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diff --git a/html/encyclopedia/mathematics.html b/html/encyclopedia/mathematics.html index e0c14d1..948183e 100644 --- a/html/encyclopedia/mathematics.html +++ b/html/encyclopedia/mathematics.html @@ -19,13 +19,17 @@ <p class="math">\(\frac{z}{y} = x\)</p> <p class="math">\(\frac{z}{x} = y\)</p> <br /> - <p class="math">\(x ^ y = z\)</p> + <p class="math">\(\frac{x}{y} = z\)</p> + <p class="math">\(zy = x\)</p> + <p class="math">\(\frac{x}{z} = y\)</p> + <br /> + <p class="math">\(x^y = z\)</p> <p class="math">\(\sqrt[y]{z} = x\)</p> <p class="math">\(log_{x}(z) = y\)</p> <br /> - <p class="math">\(x ^ n = \frac{1}{x ^ {-n}}, x \lt 0\)</p> - <p class="math">\(x ^ 0 = 1\)</p> - <p class="math">\(x ^ {\frac{a}{b}} = \sqrt[b]{x ^ a}\)</p> + <p class="math">\(x^n = \frac{1}{x^{-n}}, x \lt 0\)</p> + <p class="math">\(x^0 = 1\)</p> + <p class="math">\(x^{\frac{a}{b}} = \sqrt[b]{x^a}\)</p> <br /> <p class="math">\(\frac{x}{y} = x\frac{1}{y}\)</p> <p class="math">\(\frac{x}{y} + n = \frac{x + n y}{y}\)</p> @@ -36,23 +40,23 @@ <p class="math">\(\frac{\frac{x}{y}}{z} = \frac{x}{yz}\)</p> <p class="math">\(\frac{\frac{x}{y}}{\frac{a}{b}} = \frac{xb}{ya}\)</p> <br /> - <p class="math">\(x ^ ax ^ b = x ^ {a + b}\)</p> - <p class="math">\(\frac{x ^ a}{x ^ b} = x ^ {a - b}\)</p> - <p class="math">\(x ^ ay ^ a = (xy) ^ a\)</p> - <p class="math">\(\frac{x ^ a}{y ^ a} = (\frac{x}{y}) ^ a\)</p> - <p class="math">\((x ^ a) ^ b = x ^ {ab}\)</p> + <p class="math">\(x^ax^b = x^{a + b}\)</p> + <p class="math">\(\frac{x^a}{x^b} = x^{a - b}\)</p> + <p class="math">\(x^ay^a = (xy)^a\)</p> + <p class="math">\(\frac{x^a}{y^a} = (\frac{x}{y})^a\)</p> + <p class="math">\((x^a)^b = x^{ab}\)</p> </div> <div class="section" id="equations"> <p class="large">Ligninger</p> <p>Andengrads:</p> - <p class="math">\(y = ax ^ 2 + bx + c\)</p> + <p class="math">\(ax^2 + bx + c = 0\)</p> <p class="math">\(x = \frac{-b \pm \sqrt[2]{d}}{2a}\)</p> - <p class="math">\(d = b ^ 2 - 4ac\)</p> + <p class="math">\(d = b^2 - 4ac\)</p> </div> <div class="section" id="functions"> <p class="large">Funktioner</p> <p class="math">\(y = f(x)\)</p> - <p class="math">\(x = f ^ {-1}(y)\)</p> + <p class="math">\(x = f^{-1}(y)\)</p> <br /> <p>Lineær:</p> <p class="math">\(f(x) = ax + b\)</p> @@ -61,20 +65,20 @@ <p class="math">\(f(0) = b\)</p> <br /> <p>Eksponentiel:</p> - <p class="math">\(f(x) = ba ^ x\)</p> + <p class="math">\(f(x) = ba^x\)</p> <p class="math">\(a = \sqrt[x_1 - x_0]{\frac{y_1}{y_{0}}}\)</p> - <p class="math">\(b = \frac{y}{a ^ x}\)</p> + <p class="math">\(b = \frac{y}{a^x}\)</p> <p class="math">\(f(0) = b\)</p> <br /> <p>Potens:</p> - <p