End Area Volume Calculation

Introduction to end area volume calculation:

In math, Volume plays vital role in geometry. Volume is used to find how much space occupied by the shape. It is measured in cubic units. Understanding Area of Circle Equation is always challenging for me but thanks to all math help websites to help me out.

In this article, we shall see about calculation of cross section measurement by the average end area method.

We are going to calculate volume of cross section shape by the average end area method using formula.

Let us see about end area volume calculation in detail.

Average End Area Volume Calculation:

The volume formula for average end area is very exact method calculation only for end areas are equal. For end areas are not equal cases, this volume formula calculates slightly larger than its original values. For example, we are going to calculate volume of pyramid, the calculation of volume will be equal 50% of correct volume values.

The formula for calculation of volume by average end area:

Volume = L x `1/2` (A1 + A2) cubic meter.

L – Distance in meters

A1 and A2 – area in Square meters

This average end area calculation is used to calculate volume between two cross sections. That is, two cross sectional areas are averaged and multiplied by the length(distance) between two cross sections to get the volume. Is this topic how to solve linear equations and inequalities hard for you? Watch out for my coming posts.

Let us discuss example problems of average end area calculation.

Example Problem - Average End Area Volume Calculation:

Example Problem:

Find the volume of two cross sections using average end area method for following values.

Length is 20 m, two areas are 150 m2 , 180 m2.

Solution:

Given:

L = 20 m

A1 = 150 m2

A2 = 180 m2

Formula for calculation:

Volume = L x `1/2` (A1 + A2)

Substituting values for length and areas into above formula.

Volume = 20 x `1/2` (150 + 180)

Volume = 20 x `1/2` (330)

Volume = 20 x 165

Volume = 3300

Therefore, volume of two cross sections is 3300 m3.

Thus we solved volume calculation by using average end area method.

Percentage Variance

Introduction for percentage variance:

The percentage of the number is a method of showing the number with the denominator 100 as fraction. The percentage of the number is represented by the symbol “%” or “pct”. Percentage shows the relation of the two quantities, the first quantity is associated with the second quantity. So, first quantity should be larger than zero. But in this article we are going to see percentage variance. I like to share this Definition of Variance with you all through my article.

Equation for percentage variance is `("new value"-"previous value")/"previous"` `xx` 100

Examples for Percentage Variance:

Example 1:

The last year of the bag was soled at the price 57. In this year, the bag is selling with the price 28. Calculate percentage variance by using formula.

Solution:

Percentage variance = ` ("new value-previous value")/"previous value"` `xx` 100

= `(28-57)/57` ` xx` 100

= `-29/57` `xx` 100

= -0.5088 `xx` 100

= -50.88%

Therefore, 50.88% loss in selling of bag in this year when we compare with the last year.

Example 2:

The last year of the basket was soled at the price 39. In this year, the basket is selling with the price 58.

Solution:

Percentage variance = `("new value-previous value")/"previous value"` `xx` 100

= `(58-39)/39` `xx` 100

= `19/39` `xx` 100

= 0.4872 `xx` 100

= 48.72%

Therefore, 48.72% percentage is profit in selling of basket in this year when we compare with the last year.
I have recently faced lot of problem while learning linear equations in two variables word problems, But thank to online resources of math which helped me to learn myself easily on net.

Practice Problems for Percentage Variance:

Problem 1:

The last year of the washing machine was soled at the price 48. In this year, the washing machine is selling with the price 52. Calculate percentage variance by using formula.

Solution:

8.33% profit in selling of washing maching in this year when we compare with last year

Problem 2:

The last year of the TV was soled at the 50 . In this year, the TV is selling with the price 72. Calculate percentage variance by using formula.

Solution:

44% profin in selling of TV in this year when we compare with the last year.

Problem 3:

The last year of the laptop was soled at the price 89. In this year, the laptop is selling with price 20.

Solution:

77.53% loss in selling of laptop in this year when we compare with the last year.

Problem 4:

The last year of the computer was soled at the price 89. In this year, the computer is selling with the price 83. Calculate percentage variance by using formula.

Solution:

6.74% loss in selling of computer in this year when we compared with the last year

Information on Math Functions

Introduction to information on math functions:

In this article information on math functions, we will refer definition of a function and some worked example problems. Function is defined as a equation where the terms present in one side will vary with the terms present on the other side. For example x=5b+6c here x is a dependent variable of b and c, since b and c are independent variables.

Information on Math Function

1.Function is defined as a collection of mathematical function which produce the result after performing the calculation.

For example y=(4x+5x)+`(5x)/2` -4(x+2)

After performing the right hand side calculation which produces the result.

2.The function is used to identify or compare the relationship between two numbers

y=f(x)=x+7

Here the value y is greater than x.

