the voulme of the region are  bounded by the paraboloid x= y^2+z^2 and the half cone x= 8sqrt(y^2+z^2) is

Q: Find an equation of the line tangent to the intersection of the cylinders x² + z² = 4, y² + z² = 4…

A: The parametric form of the tangent line is  x=x0+aty=y0+btz=z0+ct where, (a,b,c) is the direction…

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

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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: Find normal line (parametric form) to the surface x^2 − 4y^2 + z^2 + y = 27 at the point (5, 1, −3

A: This question is about application of derivative

Q: Question 5. Use Green's theorem to compute the area trapped between the ellipse x2 + 4y? = 4 and the…

A: Given that the area is bounded between the ellipse x2+4y2=4 and the parabola x=22y2. The Green's…

Q: Find the average distance from the origin of a point between the two spheres x ^ 2 + y ^ 2 + z ^ 2 =…

A: We have to find average distance from origin of a point between the two given spheres.

Q: A surface has Cartesian equation :- f(xy). given by f(1.9)=6xy-5x -3y+ +7x-6y a) Use any…

A: To graph the function: z=f(x,y) where f(x,y)=6xy-5x2-3y4+7x-6y

Q: the normal line of the surface [z = (4x^2 + y^2] at the point (1,1,5) O 8x-2y+z=5 O 8x+2y+z=5…

A: We have to find the normal line of the surface.

Q: Graph  the elliptical cylinder in 3 dimensions

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Q: Draw the bifurcation diagram for x'=x^2-ax

A: Given that, x'=x^2-ax

Q: Let S be the passage of R ^ 2 defined by the parabola with equation y = 18-x ^ 2 and by the line…

A:

Q: normal is drawn to the hyperbola         x^2/a^2+y^2/b^2=1 meets the transverse axis at G. If…

A: A normal is drawn to the hyperbola meets the transverse axis at G. If perpendicular from G on the…

Q: Find a point on the surface z = 3x^2 − y^2 at which the tangent plane to this surface is parallel to…

A: We need to find the Point on the surface of  z=3x2−y2 given tangent plane to this surface is…

Q: Draw a contour map for f(x,y) = x^2 + 4y^2 where k = 3, k=8 and k=14

A: A scalar function f(x,y) is a rule that is used to associate a number, or quantity with a particular…

Q: Find the maximum and minimum values of x^2 + y^2 − 2x − 2y on the disk of radius √ 8 centered at the…

A: Given function is  fx,y=x2+y2-2x-2y where bounded region is  x2+y2≤8.

Q: Which is the equation of a sphere with a center at (1,0,-2) with a volume of 36(pi)(u^3)? a.…

A: We first defined the equation of sphere and centre,volume . Using this formula we have equation (a)…

Q: What is the center of gravity of the region bounded by the graphs of equations y = x2 -2x+1, y =…

A:

Q: Given a parabola with equation y = ax^2 where a is a constant, determine the value of a for which…

A:

Q: Find the extreme values of the function f(x, y, z) = xy + z^2 on the circle in which the plane y - x…

A: Given function is fx,y,z=xy+z2. We have to find the extreme values of the given function on the…

Q: How many cells are there in the arrangement of hyperplanes in R^d with equations xi + xj = 0 and x…

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Q: Find the parametrization of the curve defined by the intersection of the two surfaces y = x^2 − 3z^2…

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Q: Find a parameterization for a circle of radius 4 with center (-4,4,-6) in a plane parallel to the yz…

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Q: Find the area of the surface generated when the curve: =y=+on [1,2] is rotated about the x-axis. 2 0…

A: As per our guideline, we are supposed to solve only first question. Kindly repost other question as…

Q: arametrize the monkey saddle z=x^3−3xy^2 by using u=x,v=y as the parameters.  plot the image

A: Given equation is, z=x3-3xy2 Take u=x,v=y Then the equation becomes, z=u3-3uv2 The counter map is,

Q: find the points of the surface x^2-y^2+z^2=1 which corresponds to the extreme value of…

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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…