What is Word problem: Definition and 499 Discussions

In mathematics and computer science, a word problem for a set S with respect to a system of finite encodings of its elements is the algorithmic problem of deciding whether two given representatives represent the same element of the set. The problem is commonly encountered in abstract algebra, where given a presentation of an algebraic structure by generators and relators, the problem is to determine if two expressions represent the same element; a prototypical example is the word problem for groups. Less formally, the word problem in an algebra is: given a set of identities E, and two expressions x and y, is it possible to transform x into y using the identities in E as rewriting rules in both directions? While answering this question may not seem hard, the remarkable (and deep) result that emerges, in many important cases, is that the problem is undecidable.
Many, if not most all, undecidable problems in mathematics can be posed as word problems; see the list of undecidable problems for many examples.

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  1. karush

    MHB Solve Dxdy Word Problem: Height of Bulb at $(1.25, 0)$

    how high h must the bulb in the figure be if point $(1.25,0)$ is right on the edge of the illuminated region. ${x}^{2}+{y}^{2}=1$ $y' = -x/y$ $\frac{-h}{13/4}=\frac{-y}{5/4-x}=-\frac{x}{y}$ hopefully if the is setup ok what is next?
  2. D

    Word problem on finding speed based on time, distance

    Mod note: Moved the text under Relevant equations to the attempt section 1. Homework Statement Hello! Can't wrap my head around this easy problem. Would be grateful for help in spotting out my mistakes. One day, Donnie observes that the wind is blowing at 6 miles per hour. An unladen swallow...
  3. karush

    MHB Solve Trig Word Problem: Acre Parcel Sides 180 & 240 ft

    A one acre parcel has 2 sides 180 ft and 240 ft intersecting at a right angle. the other side adjacent to the 180 ft is 200 ft what is the length of the 4th side. by Pythagorean theorem $BD = 300$ so triangle ABD = $21600 \ ft^2$ thus triangle DBC = $21960 \ ft^2$ so 21960 = (1/2)(300)(h)...
  4. N

    Calculus Word Problem: Finding Rate of a Sliding Ladder with Pythagoras Theorem

    Question: Suppose a 15-foot ladder is sliding down a vertical wall, with the bottom of the ladder sliding away from the wall at a rate of 2 feet per minute. Sketch a picture of the situation, with labels x and y indicating horizontal and vertical distances, respectively. Then find the rate at...
  5. E

    Algebra Word Problem - practice problems

    Homework Statement The problem goes like this: The sum of 2 numbers is 25. If 2/3 of the smaller one is 2 more than 1/4 of the larger one, find the 2 numbers. Any hints on how to start off this one? What should I let x= be? When i attempted to solve this i let 2/3x = the smaller number and...
  6. R

    MHB Word Problem: Songs Downloaded

    My homework question is "the standard version of a song is 2.3mb and high quality is 4.2mb. There was 1120 downloads for a total of 4077mb. How many high quality songs were downloaded?" I'm having an issue creating the formula needed to solve this word problem!
  7. Euler2718

    Logarithm Depreciation Word Problem

    Homework Statement A vehicle purchase for $32,000 depreciates at a rate of 75% every 6 years. Another vehicle purchased for $16,000 depreciates at a rate of 50% every 4 years. Create an exponential function for each situation, and use the functions to algebraically determine the amount of time...
  8. U

    MHB Calculating Average Fees and Transaction Volumes Word Problem

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  9. S

    MHB How Far Does a Bouncing Ball Travel Before Stopping?

    Hi everybody, can you please help me with this question and with the working out? A ball was dropped from a height of 270 m. On each rebound, it rose to 10% of the previous height. Find the total vertical distance traveled by the ball before coming to rest. Thanks, Starkiller2301
  10. Jaco Viljoen

    Word problem x boys and y girls in a class

    Homework Statement There are x boys and y girls in a class(Class A) The girls outnumber the boys by 4. They join up with another class(Class B) in which there are twice as many boys as girls. Class B has 3 more boys and 5 less girls than class A. Which one of the following systems of equations...
  11. A

    MHB What is the Optimal Number of Birdhouses to Produce?

