Solving Variable Expressions

Introduction to solving variable expressions:

In mathematics, an expression is a finite combination of symbols that are well-formed according to the rules applicable in the context at hand. Symbols can designate values (constants), variables, operations, relations, or can constitute punctuation or other syntactic entities. The use of expressions can range from simple arithmetic operations like 3+ 5 x ((-2)^7 – 3/2) . (Source: Wikipedia)

Types of Math Solving Variable Expressions:-

In solving variable expressions to study the algebra expressions in following types are used in algebra expressions.

Variable expressions Variable expressions using word

Variable expressions  

In variable expressions means to form a number and word in expression like as add, plus, greater, less than, increase, decrease etc.

For Example,

24 increased by x?

24 + x

Variable expressions using word

In variable expressions using word means the expression numbers and word are shows the sentence formation like as add, plus , greater ,less than ,decrease etc

For Example,

Haley earned 31 bonus points. Marisol earned b more bonus points than Haley. Choose the expressions that show how many bonus points Marisol earned.

31+b

Example Problems for Solving Variable Expressions:-

Problem 1:-

Solving variable expressions for 370 added to v.

Solution:-

Adding the variable v to number 370 and form an expression as V+370

Answer:- V+370 

Problem 2:-

Solving variable expression for 28 minus w

Solution:-

Subtracting the variable w to number 28 and form an expression as 28-w. I like to share this Algebra 2 problem solver with you all through my article.

Answer: 28 –w

Problem 3:-

Solving variable expression for 703 increased by z

Solution:-

Increased the variable z to number 703 and form an expression as 703+z

Answer: 703+z

Problem 4-

Solving variable expression for 45 decreased by p

Solution:-

Decreased the variable p to number 45 and form an expression as 45-p

Answer: 45-p

Problem 5-

Talia earned 64 bonus points. Jones earned d more bonus points than Talia. Choose the expression that shows how many bonus points Jones earned.

Solution:-

Adding the jones variable d to talia earned 64 bonus points and form an expression as 64+d

Answer: 4+d

Vector Component Calculator

Introduction to vector component calculator:

The collection of ordered components are called as vector and the types of components are x component and y component. The calculator is a device that gives the output of all math operations. The vector component is also determined by calculator. Both vector components are representing the direction by sign. Now we are going to see about vectors component calculator.

Explanation for Vector Component Calculator

Vector component:

In math, the vector component is used in algebra. The x component is representing the horizontal component that is x-axis value and the y component is representing the vertical component that is y-axis value. If two vectors are present means find out the components by addition operation.

Vector component calculator:

The vector calculator is calculating the components by addition method. The x component of first vector is added with x component of second vector. Similarly the y component of first vector and second vector is added.I like to share this math homework help answers with you all through my article.

The graph representation is used in vector calculator. The calculator contains graph with in it. We can see the calculator operations stepwise.

More about Vector Component Calculator

Following steps are operations of vector calculator:

Step 1: First plotting the first vector in graph.



The first vector is plotted as above and this vector is represented with x components 5 and y components 4.

Step 2: Plotting the second vector in graph.



The second vector is plotted as above diagram.The second vector is represented with x component 6 and y component -4.

Step 3: The addition of two vectors.



The given two vectors are added by calculator. The result of vector addition in calculator is shown above.

The calculator represents the x component value is 11 that is 5 + 6 and the y component is 0 that is 4 - 4. Another application of vector calculator is magnitude and direction determination.

Array Math Definitions

Introduction to array

Let us discuss about the array math definition. The definition of array is number or objects arranged in rows and columns. The array is the main tools in the mathematics. The basic operation of the array is multiplication and division. The array is declaring the square bracket. The example of the array is [8]. Next we see the definition of an array.

Definition of the Array in Math

The definition of the diagonal array is square matrix.  A diagonal matrix having the element only in the diagonal position. The remaining position elements are zero.

`[[9,0,0],[0,5,0],[0,0,7]]`

The array of number is 3 rows and 3 columns. That is defining the B [3] [3].

Definition of row matrix

The definition of row matrix is called as the only one row. It is represents the 1 x n. the n is declare the number of columns.

Examples of row matrix: [4   5   9]

Math definition of column matrix

The column matrix is defined as the matrix contains only one column. It is declaring the up to down format. It is represents the n x 1. The n is called as the number of rows.

