Use the divergence theorem, assuming that the assumptions on T and S are satisfied Show that a region T with boundary surface S has the volume where r is the distance of a variable point P (x, y, z) on S from the origin O and Iuml is the angle between the directed line OP and the outer normal of S ...

Use the divergence theorem, assuming that the assumptions on T and S are satisfied. Show that a

Question:

Use the divergence theorem, assuming that the assumptions on T and S are satisfied.

Show that a region T with boundary surface S has the volume

-Hгc V = r cos ф dA

where r is the distance of a variable point P: (x, y, z) on S from the origin O and Ï• is the angle between the directed line OP and the outer normal of S at P.

Make a sketch. Use (2) in Sec. 10.7 with F = [x, y, z].

Fantastic news! We've Found the answer you've been seeking!

Step by Step Answer:

Related Book For book-img-for-question

Advanced Engineering Mathematics

ISBN: 978-0470458365

10th edition

Authors: Erwin Kreyszig

See More Books

Question Posted: Dec 12, 2018 11:01 AM

See More Questions

Use the Divergence Theorem to calculate ( (s F ( dS for the given vector field and surface. F = {xy, zy, x2z + z2}, S is the boundary of the box [0, 1] ( [2, 4] ( [1, 5]?
Use the Divergence Theorem to evaluate s (2x + 2y + z 2 ) dS where S is the sphere x 2 + y 2 + z 2 = 1.
Use the Divergence Theorem to calculate the surface integral S F dS; that is, calculate the flux of F across S. F = |r| r, where r = x i + y j + z k, S consists of the hemisphere z = 1 x 2 y 2...
Consider the hydrogen atom, and assume that the proton, instead of being a point- source of the Coulomb field, is uniformly charged sphere of radius R ( < < ao), so that the Coulomb potential is now...
Sachs Brands defined benefit pension plan specifies annual retirement benefits equal to: 1.6% service years final year's salary, payable at the end of each year. Angela Davenport was hired by Sachs...
How did Ford use strategic and tactical planning in its launch of the Ford Fusion? How did the company wide One Ford Plan contribute to the project-specific Launch Readiness plan? What was the role...
You invest $$17,000$ in a mutual fund recommended by a fellow Dallas Mavericks sports fan. The fund is known to have \highs and lows," but your friend virtually guarantees you will beat the market...
The rigid metal strip of negligible weight is used as part of an electromagnetic switch. If the stiffness of the springs at A and B is k, and the strip is originally horizontal when the springs are...
PT Elyksion Communication is experiencing rapid growth. The company expects earnings and dividend growth of 15% over the next two years, 13% in the third year, and constant growth of 6% for the...
Refer to the financial statements of American Eagle Outfitters given in Appendix B at the end of this book. At the bottom of each statement, the company warns readers to "Refer to Notes to...
Evaluate the surface integral S F n dA by the divergence theorem. Show the details. Solve Prob. 9 by direct integration. Data form Prob. 9 F = [x 2 , 0, z 2 ], S the surface of the box |x| 1, |y| ...
Let R and C be as in Greens theorem, r' a unit tangent vector, and n the outer unit normal vector of C (Fig. 240 in Example 4). Show that (1) may be written or where k is a unit vector perpendicular...
More companies than ever before conduct business with companies in other countries. This exercise requires students to discuss within their groups the ethicality of paying bribes to foreign...
The inverse of $A \Rightarrow B$ is the implication $eg A \Rightarrow eg B$. Explain why the inverse is equivalent to the converse.
The equity section of the statement of financial position of Lorenzo pleas at 30 September 2010 is as follows (amounts in thousands of euro): Additional information: Lorenzo plc issued 16,000 shares...
The Companies Act 1900 has been referred to as a prominent milestone in the history of company auditing. List reasons which help to explain why this Act has been given this title.
A vector field $\mathbf{F}$ is incompressible if $\operatorname{div}(\mathbf{F})=0$ and is irrotational if $\operatorname{curl}(\mathbf{F})=\mathbf{0}$. Prove that the cross product of two...
Outline the accounting treatments that are permitted by IAS 19 for actuarial gains and losses in connection with defined benefit pension plans.
Between-group variability is caused by ____ as well as treatment effect.
Dan and Diana file a joint return. Dan earned $31,000 during the year before losing his job. Diana received Social Security benefits of $5,000. a. Determine the taxable portion of the Social Security...
Provide a 95% confidence interval for the true Spearman rank correlation ( s )? The distribution of dietary intake for individual food items is often not very normally distributed. An alternative...
Perform a statistical procedure to compare the means of the three groups using the critical-value method? Nutrition Researchers compared protein intake among three groups of postmenopausal women: (1)...
What is the p-value from the test performed in Problem 12.1? Nutrition Researchers compared protein intake among three groups of postmenopausal women: (1) women eating a standard American diet (STD),...
Linux - choose how you will manage your software install packages? Analyse some advantages of using a package manager to manage software?
A firm produces output according to the production function Q = K1/2 1/2. The demand schedule for the output is P= 20 - Q. If K is fixed at 4 units, what is this firm's short-run demand curve for...
Write about the Biden administration's State of the Union address by taking one side and examining how it affects you as an individual. Discuss the policy, economic accomplishments, what he has done...

Use the divergence theorem, assuming that the assumptions on T and S are satisfied. Show that a

Question:

-Hгc V = r cos ф dA

Step by Step Answer:

F x y z div ...View the full answer

Advanced Engineering Mathematics

Students also viewed these Mathematics questions