Friday

December 19, 2014

December 19, 2014

Number of results: 17,226

**Calculus ll - Arc Length/Simpson's Rule**

Use Simpson's Rule with n=10 to estimate the arc length of the curve. Compare your answer with the value of the integral produced by your calculator. x = y + y^(1/2), 1 ≤ y ≤2
*October 15, 2010 by Morgan*

**Calculus - Simpson's Rule and Arc Length**

Can any show me step by step on how to get this? I keep on getting different answers... Thank You! Use Simpson's rule with n=10 to estimate the arc length of y=x^(-1/3), for 1 <= x < 6.
*July 31, 2014 by Chelsea*

**calc: simpson's rule & arc length**

i'm still getting this question wrong. please check for my errors: Use Simpson's Rule with n = 10 to estimate the arc length of the curve. y = tan x, 0 <or= x <or= pi/4 .. this is what i did: y' = sec(x)^2 (y')^2 = [sec(x)^2]^2 [f'(x)]^2 = sec(x)^4 Integral of sqrt( 1 + ...
*June 13, 2007 by COFFEE*

**Calculus**

use the simpson's rule with n=10 to estimate arc length of y=x^(-1/3), for 1<=x<6
*July 31, 2014 by Rick*

**Calculus**

Use Simpson's Rule with n = 10 to estimate the arc length of the curve. y = tan x, 0 < x < π/9
*February 4, 2014 by Sandy*

**Maths C**

I need to compare and contrast Weddle's Rule and Simpson's rule and outline a distinguishing difference between them. I understand Simpson's Rule but I am finding it difficult to obtain clear information about Weddle's rule.
*June 23, 2011 by Sam*

**calculus SIMPSON RULE**

Use Simpson's Rule and all the data in the following table to estimate the value of the integral . x -16 -15 -14 -13 -12 -11 -10 y -8 9 4 9 -5 -9 3
*March 14, 2011 by aj*

**Calculus II - Simpson's Rule **

Find the Error resulted from approximation by Simpson's Rule: integral (from 0 to 1) sqrt( 1+x^3) dx ... compute the result for n=8
*February 17, 2014 by Chelsea*

**calc arc length**

Find the length of the arc along f(x) = integral from 0 to x^3 sqrt(cos t) dt on the set of x [0, pi/3].
*December 19, 2012 by Liz*

**AP Calc B/C**

Find the arc length of one arch of the sine curve. I started it by doing y=sinx, y'=cosx arc length= integral of sqrt(1+cos^2x)dx from pi/2 to 3pi/2 but I don't know how to integrate that! Thank you!
*September 13, 2014 by Anon*

**Math Arc Length**

Find the arc length corresponding to an angle of a degrees on a circle radius of 4.9 Enter the exact answer. I put the arc length was 4.9api/180 got it wrong. Any help?
*October 31, 2014 by Taylor*

**multivariable calc**

Please help! Find the point where the curve r(t) = (12sint)i -(12cost)j +5k is at a distance 13pi units along the curve from the point (0,-12,0) in the direction opposite to the direction of increasing arc length. (Hint: ty -13pi for arc length)
*December 8, 2007 by Chris*

**Simpson's rule**

Is the simpson's rule always more accurate than the midpoint rule and trapezoidal rule? Not always; it is possible that the midpoint and/or trapezoidal rule determine exact values. 1. Some functions values for a function f are given below. x 0 0.5 1.0 f(x) 3 4 11 What is the ...
*October 24, 2006 by 413*

**calc**

find the arc length of f(x)=x^2/2
*March 15, 2011 by tom*

**math**

Use the Trapezoidal Rule, the Midpoint Rule, and Simpson's Rule to approximate the given integral with the specified value of n. (Round your answers to six decimal places.) The integral of e^(3sqrt(t)) sin3t dt from 0 to 4. n=8
*July 1, 2014 by sara*

**Calculus**

A pendulum swings through an arc length of 1120 cm (Swing #1). With each further swing, the arc length is reduced by 15 % State the growth factor. Calculate the length of the arc in swing #5 I think im supposed to use this formula again, but I dont know how to use it. Tn = ar^n-1
*September 21, 2011 by Anonymous*

**calculus**

Use the trapezoidal rule and simpson's rule to approximate the value of the definite integral âˆ«2,1 ln xdx; n =4
*March 6, 2012 by Anonymous*

