There are many other variables that would affect real-world riding speed, and the effort variable would also be far more complicated than represented here, but this should suffice for now. Several equations can be written using the variables defined here. For instance, to calculate the effort needed to go one kilometer (it's easier to go kilometers than miles, at least mathematically), or a thousand meters, in a given gear, the equation would look like this:
T) / G = E, where M. is the distance (in meters) of the journey, T is the circumference of the tire -- and therefore also the linear distance, G is the number of revolutions the tire goes per push of the pedal, which changes from gear to gear, and E. is the number of times the pedals have to go around, which is representative of the effort needed to push the bike forward for…...
Algebra
Like many other languages and sciences, Algebra can be useful in the explanation of real-world experiences. Linear algebra, in particular, holds a high level of relevancy in the solution of real world problems like physics equations. Since the key point of physics is to explain the world in proven observations, linear algebra is an ideal mode for discussion. Many real-world situations can be explained by algebra; for example, how does GPS work? The satellite-based Global Positioning System works by locking onto the system of three satellites and calculating a two-dimensional position from latitude and longitude, thus tracking movement. The location of objects can be determined by using linear equations to morph the data into identifiable locations, and with four or more satellites in view, altitude combines with latitude and longitude to determine the 3-D position.
A far more generic (but equally important) use of linear algebra in real world discussions is…...
By observing x on the graph, then we make the connection that the slope of x on the graph represents rate of change of the linear function.
Once we have done this, it is then possible to move to the development of a quadratic equation and see what the impact of the increase (or perhaps decrease) means to the data. Have we proven that the rate of change is linear? The graphical representation of the data may be misleading, so it would be good to be able to calculate the rate of change to see if it is significant.
We could assign to value of L1 to the year in which the students are enrolled collect this data in columnar form, still graphing it on our graph. We would then call L2 the number of students enrolled every year which corresponds to the year we have listed in L1. In this…...
mlaReference:
No Authors Listed. (1996) Achieving Mathematical Power. Mathematics Curriculum Framework. Accessed via the World Wide Web on July 17, 2005 at http://www.doe.mass.edu/frameworks/math/1996/patterns.html
Those studying physics and astronomy, and perhaps other scientific disciplines as well, are accustomed to the use of scientific shorthand and in some fields it is essential -- the example above of distance between energy waves from supernovae is a good example. There is a high level of variation in these distances, so a shorthand like the one on financial statements would be apply, but the numbers are very small so the use of shorthand is necessary. It is interesting to note, however, that even those in fields accustomed to scientific notation sometimes avoid it, as is the case with distances between objects in space.
Another group that does something similar to astronomers is the archaeologists. They have found ways to talk about years without using scientific notation, even though events often date back millions or billions of years. Yet, when discussing the science behind dating their samples, they will…...
mlaWorks Cited:
Hoflich, P.; Wheeler, J. & Khokhlov, A. (1997). Hard x-rays and gamma rays from type Ia supernovae. The Astrophysical Journal. Vol. 492 (1998) 228-245.
Lalho, J. (2010). Light quark physics from lattice QCD. The XXVIII International Symposium on Lattice Field Theory. Retrieved November 19, 2011 from http://docs.google.com/viewer?a=v&q=cache:gDvRm6TY1VMJ:arxiv.org/pdf/1106.0457+physics+1.5e+%2B+09&hl=en&gl=us&pid=bl&srcid=ADGEESj0lgK5NDCG9_6ieDz24CvN4cltyb2a6Rkcxewes9FXnLbXorx8egE4f6_a7wSR-YQXM9fvOSZ3D05z4ASakSK1f48HrDiYS0JnlOLNbF3-1-upjAM4N-DhnF8rUoEmdWRK-qQC&sig=AHIEtbQ5aUobZS_c9iSSgDQqnLuG1-Kw2Q
Algebra
All exponential functions have as domain the set of real numbers because the domain is the set of numbers that can enter the function and enable to produce a number as output. In exponential functions whatever real number can be operated. (-infinity, infinity)
You have ln (x+4) so everything is shifted by 4. The domain of ln (x+4) is now -4 < x < infinity (Shifting infinity by a finite number gives you infinity again.) So,-4 < x < infinity is the domain of ln (x+4).