    Hi everyone - this is my second post on here today! Anyway, I have a word problem, and would just like to make sure I am setting it up correctly. Tom expects to sell at least 30 birdhouses a week, at \$60 each. If he produces more than 30, he will lose \$2 per additional house. What is the...
  12. O

    Help with beginner level physics word problem

    1.The semester just started and my teacher has assigned us this question: How high of a tower could you build from the people in this class(30 people)? Include diagram. How much force would be pushing down on one of the base person's legs? 2. Note : Fg = mg 3. Here is my work so far ...
  13. kyphysics

    Solve a Word Problem: Find the Number of Marbles Jack Has

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  14. P

    MHB Rational Expression word problem

    Nancy's lawn care specializes in residential lawn cutting and fertilizing. Nancy the owner has tracked her income and expenses. She has determined that her profit can be represented by the expression $5A, where A is the area of the lawn in square metres. The time in hours that it takes her to...
  15. I

    Expectation of Continuous Random Variable [word problem]

    Homework Statement Here's the problem with the solution provided: Homework Equations Fundamental Theorem of Calculus (FToC) The Attempt at a Solution So I understand everything up to where I need to take the derivative of the integral(s). Couple of things I know is that the derivative of...
  16. K

    MHB Conics- Word problem with ellipses.

    Hi. I am given the following problem. A small bridge is shaped like a semi-ellipse. Given that its maximum height is 3m and that its foci are located 4m from the centre find the height of the bridge at a distance of 2m from its edge. So the problem give me the values b= 3 and c=4. With this we...
  17. I

    Inverse matrix word problem, matrix arithmetic

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  18. O

    MHB Distance formula question, word problem

    9:00 AM car A travels north 50 mph and is 50 miles south of car B Car B is traveling west at 20 mph Let (0,0) be initial coordinates of car B on xy plane units are in miles Plot locations of each car at 9:00 AM and 11:00 AM find distance of cars at 11:00 AM. So I use the midpoint formula but...
  19. I

    Matrices: word problem, transition matrix

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  20. M

    How Do You Formulate a Polynomial for Volume in This Prism Problem?

    Homework Statement A package sent by a courier has the shape of a square prism. The sum of the length of the prism and the perimeter of its base is 100cm. Write a polynomial function to represent the volume V of the package in terms of x. width and height are in x centimeters, length is in y...
  21. A

    What is the Proof for the Sum to Infinity of an Infinite Geometric Progression?

    Homework Statement An infinite geometric progression is such that the sum of all the terms after the nth is equal to twice the nth term. Show that the sum to infinity of the whole progression is three times the first term. Homework Equations [/B] S_{n} = \frac{a(1-r^n)}{1-r}\\ S_{\infty} =...
  22. I

    Augmented matrices word problem - tiny issue

    Homework Statement Hello! Here is the problem from Stitz-Zeager Pre-calculus book: At 9 PM, the temperature was 60F; at midnight, the temperature was 50F; and at 6 AM, the temperature was 70F . Use the technique in Example 8.2.3 to t a quadratic function to these data with the temperature...
  23. B

    Precalculus 11 Word problem- Fundraising

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  24. M

    Solving a Population Growth Problem

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  25. P

    Word Problem about Special Relativity

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  26. M

    How Do You Calculate Net Force and Coefficient of Friction in Physics Problems?

    these are technically not homework, i just need more help for my test tomorrow! I HAVE NO IDEA HOW TO DO THIS! can someone walk me through these and show me the steps! thank you :):confused: 1.A sled is being pulled to the right with a force of 28 N. A frictional force is working opposite...
  27. M

