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## Mathematical Modeling and Problem Solving schoolwork

Assignment ID Number AFFGEHU83939HD Type of Document Essay Writing Format APA/MLA/Harvard Academic Level Masters/University References/Sources 4 References

Instructions:Mathematical Modeling and Problem Solving schoolwork

MATH125: Unit 2 Submission Assignment Answer Form

Mathematical Modeling and Problem SolvingALL questions below regarding painting a bedroom must be answered.

.Show ALL step-by-step calculations, round all of your final answers correctly, and include the units of measurementFor full credit, all explanations must be given in the spaces provided. Upload this modified Answer Form to the intellipath Unit 2 Submission lesson.Make sure that you submit your work in a modified Microsoft Word document; scanned or handwritten work will not be accepted. If you need assistance, please contact your course instructor.All of the commonly used formulas for geometric objects are just the mathematical models of the characteristics of physical objects. For example, because a basketball is approximately a sphere, it can be partially modeled by its distance from one side through the center (

radius,r) and then to the other side by thediameterformula for a sphere,.D= 2rFor the two-dimensional variables of length (

L) and width (W), theperimeterandareaformulas for a rectangle are mathematical models for the distance around a rectangle (perimeter,P) and the region enclosed by the sides (area,A), respectively, as follows:

P= 2L+ 2WandA=L×WAlong with another variable, height (

H), a three-dimensional rectangular prism’svolumeandsurface areacan be measured. For example, the formulas for a common closed cardboard box’s inside space (volume,V) and outside covering (surface area,SA) are, respectively, as follows:

V = L x W x HandSA = 2(L x W) + 2(W x H) + 2(L x H)For this Submission Assignment, follow Pólya’s principles to solve your problems, as follows:

- Understand the problem.
- Devise a plan.
- Carry out the plan.
- Take a look back.
Include the following in your assignment:

- Explain your interpretation of what the problem is about.
- Develop and write down a strategy for solving this problem; show the steps in the correct order for your attempted solution.
- Did your strategy actually solve the problem? How do you know?
- Suppose that your solution did not solve the problem—what would your next action be?

Painting a BedroomThe walls and ceiling inside your bedroom need to be painted. To save money, you decide that you will paint the bedroom yourself. Use the following information to solve this problem:

- The bedroom is 17 feet long by 18 feet wide, and the ceiling is 9 feet high.
- The inside of the bedroom door will be painted the same color as the walls.
- Two coats of paint will be applied to all of the painted surfaces.
- The room has one window, measuring 3 feet, 9 inches by 4 feet, which will not be painted.

Pólya’s Principle Step 1: Understand the Problem

- Describe in detail what you understand the problem to be. In other words, what problem will you need to solve? Is there enough information to enable you to find a solution to your problem?

Show your work here: (10 points)

- Discuss different ways to construct the room that will be painted. Are there any restrictions on where the window and door will be located? Will the overall amount of paint that is needed change based on where these are placed in the room?

Show your work here: (10 points)

- List the facts that you know. First, find the room dimensions in feet that make a good model for this situation. One strategy would be to sketch the room as follows. Please use this model to complete the following table below.
(3 points)

Side AnswersLength? Width? Height?

- Using the measurements diagrammed above, label all of the rectangular faces in feet in the following table: (5
points)

Face DimensionsCeiling? ?

Face DimensionsLeft Wall? ? Right Wall? ?

Face DimensionsFront Wall? ? Back Wall? ?

- Because all of the ending values are given in feet, find the
window dimensionsin feet. Convert the length of 3 feet, 9 inches strictly into feet.The answer should be in decimal format.Do not round. Note that 12 inches are equal to 1 foot.

Face DimensionsWindow? ?

Show your work here: (5 points)Diagram 2

Wall

14.25’ by 8’

Pólya’s Principle Step 2: Devise a Plan

- Using Pólya’s technique for problem solving, describe
your planto solve this problem in detail. In other words, what is your solution strategy? Discuss the strategy, steps, formulas, and procedures that you will use to answer this problem.

Show your work here: (10 points)

Pólya’s Principle Step 3: Carry out the Plan

- Using the formula concepts and dimensions above, find the bedroom’s total painted
surface area for all of the walls.Show all of the calculations step by step, including the units of measurement, and round your final answer up to the

nearest whole measurementunit in the following table:

AnswerTotal Painted Wall Surface Area With One Coat of Paint?

Show your work here: (8 points)

- Do not forget to subtract the
window’s area. Also, determine the surface area for two coats bydoubling the painted wall’s surface area.Show all of the calculations step by step, including the units of measurement, and round your final answers up to the

nearest whole measurementunit in the following table:

ANSWERSWindow’s Area? One Coat of Wall Paint Excluding the Window’s Area? Painted Wall Surface Area With Two Coats of Paint?

Show your work here: (8 points)

- Using the formulas, concepts, and dimensions above, find the
ceiling’s painted surface area, including the surface areas for one and two coats.Show all of the calculations step by step, including the units of measurement, and round your final answers up to the

nearest whole measurementunit in the following table:

AnswersPainted Ceiling Surface Area With One Coat of Paint? Painted Ceiling Surface Area With Two Coats of Paint?

Show your work here: (8 points)

- Combining the answers from above, find the
total painted surface area, including both coats for the walls and ceiling.Show all of the calculations step by step, including the units of measurement, and round your final answer

upto thenearest whole measurementunit in the following table:

AnswerTotal Painted Surface Area With Two Coats of Paint?

