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A number decreased by 16 equals 5 times the number. Find the number.
A number decreased by 16 equals 5 times the number. Find the number. => 5 or 4 or -4 or -5..
Combinatorial Method
Alternative Proof of Binomial Theorem for Positive Integral Index (Combinatorial Method) - Alternative Proof of Binomial Theorem for Positive Integral Index (Combinatorial Method). We have, (a + b) n = (a + b) (a + b) ....... n times. The terms on the RHS are obtained by taking one letter..
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...Surd
An irrational root of a positive rational number is called a surd. Consider a number with base 'a' as a positive rational number with power of a fraction, say then Since is an n t h root, it is called a surd of order n, if it is irrational. e.g., (i) is a su..
An irrational root of a positive rational number is called a surd. Consider a number with base 'a' as a positive rational number with power of a fraction, say then Since is an n t h root, it is called a surd of order n, if it is irrational. e.g., (i) is a su..Matrices and Determinants
Summary - A matrix is defined as a rectangular array of elements. If the arrangement has m rows and n columns, then the matrix is of order mxn (read as m by n). A matrix is enclosed by a pair of parameters such as ( ) or [ ]. It is denoted by a capital letter. Two matrices are said to be comparable..
Step 1:
In the expansion of (1+x) n , the (r+1)th term is equal to..
In the expansion of (1+x) n , the (r+1)th term is equal to..Greatest Terms for Positive Integral Index
In (a + b) n , let 'a' and 'b' be both positive numbers. As r increases, the factor decreases. So long as this factor is greater than 1, T r+1 remains greater tha..
In (a + b) n , let 'a' and 'b' be both positive numbers. As r increases, the factor decreases. So long as this factor is greater than 1, T r+1 remains greater tha..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 = ..
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 = ..Expansions for Positive Integral Index
Some particular expansions for Positive Integral Index - For n N, we have: a) (a - b) n (a +(- b))..
Some particular expansions for Positive Integral Index - For n N, we have: a) (a - b) n (a +(- b))..Introduction
A binomial is an algebraic expression of two terms which are connected by the operations '+' or '-'. For example, x - y, a + 3b, x 3 + 4y etc. are binomials. We know that, For n = 1,2,3,4, the expansion of (a + b) n , has been expressed in a very systematical manner in terms of combinatorial coeffi..
A binomial is an algebraic expression of two terms which are connected by the operations '+' or '-'. For example, x - y, a + 3b, x 3 + 4y etc. are binomials. We know that, For n = 1,2,3,4, the expansion of (a + b) n , has been expressed in a very systematical manner in terms of combinatorial coeffi..See what our Users say :
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