    Universal gravitational word problem test tomorrow

    1. What is the strength of the gravitational field (in N/kg) at an orbit of 1.0 x106 m above the planet Zoklopgniald with mass of 3.45 x1026 kg and mean radius of 7.80 x107m? ANS:3.69 N/kg What is the gravitational force exerted on a 2840 kg satellite orbiting Zoklopgniald at this altitude...
  28. M

    Displacement word problem grade 11

    [b]1. while driving a lady sees a cat run on the road and it takes her 0.80s to react and put her foot on the brake. her car is traveling 25 m/s. (a)how far will the car travel before she puts her foot on the brake and (b) if when the brake is applied the car decelerates at a uniform rate of 9.3...
  29. Serious Max

    Word problem with exponential and quadratic models

    Homework Statement Homework Equations — The Attempt at a Solution Confused with (d) a little. Rocket explodes at ##h=3.85262 ## miles ## -16t^2+1400\sin(\alpha)t=3.852624*5280## ## \alpha=\arcsin\left(\dfrac{3.852624*5280+16t^2}{1400t}\right) ## But what do I do...
  30. Serious Max

    Word problem involving sinusoidal model

    Homework Statement Homework Equations y=30\sin(\dfrac{2\pi}{20}t)+270 General principal solutions: t=\left(\dfrac{\arcsin(\dfrac{1}{3}) 20}{2\pi}\right)+20k, k\in \mathbb{Z} t=1.08173+20kGeneral symmetry solutions: t=\left(-\dfrac{(\arcsin(\dfrac{1}{3})-\pi)20}{2\pi}\right)+20k, k\in...
  31. J

    Word problem using lagrange multiplier

    Homework Statement The Baraboo, Wisconsin plant of International Widget Co. uses aluminum, iron and magnesium to produce high-quality widgets. The quantity of widgets which may be produced using x tonnes of aluminum, y tonnes of iron and z tonnes of magnesium is Q(x,y,z) = xyz. the cost of raw...
  32. H

    Another Hydrodynamics word problem

    Homework Statement The pressure difference between the main pipeline and the throat of a venturri meter is 10.5 Pascals (Pa). The areas of the pipe and the constriction are 0.1 m^2 and 0.05 m^2 respectively. How many cubic meters per second are flowing in the pipe? The liquid in the pipe is...
  33. H

    Solving word problem in hydrodynamics

    1. A circular hole 2 cm in diameter is cut in the side of a large stand pipe 10 m below the water level in the standpipe. Find: a. the velocity of the efflux b. the volume discharged per unit time[/b] 2. P + 1/2 pv^2 + pgh Q = A1 V1 = A2 V2 where = a = area v =...
  34. paulmdrdo1

    MHB Is my solution for the tank word problem correct?

    please check my work here 1. The larger of the two pipes can fill a tank in 40 min. and the smaller can fill it in 50 min. while the drain is opened. Find the time required for the drain to empty the full tank if the pipes are closed. Solution...
  35. M

    MHB How to Solve a Terminal Arm Word Problem and Using Latex

    Would this be an okay way to go about solving the problem? Also, how do I use Latex?
  36. M

    MHB Word problem: initial height of projectile

    A ball is thrown from a cliff. The path of the ball modeled by the equation h = -5t^2+ 5t + 210, where h is the height, in metres, of the ball above the ground, and t is the time, in seconds, after it is thrown. How high is the cliff? Not really sure how to do this problem. I know that one of...
  37. M

    Quadratic equation word problem

    1. Problem Barkley runs a canoe-rental business on a small river in Pennsylvania. Currently, the business charges $12 per canoe and they average 36 rentals a day. A study shows that for every $.50 increase in rental price, the business can expect to lose two rentals per day. Find the price...
  38. B

    MHB Speed Required to Pass a Truck in 3 Seconds

    please help set up the equation for this problem, a car 15 ft.long overtakes a truck 30 ft. long which is traveling at the rate of 45mph. How fast must the car travel to pass the tuck in 3 seconds ?
  39. W

