How can I parametrize this 3D shape with two variables? x ≥ 0, 0 ≤ y ≤ x, x^2 + y^2 ≤ z ≤ 8−3x^2−3y^2

Q: find a parametrization of the curve. The line passing through (1, 0, 4) and (4, 1, 2)

A: Given: A line is passing through the points 1, 0, 4 and 4, 1, 2.

Q: Obtain the DE based on given conditions solve for item 1 only.

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Q: Find a parametrization for the cylinder x^2 + y^2 = 4.

A: Given: x2+y2=4

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

A: To find:

Q: Find the area of the surface obtained by rotating the curve of parametric equations x = 10 cos³ 10…

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Q: A suspension bridge with weight uniformly distributed along its length has twin towers that extend…

A: A suspension bridge with weight uniformly distributed along its length has twin towers that extend…

Q: Find the critical points of the parametric equations x = 5 – Int y = t+ Int

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Q: Show that the cylindrical equationr 2(1 − 2 sin2 θ ) + z 2= 1is a hyperboloid of one sheet.

A: The cylindrical co-ordinates is converted into rectangular co-ordinate as x=rcosθ         ⋯⋯1y=rsinθ…

Q: A container with a height of 3/2 is made by rotating the curve y = 3/2x^2, Osx<1, about the axis x =…

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Q: Solve 3x – 6 ≥ 0 graphically intwo dimensional plane.

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Q: find a parametrization for the curve. the ray (half line) with initial point (-1, 2) that passes…

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Q: Express x2y2+ z2 = 2z in cylindrical and spherical coordinates.

A: Given,

Q: A suspension bridge with weight uniformly distributed along its length has twin towers that extend…

A: Given information: The cables touch the road surface at the center of the bridge, Then image a graph…

Q: Find parametric equations for the tangent line to the curve of intersection of the paraboloid   z =…

A: The given curve is the intersection of paraboloid z = x2+y2 and ellipsoid 3x2+2y2+6z2 = 29.

Q: find the centroid of the solid formed by revolving about the x-axis the solid formed by the curve…

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Q: Find a parametrization of the curve. The vertical line passing through the point (3, 2, 0)

A: Consider the given point  3 , 2 , 0

Q: A suspension bridge with weight uniformly distributed along its length has twin towers that extend…

A: The general equation for a parabola is given as, y=kx2 Let the x-axis represents the road surface…

Q: Find a parametrization for the sphere of radius 2.

A: Consider the equation of the sphere x2+y2+z2=22. Here the sphere is centered at origin.

Q: Find the points on the hyperbolic cylinder x2 - z2 -1 = 0 that are closest to the origin. please…

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Q: Find an arc-length parametrization of the line passing through (1, 0, 1) and (1, 2, 3). Upload an…

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Q: Find a parametrization of the circle of radius 5 parallel to the yz-plane with center (-1, 4, 6).

A: The general form of a parametrization of the circle of radius r parallel to yz-plane with center…

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: Differentiate, and make sure to show all your work: y = exin(2z) %3D

A: The given question is taken from the derivative of the function in which we have to find the…

Q: 3. Calculate the centroid of the given illustration below. y-axis 7.5ft- 4ft 2ft 5ft- х-ахis 2ft

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Q: A point moves along the intersection of the elliptic paraboloid z = 3x² + 5y² and the plane y = 4.…

A: We are given the curve Z=3x2+5y2 and y=4   Now we know that the rate of change is simply derivative…

Q: find a parametrization for the curve. the ray (half line) with initial point (2, 3) that passes…

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Q: Find a parametrization of the circle of radius 6 in the XY-plane, centered at the origin, oriented…

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Q: 9. Determine the position of the centroid of a sheet of metal formed by the curve y = 4x - x² which…

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Q: Find parametric equations of the line through the point (5, 0,−2) that is parallel to the planes x…

A: Any point in three dimensional coordinate system will be of the form x1,y1,z1 . We can calculate the…

Q: Find using spherical coordinates integration zz2 + x2 + y²dzdydx V4-x

A: The conversion formulas for spherical coordinates are…

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

A: Surface area in yz-plane

Q: A point moves along the intersection of the elliptic paraboloid z = 10x? + 3y² and the plane y = 1.…

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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: A thin plate has mass 3. What is the x-moment of the plate if its center of mass has coordinates (2,…

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Q: Find parametric equations for the line pass- ng through the point P(1, –1, 3) and perpen- licular to…

A: Given that: Line is passing through P(1,-1,3) and perpendicular to the plane:       4x+3y-2z=6.

Q: Find the points on the hyperbolic cylinder x2 - z2 -1 =0 that are closest to the origin. please…

A: The parametric equation of hyperbolic cylinderx2-z2-1=0 is , x=cos hθ                          y=y…

Q: Parametrize the circle of radius 7 centered at (-2, 3) in the clockwise direction starting at…

A: Here I am attaching image so that you understand each and every step.

Q: A point moves along the intersection of the elliptic paraboloid z = 9x + 4y and the plane y = 4. At…

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Q: The plane tangent to the surface z +1= re" cos z at (1,0,0) can be represented by the equation X + y…

A: Given: z+1=xey cosz

Q: Find the equation of the sphere of radius 7 centered at (3, 5, 3). O (x – 3) + (y– 5 + (z - 31 = 7 O…

A: Let's find.

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: What does parseval's identity imply about relationship between the dot products x · y and [x]ẞ·…

A: Concept: A branch of mathematics which deals with symbols and the rules for manipulating those…

Q: 5. Find the moment of inertia of a plate covering the first-quad rant region bounded by y2- x, x-:…

A: Plot the given conditions for finding the boundary limits.

Q: What is a parametrization of a curve in the xy-plane? Does a function y = ƒ(x) always have a…

A: Parametrization of a curve in the xy-plane:Parametrization of a curve consists of both equation and…

Q: Find the parametrization for the curve  the lower half of the curve x+3=y^2

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Q: Find parametrization of the horizontal circle of radius 4 with center (5, -2, 6). r(t) = %3D

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Q: A suspension bridge with weight uniformily distributed along its length has twin towers that extend…

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Q: Find the moment of inertia of the solid formec y2 = 2x and th

A: Introduction: If a solid is formed by revolving an area about the y-axis, then the moment of inertia…