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Abū Kāmil Shujā ibn Aslam (Egypt, 10th century) in particular was the first to accept irrational numbers (often in the form of a square root, cube root or fourth root) as solutions to quadratic equations or as coefficients in an equation. [30] The 9th century Indian mathematician Sridhara wrote down rules for solving quadratic equations. [31]
A similar but more complicated method works for cubic equations, which have three resolvents and a quadratic equation (the "resolving polynomial") relating and , which one can solve by the quadratic equation, and similarly for a quartic equation (degree 4), whose resolving polynomial is a cubic, which can in turn be solved. [14]
Consumer–resource interactions are the core motif of ecological food chains or food webs, [1] and are an umbrella term for a variety of more specialized types of biological species interactions including prey-predator (see predation), host-parasite (see parasitism), plant-herbivore and victim-exploiter systems.
Just as on the demand side, the position of the supply can shift, say from a change in the price of a productive input or a technical improvement. The "Law of Supply" states that, in general, a rise in price leads to an expansion in supply and a fall in price leads to a contraction in supply.
The theory of consumer choice is the branch of microeconomics that relates preferences to consumption expenditures and to consumer demand curves.It analyzes how consumers maximize the desirability of their consumption (as measured by their preferences subject to limitations on their expenditures), by maximizing utility subject to a consumer budget constraint. [1]
The quadratic equation on a number can be solved using the well-known quadratic formula, which can be derived by completing the square. That formula always gives the roots of the quadratic equation, but the solutions are expressed in a form that often involves a quadratic irrational number, which is an algebraic fraction that can be evaluated ...
Charles Hugh Smith, writing for Business Insider, argues that while the use of credit has positive features in low amounts, but that the consumer economy and its expansion of credit produces consumer ennui because there is a marginal return to consumption, and that hyperinflation experts recommended investment in tangible goods. Smith raises ...
Supply-side economics is a macroeconomic theory postulating that economic growth can be most effectively fostered by lowering taxes, decreasing regulation, and allowing free trade. [1] [2] According to supply-side economics theory, consumers will benefit from greater supply of goods and services at lower prices, and employment will increase. [3]