How to Calculate Square Feet

How to calculate square feet :Square feet of an area is determined by multiplying length and the width of the given area . The area of regular polygons like square , rectangle , triangle etc... can be calculated by using the formula . If the dimensions of a regular polygon is given in feet then by just substituting the given dimensions in the formula the area in square feet can be calculated , if the measurements are given in any other units such as centimeter or inches or yards then we convert these units to feet and then calculate the area in square feet , similarly for a circle also if the radius is in feet we can just substitute the radius in the area formula and calculate the area in square feet ,if the radius is given in any other unit then convert that to feet and then calculate the area in square feet .

Area of composite shapes , a composite shape is a shape which can be divided into more than one of the basic shapes . An example of a composite shape or figure is shown in the picture .

Here in this picture we can see a square , a rectangle and a triangle . Area of the whole figure can be calculated by calculating the areas of each shape and then adding them . If the measurements are not in feet then we have to convert them to feet and calculate the area in square feet .

How to calculate square feet live situations .

The home we live , the school we study and mostly all other places one or the other time needs the area of floors , walls, ceilings , windows etc. in square feet to get them painted or any other purpose and usually the areas are calculated in square feet as most of the paints or coating materials have the coverage  specification mentioned in square feet like a ' x ' brand paint covers 30 square feet per liter . 

For How to calculate square feet the example here is an interior view of a room which has to be carpeted and walls painted .( all measurements are in feet )

We can see a room with a floor plan of a 

composite figure , that can be split into two rectangles as shown.

                                                          

Area of the floor in square feet to be carpeted is calculated by first learning How to calculate square feet :

Area of the floor  =  Area of rectangle 12 x 8  +  Area of rectangle 9 x 6

Area of the floor  =  96 square feet  +  54 square feet

Area of the floor  =  150 square feet .

There are all together six rectangular shaped walls as shown below .( figures not to scale )

To find the  total wall area , find the area of each wall and add them up .

   

  Area of wall 1. = ( 10 feet x 8 feet ) - ( 7 feet x 3 feet ) [ area of door ]                                                =   80 square feet  -  21 square feet  =  59 square feet

   Area of wall 2. = 10 feet  x  12 feet  =  120 square feet

   Area of wall 3. =  ( 10 feet x 14 feet ) - ( 4 feet x 5 feet ) [ area of window ]                                       =    140 square feet  -  20 square feet  =  120 square feet

   Area of wall 4. =  10 feet  x  9 feet  =  90 square feet

Area of wall 5.  =  10 feet  x  6 feet  =  60 square feet  ,  Area of wall 6.  =  10 feet  x  3 feet  =  30 square feet 

Total area of the wall to be painted  =  59  +  120  +  120  +  90  +  60  +  30  =  479 square feet .

How to calculate square feet unit conversion examples .

How to Calculate square feet  in each diagram .



The dimensions given for this square is in inches , we have to convert the inches to feet so that we can calculate the area in square feet .
12 inches = 1 feet  so   24 inches = 2 feet
Area of square is given by  A  =  s²       where  s  =  2 feet
Area of square  A  =  ( 2 feet )²      =    4 square feet

The dimensions for this triangle are in centimeters , we have to convert centimeters to feet so that we can calculate the area of triangle in square feet .
30 cm = 1 feet    and   15cm = 0.5 feet
Area of triangle is given by  A  =  1/2 b h  ,   where base b = 0.5 feet and height h = 1 feet
Area of triangle  A  =  1/2 x  0.5 feet  x  1 feet  =  0.25 square feet


This a composite shape and we have split that into basic shapes , we have two rectangles , one triangle and a semi circle.
Area of the total shape = 4 x 5 + 4 x 9 + 1/2 x 4 x 4 + 3.14 x 2²                                                                                                                   2
Area = 20 + 36 + 8 + 6.28  =  70.28 square feet


The radius of the circle is given in meters , we have to convert the meters to feet so that we can calculate the area of circle in square feet .
1 meter  =  3 feet   so   3 meters  =  9 feet
Area of circle is given by   A  =  π r²       ,    where     =  3.14 ,  radius r  =  9 feet
Area of circle  A  =  3.14  x  9²    =  3.14   x  81  =  254.34 square feet

Students can learn How to calculate square feet from the above examples and solve problems on similar lines.

