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Symbolab is an answer engine [1] that provides step-by-step solutions to mathematical problems in a range of subjects. [2] It was originally developed by Israeli start-up company EqsQuest Ltd., under whom it was released for public use in 2011. In 2020, the company was acquired by American educational technology website Course Hero. [3] [4]
On a single-step or immediate-execution calculator, the user presses a key for each operation, calculating all the intermediate results, before the final value is shown. [1] [2] [3] On an expression or formula calculator, one types in an expression and then presses a key, such as "=" or "Enter", to evaluate the expression.
The sequence of numbers involved is sometimes referred to as the hailstone sequence, hailstone numbers or hailstone numerals (because the values are usually subject to multiple descents and ascents like hailstones in a cloud), [5] or as wondrous numbers. [6] Paul Erdős said about the Collatz conjecture: "Mathematics may not be ready for such ...
To calculate a Pythagorean triple, take any term of this sequence and convert it to an improper fraction (for mixed number , the corresponding improper fraction is ). Then its numerator and denominator are the sides, b and a, of a right triangle, and the hypotenuse is b + 1. For example:
Find recurrence relations for sequences—the form of a generating function may suggest a recurrence formula. Find relationships between sequences—if the generating functions of two sequences have a similar form, then the sequences themselves may be related. Explore the asymptotic behaviour of sequences. Prove identities involving sequences.
The k th step of the algorithm gives the equation r k = r k−2 − q k r k−1. Since the recursion formula has been assumed to be correct for r k−2 and r k−1, they may be expressed in terms of the corresponding s and t variables r k = (s k−2 a + t k−2 b) − q k (s k−1 a + t k−1 b). Rearranging this equation yields the recursion ...
This table is used to store the LCS sequence for each step of the calculation. The second column and second row have been filled in with ε, because when an empty sequence is compared with a non-empty sequence, the longest common subsequence is always an empty sequence. LCS(R 1, C 1) is determined by comparing the first elements in each sequence.
Job times must be independent of the job sequence. All jobs must be processed in the first work center before going through the second work center. All jobs are equally prioritised. Johnson's rule is as follows: List the jobs and their times at each work center. Select the job with the shortest activity time.