Properties Of Hyperbola

A hyperbola is a conic section obtained on slicing a double napped cone by a plane parallel to the axis of the cone. The locus of a point from a fixed point is at a constant ratio and it is greater than one of its distance from a fixed line is called a Hyperbola.

Standard form of a hyperbola: x^2/a^2 – y^2/b^2 = 1


Hyperbola Properties Explained


Below are explained the properties of hyperbola:

The lines from the foci to any point on a hyperbola make equal angles with the tangent at that point. Hence if the surface of a reflector is generated by revolving a hyperbola about its transverse axis, all rays of light converging on one focus are reflected to the other.
The hyperbola is symmetric about x-axis, y-axis and hence the hyperbola is symmetric about the origin.
The hyperbola does not pass through the origin.
The tangent from any point (x1, y1) to the hyperbola is xx1/a2 – yy1/b2 = 1


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Important Hyperbola definitions


Focus: The fixed point is called a focus F1 (ae, 0) of the hyperbola.
Directrix : The fixed line is called the directrix of the hyperbola and its equation is x = a/e .
Transverse axis: The line segment AA' joining the vertices is called the transverse axis and the length of the transverse axis is 2a. The equation of transverse axis is y = 0.
Conjugate axis: The line segment joining the points B(0, b) and B'(0, - b) is called the conjugate axis. The length of the conjugate axis is 2b. The equation of the conjugate axis is x = 0
Centre: The point of intersection of the transverse and conjugate axes of the hyperbola is called the centre of the hyperbola. Here C(0, 0) is called the centre of the hyperbola.
Vertices: The points of intersection of the hyperbola and its transverse axis are called its vertices. The vertices of the hyperbola are A(a, 0) and A'(- a, 0).

Geometry Area Problems

Introduction :

In this article we are going to study geometry areas Area is region covered by two dimensional shapes. Based on the shape of the area we can drive the area formula of the shape. Based on the shape properties we have some formulas in below. In this section we will see brief about area of different shapes such as square, trapezoidal, square, triangles, cone, circle, parallelogram, and so on. Here we have some sample solved problems of area in geometry. Some important area formulas are listed in below sub topics. Area is amount of gap within a particular closed boundary. There are different measures to calculate the area in geometry. Now we are going to solve some area problems in geometry using the following area formulas.


Some area formulas in geometry:


In below we have some of the area formulas in geometry:

Square:

Area of the square = a *a square units

Where, a is a side of the square

Rectangle:

Area of the rectangle = l * b square units

Where, l and b is length and breadth of the rectangle with respective.

Circle:

Area of the circle = `pi ` * r2 square units

Where, r is a radius of the circle.

Triangle:

Area of the triangle = `1/2` b * h square units

Where, b is breadth and h is height of the triangle.

Trapezoidal:

Area of the trapezoidal = `1/2` * a * (b1 + b2) square units

Where, a is side length of trapezoidal , b1 is base1 and b2 is base2 of the trapezoidal.

Parallelogram:

Area of the parallelogram = b * h square units

Where, b is base and h is perpendicular height. I have recently faced lot of problem while learning Bisector of a Triangle, But thank to online resources of math which helped me to learn myself easily on net.


Some example problems using the above area formulas in geometry:

Problem 1: Can you calculate the area of a parallelogram with a base of 5 inches and a height of 8 inches.

Solution:

Given: base is 5 inches and height is 8 inches.

We know that,

Area of the parallelogram = b * h square units

Area of the parallelogram = 5 * 8 = 40 square inches.

Therefore, the area of the parallelogram is 40 square inches.

Answer: The area of the parallelogram is 40 square inches.

Problem 2: The school park has a circular pond with a diameter of 6 feet. What is the pond's area?

Solution:

Given: d = 6 feet.

Therefore, radius = `6/2 ` = 3 feet

Area of the circle = p r2 square units.

The diameter is 6 feet. Replace d by 6 in the formula.

Area = p * 3 * 3 = 3.14 * 9 = 28.26 square units.

The area of the circle is 28.26 square feet.

Answer: The area of the circle is 28.26 square feet.

One more example problem using the above area formulas in geometry:

Problem: A square playground has an area of 100 square meters. How long is each side?

Solution:

The area of a square is the side length times itself.

Consider of a number that, when multiplied by itself, gives 100:

10 × 10 = 100

Each side is 10 meters long.

