determine whether the value of the given expression is always an even integer: is an integer.

Determine whether the value of the given expression is always an even integer: ( 2 b 6 ) 2 - 1 2 b 6 - 1 , where b is an integer . => No or Yes..

Alice expressed three consecutive odd integers in a distinct way. The product of the three integers is given by the polynomial x 3 - 9 x 2 + 23 x - 15 . One of her integers is expressed as x - 3 . Find the other expressions did A..

The empirical formula of a compound is determined from the percentage composition of different elements and atomic masses of the elements. The various steps involved in determining the empirical formula are: The percentage of each element is divided by its atomic mass. This g..

>If A, B and C are the matrices which can be multiplied then (a) Matrix multiplication is not commutative, i.e., AB BA (always) (b) Associative law holds good for matrix multiplication, i.e., (AB)C = A(BC) (c) Matrix multiplication is distributive with respect to addition A(B + C) = AB + AC or (A +..

Use Rolle's Theorem to determine the value of c such that f ′ ( c ) = 0, if f ( x ) = ( x - a ) m ( x - b ) n where m , n are positive integers in the inter..

Limitations of Linear Programming - Linear programming is applicable only to problems where the constraints and objective function are linear i.e., where they can be expressed as equations which represent straight lines. In real life situations, when constraints or objective functions are..

i) An expression of the form a 0 x n + a 1 x n - 1 +....+ a n = 0, where n is a positive integer and a 0 , a 1 ,...,a n belong to some number system F, is called a polynomial in the variable x over F. ii) The degree of polynomial is defined as the highest index of the ..

From the figure it is evident that the curve repeats itself every 360 o or 2 p . This fact is expressed by saying that the function has a period of 360 o or 2 p . In symbols we write sin (x + n.360 o ) or sin (x + 2n p ), sinx = sin (x + n.360 o ) = sin (x + 2n p ), where n is any po..

From the graph it is clear that the curve repeats itself every 360 o (2 p rad). This fact is expressed by the statement that the function has a period of 360 o (2 p radians). In symbols we write cos(x + 360 o .n) = cos(x + 2 p n) = cos x where n is a positive or negative intege..

There are mainly four steps in the mathematical formulation of linear programming problem as a mathematical model. We will discuss formulation of those problems which involve only two variables. Identify the decision variables and assign symbols x and y to them. These decision variables are those q..