The parametric representation of the surface y2 - 4y + z2 = 0,0

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: 11. Use Stokes' Theorem to evaluate OF dr where F=(xz,e",y+z) on the curve that is the intersection…

A: The equation of curl is F=xz,ey,y+z. The equation of plane is 6x+3y+z=12

Q: Express the surface z = 6 cos 0 sin o, y = 7 sin 0 sin ø, z = 2 cos ¢ as a level surface f(z, y, 2)…

A: Given x= 6 cos θ sinϕ  , y = sinθ sinϕ  , z= 2cosϕ

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: Evaluate the surface integral fs F. dS where F = (4x, -2z, 2y) and S is the part of the sphere x² +…

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Q: 1. Verify Stokes' Theorem for F = (2x - y)i - yz²j - y² zk, where S is the upper half surface of the…

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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: A parametric representation of the curve of intersection of the two surfaces x2 + 5y2 - z = 0 and z…

A: The given curves are: x2+5y2-z=0 &amp; z=4y2+36 ⇒x2+5y2-(36+4y2)=0⇒x2+y2-36=0⇒x2+y2=36

Q: Evaluate the surface integral I F. dS when F(x, y, 2) = y²i+ 3x² j and S is the graph of - ža (1+æ²…

A: Here, Fx,y,z=y2i+3x2jz=121+x2-y2

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: Verify Stokes's Theorem for F = z²î+ x²j + y²k and S is the surface z2 = x2 + y², y 2 0, and 0 <…

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Q: Jse Green's theorem to evaluate the ne integral (2tan x _cos 2y³) dx + (7⁰s y + 2x (πº where is the…

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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: 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: Calculate F. dS where F = (e" sin y, e² cos y, yz²) S is the surface of the box bounded by the…

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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: (6) Calculate the surface integral SSs F · ñdS where F = (ze", –3ze"V, xy) and S is the…

A: Given that,

Q: Consider the surface F(x, y, z) = x°z³ + sin(y+z5) – 7 = 0. Find the following partial derivatives…

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Q: (b) Verify Stokes' theorem on a region which is a portion of the sphere r2 +y² +2 16 which lies…

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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: Evaluate SſF-dš where F = yi +2x j +(z-8)k and S is the surface of the solid bounded by 4x + 2y +z =…

A: By using the divergence theorem we solve the above question

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

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

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Q: Please make sure its right. calc 3 Find a parametric representation for the part of the plane z = x…

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Q: Evaluate the unoriented line integral (2æ² + y² + z²) ds along the parametric curve a : [0, 1] → R³…

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Q: The parametric representation of the surface x² – 6x + z² = 0,0 < y < 2 %3D is a) (u, v) = (3 cos u…

A: The general form of the parametric equation of the surface in three-dimensional space is given by…

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: Find all points where the surface z = xy e-* + 2y-) has a horizontal tangent plane. %3D O A. O B.…

A: Given the surface

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: 4. Obtain the equation of the tangent plane to the surface with parametric representation r(u, v) =…

A: Note: We'll answer the first question since the exact one wasn't specified. Please submit a new…

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: Consider a surface defined by F(, y, z) = 0 whose gradient is (cos(Tx), z? e", 2ze"). The equation…

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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: Sketch the section of the surface at z = 0 on y = sinx in xy-plane on [0,2x]. y = sinx 1 3 4 5 1 1 2…

A: Let's find.

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 ,…

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Q: Evaluate the area of the surface generated by revolving the curve y = 2/a, from x = 0 to x = 3. y -…

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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: 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…

Q: Cvaluate AP G is a solid in the first octant bounded by the plane y+ z = 2 and the urface y = 1 -…

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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.