Examples of column matrix:

`[[8],[11],[14]]`

Math Definition of even Array

The definition of the even array is the number of rows and column is a even number. the even number is normally divisible by two. The example of the even number is 2, 4, 6 etc. the example of the even array is,

`[[5,8],[7,6]]`

This array is the 2 x 2 array.

The definition of the 2 x 2 array is declare only 2 rows and 2 column should be followed.

2 x 2 = 2 + 2

= 4.    

Sample E Learning

Introduction to sample e learning:-

Sample e learning is important for students. Student’s does learning the sample e learning and also solve the e learning problems. Here e means `e^x` . In math exponential function means ex, where e is the significance of ex the same value again consequent.
For example,
`17e^x` this is a way to write an exponential function.
e = 2.718 is the value of e.

Basic Properties of Sample E Learning:-

In the following basic properties of  sample e learning:

`e^x e^y = e^(x+y)`
`(e^x)^p = e^(px)`
`(de^x)/(dx) = e^x`
`(de^ax)/(dx) = ae^(ax)`
`(d^n e^ax)/(dx^n) = a^n e^(ax)`
`e^x/ e^y = e^(x-y)`
`root(p)(e^x) = e^(x/p)`
`inte^x dx = e^x `

Example Problems to Sample E Learning:-

Problem 1:-

Solve the exponential function equation `e^x = 47`

Solution:-

Here the natural log is the inverses of exponential function, so use ln to get fast solve this problem.

ln `e^x` = ln 47

x = ln 47 (take natural log of 47)

= 3.850

So the answer is 3.850


Problem 2:-

Solving add the exponential equation `e^(18x) +e^(11x)`

Solution:

Given: `e^(18x) +e^(11x)`

We know the property `e^x e^y = e^(x+y)`

Take the common term e.

= `e^(18x+11x)`

= `e^(29x)`

Adding the both values and get 29x.

Finally we get an answer as `e^(29x)`


Problem 3:-

Solving whether the point (0, 1) lies on the graph of the function y = 18(4)x.

Solution:-

Substitute x = 0 in the function y = 18(4)x.

We know the property `e^x`

y = 18(4)0

= 18(1)

= 18

The y–coordinate of the point is 1, which does not match with the obtained value y = 18.

So, the graph of the function y = 18(4)x does not contain the point (0, 1).

Trigonometry Radian Measure

Introduction to trigonometry radian measure:

An angle is determined by rotating a ray about its endpoint. One way to measure angles is in radians. To signify that a given angle is in radians, a superscript c, or the abbreviation rad might be used. If no unit is given on an angle measure, the angle is assumed to be in radians. `(3pi^c)/2-=(3pi)/2 rad.-=(3pi)/2`                                                                                                                            (Source: Wikipedia)

Trigonometry Radian Measure

Middle angles of a circle contain an angle measure of 1° if it subtends an arc to be 1/360 of the boundary of the circle. These appearances of angle determine is reasonably general. Another appearance of angle determine namely in utilize is radian measure. If a middle angle subtends an arc i.e. identical toward the radius of the circle after that the middle angle contain a computing of one radian.

If a middle angle ? of a circle through radius r subtends an arc of length s, subsequently their radians establish is describing since  `theta= s/r`

Given, radius is 4 cm, and length of arc is 60 cm.

We know that the formula for radian measure of `theta=s/r` .

As a result,`theta = 60/4`

?=15

The angle of the arc is 15 radians.
I am planning to write more post on trigonometric function, distance from point to line. Keep checking my blog.
Examples for Trigonometry Radian Measure

Example 1 for trigonometry radian measure

Calculate the angle of the arc, if the radius is 6 cm, and length of arc is 120 cm

Solution:

Given, radius is 6 cm, and length of arc is 120 cm.

We know that the formula for radian measure of `theta=s/r` .

As a result,`theta = 120/6`

?=20

The angle of the arc is 20 radians.

Example 2 for trigonometry radian measure

Calculate the angle of the arc, if the radius is 8 cm, and length of arc is 135 cm

Solution:

Given, radius is 8 cm, and length of arc is 135 cm.

We know that the formula for radian measure of `theta=s/r` .

As a result,`theta = 135/8`

?=17

The angle of the arc is 17 radians.

Example 3 for trigonometry radian measure

Convert 1650 into radians

Solution:

We know that,

`(radians)/pi=(degrees)/180^0`

`radians=degrees pi/(180^0)`

`Given radians = `1650

`radians=165 pi/(180)`

Therefore,`radians=(11pi)/(12)`

Percent Discount Formula

Introduction to percent discount formula:

The word percent means out of hundred or per hundred. Percentage is a fraction with its denominator 100. The numerator of such a fraction is called rate percent.

