Exponentials and logarithms
... students will be familiar with the term exponential growth. The graph of y ka x can be plotted for some simple values of a and it can be observed that the value of a represents a growth factor. It can also be observed that the rate at which it is increasing at any point is proportional to its size ...
... students will be familiar with the term exponential growth. The graph of y ka x can be plotted for some simple values of a and it can be observed that the value of a represents a growth factor. It can also be observed that the rate at which it is increasing at any point is proportional to its size ...
![On the number of polynomials with coefficients in [n] Dorin Andrica](http://s1.studyres.com/store/data/023344871_1-db0421bb4ddb78289c0a283cc0aa29ca-300x300.png)
On the number of polynomials with coefficients in [n] Dorin Andrica
... In this paper we introduce several sequences related to polynomials of degree s having coefficients in the set {1,2,...,n}, where n is a positive integer, which factor completely over the integers. These sequences can be seen as generalizations of A006218. We provide precise methods for calculating ...
... In this paper we introduce several sequences related to polynomials of degree s having coefficients in the set {1,2,...,n}, where n is a positive integer, which factor completely over the integers. These sequences can be seen as generalizations of A006218. We provide precise methods for calculating ...
Name:
... upward, ignite them, and project them into the air. Suppose a particular star is projected from an aerial firework at a starting height of 520 feet with an initial upward velocity of 72 ft./s. How long will it take the star to reach its maximum height? How far above the group will it be? The equatio ...
... upward, ignite them, and project them into the air. Suppose a particular star is projected from an aerial firework at a starting height of 520 feet with an initial upward velocity of 72 ft./s. How long will it take the star to reach its maximum height? How far above the group will it be? The equatio ...
Math 312 Lecture Notes Linear Two
... possible behaviors of solutions in the various cases. An important property of an equilibrium point is its stability. The following describes three basic cases. • If all solutions that start close to an equilibrium converge to the equilibrium asymptotically as t → ∞, we say the equilibrium is asympt ...
... possible behaviors of solutions in the various cases. An important property of an equilibrium point is its stability. The following describes three basic cases. • If all solutions that start close to an equilibrium converge to the equilibrium asymptotically as t → ∞, we say the equilibrium is asympt ...
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.