3.There are lot of functions like

logarithmic function Example: f(x)=log x

Trigonometric function Example: f(x)= sin x

Geometric function Example `y=x^2`

Exponential function `f(x)=e^x`. Understanding square root of 7 is always challenging for me but thanks to all math help websites to help me out.

Worked Example Problems - Information on Math Functions

Example problem 1- information on math functions:

The price of one lemon and watermelon is $80 then what is the price of 5 jack fruit and 5 watermelon?

Solution:

Consider lemon as x

Watermelon as y

So from the given statement x + y = 80-------1

The price of 5 lemon and 5 watermelon, 5x + 5y = ?

We can write the above equation as

The price of 5 lemon and 5 watermelon = 5(x+y)

From the first equation we can substitute the x+y value

The price of 5 lemon and 5 watermelon =5(x+y)

= 5(80) = 400

The price of 5 lemon and 5 watermelon = $400

Example problem 2 - information on math functions

If log8=0.903 then find the value of log16?

Solution:

The number 8 can also be written as` 2^3`

They have given that log` 2^3=0.903`

3 log2=0.903

So log2=0.3010

The value of log 16 is given by `log 2^4 =4 xx log2`

`=4 xx 0.3010`

log 16 =1.204

Example problem 3- information on math functions

Calculate the value of `e^2 xx e^3` =?

Solution:

From the above statement `e^x xx e^y=e^(x+y)`

So `e^2 xx e^3=e^(2+3)=e^5=148.4`

Example problem 4- information on math functions

Consider `cos x = (2/5)` .Find out the value for sin x=?

Solution:

From the statement `sin^2 x+cos^2 x=1`

`sin^2 x=1- cos^2 x`

`sin x=sqrt(1- cos^2 x)`

=`sqrt[1-(2/5)^2]`

=`sqrt[1-(4/25)]`

=`sqrt(21/25)`

Divide Imaginary Numbers

Introduction about imaginary numbers:

The term "numbers" are used to measure the quantity. The term "numbers" are a fixed value, if it is integers or constants. It is also refer to a complex numbers, real number, imaginary numbers, etc. The complex numbers are numbers involving, there is no number that when squared equals -1. The square root of minus one is denoted by mathematical symbol ' i '. A number contains, i  am the co-efficient of that numbers are called imaginary numbers. Having problem with What is Composite Number keep reading my upcoming posts, i will try to help you.


Evaluation of Imaginary Numbers:

In the definition (`sqrt(-1)` )2should equal -1, but it does not, therefore the symbol i =`sqrt(-1)` is introduced,

i.e.,         `sqrt(-x)`      = i `sqrt(x)`  Where x is a positive number and (i)2 = -1.

The square roots of other than -1 of the negative numbers format is, `sqrt(-n)` = i`sqrt(n)` .

The important rules for symbol 'i' :

i-1 = `1/ i` = `i / (i^2)` = `i /(-1)` =  -i      ( reciprocal of symbol ' i ' is ' -i ' )

The powers of symbol ' i ' :

i1 = i

i2 = -1

i3 = i2 i = (-1)(i) = -i

i4 = i3 i= (-i)(i) = -(i)2 = -(-1) = 1

i5 = i4 i = (1)( i) = i

..........

Complex numbers are numbers involving i and are generally in the form:

iy `hArr` (real number)(i)  `hArr` imaginary number

x + iy   (real number) + (i)(real number) `hArr` complex number

Dividing Imaginary numbers

In the division of complex number operations performed through learn complex numbers online, first find out the complex conjugate of the denominator. Second we multiply the conjugate of complex number to both numerator and denominator of complex number. The conjugate of complex number of (x + iy) is (x - iy) and vice versa.

Please express your views of this topic rules for significant figures by commenting on blog.

Example 1:dividing Imaginary Numbers.

(a). `(2 + i3) /(4-i2)`

Solution:

Given:

` (2 + i3) /(4-i2)`

Dividing imaginary numbers:

`(2 + i3) /(4-i2)` = `(2 + i3) /(4-i2)` . `(4 + i2) /(4 +i2)`

= `((2 + i3)(4 + i2))/((4-i2)(4 + i2))`

= `((2 + i3)(4 + i2)) / (4^2 + 2^2)`

= `(8 + i4 + i12 -6)/(16 + 4)`

= `(2 + i16) / (20)`

= `(2)/(20)` + `i(16)/(20)`

= `1/(10)` + `i (4/5)`

Example 2:dividing Imaginary Numbers.
(a). `(6 + i2)/(-2+i3)`

Solution:

Given:

`(6 + i2)/(-2+i3)`

Dividing imaginary numbers:

`(6 + i2)/(-2+i3)`   = `(6 + i2)/(-2 + i3)` . `(-2-i3)/(-2-i3)`

= `((6 + i2)(-2-i3))/((-2 + i3)(-2-i3))`

= `(-12 +i18-4i -6)/(-2^2 + 3^2)`

= `(-20 + i14)/(4+9)`

= `(-20 + i14)/(13)`

=`(-20)/(13)` +`i(14)/(13)`    [Answer.]

