Impactful Mathematical Equations in Engineering and Technology

Objective:
Research about a Mathematical Equation that had a great impact on advancing Engineering
and technology.
Learning Outcomes:
1. Gaining the basic research skills to conduct research about a scientific topic,
2. Improving the scientific writing skills to enable students to write scientific papers or thesis,
Research Details:
1. The research topic will be assigned to each group by the instructor.
2. The report should have the following: title page, table of contents, introduction, main body,
conclusion, and references. Acknowledgment and dedication should not be included in this
report.
3. The introduction should be about the equation definition, the importance of the equation, in
which field of engineering it is used? Which type of problems it is solving?
4. The main body should present the mathematical history of the equation, its derivation, the
mathematical expression of the equation, and the parameters used in the equation. It may
include a detailed discussion of a specific practical application that utilizes this equation.
5. The conclusion may include the constraints or limitations of the equation, its relation to any
other mathematical equations, a summary of the report, and an outlook of its applications in
future.
6. Note that each figure or table in the report should have a caption, it has to be numbered, and it
has to be referenced appropriately, if taken from an external source.
7. The report including the cover page, table of contents, and references should be between 15
and 20 pages.
Evaluation Criteria:
1. Reports will be evaluated based on clarity, arrangement, accuracy, and completeness. Also, the
originality of the report will be checked to confirm avoiding any plagiarism violation.
2. Presentations will be evaluated based on clarity, arrangement, accuracy, and completeness.
3. Students will be evaluated after the presentation by questions about their project. The main
purpose of this discussion is to investigate the level of understanding of the student.
Make sure there is no plagiarism

📌 Struggling with where to start this assignment? Follow this guide to tackle your assignment easily!

Step 1: Understand the Research Requirements

This research paper requires you to analyze a mathematical equation that has significantly impacted engineering and technology. You will explore its definition, importance, history, derivation, applications, and limitations while maintaining a clear and structured scientific report format.

Step 2: Choose an Equation to Research

Your instructor will assign an equation, but some famous equations that have greatly influenced engineering include:

  • Newton’s Second Law (F = ma) – Essential in mechanical and civil engineering.
  • Maxwell’s Equations – Fundamental to electrical and communications engineering.
  • Navier-Stokes Equations – Used in fluid mechanics and aerodynamics.
  • Fourier Transform – Key in signal processing and engineering analysis.

Step 3: Structure Your Report

Your report should include the following sections:

✅ Title Page – Include the project title, course name, instructor’s name, and group members.

✅ Table of Contents – List all sections and page numbers for easy navigation.

✅ Introduction (1-2 pages)

  • Define the equation.
  • Explain its importance in engineering.
  • Identify the types of engineering problems it solves.
  • Mention industries or technologies that rely on this equation.

✅ Main Body (10-15 pages)

  • Mathematical History – Who developed it? When and why was it formulated?
  • Derivation of the Equation – Provide step-by-step derivation if applicable.
  • Mathematical Expression – Write the equation and define its parameters.
  • Practical Applications – Discuss at least one detailed engineering application. Include case studies or real-world usage.
  • Figures and Tables – Ensure all visuals are numbered, captioned, and referenced correctly.

✅ Conclusion (2-3 pages)

  • Discuss any constraints or limitations of the equation.
  • Relate the equation to other mathematical formulas.
  • Summarize key findings.
  • Provide insights into future applications in engineering and technology.

✅ References – Cite all sources in an appropriate scientific format (APA, IEEE, or as required by your instructor).

Step 4: Writing Tips for a Strong Scientific Report

✔ Maintain a clear and formal writing style. Avoid personal opinions unless relevant.
✔ Use equations, graphs, and figures effectively. Each figure should support your discussion.
✔ Keep your explanations structured. Break complex ideas into smaller sections.
✔ Ensure originality. Avoid plagiarism by properly citing all sources.

Step 5: Prepare for Your Presentation

After submitting your report, you will present your findings. To excel:

  • Summarize key points clearly. Don’t read from the slides; explain concepts.
  • Use visual aids effectively. Graphs and images help illustrate technical concepts.
  • Anticipate questions. Be ready to answer how the equation applies to different engineering fields.

By following this guide, you’ll develop strong research, writing, and presentation skills while mastering an important mathematical equation in engineering. Good luck! 🚀

Exploring Newton’s 3 Laws: A Cosmic Journey into Motion

You are going to create a Podcast/Vidcast about Newtons 3 Laws and share it with the world!
NASA’s DIY Podcast Instructions.pdf Download NASA’s DIY Podcast Instructions.pdfwill take you to NASA’s instruction’s on “Do-It-Yourself Podcasts”.
NASA videosLinks to an external site. will take you to the videos you will use to create your Podcast!
It can be just audio or both audio and video.
Have fun!!
Submit the finished project here! (Either the link to the RSS feed or the audio/video file itself)
Reference the RUBRIC Download RUBRICfor more details on grading!
I provided the links, I’ll just need a transcript written for the “podcast” thanks so much

Struggling with where to start this assignment? Follow this guide to tackle your assignment easily!

