# how to graph absolute value equations

17,762 questions-
## math

how to graph absolute value equations

*asked by Anonymous on December 12, 2010* -
## Math: Parametric Equations

Let G be the graph of the parametric equations x = cos(4t), y = sin(6t). What is the length of the smallest interval P such that the graph of these equations for all t E P produces the entire graph G? (The "E" represents the symbol for "is in" that looks

*asked by Katie on April 9, 2016* -
## Precalculus

Let G be the graph of the parametric equations x=cos(4t)and y=sin(6t). What is the length of the smallest interval I such that the graph of these equations for all t in I produces the entire graph G?

*asked by John on February 28, 2014* -
## Precalculus

Let G be the graph of the parametric equations x=cos(4t)and y=sin(6t). What is the length of the smallest interval I such that the graph of these equations for all t in I produces the entire graph G?

*asked by John on March 2, 2014* -
## Math

Let G be the graph of the parametric equations x = cos(4t), y = sin(6t). What is the length of the smallest interval P such that the graph of these equations for all t E P produces the entire graph G?

*asked by Bob on July 30, 2016* -
## Algebra-help please

Please help me graph this Absolute value x+1 inside absolute brackets -3

*asked by Cassie on August 23, 2013* -
## Algebra 1

Describe how the graphs of y = absolute value of x,and y = absolute value of X -15 are related. 1- Them graphs have the same shape. The y intercept of y = absolute x is 0, and them x intercept of the 2nd graph is -15. 2-m The graphs have the same y

*asked by Steve on December 13, 2014* -
## Algebra

I need help with solving these absolute value inequalities. I have to graph them as well. y< |x+2|+4 and y>|x+5|+3 I just don't know what to do without a coefficient in front of the absolute value!

*asked by Mimi on September 12, 2013* -
## Algebra

Pretend the parentheses are absolute value bars. What is the graph of y = (x) and its translation to the graph of y = (x + 3)+1? I know I can't post the graph picture here, but I'm confuzzled on how to solve the problem. Please explain how! Thank you so

*asked by Delia on June 8, 2009* -
## microsoft excel 2003

How would I graph equations in Microsoft Excel 2003 and the residuals? I want to graph linear, quadratic and exponential equations but I don't know how.

*asked by Nina on March 26, 2008* -
## Precalculus

Let $\mathcal{G}$ be the graph of the parametric equations \begin{align*} x &= \cos(4t),\\ y &= \sin(6t). \end{align*}What is the length of the smallest interval $I$ such that the graph of these equations for all $t\in I$ produces the entire graph

*asked by Zheng on January 31, 2017* -
## Algebra 2- Translations

Describe how the graph of y= absolute value changes when the equation is changed to y = -5 absolute value x-9 and + 12

*asked by Amy on March 5, 2014* -
## Precalculus

Let $\mathcal{G}$ be the graph of the parametric equations \begin{align*} x &= \cos(4t),\\ y &= \sin(6t). \end{align*}What is the length of the smallest interval $I$ such that the graph of these equations for all $t\in I$ produces the entire graph

*asked by Zheng on January 29, 2017* -
## MATH

Please help me!!!!!!!!!!!!!!!1 Instructions a. If needed, rewrite the following equations in slope-intercept form. * b. Indicate the slope and the y-intercept for each of the equations. c. Using graph paper and a straight edge, graph the equations. 1. y =

*asked by Austin on May 24, 2007* -
## Int Algebra

The difference of two numbers is 7. The sum of the numbers is -1. What are the numbers? I've come up with the following equations: x-y=7 and x+y=-1. I can't seem to solve because there are no numbers on the left side of the equations. Any thoughts? Let's

*asked by Rose Mata on January 26, 2007* -
## Calculus (pleas help!!!)

Find the absolute maximum and absolute minimum values of the function f(x)=(x−2)(x−5)^3+11 on each of the indicated intervals. Enter -1000 for any absolute extrema that does not exist. (A) Interval = [1,4] Absolute maximum = Absolute minimum = (B)

*asked by Cady on April 5, 2011* -
## Calculus (pleas help!!!)

