Holt McDougal Algebra 1 Solving Inequalities by Multiplying or
... contains multiplication or division, undo the operation by dividing or multiplying both sides of the inequality by the same number. The following rules show the properties of inequality for multiplying or dividing by a positive number. The rules for multiplying or dividing by a negative number appea ...
... contains multiplication or division, undo the operation by dividing or multiplying both sides of the inequality by the same number. The following rules show the properties of inequality for multiplying or dividing by a positive number. The rules for multiplying or dividing by a negative number appea ...
Most imp questions of Maths for class 12 2015
... 5. Show that the right circular cylinder of given surface and maximum volume is such that its height is equal to diameter of base. 6. Prove that the volume of largest cone that can be inscribed in a sphere of radius R is 8/27 times volume of sphere. 7. Show that the semi – vertical angle of cone of ...
... 5. Show that the right circular cylinder of given surface and maximum volume is such that its height is equal to diameter of base. 6. Prove that the volume of largest cone that can be inscribed in a sphere of radius R is 8/27 times volume of sphere. 7. Show that the semi – vertical angle of cone of ...
CONIC SECTION PART 8 of 8
... Statement-1 : Though (λ, λ + 1) there can’t be more than one normal to the parabola y2 = 4x, if λ < 2. Statement-2 : The point (λ, λ + 1) lies outside the parabola for all λ ≠ 1. Statement-1 : If x + y = k is a normal to the parabola y2 = 12x, then k is 9. Statement-2 : Equation of normal to the par ...
... Statement-1 : Though (λ, λ + 1) there can’t be more than one normal to the parabola y2 = 4x, if λ < 2. Statement-2 : The point (λ, λ + 1) lies outside the parabola for all λ ≠ 1. Statement-1 : If x + y = k is a normal to the parabola y2 = 12x, then k is 9. Statement-2 : Equation of normal to the par ...
The Group Structure of Elliptic Curves Defined over Finite Fields
... the other hand, since there are only finitely many monomials for each s (see [2, Theorem 9.2.4]), restricting an ideal to polynomials of degree ≤ s gives us a finite dimensional vector space over k. Consider the injective linear map αs : k [x]≤s /I(V )≤s − → k [x] /I(V ) = k[V ] defined by αs ([f ]) ...
... the other hand, since there are only finitely many monomials for each s (see [2, Theorem 9.2.4]), restricting an ideal to polynomials of degree ≤ s gives us a finite dimensional vector space over k. Consider the injective linear map αs : k [x]≤s /I(V )≤s − → k [x] /I(V ) = k[V ] defined by αs ([f ]) ...
An Approach to Hensel`s Lemma
... of this article, and although we have not seen anything in print, this article contains nothing new. In Section 3 we compare the computational complexities of both methods. Section 4 will provide full details of one of the proofs. The Hensel lift of a factorisation is defined above. We will now defi ...
... of this article, and although we have not seen anything in print, this article contains nothing new. In Section 3 we compare the computational complexities of both methods. Section 4 will provide full details of one of the proofs. The Hensel lift of a factorisation is defined above. We will now defi ...
Equation
In mathematics, an equation is an equality containing one or more variables. Solving the equation consists of determining which values of the variables make the equality true. In this situation, variables are also known as unknowns and the values which satisfy the equality are known as solutions. An equation differs from an identity in that an equation is not necessarily true for all possible values of the variable.There are many types of equations, and they are found in all areas of mathematics; the techniques used to examine them differ according to their type.Algebra studies two main families of equations: polynomial equations and, among them, linear equations. Polynomial equations have the form P(X) = 0, where P is a polynomial. Linear equations have the form a(x) + b = 0, where a is a linear function and b is a vector. To solve them, one uses algorithmic or geometric techniques, coming from linear algebra or mathematical analysis. Changing the domain of a function can change the problem considerably. Algebra also studies Diophantine equations where the coefficients and solutions are integers. The techniques used are different and come from number theory. These equations are difficult in general; one often searches just to find the existence or absence of a solution, and, if they exist, to count the number of solutions.Geometry uses equations to describe geometric figures. The objective is now different, as equations are used to describe geometric properties. In this context, there are two large families of equations, Cartesian equations and parametric equations.Differential equations are equations involving one or more functions and their derivatives. They are solved by finding an expression for the function that does not involve derivatives. Differential equations are used to model real-life processes in areas such as physics, chemistry, biology, and economics.The ""="" symbol was invented by Robert Recorde (1510–1558), who considered that nothing could be more equal than parallel straight lines with the same length.