**Calculus Hard Question**

A pendulum swings through an arc length of 1120 cm (Swing #1). With each further swing, the arc length is reduced by 15 % State the growth factor. Calculate the length of the arc in swing #5 I think im supposed to use this formula again, but I dont know how to use it. Tn = ar...
*September 21, 2011 by Anonymous*

**calc 3**

find the arc length of the curve r(t)= <6sqrt(2),e^t,e^(-6t)>
*September 24, 2010 by ashley*

**math**

Whats the difference between an arc [of a circle]'s length and measure? And how do you find each of them? The "measure" of an arc is the angle that it subtends from the center of the circle. Call that angle A. The length of the arc is 2 pi R * [A/(2 pi)] = R*A, if A is in ...
*March 20, 2007 by Emily*

**calculus 2**

use the simpsons rule with n=10, arc length y=^3√x, for 1<=x<6
*July 26, 2014 by sarah*

**calc II**

Find the arc length of the graph of the function over the interval [1,2].
*January 28, 2011 by Anonymous*

**calculus 2**

use the simpsons rule with n=10, arc length y=^3sqaure root x, for 1<=x<6
*July 29, 2014 by Ryan*

**math**

evaluate: cos (arc sin (4/5) - arc tan 2) with out using a calc.
*April 15, 2010 by krista*

**Calc**

Find the arc length of the graph of the function over the indicated interval. y = (x⁵/10) - (1/(6x³)) , [1,20] Thank you so much!!
*February 6, 2011 by Erica*

**Geometry**

What is the radius if: degree of measurement of arc=30 length=1/3xy(pi) My answer was 8xy. degree of measurement of arc=40 length=8/9(t)(pi) My answer was 9t. degree of measurement of arc=18 length=6(y)pi My answer was 45y. These are the questions I missed, along with my ...
*June 14, 2010 by Temperance*

**Math rem**

2.Find the length of the arc in a circle if the radius of the circle is 24cm and the degree of the arc is 90o 3.Find the length of the arc if a circle if the degree if the arc is 120o and the length of the radius is 8cm. 4. A circle has a radius of 7. Find the diameter (D) and...
*February 11, 2013 by bs*

**CALC**

what is the arc length of y=x^4/8 + 1/(4x^2) [-1,-2] i have tried this many times but i am not achieving the answer of 33/16 which is supposed to be correct....much help is appreciated
*February 3, 2009 by josh*

**Calc 2**

I'm asked to find the arc length of the curve y=3+(1/2)sinh(2x) from 0 to 1. I figured it out up to the integral of sqr(1+(cosh(2x))^2) from 0 to 1, but I'm not sure how to go on to solve it.
*April 3, 2012 by MT*

**calculus**

f(1)= 20, f(3)=13, f(5)=15, f(7)=16, f(9)=11, on [0,6] a, used midpint rule with n=5 to estimate intergral form 0 to 10 f(x)dx b, use trapezoidal rule with n=4 to estimate intergral from 1 to 9 f(x)dx c, used simpson's rule with n=4 to estimate intergal from 1 to 9 (x)dx
*December 12, 2011 by kyle*

**Calculus**

Using the trapezoid rule with n = 8 to approximate the arc length of the graph of y = 2x^3 - 2x + 1 from A(0,1) to B(2,13) you get (to three decimal places): A.) 6.900 B.) 13.896 C.) 14.093 D.) 13.688 E.) 13.697
*March 12, 2012 by Mishaka*

**Trig**

Find the radian measure of the central angle of a circle of radius r that intercepts an arc of length s.? Radius, r=16 ft Arc length, s=10 ft
*May 18, 2012 by Sue*

**maths**

find the radius of the circle if length of arc is 4p cm and angle made by the arc at the centre is 40 deg.find the area made by the arc.
*February 23, 2013 by urvashi*

**Calculus (Definite Integrals - Arclength)**

Using the trapezoid rule with n = 8 to approximate the arc length of the graph of y = 2x^3 - 2x + 1 from A(0,1) to B(2,13) you get (to three decimal places): A.) 6.900 B.) 13.896 C.) 14.093 D.) 13.688 E.) 13.697
*March 12, 2012 by Mishaka*

