Algebra Essays (Examples)

Algebra How Algebra Can Be

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 case, in order to define the degree to which the number of students changes in enrollment from year to year we could simply make the calculation as such: (our change being represented as L3)

L3 = ?List (L2)/?L1… [Read More]

Algebra the Use of Scientific

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 often use scientific notation, because that process involves radiation, carbon and other elements of physics. It can be concluded, however, from these examples, that the use of scientific notation is uncommon, and only used in highly specialized scientific fields. Even within those fields, practitioners have often developed a number of…… [Read More]

Algebra All Exponential Functions Have as Domain

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 an invalid input to the function, like dividing by zero or taking the square root of a negative number, or in this case, taking the log of zero. so we need to find the value where x-3=0, thus the asymptote occurs at x=3. The…… [Read More]

Algebra Trigonometry 10

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) = -7/2sqrt (6).

Use the reference to find the exact value of the expression

csc-

3

csc (4?/3) = csc (? + ?/3) -- csc (?/3) = -1/sin (?/3) = 1/sqrt (3/2) = -2/sqrt (3)

Answer: csc (4?/3) = -2/sqrt…… [Read More]

Algebra -- Trig Evaluate the Determinant

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 = [ 0-6 -3 | -15 ] -- 3[ 0-2 -7 | -11 ] = [ 0-0-18 | 18 ]

Converting back to system of equations:

x -- y + 4z = 6

y -- 7/2z = -11/2

18z…… [Read More]

Algebra Trig Solve the System 7x

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 + 2z) + (2x + 3z) = -12 + 5 + 7 y -- 3z -- 2x + y + 2z + 2x + 3z = 0

2z = 0 y + z = 0 y = -z

Substituting for y…… [Read More]

Algebra or Geometry Have No Use in

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 a family-owned pet grooming company. It is a relatively small company, with two shops and plans to expand to four locations after the economy settles down. The staff provides grooming and bathing services for dogs, cats, and some "exotic" mammals such as sugar gliders and hedgehogs. These services include…… [Read More]

Intermediate Algebra Background for Martha

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 an instructor. One side benefit to delivering classes through interactive video is increased socialization among the students

4b. Fox (2006) discussed the significant impact that utilizing the internet as a resource can be to furthering comprehension of a subject matter for children and adults. The writer went further to explain…… [Read More]

Representation in Algebra A Problem

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. Research 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 by understanding, abstraction, and transformation of these representations into symbolic equational forms which can be solved by algebraic algorithms" (1996, p. 1). Likewise, Laughbaum makes the point that, "Our students see relationships in their lives, but do not know that the study of functions is the tool for analyzing and understanding…… [Read More]

Coding Relational Algebra Operations Varies From School

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 to the meta-data elements which are used to describe the way that the Table is laid out. It describes the lay out and the constraints of the data in that particular SQL domain, or, in other words, it is a logical description of…… [Read More]

Intermediate Algebra the Formula Is C 4D -1 3B

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, it is important to use the formula in the real world to understand o much weight can be utilized in a boat of various length without the…… [Read More]

College Algebra

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 the nearest whole percent.

Answer: 74%

4)

a)

If

, fill in…… [Read More]

College Algebra

College Algebra

Graphing Transformations

a) Given the function f (x) = x^2 complete the following table. Must show all work for full credit.

f (x)

Show Work:

When x = 0, f (x) = f (0) = (0)^2 = 0.

When x = 1, f (x) = f (1) = (1)^2 = 1.

When x = 4, f (x) = f (4) = (4)^2 = 16.

When x = 9, f (x) = f (9) = (9)^2 = 81.

When x = 16, f (x) = f (16) = (16)^2 = 256.

b) Using the table from part a, graph the function f (x) = x^2 . For a tutorial on creating graphs in Excel and inserting graphs of functions please see the Assignment List.

c) Given the function f (x) = (x +1)^2 complete the following table. Must show all work for full credit.

f (x)

Show Work or Explain in Words:

When x = -1, f (x) = f (-1) = (-1 + 1)^2 = (0)^2 = 0.

When x = 0, f (x) = f (0) = (0 + 1)^2 = (1)^2 = 1.

When x = 3, f (x) = f (3) = (3 + 1)^2…… [Read More]

Business Math and Algebra

Managerial Math

Solve each of the following equations for the unknown variable.

a) 15x + 40 = 8x -

15x +49 = 8x

49= -7x

b) 7y - 1 = 23-5y

Y=

c) 9(2x + 8) = 20 - (x + 5)

= 15-x

d) 4(3y - 1) - 6 = 5(y + 2)

Y = (20/7)

Bob Brown bought two plots of land for a total of $110,000. On the first plot, he made a profit of 16%. On the second, he lost 4%. His total profit was $9,600. How much did he pay for each piece of land?

