Tuesday

September 23, 2014

September 23, 2014

Number of results: 104,197

**Discrete Math: Equations of a Line**

Find parametric equations for the line that passes through the point (0, -1, 1) and the midpoint of the line segment from (2, 3, -2) to (4, -1, 5). I don't know how to solve this problem.
*March 14, 2008 by Anonymous*

**Discrete Math: Equations of Line in a Plane**

I'm stuck on these questions. Can you please show me a step by step solution? 20) For each of the following, find a normal vector, a direction vector, and a point of each line. Note, normal vector means perpendicular to the direction vector. a) 3x - 6y = 14 TEXTBOOK ANSWER: ...
*March 12, 2008 by Anonymous*

**discrete math**

how do i solve linear equations? -4(k-2)+3(k+1) =7.
*September 11, 2008 by kennedy*

**Math**

In your own line of work, give one example of a discrete and one example of a continuous random variable, and describe why each is continuous or discrete.
*October 11, 2011 by Jen*

**math**

Hi, How could I find the line of best fit? I plotted each of the equations I had for a problem I'm solving. The equations were linear (y=ax+b) and quadratic (y=ax+b+c). I'm supposed to find out which line is the most appropriate for the data that is given to me. When looking ...
*March 17, 2008 by Irene*

**Elementary Math**

The temperature of a cup of coffee is a discrete or continuous random variable? Am I correct " Discrete"
*August 8, 2009 by J.J.*

**MATH**

Determine whether the situation calls for a discrete or continuous random variable. The braking time of a car Is it discrete?
*September 8, 2009 by Jalynn*

**MATH**

(A) Classify the following as an example of nominal, ordinal, interval, or ratio level of measurement, and state why it represents this level: zip codes for the state of Pennsylvania (B) Determine if this data is qualitative or quantitative: Nationality (C) In your own line of...
*November 11, 2011 by Jennifer*

**Discrete Mathematics**

3.Does it matter if we join two vertices with a straight line or a curved line when we represent a graph by drawing it on paper?
*August 8, 2013 by Joy*

**research and evaluation**

Give examples of both discrete and continuous data? What makes them different? Is the measurement of money continuous or discrete? Explain. Can discrete data be analyzed using the normal distribution? Why or why not?
*November 18, 2010 by sue*

**math**

1. A skateboard ramp has a 158º entry angle. Find the measure of ∠1. A.) 22º B.) 68º C.) 78º D.) 58º 2. Which of the following equations parallel to the line passing through A(-2, 7);B(-2, -2)? A.) y = -2 B.) y = x C.) 3x = 5 D.) -2x = 7y 3. Which of the following ...
*October 30, 2013 by kaitlyn*

**Stats**

Determine the following random variables discrete or continuous: a)Number of fish I caught during 2 hours? I said: discrete b)Temperature of a coffee cup? I said: continuous c)Height of a 2-year-old maple tree? I said: continuous d) Number of credit cards I have in my wallet? ...
*February 8, 2014 by Ashley*

**Math**

Find parametric equations and symmetric equations for the line of intersection of the given planes. x + y + z = 2, x + z = 0 X=1 y = Z= x=, y=
*April 13, 2010 by Mike*

**statistics, are my calculations correct?**

classify the following as discrete or continuous random variables: a) the time it takes to run a marathon- i think that it is discrete b) the number of fractions between one and two- i think that it is discrete? c) a pair of dice is rolled and the sum to appear on the dice is ...
*October 23, 2010 by mary- please check calculations.*

**Math**

How do I write the Symmetric Equation of a line given the following parametric equations: (where t is a scalar) x=0t y=0t z=1+1t I know normally I would solve each equation for t and set the equations equal to one another. However, I can not solve for t in the first two ...
*November 3, 2010 by Dwight*

**Math**

How do I write the Symmetric Equation of a line given the following parametric equations: (where t is a scalar) x=0t y=0t z=1+1t I know normally I would solve each equation for t and set the equations equal to one another. However, I can not solve for t in the first two ...
*November 4, 2010 by Dwight*

**math**

19. Which statement describes the relationship between the line graphs of the equations below? y=-2x+4 y=0.5x+4 A.The line graph are the same line. B.The line graph are parallel lines. C.The line graph are perpendicular lines. D.The line graphs intersect, but are not ...
*August 14, 2014 by vincent*

