Project & Resources Table of Contents Project

MAT-20037-XA121 Solve Problems with Math 2… Project & Resources Table of Contents Project Announcements Discussions Project Results JG FAQs Calendar Support Tools Project Instruc!ons Project Instruc!ons Listen # ” ! Competency In this project, you will demonstrate your mastery of the following competency: Solve prac!cal problems using basic mathema!cal calcula!ons Scenario You work for OneEarth, an environmental consul!ng company that specializes in building condi!on assessments, contaminated site remedia!on, and energy audits. Founded by an environmentally concerned ci!zen in 2010, OneEarth has emerged as the highest-quality and most comprehensive environmental services company in the region. Southern New Hampshire University (SNHU), a private nonprofit university located in Manchester, New Hampshire, in the United States, is dedicated to reducing its carbon footprint. SNHU has approached OneEarth for its assistance and exper!se in achieving this goal. Knowing of your desires to diversify your experience and professional por”olio, : your manager, Claire DeAir, has consented for you to join the team working with SNHU. You’re responsible for crea!ng a technical report based on an analysis of the data the onsite team has collected over the last few weeks to determine the cost-effec!veness of SNHU adop!ng solar energy. Direc!ons 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 Suppor!ng Materials sec!on, you will conduct a series of calcula!ons. With those calcula!ons, 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 calcula!ons and determina!ons: A calcula!on of the total electricity output of a solar panel system in kilowa”s hours (kWh) Use the following steps as a guide to making this calcula!on: How many panels fit on the roof, assuming the building is rectangular? (To make this determina!on, 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 direc!on and mul!ply 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 cen!meters? (To convert from inches to cen!meters, mul!ply the dimensions in inches by 2.54 and do not round un!l the last step of the calcula!on.) Find the number of meters for each dimension. How many panels will fit on the roof in each direc!on? Round down to the nearest panel. When calcula!ng 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 adop!ng a solar panel system that covers the en!re roof based on the average monthly sunlight? (1kW = 1000W, and 1 hour of sunlight produces 400 wa$s per panel) How many kW per hour of sunlight could be produced per solar panel? Per en!re 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 en!re solar panel system per month based on the average monthly sunlight? Per year? A calcula!on of the difference between the current electricity usage of the building and the electricity : generated by a solar panel system in kilowa” hours and in dollars generated by a solar panel system in kilowa” hours and in dollars Use the following steps as a guide to making this calcula!on: How much electricity does the building use on average annually? What is the es!mated total amount of kWh produced by the en!re 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 u!lity bill? If the energy generated is more than the energy needed to run the building, how much addi!onal savings is there for energy that can be channeled to other buildings on campus or sold back to the energy company? A determina!on 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 illustra!ng 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 defec!ve. 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 determina!on 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 calcula!on—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 en!re system cost? How much does installa!on cost? What are the government incen!ves? How does that affect the cost? What is the remaining u!lity 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 !me in years should take into account all : energy savings, not just those for the building on which the solar array is installed. energy savings, not just those for the building on which the solar array is installed. A determina!on 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 calcula!on: 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 en!re solar panel system? What is the total remaining u!lity 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 U!lity Bills for 10 Years) = Total 10-Year Saving) A recommenda!on for whether SNHU should install solar energy panels on its buildings based on your calcula!ons An explana!on of whether SNHU should invest in a solar energy system by purchasing it upfront or by leasing it (Base your response on your calcula!ons.) What to Submit Every project has a deliverable or deliverables, which are the files that must be submi$ed before your project can be assessed. For this project, you must submit the following: Technical Report (1,000–1,500 words) Using the data provided in the SNHU Site Data document in the Suppor!ng Materials sec!on, you will conduct a series of calcula!ons. Your computa!ons will inform your recommenda!ons. 