Find the absolute maximum and absolute minimum values of the function f(x)=(x−2)(x−5)^3+11 on each of the indicated intervals. Enter -1000 for any absolute extrema that does not exist. (A) Interval = [1,4] Absolute maximum = Absolute minimum = (B)

*asked by Cady on April 5, 2011* -
## Math (Solving Equations)

Find all solutions (answers should be given in simplified form). Some answers may involve the number i. *I will use lowercase l to represent absolute value lines.* 3 lx-1l + 4 = 19 We've never really worked with absolute value in solving equations before.

*asked by Leah on May 17, 2015* -
## Precalculus

Find the sum of all possible values of the constant k such that the graph of the parametric equations x=2+4cos(s) and y=k-4sin(s) intersects the graph of the parametric equations x=1+cos(t) and y=-3+sin(t) at only one point.

*asked by John on March 2, 2014* -
## Precalculus

Find the sum of all possible values of the constant k such that the graph of the parametric equations x=2+4cos(s) and y=k-4sin(s) intersects the graph of the parametric equations x=1+cos(t) and y=-3+sin(t) at only one point.

*asked by John on February 28, 2014* -
## Algebra 2

how do i do these problems???? Graph each pair of equations in the same coordinate plane. Find the coordinates of the point where the graphs intersect. Then show by substitution that the coordinate satisfy both equations. 1. 2x + 5=0 2x + y=8 Graph each

*asked by Jessica on August 17, 2010* -
## university physics

Derive absolute error in equations: 1)Derive absolute error in (e/m) e/m= 2V/B^2*R^2 2)Derive absolute error in B B=8uN(Inet)/square root 125a

*asked by Ella on November 21, 2012* -
## precalculus

To what interval I must we restrict the parameter t if the graph of the parametric equations x=t+1 y = 2t^2 +1 for t in the set I is identical to the graph of the parametric equations x = 1+ sin s y = 2- cos(2s) for s in [0,pi)?

*asked by dreidel on December 18, 2013* -
## Chemistry

How do you do the inverse of absolute temperature? My kelvin temperatures are: 298 308 318 328 338 348 358 368 378 Taking the natural log of both sides of both sides of the equation gives ln(k) = ln(A) – E/RT. Thus, a graph of the natural log of the

*asked by Angie on September 25, 2012* -
## Calculus

Okay, I have a graph of the f(x). It is a parabola that opens up. What does the graph of f(|x|) look like (the absolute value). Is it the same, or flipped or translated? Can someone describe what it looks like to me please :)

*asked by Jon on September 19, 2010* -
## Algebra(please help ASAP!)

This is a little difficult... Graph the Function y=3 less than the absolute value of x+2 Obviously you cannot show me this on a graph, but I just need help with solving the equation... Thanks!!!

*asked by Jackie on November 11, 2015* -
## math

Graph f(x)=lx-3l and x=3 on the same set of coordinate axes. Write a description of the relationship between the two graphs. i graphed absolute value of x-3 but how do you graph x=3

*asked by ANONYMOUS. on January 10, 2010* -
## calculus (gr 12)

State the absolute maximum value and the absolute minimum value of each function, if the function is defined on the interval shown. {I CANNOT POST THE GRAPH SO CAN SOMEONE EMAll ME AT miss.a.parker at hot mail(. com) SO I CAN EMAIL IT TO THEM SO YOU CAN

*asked by HELP MEE PLEASE on April 17, 2013* -
## Grade 12 Calculus

State the absolute maximum value and the absolute minimum value of each function, if the function is defined on the interval shown. {I CANNOT POST THE GRAPH SO CAN SOMEONE EMAll ME AT miss.a.parker at hot mail(. com) SO I CAN EMAIL IT TO THEM SO YOU CAN

*asked by Alexandra on April 15, 2013* -
## calculus

3. Let f be the function defined by f(x)=ln(2+sinx) for pi

*asked by Yoona on February 13, 2012* -
## math 12

desribe how the graph of each funtion compares to the graph of y = l x l (absolute value) a) y = 1 2x l b) y = l 1/2x l c) 2y = l x l d) 1/2y = l x l i don't understand when it is vertical/horizontal and when it is expansion or compression

*asked by Anonymous on September 15, 2008* -
## Algebra

analyze the graph f(x)=(x-2)^3(x-3)^2(x-4) a)end behavior: find the power function that the graph of f resembles for large values of absolute value of x

*asked by Stone on November 12, 2013* -
## Algebra

Two cell phone companies have different rate plans. Runfast has monthly charges $8 plus $8 per gig of data. B A &D’s monthly charge is $15 plus $4 per gig of data. Your task, is to determine under what circumstances each company has the better pricing.

