Rectangle,Square,Parallelogram,Trapezium,Rhombus,Triangles,Circle and semicircle



What is the value of x in log2^8 – log2^4 = log2^x ?


Sollog2^8 - log2^4 = log2^x
=>8log2 - 4log2 = xlog2
=>4log2 = xlog2
=>x = 4

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NUMBER  SYSTEM

NATURAL NUMBERS
The counting numbers are 1,2,3,4,5,6,.... are called natural numbers. The set of natural numbers is denoted by N.
Thus, N={1,2,3,4,5,6,....}
WHOLE NUMBERS
The set of natural numbers along with 0 represents whole numbers. The set of whole numbers is denoted by W.
Thus, W={0,1,2,3,4,5,.......}


INTEGERS
The set of whole numbers along with the negatives of natural numbers represents integers. The set of integers is denoted by I or Z.
Thus, I or Z={......,-3,-2,-1,0,1,2,3,......}
RATIONAL NUMBERS
The numbers in the form p/q, where p and q are both integers, q not equal to 0 and p and q have no common factors except 1 i.e. p and q are co-prime, are called rational numbers. The set of rational numbers is denoted by Q.
Thus, Q={p/q; p ,q belongs to Z , q not equal to 0}
IRRATIONAL NUMBERS
The numbers which cannot be expressed in the form p/q , where p and q are both integers and q not equal to 0, are called irrational numbers.
REAL NUMBERS
All rational and irrational numbers together called real numbers. The set of real numbers is denoted by R.





POLYGONS

The word polygon means having many sides. Therefore a closed plane figure made up of several line segments that are joined together is called a polygon.

For example, a triangle, a quadrilateral are polygons.

NB. A circle is not a polygon as it is not made of line segments.

Diagonals: The number of diagonals in a polygon of sides n is n(n-3)/2



Types of polygons
   
Regular polygons:  A polygons having all angles and all sides are equal is called a regular polygon.

Irregular polygons:  A polygon may have unequal angles and sides. Such polygons are called irregular polygon.

Name of polygons according to their sides

Name                               Number of sides

Triangle                                        3

Quadrilateral                               4

Pentagon                                       5

Hexagon                                        6

Heptagon                                       7

Octagon                                          8

Nonagon                                         9

Decagon                                        10

Types of angle of a polygon

Interior Angle:  angle formed by two adjacent sides inside the polygon.

Sum of Interior Angles in a Regular Polygon of Sides n is: 

(n-2) × 180 degree

Exterior Angle:  angle formed by two adjacent sides outside the polygon.

Sum of Exterior Angles in a Regular Polygon of Sides n is: 

360 degree

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