solve b part.. hand written plz 1: EvaluateF dS whereF = (r',,) and S is the solid boundedby the zy plane and the elliptic paraboloid z = 4 – r² - y*,a) by direct computationb) using Divergence theorem.

Answered: Image /qna-images/answer/30bdffa1-f1b2-4603-82bc-18b953afe99a.jpg

Answered: 1 : : Evaluate F dS whereF = (r",y",)…

1 : : Evaluate F dS whereF = (r",y",) and S is the solid bounded by the ry plane and the elliptic paraboloid z = 4-r² - y², a) by direct computation b) using Divergence theorem.

Elementary Geometry For College Students, 7e

7th Edition

ISBN:9781337614085

Author:Alexander, Daniel C.; Koeberlein, Geralyn M.

Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.

Chapter10: Analytic Geometry

Section10.6: The Three-dimensional Coordinate System

Problem 41E: Does the sphere x2+y2+z2=100 have symmetry with respect to the a x-axis? b xy-plane?

See similar textbooks

Related questions

Q: x2n+1 E (-1)"; (2n + 1)! 263 The series: n-0 the actual sum exists? Provide an exact answer and…

A: This is a problem of series.

Q: 5. Find the Laplace transform of the equation f" (t) + f(t) = sin bt where f(0) and f'(0) = 0 (a )…

Q: Question 7. Consider the solid in ryz-space, which contains all points (r, y, 2) whose z-coordinate…

A: Given that the solid is in xyz plane and z-coordinate satisfies 0≤z≤4-x2-y2.

Q: Consider the equation хд,и — удуи — -и with the initial condition: u(x,y) : = 2 on the circle {(x,y)…

A: Given the equation as x∂xu-y∂yu=-u (1) write down the subsidiary equation of (1)…

Q: 1. Solve the initial-boundary value problem du 2 32u 0 0 3 dx2 u(0, t) = u (4, t) = 0 t > 0 u(г,0)…

Q: Consider the function f(x) = 2/x + 5 on the interval [2, 5]. Find the average or mean slope of the…

Q: For which fields F listed below is the polynomial X4 + X3 +1€ F[X] irreducible? Select all that…

Q: dz (b) by using the Chain rule with the following information: ds Determine the z = cos (x"y^) – sin…

A: We have to find dz/ds using chain rule of differentiation.

Q: Determine the sum of the following series. (- 4)"-1 7" n=1

Q: . Solve the following problem with insulated boundaries: Uz = Uxx Ju,(0, t) = 0 lu(1, t) = 0 u(x, 0)…

Q: 34 18 Let A -29 Find a matrix S , a diagonal matrix D and S-! such that A = -54 SDS-1. S = s-1

A: Given matrix is A=3418-54-29

Q: Find the product of: (a) 6(cos=+i sin) and 2 (cos+i sin) 3

Q: 6. Compute the projections of [1, – 1,0, 1] on the vector [0, 1,0, 2]. |

A: Let v = [1, -1, 0, 1] and u = [0, 1, 0, 2]

Q: Find all solutions of quadratic congruence x^2+85x+2=0(mod401)

A: We follow the method of completing the squares of the equation x^2+85x+2. Note that 85 is odd so we…

Q: Make an table for the isometries of an equilateral triangle. The image describes the order from top…

Q: valuale (li) dt

Q: Determine the greatest common divisor of the polynomials X4 + X? + 1 and X + X³ + x² +1 in F[X],…

A: We want to find gcd of given polynomials

Q: 3 d²y +3y[ dy + dy .3 2 dx = 5x dx dx

A: We have to identify the independent variable, dependent variable , order and degree of the given…

Q: Find a basis for the range of A and describe what you are doing A = 1 7 8 18 -4 2 5 9 -17 8 -38 -60…

A: To find the basis for range space of A : Firstly we will find the row reduced echelon form of A then…

Q: Xn+e x1 = 1; xn+1 8

Q: exponential function rate of change Consider a function P(x) = 5.4 (1.05)^x a) explain what…

