Solve Problems with Math /AN

Solve problems with math project instructions

 

 

Directions

You’ve been asked to recommend whether or not SNHU should install solar energy panels on one of its buildings in Manchester, New Hampshire, to reduce the university’s carbon footprint. Using the data in the SNHU Site Data document in the Supporting Materials section, you will conduct a series of calculations. With those calculations, you will create a technical report for SNHU that explains whether the university should invest in solar energy by purchasing the system or by leasing. Your technical report should include the following calculations and determinations:

• A calculation of the total electricity output of a solar panel system in kilowatts hours (kWh)
  Use the following steps as a guide to making this calculation:

• • How many panels fit on the roof, assuming the building is rectangular? (To make this determination, determine the number of panels that can fit along one side, and the number of rows of panels that can fit along the opposite side. Round down to the nearest whole number of panels in each direction and multiply to obtain the required number of panels.)

• • • What are the dimensions of the building’s roof in meters?

• • • What are the dimensions of each solar panel in centimeters? (To convert from inches to centimeters, multiply the dimensions in inches by 2.54 and do not round until the last step of the calculation.) Find the number of meters for each dimension.

• • • How many panels will fit on the roof in each direction? Round down to the nearest panel. When calculating the number of panels, be sure that when you change from length to width on the roof, you also change from length to width on the panels.
    • Find the area of the panels in meters to make sure that the area of the panels is less than the area of the roof.

• • What is the total amount of electricity that could be produced by adopting a solar panel system that covers the entire roof based on the average monthly sunlight? (1kW = 1000W, and 1 hour of sunlight produces 400 watts per panel)

• • • How many kW per hour of sunlight could be produced per solar panel? Per entire system (based on how many panels could fit on the roof)?

• • • How many hours of sunlight are expected on average per month? Calculate the average hours based on the monthly data provided. Round down to the nearest tenth of an hour.

• • • What is the likely average amount of kWh produced per panel based on the average amount of sunlight per month? Per year? Round to the nearest hundredth kWh.

• • • What is the total amount of kWh that is produced by the entire solar panel system per month based on the average monthly sunlight? Per year?

• A calculation of the difference between the current electricity usage of the building and the electricity generated by a solar panel system in kilowatt hours and in dollars
  Use the following steps as a guide to making this calculation:

• • How much electricity does the building use on average annually?

• • What is the estimated total amount of kWh produced by the entire solar panel system on this building per year, based on the average monthly sunlight for the area?

• • Based on the average cost of electricity in the area, about how much is the annual electricity cost for the SNHU building?

• • • Is the amount of electricity generated by the solar array sufficient to cover SNHU’s yearly electricity usage?

• • • If not, what is the remaining energy needed in kW? How much would this cost in dollars? In other words, what is the remaining utility bill?
    • If the energy generated is more than the energy needed to run the building, how much additional savings is there for energy that can be channeled to other buildings on campus or sold back to the energy company?

• A determination of the likelihood of receiving a damaged panel
  SNHU expressed some concerns about receiving damaged solar panels from the manufacturer. You would like to be transparent and address these concerns by illustrating the likelihood of a damaged panel based on the size of the system SNHU would be purchasing.

The manufacturer has reported that since solar panels are complex and evolving technology, 1 out of every 1,000 manufactured solar panels is defective.

• • How many panels fit on the roof?

• • What is the probability or likelihood that SNHU will receive a damaged solar panel, based on the number of panels it would be purchasing?

• A determination of how long it would take to pay back the cost of buying the system in years
  Use the following steps as a guide to making this calculation—you can assume there will not be any required maintenance during the first 10 years:

• • What would be the upfront cost to purchase and install the solar panel system?

• • • How much does each panel cost? How much does the entire system cost?

• • • How much does installation cost?

• • • What are the government incentives? How does that affect the cost?

• • • What is the remaining utility cost, if there is one?

• • How much will your solar panels save SNHU per year?

• • How long would it take to pay back the cost of purchasing the solar panel system in years? (Years = Cost to Purchase and Install Solar Panel System / Savings Per Year) The time in years should take into account all energy savings, not just those for the building on which the solar array is installed.

• A determination of whether there is a cost savings over 10 years for leasing the solar panel system
  Use the following steps as a guide to making this calculation:

• • What is the total cost without solar for 10 years, in dollars?

• • What is the total cost with solar for 10 years, in dollars?

• • • How much does it cost to rent the entire solar panel system?

• • • What is the total remaining utility bill for 10 years?