Answer: Each side is 10 meters long.

Fractions Solving Online

Introduction :
DEFINITION:

Fraction is defined as an equal amount of one whole object. It can be represented as " a / b " where 'a' denotes the value called numerator and 'b' denotes the value called denominator and q not equal to zero.we can  easily perform these operations online

The fundamental rule of fractions is given as follows:

Multiplying both numerator and denominator by the same number because it does not change the value of the fraction. It is one of the most important steps used in dealing with equaling the fractions.by doing problems online we can quickly get the answers.


Description about fractions solving online:


Adding fractions:

There are 3 Simple Steps for solving the addition fractions:

Step 1: Make sure the bottom of the numbers that is denominators are the same or not

Step 2: Add the top numbers (the numerators). Put the answer over the same denominator as in step 1

Step 3: Simplify the fraction (if needed)

Ex:

1 / 4 + 1 / 4

Step1. The bottom numbers are already the same. Go straight to step 2.

Step2. Add the numerator and put the answer over the same denominator:

1 / 4 + 1 / 4 = (1+1) / 4 = 2 / 4

Step3. Simplify the fraction:

2 / 4 = 1 / 2

Subtracting Fractions:

There are 3 simple steps  for solving subtract fractions:

Step1 Make sure the bottom numbers (the denominators) are the same or not

Step2 Subtract the top numbers (the numerators). Put the answer over the same denominator.

Step3 Simplify the fraction.

Ex:

3 / 4 – 1 / 4

Step1 The bottom numbers are already the same. Go straight to step 2.

Step2 Then subtract the numerator and substitute the answer over the same denominator:

(3 / 4) - (1 / 4) = (3 - 1) / 4 = 2 / 4

Step3 Simplify the fraction:

2 / 4 = 1 / 2

Understanding Subtracting Mixed Numbers is always challenging for me but thanks to all math help websites to help me out.

Practice problems for fractions solving online

Multiplying Fractions:

There are 3 simple steps to multiply fractions:

Step1 Multiply the top numbers (the numerators).

Step2 Multiply the bottom numbers (the denominators).

Step3 Simplify the fraction if needed.

Ex:

1 / 2 * 2 / 5

Step1. Multiply the top numbers:

1 / 2 * 2 / 5 = 1 * 2 / = 2 /

Step2. Multiply the bottom numbers:

1 / 2 * 2 / 5 = (1 * 2) / (2 * 5) = 2 / 10

Step3. Simplify the fraction:

2 / 10 = 1 / 5

Dividing Fractions:

There are 3 Simple Steps to Divide Fractions:

Step1 Turn the second fraction into as a reciprocal of itself.

Step2 Multiply the first fraction by that reciprocal

Step3 Simplify the fraction (if needed)

Ex :

(1 / 2) / (1 / 6)

Step1 Turn the second fraction upside-down (the reciprocal):

1 / 6 = 6 / 1

Step2 Multiply the first fraction by that reciprocal:

(1 / 2) * (6 / 1) = ((1 * 6) / (2 * 1)) = 6 / 2

Step3 Simplify the fraction:

6 / 2 = 3

Check a Solution Online

Introduction to check a solution online:

In mathematics, check means the process of confirming a solution is correct or not for the given equation or inequality. Check is nothing but substitute the solution in the given question. Now, we are going to see some of the problems to check the solution online. From these problems, we can get clear view about whether the solution is correct or not for the given question. Is this topic online geometry tutor free hard for you? Watch out for my coming posts.


Problem on check a solution online:


Example problem 1:

Solve for x in the given equation and check the solution online: 5 x - 6 = 3 x - 10

Solution:

Subtract 3x on both sides of the equation

5 x - 6 = 3 x – 10

Add 6 to both sides of the equation

5 x - 6 + 6 = 3 x – 10 + 6

5x = 3x – 4

Subtract 3x on both sides of the equation

5x – 3x = 3x – 4 -3x

2x = -4

Divide by 2 on both sides of the equation

2x / 2 = -4 / 2

x = -2

The answer is x = - 2

Check:

Substitute the value x = -2 in the given equation

5 x - 6 = 3 x – 10

5 (-2) - 6 = 3(-2) – 10

-10 – 6 = -6 – 10

-16 = -16

Both the sides are equal. So, the answer is correct. I have recently faced lot of problem while learning Large Sample Size, But thank to online resources of math which helped me to learn myself easily on net.