A: (a) Here, P(x) = 5.4 (1.05)^x represents a geometric series. P(0) = 5.4 (1.05)^0 = 5.4 x 1 = 5.4…

Q: Analyze the approximate value and the exact value for (7.2, 4.02) for the function z = x³y2 sin(xy)…

A: Below given clear explanation .Have a look in hand written solution below

Q: Indepen-dent Variable Depen-dent Variable Equation Order Degree dy ²+2 = 0 d²y dy + dx e* dx2

Q: az (b) Determine the by using the Chain rule with the following information: ds z = cos (x"y) – sin…

Q: 3. Find a basis among the vectors [1, 2, 3], [2, 6, 10], [0, –3, –6],[-1,-3,-5] (which are surely…

A: Q3 asked and answered.

Q: Why do we take s=0 or s=1?

A: A normal vector to a plane is perpendicular to all vectors in the plane. If we have 2 vectors in a…

Q: Find the eigenvalues and eigenvectors of the matrix -3 11 -1 3 -7 3 -9 From smallest to largest, the…

Q: QI. Solve the following problem with insulated boundaries: U = Uxx Ju,(0, t) = 0 lu(1, t) = 0 u(x,…

Q: Prove that {4a + 126 : a, b E Z} = {4c: c € Z}.

Q: Consider the following 3 x 3 matrix A and b in R, 1 -4 8 | A = 2 -3 2 1 5 -8 1

Q: A Binary search tree was created by inserting the keys in the following order: 20, 10, 30 How many…

A: # As per the guidelines we are entitled to solve one question at a time, please resubmit the other…

Q: enter the weight of homework assignments in percent30 enter the weight of quiz assignments in…

Q: How did you get the expression for xtan-1(x)? How did you relate it with the maclaurin series of…

A: We use the Maclaurin series of tan-1x and multiply it by x on both the sides to get the Maclaurin…

Q: Find the best-fit quadratic function f(t) = co+ c¡t + czť² to the data points (0, 7), (1, 6), (2,…

Q: URopN4YwnAM-fIPV2X9hPeXZqSys?1oBw7QYjlbavbSPXbx-YCjsh_7mMmrq Week 3 Quiz Question 9 of 10 (1 point)|…

A: A logical operator on mathematical statements is a word or combination of words that combines one or…

Q: Proof [(pAq)=r] = [p=(q=r)] using the rule of replacement.

Q: Write MATLAB commands to solve the following equations. x = 4 cos 30° + VT0 sin? 30° b. y = In 10 +…

A: x=4cos(300)+10sin2(300) y=ln(10)+30sin(250)

Q: The function f.(z) = sin(2z) has one residue %3D 3) Find the absolute value of the residue of f. The…

Q: Suppose that all car owners fill when their tanks are exactly half full. At the present time, an…

A: Given that (1) The number of customers per hour arrive at a single pump gas station λ=7.5 the time…

Q: 2. The inverse Laplace Transform of the function F(s) = 4s+2 / s²+2s+5 is : (a) e* cos 2t + 2e* sin…

A: Given function is Fs=4s+2s2+2s+5

Q: Find the mass and the z-coordinate of the center of mass of the solid of density kx bounded by the…

A: Mass of solid of region D with density function δx,y,z M=∫∫∫Dδx,y,zdV To find z co ordinate we need…

Q: A. TRUE OR FALSE. Determine each of the following statements if it is true or false. Support your…

A: Given: 1. P is a prime such that p divides a2 then p divides a 2. If a3 divides c2, then a divides…

Q: Determine if the series converges or diverges without using the different tests discussed in Lesson…

A: We will use sum and condition for sum of infinite GP ( geometric progression ) a+ar…

Q: Show if the shown group is cyclic or not. If cyclic, provide its generator/s for H H = ({3* : k E…

Q: 2 Suppase G is an abeli Group of Order 6 Contauining an element' of order 3. Prove G is Cyclic. 2…

A: 1) Let , G be an abelian group of order 6. Consider , a ∈ G of order 3. By definition order of an…

