Solve x(y^2+U)Ux -y(x^2+U)Uy =(x^2-y^2)U, U(x,-x)=1

3. The Krov band is touring the UK. They have played eight dates and already their tour is a great success. Total post-gig sales (merchandising, CDs etc.) on each date have been:

1. Apply the exponential smoothing model with a coefficient of 0.4 to predict the value of post-gig sales after the next tour date (Date no. 9).
2. Compute the Mean Square Deviation (MSD).
3. Exponential smoothing with a coefficient of 0.6 was found to have a MSD = 28.592. Which model is better in terms of prediction?

1. Suppose that you work in a shoe company want to compare two materials, A and B, for use on the soles of boys' shoes. In this problem, each of ten boys in a study wore a special pair of shoes with the sole of one shoe made from Material A in column (Mat-A) and the sole on the other shoe made from Material B in column (Mat-B). The sole types were randomly assigned to account for systematic differences in wear between the left and right foot. After three months, the shoes are measured for wear

data:

• • Weight measurements were made on nine boys in column (weight lb). You know that the distribution of measurements has historically been close to normal with s= 0.2. Test if the population mean is 50 and obtain a 90% confidence interval for the mean. - (Solve manually and Minitab)
• • You want to see if these is difference between the two materials. Justify your answers by using hypothesis testing and confidence interval procedures. - (Solve manually and Minitab)
  • Compare the results from the paired procedure with those from an unpaired- (Solve manually and Minitab)

For each of the following data sets, write a system of equations to determine the coefficients of the natural cubic spline passing through the given points.

x| 2 4 7

-------------

y| 2 8 12

Find the finite-difference solution of the heat-conduction problem
PDE: ut = uxx 0 < x < 1, 0 < t < 1
BCs:
⇢
u(0, t) = 0
ux(1, t) = 0
0 < t < 1
IC: u(x, 0) = sin(pi x) 0 x  1
for t = 0.005, 0.010, 0.015 by the explicit method. Assume

Explain Polya's Theorem and the basic ideas in the proof.

The numbers used in the Trust Funds Model from this lesson are, of course, just estimates. Let’s investigate what happens if these estimates are off by 10%. To do so, answer the following questions:

Using a starting value of $3 trillion in the trust funds in 2032, with an annual rate of decline of 8.7%, how much money will be in the funds in 2040? The answer is 1448

Now let us assume the starting value of the funds was 10% less and the rate of decline was 10% greater than was estimated in the lesson. What is the estimated value of the trust funds in 2040? I need help with this specific question only. Thanks

Exhibit L.1 reports the multivariate odds ratios comparing each category to women who never had an induced abortion and had at least one pregnancy. Researchers were able to interview 845 out of 1,011 (83.5 percent) of the eligible cases and 961 out of 1,239 (78 per- cent) of the eligible controls. Of the cases, only 689 (81.5 percent) had complete information on abortion history, compared to 781 (81.3 per- cent) of the eligible controls.

Note: 1. Estimated from the data. 2. Multivariate OR adjusts for age, family history of breast cancer, religion, age at first pregnancy. 3. Both crude and multivariate odds ratio estimates risk relative to women with a least one pregnancy who never had an induced abortion. Source: Daling et al. (1994).

Calculate the crude odds ratios for each of the abortion history strata in Exhibit L.1. What is the overall increased risk of abortion after adjusting for several covariates?

Use the Chain Rule to find the indicated partial derivatives. N = p + q p + r , p = u + vw, q = v + uw, r = w + uv; ∂N ∂u , ∂N ∂v , ∂N ∂w when u = 4, v = 2, w = 8

Let x = (1,1) and y = (3,1).

1. Find an explicit hyperbolic isometry f that sends the semicircle that x and y lie on to the positive part of the imaginary axis. Write f as a composition of horizontal translations, scalings, and inversions.

2. Compute f(x) and f(y).

3. Compute d_{H^2}(f(x),f(y)) and verify that f is an isometry.

Could Anybody explain about THE CONTRACTION MAPPING THEOREM with easy definition and few easy examples ?

I am having very hard time understanding it :((

Consider the following nonlinear differential equation, which models the unforced, undamped motion of a "soft" spring that does not obey Hooke's Law. (Here x denotes the position of a block attached to the spring, and the primes denote derivatives with respect to time t.) Note: x3 means x cubed not

x''' x′′ - x + x^3 = 0

a. Transform the second-order d.e. above into an equivalent system of first-order d.e.’s.

b. Use MATLAB’s ode45 solver to generate a numerical solution of this system over the interval 0 ≤ t ≤ 6π for the following two sets of initial conditions.

i. x(0)=2,x′(0)=−3

ii. x(0) = 2, x′(0) = 0

c. Graph the two solutions on the same set of axes. Graph only x vs. t for each IVP; do not graph x′. Be sure to label the axes and the curves. Include a title that contains your name and describes the graph, something like “Numerical Solutions of x′′ +x− x3 = 0 by I. M. Smart.” (obviously your name!). Make sure to include a date/time stamp on the graph, Note: To get x′′ to appear in your title you will have to type x′′′′ in your MATLAB title command.

d. Based on your graph, which solution appears to have the longer period? Explain clearly how you arrived at your answer