Frned the poind al on 2x+y + 2' =4 n hreh bangend plana アaralle l lo tk plane x-2y +62 =5. is

Q: Use Cartesian coordinates to evaluate JIJ y² dv 2 D where D is the tetrahedron in the first octant…

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Q: HW Find the valume af theSelid beunded abave the Planc 2= x+2y+2,belw the X-y plane and Taterally…

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Q: Find ervstion for the tangen plare to the Surface an Siven by x2y?3 =12 at the point Z-2,1,3)

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Q: 1 in 1in y 1 in 3 in 1 in X

A: Consider the diagram and divide into four regions as shown below, Now, make a chart and evaluate…

Q: The plane y=2 intersects the elliptic paraboloid ē =4x ty parabobo. Fied the slope ot the fangenh to…

A: Given :     y = 2      z = 4x2 + y2

Q: Calculate fol(3z + 4y) ỉ + (5x + 2y) ) · dř where C is the circular path with center (a, b) and…

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Q: Find the moving tri hedral of f R CE) = t, 2E> at %3D

A: This is a problem of differential Geometry.

Q: Find the surface area of the part of the plane z = 5 + 7x + 2y that lies inside the cylinder x² + y?…

A: Part of the plane is z = 5 + 7x + 2y, so this is given in terms of f(x,y). If part of the plane is…

Q: Find the surface area of the part of the plane 4+ 2x + 3y that lies inside the cylinder x² + y? 9.

A: The area is given by using double integral

Q: Evaluate fs F dS, where F(r, y, z) = (2², xy, z) and S is the part of the paraboloid z = 22 + y?…

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Q: Compute x dS where S is the portion of the plane z=1+x+2y that lies over the square [0, 1] × [0, 1].…

A: We have to find the surface integral ∫sxds.

Q: Let d represent the distance from the center of the sphere 22 +y ++ 4x- 10y = 12 to the plane y = 4.…

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Q: S how that the line af intesection of the Planes and 5x-2y-Z=0 X+2y-22= 5 is Paralkel to thelime メ+3…

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Q: Find the equatioa of tangeut plane to the surface + 2y? + 3: = 21 which is puraliel to the plane 2r…

A: parallel to plane 2x+4y+6z = 3      surface x2 + 2y2 + 3z2 = 21     Let  F = x2 +2 y2 + 3z2 = 21  we…

Q: ? Find the surface area of the plane ( 15x-5z+20y%3D35) if it is in the first octant

A: Here we have to find the surface area of the plane 15x-5z+20y=35 ................... (1) for the…

Q: Find the surface area of that part of the plane 9x + 6y + z = 4 that lies inside the elliptic…

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Q: Find the surface area of the part of the plane z = 5 + 4x + 3y that lies inside the cylinder 22 + y?…

A: We have to find surface area of the plane z=5+4x+3y that lies inside the cylinder x^2+y^2=16.

Q: Find of and Duf to :- f cas,z) = In (x²+zy?+32) atp(-v34) in the direction of ã=-3i-4j-12K. -314…

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Q: Calculate f((5x + 2y)i + (4x + 7y) 3) · dr where C' is the circular path with center (a, b) and…

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Q: Find the surface area of the plane ( 15x- ? 5z+20y=D35) if it is in the first octant

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Q: a) Evaluate (-ri-yj+2z k) -n dS, where o is the portion of the paraboloid z = 3r + 3y? between the…

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Q: Use Stoke's theorem to evaluate // curlF - dS where F(x, y, z) = 2y i+ 3xj + (z – x) k and S is the…

A: The given integral is∫∫CcurlF→·dSwhere F→x,y,z=2yi^+3xj^+z-xk ^and S is theportion of y=11-3x2-3z2…

Q: Find the projection in the ry plane of the curve of intersection of the surfaces 222 = r² + y? and r…