(2 [less than] t [less than] infinity)
For your function f (t) = 5.5exp (t) the function is continuous for all values of t as exp (t) is continuous for all values t, i.e. The domain of the function is -oo < t < oo
2a. subtracting 3 on the inside the function moves it 3 units to the right, that's the only transformation.
the vertical asymptote results from…...
Algebra -- Trig --
Writer's Note: The symbol "n" should really be referred to as "pi" or "?" To prevent confusion within the problem. Also, there is a difference between "squared" and "square root." The case in these problems is to use the square root, so "sqrt (number)." I've only managed the calculations because I have presumed the indicated changes.
Using the periodic properties of trigonometric functions, find the exact value of the expression
cos-
cos (8?/5) = cos (2? + (2?/5)) = cos (2?/5) = cos (72) = 0.31
cos (8?/5) = 0.31.
The point P. On the unit circle that corresponds to a real number t is:
{ 5-2 6 squared}
} Find csc (t)
P is on the unit circle, therefore the coordinates are (cos (t), sin (t)). This leads to the following calculations:
sin (t) = -2sqrt (6)/7, and csc (t) = 1/sin (t) = 1/(-2sqrt (6)/7) = 7/(-2sqrt (6)) = -7/2sqrt (6)
Answer: csc (t) =…...
Algebra -- Trig
Evaluate the determinant: | 3-9 |
Determinant of a square matrix can be solved by the following equation: A = ad -- bc, where a = 3, b = 9, c = 6, and d = 4. Therefore, A = (3)(4) -- (9)(6) = 12 -- 54 = -42
Solve the following system of equations using matrices:
y + 4z = 6, 2x + z = 1, x + 5y + z = -9
[ 1-5-1 | -9 ]
Row 2: R2 -- 2R1 = [ 2-0-1 | 1 ] -- 2[ 1 -1-4 | 6 ] = [ 0-2 -7 | -11 ]
Row 3: R3 -- R1 = [ 1-5-1 | -9 ] -- [ 1 -1-4 | 6 ] = [ 0-6 -3 | -15 ]
New matrix:
[ 0-2 -7 | -11 ]
[ 0-6 -3 | -15 ]
Row 2: R2/2 = [ 0-1 -7/2 | -11/2 ]
Row 3: R3 -- 3R2 =…...
Algebra, Trig
Solve the system: 7x + 3y = -2, -7x -- 7y =
(7x + 3y) + (-7x -- 7y) = (-2 + 14) 7x + 3y -- 7x -- 7y = 12 -4y = 12 y = -3
Substituting y for the first equation: 7x + 3(-3) = -2 7x -- 9 = -2 7x = 7 x = 1
x = 1, y = -3.
Solve the system: x + y = -5, x -- y = 12
(x + y) + (x -- y) = (-5 + 12) x + y + x -- y = 7 2x = 7 x = 7/2
Substituting x for the first equation: 7/2 + y = -5 y = -5 -- (7/2) y = -17/2
x = 7/2, y = -17/2.
Solve the system: y -- 3z = -12, -2x + y + 2z = 5, 2x + 3z = 7
(y -- 3z) + (-2x + y +…...
Algebra Lesson Plans and Curriculum for the 7th Grade Classroom
The National Council of Teachers of Mathematics (NCTM) provides a comprehensive set of principles and standards for developing curriculum for grades K. through 12th. Chapter two of their text Principles and Standards for School Mathematics specifies the six principles considered vital for the development of a coherent math plan. The principles are general enough to apply across a wide variety of disciplines as they are "not unique to school mathematics." (p. 16). However, chapter three dealing with the ten standards, themselves, makes quite clear (and rightly so) that math, unlike other disciplines, can benefit from a truly integrated approach: "Because mathematics as a discipline is highly interconnected the areas described by the Standards overlap and are integrated." (p. 30). In other words, the standards cannot be easily divided into particular grade levels (i.e. numbers/operations in K-2, geometry in 3-5, algebra…...
mlaReferences
Algebra for All - Not with Today's Textbooks, Says AAAS. (2000). Retrived April 1, 2003, at http://www.prject2061.org/newsinfo/press/r1000426.htm.
Algebra: Some Common Misconceptions. (n.d.). Retrieved April 1, 2003 at http://www.quesnrecit.qc.ca/mst/mapco/pdf/algemisc.pdf.
Aziz, N., Pain, H.G., Brna, P. (1995). Modelling and Mending Students' Misconceptions in Translating Algebra Word PRoblems Using a Belief Revision System in Taps (Abstract).