Domain all the Real Numbers

In mathematics, the domain of definition or simply the domain of a function is the set of "input" or argument values for which the function is defined. That is, the function provides an "output" or "value" for each member of the domain. For instance, the domain of cosine is the set of all real numbers, while the domain of the square root consists only of numbers greater than or equal to 0.(Source: Wikipedia)

Domain all the real values - Example problems:

Example problem: 1
Find the domain function of f that can be defined by f (x) = -1 / ( x + 10)
Solution:
  To find the domain equate denominator to zero
  x + 10 = 0
  x = -10
Therefore the domain function of f is the set of all real values of x in the interval is(-infinity, -10) U (-10, +infinity)
Example problem: 2
 Find the domain function of f that can be defined by f(x) = x² + 6.
Solution:
 The function f(x) = x² + 6 is defined for all real values of x.
 Hence, the domain function of f(x) is the function of  "all real values of x".
 Since x² is never negative, x² + 6 is never less than 2
Example problem: 3
 Find the domain function of f that can be defined by f(t) = (1)/(t + 6)
Solution:
 The function f(t) = (1)/(t + 6) is not defined for t = -6, as this value requires division by zero.
 Hence the domain function of f(t) is the function of all the real numbers except -6
 Also, no matter how large or small t becomes, f(t) will never be equal to zero

Domain all the real values - Practice problems:

Practice problem:- 1
Find the domain of function of f that can be defined by f (x) = sqrt (-x + 16)
[Answer: Domain of function f is the set of all values of x in the interval (-infinity, 16) ]
Practice problem:- 2
Find the domain of function f defined by f (x) = sqrt( -x + 4) / [(x + 2)(x + 8)]
[Answer: domain of function f is the set of all values of x in the interval   (-infinity, -8) U    (-8, -2) U (-2, 4)] 

Properties of the Parallel Lines

Parallel lines
          The distance between the two lines will be equal and they will never intersect, such lines are said to parallel lines.

 Properties of the parallel lines
           The parallel lines will have the same slope (m1=m2)
           Here the m1 and m2 are slopes of the lines.
           When the parallel lines are cut by transversal line, then eight angles are formed

properties :

Here
                     Angle 1 = angle 3 =angle 5=angle 7
                    Angle 2= angle 4 = angle 6= angle 8.

 Adjacent angles properties:
        when  the parallel line is cut by a transversal line, then the adjacent angles sum up to 180 degrees
                   Angle 1 +angle 2= 180 degree
                   Angle 3 +angle 4= 180 degree
                   Angle 5 +angle 6= 180 degree
                   Angle 7 +angle 8= 180 degree
                Here the adjacent angles always sum up to 180 degree.

 Corresponding angles properties
       The angle in the same position around the intersection of two points is said to be corresponding angle.
          when  the parallel line is cut by a transversal line, then corresponding angles are  equal
                    Corresponding angles:
                       Angle 1 = angle 6
                       Angle 2 = angle 5
                       Angle 3 = angle 8
                       Angle 4 =angle 7

Alternate angles properties:
                   when the parallel line is cut by a transversal line then alternate angles are equal
                   So
                    Alternate interior angle
                       Angle 3 = angle 5
                       Angle 4 = angle 6
                    Alternate exterior angle
                      Angle 2 = angle 8
                      Angle 1 = angle 7


Algebra is widely used in day to day activities watch out for my forthcoming posts on hard math problems for 8th graders and cds exam 2013. I am sure they will be helpful.

Model problems:

1.Find the angle 2, when the angle 1 = 120?
Solution:
 Here angle 1 and 2 are adjacent angles
 When parallel lines is cut by a transversal line, then the    adjacent angles sum up to 180 degree
          So angle 1+angle 2 = 180
                    120 +angle 2= 180
                     Angle 2= 180-120
                    Angle 2 =60 degrees
 2.Find the angle 4, when the angle 1 = 120?
Solution:
           Here angle 3 and 4 are adjacent angles
           Angle 1= angle 3 (vertical opposite angles are equal)
           Angle 3 = 120
 When parallel lines is cut by a transversal line, then the adjacent angles sum up to 180 degree
           So angle 3+ angles 4 = 180
                       120 +angle 4= 180
                        Angle 4= 180-120
                       Angle 4 =60 degrees.

Fraction Variable Solver

A fraction (from the Latin fractus, broken) is a number that can represent part of a whole. The earliest fractions were reciprocals of integers: ancient symbols representing one part of two, one part of three, one part of four, and so on. A much later development were the common or "vulgar" fractions which are still used today (½, ?, ¾, etc.) and which consist of a numerator and a denominator.
Source – Wikipedia.


