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Grade 8 – MAFS.8.EE.3.8 MAFS-FSA Resource
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... Purpose: Teachers should utilize the ExploreLearning published Teacher Guide and Student Exploration Sheet to teach the content of this standard. This document is a supplemental resource designed to help support teachers in preparing students for content and various computer-based question mechanism ...
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... Squaring the above relation we get that (2ζ1 − 5)2(a−b) is a rational number, which is impossible for a > b. Hence, our polynomial f (X) has only simple roots, which, via Siegel’s Theorem, shows that equation (3) has only finitely many integer solutions (n, X) whenever b < a are fixed positive integ ...
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Partial differential equation



In mathematics, a partial differential equation (PDE) is a differential equation that contains unknown multivariable functions and their partial derivatives. (A special case are ordinary differential equations (ODEs), which deal with functions of a single variable and their derivatives.) PDEs are used to formulate problems involving functions of several variables, and are either solved by hand, or used to create a relevant computer model.PDEs can be used to describe a wide variety of phenomena such as sound, heat, electrostatics, electrodynamics, fluid flow, elasticity, or quantum mechanics. These seemingly distinct physical phenomena can be formalised similarly in terms of PDEs. Just as ordinary differential equations often model one-dimensional dynamical systems, partial differential equations often model multidimensional systems. PDEs find their generalisation in stochastic partial differential equations.
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