The parametric representation of the surface x² – 6x + z² = 0,0 < y < 2 %3D is a) (u, v) = (3 cos u ,3 sin u, v), 0 < u < 2n,0 < v< 2. b) ř(u,v) = (3+3 cos u, v,3 + 3 sin u), 0

Q: Find the surface area for the portion of the surface f(x,y)=1-x² + y that lies above the triangular…

A: Solution :

Q: Find parametric equations for the line tangent to the curves of intersection of the surfaces xyz =1…

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Q: Explain briefly how Vø relates to surfaces of constant o(x, y, x). Hence, use Vø to find points in…

A: For the surface of constants ϕx,y,z=k, the gradient vector ∇ϕx0,y0,z0 is orthogonal to the level…

Q: How do you calculate the area of a parametrized surface in space? Of an implicitly defined surface…

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Q: Find parametric equations for the tangent line to the curve of intersection of the paraboloid z =x²…

A: Tangent line to ellipse will be perpendicular to normals of both the surfaces Therefore,  The…

Q: (a) Integrate g(x,y,z) = Inx+y over the surface of the region cut from the plane 4x+3y+2z=1 by the…

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Q: Find the circulation of F(x, y, z) = (-y sin 2, x sin z, xy cosz +12) around the circle cut from the…

A: Given that,F(x, y, z)=(-ysinz, xsinz, xycosz+12) around the circle cut from the sphere x2+y2+z2=5 by…

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: Write parametric equations for the tangent line to the curve of intersection of the surfaces x +y +z…

A: We know that the parametric equation of a tangent line to the curve of intersection of the two…

Q: Find parametric equations for the normal line to the surface z=e2x< + 9y< at the point (0,0, 1). O x…

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Q: 14) Find the points on the surface xy- z2 = 1 that are closed to the origin. %3D

A: To find the point on the below surface that is closed to the origin. xy−z2=1

Q: Consider the surface z = 2 – xy in R³. Use the second derivative test to find the points on this…

A: Given curve z = 2-xy To find :- Use the second derivative test to find the points on this surface…

Q: 4. Graph the surface 1 = y² + z² – by first sketching at least three cross sections in each of the…

A: Graph the surface by using a 3D graphing calculator like desmos. Three cross sections in xy plane…

Q: The parametric representation of the surface x² – 8x + z? = 0,0 < y < 5 is a) ř(u, v) = (4 cos u , 4…

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Q: Find a parametric representation for the part of the cylinder y2 + z² = 36 that lies between the…

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Q: Consider the surface S parameterized by r(u, v) = (u, 2 cos(v), 4 sin(v)),0 < u < 2,0 < v < 2n. 1.…

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Q: The equation of the tangent plane to the surface f (x,y,z)= xe" cosz- z-1= 0 at the point…

A: Given surface is xeycosz-z-1=0 and the point is A1,0,0 find the equation of tangent

Q: Integrate G(x, y, z) = x over the surface given by z = x2 + y for 0 ≤ x ≤ 1, -1 ≤ y ≤ 1.

A: The function is fx,y,z=x2+y-z=0         ......1 Gx,y,z=x…

Q: An equation of the tangent plane to the surface z = In(x - 2y) at (3, 1,0) is given by z = x + 2y- 1…

A: This question is related to three dimensions geometry.

Q: Consider the surface x2 + y2 − 2xy − x + 4y − z2 + 4 = 0 at the point Po (2, −2, 5). Determine the…

A: This is a multi-variable calculus.

Q: Verify Stokes's Theorem for F = z²î + x²j + y?k and S is the surface z² = x2 + y2, y 2 0, and 0 szs…

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Q: The parametric representation of the surface y2 - 4y + z2 = 0,0 < x < 3 is a) 7(u, v) = (v, 2 + 2…

A: solution:y2-4y+z2=0 , 0≤x≤3considery2-4y+z2=0∴y2-4y+4+z2=4∴y-22+z2=22

Q: Integrate G(x, y, z) = xyz over the surface of the rectangular solid cut from the first octant by…

A: Given: G(x,y,z)=xyz We have to integrate G(x,y,z) over the surface of the rectangular solidcut from…

Q: 4. The surface described by the equation x2 + y + z² = 0 is a(an) (a) elliptic paraboloid symmetric…

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Q: a) Integrate g(x,y,z) = Inx²+y over the surface of the region cut from the plane 4x+3y+2z=1 by the…

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Q: Find a parametrization of the curve. The intersection of the surfaces z = x^2 − y^2 and z = x^2 + xy…

A: Given : The surfaces z = x2 - y2 and z = x2 + xy - 1.   To find the parameterization of the curve.