X= price of the first plot

Y= price of the second plot

X+Y= 110,000

.16x-.04y=9600

x=110,000-y

.16(110,000-y)-.04y=9600

17600-.16y-.04y=9600

y=40,000

x=110,000-40,000=70,000

A major car rental firm charges $57 a day with unlimited mileage. A discount firm offers a similar car for $24 a day plus 22 cents per mile. How far must you drive in a day in order for the cost to be the same at both firms?

Answer:

57=24+.22X

.22X=57-24

.22X=

X=33/.22

X=150 MILES.

Algebraic Operations and Applications

When solving the following questions, show each step of the solution along with the final results. If there is no work…… [Read More]

College Algebra

Solve the following quadratic equation by factoring:

A) X2 + 6x -16 = 0

(x-2) (x+8)= 0

(x+2) (x-8) = 0

x=-2, x-8

b) solve the quadratic equation 6x2 +3x-18 = 0 using the quadratic formula x= - b +/- ?(b2- 4ac)

+/- ?[32- (4*6*-18c)]

x = 3/2; x= 2

c) Compute the discriminant of the quadratic equation 2x2-3x - 5 = 0 and then write a brief sentence describing the number and type of solutions for the equation.

If x= - b +/- ?(b2- 4ac), then (b2- 4ac) is the discriminant b2- 4ac= -32- (4*2*-5) = 49

There are two solutions for the equation, 1 and 2 1/2, which one gets by plugging the discriminant into the quadratic formula and solving for x.

Use the graph of y=x2+4x-5 to answer the following:

a) Without solving the equation or factoring, determine the solution(s) to the equation, x^2 + 4x - 5 = 0, using only the graph. Answer: x= 0, x = -5. I obtained the answers by looking at the situation where y=0 and finding the value for x in those locations.

b) Does this function have a maximum or a minimum? The graph has a minimum, y= -9,…… [Read More]

Business Algebra and Math

Financial Polynomials

Solution for the problem: (-9x3 + 3x2 -- 15x)

The division process for the polynomial above can be approached in the same way as dividing whole numbers. The polynomial (-9x3 + 3x2 -- 15x) is the dividend, while (-3x) is the divisor. To easily facilitate the division process, the whole equation will be multiplied by "-1." The new equation is: (9x3 -- 3x2 + 15x) / (3x). Writing the question in long division form, begin dividing (9x3) first by (3x), which is equal to (3x2). To cancel the first part of the equation, the first part of the quotient must be negative. Thus, 3x2 becomes (-3x2). Place (-3x2) above the division bracket as shown below.

) 9x3-3x2 + 15x

Multiply (3x) by (-3x2), which is equal to 9x3. Placing 9x3 below (-9x3) then subtract them, resulting to zero. The remaining parts of the equation must be divided in a descending order. Bring down the next term, (-3x2), and divide again by the divisor 3x. Dividing (-3x2) by 3x will give the quotient x. This is placed above the division bracket and added to the equation, resulting to the yet unfinished quotient:

____- 3x2 + x

3x

) 9x3-3x2…… [Read More]

Algebra in Daily Life it

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 the given distance Plugging some numbers into this equation allows us to see how it works more clearly. Let's assume that the tires are 1.5 meters, and that in third gear they go around three times for every revolution. If the journey is one kilometer, the equation becomes: (1000 /…… [Read More]

Algebra Trigonometry

Algebra, Trig

Algebra-Trig

Find the slope of the line that goes through the following points: (-4, 6), (-8, 6)

Slope: m = (y2 -- y1) / (x2 -- x1) = (6 -- 6) / (-8 -- (-4)) = 0 / (-4) = 0

m = 0.

Determine whether the given function is even, odd or neither: f (x) = 5x^2 + x^

To test a function for even, odd, or neither property, plug in -- x for x, and simplify.

f (-x) = 5(-x)^2 + (-x)^4 = 5x^2 + x^4.

Because the final expression remains the same for -- x, it stands that the function is even.

f (x) is even.

Find the slope of the line that goes through the following points: (-1, 1), (-2, -5)

Slope: m = (y2 -- y1) / (x2 -- x1) = ((-5) -- 1) / ((-2) -- (-1)) = (-6) / (-1) = 6

Answer: m = 6.

Evaluate: f (x) = -5x + 8 at f (-3)

f (-3) = -5(-3) + 8 = 15 + 8 = 23

Answer: f (-3)…… [Read More]

Algebra Suppose You Have a

f (x) = 3 if x>2 otherwise f (x) = -2 Function: every x value corresponds to only one f (x) value

c. f (x) = 7 if x>0 or f (x) = -7 if x… [Read More]

Algebra Trig Find the Radian Measure of

Algebra, Trig

Find the radian measure of the central angle of a circle of radius r = 4 inches that intercepts an arc length s = 20 inches.

The formula for an arc length is a = r?, where'd is the arc length, ? is the central angle in radians, and r is the radius. That said, s = 20, r = 4, and ? is unknown.

= 5 radians

The central angle is 5 radians.

