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A number when increased by 6 equals 3 times the same number. Find the ..
A number when increased by 6 equals 3 times the same number. Find the number. => 4 or 2 or 5 or 3..
Sequences and Series Summary
1 , A 2 ,.....,A n are called the n arithmetic means between a and b. (vii) The sum of n A.M.s between given numbers a and b is equal to n times the A.M. between a and b. (viii) If a, b, c are in A.P., then for any k: (a) a+k, b+k, c+k are in A.P...
1 , A 2 ,.....,A n are called the n arithmetic means between a and b. (vii) The sum of n A.M.s between given numbers a and b is equal to n times the A.M. between a and b. (viii) If a, b, c are in A.P., then for any k: (a) a+k, b+k, c+k are in A.P...Operations on Matrices
Equality of Matrices - Two matrices are said to be equal if they have the same order and their corresponding elements are equal. e.g., then a = 1, b = 2, c = 3, d = 4, e = 5 and f = 6..
Equality of Matrices - Two matrices are said to be equal if they have the same order and their corresponding elements are equal. e.g., then a = 1, b = 2, c = 3, d = 4, e = 5 and f = 6..Concept of Indices with Solved Examples
Indices - We know that 64 = 2 x 2 x 2 x 2 x 2 x 2 = 2 6 We know that 64 = 2 x 2 x 2 x 2 x 2 x 2 = 2 6 Here 2 is called the base and 6 is called the power (or index or exponent). We say that "64 is equal to base 2 raised to the power 6". Similarly, i..
Indices - We know that 64 = 2 x 2 x 2 x 2 x 2 x 2 = 2 6 We know that 64 = 2 x 2 x 2 x 2 x 2 x 2 = 2 6 Here 2 is called the base and 6 is called the power (or index or exponent). We say that "64 is equal to base 2 raised to the power 6". Similarly, i..Suggested answer:
Step 1: Factor pairs of the last term are (9,-2); (-6,3); (-18,1);(-9,2);(6,-3); (18,-1). Step 2: The pair of factors whose sum is equal to the co-efficient of the middle term is (-6,3). Step 3: Rewrite the expression using these factors as Step ..
Step 1: Factor pairs of the last term are (9,-2); (-6,3); (-18,1);(-9,2);(6,-3); (18,-1). Step 2: The pair of factors whose sum is equal to the co-efficient of the middle term is (-6,3). Step 3: Rewrite the expression using these factors as Step ..Approximation
We know that the digits of a number, one by one in order from left to right decrease in value rapidly. Let us illustrate it by examples. Mass of a gold ornament is 23.473 g. Round off to (i) two decimal places, (ii) one decimal place. 23.473 g = (2 x 10) + (3 x 1) + The successi..
We know that the digits of a number, one by one in order from left to right decrease in value rapidly. Let us illustrate it by examples. Mass of a gold ornament is 23.473 g. Round off to (i) two decimal places, (ii) one decimal place. 23.473 g = (2 x 10) + (3 x 1) + The successi..Multiplication of Matrices
Let A be a matrix of order mxn. Let B be a matrix of order nxp. Then the product of the matrices A and B is of order mxp. i.e., when we multiply two matrices the number of columns of the first matrix should be equal to the number of rows of the second matrix. Two matr..
Let A be a matrix of order mxn. Let B be a matrix of order nxp. Then the product of the matrices A and B is of order mxp. i.e., when we multiply two matrices the number of columns of the first matrix should be equal to the number of rows of the second matrix. Two matr..Ratio
Ratio - Ratio is the numerical relation of one quantity to another of the same kind. To find the ratio of 2 m 25 cm to 75 cm, we first change 2 m 25 cm into cm, which equals 225 cm. Now, we have to find 225 cm to 75 cm ratio is = 3 : 1 We can write the above ..
Ratio - Ratio is the numerical relation of one quantity to another of the same kind. To find the ratio of 2 m 25 cm to 75 cm, we first change 2 m 25 cm into cm, which equals 225 cm. Now, we have to find 225 cm to 75 cm ratio is = 3 : 1 We can write the above ..Summary
The following are the steps to solve a system of linear equations using Cramer's rule. Step 1: Find the value of the determinant Step 2: If D 0, then the system has unique solution, given by Where D 1 , D 2 and D 3 are the determinants obtained from D by replacing respectively t..
The following are the steps to solve a system of linear equations using Cramer's rule. Step 1: Find the value of the determinant Step 2: If D 0, then the system has unique solution, given by Where D 1 , D 2 and D 3 are the determinants obtained from D by replacing respectively t..Some important results
or This property is known as COMPONENDO & DIVIDENDO. (6) If , then each of these ratios equals where l,m,n are real numbers. L..
or This property is known as COMPONENDO & DIVIDENDO. (6) If , then each of these ratios equals where l,m,n are real numbers. L.. Result
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