Additional Problem on check a solution online:


Example problem 2:

Solve the simultaneous equations and check the answer:

x + y = -1-----------Equation (1)
2x + y = 0-----------Equation (2)

Solution:

Step 1: From equation (1)

x + y = -1

Subtract x on both sides of the equation

x + y – x = -1 – x

y = -x – 1----------Equation (3)

Step 2: Substitute the equation (3) in equation (2)

2x + y = 0

2x + (-x – 1) = 0

2x –x – 1 = 0

x – 1 =0

Add 1 on both sides of the equation

x – 1 + 1 = 0 + 1

x = 1

Step 3: Substitute x=1 in equation (3)

y = -x – 1

y = - 1 – 1

y = -2

So, the solution is (1, -2)

Verify:

Substitute the x and y values in any one of given equation

Let us take equation (1)

x + y = -1

1 + (-2) = - 1

-1 = -1

Both the sides are equal. So, the answer is correct.

Define Associative

Introduction to algebra:

Algebra is the branch of mathematics concerning the study of the rules of operations and relations, and the constructions and concepts arising from them, including terms, polynomials, equations and algebraic structures. Together with geometry, analysis, topology, combinatorics, and number theory, algebra is one of the main branches of pure mathematics. Please express your views of this topic Factor Polynomial Calculator by commenting on blog.

Source:  Wikipedia


Concept of associative property in algebra:


The associative property in algebra also works for addition and multiplication. For addition, the associative property in algebra means that when you add three numbers, you can first add any two of the numbers and then add the third.

Associative property for addition in algebra:

First, add any two of the numbers and then add the third.

(p+q)+r=p+(q+r)

The parentheses group numbers together. Suppose you want to add 1+2+3. You could first add 1 and 2 to get 3, and then add 3 and 3 to get 6. Or you could first add 3 and 2 to get 5, and then add 5 and 1 to get 6. The results are the same in algebra addition.

If you replace p with 1, q with 2 and r with 3, the associative property in algebra of addition looks like this:

(a+b)+c=a+(b+c)

(1+2)+3=1+(2+3)

3+3=1+5

6=6

Associative property for multiplication in algebra:

First, multiply two numbers and then multiply that product by the third number.

(p*q)*r=p*(q*r) or (pq)r=p(qr)

Again, the parentheses group numbers together. Suppose you want to solve the multiplication problem 1x2x3. You could first multiply 1x2 to get 2, and then multiply 2x3 to get 6. Or you could first multiply 2x3 to get 6, and then multiply 6x1 to get 6. The results are the same.

If you replace p with 1, q with 2, and r with 3, the associative property in algebra of multiplication looks like this:

(pq)r=p(qr)

(1*2)*3=1*(2*3)

2*3=1*6

6=6

Example for associative property in algebra:

Example 1:

Which of the following is the same as (10+12)+15?

10(12+15)

(10+12)15

10+15+12+15

10+(12+15)

Solution:

Answer (4) is the correct choice. You could first add 10 and 12 to get 22, and then add 22 and 15 to get 37. Or, you could first add 12 and 15 to get 27, and then add 10 and 27 to get 37.

Example 2:

Which of the following is the same as (5x2)x3?

5(2+3)

(3+2)5

5x2+5x3

3(5x2)

Solution:

Answer (4) is the correct choice. You could first multiply 5 and 2 to get 10, and then multiply 10 and 3 to get 30. Or, you could first multiply 2 and 3 to get 6, and then multiply 6 and 5 to get 30. Is this topic algebra 2 homework solver hard for you? Watch out for my coming posts.


Practice problem for associative:


Problem 1:

Which of the following is the same as (8+2)+5?

8(2+5)

(8+2)5

8+5+2+5

8+(2+5)

Answer: 4.

Problem 2:

Which of the following is the same as (5+2)*6?

5(2+6)

(5+6)2

(5*6)+(2*6)

(5+6)+2+15

Answer: 3.

Problem 3:

Which of the following is the same as (5*2)+6?

6+(2*5)

(5+6)2

(5*6)+(2*6)

(5+6)+2

Answer: 1.

What is Coefficient of Variance

Whenever we want to compare the variability of two series which differ widely in their averages or which are measured in different units, we do not merely calculate the measures of dispersions but we calculate the coefficients of dispersion which are pure numbers independent of the units of measurement.

