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Let us know what is graphing polynomial functions

Polynomial functions are functions which has x as an input variable, made up of several terms, each term is made up of four factors, the first being a actual number coefficient, and the second being x raised to some non-negative integer power. Actually, it is kind of more complicated than that. refer to the following links to get a deeper understanding.

Polynomial functions are comparatively simple to understand. Low degree solving polynomial equations can be solved explicitly. Polynomials provide lovely examples for studying more general functions.Do you find Math Difficult get help here ....

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Let us learn how to do percentages of any given value.

How to do percentages is widely used technique throughout the business world, Percentage is denoted with the sign %, for example 50% is read as fifty percentage that an also written as 50/100 or 0.50.

Example:

In a crowd containing 200 people out of that only 50 are men.Find the percentage of men

Given that make out positions

Total number of men = 50

Total number of people = 200

Percentage of men = 50/200 = 1/4 = 0.25

= 0.25 x 100 = 25

There are 25% of men in a group for more help with Math at your fingertips

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Introduction to prepare for natural sine:
In trigonometric functions are known as circular function of an angle. They are setting to transmit the point of a triangle to lengths of the exterior of a triangle.
Natural sines are one of the trigonometric function. Trigonometric function is the division of the exterior of the right triangle formula.
The angle derived are the ratios of length of the sides of right-angled triangle contain the angle. Now we Learn Math Easily about natural sines.

Math is a Game

Do you know how to convert height to inches:

The height can be calculated in terms of centimeter, meter, and inches. The longest dimension of an object is called length of that object. They can convert meter to inches, inches to centimeter or vice versa. In this article they shall discuss about the converting height to inches. In specific they deal with conversion from (height) meter to inches and (height) centimeter to inches.

To convert from centimeter to inches, divide centimeters by 2.54, result will be in inches.

To convert from meter to inches multiply meters by 3.28, result will be in inches.

Centimeter to Inches Conversion:

Also learn how to convert meters to centimeters

Formula to convert centimeter to inches

Inches =centimeter/ 2.54.
Example:
Convert 5 centimeter in to inches.

Divide 5 centimeter by 2.54.

=5 / 2.54

=2.0 inches Find Math Homework here

Fun learning mathematics

Introduction to learning 5th grade math help:

Learning 5th grade math help is concepts having basic mathematics for 5^th grade students.5^th grade students are having basic concepts of algebra, geometry, addition, subtraction and multiplication on numbers, fractions, and decimals. Main concept of learning 5^th grade math help includes algebraic expressions and geometry. Let us see about the basic concept of 5^th grade math with an example and practice problems.

Example : The angles of the triangle are given 85° and 45°. Find the 3^rd angle of the triangle.
Given:
The two angles are 85° and 45°.
Let us assume the third angle as y° also you may refresh 4 grade math.
Steps:
We know that,
Summation of the angles = 180°.
85° + 45° + y° = 180°
130° + y° = 180°
y° =180° -130° (subtract 130° on both sides)
y° =50°
Solution: The third angle is 50°.also Get math help here

Fun learning mathematics

Introduction to line plot example

One of the important educational tools is graphs. Through graphs we can learn how to organize and interpret information. Graphs help not only to analyze information in math but also help convey information in business. Many types of graphs exist, but we use line plots to show frequency of data.

A line plot shows frequency of information along a number line with “x” mark or any other marks to show frequency. It is best to use a line plot while comparing fewer than 25 frequency information. It is a quickest and simplest way to organize data.

Steps to Follow to Plot the Examples on Line Plot

Here are few steps to show how to sketch a line plot;
Step 1 : Collect the given information which is called data for which a line plot has to be drawn. Look for those information sets that need to show frequency.
Step 2 :Group the information items that are the same and then create and label a chart to help you organize the list from the data and line plot worksheets.
Step 3 : Find an approximate scale to draw the line plot. If the scale consists of numbers, then break it into even parts.
Step 4 : Draw a horizontal line & label it according to the scale chosen. This looks similar to a number line.
Step 5 : Put a mark, say X that corresponds to the number on the scale according to the data that is organized. This is the line plot Math Problems Help.

