I circled the correct answer, could you show me how to do it using divergence and polar coordinates 1 The flux of the vector field F(x, y, z) = (y − z² + 2x³, −z + x² + 2y³, x − y²+22³) out-going from the set {(x, y, z) = R³ : x² + y² − 1 ≤ z ≤ 0} is(A)πK20(B) 00 0 03πT

1 The flux of the vector field F(x, y, z) = (y − z² + 2x³, −z + x² + 2y³, x − y²+22³) out- going from the set {(x, y, z) = R³ : x² + y² − 1 ≤ z ≤ 0} is (A) π K20 (B) 0 0 0 0 3πT

1 The flux of the vector field F(x, y, z) = (y − z² + 2x³, −z + x² + 2y³, x − y²+22³) out- going from the set {(x, y, z) = R³ : x² + y² − 1 ≤ z ≤ 0} is (A) π K20 (B) 0 0 0 0 3πT

Algebra and Trigonometry (MindTap Course List)

4th Edition

ISBN:9781305071742

Author:James Stewart, Lothar Redlin, Saleem Watson

Publisher:James Stewart, Lothar Redlin, Saleem Watson

Chapter9: Vectors In Two And Three Dimensions

Section9.FOM: Focus On Modeling: Vectors Fields

Problem 16P

See similar textbooks

Related questions

Q: 3. Please solve this for me and show every single step. I am studying and got stuck on this…

Q: Find the flux F(x, y, z) = xi + 2yj +4zk, S is the cube with vertices (1, 1, 1), (-1, -1, -1)

A: This question can be solved using Gauss divergence Theorem, which states…

Q: Give equations describing the regions below in cylindrical or spherical coordinates.(a) The unit…

Q: express the inverse transforms in terms of step functions, and then find distinct formulas the for…

Q: C = (2√3)/3 or (-2√3)/3 within the interval (-2,2)

Q: Question 3 1 pts By changing to spherical coordinates, calculate A = SSS, e(x²+y²+z²)³/2/2 dV, = 2x…

Q: 5. Submit answer Compute the surface area of the solid of revolution formed by rotating the bounded…

A: Step 1:Step 2: Step 3: Step 4:

Q: π 25. If lies in the interval <0</ and Sinh x = tan 0. Show that: 2 Cosh x= Sec 0, tanh x =Sin 0,…

A: Using the definition of hyperbolic functions, we can show that coshx=secθ, tanhx=sinθ, cothx=cscθ,…

Q: Test the series for convergence or divergence.

A: Step 1:The provided series is:∑n=1∞n!3nn2It is needed to test the series for convergence or…

Q: Ministry of Higher Education & Scientific Research Babylon University College of Engineering - Al…

A: Q1 uses the power series method where we assume a solution in the form of an infinite series and…

Q: Question 1 Let f(x) = 15 and g(x) = +5. Find the following functions and simplify your answers.…

A: Verify: Since)log4(x+2) is undefined for x=0 the only valid solution is x=4096Answer: x=4096

Q: For the volume of the region in the first octant shown in the adjacent Figure. It is bounded by the…

A: For the iterated integral ∫∫∫ dz dx dy, the limits of integration are determined by the boundaries…

Q: Please help on all questions asked. Please show all work and steps. Please circle the final answer.

A: r=−2 and r=−4

Q: Problem 1. Solving SDEs: Ornstein-Uhlenbeck process The purpose of this problem is to use Itô lemma…

Q: I want the solution with all the details if L is of rank n

Q: In the attached graph of f', and given that f(0) = -4 a) Approximate the slope of f at x = 4. b) Is…

A: //The answer above is the detailed solution of the given problem //Feel free to ask doubts if any…

Q: Consider an object moving along the parametrized curve with equations: x(t)=e² + e¯², y(t)=-* where…

A: Approach to solving the question: Detailed explanation:Examples: Key references:

Q: The cup on the 9th hole of a golf course is located dead center in the middle of a circular green…

A: QUESTION 1: x-coordinate when the ball enters the green Step 1: Find the equation of the circle…

Q: Help me with the accurate answer and solution asap pls pls thank yo u

Q: Determine whether the series is convergent or divergent. Identify b 8 Σ n = 1 (-1)-1 7 + 9n Evaluate…

Q: Find the value of the following indefinite integral: (see image)