Creating a podcast or vidcast about Newton’s 3 Laws is a fantastic project! Here’s a step-by-step guide based on NASA’s DIY Podcast instructions:

 

1. Plan Your Content:

  • Introduction: Start with a brief introduction to Newton’s 3 Laws of Motion and their importance in understanding how objects move. Mention that your podcast/vidcast will explain each law with examples from everyday life and science.
  • Newton’s First Law (Law of Inertia): Explain that an object at rest will stay at rest, and an object in motion will stay in motion unless acted upon by an external force. Use an example like a car coming to a sudden stop and how passengers lurch forward.
  • Newton’s Second Law (F=ma): Explain how force is related to mass and acceleration. For example, use a car pushing a lighter object versus a heavier one. You can also describe how rockets launch into space by applying force to overcome the Earth’s gravity.
  • Newton’s Third Law (Action and Reaction): Discuss how every action has an equal and opposite reaction. A fun example is the launch of a balloon (when air is pushed out, the balloon moves in the opposite direction).
  • Conclusion: Wrap up by summarizing the laws and explaining their relevance in fields like space travel, sports, and even our everyday activities.

2. Format:

  • Audio-Only Podcast: If you’re going for an audio podcast, you can use sound effects or music to make the experience engaging. NASA’s sound resources (like rocket launches or space sounds) could be great additions!
  • Vidcast (Audio + Video): For a vidcast, consider using visuals or animations to illustrate each of Newton’s Laws. You can integrate clips from NASA’s videos to show real-world applications of the laws in space missions or everyday situations.

3. Gather Resources:

  • Review the NASA DIY Podcast Instructions to help with structure, recording tips, and technical details. They might include how to edit, upload, and share your podcast.
  • Check out NASA Videos for content that showcases Newton’s Laws in space. You could use these clips as examples or visual aids in your vidcast.

4. Record Your Podcast/Vidcast:

  • Use a microphone or your phone to record the audio. If you’re creating a vidcast, use video editing software like iMovie, Adobe Premiere, or Windows Movie Maker to combine your narration with visuals.
  • Be clear and engaging! Speak at a comfortable pace, and consider adding a little humor or fun facts to keep your audience interested.

5. Editing:

  • Once your content is recorded, listen through to ensure clarity. Edit out any mistakes or awkward pauses.
  • Add transitions or sound effects, such as the whoosh of a rocket or the sound of a car’s brakes, to reinforce the concepts.
  • If you’re making a vidcast, sync the visuals to your audio.

6. Upload and Share:

  • Follow NASA’s instructions for uploading your podcast or vidcast. Share it with the world on platforms like YouTube, Spotify, or even a personal website.
  • Consider creating a social media post or a blog entry to promote your podcast/vidcast. Use hashtags like #NewtonsLaws #SciencePodcast #SpaceScience to reach a wider audience.

7. Engagement:

  • Encourage your listeners or viewers to share their thoughts. You could ask questions or prompt them to think about how they see Newton’s Laws in their daily lives.

This project is an opportunity to combine your knowledge of Newton’s Laws with creativity and technology to reach an audience that might be curious about physics! Let me know if you need help with anything specific while creating your podcast/vidcast!

write a report on why and how we should care for our oceans includes sсrіptural

write a report on why and how we should care for our oceans includes sсrіptural reasons why we should care about our oceans include specific things we can do to keep oceans, healthy, and white it matters
Important Info

The order was placed through a short procedure (customer skipped some order details).
Please clarify some paper details before starting to work on the order.

Type of paper and subject
Number of sources and formatting style
Type of service (writing, rewriting, etc)

Please read the 4 power points and answer these questions. 1.How do the concepts

Please read the 4 power points and answer these questions.
1.How do the concepts and laws of Physics we’ve been discussing these last 5 weeks pertain to the study of Traditional East Asian Medicine and/or to modern Allopathic medicine?
2. Has studying Biophysics affected your understanding of Traditional East Asian Medicine and/or Allopathic medicine? If so, in what ways?
3.What role do you think science in general, and biophysics particularly, has for the future of Traditional East Asia Medicine?
I would prefer if we can answer the questions more on the Heart and the Thermodynamics how are they connected to Traditional Chinese Medicine. I would touch on the other slides but more so on those two is great. Thanks

– the writer should follow the objective of the project – attached. – the writer

– the writer should follow the objective of the project – attached.
– the writer should follow the report guide format – attached.
– the writer should do some analysis for the 25 dosimeters distributed and dosimeter calibration – attached excel file.
– the writer should write the report based on the project objectives using the provided data and do some analysis and some graphs with explanations of the results acquired.

here mass=m=20g velocity=v=4t^2+3t+6m/s then force at t=2s after differentiatin

here mass=m=20g
velocity=v=4t^2+3t+6m/s
then force at t=2s
after differentiating velocity we get acceleration
differentiate v= 4t^2+3t+6 WRT t
we get dv/dt=8t+3………(1)
put t=2 in (1)
8*2+3=19
so acceleration = 19 m/s^2
we know that,
force=mass*acceleration
force=20g*19m/s^2
=380N
ans:- 380N

