1) What is the best estimate for the distance covered between t=2 s and t=10 s by using Romberg integration (based on Trapezoidal rule)? Use three different h values of 2, 4 and 8.

Describe the boundary lines for two- variable inequalities. Why are the boundary lines for two- variable inequalities with greater than and less represented by dotted lines? Provide examples.
First, define a boundary line and tell where it comes from. Then, describe what the boundary line can tell us about solutions to an inequality. You can also talk about how to know what part of a graph to shade. Finally , talk about the cases where we use each type of boundary line. ( solid and dotted/ dashed).
Real - life Relationship: If you have 100 $ available to buy party favors ( 3$ per bunch of balloons and 4 $ per bag of candy) than you can solve an inequality to find the possibilities . If x = # of bunches of balloons and y= number of bags of candy then we want to solve: 3x+ 4y<=100.
Some possible solutions are: no bunches of balloons and 25 bags of candy,20 bunches of balloons and 10 bags of candy. There are other possibilities!
Challenge: Imagine we have two boundary lines: one solid and one dashed. If they are not parallel is the point where they meet included in the solution? Why or why not?
If you are not sure, try an example, such as y < x + 1 and y < = 2x-4. Graph both boundary lines and find the point of intersection. Then , see if the coordinates satisfy both inequalities.

On 5/17/2020, a random sample of 1007 U.S. households finds that Trump has a 49% approval rating.

a) Use the 2SD method to find a 95% confidence interval estimate of the proportion of all U.S. households that approve of Trump on 5/17/2020. Show all work/steps to get the 2SD estimate. Round the margin of error to three decimal places. Work and Answer:

b) Use your answer from part (a) to fill in the red spaces below in order to write the results of the poll in these two notations:

According to the poll, on 5/17/2020, Trump has an approval rating of 49% ± _________%

According to the poll, on 5/17/2020, Trump’s approval rating was between ______% and ______%

c) If we were to use this same sample information to find a 90% confidence interval estimate instead of a 95% confidence interval estimate, then would our new 90% confidence interval be wider, or would it be narrower than the 95% estimate? Work and Answer:

solve using laPlace dy/dt+4y=40sin3t; y(0)=6 Please show all steps and write neat, thanks!

1. A tank initially contains 200 liters of saltwater, with a concentration of 2g/L salt. Saltwater with a concentration of 5g/L flows into the tank at 2L/min and the well-mixed solution flows out of the tank at the rate of 4L/min.

(a) Set up, but do NOT solve, the initial value problem whose solution will be the VOLUME OF LIQUID in the tank as a function of time

(b) Solve the IVP from the previous part and find the volume of liquid in the tank as a function of time.

(c) Set up, but do NOT solve, the initial value problem whose solution will be the MASS OF SALT in the tank as a function of time.

(d) Solve the IVP in part (c) and determine the mass of salt in the tank as a function of time (Show your work)

You are responsible for developing a supervisory training programme for a company. The following table shows the relationships between the activities that must be completed, along with estimates of the durations in days.

Table 1: Activity Times and Predecessors

Required
(a) Draw the activity network for this problem (either AON or AOA)
(b) Determine the Expected Time and Variance for each activity (show in a table).
Round off times to two decimal places where fractional.
(c) Show the activity schedule (ES, EF, LS, LF) as well as slack (in table).
(d) Determine and state the critical path for this project. This must be based on
your work in c) and not by inspection.
(e) What are the expected time and the variance of the project?
(f) What is the probability the project will be finished within 49 days?
(g) What time should be set such that there is a 99% chance of completion?
(h) What is the probability the project will take between 45 and 50 days?

MATH 383: WORKSHEET 9, WEDNESDAY APRIL 1Name:Problem 1.Write down the solution of the system of equationsc1−2c2+c3−c4=−2c2+ 2c3+ 2c4= 5c3+c4= 1c4=−1.What does the augmented coefficient matrix look like in this example?Problem 2.In this problem we will solve the system of equations−c1+c2+ 2c3−c4= 1c1+ 2c2−c3+ 0c4=−33c1−c2+c3+ 2c4= 80c1+c2+c3+c4= 2using elementary row operations.a) Write down the augmented coefficient matrix for this system of equations.

Using Matlab

1. Solve the following equations set

f1 (x1,x2) = sin (sin (x1)) +x2

f2 (x1,x2) = x1+ e^(x2)

a) Can this equation set be solved by the fixed - point method with the following expressions? And why? Show your analysis with a 2D graph.

g1 (x1,x2) = -e^(x2)

g2 (x1,x2) = -sin⁡(x1)

b) Use Newton Raphson Method with initial values x1 = -2, x2 = 1.5. (8 significant figures. Please submit the code and results.)

Geostatistics deviates from classic statistics in that Geostatistics is not tied to a population distribution model that assumes, for example, all samples of a population are normally distributed and independent from one another. Most of the earth science data (e.g., rock properties, contaminant concentrations) often do not satisfy these assumptions as they can be highly skewed and/or possess spatial correlation. a. Illustrate with the aid of diagram how and why any of such Earth Science data obtained from a given field would be skewed and possess spatial correlation. b. How would the spatial correlation property aid the Geostatistician in predicting the values of the unknown data points of a given field?

List the left and right cosets of H = {(1), (23)} in S3. Are they the same collection?

y''-2ay'+a^2y=60xe^{ax}+60x^2e^{ax}

Use the method of undetermined coefficients to find a particular solution for each equation. Then solve each equation for real general solution.

this is a non homogeneous differntial equation

1. Project flow and Report Format

The following information must be included in your report:

Abstract

Table of Content

List of Figures

List of Tables

LIST OF ABBREVIATIONS

Part 1: Introduction

Part 2: Literature Review

Part 3: Methodology

Part 4: Result and Discussion

Part 5: Conclusions

Part 6: References

Appendix

Initial Value Problem. Use Indeterminate Coefficients method for this problem:

y'' - 4y = sin(x)

where: y(0) = 4 and y'(0) = 8

On Matlab use BFGS Method to find the minimum of the following function: f(x) = x₁³ - 2x₂x₁² + x₁² - x₁using initial point (x₀, y₀) = (1, 2)^T to start, and stop when f changes less than 0.0001

2. (a) Solve the complex equation (1+?)?³−[1+?^?(?3)]=0 and list all possible solutions in Euler’s form with principal arguments.
(b) Express the complex number ?=(1−sin?+?cos?)²⁰ in Euler’s form.