What Is a Coefficient?
Date: 01/29/2004 at 09:17:25 From: victoria Subject: Numerical coefficient My book says 4xy contains a numerical coefficient which is 4. What's a coefficient?
Date: 01/29/2004 at 11:55:01 From: Doctor Ian Subject: Re: (no subject) Hi Victoria, When we have a term with a bunch of variables multiplied together, such as 2 3 xy z we sometimes multiply it by a constant factor, like 2 3 7xy z In this case, we say the the constant (7, in this case) is the "numerical coefficient" of the term. Sometimes we have parameters--symbols that look like variables, but don't really change their values. For example, suppose we know that the density of something has some value, but we don't know what it is. We might call it "D". The weight of a cube with edge length x, made of this substance, would be Dx^3 Here, the D looks like a variable, but it's really a coefficient, since whatever it is, it is, and we're not going to change it the way we would substitute different values of x. (Does that make sense? It's a little complicated, so write back if you're not quite getting it.) In this case, we would say that D is the "coefficient" of the term, but it's not a "numerical" coefficient, since we're not using numerals to represent it. Usually we talk about coefficients in conjunction with polynomials, e.g., __x^4 + __x^3 + __x^2 + __x^1 + __x^0 (Note that x^0 = 1) This is a general description of a certain kind of curve, which always looks sort of the same--but by putting different values in the slots, we can change the exact shape, to make parts of it taller or shorter, or sqeezed in or stretched out. The exponents on the variables tell us, in a general sense, what _type_ of curve we have; but the coefficients (the actual numbers we choose to put in the slots) tell us how each one of those curves differs from the others. Does this make sense? - Doctor Ian, The Math Forum http://mathforum.org/dr.math/
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