Show your work here: (5 points)

- Assuming that you can paint 100 square feet per hour, what will be the
work timeneeded to paint your bedroom?Show all of the calculations step by step, including the units of measurement, and round your final answer off to the

nearest whole houramount in the following table:

AnswerPainting Time for the Walls and Ceiling?

Show your work here: (8 points)

Pólya’s Principle Step 4: Take a Look Back

- Did this strategy actually solve the problem? How do you know? Demonstrate that
your solution is correct. In other words, explain why the values that you have created are the best times for the job. Was this the best way to solve this problem? If you had to do this again, what would you do differently? What would you do the same?Show your work here: (10 points)

RUBRIC

QUALITY OF RESPONSENO RESPONSEPOOR / UNSATISFACTORYSATISFACTORYGOODEXCELLENTC ontent (worth a maximum of 50% of the total points)Zero points: Student failed to submit the final paper.20 points out of 50: The essay illustrates poor understanding of the relevant material by failing to address or incorrectly addressing the relevant content; failing to identify or inaccurately explaining/defining key concepts/ideas; ignoring or incorrectly explaining key points/claims and the reasoning behind them; and/or incorrectly or inappropriately using terminology; and elements of the response are lacking.30 points out of 50: The essay illustrates a rudimentary understanding of the relevant material by mentioning but not full explaining the relevant content; identifying some of the key concepts/ideas though failing to fully or accurately explain many of them; using terminology, though sometimes inaccurately or inappropriately; and/or incorporating some key claims/points but failing to explain the reasoning behind them or doing so inaccurately. Elements of the required response may also be lacking.40 points out of 50: The essay illustrates solid understanding of the relevant material by correctly addressing most of the relevant content; identifying and explaining most of the key concepts/ideas; using correct terminology; explaining the reasoning behind most of the key points/claims; and/or where necessary or useful, substantiating some points with accurate examples. The answer is complete.50 points: The essay illustrates exemplary understanding of the relevant material by thoroughly and correctly addressing the relevant content; identifying and explaining all of the key concepts/ideas; using correct terminology explaining the reasoning behind key points/claims and substantiating, as necessary/useful, points with several accurate and illuminating examples. No aspects of the required answer are missing.Use of Sources (worth a maximum of 20% of the total points).Zero points: Student failed to include citations and/or references. Or the student failed to submit a final paper.5 out 20 points: Sources are seldom cited to support statements and/or format of citations are not recognizable as APA 6^{th}Edition format. There are major errors in the formation of the references and citations. And/or there is a major reliance on highly questionable. The Student fails to provide an adequate synthesis of research collected for the paper.10 out 20 points: References to scholarly sources are occasionally given; many statements seem unsubstantiated. Frequent errors in APA 6^{th}Edition format, leaving the reader confused about the source of the information. There are significant errors of the formation in the references and citations. And/or there is a significant use of highly questionable sources.15 out 20 points: Credible Scholarly sources are used effectively support claims and are, for the most part, clear and fairly represented. APA 6^{th}Edition is used with only a few minor errors. There are minor errors in reference and/or citations. And/or there is some use of questionable sources.20 points: Credible scholarly sources are used to give compelling evidence to support claims and are clearly and fairly represented. APA 6^{th}Edition format is used accurately and consistently. The student uses above the maximum required references in the development of the assignment.Grammar (worth maximum of 20% of total points)Zero points: Student failed to submit the final paper.5 points out of 20: The paper does not communicate ideas/points clearly due to inappropriate use of terminology and vague language; thoughts and sentences are disjointed or incomprehensible; organization lacking; and/or numerous grammatical, spelling/punctuation errors10 points out 20: The paper is often unclear and difficult to follow due to some inappropriate terminology and/or vague language; ideas may be fragmented, wandering and/or repetitive; poor organization; and/or some grammatical, spelling, punctuation errors15 points out of 20: The paper is mostly clear as a result of appropriate use of terminology and minimal vagueness; no tangents and no repetition; fairly good organization; almost perfect grammar, spelling, punctuation, and word usage.20 points: The paper is clear, concise, and a pleasure to read as a result of appropriate and precise use of terminology; total coherence of thoughts and presentation and logical organization; and the essay is error free.Structure of the Paper (worth 10% of total points)Zero points: Student failed to submit the final paper.3 points out of 10: Student needs to develop better formatting skills. The paper omits significant structural elements required for and APA 6^{th}edition paper. Formatting of the paper has major flaws. The paper does not conform to APA 6^{th}edition requirements whatsoever.5 points out of 10: Appearance of final paper demonstrates the student’s limited ability to format the paper. There are significant errors in formatting and/or the total omission of major components of an APA 6^{th}edition paper. They can include the omission of the cover page, abstract, and page numbers. Additionally the page has major formatting issues with spacing or paragraph formation. Font size might not conform to size requirements. The student also significantly writes too large or too short of and paper7 points out of 10: Research paper presents an above-average use of formatting skills. The paper has slight errors within the paper. This can include small errors or omissions with the cover page, abstract, page number, and headers. There could be also slight formatting issues with the document spacing or the font Additionally the paper might slightly exceed or undershoot the specific number of required written pages for the assignment.10 points: Student provides a high-caliber, formatted paper. This includes an APA 6^{th}edition cover page, abstract, page number, headers and is double spaced in 12’ Times Roman Font. Additionally, the paper conforms to the specific number of required written pages and neither goes over or under the specified length of the paper.## GET THIS PROJECT NOW BY CLICKING ON THIS LINK TO PLACE THE ORDER

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