Sunday

November 23, 2014

November 23, 2014

Number of results: 13,216

**Pre-Calculus/Calculus**

I am too embarassed to ask this Calculus (really pre-calculus) question in tutoring, because I know I should know. Is the inverse of f(x)=3x-1 actually f(x)=1/3x+1? How do I find it? What if it asks the same equation replaced with f to the -1 power (x)? I think I know how the ...
*July 1, 2008 by Molly*

**Calculus**

What is the use of Calculus? How is it use in jobs? What jobs use Calculus? Calculus is used in engineering, economics, any physical science, and in business (e.g., actuary studies and statistics).
*May 5, 2007 by Anonymous*

**Algebra**

In an interview of 50 math majors, 12 liked calculus and geometry 18 liked calculus but not algebra 4 liked calculus, algebra and geometry 25 liked calculus 15 liked geometry 10 liked algebra but neither calculus nor geometry 2 liked geometry and algebra but not calculus. Of ...
*January 11, 2010 by Anita*

**Calculus**

What is the simplest solution to the Brachistochrone problem and the Tautochrone problem involving calculus? (I know that the cycloid is the solution but I need a simple calculus proof as to why this is the case)
*May 27, 2010 by Sam*

**math**

8. In an interview of 50 math majors, 12 liked calculus and geometry 18 liked calculus but not algebra 4 liked calculus, algebra, and geometry 25 liked calculus 15 liked geometry 10 liked algebra but neither calculus nor geometry 2 liked geometry and algebra but not calculus. ...
*November 30, 2009 by poo*

**math-calculus**

1.For any function y+f(x), express dy/dx using limit notation. Give a clear explanation for your given answer. you probably meant to type y=f(x) By definition dy/dx = Limit (f(x+∆x) - f(x))/∆x as ∆x-->0 The explanation of this equation is the whole basis ...
*March 26, 2007 by Chris*

**calculus**

Can someone please tell me what the word "WHOLE" AND "IRRATIONAL" MEAN IN CALCULUS? THANKS
*September 2, 2008 by Mike*

**Math:Calculus**

Use the Fundamental Theorem of Calculus to find the derivative of g(x)=1/(1+t^5)dt in the interval 1 to x.
*November 22, 2010 by HELP!!!!*

**Calculus**

Use fundamental theorem of calculus: Int(pi/2_pi) of e^(sin(q))*cos(q)dq
*April 28, 2011 by Rachel *

**Calculus Help **

Use calculus to find the area A of the triangle with the given vertices. (0, 0), (3, 1), (1, 8) A = ????
*May 1, 2014 by Anonymous*

**Calculus, bobpursley! **

This has to do with my last Calculus problem. I need help on it..The part I replied to after you answered the question.
*September 21, 2010 by Leanna*

**Calculus**

The area is bounded by y= x^3, x= 2 is rotated around the x-axis. Find the volume using calculus.
*July 24, 2012 by Ted*

**math, calculus 2 **

Use part 1 of the Fundamental Theorem of Calculus to find the derivative of g(x)= integrate from 9x to 4x of ((u+4)/(u-1))du
*August 29, 2012 by bobby*

**Calculus Precalculus**

Answer the calculus question about Point P, 45 mph, etc. It is ALREADY posted on here.
*August 27, 2011 by Zach*

**COLLEGE CALCULUS. HELP!**

the fundamental theorem of calculus, f(x)=∫(0,x) t^3+2t^2+2dt, and find f"(x). my answer was: f'(x)=x^3+x^2+2 f"(x)=x^4/4 + 2x^3/3 + 2x it said its wrong.
*April 15, 2012 by lindsay*

**calculus**

Find the arc length of the graph of y = x from x = 0 to x = 3 using calculus.
*September 11, 2010 by Denise*

**calculus**

I need help with this calculus problem. H(S)=S/(1+S) If F 1/2, -1/2 & (a+1)? I can't figure out what this mean /?
*May 30, 2011 by Tammy*

**calculus**

Why do we end up with f(x) instead of f(t) on the second fundamental theorem of calculus?
*November 7, 2011 by Jose*

**Calculus 1**

Use the fundamental theorem of calculus to find the area bounded by f(x)=3 square root of x+2x and the x-axis between x-=0 and x=1
*December 6, 2011 by Ihg*

