Minimum Resultant (Math Help)

Einführung in die minimale Resultant

Studium der Veränderungsraten heißt Kalkül. Optimierung ist eine der Techniken in der Infinitesimalrechnung. Es wird zur Bestimmung des maximalen oder minimalen Wertes der real-Funktion. Optimierung wird auch als mathematische Programmierung bezeichnet. Zu minimieren ist das Studium der Mindestwert der echte Funktion zu finden. Zu maximieren ist die Studie den Maximalwert des realen-Funktionen zu finden. Beide minimieren und maximieren als Optimierung bezeichnet.

Minimale Resultant:-Beispiel

Beispiel 1: Finde die minimale und maximale resultierenden eines Punktes in Funktion

f(x) = 3 X ^ 3 + 9 X ^ 2-27 X - 4.

Lösung:

f ' (X) = 9 X ^ 2 + 18 x - 27 = 9 (X ^ 2 + 2 x - 3)

= 9(x + 3) (x - 1)

= 0

Bedeutet: X =-3 oder X = 1.

f ' (X) = 9 X ^ 2 + 18 x - 27.

f '' (X) = 18 X + 18.

f '' (1) = 18 + 18 = 36.

Die zweite Ableitung ist positiv. Die Funktion hat daher ein Minimum bei X = 1.

f(x) = 3 X ^ 3 + 9 X ^ 2-27 X - 4

f(1) = 3 + 9-27 - 4

=-19

Das Minimum tritt am Punkt (1,-19).

Als nächstes wird X =-3 zu bestimmen, ein Maximum oder ein Minimum?

Die zweite Ableitung ist positiv. Die Funktion hat daher ein Maximum bei X =-3.

Um die y-Koordinate--Extremwert--, dass höchstens zu finden, bewerten Sie f (-3):

f '' (X) = 18 X + 18.

f(-3) = 3(-33) + 9(-3^2) - 27(-3) - 4

=-81 + 81 + 81-4

= 77

Das Maximum tritt am Punkt (-3, 77).

Beispiel 2: Finden Sie die maximalen und minimalen resultierenden Punkte auf der Kurve y = 4 X ^ 3-42 x 2 + 72 X - 40

Lösung:

y = 4 X ^ 3-42-X ^ 2 + 72 x - 40

y'= 12 X ^ 2-84 X + 72 = 0

12 (X ^ 2-7 X + 6) = 0

12 (x-1) (x - 6) = 0

Daher x = 1 oder X = 6

y'' = 24 X - 84

Wenn X = 1, y'' = 24 (1) - 84 =-60, die negativ ist.

Daher Kurve hat einen maximalen Punkt mit X = 1.

Wenn X = 6, y'' = 144-84 = 60, das ist positiv.

Daher die Kurve hat einen minimalen Punkt mit X = 6.

Maximalwert = (der Wert von y mit X = 1) = 4-42 + 72-40 = - 6.

Mindestwert = (der Wert von y mit X = 6) = 864-1512 + 432-40 = - 256.

(1,-6) Ist daher die maximale Point und (6,-256) ist der minimale Punkt.

Minimale Resultant: - Praxis

Problem 1: Der Raum im Zeitraum t durch ein Teilchen bewegt sich in gerader Linie beschrieben wird durch gegeben.

s = t ^ 2 - 40 t ^ 3 + 30 t ^ 2 + 180t = 240, die minimale resultierenden Beschleunigungswert zu finden.

Antwort:-260

Problem 2: Finden Sie den kleinsten Wert (2 X + (8 / x ^ 2).

Antwort: 6

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Solve science notation (Dave hooks)

Default by a technique of change is to learn the a large number of simple method and easy to recognize. Here 105 = 100000, so 6 106 can be written as 7 104 = 6000000. 70000. This consideration can be write in even larger numbers simply from standard. Small numbers can write even while out of the standard. The method script is a digit in the standard of to write down that first a digit between 1 and 10, as well as at the time write 10 (to the power of a digit).

Solved example problems on the basis of assistance to standard out:

Solved example problems on the basis of aid for standard from the bottom, which is given

Example 1:

Change 123 10 ^ 6 in standard from.

Solution:

Step 1:

123 10 ^ 6 = 123000000. [Multiplication moves by 1000000, placing 6 on the right side of the decimal point]

Step 2:

Therefore, we obtain the value for 123 1000000 = 123000000

The standard of 123 10 ^ 6 is 123000000.

Step 3:

123000000 Is the final answer for the problem.

Example 2:

Change 123,123 10 ^ 8 in standard from.

Solution:

Step 1:

123.123 10 ^ 8 12312300000. = [Multiplication moves by 100000000, placing the decimal point 8 on the right side]

Step 2:

Therefore we use for 123.123 100000000 = 12312300000

The standard of 123,123 10 ^ 8 is 12312300000.

Step 3:

The final answer to the problem is 12312300000.

Example 3:

Change 0,00752 10 ^ 7 standard out.

Solution:

Step 1:

0,00752 10 ^ 7 75200. = [Multiplication moves by 10000000, that 7 right placed the decimal point]

Step 2:

Therefore, we obtain the value for 0.00752 = 10000000 75200

The standard of the 0,00752 10 ^ 7 is 75200.

Step 3:

75200 Is the final answer for the problem.

Example 4:

Change 120,12 10 ^ 4 standard out.

Solution:

Step 1:

120.12 10 ^ 4 = 1201200. [Multiply over 10000 move decimal point 4 on the right side make]

Step 2:

Therefore we use for 120.12 10000 = 1201200

The standard of the 120,12 10 ^ 4 is 1201200.

Step 3:

The final answer to the problem is 1201200.

Example 5:

Make a note of the number 4 30 000 in standard form.

Solution:

Finding: the values of a and b.

a = 4.3 (must be between 1 and 10).

b = 5 (4.3 multiply five times from 10 to 4 to provide 30 000).

Therefore, the scientific notation of 4 is 30 000 4.3 10 ^ 5

Answer: 4.3 10 ^ 5

Example 6:

43 Million in standard form to write.

Solution:

43 Million can be written as 43 000 000.

Finding: the value of a and b.

a = 4.3 (must be between 1 and 10).

b = 7, because you will have 4.3 multiply seven times to give 43 000 000.

Therefore, the scientific notation of 43 000 000 is 4.3 10 ^ 7

Answer: 4.3 10 ^ 7

Let the practice problem in standard form.

Exercises, on the basis of assistance to standard out:

Exercises, on the basis of standard guide from under the is specified,.

Problem 1:

Amendment 564 10 ^ 5 to standard out.

Answer: The final answer to the problem is 56400000.

Issue 2:

Change 0,702 10 ^ 6 in standard from.

Answer: The final answer to the problem is 702000.

Issue 3:

Change 0,001201 10 ^ 7 standard from.

Answer: The final answer to the problem is 12010.

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Writing Percentages (Math Help)

PERCENTAGE:

Finding percentages is very important chapter in mathematics as well as in our day to day life,percentage finding is a general and very very important thing in business analysis and scientific applications. as a student you know you will get percentage of marks earned in a exam in your school.

In sports as a team analyst find the percentage of success of a individual player in a tournament .A shopkeeper estimates to sell the product to certain amount to get desired percentage of profit, so such examples are common with anybody's observation.So knowing the percentage is not only important ,it is a necessity with finding percentages. we will know on which area we have to improve to get good results.knowing percentages as a person is very essential.

So how to find percentage:

x is what percent of y =(x/y) * 100

Example : jhon is scored 8 out of 10 in a subject than his percentage of marks in that subject is

Percentage of marks of jhon=(8/10) * 100 = 80

So jhon got 80 percentage of marks in the subject.

* Let quarter part of the pizza means 1/4 th part of pizza and assume the pizza as a whole as 1

So remaining pizza part is 1- 1/4 =3/4

3/4 in percentage =3/4 * 100 =75 %

Tip for you: Multiply given fraction with 100, we get percentage.

Profit Percentage:

If an item is sold for more than its buying cost, then it is known as that the item have been sold at a profit.

If the profit is often uttered as a percentage of the cost price, then it is called as the percentage profit. In this article we are going to discuss about the formula of profit percentage and the example problems to solve the profit percentage.