Fraction variable solver for Addition:

Variable Solver:

A variable solver is the way of thinker that refers to give proper solutions or values for the given fractions problems.

The following are some of the examples for Fraction variable solver in addition.

Simplify the fraction: `(3x)/7+(5x)/6`

Solution:

=` (3x)/7+(5x)/6`

The LCD for the denominators 7 and 6 is 42.

= `(6*3x)/42+(7*5x)/42`

We can express the denominators in the LCD form as

= `(18x)/42+(35x)/42`

We can simplify the numerators.

= `(18x+35x)/42`

Then by adding the numerators.

= `(53x)/42`

Simplify: `(3x)/5+(5x)/3`

Solution:

= `(3x)/5+(5x)/3`

The LCD for the denominators 5 and 3 is 15.

= `(3*3x)/15+(5*5x)/15`

We can express the denominators in the LCD form as

= `(9x)/15+(25x)/15`

We can simplify the numerators.

= `(9x+25x)/15`

Then by adding the numerators.

= `(34x)/15`

Simplify: `(2x)/5+(7x)/6`

Solution:

= `(2x)/5+(7x)/6`

The LCD for the denominators 5 and 6 is 30.

= `(6*2x)/30+(5*7x)/30`

We can express the denominators in the LCD form as

= `(12x)/30+(35x)/30`

We can simplify the numerators.

= `(12x+35x)/30`

Then by adding the numerators.

= `(47x)/30`

Fraction variable solver for Subtraction:

The following are some of the examples for Fraction variable solver in subtraction.

Simplify the fraction: `(6x+3)/12-(4x+5)/8`

Solution:

= `(6x+3)/12-(4x+5)/8`

The LCD for the denominators 12 and 8 is 24.

= `(2(6x+3))/24-(3(4x+5))/24`

We can express the denominators in the LCD form as

= `(12x+6-12x-15)/24`

We can simplify the numerators.

= `(x-9)/24`

Simplify: `(2x+3)/6-(6x+5)/5`

Solution:

= `(2x+3)/6-(6x+5)/5`

The LCD for the denominators 5 and 6 is 30.

= `(5(2x+3))/30-(6(6x+5))/30`

We can express the denominators in the LCD form as

= `(10x+15-36x-30)/30`

We can simplify the numerators.

= `(-26x-15)/30`

Simplify: `(8x+3)/12-(3x+5)/8`

Solution:

= `(8x+3)/12-(3x+5)/8`


The LCD for the denominators 12 and 8 is 24.

= `(2(8x+3)) /24-(3(3x+5)) /24`

We can express the denominators in the LCD form as

= ` (16x+6-9x-15)/24`

We can simplify the numerators.

= `(7x-9)/24`

Discrete Data

The nature of data is discrete if there are only a limited number of values probable or if there is a space on the number line between each 2 possible values.  Example, A 5 query quiz is specified in a Math class. The number of exact answers on a student's quiz is an example of discrete data.

In discrete data examples the number of exact answers would have to be one of the following: 0, 1, 2, 3, 4, or 5. there are not an endless number of values, therefore this data is discrete. Also, if we were to illustrate a number line and position each probable value on it, we would see a gap between each pair of values.

Definition of Discrete Data examples:

The discrete data is set of data having limited number of values or data points are called Discrete Data. The differing of the discrete data i.e. sets of infinite number of values is called constant Data. For example Data that can only take certain values. The number of apple in a box (you cannot have the half a student).

Examples: Number of hours prakash time spent for playing in a week this is an example of discrete data as playing period (finite) of ram will be specific.

Solved Examples on Discrete Data:

The table illustrates the set of books by Ravi. What type of graph is suitable to display the data in the table?

We use any type of graph is used to display the data
a. Bar graph
b. Histogram
c. Line graph
d. Stem-and-leaf plot

Solution:
Step 1: The data given in the table is discrete.
Step 2: Bar graphs are used to represent discrete data.
Step 3: So, a bar graph is proper to display the data shown in the table.

Problem for discrete data Examples:

The frequency tables situate for the number of worker and their salaries. Find out the distinction between the numbers of worker receiving a salary of 5000and1500.

Solution:

Step1:  The frequency column in the table specifies the number of worker who gets the particular salary.

