## Parallel Transported Lines

Symmetries of Parallel Transported LinesConsider two lines, r and r’, that are parallel transports of each other along a third line, l. Consider now the geometric figure that is formed by the three lines and look for the symmetries of that geometric figure.What can you say about the lines r and rl Do they intersect? If so, where? Look at the plane, spheres, and hyperbolic planes.If a transversal cuts two lines at congruent angles, are the lines, in fact parallel in the sense of not intersecting?Suggestions can be found on the book.Problem 9.1, 9.2 and 10.1 Due date is March 6thProblem 9.1 Side-Side-Side (SSS)Are two triangles congruent if the two triangles have congruent corresponding sides?SuggestionsStart investigating SSS by making two triangles coincide as much as possible, and see what happens. For example, in Figure 9.2, if we line up one pair of corresponding sides of the triangles, we have two different orientations for the other pairs of sides as depicted in Figure 9.2. Of course, it is up to you to determine if each of these orientations is actually possible, and to prove or disprove SSS. Again, symmetry can be very useful here. 6n a sphere, SSS doesnt work for all triangles. The counterexample in Figure 9.3 shows that no matter how small the sides of the triangle are, SSS does not hold because the three sides always determine two different triangles on a sphere. Thus, it is necessary to restrict the size of more than just the sides in order for SSS to hold on a sphere. Whatever argument you used for the plane should work for suitably defined small triangles on the sphere and all triangles on a hyperbolic plane. Make sure you see what it is in your argument that doesnt work for large triangles on a sphere.

## Ford Agency

Using matlab to do the “The Gradient Method” and “Newton’s Method”

## Planet Marketing Management

Video link : https://www.dropbox.com/s/osgf0qw222dal1w/Wild_Planet.mov?dl=0What type of research design options and strategies are leveraged at Wild Planet?Are they using Exploratory, Descriptive or Causal Research Design techniques? What specific methodologies did you notice in the video?Is there anything further you would recommend for Wild Planet marketing management to give them the information to further grow their business?

## County Building

Assuming that in 2014, Broward County had 952 miles of paved roads. Starting in 2015, the County has been building 12 miles of new paved roads each year. At this rate, how many miles of paved road will Broward County have in 2030? (Assume that no paved roads go out of service and nothing block the project.). What would be your approach to solve this problem? Elaborate. 250 words

## Alternative Hypothesis

Homeworkweek61(11.9pg.409)ThefollowingdatarepresentsthepriceofregulargasolineatselfservicestationsinfourcountiesinNewYorkCityMay17,2014ManhattenBronxQueensBrooklynnassauSuffolk2.3392.1992.2392.1592.0992.1792.2992.1392.2392.1992.1992.1592.2392.2392.1792.3592.2592.1192.1992.1592.2992.1592.2392.1592.1992.1792.2791.9992.2392.219At the .05 level of significance, is there evidence of a difference in the mean price of gasoline in the six countiesa. State the null hypothesis, state the alternative hypothesisb. using excel, analyze the gas data using the ANOVA:single factorc. explain your results comparing the F results to Fcritical and how this determines whether we can accept or reject Ho. What is your conclusion from this analysis.2. (12.5 pg. 452) A sample of 500 shoppers was selected in a large metropolitan area to determine various information concerning consumer behavior. Among the questions asked was Do you enjoy shopping for clothing? the results are summarized in the following contingency tableGENDEREnjoy Shopping for ClothingMaleFemaleTotalyes136224360no10436140Total24260500a. Is there evidence of a significant difference between the proportion of males and females who enjoy shopping for clothing at the .01 level of significance? Watch the video provided to do this problem in Excel.c. What is your answer to a) if 206 males enjoyed shopping for clothingClass Work week 6 problem.xlsx Class Work week 6 problem.xlsxFebruary 21 2020, 3:33 PM

## Mathematical Explanation

Topic: Categories of continuity: uniform continuity, absolute continuity, Lipschitz continuityThe written portion of this project should be around 5-7 pages (before references). Each write-up should include the following three components:1- Historical context/motivation.2- Detailed mathematical explanation.3- Discussion of how the results/ideas/concepts are used more broadly.In terms of writing style, write as though you were writing part of a textbook (directed to college students who are taking upper classes). In the “detailed mathematical explanation” make sure to explain any new notation, provide plenty of justification for the steps in the proof, and explain as best as you can the overall strategy of the proof.Please include a references section at the end.you can use the book I uploaded.please do not Plagiarism

## Fundamentals Of Geometry

Respond to one or more of the following in a minimum of 175 words:This week we learn about the foundations of geometry. Geometry uses various modes of thinking. Describe inductive and deductive reasoning. Provide some examples from everyday life that compare and contrast these two ways of thinking?Where in your world do you see segments, rays, and angles? If you were going to explain these geometric figures to someone how would you describe them?Discuss the different types of angles we will be learning this week and also discuss some special angle pairs.