**Calculus AP need help!**

Use Part 1 of the Fundamental Theorem of Calculus to find the derivative of the function. If f(x)= ∫(4,x^3)√(t^2+10) dt then f '(x).
*April 17, 2012 by dania*

**Calculus**

I need to take a college calculus class. Can someone direct me to a site which might help me get a good start? Thanks in advance.
*July 10, 2008 by jules*

**calculus**

Use the fundamental theorem of calculus to evaluate the following integral ∫^π/2 **the bottom is zeroe. |cosx| dx
*December 13, 2011 by Roxy*

**Calculus**

Use any calculus method to determine extrema, intervals where the function is increasing or decreasing, asymptotes,and points of inflection for y = -x^4 + 2x^3 - x + 2
*October 20, 2012 by Sissy*

**Calculus**

Find the derivative of the following function using the appropriate form of the Fundamental Theorem of Calculus. intergral s^2/(1+3s^4) ds from sqrtx to 1 F'(x)=?
*April 18, 2014 by Brady*

**Calculus**

Integrate e^(-x^2/2) dx What branch of calculus is this? Is this differential equations?
*March 7, 2008 by mathstudent*

**calculus**

Find the limit of this calculus problem.? (5x-3)/(ln(5+4e^(x)) x=inf
*November 4, 2010 by Zel*

**calculus**

How can we verify area of square and rectangle by calculus ?
*December 15, 2011 by Abay*

**Calculus**

How can I efficiently study for a Calculus test with 8 sections?
*January 17, 2012 by Meg*

**Calculus AB (AP)**

Hi, I have a calculus test tomorrow and I understand how to complete all of the problems, but I am unsure behind the reasoning of taking two derivatives. Can someone please explain the following: 1. g(x)=e^(f(x)) g'(x)=e^(f(x))f'(x) 2. f(x)=Integral from 0 to 3x of the square ...
*April 13, 2011 by Jake*

**calculus**

hello here, Please can i get direction on website to practice calculus (both differential & integral) objectives based online. thanks.
*August 19, 2009 by matrix school 2*

**Calculus**

How do I determine the area of a region bounded by a function and the x-axis if given y=cosx and interval is [0,/2]. This has to do with the Fundamental Theorem of Calculus. Thanks in advance!
*October 27, 2011 by W*

**Calculus.......plz help! =)**

Use any calculus method to determine extrema, intervals where the function is increasing or decreasing, asymptotes, and points of inflection for y = -x(x+1)^3
*October 20, 2012 by Amy*

**calculus**

Calculus A, Evaluate the following integral : (x^2+3x-2)dx
*August 2, 2011 by Iman*

**calculus**

Does anyone know of any free calculus websites? I'm taking a college class in the fall and would like to build my confidence since I am somewhat weak in math. Thank you in advance.
*July 28, 2008 by jules*

**Calculus Please Need Urgent3 :/**

Find the derivative of the following function using the appropriate form of the Fundamental Theorem of Calculus. F(x)= (s^2)/(1+3s^4)ds from sqrtx to 1 F'(x)=? Thank you so much guys!
*April 19, 2014 by Jay*

**Calculus**

In calculus, the sum of an infinite geometric series whose first term is 1/20 is given by the complex fraction 1/20 _____ 1-r where r is the common ratio between the terms. Simplify this expression.
*March 15, 2010 by Anonymous*

**COLLEGE CALCULUS. HELP!**

the fundamental theorem of calculus, f(x)=∫(0,x) t^3+2t^2+ 2 dt, and find f"(x). my answer was: f'(x)=x^3+x^2 f"(x)=3x^2+2x it said its wrong. i dont know how solve with interval, ∫(0,x)
*April 17, 2012 by MILY*

**Calculus**

Need an answer to this Calculus Question. I keep getting this type of question wrong. Thanks. Differentiate the Function: y = (3x-1)^2(2-x^4)^2 y =
*April 19, 2010 by Dave *

**Calculus**

estimate the absolute maximum and minimum values of f if any, on the stated interval, and then use calculus methods to find the exact values: f(x)=10ln(x^2+1)-8x; [0,3]
*July 31, 2010 by Mely*