In which quadrant will the angle 100 degrees lie in the standard position?

The angle of 100 degrees will lie in Quadrant II.

In which quadrant will the angle -305 degrees lie in the standard position?

The angle of -305 degrees will lie in Quadrant I.

Find the length of the arc on a circle of radius r = 5 yards intercepted by a central angle 0 = 70 degrees.

The formula for an arc length is a = r?, where'd is the arc length, ? is the central angle in radians, and r is…… [Read More]

Algebra Trig Given F X -3X

Algebra, Trig

Given f (x) = -3x + 2 and g (x) = 2x + 9: find (g 0 f)(x)

(g 0 f)(x) = 2(-3x + 2) + 9 = -6x + 4 + 9 = -6x + 13

(g 0 f)(x) = -6x + 13.

Given f (x) = 5x + 7 and g (x) = 5x -- 1: find (f 0 g)(x)

(f 0 g)(x) = 5(5x -- 1) + 7 = 25x -- 5 + 7 = 25x +

(f 0 g)(x) = 25x + 2.

Given f (x) = 5x + 4 and g (x) = 3x -- 8, find fg = f (x) * g (x) = (5x + 4)(3x -- 8) = 15x^2 -- 40x + 12x -- 32 = 15x^2 -- 28x --

fg = 15x^2 -- 28x -- 32.

Given f (x) = 2 -- 2x and g (x) = -6x + 2, find f + g f + g = f (x) + g (x) = (2 -- 2x) + (-6x + 2) = 2 -- 2x -- 6x + 2 = -8x +

f + g = -8x + 4.

Find the center and the radius of a circle, given…… [Read More]

Algebra Trig Perform the Indicated Operation and

Algebra, Trig

Perform the indicated operation and simplify completely: (x + 10)(x^2 + 9x - 8)

(x + 10)(x^2 + 9x - 8) = x^3 + 9x^2 -- 8x + 10x^2 + 90x -- 80 = x^3 + 19x^2 +82x --

Perform the indicated operation and simplify completely:

(5x + 5) / (5x + 9) + (5x + 13) / (5x+9)

(5x + 5) / (5x + 9) + (5x + 13) / (5x+9) = (5x + 5 + 5x + 13) / (5x + 9)

= (10x + 18) / (5x + 9) = 2(5x + 9) / (5x + 9) = 2

Perform the indicated operation and simplify completely:

(8x^6 + 7x^3 + 3x) + (3x^6+5x^3 -5x)

(8x^6 + 7x^3 + 3x) + (3x^6+5x^3 -5x) = 8x^6 + 7x^3 + 3x + 3x^6 + 5x^3 -- 5x

= 11x^6 + 12x^3 -- 2x

Perform the indicated operation and simplify completely: (x - 3)^

3)^3 = (x -- 3)(x --…… [Read More]

Algebra Lesson Plans and Curriculum for the

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 in 6-8, etc.). All ten standards are relevant to all grade levels from K. through 12. The only thing that changes at each particular level is the actual emphasis placed on any given standard over another.

Consider algebra - the main topic of this paper. Teaching in this area of…… [Read More]

Algebra Many Times When Purchasing

05x)

Option for Plan B:

$20 + (0.10x)

Determine the best option given two plans

Step 1: $30 + (0.05x) = $20 + (0.10x)

Step 2: Subtract (0.05x) from both sides-

$30 + (0.05x) -- (0.05x) = $20 +(0.10x) -- (0.05x) ? $30 = $20 + (0.05x)

Step 3: Subtract $20 from each side-

$30 - $20 = $20 -$20 + (0.05x) ? $10 = (0.05x)

Step 4: Divide both sides by (0.05) to isolate x:

$10 / (0.05) = (0.05x)/(0.05)

200 = x

After making 200 phone calls, both plans will break even so it doesn't matter which plan you are choosing if you are making 200 phone calls.

If you plan on making less than 200 phone calls, then one should assign a random value to x less than 200:

$30 + (0.05 x 100)= $35

$20 + (0.05 x 100) = $25

If making less than 200 calls, then Plan B. is the better option. If making more than 200 calls, then Plan A would be the better option…… [Read More]

XML Physical Evaluation of XML

One such body is the American National Standards Institute or ANSI which is a non-profit private organization that surprisingly institutes standards the industry accepts voluntarily. Other influential standards organizations include the Institute of Electrical and Electronic Engineers or IEEE and the Organization for Standardization or ISO. The IEEE was the organization that defined LAN standards in the Project 802 or the 802 series. These projects could be the blueprints that could be used to make XML more effective by using PAT Algebra Operators for query needs.