**Stats**

Classify the following as discrete or continuous random variables. (A) The time it takes to run a marathon (B) The number of fractions between 1 and 2 (C) A pair of dice is rolled, and the sum to appear on the dice is recorded (D) The length of a broad jump I got: (A) ...
*October 24, 2011 by Jennifer*

**Is this right?? Stats....**

Classify the following as discrete or continuous random variables. (A) The time it takes to run a marathon (B) The number of fractions between 1 and 2 (C) A pair of dice is rolled, and the sum to appear on the dice is recorded (D) The length of a broad jump I got: (A) ...
*October 25, 2011 by Jennifer*

**math**

Determine whether the situation calls for a discrete or continuous random variable. The number of freshmen in the required course, English 101 The braking time of a car I think the first one discrete and the second is continous is this correct?
*April 25, 2010 by KiKi*

**math-please help!**

Determine whether the situation calls for a discrete or continuous random variable. The number of freshmen in the required course, English 101 The braking time of a car I think the first one discrete and the second is continous is this correct?
*April 25, 2010 by KiKi*

**math**

Solve each system of linear equations by both graphical and algebraic line 1 x+2y=4 line 2 x-y=0
*August 21, 2011 by Abel*

**algebra**

how would i find an equation of a line that goes through points(1,6) and (3,10)?? thanks A straight line is y=mx+b Substitute the points to make two equations. 6=m(1)+b 10=m(3)+b Two equations; two unknowns, m and b. Solve for m and b, then plug back into y = mx + b. That will...
*December 22, 2006 by jasmine*

**Algebra**

Discuss the steps necessary to carry out each activity. Describe briefly what each line looks like in relation to the original given line. Answer these two questions briefly in your own words: What does it mean for one line to be parallel to another? What does it mean for one...
*February 20, 2014 by Patrice Mason*

**Math**

The number of people waiting in a line for a movie hours (x) people (y) 1 170 2 230 3 290 4 350 Is this discrete or continuous data?
*February 16, 2011 by Sally*

**Geometry**

1.) A skateboard ramp has a 158° entry angle. Find the measure of ∠1. 2.) Which of the following equations is parallel to the line passing through A(-2, 7);B(-2, -2)? 3.) Which of the following equations would graph a line parallel to 3y = 2x - x + 5? *Please help me!
*October 29, 2013 by Kaitlyn*

**math**

In triangle ABC, angle C is congruent to angle A, line BC=2x-5, line AB=x+5 and line AC=x+10. Find x. The problem didn't have a triangle drawn so i drew it myself. I tried many equations but when i substitute it it didn't work.
*November 16, 2008 by mark*

**mathematics **

If the line l has parametric equations x=5-3t, y=-2+t, z=1+9t, find the parametric equations for the line through p(5,4,-3) that is parallel to l.
*June 27, 2014 by malipa*

**Discrete Math**

There are 150 students taking Discrete Mathematics II, Calculus II, and Physics I courses. Of these 51 are taking Discrete Mathematics II, 111 are taking Calculus II, and 63 are taking Physics I. There are 41 taking Discrete Mathematics II and Calculus II, 32 students taking ...
*April 6, 2014 by Anonymous*

**math/equations**

Hi. I am having some issues with this one. Give the equation of the line that is perpendicular to the line y=x+6 and passes through point (0,-4). Thank you so very much!!!
*July 29, 2010 by amy*

**Math**

What does it mean if a line in R^3 is parallel to the xy-plane but not to any of the axes. I really don't know what this means in terms of how the parametric and symmetric equations of the line should look. Please help.
*October 27, 2010 by Kate*

**Math**

What does it mean if a line in R^3 is parallel to the xy-plane but not to any of the axes. I really don't know what this means in terms of how the parametric and symmetric equations of the line should look. Please help.
*November 2, 2010 by Kate*

**Pre- Algebra**

Given an equation of a line, how do I find equations for lines parallel to it going through specified points Simplifying the equations into slope-intercept form. 1. y= -2x -4; (1, 3) how do I write the equation of a line parallel to the given line but passing through the given...
*August 14, 2013 by Roosevelt*

**Math**

the question i need help with is: Classify the random variable as finite discrete, infinite discrete or continuous. The random variable given is the number of hours a child watches television on a given day.
*June 8, 2011 by Winnie*