**calculus**

Verify the identity: arctanx + arctan(1/x)=∏/2 using calculus theory. (Hint: Differentiate the left hand side of the identity)
*December 7, 2011 by NYSNC*

**Calculus**

I need help with these two review calculus problems for my final exam. What is the derivative of a). (5x^2+9x-7)^5 b). Lne^x^3 For a. I got 50x+45(5x^5+9x-7)^4 For b. I got 3x^2 Can you verify please?
*May 21, 2012 by Sam*

**calculus**

using the fundamental theorem of calculus what is the derivative of the definite integral from x^3 to sqrt x of (sqrt t) sin t dt
*January 2, 2011 by adela*

**Calculus I Theorem**

I factored and simplified dy/dx of 192x^5 + 96x^3 + 12x all the way down to x^2 = u = (-1/2) and (-1/6). How does the result illustrates part 1 of the Calculus Fundamental Theorem?
*May 14, 2010 by John*

**Calculus - Find volume of cylinder**

There is a cylindrical tank lying horizontally on the ground, its diameter is 8 feet, and length is 25 feet, the depth of the water currently in the tank is 2 feet. (1 gallon=231 cubic inches) How many gallons of water are in the tank? How many gallons of water will it take to...
*May 15, 2007 by Ashely*

**Calculus: Derivatives**

I'm having trouble understanding what derivatives in calculus (instantaneous speed) is. Can someone please explain it to me, or provide some easy links to learn from? Thanks!
*September 9, 2007 by Joe*

**Pre Calculus**

Pre Calculus why is sin(-20)/cos 380 equal to tan (-200)
*November 15, 2009 by Pre Calculus*

**Calculus**

for the function F(t)=ln(t^2), let f(t)=F'(t). Write the integral from a to b of f(t) dt and evaluate it with the fundamental theorem of calculus. the integral from 1 to 3 ___ dt= __
*November 30, 2011 by bob*

**Calculus I**

Hello! I am taking Calculus I and am in Sec. 4.3 of Stewart's 7th Edition. I ran across a problem that I don't understand the mechanics of, could someone show me? Thanks a bunch! For what values of the numbers a and b does the function f(x)= axe^{b(x^2)} have the maximum value...
*June 26, 2014 by DeeDee*

**Pre-Calculus**

I am in Honors Pre-Calculus and am having a hard time understanding my teacher. I feel so stupid. Does anyone have any suggestions on a website that might give me some insight into what I am doing wrong? Thanks!
*October 7, 2008 by Jill*

**CALCULUS 2**

Use calculus to find the volume of the following solid S: The base of S is an elliptical region with boundary curve 9x^2+4y^2=36. Cross-sections perpendicular to the x-axis are isosceles right triangles with hypotenuse in the base.
*February 4, 2014 by ADELINE*

**Calculus--Reiny**

Calculus - Reiny, Friday, December 23, 2011 at 6:59pm I read that as (4a^2-1)/(4a^2-16) * (2-a)/(2a-1) , my brackets are necessary = (2a+1)(2a-1)/( 4(a+2)(a-2) * (2-a)/(2a-1) the (2-a)/(a-2) are opposite, they will give you the -1 so.. = -(2a+1)/(4(a+2)) , again you have to ...
*December 25, 2011 by -Untamed-*

**calculus**

Quadratic function written in standard form where a, b, and c are constants such that a is not zero. f(x)= ax^2+bx+c Using calculus find the vertex of the parabola formed by this quadratic function. Determine under what conditions this vertex is a maximum or minumum (using ...
*May 8, 2011 by Janet*

**Calculus**

Calculus Limit Problem: Evaluate the function at the given numbers (correct to six decimal places). Use the results to guess the value of the limit, or explain why it does not exist. f(x)=cosx-1/sinx x=1, .5, .4, .3, .2, .1, .05, .01 What should I do? A table of values??
*June 22, 2010 by George*

**Maths Calculus Derivative Integral - Urgent Please**

Use 2nd Fundamental Theorem of Calculus to find derivative of f(x) = integral of 2x^2 (at the top) to x-5 (at the bottom) of square root of Sin(x)dx
*October 18, 2010 by Nick*

