Evaluate the surface integral SF · dS for the given vector field F and the oriented surface S. In other words, find the flux of F across S. For closed surfaces, use the positive (outward) orientation. F(x, y, z) = yi − xj + 2zk, S is the hemisphere x2 + y2 + z2 = 4, z ≥ 0, oriented downward
Evaluate the surface integral
| S |
for the given vector field F and the oriented surface S. In other words, find the flux of F across S. For closed surfaces, use the positive (outward) orientation.
F(x, y, z) = yi − xj + 2zk, S is the hemisphere
Expert Answer
Want to see the step-by-step answer?
Evaluation Of Integral
Integral Calculus
Other
Related Advanced Math Q&A
Q: Help me fast so that I will give good rating.
A: Given system of equations dxdt=-2x-2ydydt=-2x+y can be written as X'=AX, A=-2-2-21, X=xy trA=-1 whe...
Q: please help me
A: We are given that S is a sphere of radius 5 . And also we are given the Equation of Sphere : x2+y2+z...
Q: Consider the position function s(t) = - 4.91² + 30t + 19. Complete the following table with the appr...
A: The average velocity over a interval of time is given as follows. Vavg=sb-sab-ast is th eposition ve...
Q: 1. Plot the following vectors using arrows on an xy-graph: -- (}). v-[+]. 1 u = V = 2u, u+v. Is ever...
A: Click to see the answer
Q: (1) Use induction to prove the following for all natural numbers n: 13 + 23 +... n3 n² (n+1)² 4
A: Click to see the answer
Q: Solve the following system of equations. – x + 2y + z = 2 – x + y + 2z = 5 y – z = 4 Whi...
A: Click to see the answer
Q: The loudness level of a sound, D, in decibels, is given by the formula: D = 10log(1012I) where I ...
A: Click to see the answer
Q: 10
A: The volume of a curve y=f(x) rotated about x axis on the interval a,b is given by the equation V=∫ab...
Q: Questions A and B please
A: Given, H=a+b+c+db-c+2da+2c-d: a,b,c,d∈ℝ⊆ℝ3 ⋯⋯(1) a) Given, u=111 Consider the system, a+b+c+db-...
Q: Chris invests $8,000 at 7% simple interest for 31 years.Round your answers to the nearest cent.How m...
A: Click to see the answer
Q: I NEED THIS ASAP, THANK YOU!!
A: Note: As per Bartleby's guidelines, for more than one question asked in the main part, only one ques...
Q: 7. Consider the series a. Find all values of x fo be an open interval on the re b. Find all values o...
A: Click to see the answer
Q: Consider the Sequence below :- = 5; a, = 7 %3D For n22 An = 2an- Apaz 2anet Obtain the gene rating f...
A: Given, an=5 , n=07, n=12an-1-an-2,n≥2 This can be represented by the single equation, an=2an-1-an-2+...
Q: What is the answer to No. 2 of the Reflection part?
A: Given f:y=0 and g:y=x2+1 The domain D is given by D:x/0≤x≤2 2) Other than using definite integrals, ...
Q: Can you please help solve attached differential equations question attached below? How to find the s...
A: Click to see the answer
Q: Reverse Engineering It is given that the function y(t) = exp t) (cos 3t + 2 sin 3t) +t² exp(-t) (14)...
A: The general solution of a linear differential equation and the nature of roots is given as: Correspo...
Q: cos(n") In(4) 1. 1 2. n In(n) n%3D 6n + 3 (-1)" n=1 1 4. n - 5 3.
A: Click to see the answer
Q: D is theregion in the plane with boundary given by oriented simple closed piece-wise smooth cuyrves ...
A: Given that- F→= (P,Q,0):ℝ3→ℝ3 is a vector field and P and Q have continuous partial derivatives on ...
Q: Find the gradient Vf and the directional derivative at the point P (1,–1,2) in the direction a = (2,...
A: The given function f(x, y, z) = x3z - yx2 + z2.The gradient of a function f is defined as∇f(x, y, z)...
Q: In changing variables to spherical coordinates, the dV in I f(2, y, z) dV becomes o dp do do. Cos
A: The volume element on conversion to spherical coordinates becomes dV = ρ2sinϕdρdϕdθ
Q: Linear Algebra.
A: Given:T:ℝ2→ℝ2 is defined by Tx=AxWhere A=-3-3-1-5To find basis B for ℝ2 such that TB is diagonal. Fo...