    Kinematics Word Problem - Projectile Fired at a Stationary Vehicle

    Homework Statement A projectile is fired at a stationary vehicle. If the initial separation was 200m and the projectile traveled at a constant 75 m/s, find the acceleration the vehicle would need for a passenger to be able to reach out and calmly pull the projectile into the vehicle. (Assume...
  40. paulmdrdo1

    MHB Work Word problem - linear equation

    Forty men were engaged to finish a work in 90 days. Afer 60 days, some men stopped working. The remaining men finished the job at a same rate in 40 more days. How many men stopped? this is how far I can get to let x = number of men remained 40-x = number of men stopped Please help. thanks!
  41. paulmdrdo1

    MHB Solving Word Problem - Linear equations

    I'm solving a plenty list of exercises about application of linear equation. Currently I have solved 97% of them correctly. But there are some items I really need help with.here are they, 1. A nugget of gold and quartz weighs 100 grams. Gold weighs 19.3 g/cm3 (grams per cubic centimeter)...
  42. Petrus

    MHB What is the angle and rate of change when flying a kite?

    You fly a kite. The dragon is 15m away from you (measured horizontally) and moves right now straight up. The rope is rolled out with the speed of 4 dm / s, and 30m is unwound. (a) Draw a clear picture of the situation, and explain what all introduced designations stand for. (b) What is the...
  43. paulmdrdo1

    MHB Solve Milk & Cream Mixture Word Problem: Help Needed

    can you explain what the problem is asking for? please use single variable only. One thousand quarts of milk testing 4% butterfat are to be reduced to 3%. How many quarts of cream testing 23% butterfat must be separated from the milk to produce the required result? All...
  44. paulmdrdo1

    MHB Word problem - linear equation.

    please help me with this problem please use single variable only. The length of a rectangular swimming pool is twice its width. The pool is surrounded by a cement walk 4ft wide. If the area of the walk is 748 ft^2, determine the dimensions of the pool. let x = width of...
  45. paulmdrdo1

    MHB Another word problem - application of linear equations

    The annual sophomore class picnic is planned by a committee consisting of 17 members. A vote to determine whether the picnic should be held at the beach location or in the mountains resulted in a victory for the beach location. However, if two committee members had changed their vote from...
  46. paulmdrdo1

    MHB Word problem - Application of linear equations

    Every freshman student at a particular college is required to take an english aptitude exam. A student who passes the examination enrolls in english composition, and a student who fails the test must enroll in english fundamentals. In a freshman class of 1240 students there are more students...
  47. paulmdrdo1

    MHB Emptying and filling a tank word problem.

    I just want to make a sanity check here. here's the problem One pipe can fill a tank 45min and another can fill it in 30 min. If these two pipes are open and a third pipe is draining water from the tank, it takes 27 min to fill the tank. how low will it take the third pipe alone to empty a...
  48. P

    MHB Word problem finding dimensions (please check my answer)

    A homeowner wants to fence a rectangular play yard using 72 ft of fencing. The side of the house will be used as one side of the rectangle. Find the dimensions for which the area is a maximum and determine the maximum area. I got L=18 and W=36 So my maximum area is 648 ftIs this correct?
  49. N

    Find the displacement in a word problem

    Homework Statement A car is slowing down at a rate of 20 km/h/s. How far does it travel if its original velocity is 50 km/h and its final velocity is 5.0 m/s? Homework Equations vf2 = v02 + 2aΔx The Attempt at a Solution vf2 = v02 + 2aΔx Δx = (vf2 - v02) / 2a = (182-502) /...
  50. N

    Word Problem with Kinematics Equation

    Homework Statement An object thrown up from a cliff 10 m/s reaches a velocity of 20 m/s [down] as it lands. If acceleration due to gravity is 9.8 m/s2, what is the object's displacement? How long did it take for the object to land from the time it was thrown? Homework Equations I'm not...
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