Graphing solutions of inequalities

Today we will be studying Graphing Solutions Of Inequalities, Graph Solution Of Inequalities, Measurements-
To understand Graphing solutions of inequalities, Graph solution of inequalities, Measurements we must first understand the meaning of inequalities, inequalities can be defined as that one expression can be greater than or less than some other expression, the mathematical symbols used in inequalities are less than(<), greater than (>), less than equals to (≤) and greater than equals to (≥). The inequalities can transformed in many other ways. The direction of inequalities does not change if any number is added to both sides or if number is subtracted from both sides or both sides are multiplied and divided on both sides.
An inequality is of the form y > mx + b or y < mx + b, here x and y are the coordinates and 'm' is the slope and 'b' is the intercept.
Examples of inequalities-
y ≤ 2x + 3 or 2x – 3y < 6
As we have understood the meaning of inequalities, so now we will try to plot some of the inequalities on a graph. The examples are show below-

1)Let us take an example y ≤ 2x + 3 and plot it on the graph.
First we will plot the equal part of inequality that is y = 2x + 3, it is a straight line so after plotting
the graph will look like

                                                     This graph is for the equality part that is y = 2x + 3 but we also have to plot less than part of the inequality. To plot the less than part that is y < 2x + 3 we just shade the region.
So either we shade the region below the line on region above the, in this inequality we will shade the region below the line as 'y' is less than 2x + 3 .So after shading the region below the line graph will look like:                                                     

                                                            
                                   





So this is how we see Graph solution of inequalities.
In the next session we are going to discuss Measurements.

Relation between objects in space

SPACE:

• space is a three dimentional structure
• space is boundless and limitless.
• space contains object exist in space
• many events exist in space

objects:

• object is a physical body which is a collection of masses.

mass and weight of an object:

Mass is a measure of how much material is in an object, but weight is a measure of the gravitational force exerted on that material in a gravitational field; thus, mass and weight are proportional to each other, with the acceleration due to gravity as the proportionality constant. (know more about icse board papers 2013, here)
w=m*g
w is the weight
m is the mass.
g is the acceleration due to gravity.
g=9.8 m/sec>2

 Relation between objects in space
Relation between objects in space follows the newtons  gravitational law of gravitational
Newton's Universal Law of Gravitation states that any two objects exert a gravitational force of attraction on each other. The direction of the force is along the line joining the objects
Newton's law of gravitation resembles Coulomb's law of electrical forces, which is used to calculate the magnitude of electrical force between two charged bodies and this signifies the Object And Space Relationship.

.The magnitude of the force is proportional to the product of the gravitational masses of the objects, and inversely proportional to the square of the distance between them .
F(1,2)=(G*m1*m2)/r>2
m1 & m2 are the objects in space
m1 exerts  force F12 on m2
m2  exerts force F21 on m1
G is  the gravitational contant which is 6.67 x 10>- 11 N m>2/kg>2

• The inertial mass of an object determines the amount of force needed to produce a given acceleration of that object.
•  The gravitational mass determines the force of gravitational attraction between two bodies.

Gravitation is a natural phenomenon in which physical bodies attract with force propotional to the mass.
it is resposible for keeping all the object  in the universe in there orbit , otherwise all objects would have collide

In the next session we will discuss about Graphing solutions of inequalities.