3D calculator.

Q: Find and classify all the critical points of the surface with its equation z = 32°y – y° + 3z – 3y²…

A: Given: z = 3x2y - y3 + 3x2 -3y2 + 2

Q: Find the area of the surface generated by revolving the curve y=x^3/18, 0(<=)x(<=) 2 square root 2,…

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Q: 5- Find the area of the surface generated by revolving the curve X= (y*/4) +1/ (8y²),1<y <2 ,about…

A: Given:function: x=y44+18y2Interval: 1≤y≤2To find : Area of surface generated by revolving the curve…

Q: Let 11 be the surface with the equation = 2√/y+1 and let 12 be the sphere with 2 equation x²+ y²¹+…

A: Solution :-

Q: 9ху. Use hyperbolic functions to parametrize the intersection of the surfaces x - y = 49 and z =

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

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Q: Find and classify all the critical points of the surface with its equation z = 3x"y + y* – 3x2 – 3y?…

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Q: Sketch the surface x = 2y2 +3z2

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Q: Find the points on the sphere at which the minimum and maximum distances between the sphere…

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Q: Find the center and the radius of the sphere that has the given x2 + y2 + z2 + 10x – 7y + 2z + 26 =…

A: Given a equation of the sphere , x2+y2+z2+10x-7y+2z+26=0 To fin the center and the radius of the…

Q: classify the quadric surface given by equation and determine its standard form.−8x 2 − 8y2 + 10z2 +…

A: We have the quadratic surface : -8x2-8y2+10z2+32xy-4xz-4yz-24=0…

Q: 2.5 What is the distance between two parallel hyperplanes {r E R" | a"x = b1} and {r E R" | a"x =…

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Q: Classify the quadric surface given by equation  and  determine its standard  form. x2 + y2 + 2z2 −…

A: The quadric surface given to us is: x2+y2+2z2-2xy+4xz+4yz=16 This is compared to the general form of…

Q: The equation of the tangent plane to the surface x² 8 at the point (2,-1, 3) is Select one: O x-2…

A: In this question, we want to find the equation of the tangent plane to the given surface.

Q: 3. Find the area of the surface cut from the nose of the paraboloid x = 1-y²-z² by the yz-plane. Do…

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Q: In Exercises 25–26, find the areas of the surfaces generated by revolv-ing the curves about the…

A: Given:

Q: 2.5 What is the distance between two parallel hyperplanes {x E R" | a"x = b} and {x E R" | a"x =…

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Q: 16. The solid within the spherex² + y² + z² = 9, outside the cone z = Vx2 + y², and above the…

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Q: Classify the quadric surface ² - y² - x² + 4x = 5. 2 य

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Q: Find the points on the surface y2 = 64 + xz that are closest to the origin. %3D (х, у, 2) 3 (smaller…

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Q: Þ(x, y, z) = e¬x²-y²-z²+2yz

A: We have to solve given problem:

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

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Q: What is the shortest distance from the surface xy+3x+z^2=12 to the origin?

A: Let (x ,y, z) any point on surface. We have to minimize function f(x,y,z) = x2 + y2 + z2 under…

Q: Suppose that the Celsius temperature at the point (x, y, z) on the sphere x2 + y2 + z2 = 1 is T =…

A: We have given; The temperature T at any point (x, y, z) in space isT = 400xyz2and the unit spherex2…

Q: Find the area of the cap cut from the top of the sphere x2 + y2 + z2 = 1 by the plane z = √2/2.

A: Given equation of sphere is    x2+y2+z2=1     And the equation of plane is  z=22=12 But we know that…

Q: area of the surface obtained by rotating the curve y=x^3, x ∈ [0

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Q: Classify the quadric surface. 9x2 + 3y2 − 6z2 = 54

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Q: 5) Consider the surfaces S1 : ryz = 10 and S2 : z =r² + y and the %3D point Po = (1,2,5).

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Q: Sketch the surfaces ASSORTED 16y2 + 9z2 = 4x2

A: Solution:- We have to  Sketch the surfaces ASSORTED 16y2 + 9z2 = 4x2

Q: 3) Which type of quadric surface listed in Table 2 below is 4x² + y² + 4z² – 4y – 24z + 36 = 0?

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Q: Find the point lying on the intersection of the plane  x + (.5)y + (.25)z = 0  and the sphere  x2…

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Q: Sketch the surfaces 1.z = 1 + y2 - x2  2. z =-(x2 + y2 ) 3. 4y2 + z2 - 4x2 = 4

A: Used graphing calculator to graph:z = 1 + y^2 - x^2 from two viewing angles