**Physics**

While riding a Ferris wheel, the rider determines that the Ferris wheel makes 1.5 revolutions per minute. a) knowing that the diameter of the Ferris wheel is 100 ft, determine the angular speed (in rad/s) of the Ferris wheel. b) Determine the linear speed (in ft/s) of the ...
*October 31, 2011 by Adam*

**geometry**

arc AB is 55 degrees. the radius of the circle is 4 inches. what is the length of arc AB?
*December 8, 2010 by Anonymous*

**precalculus**

The question is...find the radian measure of the central angle of a circle of radius r that intercepts an arc of length s. Then it gives the radius r of 27 inches and an arc length s of 6 inches. How do I do that?
*February 28, 2010 by Megan*

**geomtry **

find the arc length of the minor arc withe degree of 120 and a radius of 8
*April 18, 2013 by justin *

**Bobby**

Find the length (in cm) of an arc of a circle with radius 12 cm if the arc subtends a central angle of 30°.
*January 19, 2014 by Kathy*

**calc: arc length**

Posted by COFFEE on Monday, June 11, 2007 at 11:48pm. find the exact length of this curve: y = ( x^3/6 ) + ( 1/2x ) 1/2 <or= x <or= 1 im looking over my notes, but i'm getting stuck. here's my work so far: A ( 1 , 2/3 ) B ( 1/2 , 49/48 ) y' = [1/6 (3x^2)] + [1/2 (-1x^-2...
*June 12, 2007 by COFFEE*

**geometry**

If the arc on a particular circle has an arc length of 14 inches, and the circumference of the circle is 84 inches, what is the angle measure of the arc?
*April 28, 2010 by Jayme*

**geometry**

If the arc on a particular circle has an arc length of 14 inches, and the circumference of the circle is 84 inches, what is the angle measure of the arc?
*July 12, 2010 by Superman*

**geometry**

If the arc on a particular circle has an arc length of 14 inches, and the circumference of the circle is 84 inches, what is the angle measure of the arc?
*April 4, 2011 by Anonymous*

**geometry**

Circle O above has a circumference of 240 cm and arc XW has a length of 60 cm. What is the measure of the central angle associated with arc XW?
*March 6, 2011 by jake*

**geometry**

The radius of a circle is 6cm and the arc measurement is 120 degrees, what is the length of the chord connecting the radii of the arc?
*May 6, 2011 by Dylan*

**calculus**

Find the length of the arc formed by y = (1/8)(4x^2-2ln(x)) from x=4 to x=8. I found the derivative of the function and got y'= x-(1/4x) Where I'm lost now is after plugging it into the arc length equation: integral of sqrt(1+(x-(1/4x))^2). Squaring the derivative yields me ...
*August 24, 2008 by Arc Length*

**Mathematics**

Use Simpson’s rule to estimate ∫_0^2▒〖1/8 e〗^(x^2 ) dx with a maximum error of 0.1
*October 15, 2013 by Dust*

**Geometry**

Find the arc length, of a 130 degree arc, in a circle with a diameter of 7.2 inches. Round your answer to the nearest thousandth
*May 20, 2012 by Bob*

**Geometry**

Find the arc length, of a 130 degree arc, in a circle with a diameter of 7.2 inches. Round your answer to the nearest thousandth
*May 20, 2012 by Maria*

**Calculus**

The area a meadow was approximated by measuring the length of the meadow at 30-foot intervals. THe distances measured across the meadow were 76 ft, 118 ft, 130 ft, 143 ft, 139 ft, 136 ft, 137 ft, 139 ft, 130 ft, 122 ft, and 60 ft. Use Simpson's Rule to approximate the area of ...
*February 26, 2011 by Lena*

**mathematics**

use Simpson's Rule with n=10 to approximate the area of the surface obtained by rotating the curve about the x-axis. y = xln(x) from 1 < x < 2
*June 29, 2012 by rohan*

**Math**

In a circle whose radius is 13 cm, a central angle intercepts an arc that measures 65o. What is the arc length? Round your answer to the nearest hundredth of a centimeter.
*May 9, 2014 by Judy*

**math**

What's the minimum. length of the arc on the cicumference of the earth,where a curvature of the horizon is appearent? OR---What's the max.length of cord,drawn on the cicumference of the earth,where length of the cord appears same as arc? Follow up 2nd question---At what ...
*February 6, 2011 by mike*