XML PAT Algebra Operators

The internet is based on a foundation of distributed hypertext. There is also plenty of proof that the internet could be regarded as a large distributed database where there are million to billions of queries processed daily. "XML is too slow an exchange format for any large volume of data transfer. It is fine for exchange of small amounts of data on the fly but when you get to the stage of wanting to transfer Gigabytes of data when converted to XML that mushrooms pretty rapidly. Before XML becomes any more mainstream it should be looked at now to see how compression can be adopted. It must be backward compatible…… [Read More]

Secondary General Education Case Study

Another way to help the students learn Algebra is to show them real-world problems where they can see what the purposes are for learning Algebra and how they would use Algebra. One of the ways to do this would be bring in parents or other adults that use Algebra in their day-to-day careers or jobs. They could explain why they used Algebra and how they used Algebra.

A learning objective for this subject would be "the student will use mean, median, mode and range in a set of ten problems and get seven to eight of the problems correct." The student will be able to explain or demonstrate how they arrived at their answers. They may use calculators, but still must show the steps used to find the answers.

One example that could be used in the classroom is to have each student take their pulse rate and write it down. After the entire class has listed the pulse rate of the each student in the classroom, they would list them from least to greatest and then put them in order. After they have the list, they will find the mean, median, mode and range of pulse rates. Since they…… [Read More]

Araybhata's Contributions to Mathematics &

..an approximation for ?, which is surprisingly accurate. The value given is: = 3.1416. With little doubt this is the most accurate approximation that had been given up to this point in the history of mathematics. Aryabhata found it from the circle with circumference 62832 and diameter 20000. Critics have tried to suggest that this approximation is of Greek origin. However with confidence it can be argued that the Greeks only used ? = 10 and ? = 22/7 and that no other values can be found in Greek texts." (Indian Mathematics, 2009)

There is stated by Selin (2001) in the work entitled: "Mathematics Across Cultures: The History of Non-Western Mathematics" to be "...no evidence of the method for extracting cube roots having been known earlier than Aryabhata I." (Selin, 2001)

Conclusion

Aryabhata made great contributions to mathematics and algebra and his greatest contribution to Algebra was that of his approximation for?

stated as equaling 3.1416 stated to be the most accurate approximation given at that time or previously in history. Aryabhata spent a great deal of time in examining previous mathematic and algebra study and filled in many knowledge gaps in these areas of study.… [Read More]

Education the Lesson Has a

The method the teacher uses encourages students to discover the answers for themselves rather than accept the right answer as a matter of rote learning. finally, the class is frequently divided into groups, both small and large. The groups vary to encourage maximum student interactions. Through cooperative learning the students share their suggestions and brainstorm. Finally, the teacher employs some self-directed learning strategies that allow students to ponder the equations on their own for brief periods of time. This helps the teacher make assessments during class while it also helps the students work independently.

D. The lesson addresses a variety of learning styles and intelligences.

Another major strength of this lesson is the way it addresses a variety of learning styles and intelligences. Algebra is traditionally taught using the abstract method; students must visualize the concept of alphabetical variables. The notation used in traditional algebraic equations might work for students whose linear or mathematical thinking is strong. However, students strong in visual thinking or tactile learning will benefit more from a lesson like this one. Furthermore, the current lesson uses a significant amount of verbal communications, so that students strong in intrapersonal, interpersonal, and even linguistic intelligence will benefit.

E.…… [Read More]

Modeling Real-World Data With Sinusoidal

6. The rabbits will never die.

The question was how many male/female rabbit pairs will be there after a year or 12 months?

When the experiment begun, there is a single pair of rabbits.

After duration of one month, the two rabbits have mated though they have not given birth. As a result; there is still only a single pair of rabbits.

After duration of two months, the initial pair of rabbits will give birth to another pair. There will be two pairs.

After duration of three months, the initial pair will give birth again, the second pair mate, but do not give birth. This makes three pair.

When four months will elapse, the original pair gives birth, and the pair born in the second month gives birth. The pair that is born in month in the third month will mate, but will not give birth. This will make two new pairs, thereby making a total of five pair.

After duration of five months, each pair that was alive two months earlier will give birth. This will make three new pair, totaling to eight (Anderson, Frazier, and Popendorf, 1999)

Factor Theorem:

Value a is a root of polynomial p (x)…… [Read More]

Real Number Is Assigned to Each Statement

real number is assigned to each statement written in a language, within a range from 0 to 1, where 1 means that the statement is completely true, and 0 means that the statement is completely false, while values less than 1 but greater than 0 represent that the statements are partly true, to a given, quantifiable extent. This makes it possible to analyze a distribution of statements for their truth-content, identify data patterns, make inferences and predictions, and model how processes operate.