Q: Need help, Thanks!
A: The power function that the graph of fx=anxn+an-1xn-1+...+a0 resembles for large values of x is the ...
Q: The student council at a university consists of 6 seniors, 7 juniors, 3 sophomores, and 4 freshmen. ...
A: The student council consists of 6 seniors, 7 juniors, 3 sophomores, and 4 freshmen. The number of st...
Q: Calculas 3 Surface Integral 2 problems
A: Since you have asked multiple questions, we will solve the first question for you. If you want any s...
Q: Use Stokes' Theorem to evaluate (x + y)dx + (2x – 3)dy + (y + z)dz over the boundary of the triangle...
A: Let the surface s is the plane ABD.The orientation of the surfaces and the contour G as shown in the...
Q: Please, will upvote for correct solution
A: Click to see the answer
Q: Sketch the solid whose volume is given by the iterated integral |LI dz dy dx. Then rewrite 4. the in...
A: Given ∫01∫-10∫0y2dzdydx
Q: c) For y<11, find the coordinates of each point on the graph where the tangent line to the graph at ...
A: For an equation of the curve f(x, y)=0 Slope =dydx If slope =±∞, Tangent line is vertical at this po...
Q: find a power series representation for f(x) ln(14 -x)
A: Click to see the answer
Q: Show all relevant work and cirlce final answer. Please write neatly
A: Click to see the answer
Q: Using the chart of the picture attached answer #15 (the moviegoers age is less than 65)
A: Click to see the answer
Q: A ballroom is full of people (say more than 200). What is the least number of people that you must s...
A: Click to see the answer
Q: In a study of the domestic market share of the three major automobile manufacturers A, B, and C in a...
A: There are 3 major automobile manufacturer A, B and C The transition matrix P is given by A B C ...
Q: Please, write a full clear answer of your own work and I'll rate up :)
A: Here, Curve C is equivalent to c1+c2. The point of intersections of c1 and c2 is at 0,1,0.
Q: Calculas 3 Strokes Theorem
A: Given that F=<x,y,z> To verify Stoke's Theorem: ∮C Fdx=∬S∇×F·n dS Find ∮C Fdx: First, Compute ...
Q: Suppose |AC| = |AD| and |BC| = |BD|. Then there exists a rigid motion F in a plane so that F(A) = A,...
A: Given that: AC=AD and BC=BD By joining CD,the figure is:
Q: A woman borrows $2500 and agrees to pay 8% annual simple interest on the loan. She repays the loan,...
A: Click to see the answer
Q: Please answer what k= for A-H
A: Click to see the answer
Q: How many significant figures are in each of the following measured quantities?
A: Given that : 0.0003303 m 0.0003303=3303×10-7 The number of significant figures= Number of figures wi...
Q: Sketch the region of integration. Then evaluate the iterated integral sin(x?) dx dy.
A: Click to see the answer
Q: Adjust h, k, and t to reproduce this picture, only with your ellipse being purple instead of green. ...
A: Note: According to Bartleby guidelines; for more than one question asked, only the first one is to b...
Q: Please, will upvote for correct solution!
A: Click to see the answer
Q: Need help with these problems
A: Given :- Initial speed of car (U) = 22 m/s Final speed of car (V) = 37 m/s Time taken (t) by car to...
Q: Find the characteristic equation of the given symmetric matrix, and then by inspection determine the...
A: Given matrix is A=633363336 First we will find the characteristic equation of the given matrix A=633...
Q: 8. Let 1 A = 4 -1 (a) Find the eigenvalues and the corresponding eigenvectors of A. (b) Is A diagona...
A: Click to see the answer
Q: questions c and d please
A: Answer for sub question c: The first step to find an orthogonal basis for H is to find a basis for H...
Q: 15. Graphically solve the following: тахітize p %3D 3х + 2у subject to: 0.2x + 0.1y 0, y > 0
A: Given: Maximize p(Objective Function)=p=3x+2y Subject to constraints: 0.2x+0.1y≤10.15x+0.3y≤1.510x+1...
Q: Let A be a 3 x 3 matrix such that det(A) = 2. Evaluate det(Aª) and det(2A).
A: Recall the following. If A is a n×n matrix and m be any positive scalardet k A=kndet Adet Am=det Am
Q: Mack is starting a new business called River Adventures which will provide canoes and kayaks to peop...
A: Click to see the answer
Q: Show all relevant work and cirlce final answer. Please write neatly
A: Click to see the answer