Let F = (z, 2x, y) and C is the straight segment from (0,0,0) to (1,2,3). Then ,F dř = %3D %3D

Q: Let C be the positively oriented square with vertices (0,0), (1,0), (1, 1), (0, 1). Use Green's…

A: Let's solve by using green theorem.

Q: Evaluate S. F dr where F(x, y, z) = e'i+ (xe + e²) j+ye²k and C is the line segment from (0, 2, 0)…

A: answer is in next step

Q: Let Li be the straight line segment from (0.0,1) to (1,a, 8) and let F: (z+ax, ay, x> Calculate the…

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Q: Evaluate F dr where F(r, y, z) = (2.75yz cos(ryz), 2.75rz cos(ryz), 2.75xy cos(ryz)) and C is %3D 1…

A: Here we will find out the required value.

Q: Use the Trapezoidal Rule to estimate the number of square meters of land in a lot, where x and y are…

A: The given data is: ,,

Q: Let r(t) be a positively oriented rectangle with corners (0,0), (0,1), (2,1) and (2,0) and F(r, y)…

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Q: Evaluate F. dr where F(x, Y, z) = (1.25yz cos(xyz), 1.25xz cos(xyz), 1.25xy cos(xyz)) 1 1 and C is…

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Q: Evaluate | F· dr where F(x, y, z) (4yz cos(xyz), 4xz cos(xyz), 4xy cos(xyz)) and C is the line C 1…

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Q: Evaluate the line integral xyz ds where C is the line segment joining the points (1, – 1, 1) to (1,…

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Q: Let M be the region bounded by the parabola y = r² and the line y = x + 2. %3D 6. y = r +2 5. 2,4)…

A: Given that, The shaded region bounded by the parabola y=x2 and the line y=x+2 is M.   And the region…

Q: The area bounded by the curve y= 3va and the lines z = 3 and T = 8 above the z- aris is square units…

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Q: Use Stoke's Theorem to evaluate $. F · dR, where F (x, y, z) = (z²,xy, xz) and C is the triangle in…

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Q: If C is the line segment from (1, 3) to, (0, 0), find the value of the line integral: 3y i+ 3x j) ·…

A: Given If C is the line segment from (1, 3) to, (0, 0),

Q: Evaluate the line integral / x°z ds, where C is the line segment from (0, 2,4) to

A: Line integral: - The function to be integrated is determined along a curve in the coordinate system…

Q: Let R be the trapezoid with vertices (1,-1), (3,3), (3,-3) and (9,9). Give a change of variables to…

A: Given that ,  R be the trapezoid with vertices (1,-1) , (3,3) ,(3,-3) and (9,9) . Let , the vertices…

Q: Evaluate the line integral ∫c x3 z ds, where C is the line segment from (0,8,8) to (5,7,6).

A:

Q: Use the Trapezoidal Rule to estimate the number of square meters of land, where x and y are measured…

A: The formula for Trapezoid rule is h2y0+yn+2y1+y2+y3+..... where h=b-an

Q: WX || ZY and Zs Z and Y are supplementary WXYZ is a parallelogram Given: Prove: W Y

A: It is given that,  WX ¯|| ZY¯  and ∠Z and ∠Y are supplementary To prove :- WXYZ is a parallelogram

Q: | Let C be the positively oriented square with vertices (0, 0), (2, 0), (2, 2). (0, 2). Use Green's…

A: greens theorem

Q: Let f(x, y) = 2x and C be the line segment on the plane from (0, 0) to (3, 4). Evaluate the line…

A:

Q: Let z = f(x, y) = x² – y² + xy + 2. Consider the triangular region in the xy-plane with corners at…

A: The given function is z=fx,y=x2-y2+xy+2

Q: Find all points on the surface x² + y² – z² = I at which the normal line is parallel to the line…

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

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Q: Let f(x, y) = x²y – xy. Evaluate | Vf•dr where C is any oriented curve from (4, –1) to (1,5).