**Math (Calculus)**

Use the disc method to find the volume of the solid generated by revolving the region bounded by the graphs of the equations about the indicated line. y=x^3, y=0, x=2 a)the x-axis b)the line x=4
*May 9, 2014 by Sherman*

**help!**

Can you please give me one of them so I cansolve for the other one?PLease! The general formula for a straight line is y = mx + b. Just plug the points into the equation to arrive at two equations. 6=2m+b 10=4m+b you have two equations and two unknowns. Solve them ...
*November 1, 2006 by margie*

**Physics**

Explain atomic line spectra in terms of transitions between discrete energy levels.
*February 9, 2011 by Hakuoh*

**Stats**

1.Number of people in attendance at a baseball game qualitative/ordinal qualitative/nominal quantitative/discrete quantitative/continuous 2. number of tracks on a CD qualitative/ordinal qualitative/nominal quantitative/discrete quantitative/continuous 3.eye color qualitative/...
*August 11, 2014 by Kathryn*

**Math**

What will the graph look like for a system of equations that has no solution? A. The lines will be perpendicular. B. The lines will cross at one point. C. Both equations will form the same line. D. The lines will be parallel. I think it is D..?
*April 9, 2013 by Cassie*

**maths..plse helppppppp**

Please help me to find the separate equations of the line represented by following equations: a) x^2+2(cosec a)xy-y^2=0 b) x^2+2xy. tan a-y^2=0
*December 7, 2012 by ragini*

**Vectors**

3 planes; $: x+2y-2z-6=0 %: 2x-y+z+8=0 £: 2x-y+2z+3=0 (a)(i)Find the cartesian equation for the plane @ parallel to $ and containing the point (1,1,2) (ii)Calculate the distance between $ and @ (b)(i)Find the parametric equations for the line of intersection of the planes $ ...
*April 25, 2010 by Anonymous*

**vectors**

3 planes; $: x+2y-2z-6=0 %: 2x-y+z+8=0 £: 2x-y+2z+3=0 (a)(i)Find the cartesian equation for the plane @ parallel to $ and containing the point (1,1,2) (ii)Calculate the distance between $ and @ (b)(i)Find the parametric equations for the line of intersection of the planes $ ...
*April 25, 2010 by Anonymous*

**Math**

For each of the following, find the parametric equations of the line that passes through the point P with direction vector d. In each case, find two points on the line different from P. a) P(1,1) d=(4,-4) b) P(5,0) d=(1,3) answer at the back of the book is: a) x=1+t y=1-t ; (2...
*March 23, 2009 by Steffy*

**discrete data**

Can discrete data be analyzed using a normal distribution?
*June 2, 2011 by Anonymous*

**Discrete Math**

I am really stuck on these problems. I've worked a lot of them but I can't get these. Sometimes I think I know the answer but I can't show how I got it. 1.) Solve each matrix equation for X. 2X + 5A = B 2.) Find the following matrices: a. AB b. BA A= 2 4 3 1 4 2 B= 3 2 0 -1 -3...
*February 25, 2010 by Ryan*

**Math 116**

Consider the following system of equations. y=2x-2 y-2x=9 What can you conclude about the system of equations? a. The system of equations is inconsistent. b. The system of equations is dependent. c. The system of equations is independent. d. none of these.
*June 21, 2013 by Queta*

**Adv. Math.**

Write a vector equation of the line that passes through point P and is parallel to a. Then write parametric equations of the line. P(-1, 3); a=(-6, -1) MY ANSWER: (x+1, y-3) = t(-6, -1); x= -1-6t, y=3-t P(0, 5); a=(2, -9) MY ANSWER: (x, y-5) = t(2, -9); x=2t, y=5-9t
*June 17, 2009 by James*

**Math**

Give the equation of a line perpendicular to the line y = -8x + 8 having the y-intercept 2 units below the y-intercept of the given equation. At what point the two equations cross each other?
*January 9, 2010 by Anna*

**math**

Give the equation of a line perpendicular to the line y = -8x + 8 having the y-intercept 2 units below the y-intercept of the given equation. At what point the two equations cross each other?
*February 28, 2010 by Jillian*

**calculas**

Find the equations for the tangent line and normal line to the curve for f(x)=(x^4)+(2e^x) at the point (0,2)?
*September 28, 2010 by john*