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 proposi!on should be informed and supported by your calcula!ons. You can include visual and graphical elements in your report to illustrate your proposi!ons. Suppor!ng Materials The following resource(s) may help support your work on the project: Cita!on Help Need help ci!ng your sources? Use the CfA Cita!on Guide and Cita!on Maker. SNHU Site Data This document contains the data that OneEarth’s onsite team has collected over the last few weeks to determine the cost-effec!veness of SNHU adop!ng solar energy. : Informa!on on Solar Energy Informa!on 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 In this Shapiro Library resource, you can explore solar energy. Reflect in ePor!olio Download Print Open with docReader Ac”vity Details Task: View this topic : Read all about your project here. This includes the project scenario, direc!ons for comple!ng the project, a list of what you will need to submit, and suppor!ng materials that may help you complete the project. Building Location Manchester, New Hampshire 03101 United States of America Building Roof Dimensions: 60 m x 30 m Roof Assessment of the Building The engineering team has inspected the roof and determined:   There are no obstructions on the roof; therefore, the panels can be placed close together. The building is structurally sound and can hold more than 15 kg per square meter of weight. Expected Hours of Sunlight in Manchester, NH (by Month) January February March April May June 163 168 214 227 267 287 July August September October November December 301 277 237 206 143 142 Electricity Usage for the Building Average Electricity Usage (kWh) Annually: 271,253 kWh National Average Cost of Electricity: $0.165 per kWh Note: This is a projection of the building’s energy use over the next 10 years based on the assumption that there will not be a drastic increase or decrease during that period. Solar Panels Size and Weight: 80 in x 40 in x 2 in; 50 lbs Watts: 400 Amps: 9.86A Volts: 40.6 DC Cost: $560.00 per panel Purchasing a Solar Panel System for the Building: Installation: $0.75 per watt Incentives: If you purchase the system upfront, you will receive a 30% discount on the total cost of the panels and the installation. Leasing / PPA a Solar Panel System for the Building Upfront Cost: $0.00 Monthly Payment (Including Savings): $97.00 per panel Remaining Utility Bill: $20/month Duration: 20 years Incentives: Assume that SNHU does not qualify for leasing incentives. ! Chat 24/7 with a Librarian ask@snhu.libanswers.com 844.684.0456 (toll free) Carbon Footprint. Authors: Droujkova, Maria Source: Salem Press Encyclopedia of Science, 2019. 3p. Document Type: Article Subject Terms: Ecological impact Ecology Environmental responsibility Abstract: Carbon footprint is intended to be a measure of the ecological impact of people or events. It is a calculation of total emission of greenhouse gases, typically carbon dioxide, and is often stated in units of tons per year. There is no universal mathematical method or agreed-upon set of variables that are used to calculate carbon footprint, though scientists and mathematicians estimate carbon footprints for individuals, companies, and nations. Many calculators are available on the Internet that take into account factors like the number of miles a person drives or flies, whether or not he or she uses energy efficient light bulbs, whether he or she shops for food at local stores, and what sort of technology he or she uses for electrical power. Some variables are direct, such as the carbon dioxide released by a person driving a car, while others are indirect and focus on the entire life cycle of products, such as the fuel used to produce the vegetables that a person buys at the grocery store and disposal of packaging waste. Full Text Word Count: 1578 Accession Number: 89404314 Database: Research Starters Carbon Footprint Listen American Accent Fields of Study: Fields of Study: Algebra; Data Analysis and Probability; Measurement; Representations. Summary: A carbon footprint is a mathematical calculation of a person’s or a community’s total emission of greenhouse gases per year. Carbon footprint is intended to be a measure of the ecological impact of people or events. It is a calculation of total emission of greenhouse gases, typically carbon dioxide, and is often stated in units of tons per year. There is no universal mathematical method or agreed-upon set of variables that are used to calculate carbon footprint, though scientists and mathematicians estimate carbon footprints for individuals, companies, and nations. Many calculators are available on the Internet that take into account factors like the number of miles a person drives or flies, whether or not he or she uses energy efficient light bulbs, whether he or she shops for food at local stores, and what sort of technology he or she uses for electrical power. Some variables are direct, such as the carbon dioxide released by a person driving a car, while others are indirect and focus on the entire life cycle of products, such as the fuel used to produce the vegetables that a person buys at the grocery store and disposal of packaging waste. : The notion of a carbon footprint is being considered in a wide range of areas, including the construction of low-impact homes, offices, and other buildings. The design must take into account not only the future impact of the building in terms of carbon emissions, but carbon-related production costs for the materials, labor, and energy used to build it. Mathematical modeling and optimization helps engineers and architects create efficient, useful, and sometimes even beautiful structures while reducing the overall carbon footprint. Mathematicians are also involved in the design of technology that is more energy efficient, as well as methods that allow individuals and businesses to convert to electronic documents and transactions