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Q: 4. Prove that fer*dr+xydy = f, So*(y– 0)dydr where C is the triangular curve consisting of the line…

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Q: Let P be the plane 2x + y – z = 2 and let Q(1,0,3) be a point. We want to find the minimum distance…

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Q: Evaluate x*dx C + xy dy, where C is the triangular curve consisting of the line segments from (0, 0)…

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Q: f(x, y, z) = xe z2, piecewise linear path from (0, 0, 1) to (0, 2, 0) to (1, 1, 1)

A: To Determine: calculate ∫cxez2dx Given: we have piecewise linear path from (0, 0, 1) to (0, 2, 0) to…

Q: a) Evaluate the line integral S. (2x – y) dx – (x + 3y) dy, where C is a straight line from (1,1) to…

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Q: Let f(z) = 5z + 14, and let C1 be the line segment from z = 0 to z = 2, let C2 be the line segment…

A: In this question, we calculate the complex integral along the given contour joining vertices of the…

Q: The area bounded by the curve y = In(z) and the lines z = 1 and =2 above the z -azis is %3D square…

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Q: (b) Let z(r, y) = exp(-|r|) cos r + y², where r + y /9 = 1. Show that z(r, y) has minimum points…

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Q: Evaluate R CF. dr with F(x, y, z)=(x2 + y)i – (3xz)j + (z – 4y) k, with the path C as the line…

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Q: Let C be the curve connecting (0,0) to (1,2) to (0,6) to (0,0) using straight lines. (5x*y – 3x²y+…

A: Greens theorem based problem......

Q: Use the Jacobian of a coordinate transformation to find the area of the parallelogram bounded by the…

A: We use the following transformation to find the area of the parallelogram bounded by the lines y =…

Q: Let w be the projection of u in the direction of v. That is, w = proju. The x-component of w, to 2…

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Q: Calculate (y+z)dx+ (x+ z)dy+ (x+y)dz , where C consists of line segments from (0,0,0) to (3,2,4) and…

A: We will use parametric equation of lines to find the integral

Q: Evaluate F. dr where C is the line segment from (6,,1) to (36, 1, and F = (sin (yz) + 1)i + (zzcos…

A: Whenever a Vector is given and we need to find line integral with two points mentioned, we first…

Q: Let f(x, y, z) = eª + zy² and let C be a straight line segment connecting the points (4,2,1) and…

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Q: |F - dr where C is the line segment from (6, 5,1) to (45, 1, ) and F = (sin(yz)+1)i + (zzcos(yz) +…

A: To evaluate:

Q: The plane z = 2x - y - l is tangent to the graph of z = f(x, y) at P = (5, 3). (a) Determine f (5,…

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Q: An _____ is a set of points (x, y) in a plane such that the sum of the distances between (x, y) and…

A: The sum of the distances to any point on the ellipse (x,y) from the two foci (c,0) and (-c,0) is a…

Q: Let W = Span{u} where u -2. Let y = |1, find the distance from y to W L3]

A:

Q: Let M be the region bounded by the parabola y = x² and the line y = x +2. %3D 6. y = r + 2 5. 4.…

A: Consider the given information and diagram: Let y=x2 and the line is y=x+2.

Q: Let F(x,y,z)=(2ye?,2e²,12(2-e?)). Let S be the portion of the graph z=1n(2x2+40y3+2) which is above…

A: Given that: Fx,y,z=2yez,2ez,122−ez Here S is the portion of the below graph which is above the given…

Q: B) Use Green's Theorem to evaluate F-dr, where C is the triangle with vertices (0, 0) (3,0) and (3,…

A: Explained below

Q: Let F(r, y) = yeyi+xe*vj. Evaluate the line integral | 1 F. dr where C is the closed path consisting…

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Q: Let F = (r-y, z+y+3, z2) and S y-direction. Compute {(r, y, z) : y =1-r²-z², y20} oriented in the…

A: Here orientation is positive y direction, surface is open.  During the calculation we ignore many…

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.