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Definition of linear programming problems:
The problem of minimizing or maximizing linear constraints from linear function subject is defined as the linear programming problem. These linear constraints are mayor may not be equalities. That is it may either equality or non equality.

Solving a Linear programming Problem :
The linear programming problem generally consists of three components:

• Activities of variables and their relationships.
• Objective functions
• The constraints.

Solving a Linear programming Problem :
How to find the solution set is called the feasible region for a set of linear inequalities. These concepts will be used for solving Linear programming Problem.
A programming problem consists of Business problem where one faces several limitations causing restrictions. One has to remain within the frame work of these restrictions and optimize his goals. The strategies of doing so successfully, is called solving a programming problem.
For Linear programming examples:
If the restrictions, when expressed mathematically are in the form of linear inequalities, the programming problem is called a Linear programming Problem. These restrictions are also called constraints and Get math help here
If the constraints do not have more than two variables the L.P.P Can be solved graphically.
The goals when written mathematically are called Objective functions.

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Introduction to theorems in geometry :

Geometry: Is a branch of mathematics, which is explained shapes or sizes of mathematical and geometry objects and their postulates. Geometry is important element to prove the postulates, theorems and properties.
Theorem: Theorem is one of the statement, which is proved from already exists statements. It may be postulates, proofs, theorems, definitions, etc. Those theorems are result of some truths. Its consists of logical assumption and basic rules in it. Theorem contains two elements, called as conclusions and hypotheses .
Postulate : Is a fundamental thing or basic principle or general proof of any subject. In mathematics, postulate is helpful in solving the proofs and realizes the truth of relevant topic with logically.

Theorems in Geometry:

There are many theorems in geometry properties. Few of them as follows,

• Line: A line can illustrate between two points only.
• Parallel lines:The similar plane and do not meet together which are straight lines. They may extend in any direction
• line intersection: A single point where the intersection of 2 lines meet called as intersection point.
• Midpoint:Which contains single midpoint only is a line section.
• Every line and every plane are locations of points.
• All lines include a coordinate structure.
• The process of enlarged indefinitely in a straight line with the help of any straight-line section.
• Angle: It is measure of direction, which has two rays dividing by general end.
• Vertex: The meeting point of two lines is called the vertex.
• Vertex angle: An angle is reverse to the base.
• Right angle: Every right angle is congruent angles. A right angle is greater than an acute angle and less than obtuse angle.
• Complementary angle: An angle is = single right angle.
• Supplementary angle: An angle is = two right angles.
• Bisector: It is a ray of interior angle, which bisects that angle. An angle contains single bisector only.
• If two points recline in a flat surface, the points reclines in the flat surface with the line surrounding .
• The intersection of two planes meets single line and explore yourself in Geometry World.

Significance of Math

Introduction to first in math:

Math is very important for students in their life, so first grade shows from basics, how to start math from first grade and may learn about addition of natural numbers, subtraction of natural numbers. Then the measurement basic geometry and graphs are to be teach. And they started from counting coins from initial level to dollars by showing the pictures, clock are shown in pictures and ask timing methods. Calendars dates are also identified to calculate.

Steps to Understand the first in Math:

i). Count the numbers by using fingers Do U Need free online tutor
ii) Then to see the example sums to get an idea and work out the practice problems.
Numbers counting up to 10:

1 6

2 7

3 8

4 9

5 10

Numbers counting in words up to ten:

One Six

Two Seven

Three Eight

Four Nine

Five Ten

Counting the numbers with tens in first in math:

10 60

20 70

30 80

40 90

50 100

Counting the words in tens in first in math:

Ten Sixty

Twenty Seventy

Thirty Eighty

Forty Ninety

Fifty One Hundred

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Knowledge of Math

Introduction to Grade percentage calculator:

The percentage is the fraction or the division of whole number. Percentage is generally calculated for the number 100. Percentage has the two parts namely the numerator and the denominator of the given expression. In percentage the denominator should have the value 100. Now we are going to see about the percentage calculator.