Introduction to variance of discrete random variable:

The discrete random variables have the countable values for their probability. The variance value for the discrete random variable is calculated with the help of the mean. The random variables are said to discrete random variable when the sum of their probability is one. The online produces the link between the tutor and the students. With the help of the online the students clarify their doubts. This article contains the information about the discrete random variables in the probability theory and statistics.

Formula Used for Solve Online Discrete Random Variables:

The formulas used to determine variance for the discrete random variable are

Variance = `sum p(x) (x^2) - (sum x p(x)) ^2`

In this above mentioned formula the `(sum x p(x)) ^2` is the squared value of the mean in the statistics.

In the above formula x denotes the given set of discrete random values and p(x) denotes the probability value for the discrete random variables in the statistics.Having problem with what are exponents keep reading my upcoming posts, i will try to help you.

Examples for Solve Online Discrete Random Variables:

Example 1 to solve online discrete random variables:

Predict the mean, variance and standard deviation for the discrete random variables.

x	2	4	6	8	9
P(x)	0.23	0.21	0.30	0.11	0.15

Solution:

Mean = `sum x p(x)`

Mean = 2 (0.23) +4 (0.21) +6 (0.30) +8 (0.11) + 9(0.05)

Mean = 0.46+ 0.84 + 1.8 + 0.88 + 0.45

Mean = 4. 43

Variance = `sum p(x) (x^2) - (sum x p(x)) ^2`

Variance = ((0.23) (2) (2) + (0.21) (4) (4) + (0.30) (6) (6) + (0.11) (8) (8) + (0.15) (9) (9)) - (4.43)2

Variance = (0.92+ 3.36+ 10.8 + 7.04+ 12.15) - 19.6249

Variance = 34.27 -21.5296

Variance = 46.42

The variance for the discrete random variable is 46.42.

Example 2 to solve online discrete random variables:

Predict the mean, variance and standard deviation of discrete random variables.

x	10	20	-30	40	50
P(x)	0.22	0.12	0.25	0.05	0.36

Solution:

Mean = `sum x p(x)`

Mean = 10(0.22) +20(0.12) - 30(0.25) +40(0.05) + 50(0.36)

Mean = 2.2 +2.4 -7.5+ 2+ 18

Mean = 17.1

Variance = `sum p(x) (x^2) - (sum x p(x)) ^2`

Variance = ((0.22) (10) (10) + (0.12) (20) (20) + (0.25) (-30) (-30) + (0.05) (40) (40) + (0.36) (50) (50)) - (17.1)2

Variance = (22+48+ 225 + 80 +900) -292.41

Variance = 1275 - 292.41

Variance = 982.59

The variance for the discrete random variable is 982.59.

Open Number Line

Introduction to open number line
A definition of number line is placed in the correct position of numbers. The number line is generally represented the positive and negative numbers. Number line is commonly performing by the addition and subtraction operation. The general format of the line number is {-5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5}. Next we discuss about this articles open number line.

Open Number Line

The open number line is defined the empty line used in the operations are addition and subtraction. Open number line is generally used in the three parts. Those parts are organ of open line number, positive value of open line number and negative open line number.

The positive value means larges values of the open line number it is represented the 25, 35 and etc.

The negative line number means smallest values of the open line number it is represented the -50, -75 and etc.Understanding how to solve matrices is always challenging for me but thanks to all math help websites to help me out.

Example Problem of Open Number Line

Problem 1:

Calculate the following numbers using open line numbers.

(77 + 2 + 8 + 3)

Solution

The number is 77 + 2 + 8 + 3

The above all numbers are positive number. So that numbers are move from the open line number is right side only.

Step 1: Move 2 units from right side of the open line number. The answer is 79.

Step 2: Move 8 units from right side, the answer is 87

Step 3: Move 3 units from right side, the answer is 90.

The answer of the 77 + 2 + 8 + 3 is 90.

Problem 2:

Calculate the following numbers using open line numbers.

(63 + 12 - 3)

Solution

The number is 63 + 12 - 3

The above numbers are positive and negative number. So positive numbers are move from the right side and negative number are move from left side of the open line number.

Step 1: Move 12 units from right side of the open line number. The answer is 75.

Step 2: Move 3 units from left side, the answer is 72

The answer of the 63 + 12 - 3 is 72.