Presented In the proceedings of the 7th World Conference on Artificial Intelligence in Education, AI-ED 95, Virginia, AACE. Retrieved April 1, 2003 from DAI Database.
algebra or geometry have no use in "real" life, many people think that statistical analyses have no possible real-world applications. However, as the following scenario should make clear, statistical analysis can be extremely helpful in assessing quality control issues in the workplace. Using a specific type of statistical analysis, the supervisor at a former workplace was able to reduce costs while increasing customer satisfaction.
Analysis of variance (more generally referred to as an ANOVA test) is one of the most basic statistical tests that can be applied to a data set. It is used to provide an accurate way to compare the results from different groups (defined in ways that are relevant to the issue at hand). Such comparisons are useful because they provide information that allows processes to become more efficient or to meet other goals, such as increasing customer satisfaction.
For a number of years I have worked in…...
3b. One method that can be utilized to help Martha with applying algebra to real world application is through interactions within her environment that will allow her to utilize these skills. Another method proven useful in building applicable skills and communication is online conferencing. This tool utilized in the class room can give Martha access to knowledge from other professors and learners that could not normally be possible in a standard classroom. A professor that may specialize in a specific method on how to understand certain terms or expressions would be able to share these applications with students globally through virtual conferences. Technological Horizons (1993), recant the significance of videoconferencing by reporting that the characteristics of videoconferencing may actually enhance the learning process. Teachers and administrators say that students who take distance education classes are scoring higher on basic skills tests than those who are in the same classroom with…...
mlaReferences
Fox, Christine. "Going virtual: online courses can get to people and places beyond the reach of the traditional school setting, serving the needs of students and teachers nationwide. (Using Technology to Expand Opportunity)." THE Journal (Technological Horizons In Education). 1105 Media, Inc. 2006. Retrieved September 10, 2010 from HighBeam Research: http://www.highbeam.com/doc/1G1-148856686.html
Olliges, Ralph; Sebastian Mahfood. "10. Resources.(Teaching and learning in the new millennium: transformative technologies in a transformable world)(Missouri Department of Education Commission)." Communication Research Trends. Centre for the Study of Communication and Culture. 2003. Retrieved September 10, 2010 from HighBeam Research: http://www.highbeam.com/doc/1G1-130975621.html
"CRITICAL THINKING SKILLS, MATH, SCIENCE DEMAND OF BusinessES, GLOBAL COMPETITION." U.S. Fed News Service, Including U.S. State News. HT Media Ltd. 2007. Retrieved September 10, 2010 from HighBeam Research: http://www.highbeam.com/doc/1P3-1248145301.html
"Videoconferencing bridges gaps in distance and curriculum for Alaskan students. (how the North Slope Borough School District uses VideoTelecom's MediaConferencing systems) (Multimedia)." THE Journal (Technological Horizons In Education). 1105 Media, Inc. 1993. Retrieved September 10, 2010 from HighBeam Research: http://www.highbeam.com/doc/1G1-14354264.html
2007, p. 115). Likewise, a study by Wyndhamm and Saljo found that young algebra learners were more successful in their problem-solving efforts when collaborating in a group environment. According to these researchers, "An experiment involving 14 small groups of Swedish students (usually 3 per group) aged 10, 11, and 12 years shows that these students acting in groups and creating shared contextualizations were able to solve mathematics word problems calling for real-world knowledge. esearch has shown students acting alone to have difficulty with the same types of problems" (Wyndhamm & Saljo 1997, p. 361). Other teachers report that algebra story problems can help make learning more relevant to young people's lives. For instance, according to Homann and Lulay, "Algebra story problems are an important practical application of mathematics since real-world problems usually do not arise in terms of equations but as verbal or pictorial representations. The problems are solved…...
mlaReferences
Barry, D. (1989) Dave Barry Slept Here: A Sort of History of the United States. New York:
Random House.
Dillon, R.F. & Sternberg, R.J. (1986) Cognition and Instruction. Orlando, FL: Academic
Press.
Coding relational algebra operations varies from school to school. I wrote it according to my training, but there are variations. Review and rewrite in own words so as to preclude plagiarism.
What is a relation schema? What is the difference between a relation, a relation schema, and a relational schema?
A relation schema is the basic information that describes a table or a relation. This includes the set of column names, the data within the columns, or the name associated with the entire table.
For example 'Students' would be the relation (I..e category) name.
