Area of Irregular Shaped Roof

This project makes use of calculus, specifically integration, to find the exact area of a roof garden to minimize the cost of material used in flooring it. Since the roof is of irregular shape, it is divided into four sections, the integral of each section is taken, and a relationship between the integrals is generated. Positive results are found, and the data reveal that the area of the grass floor is 175.3 m2 while the area of the wooden floor is 23.4 m2 with the total price being 2472 US dollars.

Mathematical Reconstruction of a Traffic Crash

The objective is to find the impact speeds of two motor vehicles involved in a traffic crash. The calculations take into account the approach (pre-collision) and departure (post collision) angles, as well as weights and post collision speeds of both vehicles. The data is provided by Timothy Sleyzack who investigated this traffic collision. The conclusions confirm the validity of the use of Conservation of Linear Momentum in the field of traffic crash reconstruction.

The Dangers of Lift on Parked Planes: General Aviation Airport Safety

The focus of this paper is to investigate proper aircraft management for safety on an airfield. This is accomplished by looking at lift caused by powerful winds to the aircrafts stored on an airfield, and the tension it places on the rope that secures them. This work could be used to determine when aircrafts are in high-risk and need to be stored either in hangars or moved to other airports prior to storms. The calculations used to determine these conclusions are also explored in the paper.

Calculating Probable Theoretical Offspring Genotype in Fruit Flies

Being able to calculate an offspring's theoretical genotype is critical in genetic sciences. We calculate the theoretical genotype and phenotype of fruit fly offspring. Using the product rule, we determine the probability for each trait and then for each genotype. In conclusion, we calculate 64 different genotypes that are supposed to be possible, but only 8 phenotypes are possible.

Predicting the Cost of Dental Care Using a Probability Model

This paper uses survey data to present a probability model that allows dental offices to predict patient costs. The quantitative model is useful for developing and accepting capitation rates. It accounts for whether the care is initial care or maintenance care, the type of dental care (such as operative, prosthetics, or periodontics), and different age groups, all of which affect the cost of dental treatment.

Calculating the Probability of Constitutional Isomers of Pentane

Depending on the reagent, and orientation of collisions within a chemical reaction, organic molecules can be present as different constitutional isomers of the same molecule. We can analyze the likelihood of getting a mixture of pentane with certain conformers. Based on this, we find that there are 16 potential conformers, but 13 are identical structures, meaning only three are distinct from each other. Using the product rule, we then demonstrate how to go about calculating the probability of specific conformers, including specific identical structures, being present in a mixture, and then we demonstrate that process is strictly within the three different conformers.

Possible Contamination from Rainwater in Community Pool

The project is meant to create an equation that can be used to estimate the amount of organic pollutant – bacteria - that is present in a swimming pool per day from rainwater. This equation is derived through a differential equation of the rate in minus the rate out. The created differential equation is an ordinary linear differential equation and is solved using an integration factor. The general solution is then converted into a specific equation using an initial condition. The resulting equation provides an approximate number of organic contaminants x(t) present in the pool after an amount of time in days (t). The equation finds that the pool – during its closure – has been cleaned often enough. It also provides a method to estimate the amount of contamination from rain after any other extended closures.

Evaluating the Improvement in DNA Fingerprinting

DNA fingerprinting is a forensic technique used to create patterns that are unique to a person’s DNA. Previously, these fingerprints were made from 13 different segments of DNA, but today they are made from the 20 ones. The fundamental principle of counting is used to determine how much of an improvement was made after adding the 7 additional DNA segments. It is found that this addition greatly reduces the likelihood of two people having the same exact fingerprint, therefore improving the accuracy and reliability of DNA fingerprinting.

Using Calculus to Plan an Open-Air Concert

A concert is a mass entertainment event held indoors, at concert halls, or outdoors (open-air festivals). These two formats differ greatly from each other. However, the goal of both events remains the same – to allow the audience to enjoy the musical performance. Indoor halls are designed for the best acoustics of sound. They are often circular and let sound waves travel around the inside of the building, like an echo bouncing back and forth. This makes the audience feel like they are surrounded by sound. Such places already have outlined spots for mounting music equipment with the highest efficiency. Thus, thanks to the fact that the building is engineered exactly for the purpose of conserving the sound, concert holders are not obligated with extra calculations and planning. On the other hand, open-air concerts can range from small, acoustic gatherings at municipal parks, to large music festivals that take place over several days and feature a large number of different artists. Such concerts take great amounts of planning to make sure that the stage is visible and, more importantly, audible from the entire seating area. In this paper, we investigate the physics of sound events of both formats and derive a basic formula for calculating the coverage of a sound system.

Emergency Communications Deficiency Locator

The Bi-Directional Amplifier (BDA) is the newest edition to Life Safety in the state of Florida. The Florida Fire Prevention Code (NFPA 1) section 11.10.1 states that “In all new and existing buildings, minimum radio signal strength for fire department communications shall be maintained at a level determined by the authority having jurisdiction (Committee NFPA 1: Fire Code 2018). That authority having jurisdiction for our local Tampa Bay area is the Hillsborough County Fire Rescue department and they have posted their own requirements along with the Florida Senate for emergency communication standards. All existing “Hi-rise” buildings, 75 feet tall or more, must comply by Jan. 1st 2022, all existing apartment complexes must comply by 2025, and all existing buildings that do not comply with the Hillsborough County Fire Rescue department standards were supposed to have applied for permit by December of 2019 (Senate Florida Legislature) . Several building owners are unaware of the aforementioned changes and it is extremely important to efficiently identify the buildings that do not comply with the latest regulations. To begin determining the best fix for soft spots in public safety radio transmissions I considered three separate FCC callsigns that cover the emergency radio channels around Hillsborough County. Next, I recorded the amount of Watts each tower is using to then convert to decibel gain (dB) that each tower produces. I determined that greater the power (Watts) that you push through a tower has a decreasing rate of decibels produced per watt and therefore not an option to solve the problem at hand. Then I derived an expression for “Free Space Path Loss (FSPL) in dB” that shows the dissipation of radio signal over a given distance. Using this formula, I realized I may not be able to provide an overall solution for the lack of radio signal, but I would be able to locate areas that will require the installation of a radio amplification system. Therefore, using derivative and integration techniques, I have designed a precise method for mapping areas of radio propagation around Hillsborough County, which in turn, show areas that do not receive the minimal -95dB radio strength and must have a BDA installed.