**Maths (Calculus)**

A current i = 50sin 100πt mA flows in an electrical circuit. Determine, using integral calculus, its a) Mean Value b) RMS Value each correct to 2 decimal places over the range t = 0 to t = 10 ms I need to do this two way so I was thinking of using the trapezoidal rule and...
*May 5, 2013 by Dylan James*

**math**

The length of an arc of a circle equals 1/8 of the circle's circumference. What is the diameter of the circle if the length of the arc is 3.14?
*September 17, 2014 by Irene Wu*

**math**

The length of an arc of a circle equals 1/8 of the circle's circumference. What is the diameter of the circle if the length of the arc is 3.14?
*September 16, 2014 by Irene Wu*

**physics**

A charge of 21 nC is uniformly distributed along a straight rod of length 4.3 m that is bent into a circular arc with a radius of 1.7 m. What is the magnitude of the electric field at the center of curvature of the arc?
*June 8, 2013 by Anonymous*

**calc**

I was given a decreasing concave down graph of the integral F(x) from 0-8. i have to say whether the following are greater then, less then,equal to, or unable to determine each other 1. T (greater then) M 2. T (greater then) R 3. M (less then) S 4. S ? actual integral where t=...
*January 30, 2008 by sarah*

**CALC**

I was given a decreasing concave down graph of the integral F(x) from 0-8. i have to say whether the following are greater then, less then,equal to, or unable to determine each other 1. T (greater then) M 2. T (greater then) R 3. M (less then) S 4. S ? actual integral where t=...
*January 30, 2008 by sarah*

**physics**

A meter stick is rotated about the end labeled 0.00 cm, so that the other end of the stick moves through an arc length of 7.40 cm. Through what arc length s does the 25.0-cm mark on the stick move?
*October 22, 2014 by vik*

**computer program**

where can i find a computer code for Simpson's 1/3 Rule using c++? please help. thank you.
*October 21, 2010 by Raimu*

**Geometry**

In ⊙B the length of arc ST is 3π inches and the measure of arc ST is 120. What is the radius of ⊙B?
*May 16, 2012 by Sholanda*

**McLoughlin**

1841. Describe what happened between Simpson and McLoughlin. In 1841, Simpson toured the area again and discovered that the fur trade was not expanding as he had hoped. He decided to consolidate the operations of the maritime fur trade. All coastal posts were to be closed, ...
*June 4, 2011 by Emma*

**Calc I**

How do I find the derivative for the sqrt(sin(e^(x^3)*cos(x)))??? I know this is a combination of the chain rule and product rule. Please help!
*June 30, 2013 by Coolio*

**MATHS**

Find arc length of y=logx from x=1 to x=2. dy/dx)^2=1/x^2 arc length=Int of [sqrt(1+1/x^2)]dx =Int of [sqrt(1+x^2)/x^2] =Int of [sqrt(1+x^2)]/x from x=1 to x=2. How to proceed further to integrate?
*September 11, 2013 by MS*

**Calculus**

Find arc length of y=logx from x=1 to x=2. dy/dx)^2=1/x^2 arc length=Int of [sqrt(1+1/x^2)]dx =Int of [sqrt(1+x^2)/x^2] =Int of [sqrt(1+x^2)]/x from x=1 to x=2. How to proceed further to integrate?
*September 12, 2013 by MS*

**math **

suppose the diameter of a circle has length d. the length of a chord is c and the length of the arc cut off by the cord is s. express sin(s/d) in terms of c and d
*December 1, 2011 by Anonymous*

**Physics**

When a wheel is rotated through an angle of 35 degrees, a point on the circumference travels through an arc length of 2.5 m. When the wheel is rotated through angles of 35 rad and 35 rev, the same point travels through arc lengths of 143 m and 9.0 X 10^2 m, respectively. What ...
*November 19, 2008 by Bob*

**calculus (limits)**

lim h>0 sqrt(1+h)-1/h not sure how to factor this; not allowed to use L'Hopital's Rule. (that isn't taught at my school until Calc II & I'm in Calc I).
*January 22, 2011 by John*

**PreCalculus**

Cone Problem Beginning with a circular piece of paper with a 4- inch radius, as shown in (a), cut out a sector with an arc of length x. Join the two radial edges of the remaining portion of the paper to form a cone with radius r and height h, as shown in (b). What length of ...
*January 1, 2011 by Emma*