**calculus**

Find the parametric equations for the line that contains the point (3,1,-4) and is parallel to the line r(t)=(1+2t)i+(-3-t)j+(5+5t)k
*January 15, 2013 by Zac*

**calculus**

Find equations of the tangent line and normal line to the curve at the given point. y = x^4 + 2e^x, (0,2)
*October 14, 2008 by Vishnu*

**Maths**

Consider the line defined by the parametric equations x=3d-10, y=2d+1. The y-intercept of this line can be expressed as a/b. Find a and b.
*October 27, 2013 by CHRIS*

**Discrete Mathematics**

The augmented matrix A represents a system of three real-valued equations in three unknowns. Which of the answer choices would result from the usual first step of applying Gauss-Jordan elimination?
*July 30, 2013 by Joy*

**Discrete Mathematics**

15. The augmented matrix A represents a system of three real-valued equations in three unknowns. Which of the answer choices would result from the usual first step of applying Gauss-Jordan elimination? A = (1 4 2 3) A = (2 9 13 18) A = (3 10 8 15)
*July 30, 2013 by Joy*

**math**

Which of the following equations represents the equation for the line that is parallel to the given line and passes through the given point? y= 1/5 x - 10; (15, -16) A. y = -5x +19 B. y = 1/5x + 91/5 C. y = 1/5 x - 19 D. y = 5x - 19 I do know that to be parallel the slopes ...
*April 11, 2012 by Jane*

**equations**

does it make a diffrence what two points you chooose on a stragight line to find the slope of the line
*September 3, 2008 by isaiah*

**Math 1**

Consider the following system of equations. y = 4x - 4 y - 4x = 3 What can you conclude about the system of equations? A) The system of equations is inconsistent. B) The system of equations is dependent. C) The system of equations is independent. D) none of these
*October 20, 2013 by sam*

**math**

Consider the following system of equations. y = 2x - 2 y - 2x = 7 What can you conclude about the system of equations? The system of equations is inconsistent. The system of equations is dependent. The system of equations is independent. none of these
*September 8, 2014 by robert*

**Calculus grade 12**

1. a) Write the vector and parametric equations of the line through the points A(6, -1, 5) and B(-2, -3, 6). b) Find another point on the line in (a).
*May 3, 2012 by J*

**college algebra**

Write an equation of the line parallel to the line given by 3x-2y=8 and having the same y-intercept as the line given by 2y+3x=-4 (show work) I am stuck with this problem. Can you please show me how to do these types of equations? Thank you
*February 9, 2013 by Clay*

**calculus**

use the definition of the derivative to calculate f'(x), if f(x)= SQRT(2x) and find the equations of the tangent line and the normal line to the graph of f at x=2
*November 13, 2010 by Raj*

**linear equations**

Write the equation of a line in slope-intercept form that is perpendicular to the line and passes through the point (-9, 4).
*December 14, 2011 by nick*

**Calculus**

1. a) Write the vector and parametric equations of the line through the points A(6, -1, 5) and B(-2, -3, 6). b) Find another point on the line in (a). ----- This is what I got for a) r = 6i-j+5k + t(-8i-2j+k) x = 6-8t y = -1-2t z = 5+t I need help with b)
*May 4, 2012 by J*

**precals**

find the equations of the lines to the line whose equations is y-17 / x -13 = -3 /2 If these lines each pass through the point (6,-5) Gracias`
*April 25, 2010 by treeema*

**Calc 3**

Find the parametric equations for the tangent line to the curve with the given parametric equations at specified point. x= e^t y=te^t z=te^(t^2) (1,0,0)
*November 10, 2010 by Rebecca *

**Calc 3**

Find the parametric equations for the tangent line to the curve with the given parametric equations at specified point. x= e^t y=te^t z=te^(t^2) (1,0,0)
*November 10, 2010 by Rebecca *

**Math - equations of lines**

A line has the same x-intercept as [x,y,z]=[-21,8,14]+t[-12,4,7] and the same y-intercept as [x,y,z]=[6,-8,12]+s[2,-5,4]. Write the parametric equation of the line.
*September 4, 2010 by Shaila*

**Math - equations of lines**

A line has the same x-intercept as [x,y,z]=[-21,8,14]+t[-12,4,7] and the same y-intercept as [x,y,z]=[6,-8,12]+s[2,-5,4]. Write the parametric equation of the line.
*September 5, 2010 by Shaila*

