can be rearranged in standard form as a x 2 + b x + c = 0 , {\displaystyle ax^{2}+bx+c=0\,,} where the variable x represents an unknown number, and a, b...

function of the form f ( x ) = a x 3 + b x 2 + c x + d , {\displaystyle f(x)=ax^{3}+bx^{2}+cx+d,} that is, a polynomial function of degree three. In many...

{ax}\right|\,dx=-{\frac {1}{a}}\operatorname {sgn}(\csc {ax})\ln(\left|\csc {ax}+\cot {ax}\right|)+C} when a x ∈ ( n π , n π + π ) {\displaystyle ax\in...

independent state. Political parties and elections in Åland Nordsieck, Wolfram (31 May 2022). Parties and Elections in Europe: Parliamentary Elections...

quadratic function is commonly written as: a x 2 + b x + c , {\displaystyle ax^{2}+bx+c\,,} where a, b and c are constants (coefficients or parameters),...

the form f ( x ) = a x 4 + b x 3 + c x 2 + d x + e , {\displaystyle f(x)=ax^{4}+bx^{3}+cx^{2}+dx+e,} α where a is nonzero, which is defined by a polynomial...

{\displaystyle \int {e^{ax}\left(\left(a\right)^{n}f\left(x\right)-\left(-1\right)^{n}{\frac {d^{n}f\left(x\right)}{dx^{n}}}\right)\,dx}=e^{ax}\sum...

{\begin{aligned}\int \sinh(ax)\,dx&=a^{-1}\cosh(ax)+C\\\int \cosh(ax)\,dx&=a^{-1}\sinh(ax)+C\\\int \tanh(ax)\,dx&=a^{-1}\ln(\cosh(ax))+C\\\int \coth(ax)\,dx&=a^{-1}\ln...

for example, in the quadratic equation a x 2 + b x + c = 0 , {\displaystyle ax^{2}+bx+c=0,} the variables a , b , c {\displaystyle a,b,c} are parameters...

variable x {\displaystyle x} in the polynomial a x 2 + b x + c {\displaystyle ax^{2}+bx+c} have coefficient parameters a {\displaystyle a} , b {\displaystyle...

and c is a scalar c ∈ K, then cx ∈ Null(A), since A(cx) = c(Ax) = c0 = 0. The product Ax can be written in terms of the dot product of vectors as follows:...

på Åland (in Swedish). 18 July 2013. Retrieved 17 June 2020. Nordsieck, Wolfram (2020). Parties and Elections in Europe. Books on Demand. p. 202. ISBN 9783750481343...

It is the unique positive number a such that the graph of the function y = ax has a slope of 1 at x = 0. One has e = exp ⁡ ( 1 ) , {\displaystyle e=\exp(1)...

European and Nordic Studies. Helsinki: University of Helsinki: 88. Nordsieck, Wolfram (2023). "Åland (Finland)". Archived from the original on 15 April 2024...

7 + b x 6 + c x 5 + d x 4 + e x 3 + f x 2 + g x + h = 0 , {\displaystyle ax^{7}+bx^{6}+cx^{5}+dx^{4}+ex^{3}+fx^{2}+gx+h=0,\,} where a ≠ 0. A septic function...

Rust S-Lang VBScript Visual Basic Visual FoxPro Wolfram Mathematica (Wolfram language) Microsoft Dynamics AX (X++) Reflective programming languages let programs...

a polynomial with terms of the form ⁠ a x k y m {\displaystyle \textstyle ax^{k}y^{m}} ⁠, where the exponents ⁠ k {\displaystyle k} ⁠ and ⁠ m {\displaystyle...

\triangle CYY'',} X X ′ Y Y ″ = A X C Y , {\displaystyle {XX' \over YY''}={AX \over CY},} △ D X X ″ ∼ △ B Y Y ′ , {\displaystyle \triangle DXX''\sim \triangle...

number arises for the logistic map f ( x ) = a x ( 1 − x ) {\displaystyle f(x)=ax(1-x)} with real parameter a and variable x. Tabulating the bifurcation values...

(WATerloo FORtran IV) WebAssembly WebDNA Whiley Wolfram Language Wyvern X++ (X plus plus/Microsoft Dynamics AX) X10 xBase++ (xBase plus plus) XBL XC (targets...

triangle △ABC at X, Y, Z respectively. Let the pairs of lines (BY, CZ), (CZ, AX), (AX, BY) meet at U, V, W. Triangles △ABC and △UVW are in perspective and let...

to the linear system Ax=b where x is in Rn, the Hermite normal form can solve problems about the solution to the linear system Ax=b where this time x is...

variable is an equation of the form a x 3 + b x 2 + c x + d = 0 {\displaystyle ax^{3}+bx^{2}+cx+d=0} in which a is not zero. The solutions of this equation...

(g\circ f)({\mathbf {x}})=g(f({\mathbf {x}}))=g({\mathbf {Ax}})={\mathbf {B}}({\mathbf {Ax}})=({\mathbf {BA}}){\mathbf {x}}.} The last equality follows...

{\begin{aligned}\|A\|_{\alpha ,\beta }&=\sup\{\|Ax\|_{\beta }:x\in K^{n}{\text{ with }}\|x\|_{\alpha }=1\}\\&=\sup \left\{{\frac {\|Ax\|_{\beta }}{\|x\|_{\alpha }}}:x\in...

b y , {\displaystyle {\begin{aligned}a(x+kv)+b(y-ku)&=ax+by+k(av-bu)\\&=ax+by+k(udv-vdu)\\&=ax+by,\end{aligned}}} showing that (x + kv, y − ku) is another...

then f ( a x ) {\displaystyle f(ax)} , where a {\displaystyle a} is a non-zero real number such that a x {\displaystyle ax} is within the domain of f {\displaystyle...

Plot ax = plt.figure().add_subplot(projection='3d') ax.plot(*xyzs.T, lw=0.6) ax.set_xlabel("X Axis") ax.set_ylabel("Y Axis") ax.set_zlabel("Z Axis") ax.set_title("Lorenz...

(compatibility with multiplicative inverse, and, if a = b, uniqueness modulo m). If ax ≡ b (mod m) and a is coprime to m, then the solution to this linear congruence...

x 2 + B x + C − y = 0 {\displaystyle Ax^{2}+Bx+C-y=0} has left-hand side A x 2 + B x + C − y {\displaystyle Ax^{2}+Bx+C-y} , which has four terms, and...