Q: Explain why the curve of intersection of the surfaces x2 + 3y2 − 2z2 + 2y = 4 and 2x2 + 6y2 − 4z2 −…
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Q: Find the area of the surface generated by revolving the curve y = sqrt(x + 1) , 1 <= x <= 5 about…
A: Given that the surface is generated by revolving the curve y=x+1 , 1 <= x <= 5 about the x -…
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: sketch the section of the surface
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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: Describe a surface of revolution in your own words.
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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. у %3D /5 — х, 3 <x < 5
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Q: Reduce the equation to one of the standard forms, classify the surface, and sketch it. Label at…
A: y2=16+x2+z2
Q: Determine the surface of revolution of arc y³+y=x²+6x on the interval [-5,-1] if it is revolved…
A: Use the formula of arc length to determine its length. Now use to it determine the volume generated…
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 exact area of the surface obtained by rotating the curve about the x-axis. 1 y = + /- 2x
A: Given: The equation of the curve y=x36+12x,where 12≤x≤1. Calculation: Compute the surface area as…
Q: You are given a y=sqrt(36-x^2) curve that rotates about the x-axis. What is the area of the…
A: To find the surface area of rotation of the below curve about the x-axis. y=36−x2
Q: Find an equation which describes the surface created by rotating (r, x, 0) around the r-axis. Note…
A: Our Aim is to find an equation which describes the surface created byrotating (x,x,0) around the…
Q: What is a trace of a surface?
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Q: Find an equation of the surface obtained by rotating the curve y = 1- sqrt(z) (square root of z)…
A: Given the equation of curve, y=1-z This can be written as z=1-y On squaring both sides, z=(1-y)2…
Q: Sketch the surface: x + 2y + 3z = 12.
A: First find the intersection of plane with axis then draw the plane.
Q: Find the area of the surface generated by revolving the curve about the indicated axis. 1) y = √4x -…
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Q: Find the exact area of the surface obtained by rotating the curve about the x-axis. y = √5 -x, 3 ≤ x…
A: We know that surface area obtained by rotating the curve y=f(x) about x axis between x=a & x=b…
Q: Find the area of the ellipse x^2+14 x y+245 y^2=4 by using a suitable transformation that maps to…
A: Given equation is, x2+14xy+245y2=4 The equation can be written as,…
Q: Find an equation of the surface of revolution obtained by revolving the plane curve 4x² – y² = 4…
A: The given equation of plane curve is 4x2-y2=4. Since the plane curve is rotated about x-axis,…
Q: Explain what it means for a surface to be orientable.
A: They are the surfaces for which we can define clockwise consistently. e.g. Cylinder and spheres are…
Q: ) I would need help wit
A: 22. Given, 4y2+z2-x-16y-4z+20=0
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 centroid of the triangular region cut from the first quadrant by the line x + y = 3.
A: We will find the x and y-intercept of the triangle. To find x-intercept we plug y=0 and find x…
Q: Find parametric equations for the line tangent to the curves of intersection of the surfaces xyz=1…
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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 the centroid of a thin, flat plate covering the region enclosed by the parabolas y = 2x2 and y…
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Q: Sketch the surface x = 2y2 +3z2
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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: Find the area of the surface. The surface cut from the “nose” of the paraboloid x = 1 - y2 - z2 by…
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Q: find an equation for the surface generated by revolving the curve about y-axis. y = 4x2, (z = 0)
A: I am going to solve the given problem by using some simple calculus to get the required result.
Q: Calculate the geodesic curve of the surface x^2 +y^2 -z=0
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Q: Find the exact area of surface obtained by rotating the curve about the x-axis. y=sqrt5-x 3< x <…
A: consider the equation
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: Identify a generating curve on the rz-plane for the surface of revolution with equation 1² + y² + zª…
A: The equation of the surface of revolution given is as follows:…
Q: Sketch the section of the surface at y 0. -6 -4 -2 6. -2 2 -6 -4 -6 -4 -2 -6 -4
A: The objective of the question is sketch the section of the surface at y=0.
Q: classify the quadric surface given by equation and determine its standard form.−x 2 − y2 − z2 + 4x y…
A: Given quadric Surface is -x2-y2-z2+4xy +4xz+4yz =3 Comparing it to the general form,…
Q: area of the surface obtained by rotating the curve y=x^3, x ∈ [0
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Q: What is the general process to fit random 3D points to a surface?
A: Hint: Here 3D points are given we need to plot them on a surface. Write the general process to plot…
Q: 9. y = x', 0< x< 2
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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: Find the exact area of the surface obtained by rotating the curve about the x-axis.
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Q: Sketch the section of the surface at x = 0. y - 252 = 25 -12- -8 12 -6 -4 -6 12 -4 -8 -12 6 4 4 -6-4…
A: topic - hyperbola y2-25z2= 25 is a hyperbola with vertex are (0,5,0) and (0,-5,0)
Q: Give an equation of the surface of revolution generated by revolving x In z about the z-axis.
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Q: Sketch the graph of -x + 9y² – 4z² = 36 and identify the surface. %3D
A: Given a function in terms of x, y and z. Here x and y are independent variables and z is a dependent…
Q: What is the surface generated by a straight line which moves along a fixed curve, and which remains…
A: To determine the name of the surface generated by a straight line which moves along a fixed curve,…
Sketch the surface with equation x^2 + y^2 + 2z^2 − 1 = 0.
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- Also need to know what surface it is?Find an equation of the surface of revolution obtained by revolving the plane curve 4x² – y² = 4 about the x-axis. Name the surface.What is the surface generated by a straight line which moves along a fixed curve, and which remains parallel to a fixed line not on the curve?
- Explain why the curve of intersection of the surfaces x2 + 3y2 − 2z2 + 2y = 4 and 2x2 + 6y2 − 4z2 − 3x = 2 lies in a planeFind the exact area of the surface obtained by rotating the curve about the x-axis. y = Square root (6-x), 4 ≤ x ≤ 6What is the general process to fit random 3D points to a surface?