Determine the mass of the hemisphere, Mathematics

Question 1. Use cylindrical coordinates to nd the mass of the solid of density ez which lies in the closed region  292_Determine the mass of the hemisphere.png

Question 2. The density of a hemisphere of radius a (y  0) with its base centred at the origin is given by (x; y; z) =2374_Determine the mass of the hemisphere1.png

 Determine the mass of the hemisphere. Note that sphere is not in the upper half space z > 0.

Hint: The identity cos(2θ) = cos2θ  - sin2θ may be useful.

Question 3. Determine whether or not the vector eld F(x; y; z) = 14xyi + (7x2+ 18yz)j + 9y2k is conservative. If it is conservative, nd a function f(x; y; z) such that

1240_Determine the mass of the hemisphere2.png


Question 4. Evaluate the line integral

402_Determine the mass of the hemisphere3.png

where C is the curve from (0; 0) to (0; 2) consisting of the path from (0; 0) to (1; 1) along the parabola y = x2 , followed by the path along straight line from (1; 1) to (0; 2).

Question 5. A particle starts at the point (-4,0), moves along the x-axis to (0,0) and the y-axis to (0,4) and then along the arc y =955_Determine the mass of the hemisphere4.png to the starting point. Use Green's theorem to nd the work done on this particle by the force eld F(x; y) = (18x; 6x3
+ 18xy2 ).

(Hint: Work done by a force eld F along a curve C is given by the line integral1119_Determine the mass of the hemisphere5.png

Posted Date: 2/16/2013 4:57:37 AM | Location : United States

Related Discussions:- Determine the mass of the hemisphere, Assignment Help, Ask Question on Determine the mass of the hemisphere, Get Answer, Expert's Help, Determine the mass of the hemisphere Discussions

Write discussion on Determine the mass of the hemisphere
Your posts are moderated
Related Questions
Q. Determine Z-scores and Percentiles? Ans. Z-scores help measure how far a piece of data is from the mean. More specifically, Z-scores tell how far a piece of data is fr

Provide me some Examples of solve quadratic equations by Factorization

1. A rectangular piece of cardboard measuring 26 inches by 42 inches is to be made into a box with an open top by cutting equal size squares from each comer and folding up the side

Poisson Probability Distribution -  It is a set of probabilities which is acquired for discrete events which are described as being rare. Occasions similar to binominal distri

the sides of a quad  taken at random are     x+3y-7=0              x-2y-5=0 3x+2y-7=0               7x-y+17=0  obtain the equation of the diagonals

Utilizes the definition of the limit to prove the given limit. Solution In this case both L & a are zero.  So, let ε 0 so that the following will be true. |x 2 - 0|

What is Angle Pairs in Parallel Lines ? Next, we introduce several angle pairs formed by transversals which are very important in our study of geometry. Alternate interior an

A graph with a positive slope shows that the variables depicted on the axes goes in the similar directions.