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In mathematics and statistics, sums of powers occur in a number of contexts: . Sums of squares arise in many contexts. For example, in geometry, the Pythagorean theorem involves the sum of two squares; in number theory, there are Legendre's three-square theorem and Jacobi's four-square theorem; and in statistics, the analysis of variance involves summing the squares of quantities.
In moral philosophy, instrumental and intrinsic value are the distinction between what is a means to an end and what is as an end in itself. [1] Things are deemed to have instrumental value (or extrinsic value [2]) if they help one achieve a particular end; intrinsic values, by contrast, are understood to be desirable in and of themselves.
The Bell Curve: Intelligence and Class Structure in American Life is a 1994 book by the psychologist Richard J. Herrnstein and the political scientist Charles Murray in which the authors argue that human intelligence is substantially influenced by both inherited and environmental factors and that it is a better predictor of many personal outcomes, including financial income, job performance ...
But, in the production of interest to the theory of history, people produce not freely but because they have to, since nature does not otherwise supply their wants; and the development in history of the productive power of man (that is, of man as such, of man as a species) occurs at the expense of the creative capacity of the men who are agents ...
The limits of such inherent powers were articulated in Youngstown Sheet & Tube Co. v. Sawyer. This case was a Supreme Court decision limiting the power of the president to seize private property in the absence of either specifically enumerated authority under Article Two of the United States Constitution or statutory authority conferred on him ...
In calculus, the power rule is used to differentiate functions of the form () =, whenever is a real number. Since differentiation is a linear operation on the space of differentiable functions, polynomials can also be differentiated using this rule.
In mathematics, exponentiation, denoted b n, is an operation involving two numbers: the base, b, and the exponent or power, n. [1] When n is a positive integer, exponentiation corresponds to repeated multiplication of the base: that is, b n is the product of multiplying n bases: [1] = ⏟.
In a notable study of power conducted by social psychologists John R. P. French and Bertram Raven in 1959, power is divided into five separate and distinct forms. [1] [2] They identified those five bases of power as coercive, reward, legitimate, referent, and expert.