*asked by Kim Sohyun on May 1, 2019* -
## Pre-Cal (Help Plz)

The question I've been trying to figure out is asking me to explain how the graph of (g) is obtained from the graph of (f). The graphs are as followed: - f(x)= x^(2)-4 - g(x)= [x^(2)-4] (Note: the Brackets represent absolute value symbols around the

*asked by Dom on June 8, 2016* -
## math, help

For the following set, which number has the largest absolute value? 4,-1,12,-20,19,0 Possible Answer of choice: A)0 B)19 C)-20 D)-1 wouldn't it be postive 20 but its not within the choices. What is the absolute value of -20? Absolute value is the distance

*asked by jasmine20 on February 13, 2007* -
## Algebra

Right now we are learning about absolute value inequalities. I have to solve and graph this inequality: Pretend my paranpheses are absolute value signs (x-4) + 5 is greater than or equal to 10. I assume I would take 5 away from each side first. But what

*asked by Julianna on January 31, 2009* -
## Algebra 1 (Reiny or Kuai)

1. Which x-values should I choose to graph these equations (y = x; y = -x + 6) so that they intersect? 2. The school band sells carnations on Valentine's Day for $2 each. They buy the carnations from a florist for $0.50 each, plus a $16 delivery charge. a.

*asked by Please, help me! on December 9, 2013* -
## Math

The graph of the parametric equations x=cos(t) y=sin(t) meets the graph of the parametric equations x=2+4cos(s) y=3+4sin(s) at two points. Find the slope of the line between these two points. Please help!!!! I need this done soon and I am getting nowhere

*asked by Sultan on July 30, 2016* -
## grasping algebra concepts

My book is showing the solution for graphing a system of linear equations y > 2x - 7 y is greater than or equal to -3x + 7 I see the way they graphed it and both lines intersect at one point. Did the just find -7 and +7 on the line in order to graph or did

*asked by Shawn on August 22, 2007* -
## precalculus HELP!

I posted this question before: What is the area enclosed by the graph of the absolute value(3x)+ the absolute value(4y)=12 I tried solving for y and got: y=4-x when I graphed this, I got a linear equation graph...I am wondering if I am supposed to find the

*asked by sara on December 4, 2006* -
## Precalculus

The graph of the parametric equations x=cos(t), y=sin(t) meets the graph of the parametric equations x=2+4cos(s), y=3+4sin(s), at two points. Find the slope of the line between these two points.

*asked by Phil on April 9, 2016* -
## Algrebra II

hi, thanks for reading this I have a question for finding vertical and horizontal asymptotes! as to finding the intercepts, domain, and graphing it all together... like y= 6 over (x+3) I don't quite understand the concepts and things, but if you can give

*asked by Kaz18 Tsuruoka on July 13, 2007* -
## Math

I have a graph which I need to find the equation of. It's an absolute value graph, the vertex/middle point is at (-2, 5) and 2 points that lie on the graph are (1,10) and (-5,10). It needs to be in 'y=' form. I'd appreciate it if you explained how to do

*asked by Jose on April 10, 2009* -
## Calculus

Find the absolute maximum and absolute minimum values of the function f(x)=x^3+6x^2-63x+4 on each of the indicated variables. Enter DNE for does not exist. (A) Interval = [-8,0] Absolute maximum = Absolute minimum = (B) Interval = [-5,4] Absolute maximum =

*asked by Nate on October 29, 2013* -
## pre-calculus 11

I am asked to solve the absolute value equation of |1/2x +1| =x+1 graphically. I can solve this algebraically and consider two cases for the absolute value one being positive and the other negative. I know this will be a straight line and when I solved it

*asked by george on June 10, 2015* -
## pre-calculus 11

I am asked to solve the absolute value equation of |1/2x +1| =x+1 graphically. I can solve this algebraically and consider two cases for the absolute value one being positive and the other negative. I know this will be a straight line and when I solved it

*asked by george on June 14, 2015* -
## math

help me ..... Consider the function f(x)= -cos3x -4sin3x. (a)Find the equation of the line normal to the graph of f(x) when x= pie/6 . (b)Find the x coordinates of the points on the graph of f(x) where the tangent to the graph is horizontal. (c)Find the

