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To graduate from an Arizona public high school, a student had to meet the AIMS High School Graduation Requirement. The most common way to meet this requirement was to pass the writing, reading, and mathematics content areas of the AIMS HS test. High school students had multiple opportunities to take and pass these content areas.
A prime p (where p ≠ 2, 5 when working in base 10) is called unique if there is no other prime q such that the period length of the decimal expansion of its reciprocal, 1/p, is equal to the period length of the reciprocal of q, 1/q. [8]
The reciprocal of a fraction is another fraction with the numerator and denominator exchanged. The reciprocal of 3 / 7 , for instance, is 7 / 3 . The product of a non-zero fraction and its reciprocal is 1, hence the reciprocal is the multiplicative inverse of a fraction. The reciprocal of a proper fraction is improper, and the ...
In geometry, a pole and polar are respectively a point and a line that have a unique reciprocal relationship with respect to a given conic section. Polar reciprocation in a given circle is the transformation of each point in the plane into its polar line and each line in the plane into its pole.
For example, the reciprocal of 5 is one fifth (1/5 or 0.2), and the reciprocal of 0.25 is 1 divided by 0.25, or 4. The reciprocal function, the function f(x) that maps x to 1/x, is one of the simplest examples of a function which is its own inverse (an involution). Multiplying by a number is the same as dividing by its reciprocal and vice versa ...
In calculus, the reciprocal rule gives the derivative of the reciprocal of a function f in terms of the derivative of f. The reciprocal rule can be used to show that the power rule holds for negative exponents if it has already been established for positive exponents.
If it does span , then is called the dual basis or reciprocal basis for the basis . Denoting the indexed vector sets as B = { v i } i ∈ I {\displaystyle B=\{v_{i}\}_{i\in I}} and B ∗ = { v i } i ∈ I {\displaystyle B^{*}=\{v^{i}\}_{i\in I}} , being biorthogonal means that the elements pair to have an inner product equal to 1 if the indexes ...
Then for , the expansion of () contains at least one term for each reciprocal of a positive integer with exactly prime factors (counting multiplicities) only from the set {+, +,}. It follows that the geometric series ∑ i = 0 ∞ ( x k ) i {\textstyle \sum _{i=0}^{\infty }(x_{k})^{i}} contains at least one term for each reciprocal of a ...