A: Find your answer below

Q: Calculate Se(5x + 3y) i + (4x + 3y) j) · dĩ where C is the circular path with center (a, b) and…

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Q: / (2² + y²) do, where S is the portion of the sphere r? + y? + z² = 9 in the first octant that is…

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Q: Find the area of the portion of the plane 3x − 3y + z = 12 that lies inside the cylinder y^2 + z^2 =…

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Q: Find the area of the surface. The part of the plane x + 2y + 3z = 1 that lies inside the cylinder x2…

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Q: a) Evaluate [-ri-yj+2: k) - n ds, (-a i- where a is the portion of the paraboloid z = 3r + 3y…

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Q: Find the distance from a point P(x1, y1, Z1) to the plane Ax + By + Cz = D.

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Q: Compute the surface area of the ellipse that lies on the plane z = 11 – 3x + 2y and inside the…

A: The surface area of the surface given by z=f(x,y) where (x,y) is a point from the region D in the…

Q: 2. At what point on z = a? + y? is the tangent plane parallel to 3.r – 4y + z = 7 ?

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Q: Find the area of the part of the plane 4x + 3y + z = 12 that lies in the first octant.

A: to find:- surface area, A.

Q: Use Cartesian coordinates to evaluate JJ v² av where D is the tetrahedron in the first octant…

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Q: Find the projection in the ry plane of the curve of intersection of the surfaces 2z2 = r? + y? and…

A: Let's find.

Q: A parametrization of the portion of a surface z=x²+y2 below the plane z= 16 is given by 7(u,v)=…

A: Since you have sent more than one question so we can just answer one of them because of our…

Q: O 9/ Compute I - [.lryz) , uhere s is the part g the plane y +x that lies inside the half-cylinder…

A: We know that, dS=1+∂z∂x2+∂z∂y2dydx where S is the part of plane z=y+x. ∂z∂x=1∂z∂y=1 dS=1+(1)2+(1)2…

Q: Calculate fc((7x + 6y) i + (4x + 7y) j) dr where C is the circular path with center (a, b) and…

A: The path is given as the circular with center (a, b). Now the integral is: I=∫C (7x+6y)i→ +…

Q: Find the area of the cap cut from the top of the sphere x2 + y2 + z2 = 1 by the plane z = √2/2.

A: Given equation of sphere is    x2+y2+z2=1     And the equation of plane is  z=22=12 But we know that…

Q: Which of the following is the least distance from the origin to the plane 2x + 2y + z = 1? Lütfen…

A: We have to find

Q: Suppose the plane So thet its Coordinates are a partile Pir moving in given by y=Fsinzt Plxy) where…

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Q: Find the area of the surface. The part of the plane 3x + 5y + z = 15 that lies in the first octant

A: Given plane,  3x+5y+z=15Intercepts of the plane axis are  x=5, y=3, z=15

Q: Evaluate (xr + y² + =³)? dV, where 2 is the solid hemisphere (half of the Ω sphere) enclosed by x +y…

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Q: Bounded by the paraboloid z = 10 – 3x? – 3y2 and the plane z = 4 (using polar coordinates)

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Q: Find the surface area of the part of the plane z = 4 + 6x + 2y that lies above the rectangle [1, 4]…

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Q: Evaluate Sſ Ands where A= (x+y*)î – 4xj +4yzk and s is the surface of the plane, 2x+y+2z=8 in the…

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Q: a) Evaluate (-x i - yj+ 2z k) - n dS, where o is the portion of the paraboloid z = 3r2 + 3y? between…

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Q: yz ds where o is the part of the plane x + y+ z = 1 that lies in the first octant.

A: Given The given integral ∫∫σyzds over the region x+y+z=1 that lies in the first octant can evaluated…

Q: Find the area of the surface of the part of the plane 3x + 2y + 4z = 2 that lies inside the cylinder…

A: Here, surface S has an equation of the form z=f(x,y), where (x,y)  D and f has continuous partial…

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.