Read the following instructions in order to complete this assignment, and review the example of how to complete the math required for this assignment:

Use the properties of real numbers to simplify the following expressions:

2a (a -- 5) + 4(a -- 5)

3(w -- 4) -- 5(w -- 6)

(0.3m + 35n) -- 0.8(-0.09n -- 22m)

Problem #1

2a (a-5) +4(a-5) I multiply 2a by each term inside the parentheses

2a^-10a+4(a-5) then I multiply 4 by each term inside the parentheses, and the distribution

Property removes parentheses

2a^-10a+4a-20 Now since -10a and 4a are like terms I subtract 4a from -10a to get -6a

2a^-6a-20 the expression fully simplify

Problem # 2

2w-3+3(w-4)-5(w-6) here I multiply 3…… [Read More]

Attribute Hiearchy Critique of the Journal Article

Attribute Hiearchy

Critique of the Journal Article "Using the Attribute Hierarchy Method to Make Diagnostic Inferences about Examinees' Cognitive Skills in Critical Reading" by Changjiang Wang and Martin J. Gieri

Gierl, M.J., Wang, C., & Zhou, J. (2008). Using the attribute hierarchy method to make diagnostic inferences about examinees' cognitive skills in algebra on the SAT. Journal of Technology, Learning, and Assessment, 6(6). Retrieved from http://www.jtla.org.

One problem with evaluating the effectiveness of different types of test questions is that it is often unclear why students get particular exam questions wrong (or right). The SAT is a particularly controversial and challenging test and can have a long-lasting impact upon a college applicant's life, depending on what score he or she receives. Thus, effective analysis of SAT questions for veracity is essential to be fair to the high school students that take the test.

The purpose of the study by Gierl, Wang & Zhou (2008) entitled "Using the attribute hierarchy method to make diagnostic inferences about examinees' cognitive skills in algebra on the SAT" was an attempt to provide greater clarity about the test-taking strategies used by various students on the SAT than simply analyzing the answers from a correct vs.…… [Read More]

Finance it Is With Great

Stories detailing the rise and fall of the Egyptians, the Roman Empire and other great nations proved mesmerizing and intriguing.

My interests in other areas have also been diversified; I have pursued many adventures, participated as president of many clubs, and won many competitions in music, sports, dance and more. My strength has always been academics however. During high school I was presented the unique opportunity to come to the United States and continue my education. It was here that I decided to study history initially. Though my parents pressured me to study finance or business, I found such work tedious at least initially. I did however entertain my parents and begin taking more classes in finance. This was probably the best decision I have ever made and helped create the professional I am today.

The more I learned the more I came to understand that finance was more than crunching numbers. The field of finance has a unique history all its own. Finance is an interesting and creative process, which I cam to realize after some time. I have since began to recognize how financial analysis, research and teachings can contribute to our welfare.

My desire to learn more…… [Read More]

Jaime Escalante Hero Teaching Hope

movie Stand and Deliver (Menendez & Musca, 1988), which is based on the true story of Jamie Escalante, an individual who overcame ethnic, cultural, and socioeconomic issues to become a highly successful mathematics teacher. Discuss the beliefs he held and the strategies he employed in his classroom that contributed to high achievement levels in his students.

The final report of the National Mathematics Advisory Panel (2008) presents a three-pronged argument for an effective math curricula: 1) It must foster the successful mathematical performance of students in algebra and beyond; 2) it must be taught by experienced teachers of mathematics who instructional strategies that are research-based; and, 3) the instruction of the math curriculum must accomplish the "mutually reinforcing benefits of conceptual understanding, procedural fluency, and automatic recall of facts" (National Mathematics Advisory Panel, 2008, p. xiv). Jamie Escalante began teaching before this report was released, but he knew from experience -- and instinct -- that students who do not achieve mastery of foundational concepts of mathematics will face unforgiving -- perhaps harsh -- consequences in their lives (Won, 2010).

Frontrunner Excellence. A report published in 2006 by the National Council of Teachers of Mathematics made recommendations for math curriculum that…… [Read More]

Logarithm History and Modern Applications

e. all loans. The same basic formulas using logarithms can be used to calculate the needed number of investments and/or the time period of investments at a given growth rate that will be needed in order to reach a target level of investments savings (Brown 2010). Both of these applications have very real implications for many individuals, whether they are trying to buy a home or planning for their retirement, as well as a n abundance of other issues related to personal banking. Logarithms are not only useful in highly technical scientific pursuits and investigations, then, but are directly applicable and necessary to situations that directly relate to and have an effect on people's daily lives.

What I found most interesting and surprising about the development of logarithms is that they are something that needed development in the first place. I suppose it is similar to having taken any invention that pre-existed myself a little for granted, but with something intangible like a mathematical concept, it seems even more strange that there was a time before logarithms were used -- the numbers and operations necessary for their development existed for millennia, so it seems odd that it took so long…… [Read More]

Resume Project My Strengths Include

Again, I should have a strong feel for current trends and innovations in software design and technology, including those at Microsoft and those being developed by competitors. Beyond software success, I should have many examples handy of how I have displayed leadership and effective group management in the software development environment.