Choose a discussion topic that uses physics topics covered in this module. Consi

Choose a discussion topic that uses physics topics covered in this module. Consider one of the following as good topic “starters” for discussion: (i) What were your “Aha!” moments as you worked through the material? (ii) How does this module’s content relate to your professional career? Personal life? (iii) How does this module’s content relate to current events? (iv) Did you more deeply explore a topic only covered lightly in the course materials? What did you discover? (v) What concepts (learning objectives) did you struggle with? What resources helped you overcome this hurdle? Do not post homework problems.
Create an engaging 3-paragraph initial post that ties one or more of the module’s concepts to the real world. The paragraphs should address the following points:
Paragraph 1: Describe the physics concepts/topics you have chosen to discuss from this week’s module, including, as appropriate, a reference to this week’s readings on the topics, terminology with definitions, units, conventions, etc.
Paragraph 2: Summarize one or more impacts of the physics concepts to everyday life or aviation.
Paragraph 3: Either: (i) provide a real example, e.g., from an article or documented report of the aviation impact of this physics concept, or, (ii) give “your take” on the relevance and importance of this topic from your own perspective, by providing personal points of view or related experiences.
Length. Because your initial post will be scored on the degree to which you meet these standards, there is no set minimum word requirement. However, there is a set maximum word requirement – confine your initial post to 500 words. Remember we are all reading each other’s posts, and a succinctly written post is more likely to be read and responded to, thus furthering our discussion on that topic.

Question 1 Assuming a flat surface with no air resistance, if a projectile is fi

Question 1
Assuming a flat surface with no air resistance, if a projectile is fired at an angle of 37 degrees with an initial velocity of 29 m/s, what will be the object’s maximum height? (Note: positive angles are upwards with respect to the surface, and negative angles are downwards with respect to the surface.)
Question 2Question 2
Assuming a cannon elevated 5 meters above the ground and with no air resistance, if a projectile is fired at an angle of 23 degrees with an initial velocity of 11 m/s, what will be the distance the object travels before hitting the ground? (Note: positive angles are upwards with respect to the surface, and negative angles are downwards with respect to the surface.)
Question 3Question 3
A 9-kg block is pulled across a table by a force of 84 N directed at an angle of 28 degrees with respect to the surface of the table. The coefficient of friction between the block and the table is 0.107. What is the magnitude of the force of friction? (Note: positive angles are upwards with respect to the surface, and negative angles are downwards with respect to the surface.)
Question 4Question 4
A 8-kg block is pulled across a table by a force of 55 N directed at an angle of 28 degrees with respect to the surface of the table. The coefficient of friction between the block and the table is 0.137. What is the magnitude of the horizontal acceleration of the block? (Note: positive angles are upwards with respect to the surface, and negative angles are downwards with respect to the surface.)
Question 5Question 5
A 7-kg block is sitting on a ramp angled at 3. The 7-kg block is being pulled to the right by a force of 96 N directed at an angle of 25 degrees with respect to the surface of the ramp. The coefficient of friction between the block and the ramp is 0.126. What is the magnitude of the acceleration of the block along the ramp? (Note: positive angles are upwards with respect to the surface, and negative angles are downwards with respect to the surface.)

Question 1 Assuming a flat surface with no air resistance, if a projectile is fi

Question 1
Assuming a flat surface with no air resistance, if a projectile is fired at an angle of 37 degrees with an initial velocity of 29 m/s, what will be the object’s maximum height? (Note: positive angles are upwards with respect to the surface, and negative angles are downwards with respect to the surface.)
Question 2Question 2
Assuming a cannon elevated 5 meters above the ground and with no air resistance, if a projectile is fired at an angle of 23 degrees with an initial velocity of 11 m/s, what will be the distance the object travels before hitting the ground? (Note: positive angles are upwards with respect to the surface, and negative angles are downwards with respect to the surface.)
Question 3Question 3
A 9-kg block is pulled across a table by a force of 84 N directed at an angle of 28 degrees with respect to the surface of the table. The coefficient of friction between the block and the table is 0.107. What is the magnitude of the force of friction? (Note: positive angles are upwards with respect to the surface, and negative angles are downwards with respect to the surface.)
Question 4Question 4
A 8-kg block is pulled across a table by a force of 55 N directed at an angle of 28 degrees with respect to the surface of the table. The coefficient of friction between the block and the table is 0.137. What is the magnitude of the horizontal acceleration of the block? (Note: positive angles are upwards with respect to the surface, and negative angles are downwards with respect to the surface.)
Question 5Question 5
A 7-kg block is sitting on a ramp angled at 3. The 7-kg block is being pulled to the right by a force of 96 N directed at an angle of 25 degrees with respect to the surface of the ramp. The coefficient of friction between the block and the ramp is 0.126. What is the magnitude of the acceleration of the block along the ramp? (Note: positive angles are upwards with respect to the surface, and negative angles are downwards with respect to the surface.)