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- ...[phinary]], which is base [[phi]]; others include "[[Fibonacci base]]" and base negative two. [[Binary]] is base 2. It's a favorite among computer programmers. It has just two digits: <ma2 KB (351 words) - 09:39, 1 October 2015
- ...th>\ln x=\int_1^x \frac{1}{t} \, dt</math>. It has been shown to be both [[irrational]] and [[transcendental number|transcendental]]. ==Euler's Number as the Base of Logarithms and Exponential Functions==4 KB (764 words) - 20:09, 13 March 2022
- There exist irrational numbers <math>e\approx 2.72</math> and <math>\pi \approx 3.14.</math> How c ...at specific order. Then, what is the value of <math>n,</math> expressed in base <math>10?</math>12 KB (1,784 words) - 15:49, 1 April 2021
- ...ath> inside the <math>\triangle ABC</math> a line is drawn parallel to the base <math>AB</math>, dividing the triangle into two equal areas. The logarithm of <math>.0625</math> to the base <math>2</math> is:22 KB (3,348 words) - 11:53, 22 July 2024
- The altitude drawn to the base of an isosceles triangle is <math> 8</math>, and the perimeter <math> 32</m \textbf{(B)}\ \text{may be irrational}\qquad25 KB (3,872 words) - 13:21, 20 February 2020
- ...ath>R_4</math>, the quotient <math>Q=R_{24}/R_4</math> is an integer whose base-ten representation is a sequence containing only ones and zeroes. The numbe Let <math>r</math> be the number that results when both the base and the exponent of <math>a^b</math> are tripled, where <math>a,b>0</math>.20 KB (2,814 words) - 07:15, 27 June 2021
- ...c{\log{b}}{q}=\frac{\log{c}}{r}=\log{x}</math>, all logarithms to the same base and <math>x \not= 1</math>. If <math>\frac{b^2}{ac}=x^y</math>, then <math ...ea of a trapezoid such that the shorter base, the altitude, and the longer base, in that order, are in arithmetic progression. Then:20 KB (3,108 words) - 13:14, 20 February 2020
- ...ortion, which differs from it by an integer. Hence <math>x_{k+1}</math> is irrational, completing the proof.2 KB (348 words) - 12:14, 13 February 2015
- ...an be written as a difference of two positive and less than <math>1</math> irrational numbers. ...A_3'\ldots A_n'],n\in\mathbb{N},n\ge 3</math>, has a convex polygon as its base. It is known that <math>A_1A_2'\perp A_2A_3',A_2A_3'\perp A_3A_4',</math><m10 KB (1,695 words) - 09:03, 10 May 2012
- <math> \textbf{(A)\ } \text{rational} \qquad \textbf{(B)\ } \text{irrational} \qquad \textbf{(C)\ } \text{integral} \qquad \textbf{(D)\ } \text{a perfec If the base of a rectangle is increased by <math> 10\% </math> and the area is unchange23 KB (3,556 words) - 14:35, 30 December 2023
- ...ea of a trapezoid such that the shorter base, the altitude, and the longer base, in that order, are in arithmetic progression. Then: \textbf{(C)}\ K \; \text{must be an irrational number} \qquad1 KB (197 words) - 00:36, 16 August 2023
- \textbf{(C) }\text{rational, but not integral} \qquad\textbf{(D) }\text{irrational} \qquad\textbf{(E) } \text{imaginary} </math> In the numeration system with base <math>5</math>, counting is as follows: <math>1, 2, 3, 4, 10, 11, 12, 13, 121 KB (3,242 words) - 20:27, 30 December 2020
- The base of the decimal number system is ten, meaning, for example, that <math>123 = In the binary system, which has base two, the first five positive integers are <math>1,\,10,\,11,\,100,\,101</ma26 KB (3,952 words) - 10:55, 27 July 2024
- \textbf{(D)}\ \text{equal and irrational} \qquad <math>\textbf{(A)}\ \text{base angle and vertex angle; isosceles triangle} \20 KB (3,039 words) - 21:44, 12 February 2021
- <math> \textbf{(C)}\ \text{An irrational number}\qquad </math> ...e the equation to <math>(2x)^x = 216</math>. Since <math>2x</math> is the base of the logarithm, we only need to check x-values that are positive.918 bytes (141 words) - 19:55, 11 May 2018
- ...ll positive integers that do not contain the digit <math>7</math> in their base-<math>10</math> representation. Find all polynomials <math>f</math> with no ...th> with <math>a</math> not a power of 10, and hence <math>\lg a</math> is irrational. By Dirichlet's approximation theorem, the set of multiples of <math>\lg a<4 KB (735 words) - 15:08, 18 March 2023
- ...ese well-defined functions everywhere, irrational numbers were defined. An irrational number is a number that can not be expressed as <math>\frac{a}{b}</math>. ==== Irrational numbers ====35 KB (5,884 words) - 09:25, 7 December 2024