Finally, I must prove to the interviewer that I am ready and capable enough to handle working in a team environment in an international branch of the Microsoft Corporation. I should be aware of the current trends and conditions that are specific to Shanghai and should know how to respond to questions concerning how I will adapt to the language and cultural differences. By being prepared for questions and anticipating what skills the job requires I will be able to succeed in getting my dream position.… [Read More]

Neo-Confucianism Is a Philosophy Which Was Born TEST1

Database Developer (based on job I worked on).

Syntax and Semantic Analysis

-- The Syntax errors involved misuse of keywords.

The Semantic errors involved misuse of columns and tables - there were incompatible data types.

To elaborate, the syntax refers to the structure of the program and syntactic analysis checks for errors in aspects like spelling or whether ibraces are missing in which case the program would fail syntactically.

Semantic errors, on the other hand refer to the essential meaning of the content -- whether it all makes sense and whether it is accurate (for instance writing "the sun rises in the west") is a semantic error for this is incorrect. I would have to ascertain that all data placed in tables and columns was accurate in both context and form.

b. Query Transformation

I transformed the query into simplified and standardized format based on relational algebra. Some query transformations need to be costed in order to be chosen and some not. For instance, if a table is eliminated totally from the join, then need to cost that consequent applied transformation is minimal since functional behavior is barely altered.

Table profiles are inputs to access plans. An access plan is…… [Read More]

Nursing Personal Statement for My Entire Life

Nursing: Personal Statement

For my entire life, acting as a caregiver has been an integral part of my identity. I come from Cuba, and caring for the old and sick is considered to be a very important obligation. I was the child who took care of the needs of my grandmother and grandfather as they aged, as well as my father who died all too young of cancer. As emotionally difficult as these experiences were, I felt privileged to be able to do something for the people who had given so much to me. I also learned how gratifying it was to nurse someone and to provide them with a sense of self-worth and empowerment, even when they were facing their own mortality. To make this my career would be my dream come true.

I wanted to become a nurse while still living in Cuba but unfortunately Cuban nursing schools are not able to accept many students. My dream was thwarted only temporarily and in the United States I intend to pursue my degree in the field of nursing. Nursing would allow me to use my compassion and joy in taking care of others every day. At present, I am…… [Read More]

Philosophy of Education Math Field

Philosophy of Education

Norma Cunningham

I am a nontraditional student and I am returning back to college due to a job loss. I have been given a second chance at obtaining an education. Since I have been attending college, I was accepted into the nursing program, but I turned it down. I did this because I remember my dream has always been to be a math teacher. Everyone knows teachers are not in the profession for the money, and that nurses make more money, so people may ask, why a teacher? Well, I remember when I was growing up, every time someone would ask me what I wanted to be, I always answered, a math teacher. Certain teachers that I have had in the past, and present, have helped me decide that I want to spend the rest of my life teaching math. Helping any age student to learn math gives me chills, because, like those teachers, I love solving problems and trying to figure out the right answers. Like John Travolta sang in Grease, "I've got chills, they're multiplying." Ever since I graduated in 1976, math has been my passion. I helped my children with their math throughout their…… [Read More]

National and State Subject Matter Content Standards

National and State Subject Matter Content Standards for Math

According to the California standards for high school students, the geometry curriculum contains six critical components: "to establish criteria for congruence of triangles based on rigid motions; establish criteria for similarity of triangles based on dilations and proportional reasoning; informally develop explanations of circumference, area, and volume formulas; apply the Pythagorean Theorem to the coordinate plan; prove basic geometric theorems; and extend work with probability" (Common Core Standards, California Department of Education: 69). The elucidated standards are often quite specific in terms of how students are asked to apply basic concepts such as measuring angles; understanding the different properties of parallel lines; and manipulating various polygons. Not only must the students prove theorems but they must also be able to construct such shapes using a variety of methods in a hands-on fashion (Common Core Standards, 2013, California Department of Education: 70).

Deeper understanding as well as superficial understanding must be demonstrated; the core requirements are conceptual as well as highly specific. This can be seen in regards to the definition of congruency: students must "use geometric descriptions of rigid motions to transform figures and to predict the effect of a given…… [Read More]

Why I Have Chosen Teaching as a Career

Teaching as a Career

Teaching Special Education requires a gentle temperament and devotion to the children. Maturity, regardless of age, and patience is very important. A Special Education teacher must be loving, kind, and nurturing in order to make the children feel safe and secure. He or she must also be focused and creative in teaching methods. And most importantly, present a positive role model for the children. I feel that I have the qualities and experience to become an effective Special Education teacher.

My background is vast and varied. I worked as a secretary at the University of California - Los Angeles for two years. The department in which I worked dealt with the clubs and fraternities on campus, therefore, I was constantly involved with the students and problems that arose from their activities. I spent a little over two years working as an office manager for a doctor's office. This gave me not only the opportunity to perfect my managerial skills but also provided the atmosphere to prepare me for my next employment that involved crisis situations. For the next five years I was Operations Manager for an ambulance service that provided 911 service for the county of…… [Read More]

Gordon's Adam's Petition

Gordon Adam's petition is not only well argued and properly reasoned, but, additionally, it managed to prove that all the arguments given against his petition were based on false reasoning. From the entire set of arguments, the only one that could actually be used against his argumentation was the one stating that he needed college algebra in order to "satisfy the university math requirement in order to graduate." Something like when you ask why you have to pay all kinds of different taxes: you see no real benefit, but some higher authority, in this case the state, in Gordon's case, the educational system and the college authorities, convinces you that this is necessary because it is so required!

