Reference no: EM1394308
1. Consider the integral
Express this integral in terms of one or more integrals in the order dz dx dy.
2. Consider a regular octahedron, centred at the origin, with vertices at (±1, 0, 0), (0,±1, 0), (0, 0,±1).
(a) Express the volume of this region as a single triple integral in rectangular coordinates.
(b) Express the volume of this region as a single triple integral in cylindrical coordinates.
(c) Express the volume of this region as a single triple integral in spherical coordinates.
(d) Find the ratio of the volume of the octahedron to the volume of the smallest sphere that can enclose it.
3. Consider a circular disc of radius 1 and thickness 1/10 which has a uniform density p(x, y, z) = 1.
(a) Find the moment of inertia of this disc about its central axis (that is, the line joining the centres of its two circular sides).
(b) What is the relationship of the moment of inertia about the central axis to the thickness of the disc?
4. Consider the polar coordinate transformation x = rcosθ , y = rsinθ as discussed in lectures, and let f(x, y) be a given di erentiable function.
(a) Use the chain rule to give expressions for
in terms of 
and 
.
(b) Rearrange your answer to part (a) to give 
in terms of 
.
(c) Use your answer to part (b) to show that
Make sure that you give explicit expressions for the orthogonal unit vectors ^r and ^θ . Show all working.
5. (a) Evaluate the line integral 
where C is the right half of the circle x2 + y2 = 16. Show all working.
(b) Evaluate the line integral 
where C is the curve parameterised by r(t) = 11t4i + t3j, 0≤ t≤ 1. Show all working.
(c) Evaluate the line integral
where C is the curve parameterised by r(t) = sin(Πt4)i + cos(Πt3)j, 0≤ t ≤ 1. Show all working
6. The position of an object with mass m at time t is given by
where a, b and c are constants. Find the work done on the object during this time period. Show all working.
|
Explain international financial manager at wal-mart
: Write about the international financial manager at Wal-Mart. This is the individual who is in charge of international financial management at Wal-Mart. Also, express the position they hold in the organization.
|
|
Determine minimum required sample size
: Determine the minimum required sample size if you want to be 99% confident that the sample mean is within 2 units of the population mean given sigma = 7.8. Assume the population is normally distributed.
|
|
Relationship of free energy change
: The relationship of free energy change to the concentrations of reactants and products is important because it predicts the direction of spontaneous chemical reactions.
|
|
What is the cash flow to creditors
: Zigs Industries had the following operating results for 2011: sales = $27,960; cost of goods sold = $19,360; depreciation expense = $4,940; interest expense = $2,190; dividends paid = $1,050.
|
|
Find the moment of inertia of disc
: Express the volume of this region as a single triple integral in rectangular coordinates and Express this integral in terms of one or more integrals in the order dz dx dy.
|
|
Alternative hypothesis for the specific situation
: What would be the correct null and alternative hypothesis for the following situation: The sample has a mean of 72.3 mph and a standard deviation of 7.4 mph. Use a 0.05 significance level to test the claim that the mean speed of all cars is greate..
|
|
Sample size calculation for population proportion
: In order that the sample proportion and the population proportion not differ by more than 0.05 with 95% level of confidence, what sample size should be used?
|
|
Discussion on different phospholipases
: What are the different phospholipases that act to hydrolyze the ester linkages of the groups attached to the various carbon atoms of glycerol? At which carbon atom of glycerol are you most likely to have arachidonate bound?
|
|
Define who is more entrepreneurial
: Discuss whether or not Neo forma fits into one of these theories better than the other, or can both be invoked when trying to understand this industry.
|