Algebra Basics, Equations, And Mathematical Models

1271 words - 5 pages

Background Information:A simple pendulum, such as a rock hanging from a piece of string or the inside of a grandfather clock, consists of a mass (the rock) and a support (the piece of string).When the mass is moved a small distance away from its equilibrium point (the bottom of the arc), the mass will swing back and forth in a constant amount of time called the period. One period is the amount of time required for the mass to swing all the way to the other side and then swing back to its staring point.Note: For the purpose of this assignment, we are making the simplifying assumption that our pendulum is swinging in a perfect vacuum, (i.e., there is no air resistance that will stop the pendulum).The period of a simple pendulum is normally expressed using the variable T and is measured in seconds. It can be calculated using the length of the pendulum, L, and the acceleration due to gravity, g, using this expression:The gravity that holds us on the earth and makes objects fall is familiar to all of us. What may not be quite as well-known, however, is that the acceleration due to gravity is actually determined by the mass (amount of material) and the radius of our planet (Note: The radius of a planet is the distance from the center of the planet to its surface.) If we represent the mass with the variable M (measured in kilograms) and the radius by the variable r (measured in meters), the acceleration due to gravity for a planet can be found from the expression:Where G is a constant called the Universal Gravitational Constant. This constant has the value as shown here:Search the Internet and the Cybrary to find the mass and radius of three of the nine planets in our solar system. Be sure that the masses are expressed in kilograms and the radii are expressed in meters. Using your data, calculate the gravitational acceleration on each of the three planets you selected.Note: With the masses measured in kilograms and the radii in meters, the units of gravitational acceleration would turn out to be meters per squared seconds.The formula for planetary gravitational acceleration of mass m and radius r is g =Gm/r2, G is Newton's Universal Gravitational Constant =...

Find Another Essay On Algebra Basics, Equations, and Mathematical Models

The History of Math Essay

4801 words - 19 pages well as to the applications of mathematics. He wrote textbooks on calculus, mechanics, and algebra that became models of style for writing in these areas. The success of Euler and other mathematicians in using calculus to solve mathematical and physical problems, however, only accentuated their failure to develop a satisfactory justification of its basic ideas. That is, Newton's own accounts were based on kinematics and velocities, Leibniz's

MATHEMATICS -ARA Essay

4768 words - 19 pages greatest mathematician of the 18th century was Leonhard Euler, a Swiss, who made basic contributions to calculus and to all other branches of mathematics, as well as to the applications of mathematics. He wrote textbooks on calculus, mechanics, and algebra that became models of style for writing in these areas. The success of Euler and other mathematicians in using calculus to solve mathematical and physical problems, however, only accentuated their

history of mathematics

969 words - 4 pages several mathematical advancements that are very much in use until today. Some of the concept which are part of Hindu mathematics and which are also studied today are the solutions of quadratic, cubic and quartic equations including the basic concept of infinitesimal calculus and spherical trigonometry. In general, Hindu mathematics ‘contributions to our modern-day math includes arithmetic, algebra, geometry, Mathematical logic, general mathematics

Solving the Algebraic Problem

718 words - 3 pages become better at a subject they enjoy and have motivation to study something they love? Today students study and do their homework so they can pass the class, not to sit there and actually absorb the information that teachers try to teach. Today multiple occupations don’t even utilize algebraic equations to figure out the problem at work. Multiple companies have to teach their own math because schools focus on calculus, algebra, trigonometry, etc

David Hilbert

976 words - 4 pages contain numerical, coefficients of algebra. Problem 12. Extension of Kroneker's theorem on abelian fields to the realm of algebraic rationality. Problem 13. Impossibility of solving the general equation of the 7-th degree by using functions of only two arguments. (Generalizing the impossibility of solving 5-th degree equations by the use of radicals.) Problem 14. Proofing the finiteness of certain mathematical functions. Problem 15. The

George Boole and Mathematics

657 words - 3 pages papers that he wrote about his findings.While editing booles journal gregory came to an untimely death ,due to sickness, and passed on his teachings to boole from then on. This lead to boole making a publication about math in the mid 1800’s. Boole sent in a hand full of his publications to the New Cambridge Mathematical journal with his “Researches on the Theory of Analytical Transformations.” which had a numerous amount of logic,equations