**Calculus**

Greetings, This is a question about selecting courses for my semester. I was planning to take Calculus 3 (Mostly 3-Dimensional topics involving calculus) and a C++ programing course. If you have heard of these courses, can you please tell me your thoughts about me taking these...
*January 3, 2012 by Simon*

**calculus**

Locate the position of Sun,using calculus---using differential euation on sign curve of Sun's path.
*February 6, 2011 by mike*

**To Reiny**

Reiny could you please check my Calculus post below, it says Calculus--Reiny.
*October 4, 2011 by -Untamed-*

**Differential Calculus**

Given that p=(2q^2-5)^2. when q=3, it is increased by 0.7%. find the appropriate percentage in p. solution dp = 2(2q^2-5) (2dq) dp = (4x(18-5)(0.7%) dp = 4(13)(0.7%) am lost from here is dp=52x0.7/100= 0.364% Responses Differential Calculus - bobpursley, Friday, August 14, ...
*August 14, 2009 by matrix school 2*

**Calculus I**

Section The fundamental Theorem of Calculus: Use Part I of the fundamental Theorem to compute each integral exactly. 4 | 4 / 1 + x^2 dx 0
*April 14, 2012 by Sandra Gibson*

**Calculus**

An important problem in mathematics is that of root finding: that is, given a function f (x), finding any roots of f in an interval. Exact methods exist for many functions: In the case of a linear function f (x) = ax + b, this is easy. If a ≠ 0, then x = −b /a...
*May 3, 2012 by Kim*

**calculus**

My a.p. calculus teacher doesn't know how to do this problem (like many others) so he's giving us 5 points extra credit on our test if we can figure it out, but I don't know how to do it: It's as the lim-->infinity (x+sinx)/(x+cosx) We know the answer is 1 because it's in ...
*October 22, 2006 by teamcaridee*

**gnozahs**

I removed about ten questions you posted this morning. There was no indication of what you had done, what your thinking was, or what you wanted from us. We are not going to do homework for you. If you want hints on these calculus questions, say so, or ask what you want. Just ...
*June 23, 2009 by bobpursley*

**CALCULUS**

what is the derivative of ln(x-1)? If you are studying the calculus of logarithms your question surprises me, since that is one of the most basic ones in that topic. in general if y = ln("anything") then y' = 1/"anything" * derivative of "anything" just apply this rule and let...
*May 6, 2007 by URGENT*

**Pre-Calculus/Trivia**

csc(theta)= 1/x sec(theta)= 1/ sqrt(1-x^2) cot(theta)= sqrt(1-x^2)/x What are these equations used for in real life matters or in regards to calculus? Can't seem to find the answer anywhere :/
*February 20, 2012 by Maria*

**Calculus**

An object at rest begins moving horizontally on the x-axis, starting at position x(t) = 0 feet at time t = 0 seconds.Suppose, after exactly 2 seconds we measure the position of the object to be 3 feet to the right of the origin AND measure the object to be moving to the ...
*April 11, 2013 by Rosie*

**Calculus 2**

Calculus. Mary designed a new viewing window consisting of a rectangle and a semi circle for a fresh water aquarium. The window is as follows and the top is located 10 feet below the water's surface. How much force is on the window?
*September 27, 2012 by Laura*

**Calculus**

A curve is defined by the parametric equations: x = t2 t and y = t3 3t Find the coordinates of the point(s) on the curve for which the normal to the curve is parallel to the y-axis. You must use calculus and clearly show your working, including any derivatives you need to ...
*July 18, 2014 by Daksh*

**Math/ Calculus Please HELP!!!**

An object at rest begins moving horizontally on the x-axis, starting at position x(t) = 0 feet at time t = 0 seconds.Suppose, after exactly 2 seconds we measure the position of the object to be 3 feet to the right of the origin AND measure the object to be moving to the ...
*April 2, 2013 by Marto*

**calculus(work)**

a rectangular water tank has a length 20 ft, width 10 ft , and depth 15 ft . if the tank is full , how much work does it take to pump all the water out (using calculus)?
*April 2, 2011 by tony*

**Applied Calculus-Question for Damon**

Hi, I have two other questions for Applied Calculus but they have graphs and I am unable to post them in here. Is there a way you could help me out with the questions?
*April 20, 2012 by Marie*