On the other hand, because the college authorities' argumentation is based on all kind of fallacies, clearly dismantled one by one in Gordon's argumentation, it is my opinion that Gordon should be allowed not to take his algebra class and graduate without. My own argumentation will rely, first of all, on a presentation of the facts and of the different arguments that the two parties involved have used. I will be able to show that Gordon's option is not determined by laziness…… [Read More]

Organizational Health Educational Institutions Generally Approach Organizational

Organizational Health

Educational institutions generally approach organizational improvement by addressing the performance standards to which students, educators, and administrators are held. The standards movement has been a dominant theme in educational policy arenas and in the public eye. With roots in the 1950s Cold War mentality, the thrust of educational improvement has been prodded by perceptions of international industrial and scientific competition. If the rigor of educational standards in the nation -- according to the logic of this argument -- falls below that of other countries, our economy will falter and the balance of trade will be compromised, perhaps beyond the point of recovery.

Fears for the future of the country and our citizens run deep; these fears propel a course of action that is not particularly based on rational thinking and lacks a base of evidence. The course of action adopted by educational policy makers and educational leaders in the country is this: Advanced mathematics and science are necessary if students are to be disciplined learners with refined capacity for scientific analysis and application of their learning once they enter the world of work. In this paper, I discuss this premise, its effect on the establishment of curricula, and…… [Read More]

Using Technology in a 2nd Grade Classroom to Improve Student Achievement in Math

Technology in a 2nd grade classroom to improve student achievement in math

Of late, there has been a push to bring in technology to schools where teachers as well as students would be able to reap the benefits of the World Wide Web, the Internet, and other related technologies. In many schools across the United States of America, this fact has been acknowledged and recognized, and many teachers and educators are being trained in the techniques and methods of using these technologies. However, it is also a fact that most teachers have admitted to the truth that they have not been using these technologies, simply because they do not know and they have not been taught, how to, and nor do they have the basic technical support to use these technologies effectively. Power Point, White Boards, Laptops, LCD Projectors, CDROMS, the internet, and others are some of the technologies available to students today, and if proper use were to be made of them, then the students would most definitely do better in all their tests, especially in mathematics, which is a subject that most children seem to fear. It is to be hoped that their scores would show a dramatic…… [Read More]

Problems Fostering Unemployment in America

Unemployment in America

Policy makers in the United States continuously seek the silver bullet(s) -- plural solutions because there is clear recognition that the issue is multifaceted -- that will achieve healthy levels of employment in the nation. Certainly there some paths to increasing employment in the country are less expensive than others, and proposed solutions range across a wide array of complexity and practicality. Invariably, today, education becomes a focal point for discussions and debates about how to increase employment in any nation. This is due largely to the potential promise that solutions based in education can act as levers that are sufficiently effective to induce change.

Thesis Statement

Solutions to unemployment must be developed through the perfection of the alignment between the education young American receive -- in both secondary (high school) and post-secondary (college / university) educational systems -- and the actual labor market.

In his article in The New York Times, Thomas Friedman argues that educational standards should be higher and that students, parents, and educators need to put more effort into meeting those standards. Friedman argues that there are three fundamental pillars of unemployment in the United States today: (1) Global competition for higher-paying skilled…… [Read More]

Improving Mathematics in Middle School

These include: question/answer, lecture, demonstration, discussion, individual student projects, laboratory, technological activities, and supervised practice. Previous research has demonstrated that the use of informal knowledge, real world settings and opportunities to apply mathematical thinking are effective instruction methods for introductory algebra. For this reason, instructional factors are related to achievement in algebra (p. 102).

When comparing the test scores from Japan and the United States, House and Telese (2008) found a correlations between positive beliefs in the student's mathematical ability and their test scores. Those who believed they could do well in math performed better than those who expressed a negative opinion about their skills, when compared to their peers. In addition, students who worked problems on their own had higher test scores. This supports Silver's (1998) analysis that much of the reason why American students have poorer test scores than their international peers is due to the classroom instructional practices. Teachers, currently, are not instilling confidence in their students, in their math skills, which negatively affects their test scores.

Falco, Crethar and Bauman (2008) also agree that a middle school student's attitudes towards mathematics affects their learning and test scores. In their study, students received a Skill Builders curriculum,…… [Read More]

Spiritual Principle For Unto Every

Once the concept of factoring is understood, technology can be used to assist the students with solving quadratic equations and equalities. The website (http://www.coolmath.com/algebra/) will be references, but the students will have to write explanations showing that they understand how at least two homework problems were solved.