Percentage Calculator - Steps:

• First the number given should be divided by the other number
• The second step is to multiply the answer by 100. The decimal points should be removed if any.
• To the desired position we can round off the decimal numbers.
• Hence it is easy to solve the problem in percentages.
• Do you need help with Simplifying Calculator

Percentage calculator - Example :

Find the percentage - 25 of 100?

Solution:

Let us take the given information of the percentage 25%

Now we can calculate the percentage, Do you think Math is all about calculation

25% = .25

The next step to calculate is given as,

.25 × 100 = 25.

Precalculus help

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Introduction to step by step precalculus help:-

In this article we are going to discuss about the precalculus help problems step by step concept free precalculus answers.

The process of contraction the precalculus comparable to over screening the real life problems concept and problem in precalculus answers solved are referred as review use of precalculus in the step by step process.

This article improves the knowledge the real life for precalculus and below the problems are using toll for the help with test calculus.

Put down behind the useful get review step by step help of precalculus to this article. Use of precalculus in real life solutions also show below precalculus problems solved.

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Introduction to “state statistics”

Statistics is said as numerical information in plural sense. In this sense, statistics is said as quantitative information.In this you will also find statistics problem solver . The word statistics in our every day life means different things to different people. Statistics is the science of collecting, organizing & interpreting numerical facts which they call information. Let us see how statistics is defined by different authors & what they mean in our every day life.

State Statistics by Different Authors

“Statistics is the science of counting ", says Dr. A. L. Bowley.

As per Boddington, “statistics is the collection , presentation, analysis & interpretation of numerical data".

Even different authors have defined the term statistics ,solved statistics answers.Horace scrist has been most exhaustive in defining the term. His definition states " By statistics they mean aggregates of facts affected to a marked extent by multiplicity of causes, mathematically expressed, enumerated or estimated according to reasonable standards of accuracy in a systematic manner for a predetermined purpose & placed in relation to each other ".

Do you need online statistics homework help

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Let us solve statistics answers
Statistics is the literary ability of making trenchant use of nonverbal collection relating to groups of individuals or experiments. It works with all aspects of this, including not only the compendium, analysis and representation of specified information, but also the thought of the assembling of collection, in cost of the ornamentation of surveys and experiments, get help with statistics homework online

A actuary is someone who is specially well versed in the construction of mentation indispensable for the thriving curative of statistical reasoning. Often much group somebody gained this get after play affect in any of a wares of comedian. Also get information on trigonometry help online. There is also a penalty called mathematical statistics, which is haunted with the suppositional foundation of the field.

Funny Math

Introduction to Constructions

In earlier chapters, the diagrams, which were necessary to prove a theorem or solving
exercises were not necessarily precise. They were drawn only to give you a feeling for
the situation and as an aid for proper reasoning. However, sometimes one needs an
accurate figure, geometry online for example - to draw a map of a building to be constructed, to design tools, and various parts of a machine, to draw road maps etc. To draw such figures
some basic geometrical instruments are needed. You must be having a geometry box
which contains the following:you will find how to solve geometry problems
(i) A graduated scale, on one side of which centimetres and millimetres are
marked off and on the other side inches and their parts are marked off.
(ii) A pair of set - squares, one with angles 90°, 60° and 30° and other with angles
90°, 45° and 45°.
(iii) A pair of dividers (or a divider) with adjustments.
(iv) A pair of compasses (or a compass) with provision of fitting a pencil at one
end.
Solutions to all your questions online geometry answers
(v) A protractor.

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Definition:

It studies triangle, particularly right triangles. Trigonometry deals with relationships between the studies and the angles of triangle and with the trigonometric functions get trigonometry help free.

Right Angle Triangle of Trignometry

It has three sides and the total angle is 180 degree. In the right angled triangle the side opposite to 90 degrees is called the hypotenuse and the opposite side is the side that is just opposite to angle A (the angle which is to be found), the other side is the adjacent side,take a look on free trigonometry answers for your queries so the length of the side is taken as a,b,c here a is the side length of the opposite, b is the side length of the base that is adjacent and the c is the side length of the hypotenuse. Angle of the right angle triangle will be measured in terms sin, cos, tan (we know that the total angle is 180 degree for any triangle) sin A=a/c, cos A=b/c and tan A=a/b.
The reciprocals of sin functions named the cosec ,Do not worry when there is online trigonometry homework help.cos functions named sec and tan functions is named as cot and also the inverse functions of sin is called as arcsine ,cos is called arccosine and the tan function is called as arc tan respectively .