**Math**

Cone Problem Beginning with a circular piece of paper with a 4- inch radius, as shown in (a), cut out a sector with an arc of length x. Join the two radial edges of the remaining portion of the paper to form a cone with radius r and height h, as shown in (b). What length of ...
*January 2, 2011 by Taylor*

**math advanced functions**

a) Determine the measure of the central angle that is formed by an arc length of 5 cm in a circle with a radius of 2.5cm. Express the measure in both radians and degrees, correct to one decimal place. b) Determine the arc length of a circle in part a) if the central angle is ...
*July 24, 2012 by ashley*

**social studdies**

posted this yesterday, some person replied. not sure if shes right. 1841. Describe what happened between Simpson and McLoughlin. In 1841, Simpson toured the area again and discovered that the fur trade was not expanding as he had hoped. He decided to consolidate the operations...
*June 5, 2011 by Emma*

**Calculus**

Can someone explain to me how to do these? Given the following definite integral and n=4 answer the following questions. (Round your answers to six decimal places.) 1. Use the Trapezoidal Rule to approximate the definite integral. Answer: T4= 2. Use the Midpoint Rule to ...
*September 29, 2011 by Patrick*

**geomerty**

Find the arc legnth of Arc AB. Leave your answer in terms of pi. arc is 45 degrees radius is 5
*May 4, 2013 by Izzy*

**Precalculus**

Instead of graphing the arc length against the height, Olivia decides to make graphs of Paul's x - and y - coordinates against time. Suppose paul walks 1 meter per second. How would Olivia's graph compare to her graph of arc length against the height?
*September 22, 2011 by Kate*

**calc**

Use L’Hopital’s rule to find the limit of this sequence (n^100)/(e^n) ...If you do L'Hop. Rule it would take forever, right? You would always get an (e^n) at the bottom and will have to use the L'Hop. rule 100 times to find the limit...100*n^99, 9900n^98, and etc. Is there a ...
*February 1, 2012 by lola*

**Geometry**

What is the circumference of the circle if the radius is: 5x-My answer was 57(x)pi. What is the radius if the circumference is: 30x(pi)-My answer was 2x. (x + y)pi -My answer (x+y)/7. What is the length of the arc if: radius=3 degree of measurement of arc=6- My answer was pi/9...
*June 14, 2010 by Temperance*

**Geometry **

in circle p below the lengths of the parallel chords are 20,16, and 12. Find measure of arc AB..... the chord with a length of 20 is the diameter. the chords with lengths 16 and 12 are below the diameter torwards the bottom of the circle. arc AB is the arc made up of the ...
*May 25, 2012 by John*

**math**

in circle p below the lengths of the parallel chords are 20,16, and 12. Find measure of arc AB..... the chord with a length of 20 is the diameter. the chords with lengths 16 and 12 are below the diameter torwards the bottom of the circle. arc AB is the arc made up of the ...
*May 25, 2012 by Bo*

**Calculus **

I know how to do this problem, but I'm stuck at the arc length differential. Set up an integral for the arc length of the curve. (Do not evaluate the integral) x=y^2ln(y), 1<y<2 dx/dy = 2yln(y) + y ds= sqrt (1 + (2yln(y)+y)^2 so far I have sqrt (1 + 4y^2ln(y) + 2[2y^2ln(...
*February 28, 2013 by Angie *

**Astronomy**

How large should Venus appear in arc seconds? Use the small angle formula and the diameter of Venus. Note that an arc second is a 1/60th of an arc minute, and an arc minute is a 1/60th of a degree.
*February 16, 2014 by Barbara*

**Math**

Given info: arc length = 65 m formula for arc length: s=rø s = 2pi r radius of circle: 2300 m so to find the angle would I put in 2pi(2300)= rounded to 14451 Then would I multiply: 65(360/14451) if that is right, why would I divide by 360 and multiply by 65? Could someone ...
*May 24, 2011 by Amy~ *

**calculus**

use the trapezoidal and simpson's rule to approximate the value of the definite integral ∫2,1 ln xdx; n=4 compare your result with the exact value of the integral
*March 3, 2012 by wei_g*

**calculus**

use the trapezoidal and simpson's rule to approximate the value of the definite integral ∫2,1 ln xdx; n=4 compare your result with the exact value of the integral
*March 4, 2012 by maga*