Q: Which of the following is not a property of Fourier Transfor 2 O Shifting O Frequency…

A: Given detail Which of the following is not a property of Fourier Transform? Shifting Frequency…

Q: 4. The inverse Laplace transform L-1{s/(s²+8s +20)}

Q: Solve the differential equation using Laplace transform method. y"- 4y +9y =t, y(0) = 0, y (0) = 1…

Q: 4. Expand the following functions into Taylor series at the point indicated and find their radius of…

A: Given, Different functions ,f(z) To expand the given functions into the Taylor series and then find…

Q: Solve the differential equation using Laplace Transform method. y’’ - 4y’ + 9y = t, y(0)=0, y’(0)=1

A: The given initial value problem is y''-4y'+9y=t,…

Question

solve b part.. hand written plz

1: Evaluate
F dS whereF = (r',,) and S is the solid bounded
by the zy plane and the elliptic paraboloid z = 4 – r² - y*,
a) by direct computation
b) using Divergence theorem.

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 1 Introduction

VIEW

Step 2 Step-by-Step Explanation

VIEW

Step by step

Solved in 2 steps with 2 images

SEE SOLUTION Check out a sample Q&A here

Similar questions

5. Chose the curl of f (x, Y, z) = x² i + xyzj– zk at the point (2, 1, -2). a) 2î + 2k b) – 2î-23 c) 4i-4ĵ + 2k d) –2î-2k
5. Chose the curl of ƒ (x, y, z) = x²î + xyzĵ– zk at the point (2, 1, -2). a) 2î + 2k b)-2i-2j c) 4î-4j+2k d) - 2i-2k
Suppose f(x, y) satisfies the basic existence and uniqueness theorem in some rectangular region Rof the- xy- plane . Explain why two distinct solutions of the DE y' = f (x, y) cannot intersect or be tangent to each other at a point (x,, yo) eR.
Calculate F · dr cylinder x2 + where F = xzi + 2zj – xyk and C is the intersection of the plane y = z+ 2 with y? = 4
Q1// Evaluate , F ds where F = yi + xj + 4zk and S is the surface x² + y? = 9 in the first octant bounded the plane z=0 to z=3 and y=0.
Let F(x, y, z) = (3ry², 3x²y + 4x, xe") and be an oriented surface of the solid bounded by the cylinder z² + y² = 1 and the planes z = -1 and z = 2. (i) Explain why Divergence Theorem applies. (ii) Use Divergence Theorem to compute [L, F F. ds.
Calculate fs f(x, y, z) dS, where S is the part of the plane x + y+ z 2, where x, y, z > 0, and f(x, y, z) = z. (Use symbolic notation and fractions where needed. Use natural parametrization of a function, (x, y, f (x, y)).) /| f(x, y, z) dS = Incorrect
Integrate G(x, y, z) = x + y + z over the surface of the cube cut from the first octant by the planes x = a, y = a, z = a.
Use Stokes' Theorem to evaluate of intersection of the plane x + 3y +z = 12 with the coordinate planes. (Assume that C is oriented counterclockwise as viewed from above.) F. dr where F = (x + 6z)i + (8x + y)j + (10y −z) k_and C is the curve
a surface is defined by the parametric form. S(u,v)= X(u,v)i + Y(u,v)j + Z(u,v)k, where 0<= u <=2pi and 0<= v <=1 X(u,v) = (v2+1)cos2u Y(u,v) =vsinu Z(u,v) =-(v2+1) a. determine the normal vector of the surface S b. determine the unit normal vector of S(0,1/2) that point onward
Use Stokes' Theorem to evaluate F. dr where F = (x + 7z)i + (10x + y)j + (8y − z) k_and C is the curve of intersection of the plane x + 3y + z = 18 with the coordinate planes. (Assume that C is oriented counterclockwise as viewed from above.)
6. (a) Compute directly I = f SsF·dS, where S is the surface of the sphere x² +y² + z² = 4 and F = xi + y3+ zk. (b) Check your result using the divergence theorem.