The formula used to find the profit and the profit percentage is explained below.

For finding the profit percentage first we need to find the profit of the product.

The formula used to find the profit is:

'"Profit" = "selling price (SP)" - "Cost price (CS)"'

The formula used to find the profit percentage is:

'"Profit %" ="Profit" / "Cost price" xx100%'

Examples:

Example 1: If a shopkeeper want to sold a cooler for 150 dollar and actually he got that cooler for 125 dollar(cost price) then, what is his profit percenage?

Solution:

Cooler cost price=125$

Cooler selling price=150$

Profit = Selling price - Cost price

profit=25$

Therefore, profit percentage= (profit/cost price) x 100=(25$/125$) *100 =(1/5) * 100 =20 %

So shopkeeper will get 20% profit, if he sold the cooler for $150.

Example 2: Generally in hollywood there are 750 flop pictures out of 1000 pictures per year. so the success rate of flims in hollywood is?

Solution:

Number of successful pictures =1000-750=250

sucess rate = (successful pictures/total pictures) * 100 = (250/1000)*100 =25%

So success percentage is 25 %

Example 3: 25 is what percentage of 50?

Solution:

=(25/50) * 100

=(1/2) * 100

=50 %

So 25 is 50% of 50

Example 4: in school test student has three subjects math,science and social and a student got 85, 80,90 in math , science and social subjects respectively out of 100 marks in each subject than what is his percentage of marks on that test?

Percentage = (sum of marks earned by the student / total marks ) * 100

=(85+80+90) / 300

=255/300

=85%

So student got 85% of marks on that test

Example 5: A house was bought for 80 000 dollar and is sold for 95 000 dollar. Find the percentage profit?

Solution:

Cost price = $80000

Selling price = $ 95000

Profit = SP - CP

= $95000 - $ 80000

= $ 15000

Profit % = (15000) / (80000) *100%

= 18.75%

Thus, the percentage profit is 18.75%.

Example 6: A car was bought for 300 000 dollar and is sold for 350000 dollar. Find the percentage profit?

Solution:

Given:

Cost price = $300000

Selling price = $ 350000

Profit = SP - CP

= $300000 - $ 350000

= $ 50000

Profit % = (50000) / (300000) *100%

= 16.66%

Thus, the percentage profit is 16.66%.

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Stats Box Plots Online Tutoring (Math Help)

Introduction to stats box plots online tutoring:

Stat box plot is to build the box and whisker plot; for the given statistical. It also helpful for analysis of given records and to make a comparative study. Statistics box plot is very useful for large observations and to spot outliers. Stats box plots online tutoring gives aid to you at any time, and especially stats box plot online tutoring, helps to clarify the doubts related to this topic.

Stats box plot:

For finding the statistical related results there are various ways, but the box and whisker plot gives the more accurate results. In box-and-whisker plot, the interior box represents the values from the lower to upper quartile.

Steps for stats box plots online tutoring :

Step 1: The first step is to sort out the given data.

Step 2: The second step involves find the median (Q2) entire data, if there should be two middle numbers means find the mean value, it should be the median..

Step 3: Find the upper quartile and lower quartile.

Step 4: Find Q1 and Q3 percentiles.

Step 5: Find the lower most and upper most value.

Step 6: Mark the positions of Q1 , Q2 and Q3 percentiles in the grid.

Step 7: Draw a box from lower to upper quartile through Q2.

Step 8: Draw a line from lower to higher range.

Example for stats box plots online tutoring:

Draw a stats box plots for the given data

Quality : 10, 20, 90, 20, 15, 80, 25

Quantity : 20, 30, 55, 65, 90, 105, 70

Solution given by online tutoring is as follows

Sort out the data in ascending order.

Quality : 10, 15, 20, 20, 25, 80, 90

Quantity : 20, 30, 55, 65, 70, 90, 105

Median :

In the two kinds of data there are 7 information, it is odd

Therefore,

Median (Quality) Q2 = 20.
Median (Quantity) Q2= 65
Lower Median(Q1)

Quality : 10, 15, 20, 20, 25, 80, 90

Quantity : 20, 30, 55, 65, 70, 90, 105
Lower three numbers are

Quality : 10, 15, 20

Quantity : 20, 30, 55

Middle (Quality) Q1= 15

Middle (Quality) Q1= 30

Upper Median

1, 8, 9, 17, 21, 22, 23

Upper three numbers are

Quality : 10, 15, 20, 20, 25, 80, 90

Quantity : 20, 30, 55, 65, 70, 90, 105

Upper three numbers are

Quality : 25, 80, 90

Quantity : 70, 90, 105

Middle (Quality) Q3= 80

Middle (Quantity) Q3 = 90

Maximum

Quality : 10, 15, 20, 20, 25, 80, 90

Quantity : 20, 30, 55, 65, 70, 90, 105

Maximum (Quality) = 90

Maximum (Quantity) =105

Minimum

Quality : 10, 15, 20, 20, 25, 80, 90

Quantity : 20, 30, 55, 65, 70, 90, 105

In the given data 23 is the highest value.

Minimum (Quality) = 10

Minimum (Quantity) =20

Stats box plots provided by online tutoring

Practice problem for stats box plots online tutoring:

Draw the box and whisker plot for the given set of report

Feature : 1, 8, 9, 17, 21, 22, 23, 15, 45, 34, 17

Excellence : 22, 13, 3, 5, 25, 28, 30, 17, 19, 32, 40

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is a repeating decimal a rational number (dave hook)

Introduction - Is a repeating decimal a rational number?

In math a rational number is a number that can be articulated as a ratio of 2 integers, which is in the form of 'p/q' where p and q are integers and q should not be equal to zero. Likewise, any repeating or ending decimal represents a rational number. In this article we shall argue is a repeating decimal a rational number.

Examples of rational numbers:

The following are the examples of rational numbers:

'1/4' is a rational number (1 divided by 4, or the ratio of 1 to 4)

The decimal 0.5 is a rational number ('1/2' )

1 is a rational number ('1/1' )

4 is a rational number ('4/1' )

The decimal 3.14 is a rational number ('314/10' )

The decimal 1.13 is a rational number ('113/100' )

The negative decimal -3.3 is a rational number ('-33/10' )

The repeating decimal 1.1212121212... is a rational number.

The repeating decimal 1.3333333333... is a rational number.

Is a repeating decimal a rational number?

Yes a repeating decimal is a rational number. Because the decimal extension of a rational number always either terminates after finitely many digits or begins to replicate the same series of digits more and more. Therefore any repeating decimal is a rational number.

Let us discuss the properties of rational numbers

Commutative property a+b = b+a

Associative property (a+b)+c = a+(b+c)

Additive identity a+0 = a

Multiplicative identity a (1) = a

Additive inverse a+ (-a) = 0

Multiplicative inverse (1/a) =1

Multiplication property of zero a(0)=0

Distributive property a(b+c) = ab + ac

Example problems for rational number:

Identify the rational numbers from the following.

5, 78, 5.6, 784, 0.55, 6.57575757..., 3.645548349... , 'sqrt2' , 'sqrt3' , 'pi'

Solution:

5 can be written as a ratio of 5 and 1, which is '5/1' where 1 and 5 are integers.

78 can be written as a ratio of 78 and 1, which is '78/1' where 1 and 78 are integers.

5.6 can be written as a ratio of 56 and 10, which is '56/10' where 10 and 56 are integers.

0.55 can be written as a ratio of 55 and 100, which is '55/100' where 100 and 55 are integers.

6.57575757... has a repeating decimal 5 and 7 therefore it is a rational number.

3.645548349... has a repeating decimal 3 therefore it is a rational number.

sqrt2 is equal to 1.4142135.. is not a rational number because the decimal is not repeating.

sqrt3 is equal to 1.732050.. is not a rational number because the decimal is not repeating.

'pi ' is equal to 3.14159265.... is not a rational number because the decimal is not repeating.

Here in this page we are going to discuss about operations with rational numbers. In abstract algebra, the concept of a polynomial is extended to include formal expressions in which the coefficients of the polynomial can be taken from any field. In this setting given a field F and some indeterminate X, a rational expression is any element of the field of fractions of the polynomial ring F [X].