4. By the time we are ready to learn inverse functions, students will have a review of everything learned during the school year building up to inverse functions. Again, technology will be used via (http://www.coolmath.com/algebra/). Students will again be asked to write an explanation for various homework problems demonstrating that they understand the concepts behind solving it.

Evaluation Procedures:

A quiz once per week

Midterm exam covering current quarter

Final exam covering current and previous quarters

Written homework explanations demonstrating how certain problems were solved

Review near the end of the school year for all concepts learned

End of year final exam

Resources:

http://www.coolmath.com/algebra / http://www.mathdork.com/games/asteroidsexp3/asteroidsexp3.html

Teacher handouts

Pilone, T., & Pilone, D. (2008). Head First Algebra: A Learner's Guide to Algebra (First

Edition ed.). Cambridge: O'Reilly.… [Read More]

Middle School Math Teachers Over

These exams would also tap teaching performance and other capabilities unlikely to be adequately assessed using conventional paper along with pencil instruments." (Shulman, 1986, pp. 4 -- 14)

These different elements are important, because they are providing a foundation for helping the schools to become more competitive in mathematics. As, they are working together to create a basic standard for: improving learning comprehension and provide the ability to solve more complex issues. Over the course of time, this will help to increase the student's ability to understand a wide variety of concepts. This is the point that they will be more prepared to deal with the various challenges that they are facing in the 21 century. Once this occurs, it will help them to establish a foundation for adapting to the changes that they will have to deal with from: shifts in technology and through these transformations because of globalization.

To corroborate these finding with one another Ball (2008) had similar kinds of observations. As, the author believes that Shulman is providing a basic foundation for improving the student's understanding of different mathematical concepts. They found, that there were a number of similar approaches and trends that must be embraced…… [Read More]

Digital Audio Over the Last

At the same time, digital audio recording also uses what is known as Boolean algebra and De Morgan's Theorem. Boolean algebra is when you are combining various binary codes and signals. De Morgan's Theorem is when you are complimenting various expressions in Boolean algebra, to more accurately represent the sound that is being heard. In digital recording, these two methods allow the various binary codes to be utilized, to specifically identify the different influxes in the various sounds. While, at the same time being able to provide, a more accurate recording of: the different noises. This is because you were able to combine the various formulas, to accurately reflect various sounds. Once this takes places, it means that actual audio recording that is being heard on the digital recorder; will more precisely reflect the various sounds that someone will hear. This is because the binary code and the Boolean algebra / De Morgan Theorem, are helping to precisely record the various inflections that are occurring. At which point, the overall amounts of sound quality will improve dramatically, as this device will capture the actual ranges vs. The overall wave of the sounds. (Pohlmann, n.d. )

Clearly, digital recording is changing…… [Read More]

Butts R E 2001 Galileo In

He looks at three methods: history (melding information about the diverse geographical origins of algebra with the problems themselves), multiple representations (using notation, narrative, geometric, graphical, and other representations together to build understanding), and the object concept of function (teaching functions without generalizing about how traits of an individual relate to traits of a group). The article serves to offer some inventive solutions to a common problem in math education: How to make material relevant and compelling to a breadth of students.

Martinez, a.A. (2010). Triangle sacrifice to the gods. 1-11.

The article looks at Pythagoras, particularly the mythology surrounding his life and his most famous discovery, the Pythagorean theorem. It calls into question the historical evidence on which mathematics teachers base their teaching of this theory. The author points out how very little is known about Pythagoras and how he has been canonized by the math discipline because his theory is so useful. He outlines evidence that exists about Pythagoras, taking a critical eye to where and from whom the histories were derived. The tone of the article is playful but also makes an important point. It is critical that teachers take a close look at what information they…… [Read More]

Teaching Math to Students With Disabilities Education

Education: Teaching Math to Students With Disabilities

Working with students with disabilities (SWD) can be quite challenging, especially for teachers working on a full-time basis. Almost every classroom today has one or more students dealing with either an emotional, educational, or physical disability; and teachers are likely to find themselves looking for resources or information that would enable them teach all their students in the most effective way. There are numerous special-education websites from which teachers and instructors can obtain information or lessons on teaching their respective subjects. Five websites available to the math special education teacher have been discussed in the subsequent sections of this text.

Teacher Resources

Teachers Helping Teachers: http://www.pacificnet.net/~mandel/

This online resource provides teaching information for all teachers, with a 'Special Education' segment that provides a number of activities meant specifically for instilling basic conceptual skills in learners with special needs. The activities are submitted by teachers from different parts of the country, and include study skills, current events, geography, math, and reading lessons for learners in different grades (Starr). The 'Math Game' activity, for instance, helps students with learning disabilities to improve their problem-solving skills through sportsmanship and teamwork. There also are activities geared at…… [Read More]