Define Pie Chart

Pie charts are circular graphs that have different  sections, that are used for organizing a set of data. These pie charts are represented by comparing  the data by using fractions or percentages, with each section  proportional to the fraction or percentage that it represents in the data set . These chart are generally  used in corporate reports, especially to show budget or financial data. These charts  are  so named as "Pie charts" because of its similarity  to a pie that is sliced into pieces.


Defnition of Pie chart


A Pie chart consists of a circle divided into several partitons normally it does not exceed more than 6. Area of each part is called slice .Each part  is of the same percentage of the circle as the component it reperesents is of the whole data set. Also called circle diagram  or sector graph.


Advantages of Pie charts:


Pie charts are easy to read and understand if they are designed appropriately . These pie charts are very effective to show the data , if the intent was to compare one section to another. Understanding Definition of Statistics is always challenging for me but thanks to all math help websites to help me out.

The best way to make these charts more readable is to make them fill with different colors and to display sections in clockwise direction ,from larger to smaller section.

Learning About Calculus

Introduction of learning about calculus:

In calculus there are various process is involves for create many tools of differential theoretical aspects. Geometrical and kinematic significance for first and second order derivatives were also interpreted. Now let us learn some practical aspects of differential calculus. It contains differential calculus and integral calculus. The applications of Calculus are Statistics, Science, Business and Engineering. Having problem with Left Hand Riemann Sum keep reading my upcoming posts, i will try to help you.


Concept of learning differential calculus:


At this level we shall consider about problems concerned with the applications to (i) plane geometry, (ii) theory of real functions, (iii) optimization problems and approximation problems.

Derivative as a rate measure:

If a quantity y depends on and varies with a quantity x then the rate of change of y with respect to x is dy / dx.. Example a rate of changes of current ‘i’ is di / dt and a rate of change of temperature ‘?’ is d? / dt and so on.

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Integral calculus and its applications:


The direct evaluation of definite integrals is about the limit for integral total. The integrands are very simple, direct calculation of definite integrals as the limit of integral total involves great complex. Sometimes this method involves cumbersome computations.

The formula called Second Fundamental Theorem on Calculus about that yields a practical and particular method for calculating definite integrals in case where the anti-derivative of the integrand is known. This method which was discovered by Newton and Leibnitz utilizes ‘the profound relationship’ that exists between integration and differentiation.

In this learning Integral calculus, we have the five sections dealing with the concept and applications of definite integrals:

(i)  To solve simple problems using theorem of calculus.

(ii)  Properties of definite integral.

(iii) Reduction formulae learning

(iv) Area under the curve and volume of solid of revolution about an axis.

(v)  Length of the curve and the surface area of a solid of revolution about an axis.

Surface Area Learning

Introduction to lateral surface learning:
Lateral surface area in a solid is the sum of the surface areas of all its faces without the base of the solid. Or Lateral surface area means the area of the sides only -- without the top and bottom. Lateral surface area is found for an object around its outer area. Lateral surface area are usually expressed in terms of some square units.


lateral surface area learning formula:


Formula for Lateral surface area:

Cube = 4b^2, where b is the base of a cube

Sphere is 4pr^2, where r is the radius of the sphere.

Cone = p × r × l, where r and l are the radius and slant height of the cone

Cylinder = 2prh, where r is the radius and h is the height of the cylinder

Right triangular pyramid = 3 × area of lateral faces

Pentagonal prism = 5 × area of each rectangle

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Examples for learning of lateral surface area:

Example 1:

Find the lateral surface area of a pentagonal prism, if a = 5 cm and b = 14 cm.

Solution:

Step 1: In the given figure, the base of the prism is a regular pentagon.

Step 2: All five rectangles are congruent.

Step 3: Lateral surface area of the prism = 5 × area of each rectangle

Step 4: = 5 × 5 × 14 [Substitute the values.]

Step 5: = 350

So, Lateral surface area of the pentagonal prism = 350 cm2.

Example 2:

Height and radius of the cone is 5yard and 7 yard.Find the lateral surface area of the given cone.

Solution: Lateral surface area of the cone = prl

Step 1:Slant height of the cone, l =v(25+49)      [l =vr2+h2.]

l = 8.6 yard

Step 2: Lateral surface area = 3.14 × 7 × 8.6   [As r = 7 andl = 8.6]

=

So, the lateral surface area of the cone = 189.03 sq yd.

Practice problem for lateral surface area learning;

1) Find the lateral surface area for of a sphere radius (r) = 3cm ?

Answer:  113.04

Equality Properties of Learning

Equality properties of learning:

Equal properties are the reasonable laws for actual numbers in arithmetic. These properties are used to control, stable the equations. Moreover, shorten the equations. In general, equality is defined as follows,

p = q denotes p is equal to q.
p ≠ q denotes p does not equal q.
Thus, the learning the properties of equality contain the following properties.

Based on balance equation:

a) Addition property

b) Subtraction property

c) Multiplication property

d) Division property

Based on equivalence:

a) Reflexive property

b) Symmetric property

c) Transitive property

Distributive property


1. Balance equation relation property:


The following properties are used for learning the equations with real numbers.

a) Addition property:

For learning the addition property let assume m, n, o are actual numbers. If m =n, then it can be written as m+o = n+o. similar number can add the equation of both side lacking of modifying the result of the equation.

b) Subtraction property:

For learning the subtraction property let assume x, y, z are real numbers. If x =y, then it can be written as x-z = y-z. Equal number can subtract the equation of all side without adjusting the result of the equation.

c) Multiplication property:

Let consider p, q, r are real numbers. If p =q, then it can be written as p*r = q*r. The equation of both sides can be multiplied by similar quantity without adjusting the result of the equation.

d) Division property:

Let consider p, q, r are real numbers(r =/ 0). If p =q, then it can be written as p/r = q/r. The equation of each side can be divided by same nonzero quantity without modifying the result of the equation.