Source: Wikipedia

Operations on rational numbers

Rational number is the quotient of two integers. Therefore, a rational number is a number that can be write in the form 'w/x', where w and x are integers, and x is not zero. A rational number written in this way is commonly called a fraction.

'w/x'

Where

w 'rArr' an integer

x 'rArr' a nonzero integer

'17/15', '(14)/(9x)' 'rArr' Rational numbers

An integer can be marking it as the quotient of the integer and 1, every integer is a rational number.

Note : A rational number written as a fraction can be written in decimal notation.

Examples

Below are the examples on operations with rational numbers -

Example 1:

Write '48/4' as a decimal.

Solution:
12 'rArr' This is called a terminating decimal.
4 | 48
4
08
8
0'rArr' The remainder is Zero.

'48/4' = 12

Adding operations with same denominators:

Example 2:

'8/2' + '4/2' = ?

Solution:

'8/2' + '4/2' = '8/2' + '4/2'

= '(8+4)/2'

= '(12/2)'

= '6'

Adding operations with different denominators:

Just as we add fractions, rational numbers with different denominators can also be extra. By finding out the LCM, we can take the denominators to the same number.

Example 3:

'4/3' + '3/6'

Solution:

= '4/3' + '3/6'

6 is the LCM of 3 and 6.

= '8/6' + '3/6'

= '(8+3)/6'

= '11/6'

= '11/6'

Subtraction operations with same denominators:

Just as we subtract fractions, we can subtract rational numbers with same denominator.

Example 4:

'5/6' - '2/6' = ?

Solution:

= '5/6' - '2/6'

= '(5-2)/6'

= '4/6'

= '2/3'

Subtraction operations with different denominators:

Just as we subtract fractions, rational numbers also can be taken off with different denominators. The common denominator is achieved by finding out the LCM.

Example 5:

'-5/12' + '2/6'

Solution:

= '-5/12' + '2/6'

= '-5/12' + '4/12'

= '(-5+4)/12'

= '-1/12'

Multiplication operations with same denominators:

Just alike the multiplication of whole numbers and integers, multiplication of rational number are also repeated addition.

Example 6:

'5/4*10/5'

Solution:

= '5/4*10/5'

= '(5*10)/(4*5)'

= '50/20'

= '5/2'

Multiplication operations with different denominators:

Example 7:

'5/2*10/3'

Solution:

= '5/2*10/3'

= '(5*10)/(2*3)'

= '50/6'

Practices problems

Problem 1:

'2/6+1/3' = ?

Answer: '2/3'

Problem 2:

'2/5' + '1/5'

Answer: '3/5'

Problem 3:

'7/5' - '5/5'

Answer: '2/5'

Problem 4:

'30/3' -('5/5')

Answer:'135/15' or '9'

Problem 5:

'5/3*2/3'

Answer:'10/9'

Problem 6:

'2/5*4/2'

Answer:'4/5'

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Solve Riemannian Geometry (Omkar Nayak)

Introduction to solve Riemannian geometry:

Solve Riemannian geometry refers solving the Riemannian manifolds and smooth manifolds using the Riemannian metrics. Riemannian metrics are nothing but the tangent space with the curves inner product which varies in smooth manner from point to point. To solve the Riemannian geometry we will use the Riemannian sums and Riemannian integrals method. Basically Riemannian geometry refers the elliptic geometry. Here we are going to solve the area of the curve underneath. We will see some example problems for solve Riemannian geometry.

Solve Riemannian geometry - formulas:

If we have to solve the Riemannian geometry we have to use the Riemann sums and integrals method. Using this we have to find the area of the given curve on the graph underneath. In Riemannian geometry the Riemann sums and integrals used in definite integration operation. The Riemann integral is defined by taking the limit for the given Riemann sums. It is based on Jordan measure.

If we want to use the Riemannian sums the formula is

'S = sum_(i = 1)^nf(y_i)(x_i - x_(i - 1))' Here xi - 1= y i= x. Here the choice of y i is the arbitrary.

If the y i = xi - 1 is for all i values then it is called Left Riemann sum.

If the y i = xi then it is called right Riemann sum.

The average of the above two Riemannian is called Trapezoidal sum.

If the y i = (xi - xi - 1) / 2 then we can call this as middle Riemann sum.

If we want to use the Riemannian integrals the formula is

' int_a^bf(x)dx=lim_(maxDeltax->0)sum_(k=1)^nf(x^n)Deltax'

Examples for solve Riemannian geometry:

Examples 1 for solve Riemannian geometry:

Find the area of the given curve under y = x2 among the limits 0 and 3 using Riemannian sum.

Solution:

The area below the curve of x2 among the limits 0 and 3 may be computed procedurally using the Riemann's Sum method. The interval 0 and 3 is divided into n number of sub intervals. Each sub interval gives the width of the 3/n. These are called width of the Riemann's rectangles. The sequence of all x coordinates can be defined as X1, X2 . . . , X n. Then the heights of the Riemann Rectangle boxes can be defined by the following (X1)2, (X2)2 . . . , (X n) 2. This is an important fact where Xi ='(3i) / n' .

The area of a single box will be (3 / n)(xi) 2

S =' (3 / n) xx (3 / n)^2 + . . . . + (3 / n) xx ((3i) / n) ^2+ . . . +(3 / n) xx (3)^2'

S = '27 / n^3 (1 + . . . + i^2 + . . . . + n^2)'

S = '27 / n^3((n(n + 1)(2n + 1)) / 6)'

S = '27 / n^3 ((2n^3 + 3n^2 + n) / 6)'

S =' 27 / 3 + 27 / (2n) + 27 / (6n^2 )'

S =' lim_(n-gtoo)( 27 / 3 + 27 / (2n) + 27 / (6n^2 ))'

S = '27 / 3' = 9

Examples 2 for solve Riemannian geometry:

Find the area of the curve under y = x3 among the limits 0 and 3 using Riemannian integral.

Solution:

In Riemann integrals help we can calculate the area above for the interval 0 and 3. Here

Riemann integral =' int_0^3(x^3)= (x^4 / 4)'

Now we have to take the limit is 0 and 3

If we applying the limit from 0 to 3 we get

= '3^4 / 5 - 0^4 / 4 = 81 / 4'

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Why is Geometry Important in Life (Nandan Nayak)

Introduction:

Geometry is important in life because it is the learning of space and spatial dealings is an important and necessary area of the mathematics curriculum at every evaluation levels. The geometry theories are important in life ability in much profession. The geometry offers the student with a vehicle for ornamental logical reasoning and deductive thoughts for modeling abstract problems. The study of geometry is important in life because it's increasing the logical analysis and deductive thinking, which assists us expand both mentally and mathematically.

Definition for why is geometry important in life:

This article going to explain about why geometry is important in life. Geometry is a multifaceted science, and a lot of people do not have an everyday need for its most advanced formulas. Understanding fundamental geometry is essential for day to day life, because we never know when the capability to recognize an angle or figure out the region of a room will come in handy.

Importance of geometry in life:

The world is constructing of shape and space, and geometry is its mathematics.
It is relaxed geometry is good preparation. Students have difficulty with thought if they lack adequate experience with more tangible materials and activities.
Geometry has more applications than just inside the field itself. Often students can resolve problems from other fields more easily when they represent the problems geometrically.
Uses of geometry:

Geometry is the establishments of physical mathematics presents approximately surround us. A home, a bike and everything can made by physical constraints is geometrically formed.
Geometry allows us to precisely compute physical seats and we can relate this to the convenience of mankind.
Anything can be manufacturing use of geometrical constraints like Architecture, design, engineering and building.

Example:

Let us see one example regarding why geometry important in our life. If you want to paint a room in your accommodation, you should know how much square feet of room you are going to cover by paint in order to know how much paint to buy. You should know how much square feet of lawn you contain to buy the correct amount of fertilizer or grass seed. If you required constructing a shed you would have to know how much lumber to buy so you should know the number of the square feet for the walls and the floor.

Geometry architecture is a one of the foundation of all technologies and science using the language of geometry pictures, diagrams and design. Geometry was fully depends on structure ,size and shape of the object. In every day geometry was very important in architectural through more technologies In a daily life geometry was used in th technology of computer graphics, structural engineering, Robotics technology, Machine imaging, Architectural application and animation application.

