Create the page "Difference equations" on this wiki! See also the search results found.

• LaTeX:Layout
  ...phing rules in LaTeX is very important when using display math. Notice the difference in the following: ...st equations, or even to past pages. Rather than having to manually number equations then change your text if the equation labels change, or having to manually
  30 KB (5,171 words) - 10:16, 4 April 2021
• 2007 AMC 12A Problems/Problem 17
  ...ic identities#Pythagorean Identities|Pythagorean identities]]: square both equations and add them up: This is just the cosine difference identity, which simplifies to <math>\cos (a - b) = \frac{1}{3} \Longrightar
  1,022 bytes (153 words) - 14:56, 7 August 2017
• 2004 AMC 12A Problems/Problem 14
  Let <math>d</math> be the common difference. Then <math>9</math>, <math>9+d+2=11+d</math>, <math>9+2d+20=29+2d</math> a ...h>, <math>11+d</math>, and <math>29+2d</math>. Thus, we get the following equations:
  4 KB (689 words) - 03:35, 16 January 2023
• 2003 AMC 12B Problems/Problem 24
  ...the line where <math>a<x<b</math> has slope <math>-1</math>, the positive difference in <math>y</math>-coordinates from <math>x=a</math> to <math>x=b</math> mus
  7 KB (1,183 words) - 11:47, 15 February 2016
• 2008 AMC 12B Problems/Problem 25
  ...frac{24}8=3</math>. Now we can solve for <math>r</math> by adding the two equations we just got to see that <math>2r=11</math>, or <math>r=\frac{11}2</math>.
  12 KB (2,015 words) - 20:54, 9 October 2022
• 2008 AIME II Problems
  ...aximum possible value of <math>\dfrac{a}{b}</math> for which the system of equations :(i) <math>n^2</math> can be expressed as the difference of two consecutive cubes;
  7 KB (1,167 words) - 21:33, 12 August 2020
• 2008 AMC 10A Problems/Problem 15
  Substituting equations <math>(1)</math> and <math>(2)</math> into <math>(5)</math> gives: We are asked the difference between Jan's and Ian's distances, or
  6 KB (1,033 words) - 15:19, 1 July 2021
• Dynamical Systems
  ...es of dynamical systems include the [[logistic equation]] and the [[Lorenz equations]].
  789 bytes (107 words) - 21:52, 18 October 2017
• 2008 iTest Problems
  The difference between two prime numbers is <math>11</math>. Find their sum. ...s. One of the problems Joshua and Alexis work on boils down to a system of equations:
  71 KB (11,749 words) - 01:31, 2 November 2023
• 2009 AMC 12A Problems/Problem 23
  ...about the quadratic <math>ax^2+bx+c</math> (<math>a>0</math>) that (i) the difference of the two quadratic roots equals to <math>\sqrt{\Delta}/a</math>, and (ii)
  5 KB (862 words) - 02:04, 1 April 2024
• 2010 USAMO Problems/Problem 3
  Given <math>a_1</math>, from the equations <math>a_ia_{i+1} = 2i+1,\; 1\le i\le 2n-1</math>, The same equations <math>a_ia_{i+1} = 2i+1</math> can be used to compute the
  11 KB (1,889 words) - 13:45, 4 July 2013
• 2011 AMC 12B Problems/Problem 21
  Squaring the first and second equations, <math>\frac{x^2 + 2xy + y^2}{4}=100 a^2 + 20 ab + b^2</math> Subtracting the previous two equations, <math>\frac{x^2 + 2xy + y^2}{4} - xy = \frac{x^2 - 2xy + y^2}{4} = \left(\
  3 KB (507 words) - 19:48, 4 November 2023
• 2011 AMC 10B Problems/Problem 21
  The largest difference, <math>9,</math> must be between <math>w</math> and <math>z.</math> ...ven as a possibility in the problem. This means <math>1</math> must be the difference between <math>y</math> and <math>x.</math> We can express the possible conf
  8 KB (1,303 words) - 20:29, 5 September 2022
• 2002 AMC 10B Problems/Problem 19
  ...lize that the two equations are 100 terms apart, so by subtracting the two equations in a form like... ...we get the value of the common difference of every hundred terms one hundred times. So we have to divide the answer b
  3 KB (472 words) - 14:56, 17 August 2023
• Trigonometric Equations
  It is probably good to know how to solve trigonometric equations, which often involved brute force and the use of trigonometric identities. When solving trigonometric equations, it probably doesn't get easier than this. Using the unit circle or a graph
  8 KB (1,351 words) - 20:30, 10 July 2016
• 1984 AHSME Problems/Problem 12
  <math> 2, 4, 8, 14, 22, .... </math>. We notice that the difference between succesive terms of the sequence are <math> 2, 4, 6, 8, .... </math> ...'''(2)''' and '''(2)''' from '''(3)''' yields the two-variable [[system of equations]]
  2 KB (325 words) - 18:10, 30 November 2013
• 2003 AMC 10B Problems/Problem 24
  The difference between consecutive terms is <math>(x-y)-(x+y)=-2y.</math> Therefore we can ...-\frac35.</math> Substituting the value for <math>y</math> into any of the equations, we get <math>x=-\frac98.</math> Finally,
  4 KB (779 words) - 16:16, 12 March 2024
• 1950 AHSME Problems
  The values of <math>y</math> which will satisfy the equations <cmath>\begin{array}{rcl} 2x^{2}+6x+5y+1&=&0\\ 2x+y+3&=&0 \end{array}</cmat ...qquad\\ \textbf{(D)}\ y^{2}+y-12=0\qquad \textbf{(E)}\ \text{None of these equations} </math>
  22 KB (3,306 words) - 19:50, 3 May 2023
• 2012 AMC 10A Problems/Problem 24
  Add the two equations. ...c)^2 = 9 \Rightarrow a-c = 3</math>, since <math>a-c</math> is the biggest difference. It is impossible to determine by inspection whether <math>a-b = 1</math> o
  2 KB (398 words) - 14:32, 5 December 2022
• 2012 AMC 10A Problems/Problem 17
  Using difference of cubes in the numerator and cancelling out one <math>(a-b)</math> in the An alternate method of solving the system of equations involves solving the second equation for <math>a</math>, by plugging it int
  6 KB (1,024 words) - 01:35, 1 October 2023

View (previous 20 | next 20) (20 | 50 | 100 | 250 | 500)