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

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Q: = xyz exists over a surface S c ed by the plane x-0,y%3D0,z%3D0, z=y V dS over the curve surface.

A: Given:  V= xyz x2+y2=9 To find: ∫s V ds  For solving the convergence x2+y2=9 (mod 1s) we use Chinese…

Q: Integrate F =-(y sin z)i + (x sin z)j + (xy cos z)k around the circle cut from the sphere x2 + y2 +…

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Q: Calculate F - dS where F = (e" sin y, e" cos y, yz²) S is the surface of the box bounded by the…

A: Given F¯={exsiny,excosy,yz2)

Q: Find the surface area of the parametric surface F (и, v) — (2 сos(2и) + vcos(u), 2 sin(2u) +…

A: Here, we need to find the surface area of the parametric surface                               r→(u,…

Q: 3. Find a parameterization for the surface created by rotating the portion of y = x from x 1 to x =…

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Q: 3- Find the surface area of the solid obtained by rotating the curve z= 2/4- y; 0Sysabout the…

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Q: Verify stokes theorem for F = (2x- y)i – yz'j - y zk over %3D the upper half surface of the sphere…

A: Given the field, F¯=2x-yi¯-yz2j¯-y2zk¯ S is the upper half surface of the sphere x2+y2+z2=1 bounded…

Q: Sketch the section of the surface at z = 0 on y = sinx in xy-plane on [0,27). y = sinx 4 56 1 3. 6…

A: The given equation of the curve is: y=sinx To draw the given equation on the x-y plane we need to…

Q: S is the surface with parametric equations x = Зи+ v, у — Зи— v, z = uv for (u, v) in the region D…

A: The integral of a scalar valued function can be calculated as follows, using the parametrization:…

Q: 13) Parametrize the boundary curve of the surface given by r(r, 0) = (r cos 0, r sin 0, (4- r2)) for…

A: The parametric equation of the surface is given as follows: rr, θ=r cos θ, r sin θ, 4-r2, where…

Q: 1) Let h(x, y) = x* – 4xy² – 2x² + 8y². Find and classify all local extrema of the surface using the…

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Q: The equation of the tangent plane to the surface f (x,y,z) = xecosz - z - 1= 0 at the point…

A: The answer is as follows :

Q: - S is the surface with parametric equations x = 3u+v, y = 3u-v, z = uv for (u, v) in the region D…

A: We will find out the required value.

Q: A trace of the surface +- z = 0 on the xy- plane is: O Point at (3, 2, 0) O Circle Ellipse Point at…

A: I am going to solve the given problem by using some simple calculus to get the required result.

Q: The parametric representation of the surface y2 - 4y + z2 = 0,0 <x< 3 %3D is a) F(u, v) = (v, 2 + 2…

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Q: Which of the following sets of parametric equations is for the surface obtained by rotating the…

A: For a fixed value of z, that is surface cut by a plane z=k it is a Circle, of radius 1/(10+k^2).

Q: The parametric representation of the surface x2 -8x + z2 = 0,0 < y 5 5 %3D is a) (u, v) = (4 cos u ,…

A:

Q: (a) The part of the surface z = 1+ 3x + 2y² that lies above the triangle with vertices (0,0), (0,…

A: a) Given part of surface is  z=1+3x+2y2, which lies above the triangle with vertices (0, 0), (0, 1),…

Q: Find and sketch the domain and range of the surface f(x, y, z)= ln(16-4x^2-4y^2-z^2

A: Given: The function is fx,y,z=ln16−4x2−4y2−z2 To determine: We have to find and sketch the domain…

Q: 2)Use Stokes' Theorem to evaluate | F.dr where F =2xyi- yj+2xzk and S is the first octant surface of…

A: The given problem is to evaluate the line integral in the surface of first octant with upward…

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A: Given:- A line intersects the xy plane at an x intercept of N and a y intercept of F.  To find :-…

Q: 14. Find a point on the surface z = 3x- y at which the tangent plane is parallel to the plane 6x +…

A:

Contingency Table

A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear relationship between two variables. A contingency table is indeed a type of frequency distribution table that displays two variables at the same time.

Binomial Distribution

Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.