In this article why is geometry important in architecture, We see about application of geometry architecture in daily life and technology sides.

Basic concepts of geometry important in architecture:

General application of geometry or important of geometry :

Generally geometry was used for identifying size, shape and measurement of an object.
Fining volume, surface area, area ,perimeter of the room a and also properties about shaped objects in building construction.
Also used for more technologies for example : computer graphics and CAD
Computer graphics:

In computer graphics geometry was used to design the building with help of more software technologies. And also how to transferred the object position.

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Best schools in Pune for kids (mycity children)

Pune is the second largest metropolis city in the Indian State of Maharashtra, and is well known as a centre of education across the country. The literacy rate in the city is approximately 81%, which is higher than the national average. Schools in Pune followed by three levels of education primary, secondary and senior secondary. All private schools in Pune are affiliated certificate (SSC), or the all - India either school advanced the Maharashtra Indian certificate of secondary education (ICSE) and CBSE boards. Private schools in Pune are more sought after and popular with parents for their good equipment and the use of English as a medium of instructions.

Before choosing some factors are a schools of child in in Pune, parents should keep in mind. The basic things start by looking through the infrastructure, academic results, extra - curricular activities and excellence of teachers in the school. If you are new to the area, then Internet will help you to find the best school for your child in your areas close by. Mycity4kids is one of children in connection with Web site contains complete information about the schools and even offers the possibility of payment of the fees online while sitting at home, for your money, save time and energy. You can search for the videos uploaded by parents have better idea about the school.

SCHOOL in North Pune and the lexicon schools such as PUNE CAMBRIDGE international school in East Pune CBSE and offers education best recruit. In these schools CBSE in Pune, students prompts teachers to participate in various activities of the co. Some of the ICSE-affiliated schools in Pune like JACK N JILL ENGLISH MEDIUM SCHOOL in East Pune, SAHYADRI SCHOOL in North Pune and many more are well equipped with all the necessary facilities for the students. These schools have well trained, passionate, qualified and dedicated employees who individually to ensure each student their physical and mental growth extra attention.

With the increase in the technology have many schools in Pune like BHARATI VIDYAPEETH ENGLISH MEDIUM SCHOOL in West Pune smart classroom AIDS student makes an experience of studying at the see it live before them with smart classroom started. These schools firmly believes in is that they produce the future gems for the country, therefore they are extremely responsible and committed to their job. The schools of this town create best man will not hesitate to take on new challenges and make their own way to the others follow.

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There are many nursery schools in Chennai, and so the literacy rate is more than 90% (Little Millennium)

Chennai is the capital city of the Indian state Tamil Nadu, which is located on the Coromandel Coast off the Bay of Bengal, It is also known as the "Cultural Capital of South India".

Chennai is the hub of education; it has many playschools in Chennai. Today it is able to offer appropriate education and studying to a large number of learners and every year a large number of learners come over here in order to get into various educational programs.

The nursery schools in Chennai are located near the residential places and hence they are within quick access of the kids. Here you will also get littlemillennium playschool which are efficient in offering top quality education and studying and also take care of the kids in providing them top quality academic knowledge. The Professional littlemillennium Playschool in the town has gained a name for itself through actual commitment and top quality performs in the area of educating.

One of the priority objectives of the playschools in Chennai is to set up a appropriate base of baby's room academic education and studying for the little learners so that they could get into this routine of studying and growing. Interesting and motivating academic as well as co curricular actions and applications are set in the annually program so that the youngsters could get maximum contact with the new kinds of studying ways. Different kinds of social and traditional applications and actions are performed to keep them informed with the age old lifestyle and custom of the nation which is not just rich and different but also a fundamental element of our community.

Research by scientists reveal that the development of brain is the most in the age of 1-5, that is the age when the kid lays his foundation pillar for his future. Parents are responsible for the strength of the foundation laid by the kid. A well foundation can be very well termed as a stepping stone to success. Kids have an amazing grasping power in this age range, they grasp things very easily and inculcate them in their nerves as a moral value.
All play and no work makes a jack (kid) an awesome Boy!

The most vital role that play performs is to make them active, take decisions, and do a sort of workout while playing. Nursery schools in Chennai helps child to play games which are related to their own imagined actions. If the work is play, and the tools are toys for a kid then he/she can easily learn creativity that helps children to grasp things easily using their constructive imagination.

Little millennium play school in Chennai provides better classes which are huge and well equipped, clean and sanitary cafeteria, 24*7 safe and clean water service, music and toy rooms for extracurricular activities. Students are taken to academic visits and other adventures for a fun filled studying time that helps them grow in a creative way.

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Stomach acid (math help)

Many people take over-the-counter traded antacids for a fast simple acidic stomach, but for most people, a proper diet is the best solution for overcoming acidic stomach.

Sour stomach diet myth

* Myth 1: drink milk

Many people try drinking milk sour stomach before sleep easier. But often, milk cause sour stomach during sleep ends. To understand the whole situation, we need to recognize that the problem of eating too much at meal time roots. Causes a big meal in the evening, that excess stomach acid production. Drinking milk could be a quick solution to the problem of stomach of acid. Unfortunately, milk would has a rebound action and finally the secretion of more stomach acid, allowing the acidic stomach. To solve the problem, try to adapt your diet through a small meal in the evening and have a small snack like crackers sleep before.

* Myth 2: Avoid coffee, citrus fruits and spicy food

We have said for many years that coffee, sour fruits and spicy foods worsen sour stomach can. For this reason we should avoid them in our daily diet to reduce acidic stomach. A recent study in the archives of internal medicine published in May 2006 showed that none of these myths are true. Researchers at Stanford University found that only two changes in behavior can symptoms of sour stomach their-less food and raise your head while sleeping.

Proton pump inhibitors like Nexium, Prilosec are among the most commonly prescribed drugs in the United States, but several new studies warn that the popular stomach acid reducers show the potential for serious side effects.

Issue of the archives of internal medicine explore the side effects associated with Proton pump inhibitors, including bone fractures in older women and Clostridium difficile infections which can cause life-threatening diarrhea and stomach-intestine disorder in the elderly five studies and an editorial in the may.

Overall, Proton pump inhibitors are safe, experts stressed. Nevertheless suggest instructions on unnecessary medications are prescribed, and the possible side effects not enough are taken seriously.

"Protonenpumpenhemmer safe medicines are generally. Proton pump inhibitors are commonly used and generally very well tolerated, '' said Dr. Amy Linsky, lead author of one of the studies, and general internal medicine fellow at Boston Medical Center. "But in the last few years, there is more info on some side effects that emerge them associated. Prescribe and patients should be aware, what are some of these dangers, and each patient must weigh risk vs. could use. "

Proton pump inhibitors are under the brand name Prilosec, Prevacid and Nexium, and others sold. About 113 million prescriptions for Proton pump inhibitors are each year according to an accompanying editorial filled accounting of nearly 14 billion $ sales.

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Special Purpose P-N Junction Diodes (Math Help)

How a PN Junction Diode Works

Summary of the basics or a tutorial of how a PN junction or diode works showing how does the current flow in only one direction, and how diodes can be used on their own and in transistors

Before reading this page, it is worth reading the page entitled "What is a semiconductor" - see the related articles list below the left menu. This will explain some of the basics of semiconductors and some of the terms used on this page.

The PN junction is one of the most important structures in today's electronics scene. It forms the basis of today's semiconductor technology, and was the first semiconductor device to be used. The first semiconductor diode to be used was the Cat's Whisker wireless detector used in early wireless sets. It consisted of a wire placed onto a material that was effectively a semiconductor. The point where the wire met the semiconductor then formed a small PN junction and this detected the radio signals.

The diode or PN junction was the first form of semiconductor device to be investigated in the early 1940s when the first real research was undertaken into semiconductor technology. It was found that small point contact diodes were able to rectify some of the microwave frequencies used in early radar systems and as a result they soon found many uses.

Today, the PN junction has undergone a significant amount of development. Many varieties of diode are in use in a variety of applications. In addition to this, the PN junction forms the basis of much of today's semiconductor technology where it is used in transistors, FETs, and many types of integrated circuit.