class="math">\(f(x) = bx ^ a\)</p> + <p class="math">\(f(x) = bx^a\)</p> <p class="math">\(a = \frac{log_n(y_1) - log_n(y_0)}{log_n(x_1) - log_n(x_1)}\)</p> - <p class="math">\(b = \frac{y}{x ^ a}\)</p> + <p class="math">\(b = \frac{y}{x^a}\)</p> <p class="math">\(f(0) = 0\)</p> <p class="math">\(f(1) = b\)</p> <br /> <p>Andengrads:</p> - <p class="math">\(f(x) = ax ^ 2 + bx + c\)</p> + <p class="math">\(f(x) = ax^2 + bx + c\)</p> </div> <div class="section" id="trigonometry"> <p class="large">Trigonometri</p> @@ -89,12 +93,12 @@ <p class="math">\(csc(\theta) = \frac{hypotenuse}{modliggende}\)</p> <p class="math">\(sec(\theta) = \frac{hypotenuse}{hosliggende}\)</p> <br /> - <p class="math">\(sin ^ {-1} (\frac{modliggende}{hypotenuse}) = \theta\)</p> - <p class="math">\(cos ^ {-1} (\frac{hosliggende}{hypotenuse}) = \theta\)</p> - <p class="math">\(tan ^ {-1} (\frac{modliggende}{hosliggende}) = \theta\)</p> - <p class="math">\(cot ^ {-1} (\frac{hosliggende}{modliggende}) = \theta\)</p> - <p class="math">\(csc ^ {-1} (\frac{hypotenuse}{modliggende}) = \theta\)</p> - <p class="math">\(sec ^ {-1} (\frac{hypotenuse}{hosliggende}) = \theta\)</p> + <p class="math">\(sin^{-1} (\frac{modliggende}{hypotenuse}) = \theta\)</p> + <p class="math">\(cos^{-1} (\frac{hosliggende}{hypotenuse}) = \theta\)</p> + <p class="math">\(tan^{-1} (\frac{modliggende}{hosliggende}) = \theta\)</p> + <p class="math">\(cot^{-1} (\frac{hosliggende}{modliggende}) = \theta\)</p> + <p class="math">\(csc^{-1} (\frac{hypotenuse}{modliggende}) = \theta\)</p> + <p class="math">\(sec^{-1} (\frac{hypotenuse}{hosliggende}) = \theta\)</p> <br /> <p>Forkortelser:</p> <p class="math">\(sin = sinus\)</p> @@ -103,12 +107,12 @@ <p class="math">\(cot = cotangens\)</p> <p class="math">\(csc = cosekant\)</p> <p class="math">\(sec = sekant\)</p> - <p class="math">\(arcsin = sin ^ {-1}\)</p> - <p class="math">\(arccos = cos ^ {-1}\)</p> - <p class="math">\(arctan = tan ^ {-1}\)</p> - <p class="math">\(arccot = cot ^ {-1}\)</p> - <p class="math">\(arcsec = sec ^ {-1}\)</p> - <p class="math">\(arccsc = csc ^ {-1}\)</p> + <p class="math">\(arcsin = sin^{-1}\)</p> + <p class="math">\(arccos = cos^{-1}\)</p> + <p class="math">\(arctan = tan^{-1}\)</p> + <p class="math">\(arccot = cot^{-1}\)</p> + <p class="math">\(arcsec = sec^{-1}\)</p> + <p class="math">\(arccsc = csc^{-1}\)</p> <br /> <p class="math">\(deg(rad) = \frac{rad\pi}{180}\)</p> <p class="math">\(rad(deg) = \frac{deg180}{\pi}\)</p> @@ -116,8 +120,8 @@ <p class="math">\(vinkelsum(x) = (x - 2)\pi\)</p> <p class="math">\(vinkelsum(3) = (3 - 2)\pi = \pi\)</p> <br /> - <p class="math">\(\angle A = sin ^ {-1} (\frac{a}{c}) = cos ^ {-1} (\frac{b}{c}) = tan ^ {-1} (\frac{a}{b}) = vinkelsum(3) - \angle B - \angle C\)</p> - <p class="math">\(\angle B = sin ^ {-1} (\frac{b}{c}) = cos ^ {-1} (\frac{a}{c}) = tan ^ {-1} (\frac{b}{a}) = vinkelsum(3) - \angle A - \angle C\)</p> + <p class="math">\(\angle A = sin^{-1} (\frac{a}{c}) = cos^{-1} (\frac{b}{c}) = tan^{-1} (\frac{a}{b}) = vinkelsum(3) - \angle B - \angle C\)</p> + <p class="math">\(\angle B = sin^{-1} (\frac{b}{c}) = cos^{-1} (\frac{a}{c}) = tan^{-1} (\frac{b}{a}) = vinkelsum(3) - \angle A - \angle C\)</p> <p class="math">\(\angle C = vinkelsum(3) - \angle A - \angle B\)</p> <p>I en regulær trekant:</p> <p class="math">\(\angle A = \angle B = \angle C\)</p> @@ -130,11 +134,11 @@ <p>I en regulær trekant:</p> <p class="math">\(a = b = c\)</p> <p>I en retvinklet trekant:</p> - <p class="math">\(a = \sqrt[2]{c - b ^ 2}\)</p> - <p class="math">\(b = \sqrt[2]{c - a ^ 2}\)</p> - <p class="math">\(c = \sqrt[2]{a ^ 2 + b ^ 2}\)</p> + <p class="math">\(a = \sqrt[2]{c - b^2}\)</p> + <p class="math">\(b = \sqrt[2]{c - a^2}\)</p> + <p class="math">\(c = \sqrt[2]{a^2 + b^2}\)</p> <p>I en retvinklet trekant, hvori kateterne har samme længde:</p> - <p class="math">\(a = b = \sqrt[2]{\frac{c ^ 2}{2}}\)</p> + <p class="math">\(a = b = \sqrt[2]{\frac{c^2}{2}}\)</p> <br /> <p class="math">\(O = a + b + c\)</p> <p class="math">\(A = \frac{b h}{2}\)</p> @@ -147,7 +151,7 @@ <p class="math">\(b_1 = b_0 k\)</p> <p class="math">\(c_1 = c_0 k\)</p> <p class="math">\(O_1 = O_0 k\)</p> - <p class="math">\(A_1 = A_0 k ^ 2\)</p> + <p class="math">\(A_1 = A_0 k^2\)</p> </div> <div class="section" id="constants"> <p class="large">Konstanter</p> @@ -181,12 +185,12 @@ <td class="math">\(\phi\)</td> </tr> </table> - <p class="math">\(\sqrt[2]{2} \approx \frac{1\ 414\ 213\ 562}{10 ^ 9}\)</p> - <p class="math">\(\sqrt[2]{3} \approx \frac{1\ 732\ 050\ 808}{10 ^ 9}\)</p> - <p class="math">\(e = \sum_{n = 0} ^ \infty \frac{1}{n!} \approx \frac{2\ 718\ 281\ 828}{10 ^ 9}\)</p> + <p class="math">\(\sqrt[2]{2} \approx \frac{1\ 414\ 213\ 562}{10^9}\)</p> + <p class="math">\(\sqrt[2]{3} \approx \frac{1\ 732\ 050\ 808}{10^9}\)</p> + <p class="math">\(e = \sum_{n = 0}^\infty \frac{1}{n!} \approx \frac{2\ 718\ 281\ 828}{10^9}\)</p> <p class="math">\(i = \sqrt[2]{-1}\)</p> - <p class="math">\(\pi \approx \frac{3\ 141\ 592\ 654}{10 ^ 9}\)</p> - <p class="math">\(\phi = \frac{1 + \sqrt[2]{5}}{2} \approx \frac{1\ 618\ 033\ 989}{10 ^ 9}\)</p> + <p class="math">\(\pi \approx \frac{3\ 141\ 592\ 654}{10^9}\)</p> + <p class="math">\(\phi = \frac{1 + \sqrt[2]{5}}{2} \approx \frac{1\ 618\ 033\ 989}{10^9}\)</p> </div> </div> <!--#include virtual="/include/pgftr.shtml"--> |