*asked by weloo_volley on April 24, 2012* -
## math

help me ..... Consider the function f(x)= -cos3x -4sin3x. (a)Find the equation of the line normal to the graph of f(x) when x= pie/6 . (b)Find the x coordinates of the points on the graph of f(x) where the tangent to the graph is horizontal. (c)Find the

*asked by weloo_volley on April 24, 2012* -
## math

Consider the function f(x)= -cos3x -4sin3x. (a)Find the equation of the line normal to the graph of f(x) when x= pie/6 . (b)Find the x coordinates of the points on the graph of f(x) where the tangent to the graph is horizontal. (c)Find the absolute extrema

*asked by weloo_volley on April 30, 2012* -
## math

weloo. Consider the function f(x)= -cos3x -4sin3x. (a)Find the equation of the line normal to the graph of f(x) when x= pie/6 . (b)Find the x coordinates of the points on the graph of f(x) where the tangent to the graph is horizontal. (c)Find the absolute

*asked by weloo_volley on May 8, 2012* -
## math

i can figure this out -2+|-5+6| i try inverse but im still getting it wrong ive been stuck on this fo awhile There is no inverse in the equation. the |...| means absolute value. We perform what is indicated in the |,,| and that is +1. The absolute value of

*asked by need more help please on December 6, 2006* -
## Calculus

Let f be the function defined for x >or= to 0 with f(0)=5 and f', the first derivative of f, give by f'(x)=e^(-x/4)sin(x^2). A) Use the graph of f' to determine whether the graph of f is concave up, concave down, or neither on the interval 1.7

*asked by Leanna on February 9, 2011* -
## Calculus

find the area between x=tan^2y and x=-tan^2y in -pi/4

*asked by Bethany on March 28, 2016* -
## Algebra 1 (Reiny or Kuai)

1. The school band sells carnations on Valentine's Day for $2 each. They buy the carnations from a florist for $0.50 each, plus a $16 delivery charge. a. Write a system of equations to describe the situation. A: y = 2x; y = 0.50x + 16. b. Graph the system.

*asked by Please, help me! on December 9, 2013* -
## Algebra

12. Determine if the following is a conjuction or disjunction. y + 4 < -1 or y + 2 > 8 (Points : 1) 13. State how you determined if the combination above was a conjunction or disjunction. (Points : 2) 14. Solve the problem. (Hint: You should have two

*asked by kim on April 7, 2015* -
## Explanation of Maths B Question

An example of a wine glass design, using three equations, is given below. The base of the wine glass is defined by a quadratic equation, the stem by a linear equation and the body of the glass by a square root function. The difficult part of the

*asked by Nina on July 28, 2012* -
## MATH!

How do you make a coordinate plane graph? I can't go and get my text book because its winter break! Could someone help me here? I need to know how to make one using an equation. specifically these equations y = 6x - 2 y = -3x + 5 y = ½x + 3 please I need

*asked by Austin on December 21, 2006* -
## Algebra 2

I'm working on Lesson 6: Absolute Value Equations and Inequalities Algebra 2 A Unit 2: Expressions, Equations, and Inequalities and feel confident in my first few answers, but beyond that am lost. May I have some help? **=the answer I believe to be true

*asked by Nina on September 23, 2017* -
## Algebra 1

Describe how the graphs of y =IXI nand ym = IXI -15 are related. 1- the graphs have the same shape,. The y intercept of the 2nd graph is -15 2-the graphs have the same y intercept. The 2nd graph is steeper than y= absolute x 3- the 2 graphs are the same 4-

*asked by Steve on December 7, 2014* -
## algebra

the graph of a first degree absolute value function has a Y-intercept of 3, x-intercepts of -9 and -3 , and a minimum vlaue of -3 at x=-6. on the axes provided , sketch a graph of this function.

*asked by karin on June 15, 2015* -
## Calculus I

Sketch the graph of f by hand and use your sketch to find the absolute and local maximum and minimum values of f. 18. f(x) = 1/x , 1 < x < 3 I can graph it just fine, but for my answer I got that the function has none of the above. Is this correct?

*asked by Emily on March 5, 2012* -
## precalculus

What is the area enclosed by the graph of the absolute value of (3x)+ the absolute value of (3y)=12? what area are you looking for?? ar eyou looking for the area of a cylinder or what??