The PN junction is found in many semiconductor devices today. These include:

* Diode
* Bipolar transistor
* Junction FET
* Diac
* Triac

The PN junction has the very useful property that electrons are only able to flow in one direction. As current consists of a flow of electrons, this means that current is allowed to flow only in one direction across the structure, but it is stopped from flowing in the other direction across the junction.

PN Junction

A PN junction is made from a single piece of semiconductor that is made to have two differing areas. One end is made to be P-type and the other N-type. This means that both ends of the PN-junction have different properties. One end has an excess of electrons whilst the other has an excess of holes. Where the two areas meet the electrons fill the holes and there are no free holes or electrons. This means that there are no available charge carries in this region. In view of the fact that this area is depleted of charge carriers it is known as the depletion region.

The semiconductor diode PN junction with no bias applied

The depletion region is very thin - often only few thousandths of a millimetre - but this is enough to prevent current flowing in the normal way. However it is found that different effects are noticed dependent upon the way in which the voltage is applied to the junction.

Current Flow - If the voltage is applied such that the P type area becomes positive and the N type becomes negative, holes are attracted towards the negative voltage and are assisted to jump across the depletion layer. Similarly electrons move towards the positive voltage and jump the depletion layer. Even though the holes and electrons are moving in opposite directions, they carry opposite charges and as a result they represent a current flow in the same direction.

No current flow - If the voltage is applied to the PN junction in the opposite sense no current flows. The reason for this is that the holes are attracted towards the negative potential that is applied to the P type region. Similarly the electrons are attracted towards the positive potential which is applied to the N type region. In other words the holes and electrons are attracted away from the junction itself and the depletion region increases in width. Accordingly no current flows across the PN junction.

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Exam of Logarithms in General (Nandan Nayak)

Introduction to exam of logarithms in general:

Exam of logarithm in general involves the learning and understanding of the following concepts of logarithms:-

Conversion of exponential to logarithmic form

The three laws of logarithms

The base changing formula

After learning the above topics of logarithms, the exam of logarithms in general preparation can be considered almost complete at the basic level. Essentially, one gains the application knowledge of logarithmic laws and concepts that enable one to simplify and solve logarithmic equations. The above basic logarithmic concepts help us to prove advanced logarithmic statements.

The above mentioned concepts on logarithms are briefly explained below as preparation for exam on logarithms in general.

Conversion of exponential to logarithmic forms in general:

The logarithm of a number is equal to the exponent to which the base of that logarithm must be raised in order to obtain that number.

Logarithms can be considered as a different type of representation of exponential statements.

For example, the exponential statement '6^2 = 36' can be expressed in the logarithmic form as follows:-

log '(6) 36 = 2'

In the above conversion from exponential to logarithmic form, we note the following rules:-

Base of the logarithm and the exponential form is the same.

The result in the exponential form is made the object in the logarithmic form.

The exponent in the exponential form is made the result in the logarithmic form.

The three laws of logarithms:

The three standard laws of logarithms can be stated as follows:-

First law of logarithms - the product law

The logarithm of a product of two or more numbers is equal to the sum of the logarithms of each of the numbers in the product. Thus, if 'a' and 'b' are two non-negative real numbers, and 'c' is the base of the logarithms, then,

'log (c) ab = log (c) a + log (c) b'

This law highlights that logarithms reduce multiplication to addition.
Second law of logarithms - the quotient law

The logarithm of the quotient of two numbers is equal to the difference of the logarithms of each of the two numbers. Thus, if 'a 'and 'b' are two non-negative real numbers, and 'c' is the base of the logarithms, then,

'log (c) a/b = log (c) a - log (c) b'

This law highlights that logarithms reduce division to subtraction.
Third law of logarithms - the power law

This law defines the logarithm of an exponential expression. The logarithm of an exponential expression is equal to the product of the exponent in the exponential expression and the logarithm of the base of that exponential expression.

'Log (c) a^b = b * log (c) a'

This law highlights that logarithms reduce exponents to products.

The base changing formula

The base changing formula helps us to change the base of logarithms, which is a very essential function in solving logarithmic equations. It helps to simplify logarithmic equations. By using the base changing formula, one can change the base of a logarithm to any other number or variable.

'Log (a) b = (log (c) b)/(log (c) a)'

In the above statement, the base of the logarithm is being changed from 'a' to 'c'.

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Location Theory (Math Help)

Location structure theories

Location structure theories ask for the optimal arrangement of enterprises in the area and their change with the time. To the location structure theories belong the rings of the Johann Heinrich of and from Walter all developed system of the centers of places.
Theories of the business choice of location

Theories of the business choice of location concern themselves with the optimal enterprise location, thus the location of an individual enterprise.

For the problem of the optimal operating location the motive for profit is fundamental in the free free-market economy - at which place thus can the highest profit be The enlargement of the market share, future security and subjective motives do not play however a role which can be underestimated.

If these goals are certain, the optimal location can be selected after these categories. In addition the conditions (location factors) on different spatial levels are to be compared: Which country is best suitable for the new Which And finally which municipality and where there
Neoclassical location theory

Alfred Weber set up a model for the determination of optimal locations for the industriellen individual enterprise, which is affected substantially by the location factor transport costs in his fundamental work over the location of the industries (1909). To its model from the outset critically was noticed that its premises are rather out of touch with reality, then e.g. presupposes Weber an unlimited worker offer or complete information of the decision makers over the spatial distribution of the markets and the location factors. Also Weber theory is strongly for the transport costs appropriate and neglected as substantial factor of the location decision thereby all other factors of production.

1956 extended Walter Isard of Weber location theory by Andreas substitution principle and revalued thereby the location decision to a substitution decision between factors of production in a general equilibrium model.

David M. Smith extended this theory by a variable cost model, so that in the context of a total model all space dependent costs and proceeds of the enterprises can be regarded. Smith introduced also aspects like business being able, regional policy and regional taxes into the model.

By its extensions the neoclassical location theory became more meaningful. Some the premises already criticized with Weber (purer "“homo oeconomicus", complete information, short term maximization of profit) it leads however to the fact that not all actual business location decisions can be explained satisfying by neoclassical models.

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Top convent school in Gurgaon (d.k sharma)

Alpine Convent School was set up in Gurgaon in 1996 under the able guidance of conscientious and meticulous personalities. Alpine Progressive Educational Society [Regd.] is the apex body of the school. The school believes in laying a strong foundation for children and creates an environment of self motivated learners. The school boasts of specialized Montessori Wing, primary and Middle Section with excellent infrastructure, trained and compassionate staff.
Specialities

Specialized Montessori Wing
The Preparatory wing of Alpine Convent School gives Opportunity to every child to live free from all fears and tensions. Children are exposed to Montessori Method of teaching where they are provided with great variety of materials to manipulate, experiment, play, touch and feel.
The school inculcates child oriented programs so that his /her imaginations are stimulated and creativity is encouraged. For us, every child is an 'able child' thus exploring his/her potential is our main objective. Special attention is given to enhance vocabulary and spoken English.
The wing is well equipped with
? Play station
? Audio-Visual teaching aids
? Splash pool
? Sand pit
? Sleeping Corner
? Story Room
Mont. Education at Alpine continually observe, monitor, document and evaluate children's learning and regularly report on their achievement to parents and the children themselves. The Assessment and Evaluation Programs are focused to improve learning abilities. Teachers assess children on an ongoing basis, taking into account both the process of learning and the results achieve. The teachers data gathered is recorded through the grading system, made over a period of time and measure children's achievement in relation to the learning expectations.
Discovery Learning
Children's early learning experiences have a profound effect on their development. Understanding the fact, that at kindergarten, children's receptivity to new influences and capacity to learn is at peak, the school curriculum and teaching methodology promotes Discovery Learning through Thematic Approach. The Activity Based in the Montessori wing and Project Based curriculum in primary & Middle section has been designed keeping in view the age groups of children and their heterogeneous mental level.
FOCUS:

Our focus is on growth and development of the child's- Physical, Emotional, Social, Intellectual and Creative skill. The basic skills we want our children to acquire and imbibe:
? Language & literacy skills
? Human & social skills
? Spiritual & moral skills
? Physical Skills
? Numerical skills
? Environmental skills (Ecological)
? Aesthetic & creative skills.
CURRICULUM
Our Curriculum Approach
High Quality early education leads to lasting cognitive and social benefits in children
? Meet children's social, emotional, physical, cognitive, and language development needs.
? Become good observers of children.
? Assess children's needs, interests, and abilities in order to plan appropriately.
? Use a wide range of teaching strategies that call for different learning styles by children and levels of teacher involvement.
? Create classroom communities where children learn to work together, explore and solve problems
? Establish the structure that has to be in place for teachers to teach and children to learn
? Plan meaningful learning experiences for children that build on children's interests and knowledge.
? Integrate the learning of appropriate skills, concepts, and knowledge in literacy, math, science, social studies, the arts, and technology.
The co-curricular activities
The co-curricular activities are very important for the overall development of a child. Various CO-curricular activities such debates, skits, Flower decoration, Rangoli, and creative workshops etc. are organized for an all round personality development of child. To inculcate the spirit of secularism in the students, various festivals like, Independence Day, Annual Function is Held every with 100% participation of students. Holi, Dussehra, Diwali, Id, Christmas etc. are celebrated in traditional manner.
Walk and watch for Parents
It is especially important in the early years for parents to be involved in discussions regarding their child's progress. The teachers gather information from the parents and consult with them while assessing the child's adjustment to school and achievement of the learning expectation. Parents are invited to observe the child in the Assembly, classroom activity and in the sports arena. The author is the main chair person of Alpine convent school, and posting article to full fill the needed costumers, with sufficient information about the organization.

Easy Division Problems (Omkar Nayak)

Introduction to easy division problems:

Let us see some content of easy division problems. Division is the operations in mathematics. This is one of the processes in arithmetic operation. The division is very easy for separate the group of events. The division is the opposite process of multiplication. The division problems are may be between integers or fractions. The integers are very easy to divide.

Definition:

Division is the process of dividing the objects together collection of larger objects. This process is used to easily separate from large number of objects. The division is very sufficient when compared to the subtraction. The solution is may be integer or floating. The division is signified as (/).

Steps for easy division:

Step 1: First change way of the given problem like should be written as division way.

Step 2: Next, we need to look at the first number of the given dividing number.

Step 3: Next, we want to see how many times that number divided by the given number.

Step 4: From that last step, we need to subtract the answer from the number. Repeat the step up to getting remainder as zero.

Examples:

Let us see some easy division problems.

Problem 1:

Find the easy value of the problems by division where the values are 34 and 6.

Solution:

The given values are 34 and 6.

Always dividend value should write outside and divisor value should write inside. The subtraction can be taken from left to right.

First write the problem like given below. Like the division format.
Look the first number, it is 3. So, it cannot be divided by the number of 6. So, take another digit with that.
Now the total number is 34. Put calculation how many time will multiply by 6 for getting 34.
But, the number 34 cannot get from the 6th table. But we can get below number of 30 at 5 times.

So subtract from 34. getting remainder as 4 and 5 as quotation. 4 cannot be divided by 6. So 4 is remainder.
____
6 ) 34 ( 5
30
_________
4
________

4 is remainder and 5 is quotation.

Problem 2:

Find the easy value of the problems by division where the values are 25 and 5.

Solution:

The given values are 25 and 5.

Always dividend value should write outside and divisor value should write inside. The subtraction can be taken from left to right.

First write the given problem like division format.
Look the first number It is 2. It cannot divide by 5.
So, take another number 25. The 25 can be divided by 5.
Put calculation how many times want to multiple for getting 25. It is 5 times in mathmetics multiplication table.
Subtract both answers, we are getting 0 as remainder and 5 is quotation.
___
5) 25 ( 5
25
________
0
_________

0 is remainder and 5 is quotation.

Problem 3:

Find the easy value of problems by division where the values are 12 and 6.

Solution:

The given values are 12 and 6.

Always dividend value should write outside and divisor value should write inside. The subtraction can be taken from left to right.

First write the problem as division format.
Look the first. It is 1. It cannot be divided by 6.
So take next number too. Now it is 12. It can be divided by the number of 6.
Put multiplication for getting 12. It is in 2 times from 6th table.
Now, subtract 12 from given number. Remainder 0 and the quotation is 2.
___
6)12 ( 2
12
______
0
_________

0 is remainder and 2 is quotation.

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Number of Divisors (Omkar Nayak)

Introduction to Whole Number Divisors:

A division method can be done by using the division symbol ?. The division can be otherwise said to be inverse of multiplication. The one of the major operation in mathematics is division operation. In division, a ? b = c, in that representation "a" is said to be dividend and "b" is said to be divisor and "c" is said to be quotient. The letter "c" represents the division of a by b. Here the resultant answer "c' is said to be quotient. Let us see about whole number divisors in this article.

Whole Number Divisors for the Number 80

The numbers that can divide by 80 is said to be the divisors of 80.

Let us assume that 80 can be divided by 2, 4, 5, 8, and 10.

Example 1:

Divide the whole number 80 ? 2

Solution:

Let us write the given number 80 inside the division bracket. The divisor can be put it in the left side of the division bracket.

2)80(

The number 2 should go into 8 for 4 times. So, put 4 in the right side of the bracket.

2)80(40

8

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

00

00

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

The zero can be placed just near the 4 in the quotient place.

The solution for dividing 80 by 2 is 40.

Example 2:

Divide the whole number 80 ? 4

Solution:

Let us write the given number 80 inside the division bracket. The divisor can be put it in the left side of the division bracket.

4)80(

The number 4 should go into 8 for 2 times. So, put 2 in the right side of the bracket.

4)80(20

8

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

00

00

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

The zero can be placed just near the 2 in the quotient place.

The solution for dividing 80 by 4 is 20.

More Problems to Practice for Finding the Divisors for 80

Example 3:

Divide the whole number 80 ? 5

Solution:

Let us write the given number 80 inside the division bracket. The divisor can be put it in the left side of the division bracket.

5)80(

The number 5 should go into 8 for 1 time. So, put 1 on the right side of the division bracket.

5)80(1

5

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

30

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

Then the number 5 should go into 30 for 6 times. So put 6 just near the 1 on the quotient place.

5)80(16

5

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

30

30

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

0

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

The solution for dividing 80 by 5 is 16.

Example 4:

Divide the whole number 80 ? 8

Solution:

Let us write the given number 80 inside the division bracket. The divisor can be put it in the left side of the division bracket.

10)80(

The number 8 should go into 8 for 1 time. So put 1 on the right side of the division bracket.

8)80(10

8

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

00

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

The zero can be placed just near the 1 in the quotient place.

The solution for dividing 80 by 8 is 10.

Example 5:

Divide 80 ? 10

Solution:

Let us write the given number 80 inside the division bracket. The divisor can be put it in the left side of the division bracket.

10)80(

The number 10 should go into 8 for 0 times. So, take the digit as two digits in a given number of the division bracket.

Then the number 10 should go into 80 for 8 times. So put 8 on the right side of the division bracket.

10)80(8

80

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

0

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

The solution for dividing 80 by 10 is 8.

Therefore, the divisors for the whole number 80 are 2, 4, 5, 8 and 10.

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Learn Zero (Math Help)

Introduction :

0 is the whole number preceding 1. Virtually in most of the systems, 0 was distinguished before the theme of negative things that go less than zero was admitted. It is considered to be an even number. 0 is not positive or negative as well. From a few definitions 0 is besides a natural number, and then the lonesome natural number not to followed as positive.

It is a number which measures a count or an amount of void size. Virtually altogether historiographers drop the year zero from the proleptic Gregorian and Old Style calendars, but stargazers admit it in these equivalent calendars. Nevertheless, the formulate Year Zero mayhap accustomed to depict whatsoever case believed so substantial that it processes as a fresh base point in time.

Zero when dealt as a digit:

The advanced mathematical digit 0 is generally scripted as a circle, an ellipse, or a rounded rectangle. In most innovative fonts, the tallness of the 0 case is equivalent as the remaining digits. Still, in typefaces with textual figures, the character reference are frequently shorter.

On the seven-segment displays of calculating machines, watches, and home appliances, 0 is usually penned with six line segments, although on a few past calculator models it was penned with four line segments.