The coefficients of dispersion (C.D.) based on different measures of dispersion are as follows:

Whenever we want to compare the variability of two series which differ widely in their averages or which are measured in different units, we do not merely calculate the measures of dispersions but we calculate the coefficients of dispersion which are pure numbers independent of the units of measurement.

The coefficients of dispersion (C.D.) based on different measures of dispersion are as follows:

1.  C.D. based upon range = `(L-S)/(L+S)`  , where L and S are Largest and Smallest observation in the series.

2.  C.D. based upon quartile deviation = `(Q3 - Q1)/(Q3 + Q1)`

`3. `C.D. based upon Standard deviation = `sigma/barx`


Definition of Coefficient of Variance


Coefficient of variance i.e. Coefficient of Variation is a relative measure for standard deviation. It is defined as 100 times the coefficient of dispersion based upon standard deviation is called coefficient of variation (C.V.), i.e.,

C.V.  =  `sigma/barx` x 100 .

Since it is relative measure C.V. is used to compare consistency of figures or variability of figures.

Remarks:

1. Less C.V. indicate the less variability or more consistency.

2. More C.V. indicate the more variability or less consistency.

3. According to Karl Pearson who suggested this measure, C.V. is the percentage variation in the mean, standard deviation being considered as the total variation in the mean.

Note:

With the help of C.V. we can find which salesman is more consistent in making sales, which batsman is more consistent in scoring runs, which student is more consistent in scoring marks, which worker is more consistent in production, etc.

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Example of coefficient of variance


An analysis of monthly wages paid to the workers of two firms A and B belonging to the same industry gives the following results:


Firm A
Firm B
Number of workers
500
Average daily wages
186 Rs.
175 Rs.
S.D. of daily wages
9    10
In which firm, A or B is more consistent in individual wages?

Solution:

C. V. for firm A  = `sigma/barx`` x 100 = 9/186 x 100`

` = 4.84`

C. V. for firm B  = `sigma/barx`` x 100 = 10/175 x 100`

` = 5.71`

`Since C.V. for firm B is greater than C.V. for firm A, firm A is more consistent.`

Answers For Parentheses

Introduction :

Parentheses are defined as the process of the symbols “(” and “)”. It can be generally used in grouping. Different types of parentheses are "[ ]”, " ","( )". These three types of parentheses are called as round brackets, curved brackets and oval brackets or just brackets. It can be used to mention the modifications of normal order of operations. Parenthesis is the single type of parentheses.


Example problems for answers for parentheses:

Some example problems for answers for parentheses are

Example 1:

Given:

(8+5) * (7-3)

Solution:

Step 1:

First we need to simplify the parenthesis

Step 2:

So, (8+5) = 13 and (7-3) = 4.

Step 3:

Now we have 13 * 4 = 52.

Solution to the problem is 52

Example 2:

Given:

(28+4) -5.

Solution:

Step 1:

First we need to simplify the parenthesis so,

Step 2:

(28+4) = 32.

Step 3:

Now we need to subtract 5 from 32.

Step 4:

so we get 32 -5 =27.

Solution to the problem is 27.

Example 3:

Given:

6+ (4+2).

Solution:

Step 1:

Here first we need to simplify (4+2) =6.

Step 2:

Now we need 6 with 6.

Step 3:

6+ (6) the answer is 12.

Solution to the problem is 12.

Example 4:

Given:

2x + 4xy + 5x (y + z).

Solution:

Step 1:

From this question, first we need to simplify the brackets so,

Step 2:

we multiply (y + z) with 5x. So we get 5xy +5xz.

Step 3:

Now we have 2x + 4xy + 5xy + 5xz.

Step 4:

When we add like terms we get 2x + 9xy + 5xz.

Solution to the problem is 2x + 9xy + 5xz.

Example 5:

Given:

(5*12) +11+36.

Solution:

Step 1:

First we need to simplify the parenthesis, So (5*12) = 60.

Step 2:

Now we can add 11 and 36 with 60.

Step 3:

60 + 11 + 36

Solution to the problem is 107. Understanding Decimal to Fraction Converter is always challenging for me but thanks to all math help websites to help me out.


Practice problems for answers for parentheses:

Some practice problems for answers for parentheses are

1. Simplify the parentheses (52 +12) - (12 + 10)

Answer to the problem is 40.

