Question: 5. Let E be the solid tetrahedron bounded by x = 0, y = 0, z = 0, and x+y+z = 1, and suppose that

5. Let E be the solid tetrahedron bounded by x = 0, y = 0, z = 0, and x+y+z = 1, and suppose that its topological boundary, T = 8E, is oriented with outward pointing normal. Prove for all C1 functions P, Q, R: E -T R that Ila E Pdydz + Qdzdx + Rdxdy = II L (Px + Qy + R z) dV.

Step by Step Solution

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock 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 Legal Research Analysis Questions!

Calculate Z. HR. and SR by the Redlich / Kwong equation for one of the following, and compare results with values found from suitable generalized correlations: (a) Acetylene at 300 K and 40 bar. (b)...

Let E be the solid tetrahedron bounded by x = 0, y = 0, z = 0, and x + y + z = 1, and suppose that its topological boundary, T = ÏE, is oriented with outward-pointing normal. Prove for all C1...

QUIZ... Let D be a poset and let f : D D be a monotone function. (i) Give the definition of the least pre-fixed point, fix (f), of f. Show that fix (f) is a fixed point of f. [5 marks] (ii) Show that...

Let A, B be sets. Define: (a) the Cartesian product (A B) (b) the set of relations R between A and B (c) the identity relation A on the set A [3 marks] Suppose S, T are relations between A and B, and...

Exercise 5.4(6,8,9,10) Calculus 3 ( Triple Integrals) Find the mass of the right pyramid that has a square base in the xy-plane. 1 S a: g 1, 1 g y S 1, the vertex at (0, 0,4) and density f(E, y, z) =...

there are 4 questions which all are answered I just want someone to double check them and give corrections (do please dont type it) thanks. div ( v ) = ( d /ax, a/ ay, 2 / 72). (4- 2 x42 - xe cos (y...

Question 1: Applications & Change of Variables Find the mass of a lamina bounded by y = 5%, a: = 1, and y = 0 with the density function a(m,y) = a: + 4 :1 Let E be the solid below the plane 2 = 2 and...

Mass Question 2, 16.6.9 > HW Score: 0%, 0 of Part 1 of 2 O Points: 0 of 1 Find the mass and center of mass of the thin rod with the following density function. p(x) = 3 + sin x, for OSXSI The mass is...

Exercise5.4(1,2,3,4,5,6) Calculus Question 5 0/1 pt 9 100 9 Evaluate 3xz dV where E = {(x, y, z) | 2 (3011 pt 0100 399 @l Find fff z (11/, where E is the solid tetrahedron with vertices (0,0,0),...

Please provide justification for each step: Also, I am hiring a person who can work together for this semester for Calc 2. 1. Evaluate the following antiderivatives. I. sin (x) cos'(x) dr II. sec (x)...

4. [-/16.66 Points] DETAILS MY NOTES PRACTICE ANOTHER Evaluate the triple integral. SSSE Txe dy, where E is bounded by the parabolic cylinder z = 1 - y2 and the planes z = 0, x = 1, and x = - 1. 5....

Which parts of Exercise 7.3 dealt with joint probabilities? In Exercise 7.3 Now suppose that because of the high level of ticket sales, an additional $250 second prize will also be awarded. a) Given...

Royal Company manufactures 20,000 units of part R-3 each year for use on its production line. At this level of activity, the cost per unit for part R-3 follows: Direct materials . . . . . . . . . . ....

Sander Technologies is considering a research project. If successful, the project is expected to lead to sales totaling \ ( \ $ 6 0 , 0 0 0 \ ) annually. The initial cost of the research is expected...

In a cross-sectional study, measurements are made at only one point in time. In Exercises 1116, determine whether the statement is true or false. If the statement is false, rewrite it as a true...

Let E Rn and U be relatively open in E. a) If E, then = . b) If U E 0, then U U = E.

For each of the following sets, sketch E, , and E. a) E = {(x, y) : x2 + 4y2 x2, 0

Let E be a subset of R". a) Prove that every subset A E contains a set B which is the largest subset of A that is relatively open in E. b) Prove that every subset A E is contained in a set B which...

Throughout the project, you have been asked a number of questions relating to the Balance Sheet of ABC Company. Using the Balance Sheet found below, perform a horizontal analysis. Once complete, use...

Which one of the following will decrease the net present value of a project? Group of answer choices increasing the value of each of the project's discounted cash inflows decreasing the required...

You are considering a project with an initial cost of $7,500. In years, what is the payback period for this project if the cash inflows are $1,269, $1,141, $3,929, and $4,500 a year over the next...