*asked by sara on December 3, 2006* -
## Math

At what point does the graph of the parametric equations y=3-2t, y=-2+5t intersect the graph of the parametric equations x = -1+3s,y=5-9s. The answer is the point of intersection (x,y). Please help! I am really confused!

*asked by Bob on July 29, 2016* -
## Math: Parametric Equations

The graph of the parametric equations x=cos(t) y=sin(t) meets the graph of the parametric equations x=2+4cos(s) y=3+4sin(s) at two points. Find the slope of the line between these two points. So far I've set up the system of equations cos(t)=2+4cos(s)

*asked by Katie on April 10, 2016* -
## pre - CALCULUS

Begin by graphing the standard absolute value function f(x) = | x |. Then use transformations of this graph to describe the graph the given function. h(x) = 2 | x | + 2

*asked by Ciara on April 10, 2015* -
## pre - CALCULUS

Begin by graphing the standard absolute value function f(x) = | x |. Then use transformations of this graph to describe the graph the given function. h(x) = 2 | x | + 2

*asked by Ciara on April 10, 2015* -
## Algebra2

How would you solve these absolute value equations? 1.|3x-1|=|x+4| 2.|3/k-1|=4

*asked by Unknown. on August 16, 2012* -
## Algebra

I think I am a little bit confused with this absolute value thing. When do I change the sign inside? Example f(-2)= |-2-2|. Is this equal to -4 or do I need to change a sign inside the absolute value when adding. I am trying to get some x and y values to

*asked by Lois on December 3, 2013* -
## pre-calc

find real numbers a,b,c so that the graph of the function y=ax^2+bx+c contains the points (-11,4), (2,3) , and (0,1) Write three equations, with each point in one. Then solve the three equations.

*asked by Erica on October 24, 2006* -
## Math, Year 10, Simult. Equations

How can i know if two lines/equations intersect on a graph, algebraically? For example, I have two equations: 1. -x^2 + 3x + 4, and 2. x - 4 Ty in advan.

*asked by Anonymous on June 8, 2016* -
## Math

Can someone please help/show me how to Graph linear equations?? Directions~ Graph the following linear equations by plugging in values for x, solving for y, and keeping track of your x- and y-values in a table. You should determine at least three points on

*asked by Abby on October 20, 2015* -
## Chemistry

I had to find the absolute zero from a graph with the following points: Temperature (K) / Volume (mL): 318 4.5 308 4.3 303 4.1 294 4.0 284 3.9 275 3.7 271 3.2 I graphed the points (with the temperature on the y-axis because the lab indicated a vertical

*asked by AJ on October 30, 2008* -
## algebra 1

Inequality 3 | 2x-2 | +16

*asked by karina c on June 3, 2013* -
## Calculus

Find the absolute extrema of the function. (Round your answer to three decimal places.) f(x) = xe^-x2 on [0,2] Absolute maximum value: at x = Absolute minimum value: at x =

*asked by Anonymous on July 12, 2013* -
## Calculus

Find the absolute extrema of the function. (Round your answer to three decimal places.) f(x) = xe-x2 on [0,2] Absolute maximum value: at x = Absolute minimum value: at x =

*asked by Shan on July 12, 2013* -
## Last equation question

where would I graph this?? once again I hate fractions and equations... graph the equation x=7/2 can someone help me figure this out thanks last question of the day..

*asked by Kathy on October 8, 2009* -
## Calculus

Find the absolute extrema of the function on the interval [2, 9]. (Round your answers to the nearest hundredth.) g(x)=x/(ln(x)) Absolute minimum: at x = Absolute maximum: at x =

*asked by Anonymous on July 12, 2013* -
## Math(Calculus)

Im having a real difficult time solving this question. Find the absolute extrema of the function. h(x) = e^x^(2) - 4 on [-2,2] Absolute maximum value: at x = Absolute minimum value: at x =

*asked by Chris on April 25, 2017* -
## maths

Draw the graph of y=x^2-4x-5 and use it to solve the equations. a)x^2-5x-3 b)x^2-3x-4 This should be a graph of quadratic equation. Range -3 to 5?

*asked by knuckles on November 18, 2019* -
## Physics. Error equations. Please help!

