This project utilizes integral calculus to find the volume of a longboard-style surfboard. The cost for using AirCrete as the material for the longboard will then be calculated. Due to the longboard's shape, the longboard is divided into four sections, and the volume of each is found. The final volume for the longboard with the measurements provided is approximately 3821 cubic inches. The cost of making the longboard out of AirCrete was then calculated by using ratios. The final cost for the longboard is $4.70.
Just like any thermodynamic system, combustion engines must be cooled to eliminate friction due to heat. Without proper cooling, internal components, such as connecting rods, rod bearings, and pistons can be severely damaged due to thermal expansion, leading to severe damage to the engine block or outright catastrophic failure. Modern engines are cooled using coolant, which flows through internal passageways within the engine block to pull heat away from the system. The use of coolant and external components, such as a water pump, radiator, and thermostat allow an engine to efficiently warm to standard operating temperature and remain at said temperature. Using standard calculus and differential equations, the model for the idle coolant temperature increase inside of an engine block as it approaches a steady state can be obtained. For overall application purposes, this model includes an arbitrary number of inlets and exits for coolant to flow through. This model can also be applied to air cooled or electric systems, such as small engines or electrical motors which produce a quantifiable amount of heat.
The careful monitoring of a drug’s concentration in the body of a patient is of the utmost importance in modern medicine. Many of the lifesaving medications that are administered in an emergency medicine environment have a narrow window of efficacy. This effective concentration is in an ever-changing state, as the body processes and eliminates exogenous compounds that are introduced to maintain homeostasis. To ensure the proper treatment and/or management of ailments, special attention must be given to the concentration of a given drug in the body as time progresses. These changing concentrations can be evaluated and tracked using the mathematical tools that are taught in Calculus-themed courses. In this paper, the steps required to accurately calculate the concentration of a given drug in a patient’s body will be examined. We will arrive at a formula that can reliably be used to determine this concentration at a point in time.
Almost every building in the United States has a HVAC (Heating, ventilation, and air conditioning) system that relies on balancing Velocity Pressure and calculated CFM to properly control the atmosphere in a building. This is ensured and tested by Field Engineers whose job it is to maintain the efficiency and proper output of these HVAC systems. These systems are used to improve indoor air quality, control moisture and condensation, and contaminants while satisfying comfort needs of occupants. Just with any mechanical system, HVAC systems function efficiently with multiple formulas derived from calculus and physics. Every building is equipped with a system that needs to meet a certain threshold of air movement, measured in Cubic Feet per Minute (CFM), that creates a stable and comfortable indoor atmosphere by testing and balancing these systems with Velocity Pressure. Velocity Pressure is the base reading it takes to understand and adjust air movement within a HVAC system to guarantee the overall best quality of an indoor air environment. Once a measurement of Velocity Pressure, measured in inches of water column (in-WC) using a tool called a Flow Hood or Straight Pitot Tube, is taken then you can start to calculate flow readings and test if a fan is producing the correct amount of CFM that the system was built to produce and support. This testing is done by using a series of calculus and algebraic equations that takes area and velocity into consideration. When solving these formulas, it can then be determined if a HVAC system and its fans are producing the ideal amount of airflow and air quality to accurately produce the precise environment for any building.
The application of calculus is of great importance in physics. It is used to calculate energy, acceleration, velocity, and much more. In this paper, to calculate the internal energy of an ideal gas (gas molecules) we will use Maxwell-Boltzmann statistical distribution based entirely on calculus. The technique represents the mathematical concept that depends on integration and substitution in calculus to solve a problem.
The discharge of effluents into rivers is something that has occurred a lot throughout our history, rivers like the Mississippi River and the Tiete River (São Paulo, Brazil) have been targets for many years. Therefore, in this paper I choose to show, through hard data and some assumptions, the impact of sewage dumping in water bodies, in this case the Santa Fé River, Florida and the reason why we should avoid dumping these effluents into the rivers.
Beams are extremely important structure members that are used in nearly every application where significant loads need to be supported. In mechanical and civil engineering being able to appropriately design beams to withstand the expected-to-be loads is a foundational skill. Proper beam design is what keeps large machines from failing and buildings from collapsing. One important aspect of beam design to consider is the deflection of the beam due to the applied loads. It is often useful to determine the deflection along any given point in the beam in order to make sure the loaded beam does not displace any brittle materials that may be connected to or around it such as concrete. In this paper, we investigate how to determine the displacement of due to deflection at one point along an overhanging beam
For this project, I wanted to incorporate calculus into agriculture and environmental science methods. More in detail, the problem used asked for the maximum levels of nitrogen (N) and phosphorus (P) that would be best for a current crop yield. This allowed incorporating partial derivatives, and critical points to find the maximum values for the equation. The results show that in order to demonstrate maximum crop yield production, the levels of nitrogen (N) and phosphorus (P) were to be both at 2, with the correct corresponding units. The drawback from this problem is that although the problem showed effective nitrogen and phosphorus levels, it should be determined as to whether those levels, typically in synthetic fertilizers, are more, less, or equal to the suggested amount per bushel. Adding excess nutrients onto a crop can result in nutrient in our waterways due to surface water runoff. The overall purpose would be a moral question for the farmer: Does the farmer add the levels of N and P for the maximum crop yield success, regardless of it being more than the suggested bushel amount?
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.
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.
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.
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.
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.
Implicit differentiation is used in order to find the cubic feet of water dumped into Tampa Bay per hour from the Piney Point reservoir. To get to moles from cubic feet, a series of conversions is done while Le Chatelier’s principle explains how an increase in HPO4 2- (hydrogen phosphate) in Tampa Bay is going to affect algae growth. The rate of moles of HPO4 2- is analyzed as well as the consequences that come with dumping copious amounts of fertilizer water into an aquatic environment.
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.
This project utilizes integral calculus to find the exact volume of a non-uniform cylindrical-shaped silo used to store wheat and calculate the cost of material utilized to build such silo. Due to its non-uniform shape, the silo is divided into two sections and the volume of each is calculated. The final volume for the silo with the measurements provided is approximately 2330.02 meters cubic and surface area of 1074.96 meters squared, which is considered to be a large capacity silo. With such a large capacity silo there are costs to be considered, such as the material cost which is calculated for steel.
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.
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.
