Thursday, June 10
Wednesday, June 9
Algebra
Algebra is one of the main branches of mathematics. It explains the relations and properties of quantity by means of letters and other symbols. Algebra is used to simplify the long and very complicated statements. The basic algebra has the following subtopics are
- Variables
- Expressions
- Terms
- Polynomials
- Equations.
Tuesday, June 8
Theorem in Mathematics
Theorem in Mathematics:
Congruent Supplements Theorem: When two angles are supplementary to the congruent angles or to the same angle, then the given angles are congruent.
Vertical Angle Theorem: Two angles are said as congruent even when they are vertical angles.
Alternate Interior Angle Theorem:Pairs of alternative interior angles are said as congruent when two parallel lines are cut transversely.
Consecutive Interior Angle Theorem:Pairs of consecutive interior angle are said as supplementary when two parallel lines are cut transversely.
Alternative Exterior Angle Theorem: Pairs of alternative exterior angle are said as congruent when two parallel lines are cut transversely.
Congruent Supplements Theorem: When two angles are supplementary to the congruent angles or to the same angle, then the given angles are congruent.
Vertical Angle Theorem: Two angles are said as congruent even when they are vertical angles.
Alternate Interior Angle Theorem:Pairs of alternative interior angles are said as congruent when two parallel lines are cut transversely.
Consecutive Interior Angle Theorem:Pairs of consecutive interior angle are said as supplementary when two parallel lines are cut transversely.
Alternative Exterior Angle Theorem: Pairs of alternative exterior angle are said as congruent when two parallel lines are cut transversely.
Parabola equation
X intercept and Y intercept for Parabola equation:
The general form of parabola equation is
y = ax2 + bx + c where a,b and c are parts of the parabola.
Here, x intercepts are the roots of the equation of parabola. The x intercepts are the roots of the equation 0 = ax2 + bx + c. The very common methods to solve the equation are by factoring or by quadratic formula. The y intercept is (0 , c) for parabola equation.
The general form of parabola equation is
y = ax2 + bx + c where a,b and c are parts of the parabola.
Here, x intercepts are the roots of the equation of parabola. The x intercepts are the roots of the equation 0 = ax2 + bx + c. The very common methods to solve the equation are by factoring or by quadratic formula. The y intercept is (0 , c) for parabola equation.
Thursday, June 3
Solve the equations Graphically
Solve the equations Graphically:
Check whether the pair of equations x + 3y = 6 and 2x – 3y = 12 is consistent. If so, solve them graphically.
Solution : Let us draw the graphs of the Equations (1) and (2). For this, we find two
solutions of each of the equations, which are given in Table
Plot the points A(0, 2), B(6, 0), P(0, – 4) and Q(3, – 2) on graph paper, and join the points to form the lines AB and PQ as shown in Fig below We observe that there is a point B (6, 0) common to both the lines AB and PQ. So, the solution of the pair of linear equations is x = 6 and y = 0, i.e., the given pair of equations is consistent.
Check whether the pair of equations x + 3y = 6 and 2x – 3y = 12 is consistent. If so, solve them graphically.
Solution : Let us draw the graphs of the Equations (1) and (2). For this, we find two
solutions of each of the equations, which are given in Table
Plot the points A(0, 2), B(6, 0), P(0, – 4) and Q(3, – 2) on graph paper, and join the points to form the lines AB and PQ as shown in Fig below We observe that there is a point B (6, 0) common to both the lines AB and PQ. So, the solution of the pair of linear equations is x = 6 and y = 0, i.e., the given pair of equations is consistent.
Wednesday, June 2
General Equation of a Line
General Equation of a Line:
Equation of a Straight line is also called a Linear Equation.
Graph of the equation Ax + By + C = 0 is always a straight line
Therefore, any equation of the form Ax + By + C = 0, where A and B are not zero
simultaneously is called general linear equation or general equation of a line.
Equation of a Straight line is also called a Linear Equation.
- A straight line is represented by an equation of the first degree in two variables (x and y). Conversely locus of an equation of the first degree in two variables is a straight line.
- A straight line is completely determined by its slope (direction) and a point is given through which the line must pass.
Graph of the equation Ax + By + C = 0 is always a straight line
Therefore, any equation of the form Ax + By + C = 0, where A and B are not zero
simultaneously is called general linear equation or general equation of a line.
Tuesday, June 1
Find the area of a square
Problem:
Find the area of the shaded design in below fig where ABCD is a square of side 10 cm a semicircles are drawn with each side of the square as diameter. (Use π = 3.14).
Solution : Let us mark the four unshaded regions as I, II, III and IV .Area of I + Area of III = Area of ABCD – Areas of two semicircles of each of radius 5 cm
(10×10-2×1/2×π×52)cm2= (100 – 3.14 × 25) cm2
= (100 – 78.5) cm2 = 21.5 cm2
Similarly, Area of II + Area of IV = 21.5 cm2
So, area of the shaded design = Area of ABCD – Area of (I + II + III + IV)
= (100 – 2 × 21.5) cm2 = (100 – 43) cm2 = 57 cm2
Find the area of the shaded design in below fig where ABCD is a square of side 10 cm a semicircles are drawn with each side of the square as diameter. (Use π = 3.14).
Solution : Let us mark the four unshaded regions as I, II, III and IV .Area of I + Area of III = Area of ABCD – Areas of two semicircles of each of radius 5 cm
(10×10-2×1/2×π×52)cm2= (100 – 3.14 × 25) cm2
= (100 – 78.5) cm2 = 21.5 cm2
Similarly, Area of II + Area of IV = 21.5 cm2
So, area of the shaded design = Area of ABCD – Area of (I + II + III + IV)
= (100 – 2 × 21.5) cm2 = (100 – 43) cm2 = 57 cm2
Subscribe to:
Posts (Atom)