Arithmetic Mean

Definition for Arithmetic mean
In mathematics and statistics, the arithmetic mean (or simply the mean) of a list of numbers is the sum of all of the list divided by the number of items in the list. If the list is a statistical population, then the mean of that population is called a population mean. If the list is a statistical sample, we call the resulting statistic a sample mean..
Do you know the conversion of meters to centimeters

Steps to Find out the Mean:

1. Add all the numbers (on a scratch piece of paper if needed.)

2. After we have added the numbers correctly, count how many numbers there are
(for example: 2, 3, 5, 4, 1 there are 5 numbers, right.)

3. Now divide the integer of how many of the numbers you have by the sum
(For example: 20(sum) divided by 5,(how many of the numbers) the answer would by 4
Solution to Algebra : Learn Algebra

Perimeter of a Rectangle

A rectangle is any quadrilateral with four right angles. A rectangle is a special case of a parallelogram, whose opposite sides are equal in length and parallel to each other.

Perimeter of a Rectangle can be calculated by the below formula:-

P = 2(L+W)

Where, L = length and W = width

A rectangle is cyclic. All the angles of a rectangle are congruent. The two diagonals of a Rectangle are equal and bisect each other. All the four interiors angles of a Rectangle measure 90° (right angles). The opposite sides of a rectangle are parallel to each other.

Volume of a Rectangle can be calculated by the below formula:-

V = l*w*h

Where, L = Length, W = width and H = Height.

Like wise there are many other geometrical objects, like Circle, rhombus, triangle, etc

FATHER OF GEOMETRY

Eulicid is considered the father of geometry. There are a number of other early contributors to this branch of mathematics, but it is Euclid who gave us the extraordinary mathematical text, Elements. Euclid taught for 20 to 30 years. He wrote Elements as he taught. Euclid influenced Archimedes and Appollonius, students at the library.

Geometry is a part of mathematics concerned with questions of size, shape, relative position of figures, and the properties of space. Geometry is one of the oldest sciences. In Euclid's time there was no clear distinction between physical space and geometrical space.

Ancient scientists paid special attention to constructing geometric objects that had been described in some other way. Classical instruments allowed in geometrical shapes constructions are those with compass and straightedge.

Euclidean geometry is a mathematical system attributed to the Alexandrian Greek mathematician Euclid, whose elements is the earliest known systematic discussion of geometry.

CONCENTRIC CIRCLES

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A collection of circles is said to be concentric if they have the same center. The region formed between two concentric circles is therefore an annulus.

Concentric circles are simply circles that all have the same center. They fit inside each other and are the same distance apart all the way around. In the figure above, resize either circle by dragging an orange dot and see that they both always have a common center point.

Concentric circles definition: Two or more circles which have the same center point, circles of different diameters but with the same centre point

Circles, tubes, cylindrical shafts, disks, and spheres may be concentric to one another. Concentric objects generally have different radii, as concentric object with the same radius are equal.

Below is an example image of concentric circle art.

AXIOM DEFINITION

Axiom definition is as follows:-

An axiom or postulate is a proposition that is not proved or demonstrated but considered to be either self evident, or subject to necessary decision. Axiom is a rule or a statement that is accepted as true without proof. An axiom is also called a postulate.

There are two different kinds of Axioms:-

Logical Axioms and Non Logical Axioms.

Logical axioms, being mere formula, are devoid of any meaning; but the point is that when they are interpreted in any universe, they will always hold no matter what values are assigned to the variables.

Non-logical axioms are formulas that play the role of theory-specific assumptions. Reasoning about two different structures.