2. Simplify the parentheses (5 + 3) × (2 + 8)

Answer to the problem is 128.

Live Online Math Tutoring

Live online math tutoring, a great way to learn math, interacting with well qualified net savvy tutors from all over the world at the comfort of your home or the place of your choice with the help of your desktop computer or laptop, even palmtops are getting into the act now a days. We have facilities to learn math online with lot of websites giving information on various topics but live online math tutoring is what which helps you clear your doubts on the spot with so much ease and comfort.

Tutorvista.com is one such live online tutoring company providing 24/7, 365 days service with well qualified math tutors.It is so easy to access live online math tutors from anywhere you wish, as it does not require unwieldy software's and plug-ins, it is easily accessible from any computer with Internet access.


Uses of live online tutoring


Online live math tutoring gives you a very personal tie up with the live tutor, it's only you and the tutor and no one else to interfere.  You can learn any topic,clarify any doubts with utmost ease with the use of live chat and interactive whiteboard. Any kind of questions can be asked in live sessions which is not at all possible sometimes in your class room or home tutoring as you may feel guilty and think that would be a silly question.

In live online math tutoring as you do not come face to face with the tutor you feel safe and gaurded and only in online live math tutoring you can abruptly get away from the session if you feel like the live session is of no help which is not possible while learning in class room or home.


Why live online tutoring?


It's so simple at the current scenario as most of the households have computer and Internet connection. Live online math tutoring is mostly available round the clock so accessing a tutor any time from any where is only possible with live online tutoring as all other learning media have time constraints like schools or colleges have specific timings,home tutors visit only at certain time and day.It is hygienic as you do not come in direct contact with the tutor.

Live online math tutoring requires a computer with Internet access and the interest to learn live online.After all math is an universal language.

Bias in Mathematical Terms

Introduction to bias in mathematical terms:

Bias in mathematical terms is applicable to the die or dies problem, biased dies are not give the probability of the equal number such as (2,2), example in standard die the number 3 will be appear in 6 chances (it means we have to roll the die 6 times )so the probability is 1/6.but in the biased die the number 3 will be appear 3 times in 6 rolls so the probability is 3/6=1/2


Types of bias- bias in mathematical terms:


In statistics the bias can be classified as many types

Selection bias
Systematic bias
Data-snooping bias
Statistical hypothesis testing
Sampling bias
Inductive bias
Notation bias
Publication bias
Infrastructure bias
Cognitive bias
Cognitive bias- bias in mathematical terms:

In this type only one bias we called as the conformation bias. I have recently faced lot of problem while learning Definition of Rational Number, But thank to online resources of math which helped me to learn myself easily on net.


Example problems - bias in mathematical terms:


Biased estimation is used to estimate the standard deviation of population it will be calculated by using the standard deviation of sample of size m

Solution:

Consider m=1

Here m is the standard deviation of sample size, so the standard deviation of sample size 1 will be always zero, so we cannot find the deviation for the single value, so we can tell the estimation is zero and the average of the standard deviation is zero, but in generally the population have some standard deviation value, so the above estimation will be the biased

Example 2:

Find the value of 13.39`xx` 3.45?

A) 461955

b) 461.955

c) 46.1955

D) 4619.55

Solution:

In the problem after decimal 2 digits are there (for both), therefore the product must contains 4 decimal places

1339`xx` 345=461955(here we did not consider decimal we consider only the digit)

Now take the decimal

46.1955

So the answer is c

(So here the biased question are based on the assumptions)

Online Geometry Book

Introduction:

Geometry is a construction of object according to our given measurement. Geometry books contains the collection of object  which could be square, rectangle, triangle, circle, parallelogram, cone, cylinder, cube, prism, quadrilateral. Basic geometry concepts are plane, points, rays, lines, line segment, type of lines and  angles. Main purpose of using geometry is finding area,  volume and surface of given object it may be two dimensional or three dimensional object.