Ex: (i) `3 / 5` = `3 / 5` `xx` 100% = 60 %

(ii) 0.25 = 0.25 `xx` 100% = 25%

(iii) 15% of 80 = `15 / 100` `xx` 80 = 12.

Now let us see few problems on this topic percent discount formula.

Example Problems on Percent Discount Formula.

Ex 1: What is the single discount which is equivalent to successive discounts of 20%, 15% and 10%?

Soln: Let us consider the price of an article be 100 dollars.

Therefore After the first discount 20%, it will cost = 100 – 20 = 80 dollar.

Second discount = 15%

Therefore 15% of 80 = 15 / 100 * 80 = 12

Therefore the new price = 80 – 12 = 68 dollars.

Third discount = 10%

Therefore 10% of 68 = `10 / 100` `xx` 68 = 6.8

Therefore the new price = 68 – 6.8 = 61.20 dollars

Therefore the single discount is 100 – 61.20 = 38.80%

Here one important thing is, we can get the single discount by adding all the discounts as 20 + 12 + 6.8 = 38.8%.

Ex 2: An article price is 450 dollars. It is sold at a discount of 20%. Find:

(i)                  The discount given

(ii)                The selling prize of the article.

Soln: Given: The price of the article is 450 dollars,

(i) The discount given = 450` xx 20/100` = 90 dollars.

(ii)  The selling price  = 450 – discount

= 450 – 90

= 360 dollars

Ex 3: In a sale, a shopkeeper allows 10% discount on his article. What price must he mark on an article, which costs his 750 dollar, to make a profit of 20%?

Soln: Given: Cost price = 750 dollars.

Therefore to give 10% discount and to gain 20%, his selling price should be as follows:

750 + 20% of 750

= 750 + `20 / 100``xx` 750 = 900 `=>` 90% (x) = 900

`=>` x = 900 `xx` `100 / 90` = 1000

Therefore the marked price = 1000 dollars.

Between, if you have problem on these topics Markup Formula, please browse expert math related websites for more help on Surd Definition.

Practice Problems on Percent Discount Formula.

Find a single discount for 30%, 20% and 10%
[Ans: Single discount = 50.4%]

2. A dealer is selling an article at a discount of 5% on the marked price. What is the selling price if it is marked 140 dollar?

[Ans: Selling price = 133 dollars]

Descriptive Set Theory

Introduction to descriptive set theory:
A set is a well-defined collection of things

The things belonging to a set are called it's members or elements. These elements may be objects, persons, letters, numbers or any items at all.
Well-defined means that given a member, there must be no doubt in deciding whether it belongs to, or does not belong to the given set. Example:-
A set of apples weighting 200 g or over is a well-defined.
A collection of heavy apples is not well-defined and so it not a set.
All elements are separated by a comma.
The elements should be enclosed in braces (”{ }”).
Sets are usually represented by capital letters.
The order in which the members appear is not important.
If one or more elements are repeated, the set remains the same.
A set may consist of a single member like, B = {National bird of India} = {Peacock}. If 'A' is a set and 'a' is an elements of this set, then “a belongs to A”
This article is about descriptive set theory and the topics in that.

Descriptive Set Theory-representation of a Set (notation):

A set is determined by its members or elements. This determination is brought out in the following three ways.

Roster method :-

The method of listing the elements inside the braces is called Roster method. Example :- A set of alphabets of the English language represented by P is written as :
P = {A , B , C , D , E , F , ….}

Description method :-

The method of listing a set by a well-defined statement or description is called description method.
Example :- {Vowels in English alphabet}

Set builder form :-

The method of listing the elements inside the braces by stating the rule or property or formula is known as Set builder form. Example :- If A is a set of a natural numbers less than 80, then it can be represented as, A = {x : x is a natural number and is less than 80} or as

A = {=x : x E N, x<80 br="br">
Types of Sets in Descriptive Set Theory:

Finite set

The elements are limited. Example :-
Natural number less then 60.
A = {1,2,3,4,5,6,7,.....}
Days of a week
W = {Monday, ….. , Sunday}

In finite set

Unlimited numbers of elements Example :-
Set of odd numbers
N = {1 , 3 , 5 , 7....}
Set of even numbers

E = {2 , 4 , 6 , 8....}

Empty set

No elements is represented
Set of odd numbers between 5 and 6
A = { }
30th day of February

D = { }