Modern Math

1014 words - 5 pages elementary and early middle school, students are taught the basics of math, including addition, subtraction, multiplication, division, fractions and decimals. As students continue on through middle and enter high school, the different types of math that students encounter includes algebra. “Algebra is a collection of skills and methods to solve equations and to find the unknowns” (Fawcett and Cummins 149). In algebra, variables are commonly used in this

George Boole: Boolean Algebra and Sets Theory

2031 words - 8 pages The work of George Boole on mathematical logic that gave birth to the “Boolean Algebra” was the most important contribution to the development of computer technology. We are going to see briefly, how the prodigy George Boole came from an economically modest family, to change the way we relate with logic, influencing the concept of computing and processing information. We are also going to analyse how his work in algebra revolutionised the way we

The Stages Involved in The Formulation of a Mathematical Model

1327 words - 5 pages 1) In your own words, define a mathematical model. Describe the stages involved in the formulation of mathematical models. Mathematical modelling is when a person or group uses past data and mathematical methods to predict or model future events or behaviour. This simply means that somebody looks at what has happened previously, does some maths and is then able to work out what might happen in the future. In order to create a mathematical model

Mathematical Physics

1339 words - 6 pages celestial and terrestrial bodies. In this age, the methods of Mathematical Physics were successfully used in studying mathematical models of physical phenomena. These models have something to do with electrodynamics, acoustics, theory of elasticity, hydrodynamics, aerodynamics, and other related areas. The models used were usually described using partial differential equation, integral and integrodifferential equations, variational and

A Better Mathematics Curriculum

3641 words - 15 pages the real world do not have exact solutions, but it's important to have some idea how to get approximate solutions and to know roughly the size of the error that's involved. Rather than spend an eternity on the shapes and problems that can be solved exactly, look at many problems that can't. (Algebra books are crammed with quadratic equations and 3-4-5 triangles, but cubic, quartic, and quintic equations are ignored, as well as 4-5-6 triangles

Similar Essays

Graphing, Substitution, Linear Combination Essay

542 words - 2 pages Algebra is a mathematical system. It involves letters, numbers, symbols, and a variety of equations. Equations are systems of inequality between two expressions. Thereare many types of equations. In the paragraphs below I will introduce to you three different systems of equations and how to solve them.One way to solve an equation is to graph. There are three different steps in graphing equations to solve. The first thing you want to do is put

The Important Role Of Mathematicians In Society

1626 words - 7 pages , including Thales of Miletus, Archimedes, Apollonius, Euclid, and Democritus. They began using logic to explore new mathematical concepts. Pythagoras of Samos was one of the foremost logical minds of this age. He is the inventor of abstract mathematics, and the founder of the “Pythagoras Theorem”. This theorem is still used today, in modern geometric equations The Hindu / Arabian Period (500A.D. – 1199A.D.), gave us Aryabhata the Elder and Muhammad

Untitled Essay

1834 words - 7 pages . The Greeks brought a variety of great minds to life, including Thales of Miletus, Archimedes, Apollonius, Euclid, and Democritus. They began using logic to explore new mathematical concepts. Pythagoras of Samos was one of the foremost logical minds of this age. He is the inventor of abstract mathematics, and the founder of the "Pythagoras Theorem". This theorem is still used today, in modern geometric equations The Hindu / Arabian Period (500A.D

Outline For Math That You Could Use To Be A Scholar Math Ideas For Math Outline

550 words - 3 pages Equations End of Unit IIII Material HQ 20– Sec 6.4 Quiz 15 (6.3-6.4) 26 12/06/17 Wednesday 6.8 Exponential Growth and Decay Models; Newton's Law; Logistic Growth and Decay Models HQ 21– Sec 6.5-6.6 Quiz 16 (6.5-6.6) 27 12/11/07 Monday Exam 4 on Unit IIII (Chapter 6) (Chapter 6) 28 12/13/17 Wednesday 8.1 Systems of Linear Equations: Substitution and Elimination 8.5 Partial Fraction Decomposition HQ 22– Sec 6.8 29 12/18/17 Monday Final Exam 2