Question: Let S be the surface that bounds a volume V . Show that (a) s dS = 0; (b) 1/3 s dS

Let S be the surface that bounds a volume V . Show that 

(a) ∫s dS = 0;

(b) 1/3 ∫s dS · r = V.

Step by Step Solution

★★★★★

3.31 Rating (169 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer
Step: 1 Unlock

a A corollary of the div... View full answer

blur-text-image
Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock
Step: 3 Unlock

Students Have Also Explored These Related Modern Electrodynamics Questions!

Q:

Let R = M2(Z) and let S be the subset of R where Prove that S is a subring of R. rx- y x-y y r,yez

Q:

Let S be the subspace of R2 spanned by e1 and let T be the subspace of R2 spanned by e2. Is S U T a subspace of R2? Explain.

Q:

Let S be the sample space for an experiment and let A, B with A B. Prove that Pr(A)

Q:

Math& 1 5 1 - Upsal Daily Exercises 2 4 : More related rates practice ( Section 4 . 1 ) \ table [ [ Learning objectives ] , [ Topic , Importance for future classes,Where is it used in the future? ] ,...

Q:

1. Evaluate Vu and V x Vu in each case. (h) u = sin (xyz) 2. Evaluate V . V x y and V x ( V x v) in each case. (Ov = fly)it gla)i 3. Are the parentheses needed in (14), i.e., in V x (V x v)? Explain....

Q:

8. Let S be a smooth surface enclosing a region of volume V. Show that | n . (xit yj +zk) dA=3V, where n denotes the outward unit normal on S, i, j, and k are three unit base vectors of a rectangular...

Q:

806 Chapter Fifteen OPTIMIZATION: LOCAL AND GLOBAL EXTREMA If f is not continuous or the region R is not closed and bounded, there is no guarantee that f achieves a global maximum or global minimum...

Q:

Suppose that a dimension x and the area A = 7x of a shape are differentiable functions of t. Write an equation that relates dA dx to dt dt . . . dA dx dt dtThe dimensions x and y of an object are...

Q:

878 CHAPTER 15 DIFFERENTIATION IN SEVERAL VARIABLES (e) Does P correspond to a minimum or maximum value of f? Re- fer to Figure 12 to justify your answer. Hint: Do the values of f(x, y) 2 increase or...

Q:

\f\f\f\f\f\f\f\fProblems of Calculus 1. Perimeter : P=72 m length:l=? width: w=? P=2 ( l+w ) P=72 m 2 (l+ w )=72 m l+w= 72m l+ w=36 m w=36 ml 2 Area : A=wl Replacing w in the formula of A A=wl=( 36l...

Q:

If the probability density of X is given by And Y = X2, find (a) The distribution function of Y; (b) The probability density of Y. 2xeforx0 0 elsewhere f(x) =

Q:

Compute the taxable income for 2014 in each of the following independent situations: a. Drew and Meg, ages 40 and 41, respectively, are married and file a joint return. In addition to four dependent...

Q:

What are two characteristics of the eclectic paradigm? Multiple select question. It provides a single holistic explanation of foreign direct investment. It offers a good explanation of foreign direct...

Q:

Questions 1. What mistakes did GG make? 2. Is the concept of grocery e-tailing, as attempted by GG, a sound one? Explain. Hint: You may contrast grocery e-tailing with whatAmazon.com does and how it...

Q:

Write the charge balance for a solution of H 2 SO 4 in water if H 2 SO 4 ionizes to HSO 4 and SO 2 4 - .

Q:

For a 0.1 M aqueous solution of sodium acetate, Na + CH 3 CO - 2 , one mass balance is simply [Na + ] = 0.1 M. Write a mass balance involving acetate.

Q:

(a) Following the example of Mg(OH) 2 in Section 7-5, write the equations needed to find the solubility of Ca(OH) 2 . Include activity coefficients where appropriate. Equilibrium constants are in...

Q:

If the Moran Corp. has an ROE of 11 percent and a payout ratio of 20 percent, what is its sustainable growth rate? (Do not round Intermediate calculations and enter your answer as a percent rounded...

Q:

KIN 104 - response time and dual task was there a difference in response time between the SRT single task compared to the SRT dual task? provide and explanation as to why a change was observed/not...

Q:

Voluntary settlements For a firm with outstanding debt of $126,000, classify each of the following voluntary settlements as an extension, a composition, or a combination of the two. a. Paying a group...