Standard formulas for geometric figures:

Two dimensional objects:

Square:

Perimeter of square = 4 * side
Area of square = side * side
Rectangle:

Area of rectangle = Length x width
Perimeter of rectangle = 2(Length + Width)
Triangle

Area of triangle = `1/2` (Base* height)
Perimeter of triangle = (sum of three sides)
Parallelogram

Area of parallelogram = length × breadth
Circle problems:

Area of circle = ? r2 , where r is the radius.
Circumference of triangle = 2 * ? * r
Diameter = 2 * Radius
Three dimensional objects:

Three dimensional objects are: Cone, sphere, cylinder, hemisphere, prism

Volume of cylinder = ? * R2 * h
Volume of a right circular cone = `1/3`   * ?  * R3
Volume of a sphere  = `4/3` * ? * R3
Volume of a hemisphere = `2/3` * ? * R3

Example problems:


Example 1: Find the area and perimeter of square when the side length is 5cm?

Solution:

Area of square    = (side * side)

= 5 * 5

= 25cm^2

Perimeter of square = 4 * side

= 4 * 5 = 20 cm

Example 2: Find the area and perimeter of rectangle with length 4cm, width 3 cm?

Solution:

Area of rectangle = Length x width

= 4 * 3

= 12cm^2

Perimeter of rectangle = 2(Length + width)

= 2(4 + 3)

= 14cm

Example 3: Find the area of triangle base is 4cm,height is 2cm

Solution:

Area = `1/2` (4 * 2)

= `8/2`

= 4cm^2

Example 4: Find perimeter of triangle whose side lengths are 5cm, 5cm, and 8cm?

Solution:

Perimeter = (A + B + C) (Sum of three side lengths)

A = 5, B = 5, C = 8

= (A + B + C) (Sum of three sides)

= 5 + 5 + 8 = 18cm

Example 5: Find the area and circumference of the circle when the radius is 4cm?

Solution:

Area = `pi`

= 3.14 * 4 * 4

= 50.24cm^2

Circumference = 2 * ? * r

= 2 * 3.14 * 4

= 25.12cm

Example 6: Find the area of rhombus whose diagonals are 6cm and 9cm

Solution:

Area of rhombus =`1/2` (diagonal1 * diagonal2)

= `1/2`  ( 6 * 9)

= 27cm^2

Example 7: Find the volume of cylinder whose diameter of the base is 10 cm, height is 10 cm?

Solution:

Diameter of the base is 10 cm,

Radius = `10/2`

Radius(R) = 5cm

V = Area of the base × Height = `pi` * R * R * H

= 3.14 * 5 * 5 * 40

= 3140cm^2

Statistics Questions

Introduction :

“Statistic is the numerical statement of facts, capable of analysis and interpretation.The science of statistics is the study of the principles and the methods applied in collecting, presenting, analysis and interpreting the numerical data in any field of inquiry.”  It’s also denoted as “statistics is the science of counting”.

Statistics question - Example problems:

Example for statistic question 1:

Find the mean deviation of the mean for the following data: 15, 17, 10, 13, 7, 18, 9, 6, 14, 11

Solution :

Let the mean of the given data be x1. Then,

i=1?n|X1=x| / n

=120 / 10

=12. [n=10]

The values of (x-x1 ) are 3,5,-2,1,-5,6,-3,-6,2,-1.

Therefore, the values are |x-x1| is 3,5,2,1,5,6,3,6,2,1

Mean Deviation (x1)=i=1?n|x-x1| / n   = 34/10=3.4

Hence Mean Deviation (x1)=3.4.

Understanding descriptive statistics definition is always challenging for me but thanks to all math help websites to help me out.


Practice problem for statistic question:

Statistics question word problem 1: Six boys have heights in cm, of 171, 169, 168, 166, 165. Five girls have heights in cm, 161, 160, 157, 157, 155. Draw up a frequency distribution table of the thirty possible difference in height obtained when each boy is paired with any girl. Calculate the mean of these differences and their standard deviation.

Answer:  mean 9.5 cm, Standard deviation 3.01 cm.

Acre of Land

Acre of land - Introduction:

The acre is a unit of area in a numeral of systems, with the regal and United States normal systems.Generally the used acres nowadays are the worldwide acre and, in the U.S., the survey acre. The general use of the acre is to determine tracts of land.

One acre is equal to

1 acre = 4,840 square yards

1 acre = 43,560 square feet

Acre of Land - Examples:

Acre of land - Example 1:

To build colleges in 25 acres how much of the square yards and the square feet are there in land square yards and square feet.