Postulate definition is as follows:-

A statement whose validity is accepted without proof is called a postulate. In addition to point, line plane etc, it is also necessary to start with certain other basic statements that are accepted without proof. In geometry these are called postulates.
A postulate, though itself is an unproved statement, can be cited as a reason to support a step in a proof.

To know more about Postulates click here.

PERMUTATIONS AND COMBINATIONS

INTRODUCTION TO PERMUTATIONS AND COMBINATIONS

The topic for today is Permutations and Combinations.

Certain types of probability calculations involve dividing the number of outcomes associated with an event by the total number of possible outcomes. For simple problems it is easy to count the outcomes, but in more complex situations manual counting can become laborious or impossible.

Fortunately, there are probability formula for determining the number of ways in which members of a set can be arranged. Such arrangements are referred to as permutations and combinations, depending on whether the order in which the members are arranged is a distinguishing factor.

Permutation means arrangements of things. The word arrangement is used, if the order of things is considered. The permutation of a number of objects is the number of different ways they can be ordered; i.e. which is first, second, third, etc. If you wish to choose some objects from a larger number of objects, the way you position the chosen objects is also important.

Combination means selection of things. The word selection is used, when the order of things has no importance here we need not consider the order in which objects were chosen or placed, just which objects were chosen. We could summarize permutations and combinations (very simplistically)

For information on Probability Model click here.

CONCENTRIC CIRCLES

Circles are simple closed curves which divide the plane into two regions, an interior and an exterior. Circles is one main topic under geometry basics. The circle has been known since before the beginning of recorded history. It is the basis for the wheel, which, with related inventions such as gears, makes much of modern civilization possible. The circle is a highly symmetric shape: every line through the center forms a line of reflection symmetry and it has rotational symmetry around the center for every angle.


Concentric circles are simply circles that all have the same center. They fit inside each other and are the same distance apart all the way around. In the figure above, resize either circle by dragging an orange dot and see that they both always have a common center point. The region between two concentric circles of different radii is called an annulus. Any two circles can be made concentric by inversion by picking the inversion centre as one of the limiting points. The figure below shows a concentric circles art.

Learning Probability

In the theory of probability we deal with events which are outcomes of an experiment. The word 'experiment' means an operation which can produce some well defined outcome(s):

There are two types of experiments:

(i) Deterministic (ii) Random or Probabilistic.

Deterministic Experiment: Deterministic Experiments are those experiments which when repeated under identical conditions produce the same result or outcome. When experiments in science and engineering are repeated under identical conditions, we obtain almost the same result every time.

Random or Probabilistic Experiment:If an experiment, when repeated under identical conditions, do not produce the same outcome every time but the outcome in a trial is one of the several possible outcomes, then it is known as a random or probabilistic experiment. For example, in tossing of a coin one is not sure if a head or a tail will be obtained, so it is a random experiment. Similarly, rolling an unbiased die and drawing a card from a well shuffled pack of card are examples of a random experiment.

Construction of Circumcircle of a Triangle

Today's topic is related to Construction of Circumcircle of a Triangle. Before we get into construction let us first try to know what is meant by Circumcircle of a Triangle.

Circumcircle of a Triangle: A circle passing through the vertices of a triangle is known as Circumcircle of a triangle. The centre of the circumcircle of a triangle is the point of concurrency of perpendicular bisectors of any two sides of the triangle and is known as circumcentre. The circumcentre of a triangle is equidistant from the three vertices. The distance between the circumcentre and any vertex of the triangle is the circumradius.

Listed below are the steps followed in constructing circumcircle of a triangle:-

Step 1:- Draw the given triangle ABC with the help of the given data.

Step 2:- Draw the Perpendicular Bisector of any two sides, say AB and AC of the triangle.

Step 3:- Obtain the point of intersection of the bisectors drawn in step 2 and let this point be O.

Step 4:- Draw the circle with O as centre and OA or OB or OC as radius.

The circle obtained is the required Circumcircle of Triangle ABC

Help on Differential Equation

Before we start with differential equation's let us first understand what is an equation?

What is an Equation??

A statement asserting the equality of two expressions, usually written as a linear array of symbols that are separated into left and right sides and joined by an equal sign is called an Equation.

