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

Provide a detailed report on below topics and submit all the files (Excel, word and SAP2000)

Design of Transmission towers using SAP2000

L. Houts Plastics is a large manufacturer of​ injection-molded plastics in North Carolina. An investigation of the​ company's manufacturing facility in Charlotte yields the information presented in the table below. How would the plant classify these items according to an ABC classification​ system?

​(Round dollar volume to the nearest whole number and percentage of dollar volume to two decimal​ places.)

Item Code   Avg. Inventory (units)   Value ($/unit)      Dollar Volume        % of dollar volume
1289      400                                 3.50                  _____                         ______
2347 300                                4.00                   1,200                           36.97
2349      120    2.50                     300                             9.24
2363   65   1.50                    ____                            ____
2394                   60    1.75                    105                               3.23
2395   25   1.75                    ____                            _____
6782                   20   1.15                      23                                0.71
7844   12    2.05                      25                                0.76
8210   10    2.00                      ___                                ___
8310      7      2.00                       14                                 0.43
9111                    6   3.00                      18                                 0.55

                                                                                    ___________

                                                                                            3,246

What is the highest dollar volume​ percentage?

The concept of ABC category analysis is based on

A. statistical​ sampling, i.e., sampling a few items to get control of the whole inventory.

B.controlling the maximum number of inventory items with moderate effort.

C.controlling the maximum number of inventory items with minimal effort.

D.controlling the maximum amount of money with minimal effort.

7.Find the number of{0, 1, 2}-strings of lengthn in which 0 appears an even number of times and 1 appears an odd number of times.

A student is standing still at the front doors of Maple. They start running to catch the bus at

2

1. (a) How far away is the bus stop if they reach the bus stop after accelerating from standing still until reaching maximum speed and running at that speed for 1 minute? (assume when they reach the bus stop they are at rest.)

2. (b) Suppose that the student gets to the bus stop and realizes they forgot their laptop in Maple. The next bus arrives in 2 minutes. However, they are extremely tired at this point, and their max running speed is now 6 ft/s. Can they run back to maple and return to the bus stop in time? (Assume their acceleration remains the same)

3. (c) Alternatively, suppose the student is running from Maple Hall to Sieg Hall which is 2000 feet away. Find the time (in seconds) it takes the student to travel this distance. (Assume they are at rest when they reach Sieg.) Use 7ft/s & 2 ft/s^2.

explain in your own words how to construct a perfect square trinomial, a difference of two squares and/or a polynomial with a common factor. In other words, if you were teaching a math class, how would you construct problems to practice one or more of those skills?

Choose one operation (addition, subtraction, multiplication or division) and give an example of that operation on fractions and on rational expressions (you may select an example from Chapter 6 of the text or your MML problem set). Alternatively, you may choose to work with equations containing fractions and equations containing rational expressions. Explain how the procedures are the same and/or different for the two examples.

You have learned several ways to solve quadratic equations – factoring, the square root method, completing the square and the quadratic formula. Pick one method and describe when it is and is not appropriate to use that particular method. Include an example of a problem that is easily solved using your chosen method and one that would be easier solved using a different method.