The valuate, or number, zero isn't identical as the digit zero, applied in numeric arrangements employing positional representation system. Consecutive locations of digits bear broader weights, so inwardly in a numeral the digit zero is applied to cut off a position and give advantageous weights to the leading and following digits. A zero digit isn't all of the time essential in a positional number system, for example, in the number 02.

In rarefied cases, a leading 0 may differentiate a number. This comes along in roulette in the United States, where '00' is discrete from '0' (a wager on '0' will not acquire if the ball lands in '00', and contrariwise). Sports where challengers are listed abide by this as well; a stock car listed '07' would be believed different from one numbered '7'. This is more common with single-digit numbers. With computing systems (for example, with the Unix shell BASH), a number expressly penned with a leading zero is used as a stenography to indicate an octal (base-8) representation of a number, as contrary to a decimal (base-10). Decimal fraction figures scripted with guiding zeros will expected to be represented as octal, and will bring forth mistakes -- not barely unexpected results -- if they contain '8' or '9' since these digits don't subsist in octal. Let us learn more about zero.

Learn the concept of Zero

Zero, written 0, is both a number and the mathematical figure accustomed make up that number in numerals. It acts a cardinal function in math as the linear identicalness of the whole numbers, real numbers, and many other algebraical system. As a digit, 0 is applied as a placeholder in place value systems. In the English, 0 perhaps called zero, oh, null, nil, "o", zilch, zip or nought, depending upon accent and linguistic context.

Learn the functions of Zero

The historical document, establishes rather a contrasting course towards the conception. Zero attains dim show only to disappear over again almost as if mathematicians were exploring for it as yet didn't acknowledge its key meaning even as they ascertained it.

Firstly to say most about zero is that there are two functions of zero which are both highly crucial but are fairly dissimilar.

One role is as an empty place indicant in our place-value number system. Hence in a number like 2106 the zero is used so that the positions of the 2 and 1 are correct. Clearly 216 means something rather unlike.

The second function of zero is as a number itself in the class we apply it as 0. At the same time there are also another faces of zero inside these two usages, that is to say the concept, the notation, and the name. (The name "zero" infers ultimately from the Arabic sifr which besides gives us the word "cipher".)

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Questions and answers (John Harmar)

Educational assessment is the process of documenting, usually in measurable, knowledge, skills, attitudes and beliefs. Evaluation can on the individual learner, the learning community (class, workshop, or other organized group of learners), focus facility or the education system as a whole.
Math assessment test will test its strengths and weaknesses in math skills.Some mathematical questions and answers are given in this article.

Math exam questions and answers:

(1) Evaluate: 62-(-3 + 11)

Solution:

62-(-3 + 11) = 36-8

= 28

(2) Which is larger? The sum of 12 and 11.5 (or) the difference between 22.2 and 14.4

Solution:

Sum of 12 and 11, 5 = 12 + 11.5

= 23.5

Difference between 22.2 and 14.4

= 22, 2 14.4

= 7.8

Therefore, the sum of 12 and 11.5 is greater.

(3) Release: 10 (X + 10) = 200

Solution:

10 (X + 10) = 200

10 X + (10 x 10) = 200

10 X + 100 = 200

10 X = 200

X = 20

4) Find the mean of a given data set: {4, 6, 9, 18, 15}

Solution:

My = (4 + 6 + 9 + 18 + 15) / 5

= 10.4

5) Right triangle has the legs of length 4 cm and 12 cm. What is the length of the hypotenuse?

Solution:

Given: a = 4 cm and b = 12 cm

By Pythagoras set,.

C2 = a2 + b2

C2 = 42 + 122

C2 = 16 + 144

C2 = 160

Take the square root, we get

c = m 12.65

Length of the hypotenuse = 12.65 cm

(6) Newsletter search the volume of the cone right in the face of the RADIUS is 7 cm and the height is 10 cm.

Solution:

Volume of cone = 1/3 'pi' r2 h

= 1/3 'PI' (72) 10

= 1/3 (3.14) (49) 10

= 512.87 cm3

Practice test questions and answers:

Questions:

(1) Evaluate: 82-(7 + 20)

(2) Which is larger? The sum of 10 and 15 (or) the difference of 15 and 2

3) Solve the equation: 3 (X + 5) = 30

4) Find the mean of a given data set: {21, 32, 30, 43, 41, 47}

5) Right triangle has legs length 8 cm and 12 cm. What is the length of the hypotenuse?

(6) Newsletter search the volume of the cone right in the face of the RADIUS is 8 cm and the height is 12 cm.

Answers:

1) 37 2) Die Summe von 10 und 15 3) X 5 = 4) Mittelwert = 35,67 5) c = 14,42 6) 803.84 cm3
Educational assessment is the process of documenting, usually in measurable, knowledge, skills, attitudes and beliefs. Evaluation can on the individual learner, the learning community (class, workshop, or other organized group of learners), focus facility or the education system as a whole.(Source - Wikipedia)
Math assessment test will test its strengths and weaknesses in math skills.Some mathematical questions and answers are given in this article.

Mathematics assessment test examples:

Example 1:

Find the mean of the given data set: {6, 12, 29, 18}

Solution:

My = (12 + 6 + 18 + 29) / 4

= 65 / 4

= 16.25

Example 2:

Here you find the volume of the cylinder, the face of RADIUS 12 cm or 31 cm.

Solution:

Volume of the cylinder 'pi' r2 h = cubic units.

= (3.14) * 122 * 31

= 3.14 * 144 * 31

= 14016.96 cm3

Example 3:

Find the area of the square with side length of 7 cm.

Solution:

Area of the square (a) 2 =.

(7) = 2

= 7 * 7

Area of the square = 49 cm2

Example 4:

Find the area of a triangle with base of 19 m and a height of 6 m.

Solution:

Area of a triangle = b h

= (19) (6)

= 57 m2

Example 5:

Solution: 12 (X + 6) = 120

Solution:

12 (X + 6) = 120

12 X + (12 x 6) = 120

12 X + 72 = 120

12 X = 48

X = 4

Find more at AboutAverage, statistics, and his examples. In between, if you have problem on these topics subtract binary, browse please experts math related websites for more Hilfe.Bitte share your comment

Sets to represent (math help)

Introduction for set, which represents:

Number set is a important role in mathematics. Number of records contain numbers, operations, and an equal sign, where some of the number sentences are true, and some number sets are wrong. An expression is part of a number set contains numbers and operations, but contains no equal sign. Let us learn about the set of numbers represents.

Review for number set that represents:

* 5 + 4 = 9
* 11 + 3 = 14

These are examples of the number of phrases.

If the equation satisfies the number sentence, then it is a true sentence.

* 4 + 5 = 9, which represents a true set
* 7 + 4 = 11, which represents a real set.

When Kit meets the number not the expression, then it is set wrong

* 7 + 5 = 11, representing a false set

If the number set contains no equal sign, then an expression should be.

* 5 + 4
* 3 + 7
* 4 + 11

These are examples of expressions.

Examples of record, representing numbers:

Write an expression for everyone. Then write a number sentence to solve.

Example 1:

Jim has 18 blue pins and 15 red pins. How many pins does he have in total?

Solution:

A total 18 + 15 =

18 + 15 is the expression

18 + 15 = 33 Provides the number set

This is a true sentence, because the addition of 18 and 15 33.

Example 2:

Giles bought 18 eggs. 12 Are used for breakfast. How many eggs does she have now?

Solution:

Total egg that he have now = 18-12

The term is 18-12

The number set is 18-12 = 6

This is a true sentence because is the subtraction of 18 and 12 6.

Example 3:

John has to read 12 more pages than Jimmy. Jimmy has to read 10 pages. How many pages does John have to read?

Solution:

Number of pages to read the Jimmy = 10

Number of pages to read the John = 12

Total number of pages to read John = 12 + 10

The expression is 12 + 10

12 + 10 = 22 Is the number set

This is a true sentence.

Example 4:

Jack bought 2 chocolates, 3 cookies and 9 apples. He buy as many have more apples than cookies?

Solution:

Jack bought 9 apples and 3 cookies

He bought (9-3) = 6 apples more than cookies.

Term: 9-3

Record: 9-3 = 6

To get some ideas, set that represents.