rather than using paper. These methods include using improved communication technology, faster computer networks, improved methods for digital file sharing and online collaboration, and security protocols for digital signatures and financial transactions. Manufacturers are increasingly being urged and even required to examine their practices, since manufacturing processes produce both greenhouse gasses from factory smokestacks and waste heat. Mathematicians and scientists are working on ways to recycle much of this heat for power generation. One proposed device combines a loop heat pipe, which is a passive system for moving heat from a source to another system, often over long distances, with a Tesla turbine. Patented by scientist and inventor Nikola Tesla, a Tesla turbine is driven by the boundary layer effect rather than fluid passing over blades as in conventional turbines. It is sometimes called a Prandtl layer turbine after Ludwig Prandtl, a scientist who worked extensively in developing the mathematics of aerodynamics and is credited with identifying the boundary layer. These are in turn related to the Navier–Stokes equations describing the motion of fluid substances, named for mathematicians Claude-Louis Navier and George Stokes. The Navier–Stokes equations are also of interest to pure mathematics, since many of their mathematical properties remain unproven at the beginning of the twenty-first century. Carbon Footprints of People A calculation of the carbon footprints of different aspects of people’s lives, and then the aggregate for a year, is always an estimate. For example, different towns use different methods for generating electricity. Entering data for an electric bill allows for a rough estimate of the household’s carbon footprint, but not exact numbers, which would depend on the electricity generating methods. Houses contribute to carbon footprints through their building costs, heating and cooling, water filtration, repair, and maintenance—all of which use products with carbon footprints. Travel is another major contributor to peoples’ carbon footprints. Daily commutes and longer trips with any motorized transportation contribute to carbon dioxide emissions. When computing carbon footprints, fuel production and storage costs have to be taken into consideration. A man rides a bicycle to work in an effort to reduce his carbon The food that people eat contributes to the carbon footprint if it is transported by motorized vehicles before footprint. By David Dennis being eaten. The movement of locavores (people who eat locally grown foods) aims to minimize the Scotts Valley, CC BY-SA 2.0 carbon footprint of food. Also, different farming practices may contribute more or less to the carbon (http://creativecommons.org/licenses/bysa/2.0), via Wikimedia footprint of food. Commons The objects people use contribute to their carbon footprints. Recycling and reusing reduces the need for landfills, waste processing, and waste removal, all of which have carbon footprints. There are individuals and communities who avoid waste entirely; several countries, such as Japan, have plans to mandate zero-waste practices within the next few decades. Economy and Policy There are two main strategies for addressing carbon footprints. The first strategy is to lower the carbon footprint by modifying individual behaviors, such as traveling by bike, eating locally, and recycling. The second strategy is to perform activities with negative carbon footprints, such as planting trees, to match carbon footprints of other activities. Some companies incorporate activities that offset the carbon footprint of their main production into their business plans, either lowering their profit margins or passing the cost to their customers. There are economic laws and proposals that attempt to integrate carbon footprint considerations into the economy, usually through taxes on use of fuel, energy, or emissions. Carbon dioxide emissions, in economic terms, are a negative externality (a negative effect on a party not directly involved in the economic transaction). Money collected through carbon taxes is : generally used to offset the cost to the environment. Emissions trading is another mathematics-rich area of dealing with carbon footprints economically. Governments can sell emission permits to the highest-bidding companies, matching their carbon footprints, and capping the total emission permits sold. This method allows prices of permits to fluctuate with demand, in contrast with carbon taxes in which prices are fixed and the quantities of emissions can change. Economists model the resulting behaviors, and advise policymakers based on the models’ outcomes. Marginal Abatement Cost Curve “Marginal cost” is an economic term that means the change of cost that happens when one more unit of product is made, or unit of service performed. For physical objects, the curve is often U-shaped. The first units produced are very costly because their cost production involves setting up the necessary infrastructure. As more units are produced, and the infrastructure is reused, the price goes down until the quantities of production reach such levels that the logistic difficulties drive the price per additional units higher again. A marginal abatement curve shows the cost of reducing emissions by one more unit. These curves are usually graphed in percents. For example, such a curve can be a straight line, with the cost of eliminating the first few percent of e…
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