What is the value of a so that the vector field F(x.y)=(y eX+4xy³) i+(ax²y4+ eX)j is conservative? O a. -5 O b.-6 O C. -4 O d.-3 O e. -2

Q: Is the vector field F(x, y) = 2xy+y 2xy+ xy+y*x x conservative? Select the correct answer below: O…

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Q: If the vector field v = [mz+x, -y, x]is irrotational, the mis equal to O A. 2 O B. 0 O C. 1 O D.…

A: Curl of v is zero.

Q: Q4: Find the curl of the vector field F(x, y,2) = xJyi +j+ zk at the point(2,4).

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Q: (1) Is the vector field F(x, y) = (2æ*y^ + æ) î + (2a*y³ + y) Î conservative? Support your answer…

A: Note: As per our guidelines we are supposed to answer only one question. Kindly repost other…

Q: What is the value of a so that the vector field F(x,y)=(y eX+4xy3) i+(ax?y-4+ e%) j is conservative?…

A: To find  the value of a for which F is conservative.

Q: If F (x, y) conservative = axi + byj is a vector field, then a = = b

A: It is a vector calculus problem and let us determine the curl of the given vector field  and also…

Q: What is the divergence of the vector field f=3x i+5xy j+xyz'k at the point (1, 2, 3). Select one: а.…

A: Solution:-The given vector  field is Step:-1    f=3x2i+5xy2j∧+xyz2k∧  then,  we have  to find the…

Q: What is the value of a so that the vector field F(x,y)=[y eX+4xy3) i+(ax3y4+ e%)j is conservative? О…

A: We are asked to find the value of a.

Q: Find the curl of the vector field F. F(x, y, x) = 2yz'i + 3xj +&xk O 15r4 O 15:3 O (8yz – 8]j +…

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Q: How do you determine whether a vector field in ℝ2 is conservative(has a potential function w such…

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Q: 8) The vector field Vp[x, y] = F =- has a potential function p[x, y] = a) (x² + y²)³2 b) d) Vx? +y?…

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Q: What is the value of a so that the vector field F(x.y)=(y eX+2xy4) i+(ax?y3+ e%)j is conservative? O…

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Q: Is the vector field F = y? – 2x², 2xy + 3| conserva Yes No yz Is the vector field F y? – x2 con Vy?…

A: According to the guidelines issued by the company we are supposed to answer only first question.…

Q: Jo (b) Let ƒ : IR² → R be a C² function with the property that aº f = 0. Show that the vector field…

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Q: b) Find the curl of the vector field, CurlF, if F= Axzi- By 2j+ Cx tk, %3D where the coefficients A,…

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Q: Q2. (a) Given a vector field, F = 2xyi + (x² + 3y²z)j+ (y³ + 2z)k. (i) Determine whether if F is…

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Q: Which of the following vector field is not conservative? a) Å(r, y) = yi- 3ryj b) 72r + 14(x² +…

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Q: Given the vector field F(7, y, 2) F (x, y, z) = compute the curl of F and find the values of a and…

A: curl(F)

Q: F(x.y) = (4xy, - 3y²> A V.F- 4x B VF-1 © v.F = 4x - 6y (D vi--2y

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Q: Sketch a sample of vectors for the vector field F(x, y) = 4xi + 3yj. Choose the correct answer…

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Q: 4) Determine whether the vector field hlxiy)= y?i+ 12xy-e4)T is conservative conservative, deter…

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Q: Select the irrotational vector field. O A yz î-2xz + xyz k O B. yz î + xz î + xz R OCzî + z2 + yz R…

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Q: At how many points is the vector field F(x, y, z) = (z– ,r – 2², y – x²) irrotational? Select one:…

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Q: Is the vector field F (x, y) = (2xy – y³) î + (x² – 3xy²) ĵ solenoidal, conservative, both or…

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Q: Let Σ be the sphere x2`y2`z2 “ 25 with outward orientation and let F~ be a vector field with divF~ “…

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Q: 4y V16+16g Find the divergence of the vector field F(z, 9) i+ V16z + 16g Provide your answer below

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Q: 4. Determine whether or not the vector field F(x, Y, z) = (-xye®, -xe + e° + 2y, 2z) is…

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Q: 4) Consider the conservative vector field given by: F (x, y) = (y² – ye“, 2xy – e*) A potential…

A: Given vector field is F→x,y=y2−yex,2xy−ex. We have to find the potential function that generates the…

Q: |Q19. D = yi – xj, what is the magnitude of the vector field at the point (-1, –1)?

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Q: 9. Find the flux of the vector field B(x, y,=) shown in the left figure through the square S of - yỉ…

A: The general form of a vector valued function in three dimensions is given by…

Q: For what value of the constant b is the vector field F = bxy'i+x²yj conservative? a. 0 b. 1 4 е. 1…

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Q: What is the value of a so that the vector field F(x.y)=(y eX+2xy4) i+(ax2y3+ e%) j is conservative?…

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Q: o) Find the flux of the vector field F (x,y,z) = 3xi – yj + 2zk; across o where o is

A: The given question belonging to the vector calculus  in which we have to find the value flux of the…

Q: Given the vector field F(x, y, z) = (2z3 – 4y2 + axy,x² - 8xy – bz, 6xz? –- ay + 4), compute the…

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Q: Show that the vector field F(x, Y, z) = (x² + y²)i – 2xyj is not conservative on R³.

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Q: What is the value of a so that the vector field F(xy)=(In y+2xy³) i+(ax3y2+ x/y) j is conservative?…

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Q: a) For the given a vector field A = 3x*yz a, + x*z a,+ (x*y – 2z) a, check whether given vector 'A'…

A: According to the given information, For part (a) Consider a vector field A as:

Q: 1 =(xi + yj + zk) Find the curl of the vector field x²+y? +z? 1 Vx² +y² +z² (예+f+1)- 1 -(i +j+k) x²…

A: Use the formula of determining the Curl F and substitute the values from the vector field. Partial…

Q: Determine the vector field of F. (x, y) = 12i – 4j 1

A: given isF(x,y)=12i-4jgraph of vector field of F is attached below

Q: Show that the vector field A (3x?z + y?)a,+ 2xya, + x³a, is conservative. %3D

A: Given problem:- Show that the vector field A = (3x²z+ y²)ax + 2xyay + x³az is conservative. =

Q: For the vector field F(x, y, z) = 1. a) Find curlE b) Find div E c) State whether or not the vector…

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Q: 5. If F = A × OP, where A is a constant vector field, show that V x F = 2A 6. If R = OP,r = ||R||,…

A: The solution are next step

Q: Q5: a) Show that the vector field F = (x² - y² + x)i - (2xy + y)j, is irrational.

A: Given vector field is F→=x2-y2+xi^-2xy+yj^. To show: Vector field F→=x2-y2+xi^-2xy+yj^ is…

Q: Verify if the following vector fields are conservative: 2y 21 a) A1 = (1+æ²+y² > I+x²+y² b) Ã, =…

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Q: Evaluate ∫C F . T ds for the vector field F = x2 i - y j along the curve x = y2 from (4, 2) to (1,…

A: Given information: The value of F=x2i+yj, x=y2 and from (4, 2) to (1, -1). Calculation: Consider…

Q: Given the vector field F(x,y) = [x/((x^+y^2)^(3/2)), y/((x^+y^2)^(3/2))], Find a fucntion f(x,y)…

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Q: ermine whether the vector field F(x, y, z) = (x³, 3zy², y³) is conservative on R³. If so, find a…

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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.