Solution:

Step 1:

x acre          = x * 4,840 square yards

x acre          = x * 43,560 square feet

Step 2:

25 acres = 25 * 4840 square yards = 121 000 square yards

25 acres = 25 * 43560 square feet = 1089 000 square feet

Answer:

Therefore 121 000 square yards (or) 1089000 square feet’s land are needed to build a college.

Acre of land - Example 2:

To build church in 15 acres how much of the square yards and the square feet are there in land square yards and square feet.

Solution:

Step 1:

x acre          = x * 4,840 square yards

x acre          = x * 43,560 square feet

Step 2:

15 acres = 15 * 4840 square yards = 72 600 square yards

15 acres = 15 * 43560 square feet = 653 400 square feet

Answer:

Therefore 72 600 square yards (or) 653 400 square feet’s land are needed to build a church.

Acre of Land - more Examples:

Acre of land - Example 1:

To build schools in 10 acres how much of the square yards and the square feet are there in land square yards and square feet.

Solution:

Step 1:

x acre          = x * 4,840 square yards

x acre          = x * 43,560 square feet

Step 2:

10 acres = 10 * 4840 square yards = 48400 square yards

10 acres = 10 * 43560 square feet = 435600 square feet

Answer:

Therefore 48400 square yards (or) 435600 square feet’s land are needed to build a school.

Acre of land - Example 2:

To build temple in 5 acres how much of the square yards and the square feet are there in land square yards and square feet.

Solution:

Step 1:

x acre          = x * 4,840 square yards

x acre          = x * 43,560 square feet

Step 2:

5 acres = 5 * 4840 square yards = 24 200 square yards

5 acres = 5 * 43560 square feet = 217 800 square feet

Answer:

Therefore 24 200 square yards (or) 217 800 square feet’s land are needed to build a temple.

Different Situation

Introduction :

In math, different situation questions are nothing but the questions involving the different situations. The situations may be past, current or future. In general, we can observe the different situation based questions via word problems. In this article different situation, we are going to discuss few questions based on different situations.

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Example Problems for Different Situation Questions:

The example problems for different situation questions are as follows:

Example 1:

A library consists of 600 books. Mike bought 80 more books for the library.  At present, how many books are there in the library?

Solution:

Number of books already in the library = 600

Number of books that Mike bought   =  80

Number of books in the library          = 600 + 80

= 680

Therefore, there are 680 books in the library.

Example 2:

Chris sold 1200 meatballs on Monday. He sold 600 more meatballs on Tuesday than on Monday. On Tuesday, how many meatballs did Chris sell?

Solution:

Number of meatballs on Monday = 1200

Steve sold 600 more meatballs on Tuesday

Number of meatballs on Tuesday = 1200 + 600

= 1800

Example 3:

There are 750 seats in a theater. At present, 500 seats are occupied. Calculate the percentage of seats that are occupied.

Solution:

Total number of seats   =  750

Occupied seats   =  500

Percentage of seats occupied  =  `<< 500 / 750>>`   x 100

= `<< 50/75>>`   x 100

=  66.67


Practice Problems for Different Situation Questions:

The practice problems for different situation questions are as follows:

1) A library consists of 2000 books. Milton bought 120 more books for the library.  At present, how many books are there in the library?

Answer: 2120 books

2) Kalvin sold 1310 meatballs on Monday. He sold 100 more meatballs on Tuesday than on Monday. On Tuesday, how many meatballs did Kalvin sell?

Answer: 1410 meatballs.

3) There are 450 seats in a theatre. At present, 410 seats are occupied. Calculate the percentage of seats that are occupied.

Answer: 91.1 percent.

Symbol for less than or Equal To

Introduction :

In math, the inequality shows the major task. In arithmetic it has many signs like greater than, less than, greater than or equal to and less than or equal to. In this list of symbols less than equal to symbol is `<=` . This less than equal to symbol specifies that, the term which is left hand side of the inequality is less than or equal to the term which is right of the inequality. In a number line it is mentioned as the closed dot on a number line and the arrow mark which is pointed to the left side of the dotted number.

Symbols and Rules:

Symbol – Symbol for less than or equal to.

`<=` This symbol is the specification of less than or equal to sign.
Rules – Symbol for less than or equal to:

When multiply the inequality term less than equal to sign by negative sign then the negative sign becomes positive and the positive sign becomes negative and the less than equal to sign becomes greater than equal to symbol.
When divide the inequality term less than sign by negative sign then the negative sign becomes positive and the positive sign becomes negative and the less than equal to symbol becomes greater than equal to sign.