**calculus**

Find any relative extrema and any points of inflection if they exist of f(x)=x^2+ ln x^2 showing calculus. Please show work in detail so I can follow. Thanks. The answer is no relative max or min and the points of inflection are (1,1) and (-1,1) but I'm having trouble getting ...
*May 4, 2013 by Rene*

**calculus book**

sorry i am new to this website. Do any of you know any website that offer free or cheap online book. Calculus Early Transcendentals, 10th Edition NEW! Howard Anton, Irl C. Bivens, Stephen Davis THANK U.
*August 29, 2013 by maRia*

**Calculus**

For the decomposition of Carbon 14, find the age of a prehistoric cave painting discovered in the Lascaux Caves in southern France if the amount of Carbon 14 has decayed to 14.29%...again using calculus formulas. Not sure how to use this equation (content section of course ...
*July 15, 2008 by Derek*

**math (calculus)**

you have 704m of fencing to enclose 3 adjacent plots(not the same size) you must use calculus to fine the dimensions for which the total area is as large as possible. Find the largest possible total area.
*May 4, 2011 by Ryan *

**ap calculus**

How is the ap calculus AB and BC test? Is there any online practice test?
*January 2, 2013 by maria*

**Calculus**

The curved section can be modelled by the parabola y=3x-3/4x^2 Use calculus to find the maximum height of the curved parabolic section. How do I do this step by step?
*August 22, 2010 by Sarskia*

**Calculus 2**

Calculus work problem. John bought the following corner lot. Two sides are bounded by 2 roads the back is bounded by a stream that follows the curve y = -x^3 + 8. He wants to build a house in the center of the lot. Where will that be? Please show all work
*September 27, 2012 by Laura*

**calculus**

Use Fundemental Theorem of Calculus part 1 to find the derivatives of the following: (i) F(x)=Integral ( top3, bottom x) e^-t^2 dt (ii) G(theta)=Integral ( top cos theta, bottom sin theta) 1/1-x^2 dx
*January 11, 2009 by extraordinary*

**statistics**

On this semesters final exam, john scored 72 on his calculus exam and 53 on his statistics exam. The z score for both exams was the same. Which on would he do better on? a. calculus b.statistics c. the exam scores are equivalent
*October 10, 2014 by mike*

**statistics**

On this semesters final exam, john scored 72 on his calculus exam and 53 on his statistics exam. The z score for both exams was the same. Which on would he do better on? a. calculus b.statistics c. the exam scores are equivalent
*October 11, 2014 by mike*

**Calculus**

If I derive the following, d/dt((a)S(t^2) of (s)^(1/2)ds with S being integral notation (a) being at the bottom of the notation and being a constant (t^2) being at the top of the notation ..I first apply the fundamental theorem of calculus to get.. (t^2)^(1/2) (2t) simplified ...
*November 16, 2014 by Joshua*

**Calculus Graph help!!!**

I need help with a calulus graph and figuring out its equation but it wont let me post the picture of the graphs here. so will someone who understands Calculus and their graphs super well please email me k m k underscore horse lover at hot mail dot com. no spaces and an actual...
*May 2, 2012 by kelsey*

**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*

**Calculus**

A certain calculus student hit Mrs. Evans in the head with a snowball. If the snowball is melting at the rate of 10 cubic feet per minute, at what rate is the radius of the snowball changing when the snowball is 1 foot in radius?
*November 6, 2011 by Rina*

**math**

65 men 75 women are enfolled in calculus. There are 30 business majors, 40 biology majors, 50 computer science majors, and 20 mathematics majors. No person has a double. If a single calculus student is chosen, find the probability that that the student is not a mathematics major
*September 28, 2012 by greg*

**Calculus**

At a certain factory, output Q is related to inputs u and v by the equation Q= 17u^2+(16u+17v)/(u+v)^2 If the current levels of input are u= 10 and v = 25, use calculus to estimate the change in input v that should be made to offset a decrease of .7 unit in input u so that ...
*October 8, 2013 by Rebekah*

