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In mathematics, a quadratic equation (from Latin quadratus 'square') is an equation that can be rearranged in standard form as [1] + + =, where the variable x represents an unknown number, and a, b, and c represent known numbers, where a ≠ 0. (If a = 0 and b ≠ 0 then the equation is linear, not quadratic.)
In solving mathematical equations, particularly linear simultaneous equations, differential equations and integral equations, the terminology homogeneous is often used for equations with some linear operator L on the LHS and 0 on the RHS. In contrast, an equation with a non-zero RHS is called inhomogeneous or non-homogeneous, as exemplified by ...
However the exam papers of the GCSE sometimes had a choice of questions, designed for the more able and the less able candidates. When introduced the GCSEs were graded from A to G, with a C being set as roughly equivalent to an O-Level Grade C or a CSE Grade 1 and thus achievable by roughly the top 25% of each cohort.
In set theory and its applications to logic, mathematics, and computer science, set-builder notation is a mathematical notation for describing a set by stating the properties that its members must satisfy. [1] Defining sets by properties is also known as set comprehension, set abstraction or as defining a set's intension.
The geometric series is an infinite series derived from a special type of sequence called a geometric progression.This means that it is the sum of infinitely many terms of geometric progression: starting from the initial term , and the next one being the initial term multiplied by a constant number known as the common ratio .
In 1996, Marshall Bern and Barry Hayes showed that the problem of assigning a crease pattern of mountain and valley folds in order to produce a flat origami structure starting from a flat sheet of paper is NP-complete. [18] In 1999, a theorem due to Haga provided constructions used to divide the side of a square into rational fractions. [19] [20]
The equation for describing the period: = shows the period of oscillation is independent of the amplitude, though in practice the amplitude should be small. The above equation is also valid in the case when an additional constant force is being applied on the mass, i.e. the additional constant force cannot change the period of oscillation.
The instructor then asks multiple choice or true or false questions and the students answer on their devices. [250] Depending on the software used, the answers may then be shown on a graph so students and the teacher can see the percentage of students who gave each answer and the teacher can focus on what went wrong. [251]
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