2. Equivalence relation property:


a) Reflexive property:

Let consider ‘m’ is a real number, and then it reflects by itself. That the real number equals itself as, m = m.

b) Symmetric property:

For learning the symmetric property, let consider m and n are real numbers. If m = n, then it can be written as,

n =m. The order of equality is not considered.

c) Transitive property:

Let consider m, n, and o are real numbers. If m = n and n = o, then it can be written as,

m =o. Thus, the two quantities matching to the same extent are identical to each other

3. Distributive property:

From learning of distributive property, let consider p, q, r are real numbers. Then it states that as follows,

p(q+r) = pq+pr

Angle of Depression

Introduction to Angle of Depression Learning:

Angle of depression is a term used mainly in trigonometry where “depression” means “fall” or “drop”. Angle of depression means the angle between the horizontal and the line of sight to an object beneath the horizontal. The angle of depression is mainly used for learning or obtaining the distance of the two objects where we only know their angle and an object’s distance from the ground. I like to share this Pentagon Geometry with you all through my article.

Learning Angle of Depression:

Learning angle of depression plays one of the key roles for human’s day-to-day life. The angle of depression and angle of elevation is used for seeing objects where they are high above us or low below us. The human’s should able to differentiate what is angle of depression and angle of elevation and where to use them. The some examples of angle of depression are finding an angle from top of the building a man seeing a moving car, and a man seeing a stationary car from a moving train. Please express your views of this topic Picture of an Obtuse Angle by commenting on blog.

Example for Learning Angle of Depression:

Consider an example where the distance of a tree and the airplane is to find out where the distance from the ground and the airplane is given and also we know the angle between the tree and the airplane . But the airplane is flying above the tree here we want to find the distance from the airplane and tree. From using the given data’s we can find the angle of depression where the angle for the foot of the tree and airplane’s base is acting as an angle of depression. From the angle and the distance from the ground to the airplane we can find the distance from the tree to the plane using any one of the trigonometric identities. In the case where we have to find the distance between the foot of the ground and the airplane is obtained by the same trigonometric relations.

Math Makes Sense Grade 6

Introduction to Math makes sense grade 6:

Mathematics plays a vital role in the grade of 6. Elementary level of math are easy to learn and simple to solve.  Grade 6 math, consists of algebra, arithmetic calculations, sets, measurements and graphs. In arithmetic we use numerals and variables to represent equation. The grade 6 of mathematics also solves the linear equations and also the multiplication, subtraction, addition and division of the algebra. This grade 6 math sets as basic block for solving aptitude questions. Having problem with Laplace Transform Chart keep reading my upcoming posts, i will try to help you.


Math makes sense grade 6 in algebra sample problems:


On doing the sample problems they can also solve the advanced problems in the mathematics.

Example 1 to Math makes sense grade 6:

Solve the algebraic equation from 3(-3y - 2) - (y - 3) = -10(2y + 2) + 19

Solution:

Step 1:

Given equation is 3(-3y - 2) - (y - 3) = -10(2y + 2) + 19

Step 2:

Multiply the terms

-9 y -6 - y + 3= -20y – 20 + 19

Make them as a group

-10y -3= -20y - 1

-10y + 20y = 3 -1

10y = 2

y = 2/10

y = 0.2

The Answer Y = 0.2

Example 2 Math makes sense grade 6:


Solve the equation of grade 6:

2x + 5 = 4x (3) + 15

Solution:

Eliminate the braces:

2x + 5 = 12x + 15

Subtract -5 on both the sides:

2x +5 -5 = 12 x + 15 – 5

Simplify the equation:

2x = 12x + 10

Subtract – 10 from both the sides:

2x-10= 12x + 10 – 10

On simplifying the equation:

2x-10 = 12x

Subtract – 12x on both sides to get 0 on the right hand side:

2x – 10 – 12x = 12x – 12x

On simplifying the equation we get:

-10 –10x = 0

On adding 10 on both sides:

-10 -10x +10 = 0 +10

On simplifying the equation we get,

-10x = 10

Dividing by -10 on both the sides:

-10x / -10 = 10 / -10

After dividing we get:

X = -1

Thus we got the value of x by simplifying the equation.

Mental Math Techniques

Some people are born great at maths, most of us have to work hard. But why work harder than we need too, when we can often just use a better technique to improve our maths?

Here are some techniques and rules you can use in your maths to improve your maths skills. I like to share this Mental Math Problems with you all through my article.


Estimation

This is one of the most effective techniques to help you work out roughly what sort of answer you should have. So if you need to multiply 305 x 11, then it looks hard. But 300 x 11 is really easy, so do that first to get an idea of the answer - that's 3300. Having problem with Multiplicative Inverse keep reading my upcoming posts, i will try to help you.

Break It Down

Now we know that, we use the breakdown method: 305 x 11 is the same as 300 x 11 + 5 x 11. So to our 3300 we just add 55, to get 3355 as the answer, and we can see we've worked out 305 x 11 really easily!

Multiplying by 0 is always 0

Some sums that look really hard are actually really, check this one out: 26 x 54 - 15 x 576372 x 0 + 57

Looks hard? It's easy - the answer is '0' for any sum that contains multiplying by '0' and once you know that handy little fact such sums become the easiest ones there are!