**calculus?**

Hello can u help? I need a solution to calculus problem I have $500.00 to spend on fencing for a garden. The fence for the street side costs $30.00 per foot and the other three sides cost $10.00 per foot. what dimensions will give you a rectangle for the largest possible area...
*July 14, 2012 by GiGi*

**calculus**

A rancher has 1000 feet of fencing with which to enclose two adjacent rectangular corrals with a interior partition (consider as one pen). Use calculus to determine what the external dimensions of the pen that will maximize the enclosed area. Write your answer in the form ...
*March 19, 2011 by Anonymous*

**Calculus**

Use the Fundamental Theorem of Calculus to find the area of the region bounded by the x-axis and the graph of y = 4 x3 − 4 x. Answer: (1) Use the Fundamental Theorem of Calculus to find the average value of f(x) = e0.9 x between x = 0 and x = 2. Answer: (2) Draw the ...
*December 6, 2010 by Erika*

**Calcuslus-Calculus-Calculus **

A rocket arises from its launching pad with a velocity given. By 0.1 h m/s ,where h m is the height reached by the rocket at that time.the rocket is obserrvved from 2000 m away from the launch pad.at. What rate is the distance of the roocket from observer channging when the ...
*March 16, 2011 by Mehak*

**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-calculus**

30/x^2-25 = 3/x-5-2/x+5 i be left with 30 = 3x^2-75-2x^2+50 i not sure what to do? i use the quadratic formula? math-calculus - Steve, Saturday, January 7, 2012 at 3:38pm First, you have to simplify properly: 30/(x^2-25) = 3/(x-5) - 2/(x+5) 30 = 3(x+5) - 2(x-5) You were ok ...
*January 7, 2012 by Shreya*

**calculus**

express in sinx 1 1 ---------- + -------- cscx + cotx cscx - cotx and express in cosx 1 + cot x ------- - sin^2x cscx = 1/sinx so what do i do w. that extra one on the top!?? im so confused cscx Your fractions aren't lining up. This question is also not calculus. Please do not...
*March 27, 2007 by linds*

**Calculus III**

I'm supposed to find the expression 'y', when (x^2+100)y'=23 When y(10sqrt(3))=0 Also, I have to find the indefite integral of xsqrt(19x-7), using integration tables in teh back of the book "Calculus of a Single Variable, 8th Edition." Tables are in appendix B I used the ...
*March 16, 2008 by Sean*

**physics**

Determine the acceleration and normal force of system below. Assume no friction, the mass equal to 10.0 kg and the angle equal to 60.0 degrees. Assume gravity equals 9.8 m/s/s. The picture looks like a right triangle with a box sliding down it. I am a 9th grader in conceptual ...
*December 1, 2010 by Anonymous*

**Calculus, only two problems. **

If g(x) is the inverse of f(x), g(x)=f^-1(x), such that g(3)=5 and f'(5)=4 what is the value of g'(3)????? :O 2. If g(x)is the inverse of f(x), g(x)=f^-1(x), such that f(3)=15,f(6)=3,f'(3)=-8,and f'(6)=-2. What is the value of g'(3)???????? Calculus--
*March 23, 2010 by JakeT*

**AP Calculus BC Resources**

Hi there, I was hoping if any one was familiar with any sites that have printable integration/differentiation packets? I'm hoping to use them for everyday practice. I skipped Calculus AB and need a little help. I love packets so if there are any out there (hopefully with ...
*October 26, 2006 by Ted*

**calculus help**

Is there any good calculus websites out there that teach every possible derivative there is? Such as the basic rules of differentiation, product and quotient rules, chain rule? ((I'm really bad a understanding the square roots. )) My book gives me examples but I just something...
*October 11, 2008 by student01*

**Calculus**

Hi there I am having some troubles trying to do my calculus homework and I really need help trying to do this problem from my homework: Set up the problem and do not solve: The mass of the solid bounded by the surfaces 2x^2 + 2y^2= 9, z=0, z=3 with density function p(x,y)= x^...
*December 3, 2009 by shylo*

**math (calculus)**

A room has dimensions 2.24 m (height) 5.30 m 6.55 m. A fly starting at one corner flies around, ending up at the diagonally opposite corner. (a) What is the magnitude of its displacement? (b) If the fly walks rather than flies, what is the length of the shortest path it ...
*October 9, 2012 by D*

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