Let us understand this with the help of the below example:

Example:
If one number is thrice the other and their sum is 60, find the numbers.
Solution:
Let the numbers be x and y.
x is 3 times y x = 3y …(1)
Sum of x and y is 60
x + y = 60 …(2)
Putting the value of x from (1) in (2), we get,
3y + y = 60
4y = 60
y = 15
Substituting y = 15 in (1), we get,
x = 3 x 15
= 45

The required numbers are 15 and 45.

What is Differential Equation:-

An equation involving problem on derivative (derivatives) of the dependent variable with respect to independent variable (variables) is called a differential equation.

Below is one example on Differential Equation:

A differential equation involving derivatives of the dependent variable with respect to only one independent variable is called an Ordinary Differential Equation.

Equations involving derivatives with respect to more than one independent variables, called a Partial Differential Equation.

If you liked this please leave a comment. Will be back with some more topics that can make our life easier in understanding concepts in Math and solve problems.

Empirical probability

A form of probability that is based on some event occurring, which is calculated using collected empirical evidence. An empirical probability is closely related to the relative frequency in a given probability distribution.

In order for a theory to be proved or disproved, empirical evidence must be collected. An empirical study will be performed using actual market data. For example, many empirical studies have been conducted on the capital asset pricing model (CAPM), and the results are slightly mixed.

In some analyses, the model does hold in real world situations, but most studies have disproved the model for projecting returns. Although the model is not completely valid, that is not to say there is no utility associated with using the CAPM. For instance, the CAPM is often used to estimate a company's weighted average cost of capital.

An advantage of estimating probabilities using empirical probabilities is that this procedure is relatively free of assumptions. For example, consider estimating the probability among a population of men that they satisfy two conditions:

• That they are over 6 feet in height
• That they prefer strawberry jam to raspberry jam.

A direct estimate could be found by counting the number of men who satisfy both conditions to give the empirical probability the combined condition. An alternative estimate could be found by multiplying the proportion of men who are over 6 feet in height with the proportion of men who prefer strawberry jam to raspberry jam, but this estimate relies on the assumption that the two conditions are statistically independent.

Conic Section

The locus of a point moving on a plane such that its distances from a fixed point and a fixed straight line on the plane are in constant ratio e, is called a conic.

The fixed point is called the focus and is usually denoted by S. The fixed straight line is called the directrix. The constant ratio e is called the eccentricity. The straight line on the plane passing through the focus and perpendicular to the directrix is called the axis. Therefore, the locus of a point moving on a plane such that SP/ P M = e , where PM is the perpendicular distance from p to the directrix, is called a conic.

• if e= 1 the conic is called a parabola
• if 0 <1>the conic is called an ellipse
• if e> 1 the conic is called a hyperbola.

Line and Line Segment

A line is a set of points on a directly path that extends to infinity. Any two nodes on the line can be used to name it. This type of line is known as line DE. A line segment is a division of a line that has two end points. Here we will see this line segment and line . A ray is also a section of a line.

Line, Line Segment

Line segments having two end points. These endpoints are used to put the name of the line segments. This line segment is known as segment AB.

Line Segment Angle

Definition

If V is a vector space over R or C, and L is a subset of V then L is a line segment if L can be parameterize as,

For some vectors u, v ε V, in which case the vectors u and u+v called the end points of L.

Occasionally one necessitates difference between open and the closed line segments. Then one explained the closed line segments, and the open line segment of a subset L.

More frequently than above, the concept of a line segment can define in an arranged geometry. (

Properties of Line Segments

• A line segments are connected to the non-empty set.
• If V is a topological vector space, then a protected line segment is a closed set in V.

Discrete Probability Distribution

Discrete Probability Distribution

A discrete random variable assumes each of its values with a certain probability,

Let X be a discrete random variable which takes values x₁, x₂, x₃,…x_n where p_i = P{X = x_i}

Then

X : x₁ x₂ x₃ .. x_n

P(X): p₁ p₂ p_{3 .....} p_n

is called the probability distribution of x.

Note 1:

In the probability distribution of x

Note 2:

P{X = x} is called probability mass function.