• • What are the 10-year savings? (Cost Without Solar for 10 Years – (Cost of Solar Panel Rental for 10 Years + Remaining Utility Bills for 10 Years) = Total 10-Year Saving)

• A recommendation for whether SNHU should install solar energy panels on its buildings based on your calculations

• An explanation of whether SNHU should invest in a solar energy system by purchasing it upfront or by leasing it (Base your response on your calculations.)

 

 

 

 

 

 

 

 

Supporting Materials.

 

 

 

 

Information on Solar Energy
Website: All About Solar Energy
Use this resource to learn more about everything you would need to know about solar energy.

 

Reading: Solar Energy

References

Plitnik, G. R. . B. A. . B. S. . M. A. . P. D. (2020). Solar Energy. Salem Press Encyclopedia of Science.

 

Reading: Carbon Footprint
In this Shapiro Library reading, you will learn the basics of carbon footprints, which are mathematical calculations related to individuals’ emissions of greenhouse gases.

References

Droujkova, M. (2019). Carbon Footprint. Salem Press Encyclopedia of Science.

 

 

 

More references

https://www.youtube.com/watch?v=kn83BA7cRNM

https://www.purplemath.com/modules/meanmode.htm

https://www.khanacademy.org/math/algebra-home/alg-basic-eq-ineq/alg-old-school-equations/v/averages

https://www.onlinemathlearning.com/mean-frequency-table-interval.html

https://www.khanacademy.org/math/ap-statistics/summarizing-quantitative-data-ap/mean-median-more/a/mean-as-the-balancing-point

https://www.khanacademy.org/math/ap-statistics/summarizing-quantitative-data-ap/mean-median-more/v/using-mean-to-find-missing-value

https://courses.lumenlearning.com/introstats1/

 

https://www.khanacademy.org/math/ap-statistics/summarizing-quantitative-data-ap/mean-median-more/v/impact-on-median-and-mean-when-removing-lowest-value-example

 

https://www.khanacademy.org/math/pre-algebra/pre-algebra-ratios-rates/pre-algebra-ratios-intro/v/ratio-example-problems

 

https://www.purplemath.com/modules/ratio.htm

 

https://cnx.org/contents/XeVIW7Iw@4.6:YrS9v2Z0@2/Ratios-and-Rates

https://www.purplemath.com/modules/units.htm

 

https://www.khanacademy.org/math/pre-algebra/pre-algebra-ratios-rates/pre-algebra-rates/v/introduction-to-rates

 

https://phet.colorado.edu/en/simulation/unit-rates

 

https://www.purplemath.com/modules/distance.htm

 

https://www.khanacademy.org/college-careers-more/personal-finance/pf-interest-and-debt/pf-credit-card-interest/v/annual-percentage-rate-apr-and-effective-apr?modal=1

 

https://www.khanacademy.org/college-careers-more/personal-finance/pf-interest-and-debt/pf-credit-card-interest/v/how-credit-card-interest-is-calculated?modal=1

 

https://www.youtube.com/watch?v=OyddY7DlV58

 

https://www.khanacademy.org/math/statistics-probability/probability-library/basic-theoretical-probability/a/probability-the-basics

 

https://www.khanacademy.org/math/statistics-probability/probability-library/basic-theoretical-probability/v/simple-probability

 

https://www.youtube.com/watch?v=oZCskBpHWyk

 

https://www.khanacademy.org/math/statistics-probability/probability-library/experimental-probability-lib/v/making-predictions-with-probability

 

https://courses.lumenlearning.com/wmopen-mathforliberalarts/chapter/module-1-overview/

 

https://www.youtube.com/watch?v=sxQaBpKfDRk

https://www.youtube.com/watch?v=tN9Xl1AcSv8

 

https://www.youtube.com/watch?v=ZwqOoD17_LU

https://www.youtube.com/watch?v=ldU1Fr5mSOM

https://courses.lumenlearning.com/wmopen-mathforliberalarts/chapter/introduction-data-collection-basics/

 

https://courses.lumenlearning.com/wmopen-mathforliberalarts/chapter/introduction-representing-data-graphically/

 

 

What to Submit

 

Technical Report (1,000–1,500 words)
Using the data provided in the SNHU Site Data document in the Supporting Materials section, you will conduct a series of calculations. Your computations will inform your recommendations. First, you will determine whether or not SNHU should adopt solar panels. Then, you will explain whether or not SNHU should purchase or lease a solar panel system. Specifically, you will reference and incorporate the energy output of a solar panel system, the difference between current usage and the energy generated by the system, the likelihood of a damaged panel, the costs to pay for the system, and any savings for leasing a panel. Your proposition should be informed and supported by your calculations. You can include visual and graphical elements in your report to illustrate your propositions.