A: By completing the square on 4b2y2−24aby+27a2 we have=(2b)2y2−2(6a)(2b)y+27a2By comparing with the…

Q: Please help on all asked questions. Pls show all work and steps. Please circle the final answer.…

A: I hope you are finding the material engaging and informative. If you have any questions or…

Q: Find the Laplace transform of f(t). f(t) = 8t6 + 3t4 - 2t + 5

A: The Laplace transform is an integral transform that converts a function of a real variable t (often…

Q: 2. Consider the vector force: F(x, y, z) = 2xye²i + (x²e² + y)j + (x²ye² — z)k. (A) [80%] Show that…

A: May this answer helpful to you.

Q: 1. Sketch the following piecewise function on the graph. (5 points) x<-1 3 x² -1≤ x ≤2 f(x) = = 1 ४…

A: For x < -1: f(x) = 3 ( horizontal line at y = 3 ) • We can draw a straight line (ray) through…

Q: Example: Find Fourier integral for [1 |x|1 1/

A: 1. Fourier Transform of f(x): 2. Evaluate the Fourier Integral: 3. Deducing Final Answer:…

Q: Q1/ Two plate load tests were conducted in a C-0 soil as given belo Determine the required size of a…

A: Step 1: Step 2: Step 3: Step 4:

Q: Please help on all asked questions. Please show all work and steps. Please circle the final answer.

A: Here is the step-by-step explanation:Part (a): Line [x,y,z]=t[0,0,1]Step 1: Parametric Form…

Q: 1. The average value of f(x) = ✓ on [1,4] and instantaneous rate of change at x = 16 2. f(x) =…

A: If you have any problem let me know in the comment section.

Q: 2. (i) Describe with a sketch the trace of the following curve in R² (t) = (t² sin(t), t2 cos(t)),…

A: The given curve is a parametric curve in R², defined by the function (t) = (t² sin(t), t² cos(t)).…

Q: Find parameterizations for the following objects. (Your parameterizations should, as always,be in…

A: abc d

Q: Consider an object moving along the parametrized curve with equations: x(t)=e² + e², y(t)=-* where t…

Q: 2. Consider the linear system x' = Aπ with = A-(G3). α where a -1. (a) Determine the eigenvalues in…

Q: use a graphing utility to sketch the graph of the function and then use the graph to help identify…

A: If you have any help please let me know in comment box thankyou.

Q: A ball is thrown at an angle of 45 degrees to the ground. If the ball lands 50 m away, what was the…

A: 1:

Q: Exercise 1 Given are the following planes: plane 1: 3x4y+z = 1 0 plane 2: (s, t) = ( 2 ) + ( -2 5 s+…

A: In the above diagram, the angle between the normal vectors α is what we are calculating using the…

Q: Q8 Salve: f√coshx-i.dx do Solve: So Q₂ Qio Salve S Sinho + cosho dx 4-x2 Qll Solve Sdx √ex+1 Q12 If…

A: Step 1:Step 2:Step 3:Step 4:

Q: Please help on all asked questions. Please show all work and steps. Please circle the final answer.

Q: Taylor Series Approximation Example- H.W More terms used implies better approximation f(x) 4 f(x)…

Q: A particle starts at the origin with initial velocity v (0) = (1, −1, 3). Its acceleration is a (t)…

A: Step 1: Given-The initial position of the particle is r(0)=(0,0,0) (Particle starts from rest.)The…

Q: 3. Submit answer Practice similar Calculate the integral approximation Se for So dz. L-de 4 1.…

Q: Please help on all asked questions. Please show all work and steps. Please circle the final answer.

A: (a) Parametric Equations of the LineThe vector PQ is given by:PQ=Q−P=(2−3,0−(−1),5−4)=(−1,1,1)This…

Q: Test the series for convergence or divergence.

A: Step 1: Step 2: Step 3: Step 4:

Q: Solve this page.

Q: Complete the description of the piecewise function graphed below. Use interval notation to indicate…

A: Step 1:

Q: Please help on all asked questions. Please show all work and steps. Please circle the final answer.