Note 3:

Although the probability distribution of a continuous random variable cannot be presented in tabular form, it can have a formula in the form of a function represented by f(x) usually called the probability density function.

Mixture problems

The Mixture problems are part of the algebra word problems. The mixture problems deals with two or more things mixed in different ratio and ask to find price, percentage and some other quantities. For solving mixture problems we need to know the following things,
The total amount = amount of first mixture + amount of second mixture .This formula used to find the unknown mixture amount.
We can form the equation to find unknown value by using the following formula,
(Cheaper value / dearer value) = (mean value –cheaper value)/ (dearer value –mean value)
Let us understand this with the following example on mixture problem.
f Real gold is 92.5% pure gold. How many pounds of Real Gold needs to be mixed to a 90% Gold alloy to obtain a 500g of 91% gold alloy?
Solution:
Let us take x and y be the weights of real gold and of the 90% alloy to make the 500 pounds at 91%.
That is x + y =500
The formula is,
amount₁ (%) + amount₂ (%) = (amount₁ + amount₂) (%)

92.5 % of x + 90% of y = 91% of 500
Substitute y = (500 – x) in the above equation,
We get,
92.5% of x + 90% of (500 - x) = 91% of 500
(92.5x)/100 + (90(500-x))/100 = (91(500))/100
Multiply by 100 on both sides,
92.5x+ 45000-90x=45500
Subtract 45000 on both sides,
92.5x-90x=45500-45000
2.5x=500
Divide by 2.5 on both sides,
X = 500/2.5
X = 200
Answer : 200 pounds of gold needs to make 91% of gold alloy.

Notations

A complex number is a number combination of a real and imaginary part. It can be written in the form of a + bi, where a and b are real numbers, and i is the standard imaginary unit with the property of i ² = −1. Complex numbers are containing the ordinary real numbers, but extend them by adding in extra numbers and correspondingly expanding the understanding of addition and multiplication.

Notation:

The set of all complex numbers is usually denoted with an imaginary and real part.
Complex numbers are usually written in the form of a and b.
The form is a + bi
From this part a and b are real numbers, and i is the imaginary part, which has the property i 2 = −1. The real number a is called as real part of the complex number, and the real number b is called as imaginary part.

For example:

4 + 3i is a complex number, with real part 4 and imaginary part 3. If z = a + bi, the real part a is denoted Re(z), and the imaginary part b is denoted as Im(z).
In some disciplines, the imaginary part i is instead written as j, so complex numbers are sometimes contain as a + bj or a + jb.

History of Mathematical Notation:

Below list shows history of mathematical symbols for list of symbols in history of mathematical notation:

• Beginning of notation
• Greek notation
• Chinese notation
• Indian notation
• Beginning of Arabic numerals
• North African notation
• Pre-calculus
• Calculus
• Euler

Parameters in Mathematics

The parameter in mathematics is an amount that serves to transmit functions and variables with a general variable. When a connection would be hard to explain with an equation. In different context the word may contain particular use. A variable parameter is a proper parameter whose name is close to the similar memory position as that named by the real parameter at the moment the call is complete.

Parameters in Mathematics

Mathematical functions contain one or more arguments that are chosen in the meaning by variables, while their meaning can also have parameters. The variables are mention in the record of point of view that the meaning takes, however the parameters are not For example single can define a common quadratic function through defining

f(x) = ax² + bx + c;

Here the variable x designate the function argument, however a, b, and c are parameters that establish which quadratic function single is considering. The parameter might be included into the function name to designate its dependence on the parameter; for case single may describe the bottom a logarithm by

Where a is a parameter that indicate which logarithmic function is individual used; it is not an row of the function, and will for case be a constant while considering the derived

Mathematical analysis

The integrals dependent on a limit are often measured. These are of the form

In this method, t is the row of the function F and on the right-hand parts the parameter on which the basic depends. When evaluate the integral, t is detained constant, and therefore it considered a parameter. If we are involved in the value of F for special values of t, then, we now regard as it to be a variable. The amount x is a dummy variable or variable of integration.