Representation of a Relation
(i) Roster form(i) Roster form (ii) Set builder form (iii) By tables (iv) Arrow diagram (v) By graphs (i) Roster form: The ordered pairs are listed, R = {(2, 1), (4, 2), (6, 3), (8, 4), (10, 5)} Where A = {1, 2, 3, 4, 5} and R me..
(i) Roster form(i) Roster form (ii) Set builder form (iii) By tables (iv) Arrow diagram (v) By graphs (i) Roster form: The ordered pairs are listed, R = {(2, 1), (4, 2), (6, 3), (8, 4), (10, 5)} Where A = {1, 2, 3, 4, 5} and R me..Second Method:
x 2 - 2x - 48 = x 2 - 8x + 6x - 48 = x(x - 8) + 6(x - 8) = (x - 8) (x + 6) When the coefficient of the highest power is not unity. i.e., type ax 2 bx c, when and b and c are integers. Multiply (3x + 2) (x..
x 2 - 2x - 48 = x 2 - 8x + 6x - 48 = x(x - 8) + 6(x - 8) = (x - 8) (x + 6) When the coefficient of the highest power is not unity. i.e., type ax 2 bx c, when and b and c are integers. Multiply (3x + 2) (x..(iii) Set-builder notation
f : {(x, y) : y = 4x + 5} where x belongs to real numbers. (iv) A table. The following table represents first to fifth rank holders of a class. (vi) An algebraic formula. We can use an algebraic formula to represent a function..
f : {(x, y) : y = 4x + 5} where x belongs to real numbers. (iv) A table. The following table represents first to fifth rank holders of a class. (vi) An algebraic formula. We can use an algebraic formula to represent a function..Formula
>A number of two digits p and q in that order is 7 greater than the number formed by reversing the digits. The ten's digit is p and the unit's digit is q. Then the number is 10p + q. The number formed by reversing the digits = 10q + p (10p + q) - (10q + p) = 7 A man walks for 'a' hours at..
>A number of two digits p and q in that order is 7 greater than the number formed by reversing the digits. The ten's digit is p and the unit's digit is q. Then the number is 10p + q. The number formed by reversing the digits = 10q + p (10p + q) - (10q + p) = 7 A man walks for 'a' hours at..Surd
x = 5 (iii) (iv) = (x 3 a y 6 ) 1 / 4 (x 2 / 3 y - 1 ) a = x 3 a / 4 y 3 / 2 x 2 a / 3 y - a..
x = 5 (iii) (iv) = (x 3 a y 6 ) 1 / 4 (x 2 / 3 y - 1 ) a = x 3 a / 4 y 3 / 2 x 2 a / 3 y - a..Suggested answer:
2x + y = 5 y = 5 - 2x Put x = 0, y = 5 x = 1, y = 5 - 2 = 3 x = 2, y = 5 - 4 = 1 x = 3, y = 5 - 6 =..
Ordered Pairs, Equivalence relation
Ordered Pairs - An ordered pair has a pair of elements which occur in a definite order.An ordered pair has a pair of elements which occur in a definite order. Take two numbers 3 and 5. If they form a pair (3,5) and the order of the numbers cannot be changed, these numbers are said to form..
Worked Examples on Simultaneous Equations
The fraction is . Six years hence a man's age will be three times his son's age, and three years ago he was nine times as old as his son. Find their present ages. Let the present age of the man be x years, and the present age of his son be y years. 6 years hence their a..
The fraction is . Six years hence a man's age will be three times his son's age, and three years ago he was nine times as old as his son. Find their present ages. Let the present age of the man be x years, and the present age of his son be y years. 6 years hence their a..Limits
Limits - But we are interested in finding the value of y near 2. When x = 1.9, y = 3.9 x = 1.99, y = 3.99 x = 1.999 y = 3.999 . . . . . . Similarly, when x = 2.1 y = 4.1 x = 2.01 y = 4.01 x..
Limits - But we are interested in finding the value of y near 2. When x = 1.9, y = 3.9 x = 1.99, y = 3.99 x = 1.999 y = 3.999 . . . . . . Similarly, when x = 2.1 y = 4.1 x = 2.01 y = 4.01 x..Cartesian Product
B} Similarly B x A = {(x, y) : x B, y A} If A = {3, 5}, B = {2, 4, 6}, write the Cartesian product (i) A x B (ii) B x A A x B = {(3, 2), (3, 4), (3, 6), (5, 2), (5, 4), (5, 6)} B ..
B} Similarly B x A = {(x, y) : x B, y A} If A = {3, 5}, B = {2, 4, 6}, write the Cartesian product (i) A x B (ii) B x A A x B = {(3, 2), (3, 4), (3, 6), (5, 2), (5, 4), (5, 6)} B .. Result
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