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Example Problems – less than Equal to Symbol:

Example 1 – Symbol for less than or equal to:

Find the value of x from the inequality 19a+17`<=` 23

Solution:

Given, 19a+17`<=` 23

Now add the above inequality by -17 on both sides.

19a+17`<=` 23

-17 `<=` -17

----------------------

19a `<=` 6

Now divide by 19 on both sides so, a`<=` 6/19

Example 2 – Symbol for less than or equal to:

Find the value of y from the inequality -5b+83 `>=` 3.

Solution:

Given, -5b+83 `>=` 3.

Now add -83 on both sides

-5b+83`>=` 3

-83  `gt=` -83

---------------

-5b     `>=` -80

Now multiply the above term -5b `>=` -80 by negative sign.

- (-5b `>=` -80) is 5b `<=` 80.

The answer is b`<=` 16.

Example 3 – Symbol for less than or equal to:

Find the value of y from the inequality -m+6 `>=` 4.

Solution:

Given, -m+6 `>=` 4.

Now add -6 on both sides

-m+6 `>=` 4

-6 `>=` -6

---------------

-m      `>=` -2

Now multiply the above inequality -m `>=` -2 by negative sign.

- (-m `>=` -2) becomes m`<=` 2.

m`<=` 2 is the answer.

Example 4 – Symbol for less than or equal to:

Find the value of y from the inequality -n+5 `>=` 5.

Solution:

Given, -n+5 `>=` 5.

Now add -5 on both sides

-n+5 `>=` 5

-5  `>=` -5

---------------

-n      `>=` -0

Now multiply the above inequality -n`>=` -0 by negative sign.

- (-n `>=` -0) is n `<=` 0.

n`<=` 0 is the simplified form of given inequality.

Five Steps of Problem Solving

Introduction to five steps of problem solving:

Here we are going to see the article as five steps of problem solving method.In problem solving concepts we have to do follwing steps.

First understand the problem
Find what should be calculated
Use require formula
Form the equation and plug the data.
Simplify and get the result
let us see the five steps of problem solving.

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Factoring- Five Steps of Problem Solving:

Factor x^2+8x+6=0

Solution:

Step 1:

it is in the standard form of the quadratic equation Ax2+bx+c=0

Step 2:

here A=1, B=8 and c=6, the formula for the quadratic equation is

x= `(-b+- sqrt((b^2-4ac)))/ (2a) `

Step 3:

plug a, b and c values in the above formula

So it will be look like that below,

x= `(-6+- sqrt((6^2-4xx1 xx 8)))/ (2xx1) `X= `"(-6+- sqrt((36-32)))/ (2)`

Step 4:

if we solve these equation means we get the two root valueX= `"(-6+ sqrt(4))/ (2)`X=`"(-6- sqrt(4))/ (2)`

Step 5:

so the answer is x=-2 and x=-4

Geometry- five steps of problem solving:

Find the area and perimeter of the rectangle whose length is 6cm and width is 8cm?

Solution:

Step 1:

Length of the rectangle is 6cm and width is 8cm

Step2:

Formula for area of the rectangle is ==>  length* width

Step3:

Plug the values of length and width in the above formula
Area of the rectangle => 6x8=48cm2

Step 4:

Perimeter of the rectangle formula is 2(length + breath)

Step5:

Plug the values of length and width in the above formula

Perimeter = 2(6+8) =2(14) =28cm

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Fractions - Five Steps of Problem Solving

Add `5/8+3/2`

Solution:

Step 1:

Here the denominators of the fraction are different such as 8 and 2 so we take the greatest common factor of 8 and 2

Step 2:

Here the greatest common factor is 8 it will be divided by the denominator of each fraction (8 is divided by 8 so we get 1) so we have to multiply both the numerator and denominator by 1 so we get the faction like that` (5xx1)/ (8xx1) =5/8`

Step3:

Similarly we do that in the second fraction the denominator of that fraction is 2 so 8 will be divided by 2 means we get the value as 4

Step 4:

Multiply 4 on both the numerator and denominator so the second fraction looks like that below

`(3xx4)/ (2xx4) =12/8`

Step 5:

So the two fractions have the same denominator value now we do the operation as addition

`5/8+12/8=17/8`