**Calculus**

Find parametric equations for the line through the point (0,2,2)that is parallel to the plane x+y+z = 2 and perpendicular to the line x=1+t, y=2−t, z=2t. (Use the parameter t.) (x(t), y(t), z(t)) =
*January 31, 2014 by Jale*

**math**

can someone correct these for me. 8x –4y = 16 y = 2x –4 My answer: This problem does not have a unique solution. This problem therefore is consistent and dependent These equations are the same. If you solve the first one for y, you will see that the two equations end up equal...
*December 23, 2006 by jasmine20*

**linear equations -math **

Find the equation of a line through the points (-2,3)and (-4,5)
*November 3, 2010 by Brittany *

**calculus**

Use the disk or the shell method to find the volume of the solid generated by revolving the region bounded by the graphs of the equations about each given line. y = x3 y = 0 x = 3 a)the line x = 4
*January 25, 2012 by ReinaS*

**math**

line L bisects and is perpendicular to line AB and line CD. Line AB = CD line AB = 140 and line LM = 24 what is the lenght of line NQ
*June 27, 2013 by debra*

**Calculus**

Find the parametric equations for the line of intersection of the planes x+y+z=3 and x-y+2z=2 I took the cross product of the 2 equations and got 3i-j-2k I then set z=0 and got x=5/2 and y=1/2. I got: x=5/2 +3t y=1/2-t z=-2t However, the answers are supposed to be: x=5/2-(3/2)...
*December 4, 2012 by Mackenzie*

**Math: Equations of Line in a Plane**

I'm stuck on these questions. Can you please show me a step by step solution? 20) For each of the following, find a normal vector, a direction vector, and a point of each line. Note, normal vector means perpendicular to the direction vector. a) 3x - 6y = 14 TEXTBOOK ANSWER: ...
*March 10, 2008 by Anonymous*

**8th grande transition algebra**

well, i am doing a math crossword puzzle on linear equations. I really need some help. here are the questions: what is Ax+By+C called? what are numbers used to graph a point? what is not a straight line? where does a line pass threoug the x-axes? what is the y values in a set ...
*November 18, 2009 by ktm*

**Calculus**

Find the parametric equations for the line of intersection of the planes x+y+z=3 and x-y+2z=2 I took the cross product of the 2 equations and got 3i-j-2k I then set z=0 and got x=5/2 and y=1/2. I got: x=5/2 +3t y=1/2-t z=-2t However, the answers are supposed to be: x=5/2-(3/2)...
*December 4, 2012 by Mackenzie*

**MATH/ EQUATIONS**

Hi. I have a question I need to write an equation that is parallel to the line y= -4x +3 and a y-intercept of -5. Thank you!
*July 28, 2010 by Jessica*

**math**

find the parametric equations of the line that passes through the point p(2,3,4)& parallel to the xz-plane
*December 19, 2012 by Bayeh*

**Math**

Need help on these questions! Find the slope of each line. 1. Y=x+1 Solve the equations. 2. -6+x/2=2 Simplify each expression. 3. -4(5n-5)+6(1-7n)
*December 17, 2013 by Anonymous*

**Last equations question**

The line y=0.15x+0.79 represents an estimate of the average cost of gasoline for each year. The line 0.11x-y=-0.85 estimates the price of gasoline in January of each year (Bureau of Labor Statistics, 2006). a)Do you expect the lines to be intersecting, parallel, or ...
*October 25, 2009 by Anna*

**math**

graph the line with slope 1/2 passing through the point(-5,-2) find the slope of the line 5x+5y=3 write answer in simplest from consider the line 2x-4y=4 what is the slope of a line perpendicular to this line. what jis the slope of a line parallel to this line
*February 10, 2013 by Anonymous*

**Algebra**

Write a system of inequalities to express the exterior of the triangle ABD if A=(-2,7), B=(4,0), and C=(1,-3). Please help! gracias<3 Derive equations for the three lines connecting the three points. Then change the equations to inequalities to represent the region on the ...
*December 20, 2006 by Lily*

**Calculus**

Find parametric equations for the tangent line to the curve with the given parametric equations at the specified point. x=4cos(t) y=4sin(t) z= 10cos(2t) (2sqrt2,2sqrt2,0)
*April 20, 2010 by Mike*

