![WHEN IS F[x,y] - American Mathematical Society](http://s1.studyres.com/store/data/017823178_1-6801a801f234da9ec7275765b0565209-300x300.png)
WHEN IS F[x,y] - American Mathematical Society
... Proposition 3. Let f be a linear polynomial in R = F[x, y] that is not associated to a central polynomial. Then ff is a C-atom. Proof. Let f = ax + by + c. If either a or b is 0 then / G F[y] or F[x], respectively, so ff is a C-atom by Proposition 2. Suppose now that both a and b are nonzero and // ...
... Proposition 3. Let f be a linear polynomial in R = F[x, y] that is not associated to a central polynomial. Then ff is a C-atom. Proof. Let f = ax + by + c. If either a or b is 0 then / G F[y] or F[x], respectively, so ff is a C-atom by Proposition 2. Suppose now that both a and b are nonzero and // ...
B. The Product, Quotient, and Power Properties of Logarithms
... storage buildings believes the larger area can support sales of 40 units per month. After increasing the advertising budget and enlarging the sales force, sales are expected to grow according to the model where S( t) is the expected number of sales after t months. ( a) How many sales were being m ...
... storage buildings believes the larger area can support sales of 40 units per month. After increasing the advertising budget and enlarging the sales force, sales are expected to grow according to the model where S( t) is the expected number of sales after t months. ( a) How many sales were being m ...
1. Find the smallest positive integer that is not a divisor of 31! 2. Find
... A number whose digit-sum is 1 must consist of a 1 followed by any number of 0’s (including none), but no number ending in 0 whose digit-sum is 1 can be a multiple of 17. If a number whose digit-sum is 2 were to be a multiple of 17, it would have to consist of two 1’s with some number of 0’s between ...
... A number whose digit-sum is 1 must consist of a 1 followed by any number of 0’s (including none), but no number ending in 0 whose digit-sum is 1 can be a multiple of 17. If a number whose digit-sum is 2 were to be a multiple of 17, it would have to consist of two 1’s with some number of 0’s between ...
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.