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Algebric Functions (dave hook)

Introduction to Algebric functions:

If the X,Y pair of coordinates is always some other value, then it is called as Algebric function. There are two terms used in algebraic function. They are Domain and Range. Domain is a set of all X values. Range is a set of all Y values.

A sample set of XY pairs of a function:

{ (2,4) , (3,6) , (4,8) }.

Let us see some more related terms in Algebric functions.

Example Problems on algebric function:

Problem 1:

Evaluate the algebric function: f(x) = 5x + 2 when x = 3.

Solution:

The given function is f(x) = 5x + 2

Substitute the x value in this given function.

f(3) = 5(3) + 2

= 15 + 2

f(3) = 17.

Therefore, f(x) = 17 when x = 3.

Problem 2:

Evaluate the algebric function: f(x) = x2 + x when x = -4.

Solution:

The given function is f(x) = x2 + x

Substitute the x value in this given function.

f(-4) = (-4)2 + (-4)

= 16 - 4

f(-4) = 12.

Therefore, f(x) = 12 when x = -4.

Problem 3:

Evaluate the algebric function: f(x) = x2 + 5x - 6 when x = 6.

Solution:

The given function is f(x) = x2 + 5x - 6

Substitute the x value in this given function.

f(6) = (6)2 + 5(6) - 6

= 36 + 30 - 6

f(6) = 60.

Therefore, f(x) = 60 when x = 6.

Other forms of algebric function:

The other types of algebraic functions are following.

Composite function:

Composite functions are a function in which we replace the output of one function and put it for the input of another function. The notation for composite functions are (f o g) (x) = f(g(x) , where the output of g(x) is used in the input of f(x).

Example:

Find (f o g) (x) = for the algebric function f(x) = x2 + 5x - 5 and g(x) = 4x + 3

Solution:

(f o g)(x) = f(g(x))

= f( 4x+3)

= (4x+3)2 + 5(4x+3) - 5

= (4x)2 + 24x + 32 + 20x + 15 - 5

= 16x2 + 24x + 9 + 20x + 10

= 16x2 + 44x + 19.

Linear and Quadratic function:

Linear function is a function where the highest power is always 1. The general form of linear function is f(x) = ax + b , where constants are a, b and a is not equal to 0.

Quadratic function is a function where the highest power is always 2. The general form of quadratic function is f(x) ax2 + bx + c ,where a and b, c are constants, and a is not 0.

Additional problems on i o functions algebra:

Example problem 3:

Find the value of f(1) for the function f(x) = -5x2 + x .

Solution:

The given function is f(x) =-5x2 + x.

Now, we have to find the value of f(1).

Substitute the value of x = 1 in the given function

f(1) = -5(1)2 + 1

f(1) = -5 + 1

f(1) = -4

So, the answer is f(1) = -4.

Example problem 4:

Find the ordered pairs of the function: f(x) = -5x + 4

Solution:

f(x)= -5x + 4

Substitute x=0

f (0) = -5(0) + 4

f(0) = 4

Therefore the ordered pair (x, f(0)) is (0, 4).

Substitute x = 1

f(1) = -5(1) + 4

f(1) = -1

Therefore the ordered pair (x, f(1)) is (1, -1).

Substitute x=2

f(2) = -5(2) + 4

f(2) = -6

Therefore the ordered pair (x, f(2)) is (2, -6).

Substitute x=3

f(3) = -5(3) + 4

f(3) = -11

Therefore the ordered pair (x, f(3)) is (3, -11).

The ordered pairs of the function f(x) = -5x + 4 is (0, 4), (1, -1), (2, -6), (3, -11).

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Top ten things to look for when choosing a TEFL course (TEFL Course)

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Principle of duality Contdition (math help)

Principle of duality condition:

In mathematics, duality have numerous meanings, and even though it is "a very profound and important concept in (modern) Mathematics" and "an important general theme that has manifestations in almost all areas of Mathematics", there is no single universally agreed definition that unifies all concepts of duality.

If the dual of a is B, the dual is B. As is involutional sometimes contain fixed points, dual a sometimes a itself.

(Source: Wikipedia)

Here, we will learn about the principle of duality.

Examples of principle of duality condition:

Let's look at some example problems in the principle of duality condition.

(Demorgan's law):

Can then be "a" and "b" Boolean algebra,

(a + b)' = construct "

Proof:

We have to prove the complement of a + b = construct '.

The definition of complement, is enough to show it

(a + b) + design ' = 1

(a + b).(construct "") = 0

(a + b) + design ' = (a + b) + construct "(Axiom 3 X)"

= b + a + construct (associative)

= b + (a + a').(a + b "") (Axiom 4y)

b + 1 = (a + b "") (axiom-5)

= b + (a + b "") (axiom 2y)

b + b =' + a (associative by +)

= 1 + (Axiom-5)

a = + 1 (axiom 3 X)

= 1 (Theorem 2 X)

(a + b) + design ' = 1... (1)

(a + b) 'a = ((a + b)' construct) b' associativity

(a '(a + b)) = b = (a'a + construct) b' (axioms 3 x, 4 X)

= (0 + BA') b' (axiom-5)

= (BA') b'

BB =' a' (axiom 3 X)

0.a =' (axiom 5)

= 0

(a + b) construct ' = 0.. (2)

(1) And (2), the complement of a + b is construct ' is

(a + b)' = construct "

More examples of principle of duality condition:

Boolean algebra, for all x, y 'in' B

(XY)' = X' + y'

Proof:

The definition of the complement of an element is sufficient to prove it

AB + (a ' + b') = 1

And (a ' + b') = 0

AB + (a ' + b')

= (AB + a') + b' (associativity +)

= (a + a') (b + a') + b' (axiom 4y)

= 1 (b + a') + b' (axiom-5)

= b + a' + b' (2y) or 1 a = a

b + b =' + a' (axiom 3 X)

= 1 + a' (axiom-5)

= a' + 1 (axiom 3 X)

= 1 (Theorem 2 X)

AB + (a ' + b') = 1...(1)

= (A ' + b')

b = a (a ' + b') (axiom 3y)

b = (aa ' + from ') (axiom 4 X)

b = (0 + AB') (axiom-5)

= Bab' (axiom 2y)

bb ='a (axiom 3 X)

= 0.a

a = (3 X and 2y theorem)

= 0

AB (a ' + b') = 0...(2)

(1) And (2), we have

(AB)' = a' + b'

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Earn A Keystone Homeschool Diploma

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Homeschool Biology

Teaching biology to your homeschool student can be an enjoyable experience; however, some parents do not benefit from the subject and the upper grades could be a bit more challenging. If you're the latter, there are many good options for teaching your child homeschool biology.

Drawbacks and benefits of any computer-based biology course

Benefits:

No planning involved and simple for the busy/working parent.

The majority are self-grading.

Usually includes the visually-appealing multimedia component.

Self-directed and provide the student a feeling of autonomy.

Drawbacks:

If many textbook selections are in the course, it can certainly be a bit tedious reading from your computer screen.

May not be a good solution for a kinesthetic learner or even a child with a great deal of energy. However, an easy solution to remedy this would always be by combining it that has a nature study program, which would get your active learner from home for some fresh fresh air and observation.

A sample of biology course alternatives: (Biology course are usually only at the high school level and also the elementary grade biology is included in more general technology classes).

Switched On Schoolhouse: This program is upon cd-roms and involves a combination of on- and off-computer jobs including experiments. Grades 3-9 observe each division of science on an personal survey basis, usually model by unit. Grades 10-12 target specific areas of technology: Life Science (Plants in addition to Animals, Human Anatomy in addition to Personal Care, Biology), Place and Earth Science (Geology, Climate, Space), Physical Science (Chemistry, Physics), Mother nature of Science (Scientific Method, Experimentation, Technology).

E-Tutor [http: //www. e-tutor. com: ]: This program offers independent and advised programs (with the advised program, they assign the student a certified tutor). Single courses are offered.

K12: K12 offers a open public school option (free in a few states) and a individual school option. They use a mix of internet courses and conventional textbook courses. It can be a rigorous program but they feature many options to this homeschooler, including individual highschool classes. K12 is a well-done high-quality software, but is not with regard to parents who prefer an increasingly gentle Charlotte Mason type method.

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