Where is the radius vector from p to any point on s

Assignment Help Mathematics
Reference no: EM131110760

Let be a smooth parametric surface and let P be a point such that each line that starts at P intersects S at most once. The solid angle Ω(S) subtended by S at P is the set of lines starting at P and passing through . Let S(a) be the intersection of Ω(S) with the surface of the sphere with center P and radius a. Then the measure of the solid angle (in steradians) is defined to be

|Ω(s)| = areaf s(a) / a2

Apply the Divergence Theorem to the part of Ω(S) between S(a) and to show that

|Ω(s)| = ∫s∫ (r·n) ds / r3

where is the radius vector from P to any point on S, r = |r|, and the unit normal vector is directed away from P.

48_Solid Angle.jpg

Reference no: EM131110760

Questions Cloud

What is your null hypothesis and alternate hypothesis : What is your null hypothesis? Alternate hypothesis? Is this a one-tailed or two-tailed hypothesis and why? What is the criterion z? Can you check this question?
What is the net torque about the center of the pulley : What is the net torque about the center of the pulley? What is the total angular momentum of the system 3.5 s after release? What is the angular momentum of the pulley at this time?
Evaluate her 2012 financial performance : During the year, Ms. Chen paid interest of $15,000 on the $120,000 borrowed to start the business. She paid an average tax rate of 30% during 2012. Prepare an income statement for Cathy Chen, CPA, for the year ended December 31, 2012. Evaluate her 20..
Identify the crime scenes involved : On the basis of the facts provided, identify the crime scene(s) involved. Outline the steps a forensic technician should take to process the scene.
Where is the radius vector from p to any point on s : et be a smooth parametric surface and let P be a point such that each line that starts at P intersects S at most once. Where is the radius vector from P to any point on S, r = |r|, and the unit normal vector is directed away from P.
Briefly discuss the form and informational content of each : The income statement for the year ended December 31, 2012, the balance sheets for December 31, 2012 and 2011, and the statement of retained earnings for the year ended December 31, 2012, for Technica, Inc., are given below and on the following page. ..
Messner purchased 100 shares of treasury stock : Messner issued 500 shares of its $10 par common stock for a patent. The market value of the shares on the date of the transaction was $23 per share.
What are some sources of stress for a corrections officer : What are some sources of stress for a corrections officer - what are some healthy ways to deal with stress?
Find v for the maximum n : The relative number N of gas molecules in a container that are moving at a velocity v can be shown to be

Reviews

Write a Review

Mathematics Questions & Answers

  Find the height of the solid

The length of one of the equal legs of an isosceles triangle is 8 cm less than 4 times the length of the base.  If the perimeter is 29 cm, find the length of one of the equal legs.

  Determine the total contribution to profit

Determine the total contribution to profit that lies on the objective function (profit line) as it is plotted on the graph if the company produces a combination of cases of Brand X and Brand Y.

  Explain the method use to find the amount of air

Explain the method use to find the amount of air

  How many hamburgers were sold on friday

on friday a local hamburger shop sold a c ombined total of 426 hamburgers and cheeseburgers. The number of cheeseburgers sold was two times the number of hamburgers sold. how many hamburgers were sold on friday?

  P-value approach to test hypothesis

Define Population 1 as this year and Population 2 as last year and use the p-value approach to test this hypothesis with α = 0.05.

  Write the equation expressing cost in terms of distance

the cost varies linearly with the distance and is $366 per month for 300 km driven per month, and $510 per month for 1500 km driven per month. write the equation expressing cost in terms of distance.

  Explain the kinetic energy of a moving object varies

The kinetic Energy (K) of a moving object varies jointly with its mass (m) and the square of its velocity (v). If an object has a mass of 22.5 kilograms and moving with a velocity of 20 meters per second has a kinetic energy of 4500 Joules

  Volume of solid of revolution by integration

The region R is bounded by the graphs of x-2y = 3 and x=y^2. Set up (but not evaluate) the integral that gives the volume of the solid obtained by rotating R around the line x=-1.

  Graph that fits the data

Use the given information to draw the graph of f(x) on an interval near the indicated point (x=3). If there is not enough information given, then state this fact.

  What is the probability that it will be the jack of hearts

One card will be randomly selected from a standard 52-card deck of cards. What is the probability that it will be the jack of hearts?

  What is the probability that you get one marble

A box contains 4 green, 10 red, 6 yellow, and 5 blue marbles. Four marbles are drawn from the box without replacement. What is the probability that you get one marble of each color?

  Find what is the probability it would be a student

What is the probability it would be a student, a faculty member, an admin staff member, a faculty or admin staff member and anyone except an admin staff member?

Free Assignment Quote

Assured A++ Grade

Get guaranteed satisfaction & time on delivery in every assignment order you paid with us! We ensure premium quality solution document along with free turntin report!

All rights reserved! Copyrights ©2019-2020 ExpertsMind IT Educational Pvt Ltd