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Quadratic formula. The roots of the quadratic function y = 1 2 x2 − 3x + 5 2 are the places where the graph intersects the x -axis, the values x = 1 and x = 5. They can be found via the quadratic formula. In elementary algebra, the quadratic formula is a closed-form expression describing the solutions of a quadratic equation.
For instance, the first counterexample must be odd because f(2n) = n, smaller than 2n; and it must be 3 mod 4 because f 2 (4n + 1) = 3n + 1, smaller than 4n + 1. For each starting value a which is not a counterexample to the Collatz conjecture, there is a k for which such an inequality holds, so checking the Collatz conjecture for one starting ...
The Haaland equation was proposed in 1983 by Professor S.E. Haaland of the Norwegian Institute of Technology. [9] It is used to solve directly for the Darcy–Weisbach friction factor f for a full-flowing circular pipe. It is an approximation of the implicit Colebrook–White equation, but the discrepancy from experimental data is well within ...
Equation solving. The quadratic formula, the symbolic solution of the quadratic equation ax2 + bx + c = 0. An example of using Newton–Raphson method to solve numerically the equation f(x) = 0. In mathematics, to solve an equation is to find its solutions, which are the values (numbers, functions, sets, etc.) that fulfill the condition stated ...
Solving these two quintics yields r = 1.501 x 10 9 m for L 2 and r = 1.491 x 10 9 m for L 1. The Sun–Earth Lagrangian points L 2 and L 1 are usually given as 1.5 million km from Earth. If the mass of the smaller object ( M E ) is much smaller than the mass of the larger object ( M S ), then the quintic equation can be greatly reduced and L 1 ...
Functional equation. In mathematics, a functional equation [1][2][irrelevant citation] is, in the broadest meaning, an equation in which one or several functions appear as unknowns. So, differential equations and integral equations are functional equations. However, a more restricted meaning is often used, where a functional equation is an ...
Generalizations of Fibonacci numbers. In mathematics, the Fibonacci numbers form a sequence defined recursively by: That is, after two starting values, each number is the sum of the two preceding numbers. The Fibonacci sequence has been studied extensively and generalized in many ways, for example, by starting with other numbers than 0 and 1 ...
Initial value problem. In multivariable calculus, an initial value problem[a] (IVP) is an ordinary differential equation together with an initial condition which specifies the value of the unknown function at a given point in the domain. Modeling a system in physics or other sciences frequently amounts to solving an initial value problem.