These two equations concern a lab on the measurement of E/M by the Brainbridge Method. I need to derive the absolute error for two different equations, the first one is: e/m = 2V/B2R2 treat (e/m) as a SINGLE VARIABLE when doing the derivation. The second

*asked by Kyle on November 20, 2012* -
## Math

I am struggling with absolute value functions, especially equations. I need help with these questions: 1. |x^2 - 2x - 3| - 4 2. | x^2 - 2x| = 1

*asked by Anonymous on March 28, 2019* -
## mat

Is their a free online calculator to graph linear equations? How do you graph x=y+3

*asked by Bryan on April 21, 2009* -
## Calculus

Use a graphing utility to graph the polar equation shown below. r = cos 5Θ + n cos Θ, 0 ≤ Θ ≤ π For the integers n = -5 to n = 5. As you graph these equations, you should see the graph change shape from a heart to a bell. I'm sorry. I'm having

*asked by Iris on December 6, 2016* -
## Algebra 1

What would the graph look like for y= the absolute value of 2x plus 1

*asked by Steve on December 29, 2014* -
## Algebra 1

Graph y= absolute x -2

*asked by Steve on December 7, 2014* -
## Algebra 1

What does the graph of y = absolute X-2 look like?

*asked by Steve on December 13, 2014* -
## Algebra 1

What does the graph y = - absolute value of X -4 look like.?

*asked by Steve on December 13, 2014* -
## Math

1. Suppose a and b are integers, and the absolute value of a is > than the absolute value of b. Must a be greater than b? Use examples to support your answer. 2. Do decimals have opposites? Explain. 3. For what values of x does the absolute value of x

*asked by Calla on September 22, 2013* -
## alg.

solve and graph 2x-y=4 2x-y=6 would this be x=2+0.5y x=3+0.5y and then graph as that??????? not really sure what i am doing here Put both equations in the form of y=mx +b Then observe that the slope is the same, the lines are parallel, and have no common

*asked by clueless on May 20, 2007* -
## Algebra

How can you tell an equation's real or imaginary roots just from its graph, without knowing the equation? I have to look ath the graph of a parabola, absolute value, and a negative third degree equation and do so? Are there any links that could explain

*asked by Anneliese on November 2, 2009* -
## trignometry

Some equations cannot be solved by symbolic manipulations. Use a graph to find all solutions of the equation sin 8x = 2x - 1. Show the details in a sketch of the graph.

*asked by jojo on October 24, 2015* -
## Algebra

How do you graph 2 equations and then find the common area on the graph?

*asked by Jo on May 4, 2011* -
## algebra

how do u graph equations?? it says use the ggraphing method but i don't know how to graph them

*asked by mee on January 30, 2011* -
## Calculus

f(x)=xe^(-2x) with domain 0< or equal to x< or equal to 10 find all values of x for which the graph of f is increasing and all values of x for which the graph is decreasing give the x and y coordinates if all absolute max and min points

*asked by John on November 30, 2010* -
## college algebra

On the graph, plot all relevant points for y=the absolute value of x-1. Then give the equation for a graph that shifts up 3 units and to the left 4 units. If it is a function, give its domain and range. Thank you!!

*asked by jenny on October 23, 2008* -
## math

f(x) = 0 if x

*asked by Robina on February 6, 2015* -
## Algebra

Graph the absolute value inequalities. I just can not get this. Please help! x + 2y ¡Ý 6

*asked by Shana on September 10, 2007* -
## calculus

Let M=1000. Which of the conditions is equivalent to f(x)= 1/((4x-12)^2)>M? a. absolute value of (x+3) is greater than or equal to .00158 b. absolute value of (x+3) is greater than or equal to .0553 c. absolute value of (x-3) is less than .00791 d.

*asked by Brian on September 14, 2011* -
## Calculus

Can someone explain this question to me? What intervals should I use to test whether or not the graph is concave up or down. I know that no points or equations are given so we have to estimate. Here is the URL for the graph. imgur dotcom/FdQCV

*asked by Jake on March 3, 2012* -
## calculus

2) Let g(s)= t(4−t)^1/2 on the interval [0,2]. Find the absolute maximum and absolute minimum of g(t) on this interval. Enter DNE if the absolute maximum or minimum does not exist. The absolute max occurs at t= . The absolute min occurs at t=

*asked by spud on October 17, 2014*

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