The relation schema for students may be expressed as following:
Students (sid: string, name: string, login: string, age: integer, gpa: real)
It has five fields or columns each having names or types.
The relation, in other words, is the topic / category (e..g 'student'), the relations schema is the property categories of the relation, or of the 'student' table.
A relational schema refer…...
mlaBlaha, M. Referential Integrity Is Important For Databases http://www.odbms.org/download/007.02%20Blaha%20Referential%20Integrity%20Is%20Important%20For%20Databases%20November%202005.PDF)
What is a relation schema | Answerbag http://www.answerbag.com/q_view/730085#ixzz1ncwaYsPz
SQL Authority. SQL SERVER -- Difference Between Candidate Keys and Primary Key. http://blog.sqlauthority.com/2009/05/30/sql-server-difference-between-candidate-keys-and-primary-key/
Intermediate Algebra
The formula is C=4d^-1/3b
D= 23,245 because it is the pounds
B= 13.5 because that is the height of the mast
C=4(23,245)^-1/3(13.5)
Because the exponent was negative it needed to be dropped down to the numerator. The fact that it was a fraction meant that 92980 needed to be cubed, since it was a 1/3 exponent. Then it could be multiplied with the B. value, which was 13.5 / This left the final answer to be 283.693745115.
C=4d^-1/3b
d=64b3/c3
In order to solve for D. you needed to move 4 and the variable D. To the other side. Then you have to log both sides, which leaves an exponent of 3 instead of -1/3.
This formula could definitely be very important in the real world. For one, it is needed to be able to properly sail a boat in various conditions. It is extremely important to understand the conditions in which any boat can capsize. As such,…...
College Algebra
Individual Project
Solve the following algebraically. Trial and error is not an appropriate method of solution. You must show all your work.
Solve algebraically and check your potential solutions:
x = -4 does not satisfy the equality. So the answer is only x = 5
Show the steps that you would take to solve the following algebraically:
Show your work here:
c) What potential solution did you obtain? Explain why this is not a solution.
This is not a solution because it makes the original equation indefinite. It makes the denominator zero.
The following function computes the cost, C (in millions of dollars), of implementing a city recycling project when x percent of the citizens participate.
a)
Using this model, find the cost if 60% of the citizens participate?
Answer:
million dollars
b)
Using this model, determine the percentage of participation that can be expected if $4 million is spent on this recycling project. Set up an equation and solve algebraically. Round to…...
Intersection theory, in abstract terms, is a complex mathematical framework used in algebraic geometry to understand the intricate "meetings" between shapes within a mathematical space. While its roots and applications stem from the world of shapes and equations, it can be viewed through a more metaphorical lens to gain insights into human experiences. Here's how:
Understanding Intersection:
How it helps:
Outline for an Essay on Intersection Theory
I. Introduction
Begin with a compelling hook or question that captures the reader's attention.
Define intersection theory and explain its significance in algebraic geometry.
State the thesis statement, which should articulate the main argument or purpose of the essay.
II. Background and Historical Context
Provide a brief overview of the historical development of intersection theory.
Discuss the contributions of key mathematicians, such as Bézout, Euler, and Poincaré.
Explain the role of intersection theory in resolving classical geometric problems.
III. Fundamental Concepts
Define the basic concepts of intersection theory, such as:
Intersection number
Cycle
Homology and cohomology....
One interesting topic that has been in the news recently is the use of abstract mathematical concepts in physics, specifically in the field of quantum physics.
There has been a lot of research and debate on the role of abstract mathematical structures in understanding and describing the behavior of particles at the quantum level. For example, the use of complex numbers, matrices, and abstract algebraic structures has been essential in developing the mathematical framework of quantum mechanics.
One recent development in this area is the use of category theory, a branch of mathematics that studies abstract structures and relationships between different....
Abstract Mathematics in Physics: A Transformative Force
Introduction
Mathematics has long played a pivotal role in the development of physics, offering a precise and abstract framework for understanding and describing the physical world. In recent decades, the influence of abstract mathematics in physics has grown exponentially, leading to groundbreaking insights and discoveries. This essay delves into the latest advancements in this area, examining specific examples that demonstrate the transformative power of abstract mathematics in modern physics.
String Theory and Calabi-Yau Manifolds
String theory is a promising candidate for a theory of everything that aims to unify all fundamental forces and particles. At its core,....
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