Step2: From the table, the number of worker who gets a salary $1500 is 8.

Step3: The number of worker who get a salary $5000is 25.

Step4: The difference between the number of worker who get 5000 and those who get 1500 = 25 - 8 = 17

Step5: So, 17 more workers get a salary 4200 than those who get 3900.

Special Functions in Math

Special functions are particular mathematical functions which have more or less established names and notations due to their importance in mathematical analysis, functional analysis, physics or other applications. In math, several functions are important enough to deserve their own names. Functions like algebraic and transcendental functions are elementary functions in math. The list of special functions in math is given below.

(Source: Wikipedia)

Understanding Absolute value functions is always challenging for me but thanks to all math help websites to help me out.

List of special functions in math:

Basic special functions
Number theoretic functions
Hypergeometric and related functions
Riemann Zeta and related functions
Antiderivatives of elementary functions
Elliptic and related functions
Iterated exponential and related functions
Gamma and related functions
Bessel and related functions
Other standard special functions
Miscellaneous functions

The example problems of trigonometric integral and logarithmic integral function are given below. Both trigonometric integral and logarithmic integral function are antiderivatives of elementary functions.

Example problems of special function in math:

Example 1:

Evaluate the integral int log (1 + x2) dx

Solution:

By integrating by parts method, taking log (1 + x2) as the first function and 1 as the second function, we get

 int log (1 + x2) dx  = int (log (1 + x2) . 1) dx

The above equation can be written as

 int log (1 + x2) dx  = log (1 + x2) int 1 dx - int [d/dx {log (1 + x2)} * int  1 dx] dx

= log (1 + x2) * x - int  (2x)/(1+x2) x dx

= xlog (1 + x2) - 2int (1 - 1/(1+x2) dx

= xlog(1 + x2) - 2int dx + 2int (dx)/(1+x2)

= xlog(1 + x2) - 2x +2 tan-1x + C

I am planning to write more post on Sampling Population and cbse 12th books. Keep checking my blog.

Example 2:

Integrate the trigonometric function sin-1(cos x).

Solution:

Step 1: Given function

sin-1 (cos x)

Step 2: Integrate the given function sin-1 (cos x) with respect to ' x ',

int sin-1 (cos x)dx = int sin-1{sin pi/2 - x} dx

= int (pi/2 - x)dx

= pi/2 int dx - int x dx

= (pix)/2 - x^2/2 + C

Identifying Functions in Math

The mathematical concept of a function expresses the intuitive idea that one quantity (input) completely determines another quantity (output). A function assigns a unique value to each input of a specified type. The argument and the value may be real numbers, but they can also be elements from any given sets: the domain and the co domain of the function. (Source : WIKIPEDIA)


For example, f(x) = 3x2 .Here f(x) is a function that express three time the square of the number. In this article we are going to discuss about how to identifying the function.

Representation of functions in math:

The functions in math can be represented in four ways.

Verbal
Table of values
Numerical
Graphical

The functions in math can be identified by using the table of values,graphical and verbal statements.

Example for representation of functions:

1.Verbal representation :

The cool drinks that john get from the vending machine depends upon the code that he enter when provoked.

2.Table of values:

x             0             1             2               3                    4

y             3             7            11            15                 19

3. Numerical

f(x) = 4x+3

4.Graphical

tht

Fig(i) Graph of function

In the following section,  we are going to see how for identifying the function in math when we given the table of values.

Problems on identifying the function in math:

Problem 1:

Identifying the function for the following math table of values

x         -2           -1          0             1          2

y          8           -1          0             1          8

Solution:

Given   x         -2           -1        0             1          2

y          8            1          0             1          8

When we give x = -2 we get f(x) = y = 8 = x3

x = - 1 we get f(x) = y = -1 = x3

x = 0   we get f(x) = y = 0 = x3

x = 1   we get f(x) = y = 1 = x3

x = 2   we get f(x) = y = 8 = x3

So the function for given table of values id f(x) = y = x3

Answer: y = x3


Problem 2:

Identifying the function from the following verbal statements.

The cost for activate a device is 5000 per week It also costs 6 for each unit produced in the device. Identifying the function for daily cost x of run the device as a function of the number m of units produced.

Solution:

The   cost y equals the cost of $5,000 plus the cost of producing x units.

For 1 unit the cost is $6 .So for x units 6x

So the total cost y,

y = 5000 + 6 x

Answer: y  = 5000 + 6 x