**Trigonometry**

I am trying to help my child out with a problem but yeah I am finding it veyr hard. Gabe is spending two weeks on an archaeological dig. He finds a fragment of a circular plate that his leader thinks may be valuable. The arc length of the fragment is about 1/6 the ...
*June 21, 2010 by Britt*

**PHYSICS**

4)SIMPSON DRIVES HIS CAR WITH AN AVERAGE VELOCITY OF 48.0KM/H TO THE EAST. HOW LONG WILL IT TAKE HIM TO DRIVE 144KM ON A STRAIGHT HIGHWAY? 5)LOOK BACK AT QUESTION 4 . HOW MUCH TIME WOULD SIMPSON SAVE BY INCREASING HIS AVERAGEVELOCITY TO 56.0KM/H TO THE EAST?
*September 5, 2007 by Susie*

**math**

the arc length and central angle of a circle are 10cm and 80degrees respectivly. what is the length of the radius?
*May 12, 2012 by celina*

**trigonometry**

Gabe is spending two weeks on an archaeological dig. He finds a fragment of a circular plate that his leader thinks may be valuable. The arc length of the fragment is about 1/6 the circumference of the original complete plate and measures 1.65 inches. A similar plate found ...
*May 28, 2010 by candace*

**MoRe HeLp PlEaSe!! (calc)**

Also can I get some help with this LONG, TIRESOME PROBLEM? Find the derivative using the chain rule. f(x)= ((3x-7)/(6x+3))^4 Thanks a lot! (68/(12x^2+12x+3))*[(3x-7)/(6x+3)]^3 you should double check the answer multiply 4((3x-7)/(6x+3))^3 by the derivative of (3x-7)/(6x+3), ...
*February 21, 2007 by Confused*

**Math**

I already posted this, but wanted to say that I have the answers and it is 1.68 is less than or equal to x is less than or equal to 9.10 Cone Problem Beginning with a circular piece of paper with a 4- inch radius, as shown in (a), cut out a sector with an arc of length x. Join...
*January 3, 2011 by Taylor*

**Math**

Find the arc length of y = x^4 from the origin to (1, 1). Answer in length units, correct to two decimal places, please.
*December 4, 2011 by Beth*

**Pre-calculus**

The length of the radius of a circle is 12 cm at the measure of a central angle, alpha, is 5pi/6. What is the length of the intercepted arc?
*May 12, 2013 by Anonymous*

**Calc**

The arc of the parabola y=x^2 from (1,1) to (2,4) is rotated about the y-axis. Find the area of the resulting surface.
*June 6, 2012 by Caitlin*

**Trigonometry**

Gabe is spending two weeks on an archaeological dig. He finds a fragment of a circular plate that his leader thinks may be valuable. The arc length of the fragment is about 1/6 the circumference of the original complete plate and measures 1.65 inches. A similar plate found ...
*April 19, 2010 by Anonymous*

**Math**

I think this will be the last one. Find the radius of circle C if the measure of anglePQR=24° and the length of arc PR is 8pi. Answers: a.15 b.20 c.30 d.60 e.45 The diagram looks like a circle with its center at C. At a point on the edge of the circle is Q with lines reaching ...
*September 4, 2009 by Anonymous*

**College Calc**

Problem: y=sqrtx ^1/x. Find DY/DX. ln(f(x))=lnx^1/2x or lnx to the 1/2x 1/2x lnx product rule (1/4x^2)(lnx)+(1/x)(1/2x) is the product rule correct? What do i do after this product rule?
*October 18, 2012 by Phillip*

**science**

a go-cart moves along a circular track of radius 100ft such that its speed for a short period of time , 0 is less than t which is less than 4s, is v=60(1-e^t^2)ft/s. Determine the magnitude of its acceleration when t=2s? How do you figure this out while using Simpson's rule ...
*November 3, 2008 by sarah*

**math **

how to rewrite rule in symbols: At a certain time of day,the length of a shadow s cast by an object is twice the length of the object L each length h in a copy 1/100 the length k in the original
*November 30, 2010 by ursula*

**math **

how to rewrite rule in symbols: At a certain time of day,the length of a shadow s cast by an object is twice the length of the object L each length h in a copy 1/100 the length k in the original
*November 30, 2010 by ursula*

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