**Math**

Write an equation in slope-intercept form of the line whose parametric equations are: x = (1/2)t +2/3 and y = t - 3/4. a) y = 2x - 7/12 b) y = 2x + 7/12 c) y = -2x - 7/12 d) y = -2x - 25/12 I think it is D.....?
*June 3, 2009 by Sophie*

**math**

If the cards contain the following equations, what is the probability that a student will graph a line whose slope is 3? 3y = 9x + 3 x(x + 3) = 0 3x + y = 0 x = 3y x2 + 3 = 0 y - 3x = 0
*December 13, 2010 by neisha*

**math linear equations**

would the equation in slope-intercept form of the line which passes through 0,6 and 4,3 be y = -3/4x + 6?
*May 31, 2013 by Anonymous*

**Algebra/equations**

Write an equation of the the line containing the given point and perpendicular to the given line. (7,-5); 9x+7y = 3. What I have so far. y-9=(1/9(x-3). Not sure after this.
*November 26, 2010 by AMY*

**precalc **

There is a line with two rectangular pt (3, 4)&(6,-3)write this line as a pair of parametric equations then show how you can eliminate the paparameter to return to rectangular form
*April 26, 2013 by brady*

**MAT221**

consider the line 8x-5y=-4 find the equation of the line that is perpendicular to this line and passes through the point (-4,-4) find the equation of the line that is parallel to this line and passes through the point (-4, -4) i keep getting different answers on the ...
*June 29, 2014 by Kia*

**Math - intersection of planes**

You are given the following two planes: x+4y-3z-12=0 x+6y-2z-22=0 a) Determine if the planes are parallel b) Fine the line of intersection of the two planes. c) Use the two original equations to determine two other equations that have the same solution as the original two. d) ...
*September 4, 2010 by Shaila*

**math**

Explain why the simultaneous equations y=1/2x+2 and 2y-x:4 have an infinite number of solutions. What is diffrent about these equations compared with the equations in the first question ( the equations were y=2x+3 and 5y-10x=5)? What is similar? ( include work to prove why and...
*February 24, 2011 by CJ*

**Reading**

Which line in the poem contains an example of onomatopoeia? A. Line 6 B. Line 7 C. Line 14 D. Line 15 Line 6: and you'll forget all about that broccoli you chop Line 7: Rock candy looks like beautiful glass Line 14: but spinach tastes all gritty and sandy Line 15: Taffy is ...
*November 14, 2011 by Bob*

**READING **

Which line in the poem contains an example of onomatopoeia? A. Line 6 B. Line 7 C. Line 14 D. Line 15 Line 6: and you'll forget all about that broccoli you chop Line 7: Rock candy looks like beautiful glass Line 14: but spinach tastes all gritty and sandy Line 15: Taffy is ...
*November 14, 2011 by Bob*

**math**

1)In the figure, the vertices of right-angled isosceles triangle ABC are A, B(2,0) and C(8,0) respectively. find the equations of AB and AC 2)If the x-intercept and y-intercept of the straight line L: B(y-2) =Ax+8 are -8 and 3 respectively, find a)the value of A and B b)the ...
*May 11, 2010 by Help*

**math**

Consider the following system of equations. Y = 3x – 7 Y - 3x = 5 a) The system of equations is inconsistent. b) The system of equations is dependent. c) The system of equations is independent. d) none of these
*January 27, 2013 by monet*

**Calc I **

I need to find the equations of the tangent and normal line for x^2-y^2=16, at the point (-5,3). I have to show every detail for my work...then use graphing software to enter my equations, so can anyone help me showing all the details of the work so that I can figure it out?? ...
*June 28, 2011 by Kejo, Help!!!!*

**bobpursly & countiblis,math**

I thought that we can solve anything with equations is it always polynomials. Isn't this the same thing as finding the unknown for an equation. As i said in my previous message or am i wrong. Also what about the rational expressions what are some challenges about working with ...
*March 5, 2007 by jas20*

**Discrete Math**

True or False? Homogeneous linear recurrence equations are linear combinations of power functions. I think the answer is false because although a homogeneous linear recurrence equation is a linear combination, it is composed of constant coefficients. However to solve this ...
*May 31, 2013 by Sarah*

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