Q: Question 3 (5pt): A chemical reaction. In an elementary chemical reaction, single molecules of two…

A: (a) Rewrite the differential equation (E) with separated variables The given equation…

Q: The measured receptance data around two resonant picks of a structure are tabulated in the…

Q: Show that the function f(x, y, z) = ex²+y²+z4 defined over the domain D = {(x, y)| x² + y² + z² =…

A: Given function: f(x,y,z)=ex4+y4+z4 defined over the domain: D={(x,y,z)∣x2+y2+z2=1}, has 6 global…

Q: Draw the region bounded by the curves. y = 3x2, x = 0, and y = 3 Use the disk method to find the…

Question

I circled the correct answer, could you show me how to do it using divergence and polar coordinates

1 The flux of the vector field F(x, y, z) = (y − z² + 2x³, −z + x² + 2y³, x − y²+22³) out-
going from the set {(x, y, z) = R³ : x² + y² − 1 ≤ z ≤ 0} is
(A)
π
K20
(B) 0
0 0 0
3πT

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

SEE SOLUTION Check out a sample Q&A here

Step by step

Solved in 2 steps with 3 images

SEE SOLUTION Check out a sample Q&A here

Similar questions

Find an orthonormal basis for the subspace of Euclidean 3 space below. W={(x1,x2,x3):x1+x2+x3=0}
Find a basis B for R3 such that the matrix for the linear transformation T:R3R3, T(x,y,z)=(2x2z,2y2z,3x3z), relative to B is diagonal.
Evaluate the 1-form φ = x2yz dx − z dy on the vector field V (x, y, z) = xU1(x, y, z) − yzU2(x, y, z) + 6zU3(x, y, z)..
h) Given vector field F (x, y, z) = (2x + 2y + 42) i + (2y +2x –. - 32) + (2z – 3y + 4x) k. 4. (a) Prove or disprove that f(x, Y, z) = x² + y² + z² + 2xy – 3yz + 4xz is a potential function for vector field F. (b) Find ſ, Fdr, where L is a part of the helix x = connecting the points A(3,0, 1) and (-3,0, 2) 3 cos (rt), у = 3 sin(rt), z =1+t, 0 < t < 1,
1) Find the work done by the vector field F(x, y, z) = (x², 4xy' , xy² ) on a particle that traverses the rectangle in the z = y with the vertices (0, 0, 0), (0, 3, 3) , (1, 3, 3) , and (1, 0, 0) .
Let F₁ (x, y, z) = (y, x − z² +2,−2yz) and F₂ (x, y, z) = (x − z², −y + 2, 2yz). (a) Find the curl of each vector field. (b) Which of these two vector fields is conservative? Find a potential function for the one that is. (c) Let F be either F₁ or F2 (whichever you want), and let C denote the curve shown in the figure which starts at the point (0, 1,0), stays above the circle x² + y² = 1 and spirals upwards in a clockwise direction to the point (0,1,1). Jo Find the exact value of the line integral: F. dr.
7
9. Find the flux of the vector field B(x, y,z) shown in the left figure through the square S of side 2 shown in the right figure , oriented in the j direction, where B(x, v. z)== yi +xj x²+y² S + 2 1 3
4. Match the vector fields given below with their plots. (a) F(x, y, z) = (b) F(x, y, 2) = (c) F(x, Y, z) = x² + y² (d) F(x, y, z) = (x² + y² + z²)3/2’ (x² + y² + z²)3/2' (x² + y² + 2²)3/2 Field (I) Field (II) Field (III) Field (VI)
Consider the scalar function (x, y, z) and the vector field F(x, y, z) defined as . (x, y, z) = 3zx² + 2xe³ - In(xz) F(x, y, z) = −3zx³7+5y²+4yzk (a) Evaluate V · Vò̟. (b) Evaluate V x (▼ × F). (c) Calculate the directional derivative at the point P function (x, y, z) in the direction ▼ × (▼ × F). = (1, 0, 1) of the scalar (d) Determine the equation of the tangent plane on the level surface at the point Po = (1, 0, 1). = 5
2x 2y Consider the vector field F x² + y2' x² + y² (a) If C1 is the unit circle x² + y? = 1, compute the circulation and outward flux of F on C1. (b) If C2 is the ellipse x² /2+ y² /3 = 1, compute the circulation and outward flux of F on C2.
2. Consider the vector field F(x, y, z) = 5zi - 7y3j+5xzk. (a) Calculate div F at the point (1,1,0). (b) Explain the meaning of the number you found above.